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Encyclopedia > Computational chemistry

Computational chemistry is a branch of chemistry that uses the results of theoretical chemistry incorporated into efficient computer programs to calculate the structures and properties of molecules and solids, applying these programs to complement the information obtained by actual chemical experiments, predict hitherto unobserved chemical phenomena, and solve related problems. Examples of such properties are structure (i.e. the expected positions of the constituent 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. The term computational chemistry is also sometimes used to cover any of the areas of science that overlap between computer science and chemistry. Electronic configuration theory is the largest subdiscipline of computational chemistry. Chemistry - the study of atoms, made of nuclei (conglomeration of center particles) and electrons (outer particles), and the structures they form. ... Theoretical chemistry is the use of reasoning to explain or predict chemical phenomena. ... A computer program is a collection of instructions that describe a task, or set of tasks, to be carried out by a computer. ... In science, a molecule is a group of atoms in a definite arrangement held together by chemical bonds. ... In the scientific method, an experiment (Latin: ex-+-periri, of (or from) trying), is a set of actions concerning phenomena. ... A phenomenon (plural: phenomena) is an observable event, especially something special (literally something that can be seen from the Greek word phainomenon = observable). ... In physics, interaction energy is the contribution to the total energy that is caused by an interaction between the objects being considered. ... e- redirects here. ... Charge density is the amount of electric charge per unit volume. ... The Earths magnetic field, which is approximately a dipole. ... Multipole moments in mathematics and mathematical physics are an orthogonal basis for the decomposition of a function, based on the response of a field to point sources that are brought infinitely close to each other. ... The vibrational states of a molecule can be probed in a variety of ways. ... Reactivity refers to the rate at which a chemical substance tends to undergo a chemical reaction in time. ... Extremely high resolution spectrogram of the Sun showing thousands of elemental absorption lines (fraunhofer lines) Spectroscopy is the study of the interaction between radiation (electromagnetic radiation, or light, as well as particle radiation) and matter. ... In nuclear and particle physics, the concept of a cross section is used to express the likelihood of interaction between particles. ... Scattering theory is a branch of physics and especially of quantum mechanics whose aim is the study of scattering events. ... Part of a scientific laboratory at the University of Cologne. ... Computer science, or computing science, is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ... Chemistry - the study of atoms, made of nuclei (conglomeration of center particles) and electrons (outer particles), and the structures they form. ... Electron configuration is the arrangement of electrons in an atom, molecule or other body. ...

Contents

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 described in a qualitative or approximate quantitative computational scheme.


Molecules consist of nuclei and electrons, so the methods of quantum mechanics apply. Computational chemists often attempt to solve the non-relativistic Schrödinger equation, with relativistic corrections added, although some progress has been made in solving the fully relativistic Schrödinger equation. It is, in principle, possible to solve the Schrödinger equation, in either its time-dependent form or time-independent form as appropriate for the problem in hand, but this in practice is not possible except for very small systems. 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. Present computational chemistry can routinely calculate the properties of molecules that contain no more than 10-40 electrons. Errors for energies can be less than 1 kcal/mol. For geometries, bond lengths can be predicted within a few picometres and bond angles within 0.5o. The treatment of larger molecules that contain a few dozen electrons is computationally tractable by approximate methods such as density functional theory (DFT). There is some dispute within the field whether 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 are called molecular mechanics. Fig. ... For a non-technical introduction to the topic, please see Introduction to quantum mechanics. ... Density functional theory (DFT) is a quantum mechanical method used in physics and chemistry to investigate the electronic structure of many-body systems, in particular molecules and the condensed phases. ... Classical mechanics is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. ... The term molecular mechanics refers to the use of Newtonian mechanics to model molecular systems. ...


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. There are two different aspects to computational chemistry: In mathematics, computing, linguistics, and related disciplines, an algorithm is a finite list of well-defined instructions for accomplishing some task that, given an initial state, will terminate in a defined end-state. ... Vapours of hydrogen chloride in a beaker and ammonia in a test tube meet to form a cloud of a new substance, ammonium chloride A chemical reaction is a process that results in the interconversion of chemical substances. ...

  • Computational studies can be carried out in order 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 so far entirely unknown molecules or to explore reaction mechanisms that are not readily studied by experimental means.

Thus computational chemistry can assist the experimental chemist or it can challenge the experimental chemist to find entirely new chemical objects.


Several major areas may be distinguished within computational chemistry:

  • The prediction of the molecular structure of molecules by the use of the simulation of forces to find stationary points on the energy hypersurface as the position of the nuclei is 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 (e.g. drug design).

