## SOS calculation of two-photon absorption cross-section

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wang

### SOS calculation of two-photon absorption cross-section

Dear collegues,

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

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``````@ 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
``````
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and

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``````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
@------------------------------------------------------------------------------ ``````
[/size]

According to the formula provided here http://www.sciencedirect.com/science/ar ... 1412008391
Sxx= μ01x*μ11x/(ω0101/2)+ μ01x*μ11x/(ω0101/2)=(-0.5488*(-0.07422049)+(-0.5488*(-0.07422049)))/(0.187412/2)=0.86912
Sxy= μ01x*μ11y/(ω0101/2)+ μ01y*μ11x/(ω0101/2)=(-0.5488*(-0.30508855)+(-0.0147*(-0.07422049)))/(0.187412/2)=1.7984

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``````                  +--------------------------------+
| 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
--------------------------------------------------------------- ``````
[/size]

I'm getting totally wrong values. But how could Sxx be negative, when both μ01x and μ11x 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.

wang
Posts: 1
Joined: 06 Apr 2015, 18:59
First name(s): Wang
Last name(s): Zhang
Affiliation: LKO

### Re: SOS calculation of two-photon absorption cross-section

I tried to figure it out by myself, but without success.
Could someone give me a clue where I am wrong, please?

kennethruud
Posts: 252
Joined: 27 Aug 2013, 16:42
First name(s): Kenneth
Last name(s): Ruud
Affiliation: UiT The Arctic University of Norway
Country: Norway

### Re: SOS calculation of two-photon absorption cross-section

Hi!

I am not sure I entirely understand all your questions, but hopefully addressing some or most of them:
1) Note that what you discuss at transition moments, not absorption cross sections. For transition moments, only the relative sign obtained in a single calculation is meaningful, as the sign will otherwise depend on factors such as the phase of the wave function. The fact that there is a difference in sign in the transition moment is thus nothing to be concerned about (I assume the linear and quadratic transition moments have been obtained in different calculations).
2) A two-state model is not particularly accurate compared to the full SOS expression used by Dalton in its calculation. How good or poor the two-state model will be depends on how dominated the two-photon absorption cross section is by the lowest excited state, and this again depends on your molecule.
3) In general, transition moments can be complex. For the equation for the transition moment provided in the reference paper you quote, I agree that the use of complex conjugation is somewhat superfluous as there are only real quantities. If a finite lifetime for the excited states were included in the expression for the two-photon transition moment, then the quantities may also be complex.

Hopefully this is of come use to you.

Best regards,

Kenneth

lyzhao
Posts: 74
Joined: 11 Nov 2013, 00:36
First name(s): Youzhao
Last name(s): Lan
Affiliation: Institute of Physical Chemistry
Country: China

### Re: SOS calculation of two-photon absorption cross-section

Dear Wang,
Thanks for your interest in my paper. Unfortunately, this post was blocked by our anti-spam system (I don't know why) before.
As mentioned by Prof. Kenneth, The two-states model is not accurate compared to the full SOS calculation.
It is difficult or impossible to compare the "truncated" SOS calcualtion to the "Full" SOS calculation.
The advantages and disadvantages of SOS have been also mentioned in my paper.
Please also refer to another paper with a compact discussion of SOS for one-, two-, and three-photon absorptions. (Chem. Phys. Lett. 2003v375p233)

Note: in your expression, "Sxx= μ01x*μ11x...." the star * means a multiplication sign not complex, doesn't it?
More questions about my paper, you may directly email to me.

Best regards.
Lan

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