Charge densities Mulliken definition

The method of electronegativity equalization is used to fix the charges, with Mulliken definition of electronegativity. This is related by Parr [175] to the chemical potential of an electron gas, using Kohn-Sham approximation in the framework of density functional theory. Hence, electronegativity equalization corresponds to equating chemical potentials. 

Thus this model maps density over atoms rather than spatial coordinates. If overlap is included some other definition of charge density such as Mulliken s17 may be employed. Eq. (30) and (31) are then used with this wave function to calculate the hyperfine constants as a function of the pn s. If symmetry is high enough, there will be enough hyperfine constants to determine all the p s, otherwise additional approximations may be necessary. For transition metal complexes, where spin-orbit effects are appreciable, it is necessary to include admixtures of excited-state configurations that are mixed with the ground state by the spin-orbit operator. To determine the extent of admixture, we must know the value of the spin-orbit constant X and the energy of the excited states. 

Momany s idea has led to a new definition of atomic charges. It would be possible to write volumes about atomic charges (AC), a concept that has no a precise definition in QM formalism, but is of extreme utility in practical applications. Many definitions of AC are based on manipulations of the molecular wave function, as, for example, the famous Mulliken charges. Other definitions are based on different analyses of the QM definition of the charge density, as for example Bader s charges.There are also charges derived from other theoretical approaches, such as the electronegativity equalization, or from experimental values, such as from the vibrational polar tensors. 

The 7/ / terms are the Coulomb functions introduced in eq.(104), P are the relaxed (i.e. polarized by the solvent in a self-consistent manner) elements of the density matrix P = CnC, and F are the elements of the in vacuo Fock matrix, in the form used in the semiempirical approach, but referred to the relaxed P matrix. The charges qk are drawn from P, according to the Mulliken s rules, or according to a new definition given by... 

It is arbitrary how the electron density arising from basis functions located on different atoms is divided. The Mulliken procedure can give unphysical charges and shows a strong basis set dependence. Because of these shortcomings an atom definition which does not depend on the basis set is desirable. 

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