Gross 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... 

Extended Hiickel calculations are performed with a nonorthogonalized AO basis set therefore, the spin densities are to be evaluated by gross atomic populations and not simply by squares of expansion coefficients. 

Distribution of ir-Electron, o-Electron and Total Electron Density The 7r-charge and u-charge densities as well as total electron densities in uracils and thymines have been calculated abundantly. The charge distributions or gross atomic populations for uracils and thymines calculated by different methods can be found in the following papers ... 

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 ... 

Here, Q- is the partial overlap population, namely, the electron population of the overlap region between the atomic orbitals y,- and Xj >n the MO atomic orbitals y,- and y, in the MO , and S,(, the overlap integral between atomic orbitals y,- and y . QH is the gross atomic population or the gross atomic charge on atom H and is given by the sum of the atomic orbital populations Qi. The net charge AQh is obtained from the difference between QH and the atomic number ZH, namely, the number of electrons in the neutral atom. 

A population analysis (14) is performed, and a charge-density-overlap-population matrix is calculated. The latter is an n X w matrix whose diagonal elements are gross atomic populations (its trace is P). The off-diagonal elements are overlap populations. It is convenient to define a matrix, R, of dimensions NXN whose elements are... 

Table 2 Gross atomic populations and charges for thiophene...

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... 

According to molecular orbital calculations, the interaciion is mainly electrostatic in character. Only minor variations of the gross atomic population in the associate, as compared with the isolated molecule, are found Consistent with this view, the experimental stretching frequency of the CN bond of organic nitriles in the vapor phase (where supposedly the monomeric form predominates) and in liquid state (where 70—90% are associated) are very amilar, as shown in Table 2. If the small decrease of 15—20 cm is taken as an indication for dimer formation, it may be conduded that the degree of association is similar in the pure liquid and in CCI4 solution. 

A recent comparison (33.) of quantities calculated from molecular electronic wave functions for pyrrole and pyrazole indicated that ARCANA values compared more favorably with large-scale ab initio values than those calculated by other non-rigorous methods in the case of orbital energies of occupied molecular orbitals, gross atomic populations of heteroatoms, and total overlap populations including negative overlap populations between nonbonded atoms. 

If both the M0DP0T and VRDD0 approximations are introduced, the accuracy [ see footnote page Ul9] with respect to the reference calculations is about the same as that obtained using only the M0DP0T approximation. The maximum error in the orbital energies is 0.012 a.u., in the gross atomic populations is 0.009> in the total overlap populations is 0.027 and in the dipole moment is 0.009 a.u. 

To account for the actual electronic populations of the bonded atoms the INDO gross atomic populations, PB, rather than ZB are used. Hence equation (13) becomes,... 

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