diff --git a/Project#03/figures/compound-index-restrictions2.png b/Project#03/figures/compound-index-restrictions2.png
index ccb74c9..2b9fc7d 100644
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diff --git a/Project#03/figures/eri.png b/Project#03/figures/eri.png
index 65810d8..a8e8dd6 100644
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diff --git a/Project#04/README.md b/Project#04/README.md
index 775a9ec..fabf300 100644
--- a/Project#04/README.md
+++ b/Project#04/README.md
@@ -1,77 +1,57 @@
 # Project #4: The second-order Moller-Plesset perturbation (MP2) energy
 Unlike the Hartree-Fock energy, correlation energies like the MP2 energy are usually expressed in terms of MO-basis quantities (integrals, MO energies). 
-The most expensive part of the calculation is the transformation of the two-electron integrals from the AO to the MO basis representation.  
-The purpose of this project is to understand this transformation and fundamental techniques for its efficient implementation. 
-The theoretical background and a concise set of instructions for this project may be found [[http://sirius.chem.vt.edu/~crawdad/programming/mp2.pdf|here]].
+The most expensive part of the calculation is the transformation of the two-electron integrals from the AO to the MO basis representation. 
+The purpose of this project is to understand this transformation and fundamental techniques for its efficient implementation.
+The theoretical background and a concise set of instructions for this project may be found [here](./project4-instructions.pdf).
 
 ## Step #1: Read the Two-Electron Integrals
 The Mulliken-ordered integrals are defined as:
 
-```
-EQUATION
-(\mu \nu|\lambda \sigma) \equiv \int \phi_\mu({\mathbf r_1})
-\phi_\nu({\mathbf r_1}) r_{12}^{-1} \phi_\lambda({\mathbf r_2})
-\phi_\sigma({\mathbf r_2}) d{\mathbf r_1} d{\mathbf r_2}
-```
+<img src="./figures/eri.png" height="45">
 
-Concise instructions for this step can be found in 
-[Project #3](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2303)
+Concise instructions for this step can be found in [Project #3](../Project%2303).
 
 ## Step #2: Obtain the MO Coefficients and MO Energies 
-Use the values you computed in the Hartree-Fock program of 
-[Project #3](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2303)
+Use the values you computed in the Hartree-Fock program of [Project #3](../Project%2303).
 ## Step #3: Transform the Two-Electron Integrals to the MO Basis 
 ### The Noddy Algorithm 
 
 The most straightforward expression of the AO/MO integral transformation is
 
-```
-EQUATION
-(pq|rs) = \sum_\mu \sum_\nu \sum_\lambda \sum_\sigma C_\mu^p C_\nu^q
-(\mu \nu|\lambda \sigma) C_\lambda^r C_\sigma^s
-```
+<img src="./figures/noddy-transform.png" height="50">
 
-This approach is easy to implement (hence the word "[noddy](http://www.hackerslang.com/noddy.html)" above), but is expensive due to its N<sup>8</sup> computational order.  
-Nevertheless, you should start with this algorithm to get your code working, and run timings (use the UNIX "time" command) 
-for the test cases below to get an idea of its computational cost.
+This approach is easy to implement (hence the word "[noddy](http://www.hackerslang.com/noddy.html)" above), but is expensive due to its N<sup>8</sup> computational order.  Nevertheless, you should start with this algorithm to get your code working, and run timings (use the UNIX "time" command) for the test cases below to get an idea of its computational cost.
 
-  * Hint 1: Noddy transformation code
+  * [Hint 1](./hints/hint1.md): Noddy transformation code
 ### The Smarter Algorithm
 
 Notice that none of the *C* coefficients in the above expression have any indices in common.  Thus, the summation could be rearranged such that:
-```
-EQUATION 
-(pq|rs) = \sum_\mu C_\mu^p \left[ \sum_\nu C_\nu^q \left[ \sum_\lambda  C_\lambda^r \left[ \sum_\sigma C_\sigma^s (\mu \nu|\lambda \sigma) \right] \right] \right].
-```
+
+<img src="./figures/smart-transform.png" height="60">
 
 This means that each summation within brackets could be carried out separately, 
-starting from the innermost summation over <html>&#963;</html>, if we store the results at each step.  
-This reduces the N<sup>8</sup> algorithm above to four N<sup>5</sup> steps.
+starting from the innermost summation over <html>&#963;</html>, if we store the results at each step.  This reduces the N<sup>8</sup> algorithm above to four N<sup>5</sup> steps.
 
 Be careful about the permutational symmetry of the integrals and intermediates at each step: 
 while the AO-basis integrals have eight-fold permutational symmetry, the partially transformed integrals have much less symmetry.
 
 After you have the noddy algorithm working and timed, modify it to use this smarter algorithm and time the test cases again.  Enjoy!
 
-  * Hint 2: Smarter transformation code
+  * [Hint 2](./hints/hint2.md): Smarter transformation code
 
 ## Step #4: Compute the MP2 Energy
 
-```
-EQUATION
-E_{\rm MP2} = \sum_{ij} \sum_{ab} \frac{(ia|jb) \left[ 2 (ia|jb) -
-(ib|ja) \right]}{\epsilon_i + \epsilon_j - \epsilon_a - \epsilon_b},
-```
+<img src="./figures/mp2-energy.png" height="60">
 
 where *i* and *j* denote doubly-occupied orbitals and *a* and *b* unoccupied orbitals, and the denominator involves the MO energies.
 
-  * Hint 3: Occupied versus unoccupied orbitals
+  * [Hint 3](./hints/hint3.md): Occupied versus unoccupied orbitals
 
 ## Test Cases
-The input structures, integrals, etc. for these examples are found in the [input directory](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2304/input).
+The input structures, integrals, etc. for these examples are found in the [input directory](./input).
 
-* STO-3G Water | [output](https://github.com/CrawfordGroup/ProgrammingProjects/blob/master/Project%2304/output/h2o/STO-3G/output.txt)
-* DZ Water | [output](https://github.com/CrawfordGroup/ProgrammingProjects/blob/master/Project%2304/output/h2o/DZ/output.txt)
-* DZP Water | [output](https://github.com/CrawfordGroup/ProgrammingProjects/blob/master/Project%2304/output/h2o/DZP/output.txt)
-* STO-3G Methane | [output](https://github.com/CrawfordGroup/ProgrammingProjects/blob/master/Project%2304/output/ch4/STO-3G/output.txt)
+* STO-3G Water | [output](./output/h2o/STO-3G/output.txt)
+* DZ Water | [output](./output/h2o/DZ/output.txt)
+* DZP Water | [output](./output/h2o/DZP/output.txt)
+* STO-3G Methane | [output](./output/ch4/STO-3G/output.txt)
 
diff --git a/Project#04/figures/eri.png b/Project#04/figures/eri.png
new file mode 100644
index 0000000..337967e
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diff --git a/Project#04/figures/mp2-energy.png b/Project#04/figures/mp2-energy.png
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index 0000000..1003c08
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diff --git a/Project#04/figures/noddy-transform.png b/Project#04/figures/noddy-transform.png
new file mode 100644
index 0000000..ecf954c
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diff --git a/Project#04/figures/smart-transform.png b/Project#04/figures/smart-transform.png
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diff --git a/Project#04/hints/hint1.md b/Project#04/hints/hint1.md
new file mode 100644
index 0000000..01221e1
--- /dev/null
+++ b/Project#04/hints/hint1.md
@@ -0,0 +1,37 @@
+Here's a code block that demonstrates how to carry out the AO to MO two-electron integral transformation using a single N<sup>8</sup> step.  Note that the original AO- and transformed MO-basis integrals are stored in a one-dimensional array taking full advantage of their eight-fold permutational symmetry, as described in [Project #3](../../Project%2303).
+
+Note how the loop structure in the MO-indices (*i*, *j*, *k*, and *l*) automatically takes into account the permutational symmetry of the fully transformed integrals.
+
+```c++
+  #define INDEX(i,j) ((i>j) ? (((i)*((i)+1)/2)+(j)) : (((j)*((j)+1)/2)+(i)))
+  ...
+  double *TEI_AO, *TEI_MO;
+  int i, j, k, l, ijkl;
+  int p, q, r, s, pq, rs, pqrs;
+  ...
+
+  for(i=0,ijkl=0; i < nao; i++) {
+    for(j=0; j <= i; j++) {
+      for(k=0; k <= i; k++) {
+        for(l=0; l <= (i==k ? j : k); l++,ijkl++) {
+
+          for(p=0; p < nao; p++) {
+            for(q=0; q < nao; q++) {
+              pq = INDEX(p,q);
+              for(r=0; r < nao; r++) {
+                for(s=0; s < nao; s++) {
+                  rs = INDEX(r,s);
+                  pqrs = INDEX(pq,rs);
+
+                  TEI_MO[ijkl] += C[p][i] * C[q][j] * C[r][k] * C[s][l] * TEI_AO[pqrs];
+
+                }
+              }
+            }
+          }
+
+        }
+      }
+    }
+  }
+```
diff --git a/Project#04/hints/hint2.md b/Project#04/hints/hint2.md
new file mode 100644
index 0000000..79a46dd
--- /dev/null
+++ b/Project#04/hints/hint2.md
@@ -0,0 +1,59 @@
+Here's a code block that demonstrates how to carry out the AO to MO two-electron integral transformation using four N<sup>5</sup> steps.  Note that the original AO- and transformed MO-basis integrals are stored in a one-dimensional array taking advantage of their eight-fold permutational symmetry, as described in [Project #3](../../Project%2303).  However, the half-transformed integrals, which lack bra-ket permutational symmetry, are stored in a two-dimensional array.
+
+A number of convenient functions [`mmult()`, `init_matrix()`, etc.] used in this code block can be found in the [diag.cc](http://sirius.chem.vt.edu/~crawdad/programming/diag.cc) discussed in [Project #1](../../Project%2301).
+
+```c++
+  #define INDEX(i,j) ((i>j) ? (((i)*((i)+1)/2)+(j)) : (((j)*((j)+1)/2)+(i)))
+  ...
+  double **X, **Y, **TMP, *TEI;
+  int i, j, k, l, ij, kl, ijkl, klij;
+
+  ...
+  X = init_matrix(nao, nao);
+  Y = init_matrix(nao, nao);
+
+  TMP = init_matrix((nao*(nao+1)/2),(nao*(nao+1)/2));
+  for(i=0,ij=0; i < nao; i++)
+    for(j=0; j <= i; j++,ij++) {
+      for(k=0,kl=0; k < nao; k++)
+        for(l=0; l <= k; l++,kl++) {
+          ijkl = INDEX(ij,kl);
+          X[k][l] = X[l][k] = TEI[ijkl];
+        }
+      zero_matrix(Y, nao, nao);
+      mmult(C, 1, X, 0, Y, nao, nao, nao);
+      zero_matrix(X, nao, nao);
+      mmult(Y, 0, C, 0, X, nao, nao, nao);
+      for(k=0, kl=0; k < nao; k++)
+        for(l=0; l <= k; l++, kl++)
+          TMP[kl][ij] = X[k][l];
+    }
+
+  zero_array(TEI, (nao*(nao+1)/2)*((nao*(nao+1)/2)+1)/2);
+
+  for(k=0,kl=0; k < nao; k++)
+    for(l=0; l <= k; l++,kl++) {
+      zero_matrix(X, nao, nao);
+      zero_matrix(Y, nao, nao);
+      for(i=0,ij=0; i < nao; i++)
+        for(j=0; j <=i; j++,ij++)
+          X[i][j] = X[j][i] = TMP[kl][ij];
+      zero_matrix(Y, nao, nao);
+      mmult(C, 1, X, 0, Y, nao, nao, nao);
+      zero_matrix(X, nao, nao);
+      mmult(Y, 0, C, 0, X, nao, nao, nao);
+      for(i=0, ij=0; i < nao; i++)
+        for(j=0; j <= i; j++,ij++) {
+          klij = INDEX(kl,ij);
+          TEI[klij] = X[i][j];
+        }
+    }
+
+  ...
+
+  free_matrix(X, nao);
+  free_matrix(Y, nao);
+  free_matrix(TMP, (nao*(nao+1)/2));
+
+```
+
diff --git a/Project#04/hints/hint3.md b/Project#04/hints/hint3.md
new file mode 100644
index 0000000..d6ae3ab
--- /dev/null
+++ b/Project#04/hints/hint3.md
@@ -0,0 +1,20 @@
+The following code block illustrates a simple-minded MP2 energy calculation with the two-electron integrals stored in a one-dimensional array.  The molecular orbitals are assumed to be ordered with all doubly-occupied orbitals first, followed by the unoccupied/virtual orbitals.  Notice the difference in limits of the loops over *i* and *a*:
+
+```c++
+  Emp2 = 0.0;
+  for(i=0; i < ndocc; i++) {
+    for(a=ndocc; a < nao; a++) {
+      ia = INDEX(i,a);
+      for(j=0; j < ndocc; j++) {
+        ja = INDEX(j,a);
+        for(b=ndocc; b < nao; b++) {
+          jb = INDEX(j,b);
+          ib = INDEX(i,b);
+          iajb = INDEX(ia,jb);
+          ibja = INDEX(ib,ja);
+          Emp2 += TEI[iajb] * (2 * TEI[iajb] - TEI[ibja])/(eps[i] + eps[j] - eps[a] - eps[b]);
+        }
+      }
+    }
+  }
+```
diff --git a/Project#04/project4-instructions.pdf b/Project#04/project4-instructions.pdf
new file mode 100644
index 0000000..6a8da0b
Binary files /dev/null and b/Project#04/project4-instructions.pdf differ
diff --git a/Project#05/README.md b/Project#05/README.md
index 2d3a74a..d4ee632 100644
--- a/Project#05/README.md
+++ b/Project#05/README.md
@@ -3,56 +3,33 @@ The coupled cluster model provides a higher level of accuracy beyond the MP2 app
 ## Step #1: Preparing the Spin-Orbital Basis Integrals 
 Each term in the equations given in the above paper by Stanton et al. depends on the T<sub>1</sub> or T<sub>2</sub> 
 amplitudes as well as Fock-matrix elements and antisymmetrized, Dirac-notation two-electron integrals, all given in the molecular spin-orbital basis 
-(as opposed to the spatial-orbital basis used in the earlier [MP2 Project](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2304).
+(as opposed to the spatial-orbital basis used in the earlier [MP2 Project](../Project%2304).
 Thus, the transformation of the AO-basis integrals into the spatial-MO basis must also include their translation into the spin-orbital basis:
 
-```
-EQUATION
-\begin{eqnarray*}
-\langle p q | r s \rangle & \equiv & \int d{\mathbf r}_1 d{\mathbf r}_2 d\omega_1 d\omega_1 \phi_p({\mathbf r}_1)\sigma_p(\omega_1) \phi_q({\mathbf r}_2)\sigma_q(\omega_2) \frac{1}{{\mathbf r}_{12}} \phi_r({\mathbf r}_1)\sigma_r(\omega_1) \phi_s({\mathbf r}_2)\sigma_s(\omega_2) \\
-& \equiv & \int d{\mathbf r}_1 d{\mathbf r}_2 \phi_p({\mathbf r}_1) \phi_q({\mathbf r}_2) \frac{1}{{\mathbf r}_{12}} \phi_r({\mathbf r}_1) \phi_s({\mathbf r}_2) \int d\omega_1 d\omega_1 \sigma_p(\omega_1) \sigma_q(\omega_2) \sigma_r(\omega_1) \sigma_s(\omega_2) \\
-& \equiv & (p r | q s)  \int d\omega_1 d\omega_1 \sigma_p(\omega_1) \sigma_q(\omega_2) \sigma_r(\omega_1) \sigma_s(\omega_2)
-\end{eqnarry*}
-```
+<img src="./figures/spin-orbital-eri.png" height="160">
 
-
-Thus, if you know the ordering of the orbitals (e.g. all occupied orbitals before virtual orbitals, perhaps alternating between alpha and beta spins), it is straightforward to carry out the integration over the spin components (the sigmas) in the above expression.  Thus, each spatial-orbital MO-basis two-electron integral translates to 16 possible spin-orbital integrals, only four of which are non-zero.
+Thus, if you know the ordering of the orbitals (e.g. all occupied orbitals before virtual orbitals, perhaps alternating between alpha and beta spins), it is straightforward to carry out the integration over the spin components (the &sigma;'s) in the above expression.  Thus, each spatial-orbital MO-basis two-electron integral translates to 16 possible spin-orbital integrals, only four of which are non-zero.
 
