Summary. Scaled freq for S and H

 ## S U M M A R Y   O F   R E S P O N S E S :  ##
 Warning: long!
 Here is the summary of the responses I received. Thank you very much
 to all that responded.
 ## Original posting: ##
 ## From: "Leif Haldor Bjerkeseth . Organisk Kjemi" <bjerkese>
 Subject: G90/92. Scaled Freq. Correct. for H and S.
 To: chemistry()at()
 Date: Wed, 10 Feb 1993 16:55:05 +0100 (MET)
 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.
 Leif Haldor
  Leif Haldor Bjerkeseth, Dept.Org.Chem., NTH, UNIT, N-7034 TRONDHEIM
  Phone: +47 7 59 39 67  //  Prefered E-mail address: bjerkese()at()
  Fax:   +47 7 59 42 56  //
 ## Responses: ##
 ## From: culmer()at() (Charles Ulmer)
   I would be greatful if you could summarize for the list any of the
 responces that you receive concerning programs which use scaled freq.
 to estimate thermodynamic properties.  I too am tired of entering all
 the data into Excel...
  Charles W. Ulmer
  D.A.Smith Group
  University of Toledo
  Toledo, OH, 43606
 ## From: Louis.Grace()at()
 I have been editing my gaussian output files in Word.  When I have the
 sections I want (frequencies and displacements, for example) I then
 change all the spaces into tabs.  I then use Excel to manipulate the data.
 One can probably use Lotus 1-2-3 or a host of other programs, too.
 Depending on what you wish to extract from the file and in what format
 you would like to have it, you may need to make a set of macros for
 transposing and rearranging things.  Have fun!
                                              Louis Grace
                                              Department of Chemistry
                                              The University of Michigan
                                              Ann Arbor, Michigan   48104
 ## From: zheng()at()
   Hi, I remember that in one paper Prof. Pople demonstrated scaling of
 frequencies has little effect on thermodynamical properties calculated. If you
 wnat to compare the calculated frequencies with experiemntal data, scaling is
 usefull. Otherwise, scaling is not needed.
      Yajun Zheng
 ## From: Bundens Jeanne W <jbundens()at()>
 	There is a derivation from Hehre's book for scaling freq and
 correcting for zpve and to standard temp. If you don't get other
 responses I could send you the short code that does that much and you
 can modify it. As for extracting frequencies from Gaussian output, we
 get by in UNIX with the convenient grep command and pipe the results to
 a file to be read by the program. I'd be interested in your other
 		Jeanne Bundens
 From: jan()at() (Jan Jensen)
 Dear Dr. Bjerkeseth,
 	With regard to using scaled frequencies to calculate thermodynamical
 properties I have one suggestion.  The US version of the quantum chemistry
 program GAMESS allows the input of a scale factor for the frequencies,
 and the scaled frequencies are then used to calculate the ZPE, etc.  It
 is also possible to type in the frequencies in the input, if you don't
 want to recalculate a hessian or have done so with another program.
 All this is done in $FORCE, in case you are familiar with GAMESS input. If you
 have access to this code this may be a good solution.  If not, it may be
 too much work to to set up the code to scale a few frequencies.  However, I
 would be happy to let you know how to get it, if you are interested.
 			Best regards,
 					Jan H. Jensen (grad. student)
 					Department of Chemistry
 					Iowa State University
 					Ames, Iowa
 ## From: "J.S. Kwiatkowski" <JSKWIAT()at()PLTUMK11.bitnet>
 Hi Leif,
  I just read your e-mail concerning the calculation of thermodynamic
 properties using the scaled frequencies from Gaussian.
  It is my pleasure to inform you that I wrote a short program
 to compute these properties using frequencies given as the input
 data (so you can use scaled, unscaled, experimental frequencies etc.).
 The program is written in fortran, it is a very short (the program
 reproduce exactly the results from the Gaussian programs at T = 298.15
 K). Using my program you can compute the thermodynamic properties at
 any temperature.
  If you are interested in this program, please reply me this
 Yours   Staszek (J.S. Kwiatkowski)
 ## From: "J.S. Kwiatkowski" <JSKWIAT()at()PLTUMK11.bitnet>
 Program THERM calculate thermodynamic functions: capacity Cp and enrtopies
 (trans,rot,vibr,tot) at any temperature. To prepare input data it is necessary
 to know the rotational constants (A,B,C), molecular mass, and frequencies
 of a molecule.
 ## From: ckf()at() (Charles Foley)
 Leif -
 You should contact Lee Bartolotti at the North Carolina Supercomputing
 Center here in the U.S.  Lee has written a program that will calculate
 thermodynamice properties at a given temperature using a starting geometry
 and frequencies.  The program has been modified by Dave Deerfield at the
 Pittsburgh Supercomputing Center to read frequency and geometry information
 directly from a Gaussian 90/92 output file.  I'm not sure if the frequencies
 are scaled however.
 You can reach Lee Bartolotti at e-mail address: bartolot()at()
 Charles K. Foley, Ph.D.
 Cray Research, Inc.
 P.O. Box 12746
 Research Triangle Park, NC 27709
 (919) 544-6267 							o
 ckf()at()					       [\.
 ## From: Lee Bartolotti <bartolot()at()>
 [Response from Dr. Bartolotti to E-mail from me. LH]
 In response to your e-mail request, I am sending you a copy of the program
 which will read Gaussian output files and calculated various thermodynamic
 properties.  It was just thrown together and could be made cleaner but
 it is functional.  Not all output is well documented. For instance, the
 zero point energy is output as "ev0", and "delta h" is the
 change in
 enthalpy going from OK to the temperature of interest ("delta h"
 is given in the book by Hehre et al).
