Molecular Geometry Predictions

This chapter is devoted to the determination of molecular geometries of stable molecules, transition states (TSs), and other meta-stable states by using the quantum chemical techniques of geometry optimization. Fundamental concepts of the methods of geometry optimization of equilibrium structures, search for TSs and conical intersections, and avoided crossings and basics of their theory and applications have been discussed in this chapter. The chapter starts with the introduction to potential energy surfaces and proceeds on to discuss the Hartree–Fock and density functional theory methods of determining their first and second derivatives called the gradients and the Hessian, respectively. Different methods of finding energy minima of stable structures that use energy, gradients and Hessian, individually or in combination, such as the method of conjugate gradient, quasi-Newton–Raphson method, etc., and large varieties of methods for Hessian updating such as MS, BFGS, GDIIS and trust radius method, etc., have been described. Quadratic synchronous transit (QSTn) methods such as the QST2 and QST3, etc., for the TSs and the Lagrange–Newton methods for the conical intersections have also been discussed. Practical aspects of optimization such as choice of coordinates, starting geometries and Hessians, quantum chemical method and basis sets, etc., and testing the character of the stationary point have been discussed. At the end of the chapter, a set of examples to illustrate the steps involved in the optimization of molecular geometries and TSs have been given.