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I want to implement in my program Chemcraft the computation of entropy and Gibbs energy of molecules in approximation "rigid rotor - harmonic oscillator", by the molecular parameters (molecular geometry, vibrational frequencies) computed by QC packages like Gaussian (the main goal is cutting/increasing low frequencies for better results). Some peole suggested this link to the program ASE.

Here it is written, that the formulas from the following book were used: C.J. Cramer. Essentials of Computational Chemistry, Second Edition. Wiley, 2004. In this book I found the following formulas:

enter image description here

This formula does not contain heat capacities C. At the ASE website the following formula is provided:

enter image description here

I don't understand, why here is provided not the heat capacity, but its integral. I don't remember what I had studied at the courses of physical chemistry. The program Gaussian computes thermodinamical functions and prints them as follows:

                       E (Thermal)             CV                S
                        KCal/Mol        Cal/Mol-Kelvin    Cal/Mol-  Kelvin
 Total                   98.006             46.365            123.966
 Electronic               0.000              0.000              0.000
 Translational            0.889              2.981             41.193
 Rotational               0.889              2.981             31.040
 Vibrational             96.228             40.403             51.733
 Vibration     1          0.593              1.986              7.306
 Vibration     2          0.593              1.984              5.881
 Vibration     3          0.594              1.981              5.310
 Vibration     4          0.596              1.975              4.563

It is not fully clear for me, the term "CV" means Cv or C*V? Sorry for stupid question.

Currently my program computes entropy correctly (the results are equal to the values provided by Gaussian and most other programs), and Cv(trans) and Cv(rot) too, but the value Cv(vib) or its integral do not match the Gaussian output. Can you suggest, what means the Cv(vibrational) in the Gaussian output (the heat capacity or maybe its integral), and how it should be computed?

One more question relates to the algorithm of computation of vibrational entropy by frequencies. I found full match of the S values produced by my program and several other packages (Gaussian, Priroda, Psi, QChem, Spartan), but there is some diffence (10-30%) with the S values produced by Orca package. I have heard that Orca uses QRRHO approximation of Grimme. If so, is it considered better than the standard RRHO approximation?

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  • $\begingroup$ CV looks like $C_\mathrm{V}$ - the molar heat capacity at constant volume. Or rather contributions of respective degrees of freedom to it. $\endgroup$
    – Poutnik
    Commented Mar 24, 2023 at 10:24
  • $\begingroup$ The Q's are the partition functions so you can calculate the thermodynamic parameters directly from these if you have the rotational and vibrational frequencies. Any good phys. chem./stat. mech/spectroscopy text book will explain these. Note also that the values in the table are in calories so not (SI) units. $\endgroup$
    – porphyrin
    Commented Mar 24, 2023 at 11:43
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    $\begingroup$ I think there is a white paper on the Gaussian website about all the thermochemistry and how to read the table. $\endgroup$ Commented Mar 25, 2023 at 1:17
  • $\begingroup$ Would you please be able to copy and paste that Gaussian output into a code block? It doesn't show up on browsers that don't load images, and on screen readers which blind people use. $\endgroup$ Commented Mar 25, 2023 at 1:30
  • $\begingroup$ @Nike Dattani, I tried to paste the Gaussian code with code block, but only the header of the table was shown correctly, the remaining text below was unformated. Sorry I do not know well how this site works. $\endgroup$
    – Linkey
    Commented Mar 25, 2023 at 7:21

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