Computational chemistry

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A molecular mechanics potential energy function, and it is used by programs like Folding@Home to simulate how molecules move and behave.

Computational chemistry is a branch of chemistry that uses computer science to help solve chemical problems. These programs calculate the structures and properties of molecules and solids. Computational chemistry normally complements the information obtained by chemical experiments. It can predict chemical phenomena that have not yet been observed. It is widely used in the design of new drugs and materials.

Computational chemistry can predict structure (that is, the expected positions of the molecule's atoms), absolute and relative (interaction) energies, electronic charge distributions, dipoles and higher multipole moments, vibrational frequencies, reactivity or other spectroscopic quantities, and cross sections for collision with other particles.

Computational chemistry looks at both static and dynamic systems. In all cases, as the size of the system being studied grows, the computer time and other resources (such as memory and disk space) used also grows. That system can be a single molecule, a group of molecules, or a solid. Computational chemistry methods range from highly accurate to very approximate. Highly accurate methods are typically feasible only for small systems.

Both ab initio and semi-empirical approaches use approximations. These range from simplified forms of the first-principles equations that are easier or faster to solve, to approximations limiting the size of the system (for example, periodic boundary conditions), to fundamental approximations to the underlying equations that are required to achieve any solution to them at all. For example, most ab initio calculations make the Born–Oppenheimer approximation, which greatly simplifies the underlying Schrödinger equation by freezing the nuclei in place during the calculation. In principle, ab initio methods eventually converge to the exact solution of the underlying equations as the number of approximations is reduced. In practice, however, it is impossible to eliminate all approximations, and residual error inevitably remains. The goal of computational chemistry is to minimize this residual error while keeping the calculations to a size that a computer can perform.

History[change | edit source]

In 1927, Walter Heitler and Fritz London made the first theoretical chemistry calculations. They built on the founding discoveries and theories in the history of quantum mechanics. Influential books in the early development of computational quantum chemistry include Linus Pauling and E. Bright Wilson's 1935 Introduction to Quantum Mechanics – with Applications to Chemistry, Eyring, Walter and Kimball's 1944 Quantum Chemistry, Heitler's 1945 Elementary Wave Mechanics – with Applications to Quantum Chemistry, and later Coulson's 1952 textbook Valence, each of which served as primary references for chemists in the decades to follow.

The development of efficient computer technology in the 1940s made calculating elaborate wave equations for complex atomic systems possible. In the early 1950s, the first semi-empirical atomic orbital calculations were carried out. Theoretical chemists used the early digital computers a lot. Smith and Sutcliffe wrote a very detailed account of such use in the United Kingdom.[1] The first ab initio Hartree–Fock calculations on molecules with two atoms (diatomic) were carried out in 1956 at MIT, using a basis set of Slater orbitals. For molecules with two atoms, a systematic study using a minimum basis set and the first calculation with a larger basis set were published by Ransil and Nesbet respectively in 1960.[2] The first polyatomic calculations using Gaussian orbitals were carried out in the late 1950s. The first configuration interaction calculations were carried out in Cambridge on the EDSAC computer in the 1950s using Gaussian orbitals by Boys and coworkers.[3] By 1971, when a bibliography of ab initio calculations was published,[4] the largest molecules included were naphthalene and azulene.[5][6] Abstracts of many earlier developments in ab initio theory have been published by Schaefer.[7]

In 1964, Hückel method calculations (using a simple linear combination of atomic orbitals (LCAO) method for the determination of electron energies of molecular orbitals of π electrons in conjugated hydrocarbon systems) were generated on computers at Berkeley and Oxford. They worked on molecules ranging in complexity from butadiene and benzene to ovalene.[8] These empirical methods were replaced in the 1960s by semi-empirical methods such as CNDO.[9]

In the early 1970s, efficient ab initio computer programs such as ATMOL, GAUSSIAN, IBMOL, and POLYAYTOM, began to be used to speed up ab initio calculations of molecular orbitals. Of these four programs, only GAUSSIAN, now massively expanded, is still in use. But many other programs are now in use. At the same time, the methods of molecular mechanics, such as MM2, were developed, primarily by Norman Allinger.[10]

One of the first mentions of the term "computational chemistry" can be found in the 1970 book Computers and Their Role in the Physical Sciences by Sidney Fernbach and Abraham Haskell Taub, where they state "It seems, therefore, that 'computational chemistry' can finally be more and more of a reality."[11] During the 1970s, computational chemistry adopted many different methods.[12] The Journal of Computational Chemistry was first published in 1980.

Different from theoretical chemistry[change | edit source]

Chemists define theoretical chemistry as a mathematical description of chemistry. Computational chemistry uses mathematical methods that are well developed. These methods are automated as computer programs. In theoretical chemistry, chemists, physicists and mathematicians 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 answer specific chemical questions.