 Don't forget that you must also create the spin-orbital Fock matrix:
 
-```
-EQUATION
-f_{pq} = h_{pq} + \sum_m^{\rm occ} \langle pm || qm \rangle
-```
+<img src="./figures/spin-orbital-fock.png" height="60">
 
 Suggestion: For simplicity, store the two-electron integrals in a four-dimensional array.  This will greatly facilitate debugging of the complicated CCSD equations.
 
-  * Hint: Sample spatial- to spin-orbital translation code.
+  * [Hint 1](./hints/hint1.md): Sample spatial- to spin-orbital translation code.
 
 ## Step #2: Build the Initial-Guess Cluster Amplitudes 
 For Hartree-Fock reference determinants, the most common initial guess for the cluster amplitudes are the Moller-Plesset first-order perturbed wave function:
-```
-EQUATION
-t_i^a = 0
-```
-
-```
-EQUATION
-t_{ij}^{ab} = \frac{\langle ij || ab \rangle}{\epsilon_i + \epsilon_j - \epsilon_a - \epsilon_b}
 
-```
+<img src="./figures/init-t-amps.png" height="120">
 
 Note that if you have constructed the Fock matrix, two-electron integrals, and initial-guess amplitudes correctly at this point, 
-you should be able to compute the MP2 correlation energy using the simple spin-orbital expression and get identical results to those from 
-[Project #4] (https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2304):
+you should be able to compute the MP2 correlation energy using the simple spin-orbital expression and get identical results to those from [Project #4](../Project%2304):
 
-```
-EQUATION
-E_{\rm MP2} = \frac{1}{4} \sum_{ijab} \langle ij||ab\rangle t_{ij}^{ab}
-```
+<img src="./figures/mp2-energy.png" height="60">
 
 ## Step #3: Calculate the CC Intermediates 
-Use the spin-orbital Eqs. 3-13 from Stanton's paper to build the two-index (F) and four-index (W) intermediates, as well as the effective doubles (labelled with the Greek letter tau).
+Use the spin-orbital Eqs. 3-13 from Stanton's paper to build the two-index (F) and four-index (W) intermediates, as well as the effective doubles (labelled with the Greek letter &tau;).
 
 ## Step #4: Compute the Updated Cluster Amplitudes 
 Use Eqs. 1 and 2 from Stanton's paper to compute the updated T<sub>1</sub> and T<sub>2</sub> cluster amplitudes.
@@ -60,18 +37,16 @@ Use Eqs. 1 and 2 from Stanton's paper to compute the updated T<sub>1</sub> and T
 ## Step #5: Check for Convergence and Iterate 
 Calculate the current CC correlation energy:
 
-```
-EQUATION
-E_{\rm CC} = \sum_{ia} f_{ia} t_i^a + \frac{1}{4} \sum_{ijab} \langle ij||ab\rangle t_{ij}^{ab} + \frac{1}{2} \sum_{ijab} \langle ij||ab\rangle t_i^a t_j^b
-```
-Compare energies and cluster amplitudes (using RMS differences) between iterations to check for convergence to some specified cutoff.  
+<img src="./figures/cc-correlation-energy.png" height="60">
+
+Compare energies and cluster amplitudes (using RMS differences) between iterations to check for convergence to some specified cutoff.
 If convergence is reached, you're done; if not, return to Step #3 and continue.
 
 ## Test Cases 
 The input structures, integrals, etc. for these examples are found in the 
-[input directory](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2305/input).
+[input directory](./input).
 
-* STO-3G Water | [output](https://github.com/CrawfordGroup/ProgrammingProjects/blob/master/Project%2305/output/h2o/STO-3G/output.txt)
-* DZ Water | [output](https://github.com/CrawfordGroup/ProgrammingProjects/blob/master/Project%2305/output/h2o/DZ/output.txt)
-* DZP Water | [output](https://github.com/CrawfordGroup/ProgrammingProjects/blob/master/Project%2305/output/h2o/DZP/output.txt)
-* STO-3G Methane | [output](https://github.com/CrawfordGroup/ProgrammingProjects/blob/master/Project%2305/output/ch4/STO-3G/output.txt)
+* STO-3G Water | [output](./output/h2o/STO-3G/output.txt)
+* DZ Water | [output](./output/h2o/DZ/output.txt)
+* DZP Water | [output](./output/h2o/DZP/output.txt)
+* STO-3G Methane | [output](./output/ch4/STO-3G/output.txt)
diff --git a/Project#05/figures/cc-correlation-energy.png b/Project#05/figures/cc-correlation-energy.png
new file mode 100644
index 0000000..0be10b2
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diff --git a/Project#05/figures/init-t-amps.png b/Project#05/figures/init-t-amps.png
new file mode 100644
index 0000000..9d8e797
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diff --git a/Project#05/figures/mp2-energy.png b/Project#05/figures/mp2-energy.png
new file mode 100644
index 0000000..cae007a
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diff --git a/Project#05/figures/spin-orbital-eri.png b/Project#05/figures/spin-orbital-eri.png
new file mode 100644
index 0000000..5ae01a5
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diff --git a/Project#05/figures/spin-orbital-fock.png b/Project#05/figures/spin-orbital-fock.png
new file mode 100644
index 0000000..69e8771
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diff --git a/Project#05/hints/hint1.md b/Project#05/hints/hint1.md
new file mode 100644
index 0000000..6483590
--- /dev/null
+++ b/Project#05/hints/hint1.md
@@ -0,0 +1,19 @@
+This block of code takes the one-dimensional array of MO-basis spatial-orbital two-electron integrals we've been using thus far and translates it to a four-dimensional array of antisymmetrized integrals over spin-orbitals.  Note that alpha and beta spin functions alternate here, with even-numbered orbitals corresponding to alpha, and odd-numbered to beta.  The variable `nmo` is the number of spin orbitals, and the `INDEX` function is the same as that [used before](../../Project%2303/hints/hint7-2.md).
+
+```c++
+  /* Translate integrals to spin-orbital basis */
+  for(p=0; p < nmo; p++)
+    for(q=0; q < nmo; q++)
+      for(r=0; r < nmo; r++)
+        for(s=0; s < nmo; s++) {
+          pr = INDEX(p/2,r/2);
+          qs = INDEX(q/2,s/2);
+          prqs = INDEX(pr,qs);
+          value1 = TEI[prqs] * (p%2 == r%2) * (q%2 == s%2);
+          ps = INDEX(p/2,s/2);
+          qr = INDEX(q/2,r/2);
+          psqr = INDEX(ps,qr);
+          value2 = TEI[psqr] * (p%2 == s%2) * (q%2 == r%2);
+          ints[p][q][r][s] = value1 - value2;
+        }
+```
diff --git a/Project#06/README.md b/Project#06/README.md
index 7fd07b3..effecf3 100644
--- a/Project#06/README.md
+++ b/Project#06/README.md
@@ -1,60 +1,37 @@
 # Project #6: A perturbative triples correction to CCSD: CCSD(T)
 
 The CCSD(T) method is often referred to as the "gold standard" of quantum chemistry for its high accuracy and reliability.  The purpose of this project is to illustrate the fundamental aspects of an efficient implementation of the (T) energy correction.  This project builds upon the results of 
-[Project #5](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2305).
+[Project #5](../Project%2305).
 
 The spin-orbital expression for the (T) correction, using the same notation as in 
-[Project #5](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2305), is:
-
-```
-EQUATION
-E_{\rm (T)} = \frac{1}{36} \sum_{ijkabc} t_{ijk}^{abc}(c) D_{ijk}^{abc} \left[ t_{ijk}^{abc}(c) + t_{ijk}^{abc}(d) \right],
-```
+[Project #5](../Project%2305), is:
 
+<img src="./figures/t-correction.png" height="60">
 
 where 
 
-```
-EQUATION
-D_{ijk}^{abc} = f_{ii} + f_{jj} + f_{kk} - f_{aa} - f_{bb} - f_{cc},
-```
-
+<img src="./figures/D.png" height="30">
 
 the "disconnected" triples are defined as
 
-```
-EQUATION
-D_{ijk}^{abc} t_{ijk}^{abc}(d) = P(i/jk) P(a/bc) t_i^a \langle jk || bc \rangle,
-```
-
+<img src="./figures/disconnected-triples.png" height="30">
 
 and the "connected" triples as
 
-```
-EQUATION
-D_{ijk}^{abc} t_{ijk}^{abc}(c) = P(i/jk) P(a/bc) \left[ \sum_e t_{jk}^{ae} \langle ei||bc \rangle - \sum_m t_{im}^{bc} \langle ma||jk \rangle \right].
-```
-
+<img src="./figures/connected-triples.png" height="70">
 
 The three-index permutation operator is defined by its action on an algebraic function as
 
-```
-EQUATION
-P(p/qr) f(pqr) = f(pqr) - f(qpr) - f(rqp).
-```
-
+<img src="./figures/three-index-permutation.png" height="25">
 
 The total energy is
 
-```
-EQUATION
-E_{\rm total} = E_{\rm SCF} + E_{\rm CCSD} + E_{\rm (T)}.
-```
-
+<img src="./figures/total-energy.png" height="25">
 
 ## Algorithm #1: Full Storage of Triples
 
 The most straightforward approach to evaluation of the (T) energy correction is to compute and store explicitly the connected and disconnected triples and plug them into the energy expression above. Store the triples amplitudes as six-dimensional arrays over occupied and virtual spin orbitals. 
+
 ## Algorithm #2: Avoided Storage of Triples
 
