In this module, we will be dealing with the techniques used in solving the non-relativistic Schrödinger equation for estimating molecular energy levels and wavefunctions.

In the initial lectures, the basic formulae relevant to the Hartree-Fock method and the extensions beyond the Hartree-Fork (HF) method are outlined. The form of the molecular hamiltonian, Slater type orbitals (STOs) and the linear combinations of Gaussians (GTOs) to represent the STOs are outlined. The formulae for overlap, electron kinetic energy, nuclear attraction energy and electron repulsion integrals are given. The extensions of HF methods to include electron correlation, the many body perturbation methods and the coupled cluster methods are considered next. The methods using density functional theory have become very popular of late and are considered in a separate chapter. The public domain softwares to do the ab initio and semi empirical calculations (such as the Huckel, extended Huckel, CNDO, etc) are considered next. There are different convenient methods for providing inputs to these programs. This is the minimum ability that one has to master to get useful results for molecules of one’s interest. Computation of single point energies and the energy for an “optimized” or the “best” molecular geometry is considered next. With the voluminous results that one gets using these programs, the analysis can be quite involved.

Several public domain softwares are available to show the results pictorially. The main objects of interest are the energy levels and wave functions. Contours of wave functions, electron densities and electrostatic potentials can be plotted. Net charges on atoms and surfaces containing or enclosing a given amount of charge can be calculated from the electronic charge densities.  By calculating the molecular energies at a few points in the neighbourhood of the equilibrium molecular geometry, the local potential energy surface (PES) can be estimated. Using this PES, an estimate of vibrational frequencies of the molecule can be made. Using models for molecular shapes and the three moments of inertia of the molecule, the rotational energy levels can also be estimated. Using all the data on molecular energy levels, molecular partition functions and the gas phase thermodynamic functions can be calculated at the ambient temperature. By exploring the PES in the region where the molecule is likely to fragment, the structure of transition states for dissociation (and analogously for association) can be studied. By placing the molecule in suitable cavities (dielectric medium) calculations can be made for taking into account the effect of the medium. The energy levels, wave function and molecular moments change due to the effect of solvation and the estimates of solvent effects are possible.