Net atomic population

The values are called the net atomic populations and the overlap population. Chemists speak of the charges on atoms in molecules, and Mulliken s second contribution was to propose a method of partitioning the overlap population between contributing atoms. He proposed that the overlap populations be divided equally between participating atoms, so giving the gross atomic populations of... 

Equation 6.55 represents the Mulliken population analysis, where the first sum in the parentheses containing only quadratic terms is called net atomic population, the second sum is the overlap population, and nA is the total sum of all electrons associated with atom A, the gross atomic population (Mulliken, 1955, 1962). Note the difference between Equation 6.54 and Equation 6.55 in the former the summation includes all AOs of the molecule, while in the latter the sum is confined to those AOs that belong to atom A. Obviously ... 

Now we can break the two terms in Eq. [7] into sums over specific atoms. Summing over only the AOs centered on atom k in the first term, we obtain the net atomic population n k), Eq. [8]. 

The net atomic population, n(k), does not include any of the electron density associated with the overlap population, N(k,l). It is clear that some of these electrons in the overlap population belong to atom k and the remaining electrons belong to atom /. Furthermore, these should be added to n k) and (/) to get the total number of electrons on each atom. Arbitrarily, Mulliken divided this overlap population evenly between the two atoms resulting in the gross atomic population N(k) for atom k, Eq. [10]. 

The net atomic population neglects the electrons associated with the overlap between two atoms. Mulliken arbitrarily divided the overlap population equally between the two atoms, producing the gross atomic population... 

Strictly speaking, the 3p and 2p net atomic orbital populations calculated by the STO-3G basis using the GAUSSIAN 90 are plotted in Figs. 13a and b, respectively. The maximum values of I Qi 2 for 3p and 2p net atomic populations are also indicated in Figs. 13a and... 

Net atomic population 105 Newton method 234 Newton s laws 11... 

Table 16-1. Energies, electric dipolar moments, net atomic populations, vibrational polarizabilities and mean vibrational molecular polarization, magnetizability and contributions thereto, isotropic g tensor and nuclear and electronic paramagnetic and diamagnetic contributions thereto, principal moments of inertia and rotational parameters calculated for H2 C N2 in seven structural isomers... 

The reason for these problems is the imbalance of overlap populations and the net atomic populations, and this imbalance is due primarily to the arbitrary equal distribution of the overlap population between atoms involved. In spite of these two problems, which have to be remembered when analyzing populations of orbitals and atoms, MPA is still frequently used for electron population analysis. 

Figure 3. Net atomic and overlap populations for the low-spin form of C54.

Atomic populations and net charges defined according to Mulliken 112>. 

In this equation, q = q C ) + ( 2)] is one-half the sum of the charges of the electron-richest bonded C atoms in each alkane molecule, expressed by means of the appropriate formulas given in Table 7.1. The net atomic charges qc and qc are both positive because n < 0. A decreasing ratio qc/q°c thus means that a carbon atom gains electronic charge with respect to that of ethane. Figure 7.1 indicates that the IPs of the alkanes are lowered as the joint electron population of the electron-richest pair of atoms increases. 

In equation (A.77) is defined the atomic orbital population P,-. Summing all of the P, that belong to the same atom, I, yields the atomic population / [equation (A.78)]. The net charge qj on atom I is just the difference between the nuclear charge Zi and the atomic population,... 

Fig. 12. Total net charges in uracil calculated by different methods (from top to bottom w-HMO + a-Del Re, w-SCF MO + a-Del Re, EHT, IEHT, CNDO/2, nonempirical). Data taken from Pullman and Pullman1 222-223 228 and from Stewart229 (nonempirical). Experimental229 net gross valence atomic populations for uracil are underlined [two sets of experimental numbers were obtained by the use of the L-shell standard STO s and L-shell SCF AO s scattering factors (in brackets), respectively]. The estimated standard deviations referring to the last decimal place are given in parentheses.

The MOs in the diatomic molecules discussed above have only two coefficients, so their chemical interpretation poses few problems. The situation becomes slightly more complicated when the molecule is polyatomic or when each atom uses more than one AO. Overlap population and net atomic charges can then be used to give a rough idea of the electronic distribution in the molecule. 

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... 

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