Atomic Charges.

The problem of deriving atomic charges from the results of ab Initio MO calculations has been studied by the use of several reported methods: Mulliken population analysis, the minimal basis set (MBS) procedure, the natural population analysis (NPA), two electrostatic potential fitting methods, M-K and ChelpG, the Hirshfeld population analysis, and CM5 (charge model 5), which is related to the Hirshfeld method. The first set of studies were concerned with hydrogen charges. It was found that the MBS charges were linearly related to the Hirshfeld charges. The Hirshfeld, CM5, and MBS methods, but not the others, provided an excellent correlation for H atomic charge with the H-C-H bond angle, and with calculated gas-phase acidity. The two methods that were linearly related and gave hydrogen charges in agreement with an experimental study of partially deuterated methanes are MBS and Hirshfeld. In order to see which of the two methods is the more satisfactory, the methanol dimer was examined. The calculated H bond energy was 6.2 kcal/mol, which was in good agreement with studies of hydrogen bonds. The Coulombic interaction for the O···H bond was estimated using the MBS and Hirshfeld charges. The latter gave a calculated energy of 3-6 kcal/mol, whereas MBS gave an energy of ∼35 kcal/mol. Clearly, the Hirshfeld method is more satisfactory and should be the method of choice.