Running parameters

Functions covered:

• dIdV
• dIdV_tilt
• STM (use MSTM instead)
• MSTM
• IETS_complex

dI/dV (no tilting of orbitals)

dIdV( V, WF, eta ,eig, R, Rat, coes, orbs='sp', s=0.0, px =0.0, py=0.0, pz=0.0, dxz=0.0, dyz=0.0, dz2=0.0)

V # applied sample bias = (energy vs. the Fermi Level in eV).

WF # the Work-function (normally ~5 eV gives reasonable results).

eta # Width of the Lorentzian function for energy smearing depending on system it can reach various values: for single molecular orbital very low number -- 1e-6 eV; For standard slabs -- 0.05-0.1 eV; For low layered or small slabs -- 0.3-0.5 eV.

eig # eigenenergies of sample states (=molecular orbitals) (given by 1st output of 3 of the reading procedure).

R #input of points in which you calculate dI/dV (relaxed via PP-AFM -- you need to have linked PPAFM part and GridUtils of PPAFM to get them; or nonrelaxed via ReadSTM.mkSpaceGrid).

Rat # position of atoms of the sample (given by 3rdt output of 3 of the reading procedure).

coes # LCAO coefficients (given by 2nd output of 3 of the reading procedure).

orbs='sp' # the same as in Reading parameters

s=0.0 # <0.0,1.0> -- contribution to the tunneling to/from s orbital on the PP.

px=0.0 # <0.0,1.0> -- contribution to the tunneling to/from px orbital on the PP.

py=0.0 # <0.0,1.0> -- contribution to the tunneling to/from py orbital on the PP.

pz=0.0 # <0.0,1.0> -- contribution to the tunneling to/from pz orbital on the PP.

dxz=0.0 # <0.0,1.0> -- contribution to the tunneling to/from dxz orbital on the PP.

dyz=0.0 # <0.0,1.0> -- contribution to the tunneling to/from dyz orbital on the PP.

dz2=0.0 # <0.0,1.0> -- contribution to the tunneling to/from dz2 orbital on the PP.

dI/dV with tilting orbitals (as PP relaxes)

dIdV_tilt( V, WF, eta ,eig, R, R0, Rat, coes, orbs='sp', pz=0.0, pxy =0.0, dz2=0.0, dxyz=0.0, len_R=4.0, al=1.0)

Note: every parameter: V-coes no change as above

orbs='sp' # only 'sp' works here

pz=0.0 # <0.0,1.0> -- contribution to the tunneling to/from tilting pz orbital on the PP.

pxy=0.0 # <0.0,1.0> -- contribution to the tunneling to/from tilting px and py orbitals on the PP.

dz2=0.0 # <0.0,1.0> -- contribution to the tunneling to/from dz2 orbital on the PP.

dxyz=0.0 # <0.0,1.0> -- contribution to the tunneling to/from tilting dxz and dyz orbitals on the PP.

len_R=4.0 # length of the PP-tip "bond"; 4 Å is an standard length in PPAFM calculations

al=1.0 # (0.0,2.0> -- rescalling constants of the tilting; 1.0 -- tilts with the same angle as the PP; 2.0 -- tilts twice as fast; 0.5 -- tilts twice as slow.

STM (no tilting of orbitals) :

STM( V, nV, WF, eta ,eig, R, Rat, coes, orbs='sp', s=0.0, px =0.0, py=0.0, pz=0.0, dxz=0.0, dyz=0.0, dz2=0.0, WF_decay=1.0)

note: RATHER USE MSTM INSTEAD - it calculates all the dI/dV and STM images from 0 to given Voltage for the same computational cost.

note: everything the same as dI/dV except for:

nV # number of dI/dV steps - should be approx. V/eta +1 ; STM is rectangular integrated from the dI/dV;

WF_decay=1.0 # How the Workfunction (barrier and therefore tunneling decay) is changing with increasing/decreasing voltage for each dI/dV step; 1.0 -- the change of the tunneling decay scales with the voltage (at V=1.0 is WF=4.0 eV); 0.0 -- no change with the voltage.

MSTM (no tilting orbitals)

MSTM( Vmin, Vmax, dV, WF, eta ,eig, R, Rat, coes, orbs='sp', s=1.0, px =0.0, py=0.0, pz=0.0, dxy=0.0, dxz=0.0, dyz=0.0, dz2=0.0, WF_decay=1.0)*:

note: everything the same in dI/dV, except for:

Vmin # minimal voltage from which the STM scan over all voltages is integrated. Maximally 0: Vmin = Vmin if Vmin <= 0.0 else 0.0;

Vmax # maximal voltage to which the STM scan over all voltages is integrated. Minimally 0: Vmax = Vmax if Vmax >= 0.0 else 0.0;

dV # division, between the calculated dI/dV steps - should be approx. eta ; STM is rectangular integrated from the dI/dV;

WF_decay=1.0 # How the Workfunction (barrier and therefore tunneling decay) is changing with increasing/decreasing voltage for each dI/dV step; 1.0 -- the change of the tunneling decay scales with the voltage (at V=1.0 is WF=4.0 eV); 0.0 -- no change with the voltage.

IETS (no tilting of orbitals)

**IETS_complex( V, WF, eta ,eig, R, Rat, coes, orbs='sp', s=0.0, px =0.0, py=0.0, pz=0.0, dxz=0.0, dyz=0.0, dz2=0.0, Amp=0.05)

V - voltage # = (energy vs. the Fermi Level in eV);

WF # - workfunction (normally ~5 eV gives reasonable results),

eta # - energy smearing (0.5-0.30 eV) depending on system (for single orbital very low number

eig # - eigenenergies of sample states (=molecular orbitals)

R #input of points in whish you calculate dI/dV (relaxed via PP afm, or nonrelaxed via mkSpaceGrid)

coes # LCAO coefficients from reading procedures.

orbs # = 'sp' orbitals of the sample (spd don't work at the moment) s and/or px and/or py and/or pz orbitals at the PP

Amp # =0.05 amplitude of vibrations in x and y directions (the same as in PPAFM)

M #= 16 effectiva mass of the vibrating molecule/atom ; in Atomic Units (16 for oxygen)

• inner variables and explanation :
  • denomin** # = 1/w_vib^2
  • IETS = 1/w_vib1^2 * d(dI/dV)/dvib1+ 1/w_vib2^2 *d(dI/dV)/dvib2 ;
  • last part: 1/w_vib3^2 *d(dI/dV)/dvib3 is not connected with Frustrated translation