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