Definition of computational chemistry[change | edit source]

There are two different aspects to computational chemistry:

  • Computational studies can be carried out to find a starting point for a laboratory synthesis, or to assist in understanding experimental data, such as the position and source of spectroscopic peaks.
  • Computational studies can be used to predict the possibility of molecules not yet discovered or to explore reaction mechanisms that are difficult to study in chemical experiments.

So, computational chemistry can assist experimental chemists. It also can challenge experimental chemists to find entirely new chemical objects.

Computational chemistry has five major parts:

  • The prediction molecules' structure by the use of the simulation of forces, or more accurate quantum chemical methods, to find stationary points on the energy surface as the positions of the nuclei are varied.
  • Storing and searching for data on chemical entities (see chemical databases).
  • Identifying correlations between chemical structures and properties (see QSPR and QSAR).
  • Computational approaches to help in the efficient synthesis of compounds.
  • Computational approaches to design molecules that interact in specific ways with other molecules (for example, drug design and catalysis).

Methods[change | edit source]

A single molecular formula can represent a number of molecular isomers. Each isomer is a local minimum on the energy surface (called the potential energy surface) created from the total energy (that is, the electronic energy, plus the repulsion energy between the nuclei) as a function of the positions of all the nuclei. A stationary point is a geometry where the derivative of the energy with respect to all displacements of the nuclei is zero.[note 1] The local minimum that is lowest is called the "global minimum" and corresponds to the most stable isomer. If there is one particular coordinate change that leads to a decrease in the total energy in both directions, the stationary point is a transition structure and the coordinate is the reaction coordinate. This process of determining stationary points is called "geometry optimization".

As computers grew more powerful, mathematicians discovered efficient ways to calculate the first derivatives of the energy with respect to all atomic coordinates. The allowed chemists to determine molecular structure by geometry optimization. Evaluation of the related second derivatives allows the prediction of vibrational frequencies by estimating harmonic motion. Second derivatives also identify stationary points in molecular vibration. The frequencies are related to the eigenvalues of the Hessian matrix, which contains second derivatives. If the eigenvalues are all positive, then the frequencies are all real and the stationary point is a local minimum. If one eigenvalue is negative (i.e., an imaginary frequency), then the stationary point is a transition structure. If more than one eigenvalue is negative, then the stationary point is a more complex one, and is usually of little interest. However, most experimental chemists are looking solely for local minima and transition structures.

Approximate solutions of the time-dependent Schrödinger equation give the total energy of the system, usually with no relativistic terms included. The Born–Oppenheimer approximation, which allows for the separation of electronic and nuclear motions, can simplify the Schrödinger equation. With this simplification, the total energy is a sum of the electronic energy at fixed nuclei positions and the repulsion energy of the nuclei.[note 2] For very large systems, the relative total energies can be compared using molecular mechanics.

Other pages[change | edit source]

Notes[change | edit source]

  1. A local (energy) minimum is a stationary point where all such displacements lead to an increase in energy.
  2. A notable exception are certain approaches called direct quantum chemistry, which treat electrons and nuclei on a common footing. Density functional methods and semi-empirical methods are variants of this.

References[change | edit source]

  1. Smith, S. J.; Sutcliffe B. T., (1997). "The development of Computational Chemistry in the United Kingdom". Reviews in Computational Chemistry 70: 271–316.
  2. Schaefer, Henry F. III (1972). The electronic structure of atoms and molecules. Reading, Massachusetss: Addison-Wesley Publishing Co.. pp. 146.
  3. Boys, S. F.; Cook G. B., Reeves C. M., Shavitt, I. (1956). "Automatic fundamental calculations of molecular structure". Nature 178 (2): 1207. doi:10.1038/1781207a0.
  4. Richards, W. G.; Walker T. E. H and Hinkley R. K. (1971). A bibliography of ab initio molecular wave functions. Oxford: Clarendon Press.
  5. Preuss, H. (1968). International Journal of Quantum Chemistry 2: 651.
  6. Buenker, R. J.; Peyerimhoff S. D. (1969). Chemical Physics Letters 3: 37.
  7. Schaefer, Henry F. III (1984). Quantum Chemistry. Oxford: Clarendon Press.
  8. Streitwieser, A.; Brauman J. I. and Coulson C. A. (1965). Supplementary Tables of Molecular Orbital Calculations. Oxford: Pergamon Press.
  9. Pople, John A.; David L. Beveridge (1970). Approximate Molecular Orbital Theory. New York: McGraw Hill.
  10. Allinger, Norman (1977). "Conformational analysis. 130. MM2. A hydrocarbon force field utilizing V1 and V2 torsional terms". Journal of the American Chemical Society 99 (25): 8127–8134. doi:10.1021/ja00467a001.
  11. Fernbach, Sidney; Taub, Abraham Haskell (1970). Computers and Their Role in the Physical Sciences. Routledge. ISBN 0677140304.
  12. Reviews in Computational Chemistry vol 1, preface

Other websites[change | edit source]