Computational Chemistry starts by arguing that the uses of computers in chemistry are many and varied. This ranges from the modelling of solid state systems to the design of complex molecules which can be used as drugs. This text introduces the many methods currently used by practising computational chemists and shows the value of computers in modern chemical research. The text describes the various computational techniques available and explains how they can be applied to single molecules, to assemblies of molecules, and to molecules undergoing reaction. An introductory chapter outlines the hardware and software available, and looks at some applications and developments. Subsequent chapters cover quantum mechanics, molecular mechanics, statistical mechanics, the modelling of biomolecules, and drug design. Whilst emphasizing the use of computers to model biological systems, the chapters explain how the methods can be applied to a whole range of chemical problems.

### Chapter

## Quantum Chemistry

This chapter discusses quantum chemistry. Pretty much all of computational chemistry relies on quantum mechanics in the sense that molecular systems follow the laws of quantum mechanics. But ‘quantum chemistry‘ has a more specific meaning: it is the study of chemistry through the use of approximate solutions to the electronic Schrödinger equation. The chapter describes the background and principles of quantum chemistry, with a focus on the conceptually most important approximate approach, which is Hartree–Fock theory. In principle, the time-dependent Schrödinger equation could be used to predict what happens in chemical reactions. The basic approximation in Hartree–Fock theory is an assumption that electrons move independently of one another throughout the molecular system. The chapter then looks at the calculation of a Hartree–Fock wavefunction.

### Chapter

## Molecular Mechanics Methods

This chapter evaluates molecular mechanics methods. In this approach, a known chemical bonding pattern is assumed and used to define preferred bond lengths and angles, and thereby an energy expression that takes into account distortions away from these ideal values. For a given bonding environment, the type of energy terms needed, and the numerical parameters within the energy expression, are transferable from one system to another. Hence, general forcefields can be constructed with quite general applicability. The chapter describes how the energy terms and parameters are chosen, based on input from experiment and quantum chemistry. Molecular mechanics can be applied to large systems due to its efficiency, allowing calculations on liquids, solutions, and solids. This frequently makes use of periodically repeating models and the chapter looks at special measures needed to treat such models. Finally, it discusses the type of software used for molecular mechanics.

### Chapter

## Hybrid and Multi-Scale Methods

This chapter addresses hybrid and multi-scale methods. Chemistry of a ‘core’ system is frequently perturbed by the ‘environment’. If the perturbation is weak, as is often the case, it is acceptable to perform calculations on the core part only. The effects of the environment can in many cases be described using continuum models, which can conveniently be coupled to quantum chemical calculations. It is also possible to devise hybrid methods, in which the atoms making up the core and the environment in the model are treated at different levels of theory. One very popular family of hybrid methods treats the core quantum mechanically (QM) and the environment with molecular mechanics (MM), and these methods are referred to as QM/MM methods.

### Chapter

## Quantum mechanics

This chapter discusses quantum mechanics. Quantum mechanics provides molecular wave functions in the form of coefficients which multiply known basis functions. The wave functions which satisfy the Schrödinger equation for the hydrogen atom are sometimes called orbitals. A hydrogenic atomic orbital is thus merely a three-dimensional mathematical function from which we can calculate the energy or other properties of the single electron system. Most applications involve computing the energy of a molecule for a given arrangement of atomic nuclei. The calculations of energy properties are now of comparable accuracy to experimental determinations. This is certainly true for geometries and static properties, but reactivities are more of a problem. The chapter looks at spin-orbitals, molecular orbitals, matrix elements, and correlation energy.