<p>I was hoping to ask for clarification of the
“temperature correction” feature in the</p>
<p><a href="https://brehm-research.de/files/spec_tutorial_2018.pdf" target="_blank">https://brehm-research.de/files/spec_tutorial_2018.pdf</a></p>
<p>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.<br />
<br />
</p>
<p style="text-indent: -0.25in;">1)<span style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-size-adjust: none; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-variant-position: normal; font-variant-emoji: normal; font-stretch: normal; font-size: 7pt; line-height: normal; font-family: "Times New Roman";"> </span>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.” <br />
<br />
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<br />
<br />
absorbance cross section = constants*integral( S * line shape
function)<br />
<br />
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.<br />
<br />
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?<br />
<br />
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,<br />
<br />
absorption line shape = constants* sum over states *
probabilities* (dipole matrix element**2) * Dirac delta of
energies<br />
<br />
I think this matches the intended units.<br />
<br />
</p>
<p style="text-indent: -0.25in;">2)<span style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-size-adjust: none; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-variant-position: normal; font-variant-emoji: normal; font-stretch: normal; font-size: 7pt; line-height: normal; font-family: "Times New Roman";"> </span>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?<br />
<br />
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?</p>
<p></p>
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