 Note that each T<sub>3</sub> amplitude depends on all the T<sub>1</sub> and T<sub>2</sub> amplitudes, **not** on other triples.  This suggests that the calculation of the T<sub>3</sub> amplitudes appearing in the energy expression could proceed one amplitude at a time:
@@ -95,13 +72,13 @@ This algorithm reduces the storage (memory and disk) requirements of the (T) cor
   End i loop
 ```
 
-This approach requires more storage (on the order v<sup>3</sup>) than the one-at-a-time approach, but can be considerably faster of modern high-performance computers.  A good discussion of the most efficient algorithm can be found in A. P. Rendell, T. J. Lee, A. Komornicki, //Chem. Phys. Lett.// **178**, 462-470 (1991).
+This approach requires more storage [O(v<sup>3</sup>)] than the one-at-a-time approach, but can be considerably faster for modern high-performance computers.  A good discussion of the most efficient algorithm can be found in A. P. Rendell, T. J. Lee, A. Komornicki, //Chem. Phys. Lett.// **178**, 462-470 (1991).
 
 ## Test Cases
-The input structures, integrals, etc. for these examples may be found in the [input](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2306/input) 
-directory, the CCSD Energies can be found in [Project #5](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2305).
+The input structures, integrals, etc. for these examples may be found in the [input](./input) 
+directory, the CCSD Energies can be found in [Project #5](../Project%2305).
 
-* STO-3G Water | [Output](https://github.com/CrawfordGroup/ProgrammingProjects/blob/master/Project%2306/output/h2o/STO-3G/output.txt) 
-* DZ Water | [Output](https://github.com/CrawfordGroup/ProgrammingProjects/blob/master/Project%2306/output/h2o/DZ/output.txt) 
-* DZP Water | [Output](https://github.com/CrawfordGroup/ProgrammingProjects/blob/master/Project%2306/output/h2o/DZP/output.txt) 
-* STO-3G Methane | [Output](https://github.com/CrawfordGroup/ProgrammingProjects/blob/master/Project%2306/output/ch4/STO-3G/output.txt) 
+* STO-3G Water | [Output](./output/h2o/STO-3G/output.txt) 
+* DZ Water | [Output](./output/h2o/DZ/output.txt) 
+* DZP Water | [Output](./output/h2o/DZP/output.txt) 
+* STO-3G Methane | [Output](./output/ch4/STO-3G/output.txt) 
diff --git a/Project#06/figures/D.png b/Project#06/figures/D.png
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diff --git a/Project#06/figures/total-energy.png b/Project#06/figures/total-energy.png
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diff --git a/Project#08/README.md b/Project#08/README.md
index a26270b..dc85873 100644
--- a/Project#08/README.md
+++ b/Project#08/README.md
@@ -1,6 +1,6 @@
 # Project #8: DIIS extrapolation for the SCF procedure
 
-The convergence of the self-consistent field (SCF) algorithm presented in Project #3 is rather slow.  
+The convergence of the self-consistent field (SCF) algorithm presented in [Project #3](../Project%2303) is rather slow.
 Even the STO-3G H<sub>2</sub>O example requires more than 20 iterations to converge the RMS density difference to a relatively loose threshold of 10<sup>-8</sup>.
 One of the most effective methods for speeding up such iterative sequences is the 
 "Direct Inversion in the Iterative Subspace (DIIS)" approach, which was 
@@ -11,110 +11,64 @@ a new guess may be constructed as a simple linear combination of the previous fe
 where the coefficients of such an extrapolation are determined from Lagrangian minimization procedure.
 
 The purpose of this programming project is to implement the Pulay DIIS procedure within the SCF algorithm from 
-[Project #3](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2303).
+[Project #3](../Project%2303).
 
 ## Working Equations
 
 Given a series of Fock matrices, <b><i>F<sub>i</sub></i></b> (expressed in the AO basis set), a new approximation to the converged solution may be written as
 
-```
-EQUATION
-{\mathbf F}' = \sum_i c_i {\mathbf F}_i
-```
-
+<img src="./figures/new-approx-fock.png" height="40">
 
 by requiring that the corresponding extrapolated "error" matrix
 
-```
-EQUATION
-{\mathbf e}' = \sum_i c_i {\mathbf e}_i \approx {\mathbf 0}
-```
-
+<img src="./figures/error-matrix.png" height="40">
 
 is approximately the zero matrix in a least-squares sense.  The error matrix for each iteration is given by
 
-```
-EQUATION
-{\mathbf e_i} \equiv {\mathbf F}_i {\mathbf D}_i {\mathbf S} - {\mathbf S} {\mathbf D}_i {\mathbf F}_i,
-```
-
+<img src="./figures/iter-error-matrix.png" height="20">
 
 where <b><i>D<sub>i</sub></i></b> is the AO-basis density matrix used to construct 
-<b><i>F<sub>i</sub></i></b>, and  ** *S* ** is the AO-basis overlap matrix.  Minimization of ** *e'* ** under the constraint that 
-
-```
-EQUATION
-\sum_i c_i = 1
-```
+<b><i>F<sub>i</sub></i></b>, and  <b><i>S</i></b> is the AO-basis overlap matrix.  Minimization of <b><i>e'</i></b> under the constraint that 
 
+<img src="./figures/constraint.png" height="45">
 
 leads to the following system of linear equations for the c<sub>i</sub>:
 
-```
-EQUATION
-\left(
-\begin{array}{ccccc}
-B_{11} & B_{12} & \ldots & B_{1m} & -1 \\
-B_{21} & B_{22} & \ldots & B_{2m} & -1 \\
-\ldots & \ldots & \ldots & \ldots & -1 \\
-B_{m1} & B_{m2} & \ldots & B_{mm} & -1 \\
--1 & -1 & \ldots & -1 & 0 \\
-\end{array}
-\right) \left(
-\begin{array}{c}
-c_1 \\
-c_2 \\
-\ldots \\
-c_m \\
-\lambda
-\end{array}
-\right) = \left(
-\begin{array}{c}
-0 \\
-0 \\
-\ldots \\
-0 \\
--1 \\
-\end{array}
-\right),
-```
-
-where lambda is a Lagrangian multiplier and the elements <b>B<sub>ij</sub></b> are computed as dot products of error matrices:
+<img src="./figures/sys-lin-eqn-ci.png" height="125">
 
-```
-EQUATION
-B_{ij} \equiv {\mathbf e}_i \cdot {\mathbf e}_j.
-```
+where lambda is a Lagrangian multiplier and the elements <i>B<sub>ij</sub></i> are computed as dot products of error matrices:
 
+<img src="./figures/Bij.png" height="20">
 
 ## Step #1: Compute the Error Matrix in Each Iteration
 
-Compute the error matrix for the current iteration using the matrix equation  for **e**<sub>i</sub> given above.  
-Note that the density matrix you use must be the same one used to construct the corresponding Fock matrix.  
+Compute the error matrix for the current iteration using the matrix equation  for <b><i>e<sub>i</sub></i></b> given above.
+Note that the density matrix you use must be the same one used to construct the corresponding Fock matrix.
 If you print the error matrix in each iteration, you should be able to note that it gradually falls to zero as the SCF procedure converges.
 
 ## Step #2: Build the B Matrix and Solve the Linear Equations
 
-After you have computed at least two error matrices, it is possible to begin the DIIS extrapolation procedure.  
+After you have computed at least two error matrices, it is possible to begin the DIIS extrapolation procedure.
 Compute the B matrix above for all of the current error matrices. 
 (Note that the matrix is symmetric, so one need only compute the lower triangle to get the entire matrix).
 
 Next, use a standard linear-equation solver (such as the DGESV function in the LAPACK library, 
 to which PSI4 has an interface named C_DGESV) to compute the <b>c<sub>i</sub></b> coefficients. 
 (NB: If you use the LAPACK solver, or any LAPACK or BLAS function for that matter, you must use matrices allocated as contiguous memory, 
-as discussed in [Project #7](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2307#usefulPsiFeatures)).
+as discussed in [Project #7](../Project%2307)).
 
 ## Step #3: Compute the New Fock Matrix
 
-Build a new Fock matrix using the equation for ** *F'* ** above and continue with the SCF procedure as usual.  
-This implies that one must store all of the Fock matrices corresponding to each of the error matrices used in constructing the B matrix above.  Note:
+Build a new Fock matrix using the equation for <b><i>F'</i></b> above and continue with the SCF procedure as usual.
+This implies that one must store all of the Fock matrices corresponding to each of the error matrices used in constructing the B matrix above.
+Note:
 
   * Do **not** use the extrapolated Fock matrix to compute error matrices for subsequent DIIS steps.
   * Keep only a relatively small number of error matrices; six to eight are reasonable for closed-shell SCF calculations. When the chosen number of error
   matrices is exceeded delete the oldest error matrix.
 
-Once the procedure is complete and working correctly, you should notice a considerable reduction in the number of SCF cycles required to achieve convergence.  
-For example, for the STO-3G/H2O test case from [Project #3](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2303), 
+Once the procedure is complete and working correctly, you should notice a considerable reduction in the number of SCF cycles required to achieve convergence.
+For example, for the STO-3G/H<sub>2</sub>O test case from [Project #3](../Project%2303), 
 the simple SCF algorithm converges to 10<sup>-12</sup> in the density in 39 iterations:
 ```
  Iter        E(elec)              E(tot)               Delta(E)             RMS(D)
diff --git a/Project#08/figures/Bij.png b/Project#08/figures/Bij.png
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diff --git a/Project#09/README.md b/Project#09/README.md
index f3a37a7..1a01dbd 100644
--- a/Project#09/README.md
+++ b/Project#09/README.md
@@ -3,11 +3,11 @@
 The use of point-group symmetry in quantum chemical calculations can lead to exceptionally efficient programs, 
 both in terms of their memory/disk usage and their computing times.  If a molecule has even one element of symmetry, 
 for example, this can reduce the number of wave function parameters that must be stored by up to a factor of two (the order of the point group) 
-and the computing effort by up to a factor of four (the square of the order of the point group).   
+and the computing effort by up to a factor of four (the square of the order of the point group).
 Most quantum chemical programs can take advantage of Abelian symmetry -- more accurately, 
 D<sub>2h</sub> and its subgroups -- which means that higher symmetry structures can yield up to a factor of 64 reduction in the computational costs.
 
-The purpose of this project is to take advantage of basic point-group symmetry in an SCF calculation.  
+The purpose of this project is to take advantage of basic point-group symmetry in an SCF calculation.
 While the most efficient programs will store only the symmetry-allowed sets of two-electron integrals, 
 for the purposes of this project we'll deal only with the one-electron (two-index) components.
 
@@ -15,22 +15,19 @@ for the purposes of this project we'll deal only with the one-electron (two-inde
 
 The vanishing integral rule of point-group theory may be stated as follows for Abelian groups:
 
-```
-EQUATION
-\langle \phi_i | \hat{A} |\phi_j \rangle = 0 \ \ \ \ {\rm if} \ \ \ \ \Gamma_A \neq \Gamma_{\phi_i} \otimes \Gamma_{\phi_j},
-```
+<img src="./figures/point-group-rule.png" height="30">
 
-where <html>&Gamma;<sub>X</sub></html> denotes the irreducible representation (irrep) of entity X.  
+where <html>&Gamma;<sub>X</sub></html> denotes the irreducible representation (irrep) of entity X.
 That is, unless the direct product of the irreps of the functions or operators in the integrand contains the totally symmetric irrep, the integral must be zero.
 
 The vanishing integral rule of group theory may be readily applied to the various integrals and wave-function parameters in the SCF procedure 
-** *if* ** the AO-basis functions over which the they are evaluated have been properly symmetrized 
+<b><i>if</i></b> the AO-basis functions over which the they are evaluated have been properly symmetrized 
 [i.e. used to form symmetry-adapted linear combinations, normally referred to as symmetry orbitals (SOs)].
 
-For example, consider the H<sub>2</sub>O test case with the STO-3G basis set as given in Project #3.  The AO 
+For example, consider the H<sub>2</sub>O test case with the STO-3G basis set as given in [Project #3](../Project%2303).  The AO 
 ([contracted Gaussian](http://sirius.chem.vt.edu/wiki/lib/exe/fetch.php?media=basis_sets.pdf)) basis functions 
 on the oxygen atom consist of 1s, 2s, 2p<sub>x</sub>, 2p<sub>y</sub>, and 2p<sub>z</sub> orbitals, 
-which those for each hydrogen atom consist of only the 1s, giving a total of seven AOs.  
+which those for each hydrogen atom consist of only the 1s, giving a total of seven AOs.
 If we take oxygen to be the first atom and ignore the C<sub>2v</sub> point group symmetry of the molecule, 
 the resulting overlap integral matrix looks like:
 
@@ -48,20 +45,20 @@ the resulting overlap integral matrix looks like:
 The first five row/column indices correspond to the basis functions on the oxygen (in the order listed above),
 while rows/columns six and seven correspond to the basis functions on each hydrogen. 
 Thus, the 1-2 element is the overlap integral between the 1s and 2s orbitals on the oxygen, 
-while element 3-7 is the overlap integral between the oxygen 2p<sub>x</sub> orbital and the second hydrogen 1s orbital.  
+while element 3-7 is the overlap integral between the oxygen 2p<sub>x</sub> orbital and the second hydrogen 1s orbital.
 
 Points to note about this matrix:
-  - The 1s and 2s orbitals on oxygen are not orthogonal to one another, but both are orthogonal to all three p-type orbitals.  
+  - The 1s and 2s orbitals on oxygen are not orthogonal to one another, but both are orthogonal to all three p-type orbitals.
   This occurs because, in Cartesian Gaussian basis sets, 
   orthogonality is generally obtained only between functions of different angular momenta on the same atomic center.
   - The 1s orbitals on the hydrogens have the same overlap integral (to within a sign) 
-  with all the orbitals on the oxygen because they are ** *symmetry equivalent* ** .  
+  with all the orbitals on the oxygen because they are <b><i>symmetry equivalent</i></b>.
   However, the 1s orbitals alone do not transform as irreps of the C<sub>2v</sub> point group.
-  - The hydrogen 1s orbitals are orthogonal to the 2p<sub>z</sub> orbital on the oxygen (cf. elements 5-6 and 5-7).  
+  - The hydrogen 1s orbitals are orthogonal to the 2p<sub>z</sub> orbital on the oxygen (cf. elements 5-6 and 5-7).
   This is because the water molecule was arbitrarily oriented in the xy-plane to compute the above integrals; 
   thus the 2p<sub>z</sub> orbital is perpendicular to the molecular plane containing the hydrogen 1s orbitals.
 
-What happens if we turn on symmetry, i.e. take linear combinations of the AO to obtain SOs?  
+What happens if we turn on symmetry, i.e. take linear combinations of the AO to obtain SOs?
 If we orient the molecule oriented in the yz-plane, so that the z-axis corresponds to the C<sub>2</sub> rotation axis, 
 we find that the AOs transform as the following irreps:
 
@@ -75,7 +72,7 @@ we find that the AOs transform as the following irreps:
 |  H<sub>1</sub> 1s + H<sub>2</sub> 1s  |  A<sub>1</sub>  |
 |  H<sub>1</sub> 1s - H<sub>2</sub> 1s  |  B<sub>2</sub>  |
 
-Thus, after symmetrization, there are four A<sub>1</sub> SOs, one B<sub>1</sub> SO, and two B<sub>2</sub> SOs.  
+Thus, after symmetrization, there are four A<sub>1</sub> SOs, one B<sub>1</sub> SO, and two B<sub>2</sub> SOs.
 (The STO-3G basis set contains no A<sub>2</sub> orbitals.  One must include at least d-type functions on the oxygen and/or 
 p-type functions on the hydrogens to obtain A<sub>2</sub> orbitals.)  Note that a normalization factor of 1/sqrt(2) should be included for the H 1s SOs above.
 
