I'm sorry in advance for asking, probably, stupid questions, because I'm

quite new in quantum chemistry.

I would like to ask your help, because I cannot understand how components of two-photon transition matrix

are calculated, even in the simpliest case - for the ground state-1st excited state transition.

Probably I'm missing something very obvious, but I could find out what.

Just for example I took water and calculated μ01 and μ11

Code: Select all

```
@ Transition moment <B | A - <A> | C> in a.u. for
@ A operator label, symmetry, spin: XDIPLEN 1 0
@ B excited state no., symmetry, spin: 1 1 0
@ C excited state no., symmetry, spin: 1 1 0
@ B and C excitation energies, moment: 0.18741243 0.18741243 -0.07422049
@ Transition moment <B | A - <A> | C> in a.u. for
@ A operator label, symmetry, spin: YDIPLEN 1 0
@ B excited state no., symmetry, spin: 1 1 0
@ C excited state no., symmetry, spin: 1 1 0
@ B and C excitation energies, moment: 0.18741243 0.18741243 -0.30508855
@ Transition moment <B | A - <A> | C> in a.u. for
@ A operator label, symmetry, spin: ZDIPLEN 1 0
@ B excited state no., symmetry, spin: 1 1 0
@ C excited state no., symmetry, spin: 1 1 0
@ B and C excitation energies, moment: 0.18741243 0.18741243 0.00000000
```

and

Code: Select all

```
Electric transition dipole moments (au)
---------------------------------------
@ Mode Frequency Velocity/Frequency Length
@ No. (au) x y z x y z
@==============================================================================
@ 1 0.187412 -0.6667 -0.0124 0.0000 -0.5488 -0.0147 0.0000
@------------------------------------------------------------------------------
```

According to the formula provided here http://www.sciencedirect.com/science/ar ... 1412008391

Sxx= μ01

_{x}*μ11

_{x}/(ω

_{01}-ω

_{01}/2)+ μ01

_{x}*μ11

_{x}/(ω

_{01}-ω

_{01}/2)=(-0.5488*(-0.07422049)+(-0.5488*(-0.07422049)))/(0.187412/2)=0.86912

Sxy= μ01

_{x}*μ11

_{y}/(ω

_{01}-ω

_{01}/2)+ μ01

_{y}*μ11

_{x}/(ω

_{01}-ω

_{01}/2)=(-0.5488*(-0.30508855)+(-0.0147*(-0.07422049)))/(0.187412/2)=1.7984

Code: Select all

```
+--------------------------------+
| Two-photon transition tensor S |
+--------------------------------+
---------------------------------------------------------------
Sym No Energy Sxx Syy Szz Sxy Sxz Syz
---------------------------------------------------------------
1 1 5.10 -1.2 -0.3 0.0 -3.3 -0.0 0.0
---------------------------------------------------------------
```

I'm getting totally wrong values. But how could Sxx be negative, when both μ01

_{x}and μ11

_{x}are negative?

And what does asterix in equation for δ(ω) means? Is it comples conjugation? The expression for Sab includes only real numbers....

Any help will be greatly appreciated.