From chemistry-request@ccl.net Thu Apr 15 17:28:20 2004 Received: from freyr.chem.washington.edu (freyr.chem.washington.edu [128.95.128.138]) by server.ccl.net (8.12.8/8.12.8) with ESMTP id i3FMSJuR000566 for ; Thu, 15 Apr 2004 17:28:19 -0500 Received: from freyr.chem.washington.edu (localhost [127.0.0.1]) by freyr.chem.washington.edu (8.12.8/8.12.8) with ESMTP id i3FMLr3E009022 for ; Thu, 15 Apr 2004 15:21:53 -0700 Received: from localhost (fer@localhost) by freyr.chem.washington.edu (8.12.8/8.12.8/Submit) with ESMTP id i3FMLpXh009018 for ; Thu, 15 Apr 2004 15:21:53 -0700 Date: Thu, 15 Apr 2004 15:21:50 -0700 (PDT) From: "Fernando D. Vila" To: Computational Chemistry List Subject: Finite Fields in Gaussian Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Spam-Status: No, hits=-0.5 required=7.5 tests=SMILEY autolearn=no version=2.61 X-Spam-Checker-Version: SpamAssassin 2.61 (1.212.2.1-2003-12-09-exp) on servernd.ccl.net Hello everybody.. I have pretty much exhausted all other alternatives, so here I'm asking the CCL community... I have been using the Field keyword in Gaussian for many years, mostly to calculate multipole moments and dipole and quadrupole polarizabilities. Now I wanted to calculate some hyperpolarizabilities using the following formulas: E = E0 - mu0_i F_i - 1/2 alp_ij F_i F_j - 1/6 bet_ijk F_i F_j F_k mu_i = m0_i + alp_ij F_j + 1/2 bet_ijk F_j F_k where F_i is the perturbing electric field in the i direction, E is the total energy including the perturbation, E0 is the energy without the perturbation, mu, alp and bet are the dipole, polarizability and hyperpolarizability. The summation over the i, j, k indices is implied. To verify that the finite differences were giving me a small error I decided to check by calculating NH3 at HF level (Gaussian produces analytic values at this level). Here are the results: Dipole=0.,0.,-0.7000795 Polar=9.4875931,0.,9.4875931,0.,0.,9.799189 HyperPolar=0.,-14.2904879,0.,14.2904879,-3.6541021,0.,-3.6541021,0.,0.,-19.6122974 If I now apply a finite electric field along the z axis and fit the results to a polymomial I get: For the energy: -56.200911807600 -0.700079533332 * F -4.899299996216 * F^2 3.333331240659 * F^3 -400.002401571933 * F^4 For the dipole moment: -0.700079500000 -9.799183333333 * F 9.783333333291 * F^2 -466.666666569064 * F^3 66666.666631576154 * F^4 If you compare the coefficients of this polymomials with the coefficients in the formulas above you will see that there are many sign differences with respect to the analytic results I showed above. This problem is not new to me and the Gaussian manual very helpfully :-P informs us that "the coefficients are those of the Cartesian operator matrices; be careful of the choice of sign convention when interpreting the results". Before I had always assumed that although Gaussian says that is adding an electric field, what is actually doing is adding a potential gradient ( dV/di = V_i = -F_i ). This assumption always gave me correct results, but now it is totally irreconciliable with the sign I get for the hyperpolarizability. So finally, my question: what is the CORRECT FORM of the perturbation introduced by the Gaussian keyword Field. Cheers and I will really appreciate any comments (Doug Fox, are you there?? :-) Fer. "The biggest cause of trouble in the world today is that the stupid people are so sure about things and the intelligent folks are so full of doubts." Bertrand Russell ******************************************************************************* 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 *******************************************************************************