Mulliken net atomic charges

Figure 5.2. Comparison between the carbon-13 NMR shifts (ppm from TMS) of selected primary, secondary, and tertiary sp carbon atoms and Mulliken net atomic charges (in me units).

Because Equation 6.53, which is sometimes called the Coulson scheme for net atomic charges, is based on the NDDO approximation, it cannot be applied properly for ab initio methods. Here, a standard scheme to quantify net atomic charges is Mulliken population analysis (Mulliken, 1955 1962), despite some well-known deflciences such as its strong dependence on the basis set and its apparent lack of convergence with increasing basis set size. Nonetheless, Mulliken charges may... 

The net atomic charge statistics in Table 6.4 reveal surprisingly large differences between the individual methods, and in particular between the semiempirical results based on the Coulson scheme (Section IV.E, Equation 6.53) and the ab initio results derived through the Mulliken... 

Charge Distribution. In Table 7 the net atomic charges on the two carbon atoms (not related by symmetry) and on the hydrogen are shown for all four PDA structures studied. These charges have been calculated again with a Mulliken-type population analysis of HF Bloch functions obtained with an electrostatically balanced (N—16)77 truncation procedure. We found that the charge distributions are also very sensitive to the method of truncation as well as to a proper convergence with respect to N. 

There has been considerable effort directed towards the assessment of the covalency or ionicity of various solids. The output of standard ab initio (SCF) Hartree-Fock-Roothaan calculations contains Mulliken (1955) charge distribution analysis parameters such as the atomic-orbital populations, net atomic charges, and bond overlap populations deseribed earlier (Chapter 3), which are often used to discuss the relative covalency or ionicity of materials. Considerable caution is required in using such parameters, however, since net atomic charges and other such quantities are not quantum-mechanical observables that is, they cannot even in principle be measured, and are highly basis-set dependent, as noted by Hehre et al. (1986 pp. 336-41). This is illustrated for molecules more relevant to mineralogy in Table 7.1, in which a number of properties of CO2 and SiOj are shown calculated at various basis-set levels. It is clear... 

An extensive study has recently been made of [WgXgXg]2- clusters, comparing DF theory, Huckel MO results, an experimental luminescence and absorption bands [101]. Here we focus mainly on the NR vs R consequences. The Mulliken populations and net atomic charges of the [WgXgX ]2 clusters obtained from NR and R DV calculations are presented in Table VI. The symmetry type of the frontier orbitals and the gap between the HOMO and LUMO are summarized in Table VII experimental absorption edge and emission maxima are also included. The atomic orbital compositions of the HOMO and LUMO from the two calculations differ primarily in their W 5d content, in the order NR> R as expected. 

Table VII Mulliken populations and net atomic charges in cluster models of annite. Sip and Fep indicate atoms in groups at periphery of cluster.

Electrostatic descriptors Net atomic charge on atom A (Mulliken charge)... 

One should not put too much reliance on numbers calculated by population analysis. Mulliken s assignment of half the overlap population to each basis function is arbitrary and sometimes leads to unphysical results (see MulUken and Ermler, Diatomic Molecules, pages 36-38, 88-89). Moreover, a small change in basis set can produce a large change in the calculated net charges. For example, net atomic charges on each H atom in CH4, NH3, H2O, and HF calculated from HF/STO-3G and HF/3-21G wave functions are (Hehre et al.. Section 6.6.2)... 

Table 11 Net Atomic Charges (q) and Spin Moments (p) According to Mulliken Partition of Spin Densitiy in KMnFs Evaluated...

An improvement on Mulliken population analysis (MPA) is natural population analysis (NPA) [A. E. Reed, R. B. Weinstcx k, and F. Weinhold, J. Chem. Phys., 83, 735 (1985)], which uses ideas related to natural orbitals (Pilar, Section 10-7). Here, one first calculates a set of orthonormal natural atomic orbitals (NAOs) from the AO basis set Xr The NAOs are then used to compute a set of orthonormal natural bond orbitals (NBOs), where each occupied NBO is classifiable as a core, lone pair, or bond orbital. Using these NBOs, one carries out a population analysis. NPA net atomic charges show less basis-set dependence than those from Mulliken population analysis. Other methods of assigning net atomic charges are discussed in the next section. Still another method of population analysis that yields net atomic charges is Lowdin population analysis (Cramer, Section 9.1.3.2). 

When 5 = 3, the resulting net atomic charges are almost undistinguishable from the Mulliken charges that are obtained in an MP2/6-31G calculation, which requires a 1000-fold longer time than the EHT calculation. 

---