To meet Wikipedias content policies, the external links section for this article may require cleanup. ... Positive linear correlations between 1000 pairs of numbers. ... Chemical structure refers to the spatial arrangement of atoms in a molecule and the chemical bonds that hold the atoms together. ... The Quantitative Structure Property Relationship (QSPR) is used in the field of chemistry, and relates bio-physico-chemical properties of chemical compounds to their structures. ... QSAR (Quantitative Structure-Activity Relationship, sometimes the A stands also for Affinity=reactivity) is the quantitative correlation of the biological (ecological, toxicological or pharmacological) activity to the structure of chemical compounds, which allows the prediction of the so-called drug efficacy of a structurally related compound. ... Drug design is the approach of finding drugs by design, based on their biological targets. ...

History

Building on the founding discoveries and theories in the history of quantum mechanics, the first theoretical calculations in chemistry were those of Walter Heitler and Fritz London in 1927. In this direction, a few books that were influential in the early development of computational quantum chemistry include: Pauling and 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. Niels Bohr’s 1913 quantum model of the atom, which incorporated an explanation of Johannes Rydbergs 1888 formula, Max Planck’s 1900 quantum hypothesis, i. ... Walter Heinrich Heitler (02. ... Fritz Wolfgang London (March 7, 1900–March 30, 1954) was a German-born American physicist for whom the London force is named. ... Linus Carl Pauling (February 28, 1901 – August 19, 1994) was an American quantum chemist and biochemist. ... Henry Eyring (February 20, 1901 - December 26, 1981) was a Mexican-American theoretical chemist whose primary contribution was in the study of chemical reaction rates and intermediates. ... Charles Alfred Coulson (1910-1974) was a prominent researcher in the field of theoretical chemistry. ...


With the development of efficient computer technology in the 1940s the solutions of elaborate wave equations for complex atomic systems began to be a realizable objective. In the early 1950s, the first semi-empirical atomic orbital calculations were carried out. 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.[1] The first ab initio Hartree-Fock calculations on diatomic molecules were carried out in 1956 at MIT using a basis set of Slater orbitals. 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 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 II 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 vy Schaefer.[7] The NASA Columbia Supercomputer. ... The wave equation is an important partial differential equation that describes the propagation of a variety of waves, such as sound waves, light waves and water waves. ... Properties In chemistry and physics, an atom (Greek ἄτομος or átomos meaning indivisible) is the smallest particle still characterizing a chemical element. ... Configuration interaction (CI) is a post Hartree-Fock linear variational method for solving the nonrelativistic Schrödinger equation within the Born-Oppenheimer approximation for a quantum chemical multi-electron system. ... Samuel Francis Boys (20 December 1911-16 October 1972) was born in Pudsey, Yorkshire, United Kingdom. ... Naphthalene (not to be confused with naphtha) (also known as naphthalin, naphthaline, tar camphor, white tar, albocarbon, or naphthene), is a crystalline, aromatic, white, solid hydrocarbon, best known as the primary ingredient of mothballs. ... Categories: Stub ...


In 1964, Hückel method calculations, which are a simple LCAO method for the determination of electron energies of molecular orbitals of π electrons in conjugated hydrocarbon systems, ranging from simple systems such as butadiene and benzene to ovalene with 10 fused six-membered rings , were generated on computers at Berkeley and Oxford.[8] In the early 1970s, efficient computer programs such as ATMOL, POLYAYTOM, IBMOL, and GAUSSIAN, etc., began to be used to speed up the calculations of molecular orbitals. Butadiene can refer to either one of two hydrocarbon chemical compounds which are alkenes that are isomers of each other. ... Benzene is an organic chemical compound with the formula C6H6. ... Ovalene is a polycyclic aromatic hydrocarbon with a formula of C32H14, which consists of ten peri-fused six-member rings. ... Generally, the word gaussian pertains to Carl Friedrich Gauss and his ideas. ...


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.”[9] On these early developments, the science computational chemistry began emerging as a distinct discipline in about 1979.[10] During 1980s, the basic science of computational chemistry began to assemble. The Journal of Computational Chemistry, for example, was first published in 1980. The Journal of Computational Chemistry is a peer-reviewed scientific journal, published since 1980 by John Wiley & Sons. ...


Molecular structure

A given 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 (electronic energy plus repulsion energy between the nuclei) as a function of the coordinates of all the nuclei. 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. A potential energy surface is generally used within the adiabatic or Born–Oppenheimer approximation in quantum mechanics and statistical mechanics to model chemical reactions and interactions in simple chemical and physical systems. ... The transition state of a chemical reaction is a particular configuration along the reaction coordinate. ... In chemistry, a reaction coordinate is an abstract one-dimensional coordinate system which represents progress along a reaction pathway. ...


