Computational chemistry

Computational chemistry is a branch of theoretical chemistry whose major goals are to create efficient mathematical approximations and computer programs that calculate the properties of molecules (such as total energy, dipole moment, vibrational frequencies) and to apply these programs to concrete chemical objects. The term is also sometimes used to cover the areas of overlap between computer science and chemistry.

Contents

1 Introduction

2 Ab initio methods

3 Semiempirical methods

3.1 Molecular mechanics and dynamics

4 Solid state methods

Introduction

The term theoretical chemistry may be defined as a mathematical description of chemistry, whereas computational chemistry is usually used when a mathematical method is sufficiently well developed that it can be automated for implementation on a computer. Note that the words exact and perfect do not appear here, as very few aspects of chemistry can be computed exactly. Almost every aspect of chemistry, however, can be and has been described in a qualitative or approximate quantitative computational scheme.

It is, in principle, possible to use one very accurate method and apply it to all molecules. Although such methods are well-known and available in many programs, the computational cost of their use grows factorially (even faster than exponentially) with the number of electrons. Therefore, a great number of approximate methods strive to achieve the best trade-off between accuracy and computational cost. Present computational chemistry can routinely and very accurately calculate the properties of molecules that contain no more than 10-20 electrons. The treatment of molecules that contain a few dozen electrons is computationally tractable by approximate methods such as DFT. There is some dispute within the field whether the latter methods are sufficient to describe complex chemical reactions, such as those in biochemistry.

In theoretical chemistry, chemists and physicists together develop algorithms and computer programs to predict atomic and molecular properties and reaction paths for chemical reactions. Computational chemists, in contrast, may simply apply existing computer programs and methodologies to specific chemical questions. There are two different approaches in doing this:

Computational studies can be carried out in order to find a starting point for a laboratory synthesis
Computational studies can be used to explore reaction mechanisms and explain observations of laboratory reactions

Several major areas may be distinguished within computational chemistry:

The computational representation of atoms and molecules
Storing and searching for data on chemical entities (see chemical databases)
Identifying correlations between chemical structures and properties (see QSPR and QSAR)
Theoretical elucidation of structures based on the simulation of forces
Computational approaches to help in the efficient synthesis of compounds
Computational approaches to design molecules that interact in specific ways with other molecules (e.g. drug design)

Ab initio methods

The programs used in computational chemistry are based on many different quantum-chemical methods that solve the molecular Schrödinger equation. Methods that do not include empirical or semi-empirical parameters in their equations - are derived directly from theoretical principles, with no inclusion of experimental data - are generally called ab initio methods. Most of the time this is referring to approximate quantum mechanical calculations. The approximations made in these cases, however, are usually mathematical in nature, such as using a simpler functional form or getting an approximate solution for a complicated differential equation.

The most common type of ab initio calculation is called a Hartree-Fock (HF) calculation, in which the Coulombic electron-electron repulsion is not specifically taken into account. Only its net effect is included in the calculation. This is a variational calculation, therefore the obtained approximate energies, expressed in terms of the system's wave function, are always equal to or greater than the exact energy, and tend to a limiting value called the Hartree-Fock limit. Many types of calculations begin with a HF calculation and subsequnetly correct for electron-electron repulsion, referred to also as correlation. Møller-Plesset perturbation theory (MP) and Coupled cluster (CC) are examples of such methods.

A method that avoids making the varaitional overestimation of HF in the first place is Quantum Monte Carlo (QMC), in its variational, diffusion, and Green's functions flavors. These methods work with an explicitly correlated wave function and evaluate integrals numerically using a Monte Carlo integration. Such calculations can be very time consuming, but they are probably the most accurate methods known today.

An alternative ab initio method is Density Functional Theory (DFT), in which the total energy is expressed in terms of the total electron density, rather than the wave function. In this type of calculation, there is an approximate hamiltonian and an approximate expression for the total electron density.

Ab initio methods have the advantage that they can be made to converge to the exact solution, when all approximations are sufficiently small in magnitude. The convergence, however, is not montonic, and sometimes the smallest calculation gives the best result for some properties. The bad side of ab initio methods is their cost. They often take enormous amounts of computer time, memory, and disk space. The HF method scales as N⁴ (N is the number of basis functions) – a calculation twice as big takes 16 times as long to complete – and correlated calculations often scale much faster.

The most popular classes of ab initio methods:

Semiempirical methods

Within the framework of Hartree-Fock calculations, some pieces of information (such as two-elecron integrals) are sometimes approximated or completely omitted. In order to correct for this loss, semiempirical methods are parametrized, that is their results are fit by a set of parameters in such a way, as to produce results the best agree with experimental data.

Semiempirical calcualtions are much faster than their ab initio counterparts. Their results, however, can be very wrong if the molecule being computed is not similar enough to the molecules in the database used to parametrize the method.

Semiempirical calculations have been very successful in the description of organic chemistry, where only a few elements are used extensively and molecules are of moderate size.

Molecular mechanics and dynamics

In many cases, large molecular systems can be modelled succesfully avoiding quantum mechanical calculations entirely. Molecular mechanics simulations, for example, use a single classical expression for the energy of a compound, for instance the harmonic oscillator. All constants appearing in the equations must be obtained beforehand from experimental data or ab initio calculations.

The database of compounds used for parameterization - (the resulting set of parameters and functions is called the force field) - is crucial to the success of molecular mechanics calculations. A force field parameterized against a specific class of molecules, for instance proteins, would be expected to only have any relevance when describing other proteins.

Molecular dynamics examines the time-dependent behavior of systems, including vibrations or Brownian motion, most often wth a classical mechanical description as well.

Solid state methods

The electronic structure of a crystal is in general described by a band structure, which defines the energies of electron orbitals for each point in the Brillouin zone. Ab initio and semiempirical calculations yield orbital energies, therefore they can be applied to band structure calculations. Since it is time consuming to calculate the energy for a molecule, it is even more time consuming to calculate them for the entire list of points in the Brillouin zone

Software packages

A number of software packages that are self-sufficient and include many quantum-chemical methods are available. Among the most widely used are:

References

Daid Young's Introduction to Computational Chemistry (http://www.ccl.net/cca/documents/dyoung/topics-orig/compchem.html)
F. Jensen Introduction to Computational Chemistry, John Wiley & Sons (1999)
T. Clark A Handbook of Computational Chemistry, Wiley, New York (1985)