Re: scaled frequencies for S and H

[topper : at : haydn.chm.uri.edu (Robert Q. Topper)]

 >Leif Haldor writes:
 >You have to scale the frequencies you get from Gaussian by about 0.9.
 >The enthalphy, entropy and ZPE among other thermodynamical properties
 >calculated by Gaussian depend upon the frequencies. Does someone on this
 >list know how you can compute the thermodynamical properties using scaled
 >frequencies in Gaussian? Probably not possible? If so, has someone written
 >a program to extract the frequencies from the outputfile or chk-file,
 >correct for the scaling and then compute the thermodynamical properties?
 >Or do I have to use Lotus 1-2-3 or Excel after looking up the litterature
 >references for all the formulas.
 >Robert Topper responds:
 >You can certainly estimate thermochemical properties from the frequencies
 >you get from Gaussian. However, you will have to use the rigid-rotator/
 >harmonic oscillator (RRHO) approximation to the partition function, which
 >requires the three principal moments of inertia as well as the
 >harmonic frequencies. These can be calculated from the molecular
 >geometry and masses.  Also, the calculation may only
 >be semi-quantitative, unless you have a fancy way of estimating the
 >partition function.  (Significantly more and detailed information has
 been deleted from this response - DAS.)
 And Doug Smith adds:
 >In a recent manuscript we wrote:
 >"Each HF/6-31G* optimization, and for the monomers the MP2/6-31G*
 >optimizations, were followed by normal frequency analysis to make sure an
 >energy minimum was obtained and for calculating free energies at 298
 >K and one atmosphere.  In the free energy calculations the thermal
 >correction to the enthalpy, H(T) and entropy, S(T) were calculated in the
 >rigid rotor, harmonic oscillator approximation.  Ideal gas behavior
 >was accepted in the imidazole protonation reaction and for the formation
 >of monohydrates.  The thermal energy contributions were calculated using
 >classical statistical thermodynamic functions.  The total entropy
 >for PyW(pi) and Im(3)W without any molecular symmetry contain a term
 >of RTln2 due to the entropy of mixing."
 >Taken from:  Nagy, P. I.; Durant, G. J.; Smith, D. A. "Theoretical
 Studies
 >on Hydration of Pyrrole, Imidazole and Protonated Imidazole in the Gas
 >Phase and Aqueous Solution," J. Am. Chem. Soc., in press.
 >Doug
 Doug, Please understand that I have nothing agains the classical
 rigid-rotator/quantum harmonic-oscillator approximation,
 which enjoys widespread use. (A paper I saw by J. Gao on the
 Menshutskin reaction [JACS 113, 7796 (1991)] comes to mind). Also,
 Don Truhlar (with whom I did the quantum Monte Carlo work) and
 Bruce Garrett have been using this approximation for many years
 in rate constant and isotope effect calculations for polyatomic molecules,
 often with great success. However, if a molecule can undergo internal
 rotations at room temperature, or the molecule is an ionic complex
 of some kind (large-amplitude, low-frequency stretches),
 the CRR/QHO approximation has less chance of working well.
 Moreover, anharmonicities can sometimes have a big effect on the
 zero-point energy, and thus affect the quality of the thermochemical
 calculations. This is my main point...and the point of our JCP article.
 My second point is that the use of scaled freqencies may be numerically
 justified, but has never been actually tested against exact calculations
 of free energies, at least not to my knowledge. Personally, if I were going
 to calculate thermochemical properties from a Gaussian calculation, I'd
 use the classical rigid rotator for the rotations, calculate some cubic
 and quartic force constants using Gaussian (assuming I had enough
 computer time), and use the expression given for the vibrational partition
 function in Truhlar and Issacson, JCP 94, 357 (1991). At least then
 the zero-point energy would be accurate, and so then presumably would be
 the room-temperature thermochemical values (again, assuming no internal
 rotations....). Moreover, only a subset of the force field is needed
 for the aforementioned approximate form.
 -rqt
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             *  Robert Q. Topper, Ph.D.     *
             *  Department of Chemistry     *
             *  University of Rhode Island  *
             *  Kingston, RI 02881 USA      *
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