The determination of molecular structure by geometry optimization became routine only when 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 assumed. In some ways more importantly it allows the characterisation of stationary points. The frequencies are related to the eigenvalues of the matrix of second derivatives (the Hessian matrix). 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 (an imaginary frequency), the stationary point is a transition structure. If more than one eigenvalue is negative the stationary point is a more complex one, and usually of little interest. When found, it is necessary to move the search away from it, if we are looking for local minima and transition structures.


The total energy is determined by approximate solutions of the time-dependent Schrödinger equation, usually with no relativistic terms included, and making use of the Born-Oppenheimer approximation which, based on the much higher velocity of the electrons in comparison with the nuclei, allows the separation of electronic and nuclear motions, and simplifies the Schrödinger equation. This leads to evaluating the total energy as a sum of the electronic energy at fixed nuclei positions plus 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: The Born-Oppenheimer approximation, also known as the adiabatic approximation, is a technique used in quantum chemistry and condensed matter physics in order to de-couple the motion of nuclei and electrons (i. ... Direct quantum chemistry covers a set of quantum chemical methods not using the Born-Oppenheimer representation. ...


Ab initio methods

The programs used in computational chemistry are based on many different quantum-chemical methods that solve the molecular Schrödinger equation associated with the molecular Hamiltonian. Methods that do not include any empirical or semi-empirical parameters in their equations - being derived directly from theoretical principles, with no inclusion of experimental data - are called ab initio methods. 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. If numerical iterative methods have to be employed, the aim is to iterate until full machine accuracy is obtained (the best that is possible with a finite word length on the computer, and whithin the mathematical and/or physical approximations made). Ab initio quantum chemistry methods are computational chemistry methods based on quantum chemistry. ... Quantum chemistry is a branch of theoretical chemistry, which applies quantum mechanics and quantum field theory to address issues and problems in chemistry. ... For a non-technical introduction to the topic, please see Introduction to quantum mechanics. ... The molecular Hamiltonian is an operator in quantum chemistry and atomic, molecular, and optical physics which describes the motions of electrons and nuclei in a polyatomic molecule. ... Ab Initio Software Corporation was founded in the mid 1990s by the former CEO, Sheryl Handler, and several other former employees of Thinking Machines Corporation, after the bankruptcy of that company. ...

Diagram illustrating various ab initio electronic structure methods in terms of energy.
Diagram illustrating various ab initio electronic structure methods in terms of energy.

The simplest type of ab initio electronic structure calculation is the Hartree-Fock (HF) scheme, 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 to a limit called the Hartree-Fock limit. Many types of calculations, known as post-Hartree-Fock methods, begin with a Hartree-Fock calculation and subsequently correct for electron-electron repulsion, referred to also as electronic correlation. As these methods are pushed to the limit, they approach the exact solution of the non-relativistic Schrödinger equation. In order to obtain exact agreement with experiment, it is necessary to include relativistic and spin orbit terms, both of which are only really important for heavy atoms. In all of these approaches, in addition to the choice of method, it is necessary to choose a basis set. This is a set of functions, usually centred on the different atoms in the molecule, which are used to expand the molecular orbitals with the LCAO ansatz. Ab initio methods need to define a level of theory (the method) and a basis set. Image File history File links Diagram illustrating electron correlation energy in terms of various levels of theory. ... Image File history File links Diagram illustrating electron correlation energy in terms of various levels of theory. ... In computational physics and computational chemistry, the Hartree-Fock (HF) or self-consistent field (SCF) calculation scheme is a self-consistent iterative variational procedure to calculate the Slater determinant (or the molecular orbitals which it is made of) for which the expectation value of the electronic molecular Hamiltonian is minimum. ... In computational chemistry, Post-Hartree-Fock methods are the set of methods developed to improve on the Hartree-Fock (HF), or self-consistent field (SCF) method for diagonalizing the electronic Hamiltonian describing the electronic structure of molecules. ... Electronic correlation refers to the interaction between electrons in a quantum system whose electronic structure is being considered. ... In modern computational chemistry, quantum chemical calculations are typically performed within a finite set of basis functions. ... This article may be too technical for most readers to understand. ... Ansatz (Ger. ...


