ABSTRACT
This chapter deals with molecular orbital theory (MOT) and valence bond approach to the formation of diatomic molecules but first of all discusses and derives the Born–Oppenheìmer approximation in detail. After this, Schrödinger equation has been applied to the hydrogen molecule ion, which consists of two nuclei and one electron. Very important mathematical conclusions have been obtained for energy of the system with the help of secular equations and determinant. With the help of the mathematical equations, it can be written that whole of the binding energy of hydrogen ion is because of resonance energy k and the overlap integral ‘s’ has been neglected. In this chapter, we have also evaluated/computed the value of overlap integral and coulomb integral considering the confocal ellipsoidal coordinates. Mathematical expression for resonance integral or exchange integral has also been derived. We have also derived the value of Ψ and Ψ2 (probability of finding the electron at a place/region). This chapter also discusses the mathematical expression for hydrogen molecule for spin independent system. Linear combination of atomic orbitals has also been discussed for finding the molecular wave function. MOT and valence bond theory (VBT) have also been explained mathematically to have the clear insight into. It also includes configuration interaction, comparison of MOT and VBT, symmetric and antisymmetric wave functions, Pauli’s exclusion principle, antisymmetric wave function and Slater determinant, bonding and antibonding orbitals, and electron density in molecular hydrogen (mathematically for better understanding). This chapter has discussed the excited state of hydrogen molecules also giving the mathematical background. The electronic transition in hydrogen molecule has also been provided on mathematical basis. Homo polar diatomic molecules have also been discussed in detail. It deals with molecules having s and p valence atomic orbitals, electronic configuration of homonuclear diatomic molecules and heteropolar diatomic molecules. At the end of the chapter, references, solved problems, and questions on concepts have been given.
