A Simple Potential Model Criterion for the Quality of Atomic Charges Anselmo E. de Oliveira, Paulo H. Guadagnini, Roberto L. A. Haiduke, and Roy E. Bruns* Instituto de Quı ´mica, UniVersidade Estadual de Campinas, CP 6154, 13083-970 Campinas, SP, Brazil ReceiVed: December 17, 1998 The simple potential model has been shown to be useful in relating core electron binding energies measured in the X-ray region with mean dipole moment derivatives obtained from experimental infrared vibrational intensities. The importance of including relaxation corrections to the experimental 1s ionization energies of sp, sp 2 , and sp 3 hybridized carbon atoms are investigated here. Although relaxation energies obtained from 6-31G(d,p) and 6-311++G(3df,3p) basis sets using ΔSCF calculations show differences of about 1 eV for most molecules studied, relative differences are of the order of 0.1 eV. Exceptions are the CO, CO 2 , COS, and CS 2 molecules where discrepancies are larger. Relaxation energy corrections improve simple potential model fits with mean dipole moment derivatives for all carbon atom models but is most pronounced for the sp hybridized atoms. The simple potential model corrected for relaxation energies is investigated as a criterion for testing the quality of Mulliken, CHELPG, Bader and GAPT carbon atomic charges calculated from MP2/ 6-311++G(3d,3p) wave functions. The GAPT charges are in excellent agreement with the experimental mean dipole moment derivatives (within 0.067e) and provide superior statistical fits to the simple potential model when compared with those obtained for the other charges. Introduction Recently, the simple potential model 1 proposed 30 years ago by Siegbahn and collaborators has been shown to be useful in relating core electron binding energies measured in the X-ray region with polar tensor invariant quantities obtained from experimental infrared vibrational intensities. 2 Separate models relating the carbon 1s core electron binding energies to their mean dipole moment derivatives were found for sp, sp 2 , and sp 3 hybridized atoms. Furthermore, the models’ parameter values were shown to be inversely dependent on the carbon atom covalent radii and identified with the Coulomb repulsion integrals involving core and valence electrons. This was confirmed in our later study relating 2p and 3p electron ionization energies of Si and Ge with their atomic polar tensor matrix traces. 3 The potential model is expected to accurately relate core electron binding energies and mean dipole moment derivatives if two conditions are fulfilled: (1) the relaxation energies of the ionization process being investigated are negligible or constant and (2) the mean dipole moment derivatives can be identified with atomic charges. These two assumptions are investigated in this work. To maintain its simplicity and usefulness for the interpretation of experimental results, the potential model was not designed to contemplate the reorganization of electron densities in molecules during the ionization process. Relaxation energies can be used to adjust the experimental ionization energies to compensate for this reorganization so that the modified energies are appropriate for use in simple potential model applications. These adjustments, whether using values calculated from either the empirical equivalent cores method 4-6 or the ΔSCF method 7-9 from 6-31G(d,p) wave functions, improve agreement of potential model fits of experimental carbon mean dipole moment deriva- tives to experimental 1s carbon atom ionization energies of the fluorochloromethanes. 2,10 However, the relaxation energies calculated by each of these methods are not constant. For example, 6-31G(d,p) ΔSCF relaxation energies for the fluoro- chloromethanes have variations, more than an order of magni- tude larger than the estimated experimental errors in their measured ionization energies. Further improvement of the potential model fits might be expected, especially for molecules with sp hybridized carbon atoms since their 1s ionization energies for CO, CO 2 , OCS, and CS 2 were found to result in large deviations when mean experimental dipole moment derivatives are used as atomic charges. Here more extensive wave functions, calculated with a 6-311++G(3d,3p) basis set are applied to the 1s ionization energies investigated in our previous work in order to further test the importance of relaxation effects on simple potential model applications. The second assumption is not so easily tested. There is no universally accepted method of calculating atomic charges, and no experimental technique is available to measure them directly. The mean dipole moment derivative, on the other hand, can be determined using only experimental fundamental vibrational frequency and infrared intensity data and common molecular parameters obtained from experimental sources, such as atomic masses, molecular dipole moments, bond distances, and angles between bonds. Futhermore, it can be calculated from the same molecular orbital wave functions used to calculate other kinds of charge estimates. In fact, population analysis using mean dipole moment derivatives, also called GAPT (generalized atomic polar tensor) charges, has been proposed by Cioslowski 11 and does not require any direct reference to the basis set used to calculated the molecular wave function. However, dipole moment derivatives, just as dipole moments, have not been considered reliable sources of atomic charge values since molecules do not appear to be describable by spherical nonde- formable charge distributions centered on their nuclei. Besides the static contribution, results of molecular orbital calculations * Corresponding author. Fax: 55-19-788-3023. E-mail: bruns@ iqm.unicamp.br. 4918 J. Phys. Chem. A 1999, 103, 4918-4924 10.1021/jp984777e CCC: $18.00 © 1999 American Chemical Society Published on Web 06/06/1999