The Hartree-Fock wave function is a single configuration or determinant. In some cases, particularly for bond breaking processes, this is quite inadequate and several configurations need to be used. Here the coefficients of the configurations and the coefficients of the basis functions are optimized together. In quantum chemistry, the Multi-configurational self-consistent field or MCSCF method is a method used is to generate qualitatively correct reference states of molecules in cases where Hartree-Fock and Density Functional Theort are not adequate (e. ...


The total molecular energy can be evaluated as a function of the molecular geometry, in other words the potential energy surface. Geometry of the water molecule Molecular geometry or molecular structure is the three dimensional arrangement of the atoms that constitute a molecule, inferred from the spectroscopic studies of the compound. ... A potential energy surface is generally used within the adiabatic or Born–Oppenheimer approximation in quantum mechanics and statistical mechanics to model chemical reactions and interactions in simple chemical and physical systems. ...


Example: Is Si2H2 like acetylene (C2H2)?

A series of ab initio studies of Si2H2 shows clearly the power of ab initio computational chemistry. They go back over 20 years, and most of the main conclusions were reached by 1995. The methods used were mostly post-Hartree-Fock, particularly Configuration interaction (CI) and Coupled cluster (CC). Initially the question was whether disilyne, Si2H2 had the same structure as ethyne (acetylene), C2H2. Slowly (because this started before geometry optimization was widespread), it became clear that linear Si2H2 was a transition structure between two equivalent trans-bent structures and that it was rather high in energy. The ground state was predicted to be a four-membered ring bent into a 'butterfly' structure with hydrogen atoms bridged between the two silicon atoms. Interest then moved to look at whether structures equivalent to vinylidene - Si=SiH2 - existed. This structure is predicted to be a local minimum, i. e. an isomer of Si2H2, lying higher in energy than the ground state but below the energy of the trans-bent isomer. Then surprisingly a new isomer was predicted by Brenda Colegrove in Henry F. Schaefer, III's group.[11] This prediction was so surprising that it needed extensive calculations to confirm it. It requires post Hartree-Fock methods to obtain a local minimum for this structure. It does not exist on the Hartree-Fock energy hypersurface. The new isomer is a planar structure with one bridging hydrogen atom and one terminal hydrogen atom, cis to the bridging atom. Its energy is above the ground state but below that of the other isomers.[12] Similar results were later obtained for Ge2H2.[13] More interestingly, similar results were obtained for Al2H2[14] (and then Ga2H2)[15] which has two electrons less than the Group 14 molecules. The only difference is that the four-membered ring ground state is planar and not bent. The cis-mono-bridged and vinylidene-like isomers are present. Experimental work on these molecules is not easy, but matrix isolation spectroscopy of the products of the reaction of hydrogen atoms and silicon and aluminium surfaces has found the ground state ring structures and the cis-mono-bridged structures for Si2H2 and Al2H2. Theoretical predictions of the vibrational frequencies were crucial in understanding the experimental observations of the spectra of a mixture of compounds. This may appear to be an obscure area of chemistry, but the differences between carbon and silicon chemistry is always a lively question, as are the differences between group 13 and group 14 (mainly the B and C differences). The silicon and germanium compounds were the subject of a Journal of Chemical Education article.[16] In computational chemistry, Post-Hartree-Fock methods are the set of methods developed to improve on the Hartree-Fock (HF), or self-consistent field (SCF) method for diagonalizing the electronic Hamiltonian describing the electronic structure of molecules. ... Configuration interaction (CI) is a post Hartree-Fock linear variational method for solving the nonrelativistic Schrödinger equation within the Born-Oppenheimer approximation for a quantum chemical multi-electron system. ... This article needs to be cleaned up to conform to a higher standard of quality. ... The chemical compound acetylene, also called ethyne, was discovered in 1836 by Edmund Davy, in England; its chemical formula is C2H2 and its structure is: Acetylene is a colorless and extremely flammable gas at standard temperature and pressure and has a pleasantly sweet ethereal odor. ... Henry F. Schaefer III was born in Grand Rapids, Michigan in 1944. ... In computational chemistry, Post-Hartree-Fock methods are the set of methods developed to improve on the Hartree-Fock (HF), or self-consistent field (SCF) method. ... In computational physics and computational chemistry, the Hartree-Fock (HF) or self-consistent field (SCF) calculation scheme is a self-consistent iterative variational procedure to calculate the Slater determinant (or the molecular orbitals which it is made of) for which the expectation value of the electronic molecular Hamiltonian is minimum. ...


