Wave function analysis electrostatic potential

The electrostatic potential F(r,) at a given point i created in the neighboring space by the nuclear charges and the electronic distribution of a molecule can be calculated from the molecular wave function (strictly speaking from the corresponding first-order density function). As this quantity is directly obtainable from the wave function, it does not suffer from the drawbacks inherent in the classical population analysis. 

Several schemes for the analysis of the wave function have been proposed. The most commonly used are those proposed by Mulliken and Lbwdin, those based on natural bond orbital theory (NBO), the Bader AIM theory, and the fitting of the electrostatic potential. 

In the same spirit, we report here an attempt to utilize for the study of molecular interactions the analysis of the electrostatic potential (produced in the surrounding space) which can be calculated from the wave function of the isolated molecule. The electrostatic molecular potential is generally a rather complex function of the point, and for this reason much of the material is presented in graphic form, as this permits a quick and easy visualization of the outstanding features, although some emphasis is also given to analytic representations of the electrostatic potential as well as to their convergence properties. 

Recently Pack, Wang and Rein51) published a convergence analysis of analytical expansions of the electrostatic potential on parallel lines to the present one. These authors compare with the exact expansion the one-center one and a segmental atomic expansion (centered at the nuclei). Convergence is tested on pyridine (semiempirical iterative extended Hiickel wave function) along the symmetry axis with expansion truncated after the octopole term. Their results are comparable to those reported here in particualr, the segmental expansion appears quite reasonable)). 

For the calculation of the electrostatic term the system under study is characterized by two dielectric constants, in the interior of the cavity the constant will have a value of unity, and in the exterior the value of the dielectric constant of the solvent. From this point the total electrostatic potential is evaluated. Beyond the mere classical outlining of the problem, Quantum Mechanics allows us to examine more deeply the analysis of the solute inserted in the field of reaction of the solvent, making the relevant modifications in the quantum mechanical equations of the system under study with a view to introducing a term due to the solvent reaction field. This permits a widening of the benefits which the use of the continuum methods grant to other facilities provided for a quantical treatment of the system, such as the optimization of the solute geometry the analysis of its wave function, the obtaining of its harmonic frequencies, " etc. all of which in the presence of the solvent. In this way a full analysis of the interaction solute-solvent can be reached at low computational cost. 

Population analysis in semiempirical methods fall into two categories. Methods including overlap in the Fock equations use the Mulliken population analysis. The majority of semiempirical methods uses the ZDO approximation, and the net charges are interpreted on the basis of symmetrically orthog-onalized AOs. It is pointed out that this interpretation is not exactly valid, because of truncation and empirical adjustment. But the corresponding nonsymmetrical orthogonalization is not uniquely defined. Charge models based on semiempirical wave functions play an important role in the calculation of molecular electrostatic potentials for reactivity. 

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