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Description Table of Contents Product Details Click on the cover image above to read some pages of this book! Water A Comprehensive Guide for Brewers. In Stock. In the early s, the first semi-empirical atomic orbital calculations were performed. Theoretical chemists became extensive users of the early digital computers. A very detailed account of such use in the United Kingdom is given by Smith and Sutcliffe. For diatomic molecules, 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 The first configuration interaction calculations were performed in Cambridge on the EDSAC computer in the s using Gaussian orbitals by Boys and coworkers.
Of these four programs, only Gaussian, now vastly 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 force field , were developed, primarily by Norman Allinger. One of the first mentions of the term computational chemistry can be found in the 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.
Computational chemistry has featured in several Nobel Prize awards, most notably in and Walter Kohn , "for his development of the density-functional theory", and John Pople , "for his development of computational methods in quantum chemistry", received the Nobel Prize in Chemistry.
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. 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 specific chemical questions. Thus, computational chemistry can assist the experimental chemist or it can challenge the experimental chemist to find entirely new chemical objects. The words exact and perfect do not apply here, as very few aspects of chemistry can be computed exactly. However, almost every aspect of chemistry can be described in a qualitative or approximate quantitative computational scheme.
Molecules consist of nuclei and electrons, so the methods of quantum mechanics apply. Therefore, a great number of approximate methods strive to achieve the best trade-off between accuracy and computational cost. Accuracy can always be improved with greater computational cost. Significant errors can present themselves in ab initio models comprising many electrons, due to the computational cost of full relativistic-inclusive methods.
This complicates the study of molecules interacting with high atomic mass unit atoms, such as transitional metals and their catalytic properties. For geometries, bond lengths can be predicted within a few picometres and bond angles within 0. The treatment of larger molecules that contain a few dozen atoms is computationally tractable by more approximate methods such as density functional theory DFT. There is some dispute within the field whether or not the latter methods are sufficient to describe complex chemical reactions, such as those in biochemistry.
Large molecules can be studied by semi-empirical approximate methods. Even larger molecules are treated by classical mechanics methods that use what are called molecular mechanics MM. One molecular formula can represent more than one molecular isomer: a set of isomers. Each isomer is a local minimum on the energy surface called the potential energy surface created from the total energy i. A stationary point is a geometry such that the derivative of the energy with respect to all displacements of the nuclei is zero. A local energy minimum is a stationary point where all such displacements lead to an increase in energy.
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.
The determination of molecular structure by geometry optimization became routine only after efficient methods for calculating the first derivatives of the energy with respect to all atomic coordinates became available. Evaluation of the related second derivatives allows the prediction of vibrational frequencies if harmonic motion is estimated. More importantly, it allows for the characterization of stationary points. 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. If more than one eigenvalue is negative, then the stationary point is a more complex one, and is usually of little interest.
When one of these is found, it is necessary to move the search away from it if the experimenter is looking solely for local minima and transition structures. This leads to the evaluation of the total energy as a sum of the electronic energy at fixed nuclei positions and the repulsion energy of the nuclei.
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 on the major theme. For very large systems, the relative total energies can be compared using molecular mechanics. The ways of determining the total energy to predict molecular structures are:.
This does not imply that the solution is an exact one; they are all approximate quantum mechanical calculations. It means that a particular approximation is rigorously defined on first principles quantum theory and then solved within an error margin that is qualitatively known beforehand. The simplest type of ab initio electronic structure calculation is the Hartree—Fock method HF , an extension of molecular orbital theory , in which the correlated electron-electron repulsion is not specifically taken into account; only its average effect is included in the calculation.
As the basis set size is increased, the energy and wave function tend towards a limit called the Hartree—Fock limit.
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Many types of calculations termed post-Hartree—Fock methods begin with a Hartree—Fock calculation and subsequently correct for electron-electron repulsion, referred to also as electronic correlation. To obtain exact agreement with experiment, it is necessary to include relativistic and spin orbit terms, both of which are far more important for heavy atoms. In all of these approaches, along with choice of method, it is necessary to choose a basis set. This is a set of functions, usually centered on the different atoms in the molecule, which are used to expand the molecular orbitals with the linear combination of atomic orbitals LCAO molecular orbital method ansatz.
Ab initio methods need to define a level of theory the method and a basis set. The Hartree—Fock wave function is a single configuration or determinant. In some cases, particularly for bond breaking processes, this is inadequate, and several configurations must be used.
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Here, the coefficients of the configurations, and of the basis functions, are optimized together. The total molecular energy can be evaluated as a function of the molecular geometry ; in other words, the potential energy surface. Such a surface can be used for reaction dynamics. The stationary points of the surface lead to predictions of different isomers and the transition structures for conversion between isomers, but these can be determined without a full knowledge of the complete surface.
A particularly important objective, called computational thermochemistry , is to calculate thermochemical quantities such as the enthalpy of formation to chemical accuracy. To reach that accuracy in an economic way it is necessary to use a series of post-Hartree—Fock methods and combine the results.
Case, J. Chen, D. Case, C.
- Associate Research Professor, Chemistry.
- Density functional theory;
- Department of Integrative Structural and Computational Biology;
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DFT in a nutshell
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