Density Functional methods

Density functional theory (DFT) methods are often considered to be ab initio methods for determining the molecular electronic structure, even though many of the most common functionals use parameters derived from empirical data, or from more complex calculations. This means that they could also be called semi-empirical methods. It is best to treat them as a class on their own. In DFT, 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. DFT methods can be very accurate for little computational cost. The drawback is, that unlike ab initio methods, there is no systematic way to improve the methods by improving the form of the functional. Density functional theory (DFT) is a quantum mechanical method used in physics and chemistry to investigate the electronic structure of many-body systems, in particular molecules and the condensed phases. ... Ab Initio Software Corporation was founded in the mid 1990s by the former CEO, Sheryl Handler, and several other former employees of Thinking Machines Corporation, after the bankruptcy of that company. ... Generally, functional refers to something with and able to fulfill its purpose or function. ... In quantum mechanics, and in particular in quantum chemistry, the electronic density corresponding to an N-electron wavefunction is the one-electron function given by In the case is a Slater determinant made of N spin orbitals : The two-electron electronic density is given by Those quantities are particulary important... The quantum Hamiltonian is the physical state of a system, which may be characterized as a ray in an abstract Hilbert space (or, in the case of ensembles, as a trace class operator with trace 1). ...


Semi-empirical and empirical methods

Main article: Semi-empirical quantum chemistry methods

Semi-empirical quantum chemistry methods are based on the Hartree-Fock formalism, but make many approximations and obtain some parameters from empirical data. They are very important in computational chemistry for treating large molecules where the full Hartree-Fock method without the approximations is too expensive. The use of empirical parameters appears to allow some inclusion of correlation effects into the methods. Semi-empirical quantum chemistry methods are based on the Hartree-Fock formalism, but make many approximations and obtain some parameters from empirical data. ... Quantum chemistry is a branch of theoretical chemistry, which applies quantum mechanics and quantum field theory to address issues and problems in chemistry. ... In computational physics and computational chemistry, the Hartree-Fock (HF) or self-consistent field (SCF) calculation scheme is a self-consistent iterative variational procedure to calculate the Slater determinant (or the molecular orbitals which it is made of) for which the expectation value of the electronic molecular Hamiltonian is minimum. ...


Semi-empirical methods follow what are often called empirical methods where the two-electron part of the Hamiltonian is not explicitly included. For π-electron systems, this was the Hückel method proposed by Erich Hückel, and for all valence electron systems, the Extended Hückel method proposed by Roald Hoffmann. In physics, Hamiltonian has distinct but closely related meanings. ... The Hückel method was proposed by Erich Hückel in 1930. ... Erich Armand Arthur Joseph Hückel (August 9, 1896 - February 16, 1980) was a German physicist and physical chemist. ... The extended Huckel method is a way of determining the structural geometry of an organic molecule. ... Roald Hoffmann (born July 18, 1937 as Roald Safran --- Hoffmann is the surname of his stepfather) is an American theoretical chemist of Polish-Jewish origin. ...


Molecular mechanics

Main article: Molecular mechanics

In many cases, large molecular systems can be modeled successfully while 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 term molecular mechanics refers to the use of Newtonian mechanics to model molecular systems. ... The term molecular mechanics refers to the use of Newtonian mechanics to model molecular systems. ... In classical mechanics, a Harmonic oscillator is a system which, when displaced from its equilibrium position, experiences a restoring force proportional to the displacement according to Hookes law: where is a positive constant. ...


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 molecules of the same class. A force field is used to minimize the bond stretching energy of this ethane molecule. ...


Interpreting molecular wave functions

The Atoms in Molecules model developed by Richard Bader was developed in order to effectively link the quantum mechanical picture of a molecule, as an electronic wavefunction, to chemically useful older models such as the theory of Lewis pairs and the valence bond model. Bader has demonstrated that these empirically useful models are connected with the topology of the quantum charge density. This method improves on the use of Mulliken population analysis. The Atoms in Molecules or Atoms-in-Molecules approach is a quantum chemical model that characterizes the chemical bonding of a system based on the topology of the quantum charge density. ... Richard F. W. Bader is a quantum chemist, noted for his work on the Atoms in Molecules approach. ... A Lewis electron pair is a pair of electrons with opposite spins located in a molecule. ... In chemistry, valence bond theory explains the nature of a chemical bond in a molecule in terms of atomic valencies. ... A Möbius strip, an object with only one surface and one edge; such shapes are an object of study in topology. ... Mulliken charges arise from the Mulliken population analysis and provide a means of estimating partial atomic charges from calculations carried out by the methods of computational chemistry, particularly those based on the linear combination of atomic orbitals molecular orbital method. ...


