The density matrix in self-consistent field theory II. Applications in the molecular orbital theory of conjugated systems

Abstract

The methods of a previous paper (McWeeny 1956) are applied in the theory of conjugated systems. The density matrix-which in this case is the array of 'charges' and 'bond orders'-may be calculated for a general $\pi $-electron system, in self-consistent field (s.c.f.) approximation, by iterative refinement of an initial estimate. In choosing an initial estimate it is possible to make use of known Huckel theory solutions for simple hydrocarbons, building up approximations for the more complicated systems by changing parameters (describing, for example, the insertion of hetero-atoms or the inter-connexion of different fragments). This may be done by a density matrix perturbation method which avoids all reference to the wave function itself (section 3). In this way, Huckel approximations for rather general systems can be written down with very little calculation (section 4), and at the same time, there are interesting chemical applications along the lines of Coulson & Longuet-Higgins (1947 a, b; 1948 a, b). Finally, self-consistency can be introduced (section 5) and the perturbation method can be carried over into the s.c.f. theory; this permits a rather more realistic discussion of chemical properties and explains the success, in certain cases, of the simple Huckel approach.