Recent years have seen an increase in the number of people doing theoretical chemistry. Many of these newcomers are part time theoreticians, who work on other aspects of chemistry as well. This increase has been facilitated by the development of computer software which is increasingly easy to use. It is now easy enough to do computational chemistry that you do not have to know what you are doing to do a computation. As a result, many people don't understand even the most basic description of how the calculation is done and are therefore sucessufully doing a lot of work which is, frankly, garbage.

Many universities are now offering classes, which are an overview of various aspects of computational chemistry. Since we have had many people wanting to start doing computations before they have had even an introductory course, this document has been written as step one in understanding what computational chemistry is about. Note that this is not intended to teach the fundamentals of chemistry, quantum mechanics or mathematics, only most basic description of how chemical computations are done. The term theoretical chemistry may be defined as the mathematical description of chemistry. The term 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 in these definitions.

Very few aspects of chemistry can be computed exactly, but almost every aspect of chemistry has been described in a qualitative or approximate quantitative computational scheme. the biggest mistake that a computational chemists can make is to assume that any computed number is exact. However, just as not all spectra are perfectly resolved, often a qualitative or approximate computation can give useful insight into chemistry if you understand what it tells you and what it doesn't. Although most chemists avoid the true paper pencil type of theoretical chemistry, keep in mind that this is what many nobel prizes have been awarded for. This name is given to computations which are derived directly from theoretical principles, with no inclusion of experimental data.

Most of the time this is referring to an approximate quantum mechanical calculation. The approximations made are usually mathematical approximations, such as using a simpler functional form for a function or getting an approximate solution to a differential equation. The most common type of ab initio calculation is called a hartree fock calculation abbreviated hf , in which the primary approximation is called the central field approximation. This means that the coulombic electron electron repulsion is not specifically taken into account. This is a variational calculation, meaning that the approximate energies calculated are all equal to or greater than the exact energy. Because of the central field approximation, the energies from hf calculations are always greater than the exact energy and tend to a limiting value called the hartree fock limit. The second approximation in hf calculations is that the wave function must be described by some functional form, which is only known exactly for a few one electron systems.

The functions used most often are linear combinations of slater type orbitals exp ax or gaussian type orbitals exp ax^2 , abbreviated sto and gto. The wave function is formed from linear combinations of atomic orbitals or more often from linear combinations of basis functions. Because of this approximation, most hf calculations give a computed energy greater than the hartree fock limit. The exact set of basis functions used is often specified by an abbreviation, such as sto 3g or 6 311++g .

A number of types of calculations begin with a hf calculation then correct for the explicit electron electron repulsion, referred to as correlation. Some of these methods are mohlar plesset perturbation theory mpn, where n is the order of correction , the generalized valence bond gvb method, multi configurations self consistent field mcscf , configuration interaction ci and coupled cluster theory cc. A method, which avoids making the hf mistakes in the first place is called quantum monte carlo qmc. These methods work with an explicitly correlated wave function and evaluate integrals numerically using a monte carlo integration. These 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 wavefunction. In this type of calculation, there is an approximate hamiltonian and an approximate expression for the total electron density.

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The good side of ab initio methods is that they eventually converge to the exact solution, once all of the approximations are made sufficiently small in magnitude. These methods often take enormous amounts of computer cpu time, memory and disk space. Where n is the number of basis functions, so a calculation twice as big takes 16 times as long to complete.

In practice, extremely accurate solutions are only obtainable when the molecule contains half a dozen electrons or less. In general, ab initio calculations give very good qualitative results and can give increasingly accurate quantitative results as the molecules in question become smaller. Semiempirical calculations are set up with the same general structure as a hf calculation. Within this framework, certain pieces of information, such as two electron integrals, are approximated or completely omitted.

In order to correct for the errors introduced by omitting part of the calculation, the method is parameterized, by curve fitting in a few parameters or numbers, in order to give the best possible agreement with experimental data. The good side of semiempirical calculations is that they are much faster than the ab initio calculations. If the molecule being computed is similar to molecules in the data base used to parameterize the method, then the results may be very good. If the molecule being computed is significantly different from anything in the parameterization set, the answers may be very poor. Semiempirical calculations have been very successful in the description of organic chemistry, where there are only a few elements used extensively and the molecules are of moderate size.

However, semiempirical methods have been devised specifically for the description of inorganic chemistry as well. The electronic structure of an infinite crystal is defined by a band structure plot, which gives energies of electron orbitals for each point in k space, called the brillouin zone. Since ab initio and semiempirical calculations yield orbital energies, they can be applied to band structure calculations. However, if it is time consuming to calculate the energy for a molecule, it is even more time consuming to calculate energies for a list of points in the brillouin zone. Band structure calculations have been done for very complicated systems, however the software is not yet automated enough or sufficiently fast that anyone does band structures casually.

If you want to do band structure calculations, you had better expect to put a lot of time into your efforts. If a molecule is too big to effectively use a semiempirical treatment, it is still possible to model it's behavior by avoiding quantum mechanics totally. The methods referred to as molecular mechanics set up a simple algebraic expression for the total energy of a compound, with no necessity to compute a wave function or total electron density.

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