Computational chemical methods in solid state physics

Computational chemical methods can be applied to solid state physics problems. 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 semi-empirical 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. Computational chemical methods in solid state physics follow the same approach as they do for molecules, but with two differences. ... Solid-state physics, the largest branch of condensed matter physics, is the study of rigid matter, or solids. ... In solid state physics, the electronic band structure, or simply band structure, refers to the dispersion relation (the relation between energy versus momentum) of electrons in a crystal. ... In mathematics and solid state physics, the first Brillouin zone is the primitive cell in the reciprocal lattice in momentum space. ...


Chemical dynamics

Once the electronic and nuclear variables are separated (within the Born-Oppenheimer representation), in the time-dependent approach, the wave packet corresponding to the nuclear degrees of freedom is propagated via the time evolution operator (physics) associated to the time-dependent Schrödinger equation (for the full molecular Hamiltonian). In the complementary energy-dependent approach, the time-independent Schrödinger equation is solved using the scattering theory formalism. The potential respresenting the interatomic interaction is given by the potential energy surfaces. In general, the potential energy surfaces are coupled via the vibronic coupling terms. Geometry of the water molecule Molecular geometry or molecular structure is the three dimensional arrangement of the atoms that constitute a molecule, inferred from the spectroscopic studies of the compound. ... In mathematics, separation of variables is any of several methods for solving ordinary and partial differential equations, in which algebra allows one to re-write an equation so that each of two variables occurs on a different side of the equation. ... The wave packet is one of the most widely misunderstood and misused concepts in physics. ... Degrees of freedom is a general term used in explaining dependence on parameters, and implying the possibility of counting the number of those parameters. ... For a system with internal state (also called stateful system), time evolution means the change of state brought about by the passage of time. ... In mathematical formulations of quantum mechanics, an operator is a linear transformation from a Hilbert space to itself. ... For a non-technical introduction to the topic, please see Introduction to quantum mechanics. ... The molecular Hamiltonian is an operator in quantum chemistry and atomic, molecular, and optical physics which describes the motions of electrons and nuclei in a polyatomic molecule. ... In physics, complementarity is a basic principle of quantum theory closely identified with the Copenhagen interpretation, and refers to effects such as the wave-particle duality, in which different measurements made on a system reveal it to have either particle-like or wave-like properties. ... For a non-technical introduction to the topic, please see Introduction to quantum mechanics. ... Scattering theory is a branch of physics and especially of quantum mechanics whose aim is the study of scattering events. ... A potential energy surface is generally used within the adiabatic or Born–Oppenheimer approximation in quantum mechanics and statistical mechanics to model chemical reactions and interactions in simple chemical and physical systems. ... A potential energy surface is generally used within the adiabatic or Born–Oppenheimer approximation in quantum mechanics and statistical mechanics to model chemical reactions and interactions in simple chemical and physical systems. ... In theoretical chemistry, the vibronic coupling terms (which are neglected within the Born-Oppenheimer approximation) are proportional to the interaction between electronic and nuclear motions of molecules. ...


The most popular methods for propagating the wave packet associated to the molecular geometry are The wave packet is one of the most widely misunderstood and misused concepts in physics. ... Geometry of the water molecule Molecular geometry or molecular structure is the three dimensional arrangement of the atoms that constitute a molecule, inferred from the spectroscopic studies of the compound. ...

  • the split operator technique,
  • the Multi-Configuration Time-Dependent Hartree method (MCTDH),
  • the semiclassical method.

Molecular dynamics (MD) examines (using Newton's laws of motion) the time-dependent behavior of systems, including vibrations or Brownian motion, using a classical mechanical description. MD combined with density functional theory leads to the Car-Parrinello method. MCTDH stands for Multi Configuration Time Dependent Hartree. ... In physics, the adjective semiclassical has different precise meanings depending on the context. ... Molecular dynamics (MD) is a form of computer simulation where atoms and molecules are allowed to interact for a period of time under known laws of physics. ... Newtons First and Second laws, in Latin, from the original 1687 edition of the Principia Mathematica. ... Density functional theory (DFT) is a quantum mechanical method used in physics and chemistry to investigate the electronic structure of many-body systems, in particular molecules and the condensed phases. ... The Car-Parrinello method in computational chemistry is a type of ab initio (first principles) molecular dynamics, usually employing periodic boundary conditions, planewave basis sets, and DFT. In slight contrast to Born-Oppenheimer molecular dynamics wherein the nuclear (ions) and electronic degrees of freedom are separated and conventional matrix diagonalization...


