The calculation of electronic charges in molecules using a simplified semi-empirical 'atoms in molecules' method

• Main Author: Evans, Donald Andrew
• Published: University of Warwick 1974
• Subjects: 500; QD Chemistry
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.595036

This thesis describes an approach to the problem of computing electronic charge distributions in molecules. The molecule is treated as a collection of atoms in assumed valence states. Sigma and pi electrons are separated from each other. The sigma electron distribution is computed using a valence state scheme the essence of which is a system of orbital charge equations, a unique equation for each type of bond. The form of orbital charge equation for a bond X - Y described by an M.O. Ψ = ciϕi + cjϕj where ϕi and ϕj are the bonding A.O.'s (usually hybrid) on X and Y respectively is N(XY) = kYXNyT - KXYNXT + IXY where N(XY) is the charge in orbital ϕi in the bond X-Y. kYX, kXY, IXY are all parameters and NXT, NYT are the total charges on X and Y excluding the charges in ϕi and ϕj. The interaction of the sigma electrons with the pi electrons is described in two ways. In the first method the interaction occurs through charge dependent inductive parameters hX in the expression αX = αC + kXβCC The sigma electron calculation is linked to a H.M.O. calculation to form an iterative method, the iterative self-consistent charge method - I.S.C.C.M. In the second approach a P.P.P. (σ + π) method is developed in which the sigma distribution provides a potential framework for the pi electrons. The Wμ terms in the diagonal matrix elements of the P.P.P. method are interpreted as valence state ionisation potentials (V.S.I.P.'s) of the pi orbitals and are expressed as functions of the charge distribution, sigma and pi. The advantages and disadvantages of the two approaches are discussed and the charges obtained using both methods are compared with other results in the literature.