Understanding the physics behind the two-photon cross section calculation
Dear all,
I have successfully calculated two-photon absorption cross sections of several molecules for several excited states. Because of research issues, I would like to understand how Dalton calculates sigma, i.e. the two-photon absorption cross section.
I read the original papers from where the Dalton developers started the implementation, but still some data, printed in the output, is not clear to me. Especially, below you can find the corresponding part of the output I'm interested in.
I understood that sigma is proportional to the square modulus of the transition dipole tensor S, that Dalton calculates somehow (how??) resulting in a symmetric 3X3 matrix (values: Sxx, Syy, Szz, Sxy, Sxz, Syz). What I do not understand, apart from how Dalton calculates the values of such tensor, is how sigma is finally calculated:
sigma = 8pi^3alpha^2hbar/e^4 * E^2*D
The first factor contains an unknown alpha (to what it refers?), than E^2 (what is E?) and finally D, defined as the transition probability, with a formula for linearly polarized light and another for circularly polarized light. D is, in any case, a function of Df (D final state??) and Dg (D ground state??). Df and Dg are, in turn, summations over i,j of products between, I guess, values of the S tensor, finally divided by 30. What is the meaning of i and j subscripts? Should I consider Df as expression containing only the diagonal terms of the tensor S, and Dg as expression containing only the off-diagonal terms of S?
If anybody can help, thank you a lot!
Best, Marco