Software packages

A number of self-sufficient software packages include many quantum-chemical methods, and in some cases molecular mechanics methods. The following table illustrates the capabilities of the most versatile software packages that show an entry in two or more columns of the table. There are separate lists for specialized programs, such as:-

Package Molecular Mechanics Semi-Empirical Hartree-Fock Post-Hartree-Fock methods Density Functional Theory
ACES N N Y Y N
CADPAC N N Y Y Y
COLUMBUS N N Y Y N
DALTON N N Y Y Y
GAMESS (UK) N Y Y Y Y
GAMESS (US) Y(*) Y Y Y Y
GAUSSIAN Y Y Y Y Y
JAGUAR Y N Y Y Y
MATERIALS STUDIO Y Y N N Y
MOLCAS Y Y Y Y Y
MOLPRO N N Y Y Y
MPQC N N Y Y Y
NWChem Y N Y Y Y
PLATO Y N N N Y
PQS Y Y Y Y Y
PSI N N Y Y N
Q-Chem Y N Y Y Y
TURBOMOLE Y N Y Y Y

(*) Through interface to TINKER Density functional theory (DFT) is a quantum mechanical method used in physics and chemistry to investigate the electronic structure of many-body systems, in particular molecules and the condensed phases. ... Semi-empirical quantum chemistry methods are based on the Hartree-Fock formalism, but make many approximations and obtain some parameters from empirical data. ... Computational chemical methods in solid state physics follow the same approach as they do for molecules, but with two differences. ... VB computer programs for modern valence bond calculations:- CRUNCH is by Gordon A. Gallup and his group. ... Min - Optimization, MD - Molecular Dynamics, MC - Monte Carlo, QM - Quantum mechanics. ... The term molecular mechanics refers to the use of Newtonian mechanics to model molecular systems. ... Semi-empirical quantum chemistry methods are based on the Hartree-Fock formalism, but make many approximations and obtain some parameters from empirical data. ... In computational physics and computational chemistry, the Hartree-Fock (HF) or self-consistent field (SCF) calculation scheme is a self-consistent iterative variational procedure to calculate the Slater determinant (or the molecular orbitals which it is made of) for which the expectation value of the electronic molecular Hamiltonian is minimum. ... In computational chemistry, Post-Hartree-Fock methods are the set of methods developed to improve on the Hartree-Fock (HF), or self-consistent field (SCF) method. ... Density functional theory (DFT) is a quantum mechanical method used in physics and chemistry to investigate the electronic structure of many-body systems, in particular molecules and the condensed phases. ... Aces II (Advanced Concepts in Electronic Structure Theory) is a computational chemistry package written and maintained by the research group of Rod Bartlett, at the Quantum Theory Project at the University of Florida. ... CADPAC, the Cambridge Analytic Derivatives Package, is a suite of programs for ab initio computational chemistry calculations. ... Look up columbus in Wiktionary, the free dictionary. ... Dalton is an both an English name and surname that means from the valley town, and an Irish name probably derived from Norman French dAuthon and is still spelt Dalton or DAlton by some, although this may be an affectation added or reinstated in recent generations. ... GAMESS (UK) is a computational chemistry software program that stands for General Atomic and Molecular Electronic Structure System. ... GAMESS (US) is a computational chemistry software program that stands for General Atomic and Molecular Electronic Structure System. ... Generally, the word gaussian pertains to Carl Friedrich Gauss and his ideas. ... For other uses, see Jaguar (disambiguation). ... MOLCAS is an ab initio computational chemistry program, developed at Lund University. ... MOLPRO is a software package used for accurate quantum chemical ab initio calculations. ... MPQC is a computational chemistry software program. ... NWChem is a computational chemistry software package. ... PLATO, which stands for Package for Linear combination of ATomic Orbitals, is a suite of programs designed and written by Andrew Horsfield and Steven Kenny. ... PQS is a general purpose quantum chemistry program. ... PSI is a computational chemistry package originally written by the research group of H. F. Schaefer III. Primary development of PSI3 has been carried out by Daniel Crawford, David Sherrill, Edward Valeev, and Rollin King. ... Q-Chem is a computational chemistry software program. ... TURBOMOLE is a Quantum chemistry ab initio program package, developed at the group of Prof. ... Tinker may mean: n. ...


