Ab initio calculations of hyperfine coupling constants.

This thesis is concerned with the calculation of spin density distributions in molecular species with an unpaired electron. The ab initio Unrestricted Hartree Pock method with single spin annihilation is used for this purpose and the construction of the wavefunction and methods by which the energy may be minimised and the hyperfine coupling constants evaluated are discussed. The atomic basis sets used are represented by combinations of Gaussian type orbitals; sufficiently large expansions are used to ensure that the wavefunction is of the accuracy required. A mixed basis approach, where smaller Gaussian expansions are used for the two electron multicentre integrals than for the other integrals, is also put forward as a reasonable approximation which results in a considerable reduction in computational times. The merits of the Roothaan, steepest descents and conjugate gradient methods, in minimising the energy, are analysed for the CN radical, leading to the conclusion that a combination of the Roothaan and conjugate gradient methods should be employed. In Chapter 2 the UHF method is used to calculate the isotropic hyperfine coupling constants of NH+3, CH3, BH-3 and the importance of optimisation and the out-of-plane zero point energy vibration is emphasised. The third chapter deals with the calculation of anisotropic coupling constants, demonstrating the value of the anisotropic coupling constants, and their directions, in supporting experimental assignments. A mixed basis approach is then applied to AIH-3, SiH3, PH+3 and associated radicals, using small expansions fitted by a least squares technique. The retention of accuracy in the calculated coupling constants combined with the considerable time saving suggests that the technique may prove very useful. The final chapter is concerned with large scale calculations on pyrazine systems using the mixed basis method.