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# Wave function calculations on small molecules

### Abstract

The ab initio calculation of wave functions for small polyatomic molecules is now feasible but is time-consuming, expensive and limited in accuracy. The most frequently used approach is that of molecular orbital (MO) theory, using the self-consistent field (SCF) method with a linear combination of atomic orbitals (LCAO) approximation to the HO's. On the other hand, semiempirical methods have been widely used and have yielded extremely interesting results in spite of the fact that they have often been based on flimsy theoretical foundations. The first and best known calculations of this type were of course initiated by Huckel and refer to the n-electrons of conjugated molecules. Later semiempirical SCF LCAO MO calculations, in which electron interaction effects are more properly taken into account, were done on n-electron systems. Then the Huckel type LCAO MO method, and later the approximate SCF HO scheme, were applied to more general systems. In this work a new semi-empirical SCF scheme is presented in which an attempt is made to produce a method as close to ab initio procedures as possible. A particular basis of orthogonalised orbitals is chosen to render valid, with a reasonable degree of accuracy, the integral approximations made. The use of a particular set of integral approximations allows the simulation of the results of non-empirical calculations. The semi-empirical calculations described in this work are less empirical than any previously performed on more general systems; this allows the scheme to be built on a sounder basis than other semi-empirical schemes which include all electrons. Results are presented to show that with a relatively simple method of estimating the larger two-electron integrals, over an orthogonal basis, reasonable results can be obtained for small polyatomic molecules. As well as giving good results the method is used as a basis for examining the foundations of more empirical calculations. Two approaches are used to obtain wave functions, the SCF MO LCAO and the self-consistent group function (SCGF) method. It is found that SCGF method has several advantages over the ordinary SCF HO LCAO method in the performance of semi-empirical calculations.