 This program will also read input from the following file format
 (which makes compatable with other programs)
 [format deleted. LH]
 Here, the first line tells the program if the molecule is linear or not,
 the symmetry number (1 in this case) and the temperature.  The next set
 of data gives the Cartesian coordinates (in Angstroms).  A blank line
 separates the the input of the vibrational frequencies (in 1/cm).
 If you want to scale the frequencies, you can do in subroutine thermo,
 at the "do 10" loop.  Just multiply "FREQ(i)" by the scale
  ||  Lee Bartolotti                   North Carolina Supercomputing Center   ||
  ||  Computational Scientist          3021 Cornwallis Rd.                    ||
  ||  Research Institute               Research Triangle Park, NC 27709       ||
  ||  bartolot()at()
  ||  (919) 248-1185                                                          ||
 c     This program calculates the thermo-chemical properties of a molecule
 c     given its Cartesian coordinates and vibrational spectrum.
 C     The program was originally written by:
 C              Dr. Lee Bartolotti
 C              North Carolina Supercomputing Center
 C              bartolot()at()
 C              919-248-1185
 C     Bastardized by:
 C              Dr. David W. Deerfield II
 C              Pittsburgh Supercomputing Center
 C              deerfiel()at()
 C              412-268-6102
 ## From: topper()at()HAYDN.CHM.URI.EDU (Robert Q. Topper)
 Dear Leif,
 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.
 My coworkers and I have recently written a paper on the calculation of
 thermochemical properties from potential energy surfaces
 using various methods, and the article will appear soon in
 the Journal of Chemical Physics (March 15 is the approximate date).
 In that paper, we compare the RRHO approximation of the free energy
 to calculations made using perturbation theory to treat the vibrations
 and to (exact) Fourier path-integral quantum Monte Carlo calculations
 for potential energy models of gas-phase H2O, D2O, H2S, and H2Se.
 However, we did not use "scaled" frequencies; we used the actual
 mode harmonic oscillator frequencies. These resulted in partition
 functions which were off by as much as 30% from "exact" values
 (looking at temperatures between 200 and 4000 K).
 There's no telling whether using scaled frequencies would make
 the partition functions more accurate or less accurate, at least not
 from first principles.
 I would be glad to send you a preprint of our work if you are interested
 (this is the same article that many people on the list have asked for
 in the context of coordinate transformations).
 Also, Martin, Francois and Gijbels have recently calculated thermochemical
 properties for H2O using Gaussian. A good reference is:
 Martin, Francois, and Gijbels, J. Chem. Phys. 96, 7633 (1992)
 Our work indicates that their calculations (which use vibrational
 perturbation theory in combination with a quantum non-rigid rotator
 calculation) are quite accurate up to 2400K.  However, for molecules
 which can undergo internal rotations at the temperature of interest,
 all bets are off! Also, beware of very low-frequency (floppy) vibrations.
 A very useful approximate "harmonic" form for the vibrational
 partition function (if you know the zero-point energy and the
 fundamentals) is given in
 D.G. Truhlar and A.D. Isaacson, J. Chem. Phys. 94, 357 (1991)
 and you may also want to look at the JANAF tables;
 M.W. Chase Jr., JANAF Thermochemical Tables, 3rd ed. (ACS and APS
 for the National Bureau of Standards, New York, 1985).
 -Hope this helps!
             *  Robert Q. Topper, Ph.D.     *
             *  Department of Chemistry     *
             *  University of Rhode Island  *
             *  Kingston, RI 02881 USA      *
             *  rtopper()at() OR      *
             *  topper()at()    *
             *  (401) 792-2597 [office]     *
             *  (401) 792-5072 [FAX]        *
 ## From: topper()at() (Robert Q. Topper)
 Leif, you may also want to look at
 J. Gao, J.Am. Chem. Soc. 113, 7796 (1991)
 for thermochemical calculations of the Menshutkin reaction in solution
 using Gaussian.
 [original posting deleted. LH]
 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.)
 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.
 Douglas A. Smith
 Assistant Professor of Chemistry
 The University of Toledo
 Toledo, OH  43606-3390
 voice    419-537-2116
 fax      419-537-4033
 email    dsmith()at()
 ## From: topper()at() (Robert Q. Topper)
 [In response to the message above Robert Topper responded: LH]
 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.
             *  Robert Q. Topper, Ph.D.     *
             *  Department of Chemistry     *
             *  University of Rhode Island  *
             *  Kingston, RI 02881 USA      *
             *  rtopper()at() OR      *
             *  topper()at()    *
             *  (401) 792-2597 [office]     *
             *  (401) 792-5072 [FAX]        *
 I think I will mention another solution to the problem mentioned in my
 original posting. If I could scale the frequencies in Gaussian that
 would be the best. It should be possible to take a copy of the link
 that performs the thermo-calculations, modify the procedure THERMO to
 calculate both scaled and unscaled thermodynamical properties (include
 the scale factor in the code) and recompile the link under another
 name and then change the route to use this new link instead of the
 standard one.
 Such a procedure is something that would have been very nice to
 have in the original Gaussian. Probably something to put into
 it in the next version, Mike Frisch ? (e.g in combination with the
 Again, thank you very much to all that responded.
 Leif Haldor
  Leif Haldor Bjerkeseth, Dep.Org.Chem., NTH, UNIT, N-7034 TRONDHEIM, Norway
  Phone: +47 7 59 39 67  //  Prefered E-mail adress: bjerkese()at()
  Fax:   +47 7 59 42 56  //