@@ -107,13 +104,13 @@ The PSI checkpoint file contains a great deal of useful symmetry information. To
 
 ## Storing One-Electron Integrals with Symmetry
 
-The block-diagonal structure above implies that one need only store and use the sub-matrices of the integrals rather than the full matrix.  
+The block-diagonal structure above implies that one need only store and use the sub-matrices of the integrals rather than the full matrix.
 One way of doing this is to store the one-electron integrals as an array of smaller matrices, 
 the size of which is dictated by the number of SOs per irrep.  For example, here's a code snippet that will extract the one-electron integrals 
-from the appropriate file (as was done in [Project #7](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2307) ), 
+from the appropriate file (as was done in [Project #7](../Project%2307) ), 
 but stores them in an array of matrices:
 
-```cpp
+```c++
   int ntri, nirreps;
   double *scratch;
   double ***S;
@@ -138,9 +135,9 @@ but stores them in an array of matrices:
 ```
 
 Notice how S is now a `double ***` -- i.e. an array of matrices.  This code uses the same `INDEX()` function found in 
-[Project #3](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2303), 
-and the sopi array is the integer array of SOs per irrep obtained using the `chkpt_rd_sopi()` function.  
-The `symm_offset` array is useful for converting between ** *relative* ** orbital indices and ** *absolute* ** orbital indices.  
+[Project #3](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2303),
+and the sopi array is the integer array of SOs per irrep obtained using the `chkpt_rd_sopi()` function.
+The `symm_offset` array is useful for converting between <b><i>relative</i></b> orbital indices and <b><i>absolute</i></b> orbital indices.
 (For example, orbital 0 in the B<sub>2</sub> irrep block corresponds to orbital 5 
 in the full list of orbitals; the first number is the relative index, the second is the absolute index.)
 
@@ -149,28 +146,23 @@ in the full list of orbitals; the first number is the relative index, the second
 If we store the integral, MO coefficient, density, and Fock matrices in the block-diagonal structure described above, 
 we may compute matrix products of these quantities separately for each diagonal block.  For example, the matrix product may be written as:
 
-```
-EQUATION
-{\mathbf C} = {\mathbf A} {\mathbf B} = \bigoplus_h {\mathbf C}_h = \bigoplus_h {\mathbf A}_h {\mathbf B}_h,
-```
+<img src="./figures/matrix-product.png" height="40">
 
-where *h* denotes a particular irrep of the point group and <b><i>C</i></b><sub>h</sub> denotes the *h*-th irrep subblock of the full matrix ** *C* ** .  
+where *h* denotes a particular irrep of the point group and <b><i>C</i></b><sub>h</sub> denotes the *h*-th irrep subblock of the full matrix <b><i>C</i></b>.
 (The notation of the large plus with a circle around it indicates a direct sum.)
 
 ## Occupied Orbitals and the Density Matrix
 
 The calculation of the density matrix requires information about the number of occupied orbitals:
 
-```
-EQUATION
-D_{\mu\nu} = \sum_m^{\rm occ.} \left( {\mathbf C} \right)_\mu^m \left( {\mathbf C} \right)_\nu^m
-```
+<img src="./figures/density-matrix.png" height="50">
+
 In a calculation without symmetry, one need only know the number of electrons (equivalently, the atomic numbers of the atoms and the overall molecular charge) 
 to evaluate this expression.  However, if the density and MO coefficient matrices are stored in symmetry-blocked form, 
-as above, one needs to know the number of occupied MOs in each irrep.  
+as above, one needs to know the number of occupied MOs in each irrep.
 
 For the case of the C<sub>2v</sub> water molecule, which has two <html>&sigma;</html> O-H bonds, two oxygen lone pairs, 
-and one oxygen core orbital, the orbital occupations are not difficult to determine, given the above information about the number of SOs in each irrep.  
+and one oxygen core orbital, the orbital occupations are not difficult to determine, given the above information about the number of SOs in each irrep.
 Since the MOs are constructed as linear combinations of the SOs, and only SOs of the same irrep can combine, we may rationalize the occupied orbitals of 
 H<sub>2</sub>O as follows:
 
@@ -184,9 +176,9 @@ H<sub>2</sub>O as follows:
 
 Thus, for the water molecule, there are 3 A<sub>1</sub>, 1 B<sub>1</sub>, and 1 B<sub>2</sub> occupied orbitals.
 
-Determining the occupations automatically is sometimes a difficult task, especially for molecules with unusual bonding patterns.  
+Determining the occupations automatically is sometimes a difficult task, especially for molecules with unusual bonding patterns.
 Many SCF programs will simply take the core Hamiltonian matrix (often used as the initial guess for the Fock matrix), 
-diagonalize it (in the othogonal AO basis) in each irrep block, and identify the lowest eigenvalues in each irrep as occupied.  
+diagonalize it (in the othogonal AO basis) in each irrep block, and identify the lowest eigenvalues in each irrep as occupied.
 However, this approach often fails for many molecules (especially those with open shells) because of near-degeneracies 
 that may not be adequately described by the simple core Hamiltonian.  Thus, some programs will make use of more 
 sophisticated guesses at the Fock matrix, e.g. Hueckel orbitals or other (semi)empirical forms.
@@ -195,12 +187,9 @@ sophisticated guesses at the Fock matrix, e.g. Hueckel orbitals or other (semi)e
 
 The only portion of the SCF procedure involving two-electron integrals is the Fock-matrix build:
 
-```
-EQUATION
-F_{\mu\nu} = H^{\rm core}_{\mu\nu} + \sum_{\lambda\sigma}^{\rm AO} D^{i-1}_{\lambda\sigma} \left[ 2 (\mu\nu | \lambda\sigma) - (\mu\lambda|\nu\sigma) \right],
-```
+<img src="./figures/fock-build.png" height="60">
 
-where the notation used in [Project #3](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2303) is retained above.  
+where the notation used in [Project #3](../Project%2303) is retained above.
 If the Fock matrix and density matrix are stored in a symmetry-blocked manner similar to the overlap matrix above, 
 then one may limit the corresponding loops only to the symmetry-allowed combinations, e.g. the irreps of <html>&mu;</html> and 
 <html>&nu;</html> must match for F<html><sub>&mu;&nu;</sub></html> to be non-zero and the irreps of <html>&lambda;</html> 
@@ -208,4 +197,4 @@ and <html>&sigma;</html> must match for D<html><sub>&lambda;&sigma;</sub></html>
 Note, however, that, because of the symmetries in the two-electron integrals, 
 the irrep of <html>&lambda;</html> and <html>&sigma;</html> do not necessarily have to match that of <html>&mu;</html> and <html>&nu;</html>.
 
-  * Hint: Fock-Build Code
+  * [Hint](./hints/hint1.md): Fock-Build Code
diff --git a/Project#09/figures/density-matrix.png b/Project#09/figures/density-matrix.png
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diff --git a/Project#09/figures/fock-build.png b/Project#09/figures/fock-build.png
new file mode 100644
index 0000000..90eb475
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diff --git a/Project#09/figures/matrix-product.png b/Project#09/figures/matrix-product.png
new file mode 100644
index 0000000..aaa4ff7
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diff --git a/Project#09/figures/point-group-rule.png b/Project#09/figures/point-group-rule.png
new file mode 100644
index 0000000..a4ae26b
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diff --git a/Project#09/hints/hint1.md b/Project#09/hints/hint1.md
new file mode 100644
index 0000000..670bf7d
--- /dev/null
+++ b/Project#09/hints/hint1.md
@@ -0,0 +1,28 @@
+```c++
+    for(h=0; h < nirreps; h++) {
+      for(i=0; i < sopi[h]; i++) {
+        I = symm_offset[h] + i;
+        for(j=0; j < sopi[h]; j++) {
+          J = symm_offset[h] + j;
+          F[h][i][j] = H[h][i][j];
+
+          for(g=0; g < nirreps; g++) {
+            for(k=0; k < sopi[g]; k++) {
+              K = symm_offset[g] + k;
+              for(l=0; l < sopi[g]; l++) {
+                L = symm_offset[g] + l;
+
+                ij = INDEX(I,J); kl = INDEX(K,L);
+                ijkl = INDEX(ij,kl);
+                ik = INDEX(I,K); jl = INDEX(J,L);
+                ikjl = INDEX(ik,jl);
+
+                F[h][i][j] += D[g][k][l] * (2.0 * TEI[ijkl] - TEI[ikjl]);
+              }
+            }
+
+          }
+        }
+      }
+    }
+```
diff --git a/Project#10/README.md b/Project#10/README.md
index 808e9f7..48e85fe 100644
--- a/Project#10/README.md
+++ b/Project#10/README.md
@@ -12,10 +12,7 @@ zero as the equations converge.  In the SCF procedure, we use the atomic-orbital
 representation of the occupied-virtual block of the Fock matrix. In the CC method, we
 could choose the difference between successive sets of cluster amplitudes:
 
-```
-EQUATION
-{\mathbf e}_i = {\mathbf T}_{i+1} - {\mathbf T}_i,
-```
+<img src="./figures/error-vector.png" height="20">
 
 where <b>T</b><sub>i</sub> represents a vector containing all the cluster amplitudes for the *i*-th iteration.
 
@@ -23,8 +20,8 @@ There are three important points to note about this choice of error vector:
   * Defining the error vectors as differences between successive sets of amplitudes
     implies that one cannot begin the DIIS extrapolation until at least three
     iterations are complete.
-  * Just as in the SCF DIIS procedure, error vectors should only be computed using *
-    **non-extrapolated** * sets of cluster amplitudes.
+  * Just as in the SCF DIIS procedure, error vectors should only be computed using
+    <b><i>non-extrapolated</i></b> sets of cluster amplitudes.
   * The set of cluster amplitudes can require substantial memory for larger
     molecules; hence, the choice of the number of error vectors used in the CC DIIS
     procedure is potentially dependent on the available storage (disk and memory).
@@ -32,48 +29,15 @@ There are three important points to note about this choice of error vector:
 ## Extrapolation
 Given the above definition of the error vectors, the set of linear equations to be solved is the same as that for the SCF DIIS procedure:
 
-```
-EQUATION
-\left(
-\begin{array}{ccccc}
-B_{11} & B_{12} & \ldots & B_{1m} & -1 \\
-B_{21} & B_{22} & \ldots & B_{2m} & -1 \\
-\ldots & \ldots & \ldots & \ldots & -1 \\
-B_{m1} & B_{m2} & \ldots & B_{mm} & -1 \\
--1 & -1 & \ldots & -1 & 0 \\
-\end{array}
-\right) \left(
-\begin{array}{c}
-c_1 \\
-c_2 \\
-\ldots \\
-c_m \\
-\lambda
-\end{array}
-\right) = \left(
-\begin{array}{c}
-0 \\
-0 \\
-\ldots \\
-0 \\
--1 \\
-\end{array}
-\right),
-```
+<img src="./figures/sys-lin-eqn-ci.png" height="125">
 
-where lambda is a Lagrangian multiplier and the elements <i>B<sub>ij</sub></i> are computed as dot products of error matrices:
+where &lambda; is a Lagrangian multiplier and the elements <i>B<sub>ij</sub></i> are computed as dot products of error matrices:
 
-```
-EQUATION
-B_{ij} \equiv {\mathbf e}_i \cdot {\mathbf e}_j.
-```
+<img src="./figures/Bij.png" height="20">
 
 A new set of cluster amplitudes is then obtained as a linear combinations of older amplitudes using the coefficients from the linear equations above:
 
-```
-EQUATION
-{\mathbf T}_{\rm new} = \sum_i c_i {\mathbf T}_i
-```
+<img src="./figures/new-t-amps.png" height="50">
 
 Again: The extrapolated cluster amplitudes should be used only in the CC amplitude equations, not to compute subsequent error vectors.
 
@@ -81,8 +45,7 @@ Again: The extrapolated cluster amplitudes should be used only in the CC amplitu
 Once the procedure is working, you should observe a considerable reduction in the
 number of iterations required to converge the CC amplitude equations to a given
 tolerance.  For example, without DIIS extrapolation, the STO-3G H<sub>2</sub>O test
-case from [Project #5](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2305) 
-converges in 38 iterations to a
+case from [Project #5](../Project%2305) converges in 38 iterations to a
 precision of 10<sup>-12</sup>:
 
 ```
diff --git a/Project#10/figures/Bij.png b/Project#10/figures/Bij.png
new file mode 100644
index 0000000..e8e0a7b
Binary files /dev/null and b/Project#10/figures/Bij.png differ
diff --git a/Project#10/figures/error-vector.png b/Project#10/figures/error-vector.png
new file mode 100644
index 0000000..2c54b20
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diff --git a/Project#10/figures/new-t-amps.png b/Project#10/figures/new-t-amps.png
new file mode 100644
index 0000000..8782089
Binary files /dev/null and b/Project#10/figures/new-t-amps.png differ
diff --git a/Project#10/figures/sys-lin-eqn-ci.png b/Project#10/figures/sys-lin-eqn-ci.png
new file mode 100644
index 0000000..9bdf555
Binary files /dev/null and b/Project#10/figures/sys-lin-eqn-ci.png differ
diff --git a/Project#11/README.md b/Project#11/README.md
index e963872..944698a 100644
--- a/Project#11/README.md
+++ b/Project#11/README.md
@@ -26,22 +26,18 @@ physical memory available on workstations or supercomputer nodes.
 The purpose of this project is to consider and implement an "out-of-core" SCF
 algorithm, that is, an approach that minimizes the core-memory requirements of
 the program by reading the two-electron repulsion integrals from disk in
-batches when only they are needed.((An alternative approach is the so-called
+batches when only they are needed (An alternative approach is the so-called
 "direct" SCF, in which the two-electron integrals are re-computed in each SCF
-iteration rather than stored on disk.))
+iteration rather than stored on disk)
 
 ## The Fock Matrix Build
 
 At the heart of the SCF procedure is the expensive Fock-matrix term:
 
-```
-EQUATION
-F_{ij} = H^{\rm core}_{ij} + \sum_{kl}^{\rm AO} D_{kl} \left[ 2 (ij|kl) - (ik|jl) \right],
-```
+<img src="./figures/fock-matrix.png" height="60">
 
 where we use *i*, *j*, *k*, and *l* to denote AO-basis indices.  As described
-in [Project #3](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2303), a simple algorithm for
-evaluating this matrix is:
+in [Project #3](../Project%2303), a simple algorithm for evaluating this matrix is:
 
 ```cpp
 for(i=0; i < nao; i++)
@@ -63,10 +59,9 @@ for(i=0; i < nao; i++)
 
 This algorithm hinges on the fact that all the two-electron integrals are
 immediately available in the TEI array (which takes advantage of permutational
-symmetry).  In 
-[Project #7](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2307) 
-you made use of the following code, which reads the integrals into the TEI
-array in batches (sometimes referred to in PSI as "buffers"):
+symmetry).  In [Project #7](../Project%2307) you made use of the following code, 
+which reads the integrals into the TEI array in batches (sometimes referred to 
+in PSI as "buffers"):
 
