[CP2K-user] [CP2K:21454] Meaning of TRAVIS Temperature Correction

[Robert Molt]

I was hoping to ask for clarification of the “temperature correction” 
feature in the

https://brehm-research.de/files/spec_tutorial_2018.pdf

I have been relying on the TRAVIS article and McQuarrie’s Statistical 
Mechanics to follow the reasoning, but I am unable to understand certain 
pieces.

1)     I will begin by trying to clarify terms. It seems like the 
“absorbance” (using the word in the output file) has units of cm*km/mol . 
These particular units are effectively (length**2/mol), which is what I 
would personally call an “absorption cross section.” 

I might have naively assumed that the output would be what I call an 
“integrated line strength” or just a “line strength,” often denoted by the 
letter S. This has units of length/mol, usually km/mol. The relationship 
between an integrated line strength and an absorbance cross section is

absorbance cross section = constants*integral( S * line shape function)

where the integral is over frequency, and the line shape function is 
usually Gaussian/Lorentz/Voigt/etc. This is what I am used to doing in my 
field (using linear response theory for anharmonic vibrational perturbation 
theory). However, I *think* CP2K is using a different convention.

I note that the absorbance term has exactly the units I would want to use 
inside the integral: an S value (units of km/mol) multiplied by the line 
shape function (units of cm-1). This makes me think that the “absorbance” 
is the integrand of the broadening function?

I *think* CP2K is actually using a different system, based on reading 
McQuarrie. I am guessing , like in the first time-correlation function 
formalism chapter equation 21-18,

absorption line shape = constants* sum over states * probabilities* (dipole 
matrix element**2) * Dirac delta of energies

I think this matches the intended units.

2)    Preliminaries aside, I do not understand what the temperature 
correction is in the code. The units for the “not corrected” absorbance are 
(K*cm*km/mol). I ran an AIMD calculation at 500K without the temperature 
correction, and the “absorbance values” are the same as the 
temperature-corrected values if one divides by 500K. It seems like the 
difference for “temperature correction” is dividing by the temperature? Is 
this correct?

Regardless, can you point me to the relevant equations in some paper/book 
to explain how temperature is affecting the “absorbance” in a linear manner?

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