See also

In modern computational chemistry, quantum chemical calculations are typically performed within a finite set of basis functions. ... Map of the human X chromosome (from the NCBI website). ... Cheminformatics (also known as chemoinformatics and chemical informatics) is the use of computer and informational techniques, applied to a range of problems in the field of chemistry. ... The Computation Chemistry List (CCL) was established on January 11, 1991, as an independent electronic forum for chemistry researchers and educators from around the world. ... The International Academy of Quantum Molecular Science was created in Menton in 1967, with Professors Raymond Daudel (France), Per-Olov Löwdin (Sweden), Robert G. Parr (USA), John A. Pople (USA) and Bernard Pullman (France) as its founding members, under the inspiration and with the support of Professor Louis de... This is a list of important publications in chemistry, organized by field. ... The backbone dihedral angles are included in the molecular model of a protein. ... Monte Carlo molecular modeling, particularly Metropolis Monte Carlo simulation is the application of Monte Carlo methods to problems which would otherwise be solved by molecular dynamics. ... Quantum chemistry is a branch of theoretical chemistry, which applies quantum mechanics and quantum field theory to address issues and problems in chemistry. ... Scientific computing (or computational science) is the field of study concerned with constructing mathematical models and numerical solution techniques and using computers to analyze and solve scientific and engineering problems. ... Statistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ...

Cited References

  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., 146. 
  3. ^ Boys, S. F.; Cook G. B., Reeves C. M., Shavitt, I. (1956). "Automatic fundamental calculations of molecular structure". Nature 178 (2): 1207. 
  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. ^ Fernbach, Sidney; Taub, Abraham Haskell (1970). Computers and Their Role in the Physical Sciences. Routledge. ISBN 0677140304. 
  10. ^ Reviews in Computational Chemistry vol 1, preface
  11. ^ Colegrove, B. T.; Schaefer, Henry F. III (1990). "Disilyne (Si2H2) revisited". Journal of Physical Chemistry 94: 5593. 
  12. ^ Grev, R. S.; Schaefer, Henry F. III (1992). "The remarkable monobridged structure of Si2H2". Journal of Chemical Physics 97: 7990. 
  13. ^ Palágyi, Zoltán; Schaefer, Henry F. III, Kapuy, Ede (1993). "Ge2H2: A Molecule with a low-lying monobridged equilibrium geometry". Journal of the American Chemical Society 115: 6901 - 6903. 
  14. ^ Stephens, J. C.; Bolton, E. E.,Schaefer, H. F. III, and Andrews, L. (1997). "Quantum mechanical frequencies and matrix assignments to Al2H2". Journal of Chemical Physics 107: 119 - 223. 
  15. ^ Palágyi, Zoltán; Schaefer, Henry F. III, Kapuy, Ede (1993). "Ga2H2: planar dibridged, vinylidene-like, monobridged and trans equilibrium geometries". Chemical Physics Letters 203: 195 - 200. 
  16. ^ DeLeeuw, B. J.; Grev, R. S. and Schaefer, Henry F. III (1992). "A comparison and contrast of selected saturated and unsaturated hydrides of group 14 elements". Journal of Chemical Education 69: 441. 

The International Journal of Quantum Chemistry is an international peer-reviewed scientific journal publishing original, primary research and review articles on all aspects of quantum chemistry, defined as Theory and Computation in Chemistry, Physics, and Molecular Biology. [1] The impact factor of the journal is 1. ... Chemical Physics Letters is a peer-reviewed scientific journal, published since 1967 by Elsevier. ... Charles Alfred Coulson (1910-1974) was a prominent researcher in the field of theoretical chemistry. ... Henry F. Schaefer III was born in Grand Rapids, Michigan in 1944. ...

Other references

  • T. Clark A Handbook of Computational Chemistry, Wiley, New York (1985)
  • C. J. Cramer Essentials of Computational Chemistry, John Wiley & Sons (2002)
  • R. Dronskowski Computational Chemistry of Solid State Materials, Wiley-VCH (2005)
  • F. Jensen Introduction to Computational Chemistry, John Wiley & Sons (1999)
  • D. Rogers Computational Chemistry Using the PC, 3rd Edition, John Wiley & Sons (2003)
  • A. Szabo, N.S. Ostlund, Modern Quantum Chemistry, McGraw-Hill (1982)
  • D. Young Computational Chemistry: A Practical Guide for Applying Techniques to Real World Problems, John Wiley & Sons (2001)
  • David Young's Introduction to Computational Chemistry

External links


  Results from FactBites:
 
Encyclopedia4U - Computational chemistry - Encyclopedia Article (433 words)
Computational chemistry is the branch of theoretical chemistry whose major goals are to create efficient 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 programs used in computational chemistry are based on many different quantum-chemical methods that solve the molecular Schrödinger equation.
The opinion that computational chemistry would be ultimately able to predict mechanisms of such complex processes as biochemical reactions is now looked upon as unjustifiably optimistic.
  More results at FactBites »

 
 

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