ABSTRACT
It is to be noted that we have derived the matrix form of Roothaan’s equation and also Roothaan’s method for quantum mechanical computation in one dimension in this chapter. We have also dealt with shapes of molecules for which hybridisation has been incorporated. Fock matrix element has also been provided. The chapter also provides the electronic energy, solution of Roothaan’s equation for helium atom with mathematical clarity. It also consists of derivation of sp 3, sp 2, and sp hybridisation in detail and shapes of the molecules with regard to different hybridisation. It beautifully explains the hybridisation in H2O. This chapter deals with ab initio calculations and semi-empirical methods of computation. This chapter also provides the mathematical idea of valence electrons, zero differential overlap, π-electron evaluation, invariance under transformation, complete neglect of differential overlap parametrisation, intermediate neglect of differential overlap, and also the mathematical form of neglect of diatomic differential overlap. The Pariser–Parr–Pople (PPP) method has been provided to supply the satisfactory description of conjugated systems in the excited states. The method includes electron correlation, electron repulsion, and employs wave functions describing pure spin states. The mathematical formulation of the PPP method has been given in clear and lucid way. The end of this chapter describes the references, brain teasing problems, and questions on concepts.