 ```cpp
   iwl_buf_init(&InBuf, PSIF_SO_TEI, 1e-14, 1, 0);
@@ -117,47 +112,36 @@ each individual integral to the Fock matrix:
   iwl_buf_close(&InBuf, 1);
 ```
 
-Thus a given integral, (ij|kl), would contribute to **//at least two//** Fock matrix elements as:
+Thus a given integral, (ij|kl), would contribute to <b><i>at least two</i></b> Fock matrix elements as:
+
+<img src="./figures/fock-contribution-1.png" height="20">
 
-```
-EQUATION
-F_{ij} \leftarrow +2 * D_{kl} (ij|kl)
-```
 and
 
-```
-EQUATION
-F_{ik} \leftarrow - D_{jl} (ij|kl).
-```
+<img src="./figures/fock-contribution-2.png" height="20">
 
 ## Handling Permutational Symmetry
 
 The most difficult aspect of the out-of-core algorithm is the fact that file contains only the permutationally unique integrals,
 *(ij|kl)*, such that:
-```
-EQUATION
-i \geq j,\ \ \ \ \ k \geq l,\ \ \ \ \ \ {\rm and}\ \ \ \ \ \ ij \geq kl,
-```
+
+<img src="./figures/index-restrictions.png" height="20">
+
 where
 
-```
-EQUATION
-ij \equiv i(i+1)/2 + j\ \ \ \ \ \ {\rm and} \ \ \ \ \ \ kl \equiv k(k+1)/2 + l.
-```
+<img src="./figures/compound-indices.png" height="22.5">
+
 Thus, when determining the contribution of a given integral to various elements
 of the Fock matrix, one must consider all possible unique permutations of the
 indices, *i*, *j*, *k*, and *l*.  Note, however, that coincidences among the
 indices can limit the number of possibilities.  For example, if one encountered
-the integral *(22|11)*, it would contribute to a total of * **four** * Fock
+the integral *(22|11)*, it would contribute to a total of <b><i>four</i></b> Fock
 matrix elements, viz.
 
-```
-EQUATION
-F_{22} \leftarrow 2 D_{11} (22|11),\ \ \ F_{21} \leftarrow - D_{21} (22|11),\ \ \ F_{11} \leftarrow 2 D_{22} (22|11),\ \ \ {\rm and}\ \ \ F_{12} \leftarrow -D_{12} (22|11).
-```
+<img src="./figures/fock-contribution-3.png" height="20">
 
 All such cases must be included in the algorithm to obtain a correct Fock matrix.
 
 ## Additional Reading
-  * J. Almlof, K. Faegri, and K. Korsell, "Principles for a Direct SCF Approach to LCAO-MO //Ab Initio// Calculations," //J. Comp. Chem.// **3**, 385-399 (1982).
+  * J. Almlof, K. Faegri, and K. Korsell, "Principles for a Direct SCF Approach to LCAO-MO *Ab Initio* Calculations," *J. Comp. Chem.* **3**, 385-399 (1982).
 
diff --git a/Project#11/figures/compound-indices.png b/Project#11/figures/compound-indices.png
new file mode 100644
index 0000000..714c307
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diff --git a/Project#11/figures/fock-contribution-1.png b/Project#11/figures/fock-contribution-1.png
new file mode 100644
index 0000000..4e7a2a2
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diff --git a/Project#11/figures/fock-contribution-2.png b/Project#11/figures/fock-contribution-2.png
new file mode 100644
index 0000000..5c69e70
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diff --git a/Project#11/figures/fock-contribution-3.png b/Project#11/figures/fock-contribution-3.png
new file mode 100644
index 0000000..3234c8a
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diff --git a/Project#11/figures/fock-matrix.png b/Project#11/figures/fock-matrix.png
new file mode 100644
index 0000000..82afe61
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diff --git a/Project#11/figures/index-restrictions.png b/Project#11/figures/index-restrictions.png
new file mode 100644
index 0000000..d9cfed7
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diff --git a/Project#12/README.md b/Project#12/README.md
index 2725558..c0e76cd 100644
--- a/Project#12/README.md
+++ b/Project#12/README.md
@@ -6,7 +6,7 @@ and time-dependent Hartree-Fock (TDHF), which is also known as the random-phase
 approximation (RPA). The purpose of this project is to develop simple
 implementations of these two methods and to understand the basic differences
 between them.  This project assumes you have completed at least the
-[CCSD programming project](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2305).
+[CCSD programming project](../Project%2305).
 
 You can read more about these methods in 
 [J.B. Foresman, M. Head-Gordon, J.A. Pople, and M.J. Frisch, J. Phys. Chem. 96, 135-141 (1992)](http://pubs.acs.org/doi/pdf/10.1021/j100180a030) (CIS) 
@@ -18,39 +18,27 @@ The fundamental idea behind CIS is the representation of the excited-state wave
 functions as linear combinations of singly excited determinants relative to the
 Hartree-Fock reference wave function, *viz.*
 
-```
-EQUATION
-\[ |\Psi(m)\rangle = \sum_{jb} c_j^b(m) \{ a^+_b a_j \} |\Phi_0\rangle = \sum_{jb} c_j^b(m) |\phi_j^b\rangle, \]
-```
+<img src="./figures/singly-excited-determinant.png" height="50">
 
 where *m* identifies the various excited states, and we will use *i* and *j*
 (*a* and *b*) to denote occupied (unoccupied) spin-orbitals. Inserting this
 into the Schr<html>&ouml;</html>dinger equation and left-projecting onto a
 particular singly excited determinant gives
 
-```
-EQUATION
-\sum_{jb} \langle \phi_i^a|H|\phi_j^b\rangle c_j^b(m) = E(m) c_i^a(m).
-```
+<img src="./figures/excited-det-schrod-eqn.png" height="50">
 
 If we recognize that we have one of these equations for every combination of
 *i* and *a* spin-orbitals, then this equation may be viewed as a matrix
 eigenvalue problem:
 
-```
-EQUATION
-\[ {\mathbf {\underline{\underline H}}}\ {\mathbf {\underline c}}(m) = E(m) {\mathbf {\underline c}}(m). \]
-```
+<img src="./figures/matrix-eigenvalue-problem.png" height="25">
 
 To solve this equation, we need an expression for the matrix elements in terms
 of things we already know, i.e. Fock matrix elements and two-electron
 integrals.  This can be done using either algebraic or diagrammatic techniques
 to obtain (in the spin-orbital notation of previous projects):
 
-```
-EQUATION
-\langle \phi_i^a | H | \phi_j^b \rangle = H_{ia,jb} = f_{ab} \delta_{ij} - f_{ij} \delta_{ab} + \langle aj || ib \rangle.
-```
+<img src="./figures/matrix-elements.png" height="30">
 
 Our task is then relatively simple: Build the Hamiltonian matrix (expressed in
 the basis of all singly excited determinants) using the above expression and
@@ -60,7 +48,7 @@ occupied orbitals times the number of unoccupied orbitals.  For our
 STO-3G/H<sub>2</sub>O test case, with its ten occupied and four unoccupied
 spin-orbitals, the matrix will be 40 x 40.
 
-  * Hint: CIS Hamiltonian for STO-3G H<sub>2</sub>O
+  * [Hint](./hints/hint1.md): CIS Hamiltonian for STO-3G H<sub>2</sub>O
 
 Make sure you can compute the correct CIS excitation energies for each of the
 four test cases provided at the end of the page.  Before you move on to the
@@ -84,121 +72,29 @@ from a simple two-electron/two-orbital example (such as the *1s 2s* excited
 state configuration of the He atom).  One can easily show that the four
 possible determinants arising from this configuration,
 
-```
-EQUATION
-\[ \left|
-\begin{array}{cc}
-\uparrow &  \\
-\hline
-\uparrow & \\
-\hline
-\end{array}
-\right\rangle,\ \ 
-\left|
-\begin{array}{cc}
-& \downarrow \\
-\hline
-& \downarrow \\
-\hline
-\end{array}
-\right\rangle,\ \ 
-\left|
-\begin{array}{cc}
-\uparrow &  \\
-\hline
-& \downarrow\\
-\hline
-\end{array}
-\right\rangle,\ \ 
-\left|
-\begin{array}{cc}
- & \downarrow \\
-\hline
-\uparrow & \\
-\hline
-\end{array}
-\right\rangle,\ \ \]
-```
+<img src="./figures/four-possible-determinants.png" height="50">
 
 are components of one singlet and one triplet in the following combinations:
 
-```
-EQUATION
-\[ |\Phi^3_1\rangle = \left|
-\begin{array}{cc}
-\uparrow &  \\
-\hline
-\uparrow & \\
-\hline
-\end{array}
-\right\rangle,\ \ 
-|\Phi^3_{-1}\rangle = \left|
-\begin{array}{cc}
-& \downarrow \\
-\hline
-& \downarrow\\
-\hline
-\end{array}
-\right\rangle,\ \ 
-|\Phi^3_{0}\rangle = 
-\frac{1}{\sqrt{2}}\left\{
-\left|
-\begin{array}{cc}
-\uparrow & \\
-\hline
-& \downarrow\\
-\hline
-\end{array}
-\right\rangle -
-\left|
-\begin{array}{cc}
-& \downarrow \\
-\hline
-\uparrow & \\
-\hline
-\end{array}
-\right\rangle\right\},\ \ {\rm and}\ \ 
-|\Phi^1_{0}\rangle = 
-\frac{1}{\sqrt{2}}\left\{
-\left|
-\begin{array}{cc}
-\uparrow & \\
-\hline
-& \downarrow\\
-\hline
-\end{array}
-\right\rangle +
-\left|
-\begin{array}{cc}
-& \downarrow \\
-\hline
-\uparrow & \\
-\hline
-\end{array}
-\right\rangle\right\}, \]
-```
+<img src="./figures/triplet-combinations.png" height="50">
+
+<img src="./figures/singlet-combinations.png" height="50">
 
 where the superscript is the spin multiplicity (*2S+1*) and the subscript is
 the *M<sub>S</sub>* value of the wave function.  So, if we wanted to compute
 only the eigenvalues and eigenfunctions corresponding spin singlets in our CIS
-calculation, we could introduce the restriction on our CIS coefficients that
-<html>&alpha;</html> and <html>&beta;</html> excitations involving the same
-*spatial* orbitals must be identical (including the sign).  Similarly, if we
-wanted only triplets, we could require that the <html>&alpha;</html> and
-<html>&beta;</html> excitations have the same magnitude but opposite signs.
+calculation, we could introduce the restriction on our CIS coefficients that <html>&alpha;</html> 
+and <html>&beta;</html> excitations involving the same <i>spatial</i> orbitals 
+must be identical (including the sign).  Similarly, if we wanted only triplets, 
+we could require that the <html>&alpha;</html> and <html>&beta;</html> excitations 
+have the same magnitude but opposite signs.
 
 Let's begin with the singlets.  Starting from the spin-orbital eigenvalue
 expression and the equation for the CIS Hamiltonian matrix elements in the
-previous section, we may write a spin-factored equation for the
-<html>&alpha;</html> coefficients as
+previous section, we may write a spin-factored equation for the <html>&alpha;</html> 
+coefficients as
 
-```
-EQUATION
-c_{i_\alpha}^{a_\alpha}(m) E(m) = \sum_{j_\alpha b_\alpha} 
-\left[ f_{a_\alpha b_\alpha} \delta_{i_\alpha j_\alpha} - f_{i_\alpha j_\alpha} \delta_{a_\alpha b_\alpha} + \langle a_\alpha j_\alpha || i_\alpha b_\alpha \rangle \right]
-c_{j_\alpha}^{b_\alpha}(m) + \sum_{j_\beta b_\beta} \langle a_\alpha j_\beta ||
-i_\alpha b_\beta \rangle c_{j_\beta}^{b_\beta}(m).
-```
+<img src="./figures/spin-factored-eqn.png" height="55">
 
 Note that the mix-spin cases (where *j=*<html>&alpha;</html> and
 *b=*<html>&beta;</html> or *vice versa*) do not contribute since the Fock
@@ -207,39 +103,27 @@ carry out spin integration on the integrals in the above expression and assume
 that the <html>&alpha;</html> and <html>&beta;</html> CI coefficients are
 identical for the same spatial orbitals, i.e.,
 
-```
-EQUATION
-c_{i_\alpha}^{a_\alpha}(m) = c_{i_\beta}^{a_\beta}(m).
-```
+<img src="./figures/identical-ci-coeff.png" height="30">
 
-we obtain the ***spatial orbital*** expression
+we obtain the <b><i>spatial orbital</i></b> expression
 
-```
-EQUATION
-c_i^a(m) E(m) = \sum_{jb} \left[ f_{ab} \delta_{ij} - f_{ij} \delta_{ab} + 2 <aj|ib> - <aj|bi> \right] c_j^b(m).
-```
+<img src="./figures/spatial-orbital-expression.png" height="50">
 
 The part in brackets above is an expression for the spatial-orbital CIS
 Hamiltonian, spin-adapted for singlet excited states, and diagonalization of
 this matrix will yield only the singlet eigenvalues you obtained from your
 spin-orbital matrix earlier.
 
-  * Hint: Spin-adapted CIS singlet Hamiltonian for STO-3G H<sub>2</sub>O
+  * [Hint](./hints/hint2.md): Spin-adapted CIS singlet Hamiltonian for STO-3G H<sub>2</sub>O
 
 How about the triplets?  We use exactly the same spin-factorization, but
 instead require
 
-```
-EQUATION
-c_{i_\alpha}^{a_\alpha}(m) = -c_{i_\beta}^{a_\beta}(m).
-```
+<img src="./figures/inverse-ci-coeff.png" height="30">
 
 This yields a slightly simpler Hamiltonian:
 
-```
-EQUATION
-c_i^a(m) E(m) = \sum_{jb} \left[ f_{ab} \delta_{ij} - f_{ij} \delta_{ab} - <aj|bi> \right] c_j^b(m),
-```
+<img src="./figures/simpler-hamiltonian.png" height="50">
 
 which, upon diagonalization, will yield only the triplet eigenvalues (but each only occurring once) from your earlier diagonalziation.
 
@@ -266,47 +150,23 @@ TDHF/RPA wave function expansion in terms of orbital rotations instead of
 Slater determinants, but that's a discussion for another day.)  The TDHF/RPA
 eigenvalue equations take the form
 
-```
-EQUATION
-\left(
-\begin{array}{cc}
-{\mathbf {\underline{\underline A}}} & {\mathbf {\underline{\underline B}}} \\
--{\mathbf {\underline{\underline B}}} & - {\mathbf {\underline{\underline A}}} \\
-\end{array}
-\right) \left(
-\begin{array}{c}
-{\mathbf {\underline X}} \\
-{\mathbf {\underline Y}} \\
-\end{array}
-\right) = E \left(
-\begin{array}{c}
-{\mathbf {\underline X}} \\
-{\mathbf {\underline Y}} \\
-\end{array}
-\right).
-```
+<img src="./figures/tdhf-eqn.png" height="50">
 
 The definition of the ***A*** matrix is just the CIS matrix itself, *viz.*
 
-```
-EQUATION
-A_{ia,jb} \equiv \langle \phi_i^a | H | \phi_j^b \rangle = f_{ab} \delta_{ij} - f_{ij} \delta_{ab} + \langle aj || ib \rangle,
-```
+<img src="./figures/A-matrix.png" height="30">
 
 while **X** and **Y** are the parameters of single excitations and
 de-excitations, respectively, and the ***B*** matrix is simply
 
-```
-EQUATION
-B_{ia,jb} \equiv \langle ab || ij \rangle.
-```
+<img src="./figures/B-matrix.png" height="25">
 
 Thus, the row/column dimension of the TDHF/RPA Hamiltonian is twice that of the
 CIS Hamiltonian, and the matrix is non-symmetric (so you must be careful about
 the diagonalization function you choose).  Do you obtain twice as many
 excitation energies?
 
-  * Hint: TDHF/RPA Hamiltonian for STO-3G H<sub>2</sub>O
+  * [Hint](./hints/hint3.md): TDHF/RPA Hamiltonian for STO-3G H<sub>2</sub>O
 
 ## A Better Approach to Solving the TDHF/RPA Eigenvalue Equations
 
@@ -316,57 +176,28 @@ Hamiltonian storage cost), one can rearrange the eigenvalue equations.  First
 write eigenvalue equation two separate equations, each in terms of the
 submatrices **A** and **B**:
 
-```
-EQUATION
-\[ {\mathbf {\underline{\underline A}}} {\mathbf {\underline X}} + {\mathbf {\underline{\underline B}}} {\mathbf {\underline Y}} = E {\mathbf {\underline X}} \] 
-```
+<img src="./figures/smarter-tdhf-1.png" height="22.5">
 
 and
 
-```
-EQUATION
-\[ 
--{\mathbf {\underline{\underline B}}} {\mathbf {\underline X}} - {\mathbf {\underline{\underline A}}} {\mathbf {\underline Y}} = E {\mathbf {\underline Y}}. \]
-```
+<img src="./figures/smarter-tdhf-2.png" height="22.5">
 
 Now take +/- combinations of these equations to obtain
 
-```
-EQUATION
-\[ 
-({\mathbf {\underline{\underline A}}} - {\mathbf {\underline{\underline B}}})
-({\mathbf {\underline X}} - {\mathbf {\underline Y}}) 
-= E ({\mathbf {\underline X}} + {\mathbf {\underline Y}}) \]
-```
+<img src="./figures/smarter-tdhf-3.png" height="22.5">
 
 and
 
-```
-EQUATION
-\[ ({\mathbf {\underline{\underline A}}} + {\mathbf {\underline{\underline B}}})
-({\mathbf {\underline X}} + {\mathbf {\underline Y}}) 
-= E ({\mathbf {\underline X}} - {\mathbf {\underline Y}}). \]
-```
+<img src="./figures/smarter-tdhf-4.png" height="22.5">
 
 Solve for ***(X+Y)*** in the second equation:
 
-```
-EQUATION
-\[ ({\mathbf {\underline X}} + {\mathbf {\underline Y}}) 
-= E ({\mathbf {\underline{\underline A}}} + {\mathbf {\underline{\underline B}}})^{-1} 
-({\mathbf {\underline X}} - {\mathbf {\underline Y}}). \]
-```
+<img src="./figures/smarter-tdhf-5.png" height="25">
 
 Insert this result into the first equation, rearrange a bit, and finally
 obtain:
 
-```
-EQUATION
-\[ ({\mathbf {\underline{\underline A}}} + {\mathbf {\underline{\underline B}}}) 
-({\mathbf {\underline{\underline A}}} - {\mathbf {\underline{\underline B}}})
-({\mathbf {\underline X}} - {\mathbf {\underline Y}}) 
-= E^2 ({\mathbf {\underline X}} - {\mathbf {\underline Y}}). \]
-```
+<img src="./figures/smarter-tdhf-6.png" height="25">
 
 This is an eigenvalue equation of the same dimension as the CIS eigenvalue
 equation (number of occupied orbitals times number of unoccupied orbitals),
@@ -379,12 +210,12 @@ approach, for all four test cases below.
 
 ## Test Cases
 The input structures, integrals, etc. for these examples may be found in the 
