*From*: "Fernando D. Vila" <fer;at;freyr.chem.washington.edu>*Subject*: Finite Field PT in Gaussian*Date*: Wed, 8 May 2002 13:32:36 -0700 (PDT)

Hi.. I don't send questions to the CCL very often, but it looks like this week I'm going to send a couple.. And this one is looong.. :-) I have been trying to calculate the dipole-quadrupole (A) and quadrupole-quadrupole (C) polarizabilities of water by means of Finite Field Perturbation Theory (FFPT) using Gaussian 98 Rev A.7. I have previous experience with this method, I've used it to calculate dipole moments and dipole polarizabilities. Now I've run into some trouble because I need to transform the Cartesian-based properties that Gaussian generates into the traceless ones. Right now I'm pretty confused, so I'll try to explain the problem as clearly as I can. I think the main question is: what is the expression of the perturbation Hamiltonian used by Gaussian?? I have found that when a dipole perturbation is applied (lets say, in the z direction), the perturbed energy can be written as: E = E0 + Mz * Vz where E0 is the unperturbed energy, Mz is the Cartesian z component of the dipole moment and Vz is the magnitude of the perturbation. I have checked and the Mz moment is identical to the one reported at the end by Gaussian. This is reasonable, the problem comes when you check that for a quadrupole perturbation the SAME formula is valid. Now, if the standard Cartesian perturbation Hamiltonian was used, the formula should be E = E0 + 1/2 * Mzz * Vzz I did the same for the octupole and the hexadecapole and the apparent Hamiltonian used by Gaussian is H' = Mi * Vi + Mij * Vij + Mijk * Vijk + Mijkl * Vijkl where the repeated indices are summed. This series is missing the 1/n! coefficients in front of each term. I tried checking if these coefficients are folded into the Cartesian moments, but this is not the case: when the Cartesian moments are used to calculate the traceless moments, the results are exactly correct, so no coefficients are included (the moments are simple the Cartesian components). Since I don't know what perturbation is being used, I can't derive the transformation relation that would take the Cartesian components of, say, the dipole-quadrupole polarizability and give me the ones associated with the traceless operators. What is really frustrating is that the Gaussian manual is extremely terse in the explanation of what is being done. Moreover, I've found that the warning in the manual regarding the sign ("be careful of the choice of sign convention when interpreting the results") is quite misleading: according to usual standards, what Gaussian is using are not electric fields but potential gradients. Let me say, finally, that I have actually gone into the code to see if there were any more explanatory comments, without success.. Hope anybody can help, thanks in advance.. Fer. ******************************************************************************* Fernando D. Vila Voice (206)616-3207 Department of Chemistry Fax (206)685-8665 University of Washington E-mail fdv;at;u.washington.edu Seattle, WA 98195, USA WWW http://faculty.washington.edu/fdv *******************************************************************************