Introduction to Computational Chemistry

Frank Jensen

• Publisher: Wiley
• Year: 2016
• ISBN:
  9781118825952
• Edition: 3
• Topic: Naturwissenschaften
• Subtopic: Physikalische & theoretische Chemie

Introduction to Computational Chemistry 3rd Edition provides a comprehensive account of the fundamental principles underlying different computational methods. Fully revised and updated throughout to reflect important method developments and improvements since publication of the previous edition, this timely update includes the following significant revisions and new topics:

• Polarizable force fields
• Tight-binding DFT
• More extensive DFT functionals, excited states and time dependent molecular properties
• Accelerated Molecular Dynamics methods
• Tensor decomposition methods
• Cluster analysis
• Reduced scaling and reduced prefactor methods

Additional information is available at: www.wiley.com/go/jensen/computationalchemistry3

1
Introduction

Chemistry is the science dealing with construction, transformation and properties of molecules. Theoretical chemistry is the subfield where mathematical methods are combined with fundamental laws of physics to study processes of chemical relevance.^1–7

Molecules are traditionally considered as “composed” of atoms or, in a more general sense, as a collection of charged particles, positive nuclei and negative electrons. The only important physical force for chemical phenomena is the Coulomb interaction between these charged particles. Molecules differ because they contain different nuclei and numbers of electrons, or because the nuclear centers are at different geometrical positions. The latter may be “chemically different” molecules such as ethanol and dimethyl ether or different “conformations” of, for example, butane.

Given a set of nuclei and electrons, theoretical chemistry can attempt to calculate things such as:

• Which geometrical arrangements of the nuclei correspond to stable molecules?
• What are their relative energies?
• What are their properties (dipole moment, polarizability, NMR coupling constants, etc.)?
• What is the rate at which one stable molecule can transform into another?
• What is the time dependence of molecular structures and properties?
• How do different molecules interact?

The only systems that can be solved exactly are those composed of only one or two particles, where the latter can be separated into two pseudo one-particle problems by introducing a “center of mass” coordinate system. Numerical solutions to a given accuracy (which may be so high that the solutions are essentially “exact”) can be generated for many-body systems, by performing a very large number of mathematical operations. Prior to the advent of electronic computers (i.e. before 1950), the number of systems that could be treated with a high accuracy was thus very limited. During the 1960s and 1970s, electronic computers evolved from a few very expensive, difficult to use, machines to become generally available for researchers all over the world. The performance for a given price has been steadily increasing since and the use of computers is now widespread in many branches of science. This has spawned a new field in chemistry, computational chemistry, where the computer is used as an “experimental” tool, much like, for example, an NMR (nuclear magnetic resonance) spectrometer.

Computational chemistry is focused on obtaining results relevant to chemical problems, not directly at developing new theoretical methods. There is of course a strong interplay between traditional theoretical chemistry and computational chemistry. Developing new theoretical models may enable new problems to be studied, and results from calculations may reveal limitations and suggest improvements in the underlying theory. Depending on the accuracy wanted, and the nature of the system at hand, one can today obtain useful information for systems containing up to several thousand particles. One of the main problems in computational chemistry is selecting a suitable level of theory for a given problem and to be able to evaluate the quality of the obtained results. The present book will try to put the variety of modern computational methods into perspective, hopefully giving the reader a chance of estimating which types of problems can benefit from calculations.

1.1 Fundamental Issues

Before embarking on a detailed description of the theoretical methods in computational chemistry, it may be useful to take a wider look at the background for the theoretical models and how they relate to methods in other parts of science, such as physics and astronomy.

A very large fraction of the computational resources in chemistry and physics is used in solving the so-called many-body problem. The essence of the problem is that two-particle systems can in many cases be solved exactly by mathematical methods, producing solutions in terms of analytical functions. Systems composed of more than two particles cannot be solved by analytical methods. Computational methods can, however, pro...