-[input directory](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2312/input).
+[input directory](./input).
 
 | Test Case | CIS | RPA (Method 1) | RPA (Method 2) |
 |-----------|-----|----------------|----------------|
-| STO-3G Water | [output](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2312/output/h2o/STO-3G/output_cis.txt) | [output](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2312/output/h2o/STO-3G/output_rpa1.txt) | [output](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2312/output/h2o/STO-3G/output_rpa2.txt) |
-| DZ Water | [output](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2312/output/h2o/DZ/output_cis.txt) | [output](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2312/output/h2o/DZ/output_rpa1.txt) | [output](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2312/output/h2o/DZ/output_rpa2.txt) |
-| DZP Water | [output](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2312/output/h2o/DZP/output_cis.txt) | [output](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2312/output/h2o/DZP/output_rpa1.txt) | [output](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2312/output/h2o/DZP/output_rpa2.txt) |
-| STO-3G Methane | [output](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2312/output/ch4/STO-3G/output_cis.txt) | [output](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2312/output/ch4/STO-3G/output_rpa1.txt) | [output](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2312/output/ch4/STO-3G/output_rpa2.txt) |
+| STO-3G Water | [output](./output/h2o/STO-3G/output_cis.txt) | [output](./output/h2o/STO-3G/output_rpa1.txt) | [output](./output/h2o/STO-3G/output_rpa2.txt) |
+| DZ Water | [output](./output/h2o/DZ/output_cis.txt) | [output](./output/h2o/DZ/output_rpa1.txt) | [output](./output/h2o/DZ/output_rpa2.txt) |
+| DZP Water | [output](./output/h2o/DZP/output_cis.txt) | [output](./output/h2o/DZP/output_rpa1.txt) | [output](./output/h2o/DZP/output_rpa2.txt) |
+| STO-3G Methane | [output](./output/ch4/STO-3G/output_cis.txt) | [output](./output/ch4/STO-3G/output_rpa1.txt) | [output](./output/ch4/STO-3G/output_rpa2.txt) |
 
diff --git a/Project#12/figures/A-matrix.png b/Project#12/figures/A-matrix.png
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diff --git a/Project#12/figures/simpler-hamiltonian.png b/Project#12/figures/simpler-hamiltonian.png
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diff --git a/Project#12/figures/singlet-combinations.png b/Project#12/figures/singlet-combinations.png
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diff --git a/Project#12/figures/singlet-triplet-combinations.png b/Project#12/figures/singlet-triplet-combinations.png
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diff --git a/Project#12/figures/singly-excited-determinant.png b/Project#12/figures/singly-excited-determinant.png
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diff --git a/Project#12/figures/smarter-tdhf-1.png b/Project#12/figures/smarter-tdhf-1.png
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diff --git a/Project#12/figures/smarter-tdhf-2.png b/Project#12/figures/smarter-tdhf-2.png
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diff --git a/Project#12/figures/smarter-tdhf-3.png b/Project#12/figures/smarter-tdhf-3.png
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diff --git a/Project#12/figures/smarter-tdhf-4.png b/Project#12/figures/smarter-tdhf-4.png
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diff --git a/Project#12/figures/spatial-orbital-expression.png b/Project#12/figures/spatial-orbital-expression.png
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diff --git a/Project#12/figures/spin-factored-eqn.png b/Project#12/figures/spin-factored-eqn.png
new file mode 100644
index 0000000..f0167ff
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diff --git a/Project#12/figures/tdhf-eqn.png b/Project#12/figures/tdhf-eqn.png
new file mode 100644
index 0000000..318b921
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diff --git a/Project#12/figures/triplet-combinations.png b/Project#12/figures/triplet-combinations.png
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diff --git a/Project#12/hints/hint1.md b/Project#12/hints/hint1.md
new file mode 100644
index 0000000..a05b2d7
--- /dev/null
+++ b/Project#12/hints/hint1.md
@@ -0,0 +1,174 @@
+Here is the CIS matrix for the same H<sub>2</sub>O STO-3G test case we've been using throughout these projects.  Note that the row/column ordering follows *i* and *a* combinations with *a* as the faster-running index (i.e., *a* indexes the inner loop).  Thus the first row/column corresponds to *i=0* and *a=0* and the second row/column to *i=0* and *a=1*.  Notice that the matrix is diagonally dominant --- that is, the largest element on any row/column combination is the diagonal entry --- and that all the diagonal elements are positive.
+```
+           1           2           3           4           5           6           7           8           9          10
+
+    1  19.9847006   0.0000000   0.0000000   0.0000000   0.0000000   0.0261967   0.0000000  -0.0000000   0.0172405   0.0000000
+    2   0.0000000  19.9585039   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0074145
+    3   0.0000000   0.0000000  20.0308559   0.0000000   0.0000000  -0.0000000   0.0000000   0.0195218   0.0000000   0.0000000
+    4   0.0000000   0.0000000   0.0000000  20.0113341   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000
+    5   0.0000000   0.0000000   0.0000000   0.0000000  19.9585039   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+    6   0.0261967   0.0000000  -0.0000000   0.0000000   0.0000000  19.9847006   0.0000000   0.0000000   0.0098259   0.0000000
+    7   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  20.0113341   0.0000000   0.0000000   0.0000000
+    8  -0.0000000   0.0000000   0.0195218   0.0000000   0.0000000   0.0000000   0.0000000  20.0308559   0.0000000   0.0000000
+    9   0.0172405   0.0000000   0.0000000   0.0000000   0.0000000   0.0098259   0.0000000   0.0000000   1.1883321   0.0000000
+   10   0.0000000   0.0074145   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   1.0931793
+   11   0.0000000   0.0000000   0.0280239   0.0000000   0.0000000   0.0000000   0.0000000   0.0191033   0.0000000   0.0000000
+   12   0.0000000  -0.0000000   0.0000000   0.0089205   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   13   0.0000000   0.0000000   0.0000000   0.0000000   0.0074145   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000
+   14   0.0098259   0.0000000   0.0000000   0.0000000   0.0000000   0.0172405   0.0000000   0.0000000   0.0951527   0.0000000
+   15   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0089205   0.0000000   0.0000000   0.0000000
+   16   0.0000000   0.0000000   0.0191033   0.0000000   0.0000000   0.0000000   0.0000000   0.0280239  -0.0000000   0.0000000
+   17  -0.0000000   0.0000000  -0.0046225   0.0000000   0.0000000  -0.0000000   0.0000000   0.0030386   0.0000000   0.0000000
+   18   0.0000000  -0.0000000   0.0000000  -0.0076611   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000
+   19  -0.0134310   0.0000000  -0.0000000   0.0000000   0.0000000  -0.0057699   0.0000000   0.0000000  -0.0178319   0.0000000
+   20   0.0000000  -0.0076611   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0867137
+   21   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0076611   0.0000000   0.0000000   0.0000000
+   22  -0.0000000   0.0000000   0.0030386   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0046225   0.0000000   0.0000000
+   23   0.0000000   0.0000000   0.0000000   0.0000000  -0.0076611   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000
+   24  -0.0057699   0.0000000   0.0000000   0.0000000   0.0000000  -0.0134310   0.0000000  -0.0000000   0.0688817   0.0000000
+   25   0.0197793   0.0000000  -0.0000000   0.0000000   0.0000000   0.0017709   0.0000000   0.0000000  -0.0117148   0.0000000
+   26   0.0000000   0.0180084   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0485372
+   27   0.0000000   0.0000000   0.0149879   0.0000000   0.0000000   0.0000000   0.0000000   0.0112477   0.0000000   0.0000000
+   28   0.0000000  -0.0000000   0.0000000   0.0037402   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000
+   29   0.0000000   0.0000000   0.0000000   0.0000000   0.0180084   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000
+   30   0.0017709   0.0000000   0.0000000   0.0000000   0.0000000   0.0197793   0.0000000  -0.0000000  -0.0602520   0.0000000
+   31   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0037402   0.0000000   0.0000000   0.0000000
+   32   0.0000000   0.0000000   0.0112477   0.0000000   0.0000000   0.0000000   0.0000000   0.0149879   0.0000000   0.0000000
+   33  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000
+   34   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   35   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   36   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   37   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   38  -0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000
+   39   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000
+   40   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000  -0.0000000   0.0000000
+
+          11          12          13          14          15          16          17          18          19          20
+
+    1   0.0000000   0.0000000   0.0000000   0.0098259   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0134310   0.0000000
+    2   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0076611
+    3   0.0280239   0.0000000   0.0000000   0.0000000   0.0000000   0.0191033  -0.0046225   0.0000000  -0.0000000   0.0000000
+    4   0.0000000   0.0089205   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0076611   0.0000000  -0.0000000
+    5   0.0000000   0.0000000   0.0074145   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+    6   0.0000000   0.0000000   0.0000000   0.0172405   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0057699   0.0000000
+    7   0.0000000   0.0000000  -0.0000000   0.0000000   0.0089205   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+    8   0.0191033   0.0000000   0.0000000   0.0000000   0.0000000   0.0280239   0.0030386   0.0000000   0.0000000   0.0000000
+    9   0.0000000   0.0000000   0.0000000   0.0951527   0.0000000  -0.0000000   0.0000000   0.0000000  -0.0178319   0.0000000
+   10   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0867137
+   11   1.2566569   0.0000000   0.0000000  -0.0000000   0.0000000   0.0678165  -0.0564572   0.0000000   0.0000000   0.0000000
+   12   0.0000000   1.1888405   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0867137   0.0000000   0.0000000
+   13   0.0000000   0.0000000   1.0931793   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   14  -0.0000000   0.0000000   0.0000000   1.1883321   0.0000000   0.0000000   0.0000000   0.0000000   0.0688817   0.0000000
+   15   0.0000000   0.0000000   0.0000000   0.0000000   1.1888405   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   16   0.0678165   0.0000000   0.0000000   0.0000000   0.0000000   1.2566569   0.0302565   0.0000000  -0.0000000   0.0000000
+   17  -0.0564572   0.0000000   0.0000000   0.0000000   0.0000000   0.0302565   0.5507646   0.0000000   0.0000000   0.0000000
+   18   0.0000000  -0.0867137   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.4757743   0.0000000   0.0000000
+   19   0.0000000   0.0000000   0.0000000   0.0688817   0.0000000  -0.0000000   0.0000000   0.0000000   0.7122157   0.0000000
+   20   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.5527668
+   21   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0867137   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   22   0.0302565   0.0000000   0.0000000   0.0000000   0.0000000  -0.0564572   0.0749902   0.0000000   0.0000000   0.0000000
+   23   0.0000000   0.0000000  -0.0867137   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   24  -0.0000000   0.0000000   0.0000000  -0.0178319   0.0000000   0.0000000   0.0000000   0.0000000   0.1594489   0.0000000
+   25   0.0000000   0.0000000   0.0000000  -0.0602520   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0383679   0.0000000
+   26   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0615255
+   27  -0.0011401   0.0000000   0.0000000   0.0000000   0.0000000   0.0171886   0.0073884   0.0000000  -0.0000000   0.0000000
+   28   0.0000000  -0.0183287   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0615255   0.0000000  -0.0000000
+   29   0.0000000   0.0000000   0.0485372   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   30   0.0000000   0.0000000   0.0000000  -0.0117148   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0998933   0.0000000
+   31   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0183287   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   32   0.0171886   0.0000000   0.0000000   0.0000000   0.0000000  -0.0011401  -0.0541371   0.0000000   0.0000000   0.0000000
+   33   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000   0.0000000
+   34   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000
+   35   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000
+   36   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000
+   37   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   38  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0000000   0.0000000
+   39   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   40   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0000000   0.0000000
+
+          21          22          23          24          25          26          27          28          29          30
+
+    1   0.0000000  -0.0000000   0.0000000  -0.0057699   0.0197793   0.0000000   0.0000000   0.0000000   0.0000000   0.0017709
+    2   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0180084   0.0000000  -0.0000000   0.0000000   0.0000000
+    3   0.0000000   0.0030386   0.0000000   0.0000000  -0.0000000   0.0000000   0.0149879   0.0000000   0.0000000   0.0000000
+    4   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0037402   0.0000000   0.0000000
+    5  -0.0000000   0.0000000  -0.0076611   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0180084   0.0000000
+    6   0.0000000  -0.0000000   0.0000000  -0.0134310   0.0017709   0.0000000   0.0000000   0.0000000   0.0000000   0.0197793
+    7  -0.0076611   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000
+    8   0.0000000  -0.0046225   0.0000000  -0.0000000   0.0000000   0.0000000   0.0112477   0.0000000   0.0000000  -0.0000000
+    9   0.0000000   0.0000000   0.0000000   0.0688817  -0.0117148   0.0000000   0.0000000   0.0000000   0.0000000  -0.0602520
+   10   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0485372   0.0000000  -0.0000000   0.0000000   0.0000000
+   11   0.0000000   0.0302565   0.0000000  -0.0000000   0.0000000   0.0000000  -0.0011401   0.0000000   0.0000000   0.0000000
+   12   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0183287   0.0000000   0.0000000
+   13  -0.0000000   0.0000000  -0.0867137   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0485372   0.0000000
+   14   0.0000000   0.0000000   0.0000000  -0.0178319  -0.0602520   0.0000000   0.0000000   0.0000000   0.0000000  -0.0117148
+   15  -0.0867137   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000
+   16   0.0000000  -0.0564572   0.0000000   0.0000000   0.0000000   0.0000000   0.0171886   0.0000000   0.0000000   0.0000000
+   17   0.0000000   0.0749902   0.0000000   0.0000000  -0.0000000   0.0000000   0.0073884   0.0000000   0.0000000  -0.0000000
+   18   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0615255   0.0000000   0.0000000
+   19   0.0000000   0.0000000   0.0000000   0.1594489  -0.0383679   0.0000000  -0.0000000   0.0000000   0.0000000  -0.0998933
+   20   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0615255   0.0000000  -0.0000000   0.0000000   0.0000000
