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Merge pull request CrawfordGroup#11 from CrawfordGroup/proj-1-final
Project 1: Changed Image Sizes
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Diff for: Project#01/README.md

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@@ -27,7 +27,7 @@ After downloading the file to your computer (to a file called “geom.dat”, fo
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## Step 2: Bond Lengths
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Calculate the interatomic distances using the expression:
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![Bond Lengths](./figures/distances.png)
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<img src="./figures/distances.png" width="400">
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where x, y, and z are Cartesian coordinates and i and j denote atomic indices.
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## Step 3: Bond Angles
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Calculate all possible bond angles. For example, the angle, &phi;<sub>ijk</sub>, between atoms i-j-k, where j is the central atom is given by:
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![Bond Angles](./figures/bond-angle.png)
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<img src="./figures/bond-angle.png" width="150">
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where the e&#8407;<sub>ij</sub> are unit vectors between the atoms, e.g.,
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![Unit Vectors](./figures/unit-vectors.png)
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<img src="./figures/unit-vectors.png" width="600">
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- [Hint 1](./hints/hint3-1.md): Memory allocation for the unit vectors
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- [Hint 2](./hints/hint3-2.md): Avoiding a divide-by-zero
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## Step 4: Out-of-Plane Angles
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Calculate all possible out-of-plane angles. For example, the angle &theta;<sub>ijkl</sub> for atom i out of the plane containing atoms j-k-l (with k as the central atom, connected to i) is given by:
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![Out-of-Plane Angles](./figures/oop-angle.png)
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<img src="./figures/oop-angle.png" width="200">
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- [Hint 1](./hints/hint4-1.md): Memory allocation?
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- [Hint 2](./hints/hint4-2.md): Cross products
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## Step 5: Torsion/Dihedral Angles
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Calculate all possible torsional angles. For example, the torsional angle &tau;<sub>ijkl</sub> for the atom connectivity i-j-k-l is given by:
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![Torsion/Dihedral Angles](./figures/torsion-angle.png)
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<img src="./figures/torsion-angle.png" width="250">
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Can you also determine the sign of the torsional angle?
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## Step 6: Center-of-Mass Translation
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Find the center of mass of the molecule:
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![Center of Mass](./figures/center-of-mass.png)
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<img src="./figures/center-of-mass.png" width="600">
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where m<sub>i</sub> is the mass of atom i and the summation runs over all atoms in the molecule.
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Diagonal:
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![Diagonal](./figures/inertia-diag.png)
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<img src="./figures/inertia-diag.png" width="750">
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Off-diagonal:
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![Off-diagonal](./figures/inertia-off-diag.png)
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<img src="./figures/inertia-off-diag.png" width="600">
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Diagonalize the inertia tensor to obtain the principal moments of inertia:
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![Principal Moments of Inertia](./figures/principal-mom-of-inertia.png)
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<img src="./figures/principal-mom-of-inertia.png" width="125">
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Report the moments of inertia in amu bohr<sup>2</sup>, amu &#8491;<sup>2</sup>, and g cm<sup>2</sup>.
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## Step 8: Rotational Constants
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Compute the rotational constants in cm<sup>-1</sup> and MHz:
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![Rotational Constants](./figures/rot-const.png)
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<img src="./figures/rot-const.png" width="100">
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- [Solution](./hints/step8-solution.md)
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