+   21   0.4757743   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   22   0.0000000   0.5507646   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0541371   0.0000000   0.0000000  -0.0000000
+   23   0.0000000   0.0000000   0.5527668   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0615255   0.0000000
+   24   0.0000000   0.0000000   0.0000000   0.7122157  -0.0998933   0.0000000   0.0000000   0.0000000   0.0000000  -0.0383679
+   25   0.0000000  -0.0000000   0.0000000  -0.0998933   0.4658980   0.0000000   0.0000000   0.0000000   0.0000000   0.0955699
+   26   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.3703281   0.0000000  -0.0000000   0.0000000   0.0000000
+   27   0.0000000  -0.0541371   0.0000000   0.0000000   0.0000000   0.0000000   0.5152458   0.0000000   0.0000000   0.0000000
+   28   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.4442931   0.0000000   0.0000000
+   29   0.0000000   0.0000000   0.0615255   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.3703281   0.0000000
+   30   0.0000000  -0.0000000   0.0000000  -0.0383679   0.0955699   0.0000000   0.0000000   0.0000000   0.0000000   0.4658980
+   31   0.0615255   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000
+   32   0.0000000   0.0073884   0.0000000  -0.0000000   0.0000000   0.0000000   0.0709527   0.0000000   0.0000000   0.0000000
+   33   0.0000000  -0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000
+   34   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000
+   35   0.0000000  -0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   36   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   37  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   38   0.0000000  -0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   39   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000
+   40   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+
+          31          32          33          34          35          36          37          38          39          40
+
+    1   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000
+    2   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+    3   0.0000000   0.0112477   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000
+    4   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+    5  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000
+    6   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000
+    7   0.0037402   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000
+    8   0.0000000   0.0149879  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000
+    9   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0000000
+   10   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   11   0.0000000   0.0171886   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000
+   12   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   13  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   14   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   15  -0.0183287   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   16   0.0000000  -0.0011401  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   17   0.0000000  -0.0541371  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0000000
+   18   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   19   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0000000
+   20   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   21   0.0615255   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000
+   22   0.0000000   0.0073884  -0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000
+   23  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000
+   24   0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0000000
+   25   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   26   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   27   0.0000000   0.0709527  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   28   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   29  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000
+   30   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   31   0.4442931   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000
+   32   0.0000000   0.5152458   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000
+   33   0.0000000   0.0000000   0.3218586   0.0000000   0.0000000   0.0000000   0.0000000   0.0346031   0.0000000  -0.0000000
+   34   0.0000000   0.0000000   0.0000000   0.2872555   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   35   0.0000000   0.0000000   0.0000000   0.0000000   0.3910304   0.0000000   0.0000000  -0.0000000   0.0000000   0.0250414
+   36   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.3659890   0.0000000   0.0000000   0.0000000   0.0000000
+   37  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.2872555   0.0000000   0.0000000   0.0000000
+   38   0.0000000  -0.0000000   0.0346031   0.0000000  -0.0000000   0.0000000   0.0000000   0.3218586   0.0000000   0.0000000
+   39   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.3659890   0.0000000
+   40   0.0000000   0.0000000  -0.0000000   0.0000000   0.0250414   0.0000000   0.0000000   0.0000000   0.0000000   0.3910304
+```
diff --git a/Project#12/hints/hint2.md b/Project#12/hints/hint2.md
new file mode 100644
index 0000000..f14b3fc
--- /dev/null
+++ b/Project#12/hints/hint2.md
@@ -0,0 +1,15 @@
+Here is the CIS spin-adapted singlet matrix for the H<sub>2</sub>O STO-3G test case.  Note that the row/column ordering follows *i* and *a* combinations with *a* as the faster-running index (i.e., *a* indexes the inner loop).  Thus the first row/column corresponds to *i=0* and *a=0* and the second row/column to *i=0* and *a=1*.  Notice that the matrix is diagonally dominant --- that is, the largest element on any row/column combination is the diagonal entry --- and that all the diagonal elements are positive.
+```
+           1           2           3           4           5           6           7           8           9          10
+
+    1  19.9585039   0.0000000   0.0074145  -0.0000000  -0.0000000  -0.0076611   0.0180084  -0.0000000  -0.0000000   0.0000000
+    2   0.0000000  20.0113341  -0.0000000   0.0089205  -0.0076611  -0.0000000  -0.0000000   0.0037402   0.0000000  -0.0000000
+    3   0.0074145  -0.0000000   1.0931793   0.0000000  -0.0000000  -0.0867137   0.0485372  -0.0000000   0.0000000   0.0000000
+    4  -0.0000000   0.0089205   0.0000000   1.1888405  -0.0867137   0.0000000  -0.0000000  -0.0183287   0.0000000   0.0000000
+    5  -0.0000000  -0.0076611  -0.0000000  -0.0867137   0.4757743   0.0000000   0.0000000   0.0615255  -0.0000000   0.0000000
+    6  -0.0076611  -0.0000000  -0.0867137   0.0000000   0.0000000   0.5527668   0.0615255  -0.0000000   0.0000000  -0.0000000
+    7   0.0180084  -0.0000000   0.0485372  -0.0000000   0.0000000   0.0615255   0.3703281  -0.0000000   0.0000000  -0.0000000
+    8  -0.0000000   0.0037402  -0.0000000  -0.0183287   0.0615255  -0.0000000  -0.0000000   0.4442931  -0.0000000   0.0000000
+    9  -0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000  -0.0000000   0.2872555   0.0000000
+   10   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000  -0.0000000   0.0000000   0.0000000   0.3659890
+```
diff --git a/Project#12/hints/hint3.md b/Project#12/hints/hint3.md
new file mode 100644
index 0000000..13b0e43
--- /dev/null
+++ b/Project#12/hints/hint3.md
@@ -0,0 +1,666 @@
+Here is the TDHF/RPA version of the H<sub>2</sub>O STO-3G Hamitlonian.  The row/column ordering is the same as for CIS above, but there two blocks of *i/a* pairs, one for each of the ***A*** and ***B*** submatrices.  This matrix is also diagonally dominant, but not all the diagonal elements are positive.
+```
+           1           2           3           4           5           6           7           8           9          10
+
+    1  19.9847006   0.0000000   0.0000000   0.0000000   0.0000000   0.0261967   0.0000000  -0.0000000   0.0172405   0.0000000
+    2   0.0000000  19.9585039   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0074145
+    3   0.0000000   0.0000000  20.0308559   0.0000000   0.0000000  -0.0000000   0.0000000   0.0195218   0.0000000   0.0000000
+    4   0.0000000   0.0000000   0.0000000  20.0113341   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000
+    5   0.0000000   0.0000000   0.0000000   0.0000000  19.9585039   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+    6   0.0261967   0.0000000  -0.0000000   0.0000000   0.0000000  19.9847006   0.0000000   0.0000000   0.0098259   0.0000000
+    7   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  20.0113341   0.0000000   0.0000000   0.0000000
+    8  -0.0000000   0.0000000   0.0195218   0.0000000   0.0000000   0.0000000   0.0000000  20.0308559   0.0000000   0.0000000
+    9   0.0172405   0.0000000   0.0000000   0.0000000   0.0000000   0.0098259   0.0000000   0.0000000   1.1883321   0.0000000
+   10   0.0000000   0.0074145   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   1.0931793
+   11   0.0000000   0.0000000   0.0280239   0.0000000   0.0000000   0.0000000   0.0000000   0.0191033   0.0000000   0.0000000
+   12   0.0000000  -0.0000000   0.0000000   0.0089205   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   13   0.0000000   0.0000000   0.0000000   0.0000000   0.0074145   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000
+   14   0.0098259   0.0000000   0.0000000   0.0000000   0.0000000   0.0172405   0.0000000   0.0000000   0.0951527   0.0000000
+   15   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0089205   0.0000000   0.0000000   0.0000000
+   16   0.0000000   0.0000000   0.0191033   0.0000000   0.0000000   0.0000000   0.0000000   0.0280239  -0.0000000   0.0000000
+   17  -0.0000000   0.0000000  -0.0046225   0.0000000   0.0000000  -0.0000000   0.0000000   0.0030386   0.0000000   0.0000000
+   18   0.0000000  -0.0000000   0.0000000  -0.0076611   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000
+   19  -0.0134310   0.0000000  -0.0000000   0.0000000   0.0000000  -0.0057699   0.0000000   0.0000000  -0.0178319   0.0000000
+   20   0.0000000  -0.0076611   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0867137
+   21   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0076611   0.0000000   0.0000000   0.0000000
+   22  -0.0000000   0.0000000   0.0030386   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0046225   0.0000000   0.0000000
+   23   0.0000000   0.0000000   0.0000000   0.0000000  -0.0076611   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000
+   24  -0.0057699   0.0000000   0.0000000   0.0000000   0.0000000  -0.0134310   0.0000000  -0.0000000   0.0688817   0.0000000
+   25   0.0197793   0.0000000  -0.0000000   0.0000000   0.0000000   0.0017709   0.0000000   0.0000000  -0.0117148   0.0000000
+   26   0.0000000   0.0180084   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0485372
+   27   0.0000000   0.0000000   0.0149879   0.0000000   0.0000000   0.0000000   0.0000000   0.0112477   0.0000000   0.0000000
+   28   0.0000000  -0.0000000   0.0000000   0.0037402   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000
+   29   0.0000000   0.0000000   0.0000000   0.0000000   0.0180084   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000
+   30   0.0017709   0.0000000   0.0000000   0.0000000   0.0000000   0.0197793   0.0000000  -0.0000000  -0.0602520   0.0000000
+   31   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0037402   0.0000000   0.0000000   0.0000000
+   32   0.0000000   0.0000000   0.0112477   0.0000000   0.0000000   0.0000000   0.0000000   0.0149879   0.0000000   0.0000000
+   33  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000
+   34   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   35   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   36   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   37   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   38  -0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000
+   39   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000
+   40   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000  -0.0000000   0.0000000
+   41  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0261967  -0.0000000   0.0000000  -0.0000000  -0.0000000
+   42  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0261967  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000
+   43  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0195218  -0.0000000  -0.0000000
+   44  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0195218  -0.0000000  -0.0000000  -0.0000000
+   45  -0.0000000   0.0261967  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0098259
+   46  -0.0261967  -0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0098259  -0.0000000
+   47  -0.0000000  -0.0000000  -0.0000000   0.0195218  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000
+   48   0.0000000  -0.0000000  -0.0195218  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000
+   49  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0098259  -0.0000000  -0.0000000  -0.0000000  -0.0000000
+   50  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0098259  -0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0000000
+   51   0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0191033  -0.0000000  -0.0000000
+   52  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000   0.0191033  -0.0000000  -0.0000000  -0.0000000
+   53  -0.0000000   0.0098259  -0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0951527
+   54  -0.0098259  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0951527  -0.0000000
+   55  -0.0000000   0.0000000  -0.0000000   0.0191033  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000
+   56  -0.0000000  -0.0000000  -0.0191033  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000
+   57  -0.0000000  -0.0000000  -0.0088085  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0030386  -0.0000000  -0.0000000
+   58  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0057699  -0.0000000  -0.0000000  -0.0000000
+   59   0.0088085   0.0000000  -0.0000000  -0.0000000   0.0000000   0.0057699  -0.0000000  -0.0000000  -0.0386252  -0.0000000
+   60   0.0000000   0.0000000  -0.0000000  -0.0000000   0.0030386   0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0000000
+   61  -0.0000000  -0.0000000  -0.0000000  -0.0057699  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000
+   62   0.0000000  -0.0000000  -0.0030386  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0088085  -0.0000000  -0.0000000
+   63   0.0000000   0.0030386  -0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0302565
+   64   0.0057699   0.0000000  -0.0000000  -0.0000000   0.0000000   0.0088085  -0.0000000  -0.0000000  -0.0688817  -0.0000000
+   65  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0017709  -0.0000000  -0.0000000  -0.0000000  -0.0000000
+   66  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0017709  -0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0000000
+   67  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0112477   0.0000000  -0.0000000
+   68  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000   0.0112477  -0.0000000  -0.0000000  -0.0000000
+   69  -0.0000000   0.0017709  -0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0602520
+   70  -0.0017709  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000   0.0602520  -0.0000000
+   71  -0.0000000   0.0000000  -0.0000000   0.0112477  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000
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+
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+   53   0.0000000  -0.0000000   0.0867137  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0485372  -0.0000000
+   54  -0.0000000  -0.0000000  -0.0000000   0.0178319   0.0602520  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0117148
+   55   0.0867137  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000
+   56  -0.0000000   0.0564572  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0171886  -0.0000000  -0.0000000  -0.0000000
+   57  -0.0000000  -0.0749902  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0073884  -0.0000000  -0.0000000   0.0000000
+   58  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0615255  -0.0000000  -0.0000000
+   59  -0.0000000  -0.0000000  -0.0000000  -0.1594489   0.0383679  -0.0000000   0.0000000  -0.0000000  -0.0000000   0.0998933
+   60  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0615255  -0.0000000   0.0000000  -0.0000000  -0.0000000
+   61  -0.4757743  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000
+   62  -0.0000000  -0.5507646  -0.0000000  -0.0000000   0.0000000  -0.0000000   0.0541371  -0.0000000  -0.0000000   0.0000000
+   63  -0.0000000  -0.0000000  -0.5527668  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0615255  -0.0000000
+   64  -0.0000000  -0.0000000  -0.0000000  -0.7122157   0.0998933  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0383679
+   65  -0.0000000   0.0000000  -0.0000000   0.0998933  -0.4658980  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0955699
+   66  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.3703281  -0.0000000   0.0000000  -0.0000000  -0.0000000
+   67  -0.0000000   0.0541371  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.5152458  -0.0000000  -0.0000000  -0.0000000
+   68  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.4442931  -0.0000000  -0.0000000
+   69  -0.0000000  -0.0000000  -0.0615255  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.3703281  -0.0000000
+   70  -0.0000000   0.0000000  -0.0000000   0.0383679  -0.0955699  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.4658980
+   71  -0.0615255  -0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000
+   72  -0.0000000  -0.0073884  -0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0709527  -0.0000000  -0.0000000  -0.0000000
+   73  -0.0000000   0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0000000
+   74  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000
+   75  -0.0000000   0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000
+   76  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000
+   77   0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000
+   78  -0.0000000   0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000
+   79  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000
+   80  -0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000
+
+          71          72          73          74          75          76          77          78          79          80
+
+    1   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000
+    2  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+    3   0.0000000   0.0112477  -0.0000000  -0.0000000   0.0000000   0.0000000  -0.0000000  -0.0000000   0.0000000   0.0000000
+    4  -0.0112477   0.0000000  -0.0000000  -0.0000000   0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000
+    5   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+    6   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+    7   0.0000000   0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000   0.0000000
+    8   0.0000000   0.0000000  -0.0000000  -0.0000000   0.0000000   0.0000000  -0.0000000  -0.0000000   0.0000000   0.0000000
+    9   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0000000
+   10  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   11   0.0000000   0.0171886   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000
+   12  -0.0171886   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000
+   13   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   14   0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000
+   15   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   16   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   17   0.0000000  -0.0541371   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0000000
+   18   0.0998933   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   19   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0000000
+   20  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   21   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   22   0.0000000   0.0457562  -0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   23   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   24   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000
+   25   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   26  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0000000   0.0000000
+   27   0.0000000   0.0709527  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   28  -0.0709527   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0000000   0.0000000
+   29   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   30   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   31   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   32   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0000000
+   33   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0346031   0.0000000  -0.0000000
+   34  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0346031   0.0000000   0.0000000   0.0000000
+   35   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000   0.0250414
+   36  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0250414   0.0000000
+   37   0.0000000   0.0000000   0.0000000  -0.0346031   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   38   0.0000000  -0.0000000   0.0346031   0.0000000  -0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   39   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000  -0.0250414   0.0000000   0.0000000   0.0000000   0.0000000
+   40   0.0000000   0.0000000  -0.0000000   0.0000000   0.0250414   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
+   41  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000
+   42  -0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000
+   43  -0.0000000  -0.0112477  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000
+   44  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000
+   45   0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0000000
+   46  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000
+   47  -0.0037402  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000
+   48  -0.0000000  -0.0149879   0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000
+   49  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000   0.0000000
+   50  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000
+   51  -0.0000000  -0.0171886  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000
+   52  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000
+   53   0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000
+   54  -0.0000000  -0.0000000   0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000
+   55   0.0183287  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000
+   56  -0.0000000   0.0011401   0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000
+   57  -0.0000000   0.0541371   0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000   0.0000000
+   58  -0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000
+   59  -0.0000000  -0.0000000   0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000   0.0000000
+   60  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000
+   61  -0.0615255  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0000000
+   62  -0.0000000  -0.0073884   0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000
+   63   0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000
+   64  -0.0000000   0.0000000   0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000   0.0000000
+   65  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000
+   66  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000
+   67  -0.0000000  -0.0709527   0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000
+   68  -0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000
+   69   0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000
+   70  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000
+   71  -0.4442931  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000  -0.0000000
+   72  -0.0000000  -0.5152458  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0000000
+   73  -0.0000000  -0.0000000  -0.3218586  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0346031  -0.0000000   0.0000000
+   74  -0.0000000  -0.0000000  -0.0000000  -0.2872555  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000
+   75  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.3910304  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0250414
+   76  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.3659890  -0.0000000  -0.0000000  -0.0000000  -0.0000000
+   77   0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.2872555  -0.0000000  -0.0000000  -0.0000000
+   78  -0.0000000   0.0000000  -0.0346031  -0.0000000   0.0000000  -0.0000000  -0.0000000  -0.3218586  -0.0000000  -0.0000000
+   79  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.3659890  -0.0000000
+   80  -0.0000000  -0.0000000   0.0000000  -0.0000000  -0.0250414  -0.0000000  -0.0000000  -0.0000000  -0.0000000  -0.3910304
+```
diff --git a/Project#13/README.md b/Project#13/README.md
index 1b5532e..27d1be7 100644
--- a/Project#13/README.md
+++ b/Project#13/README.md
@@ -9,7 +9,7 @@ algorithm to allow computation of several eigenvalues simultaneously rather
 than one at a time<sup id="r2">[2](#f2)</sup>. The
 purpose of this project is to illustrate the use of what is now called the
 Davidson-Liu algorithm in the context of a 
-[CIS computation](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2312).
+[CIS computation](../Project%2312).
 
 ## The Basic Algorithm
 
@@ -29,26 +29,19 @@ from a well-chosen subspace of the full determinantal space.
 
 Compute a representation of the Hamiltonian within the space of guess vectors,
 
-```
-EQUATION
-G_{ij} \equiv \langle {\mathbf b}_i | H | {\mathbf b}_j \rangle = 
-\langle {\mathbf b}_i | H {\mathbf b}_j \rangle = \langle {\mathbf b}_i | {\mathbf \sigma}_j \rangle,\ \ 1\leq i,j \leq L
-```
+<img src="./figures/guess-vector-hamiltonian.png" height="22.5">
+
 and then diagonalize this so-called "subspace Hamiltonian",
 
-```
-EQUATION
-{\mathbf G} \alpha^k = \lambda^k \alpha^k,\ \ k=1,2,\cdots,M
-```
+<img src="./figures/diag-subspace-hamiltonian.png" height="25">
+
 where *M* is the number of roots of interest. The current estimate of each of
 the *M* eigenvectors we want is a linear combination of the guess vectors,
 with the &alpha;<sup>k</sup> subspace eigenvectors providing the
 coefficients, *viz.*
 
-```
-EQUATION
-{\mathbf c}^k = \sum_i^L \alpha_i^k {\mathbf b}_i.
-```
+<img src="./figures/coefficients.png" height="60">
+
 The dimension of ***G*** is typically very small (perhaps a dozen times the
 number of guess vectors, *L*), so one can used a standard diagonalization
 package (such as DSYEV in LAPACK) for this task.  Note that the most expensive
@@ -62,16 +55,12 @@ elements must be computed "on the fly" during the computation of each
 
 Build a set of "correction vectors",
 
-```
-EQUATION
-\delta^k_I \equiv \left(\lambda^k - H_{II}\right)^{-1} r_I^k, \ \ I=1,2,\cdots,N
-```
+<img src="./figures/correction-vectors.png" height="30">
+
 where the "residual" vectors are defined as
 
-```
-EQUATION
-{\mathbf r}^k \equiv \sum_{i=1}^L \alpha^k_i\left( {\mathbf H} - \lambda^k \right) {\mathbf b}_i,
-```
+<img src="./figures/residual-vectors.png" height="60">
+
 and *N* is the dimension of the Hamiltonian (i.e. the number of determinants).
 The inverse appearing in the definition of the correction vectors is commonly
 referred to as the "preconditioner". Notice that the residual vectors are so
@@ -92,21 +81,17 @@ Return to step #2 and continue.
 ## CIS Sigma Equation
 
 We will focus on the spin-adapted singlet formulation of CIS, 
-for which the <b>&sigma;</b> = <b>H c</b>equation was given in 
-[Project 12](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2312):
+for which the <b>&sigma;</b> = <b>H c</b> equation was given in 
+[Project 12](../Project%2312):
 
-```
-EQUATION
-\sigma(m)_{ia} = \sum_{jb} H_{ia,jb} c_j^b(m) = \sum_{jb} \left[ f_{ab} \delta_{ij} - f_{ij} \delta_{ab} + 2 <aj|ib> - <aj|bi> \right] c_j^b(m).
-```
+<img src="./figures/spin-adapted-cis-eqn.png" height="50">
 
 ## Unit Guess Vectors
 
 What should we choose for guess vectors?  As noted above, the simplest choice
 is probably a set of unit vectors, one for each eigenvalue you want.  But in
 what position of the vector should we put the 1?  For a hint, look at the
-structure of the 
-[spin-adapted singlet CIS Hamiltonian](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2312/hints/hint1.2)  
+structure of the [spin-adapted singlet CIS Hamiltonian](../Project%2312/hints/hint2.md)  
 for the H<sub>2</sub>O STO-3G test case and note that it is
 strongly diagonally dominant.  Thus, if the diagonal elements are reasonable
 approximations to the true eigenvalues, and we want to compute only the lowest
@@ -120,13 +105,9 @@ dimension to something more manageable before continuing the Davidson-Liu
 algorithm.  A typical choice is to collapse to the current best set of guesses
 using the equation given above for the current final eigenvectors:
 
-```
-EQUATION
-{\mathbf c}^k = \sum_i^L \alpha_i^k {\mathbf b}_i.
-```
-
+<img src="./figures/final-eigenvectors.png" height="60">
 
 #### References
- - <b id="f1">1</b>: E.R. Davidson, "The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices," *J. Comput. Phys.* **17**, 87 (1975).[up](#r1)
- - <b id="f2">2</b>: B.Liu, "The simultaneous expansion method for the iterative solution of several of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices," Technical Report LBL-8158, Lawrence Berkeley Laboratory, University of California, Berkeley, 1978.[up](#r2)
- - <b id="f3">3</b>: C.D. Sherrill, "The Configuration Interaction Method: Advances in Highly Correlated Approaches," *Adv. Quantum Chem.* **34**, 143 (1998). [up](#r3)
+ - <b id="f1">1</b>: E.R. Davidson, "The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices," *J. Comput. Phys.* **17**, 87 (1975). [(return to text)](#r1)
+ - <b id="f2">2</b>: B.Liu, "The simultaneous expansion method for the iterative solution of several of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices," Technical Report LBL-8158, Lawrence Berkeley Laboratory, University of California, Berkeley, 1978. [(return to text)](#r2)
+ - <b id="f3">3</b>: C.D. Sherrill, "The Configuration Interaction Method: Advances in Highly Correlated Approaches," *Adv. Quantum Chem.* **34**, 143 (1998). [(return to text)](#r3)
diff --git a/Project#13/figures/coefficients.png b/Project#13/figures/coefficients.png
new file mode 100644
index 0000000..09b91cf
Binary files /dev/null and b/Project#13/figures/coefficients.png differ
diff --git a/Project#13/figures/correction-vectors.png b/Project#13/figures/correction-vectors.png
new file mode 100644
index 0000000..229b957
Binary files /dev/null and b/Project#13/figures/correction-vectors.png differ
diff --git a/Project#13/figures/diag-subspace-hamiltonian.png b/Project#13/figures/diag-subspace-hamiltonian.png
new file mode 100644
index 0000000..41fc305
Binary files /dev/null and b/Project#13/figures/diag-subspace-hamiltonian.png differ
diff --git a/Project#13/figures/final-eigenvectors.png b/Project#13/figures/final-eigenvectors.png
new file mode 100644
index 0000000..936621f
Binary files /dev/null and b/Project#13/figures/final-eigenvectors.png differ
diff --git a/Project#13/figures/guess-vector-hamiltonian.png b/Project#13/figures/guess-vector-hamiltonian.png
new file mode 100644
index 0000000..a4add57
Binary files /dev/null and b/Project#13/figures/guess-vector-hamiltonian.png differ
diff --git a/Project#13/figures/residual-vectors.png b/Project#13/figures/residual-vectors.png
new file mode 100644
index 0000000..1438091
Binary files /dev/null and b/Project#13/figures/residual-vectors.png differ
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