Computational chemistry

Computational chemistry is a branch of chemistry that uses computer simulation to assist in solving chemical problems. It uses methods of theoretical chemistry , incorporated into effective computer programs , to calculate the structures and properties of molecules and solids. It is necessary because of the recent relative results concerning the hydrogen molecular ion (the dihydrogen cation , see references therein for more details), the quantum many-body problem can not be solved analytically, much less in closed form. While computational results Normally complement the information Obtained by chemical experimentspredictable hitherto unobserved chemical phenomena . It is widely used in the design of new drugs and materials.

Examples of such properties are structure, absolute and relative (interaction) energies , electronic charge density distributions, dipoles and higher multipole moments , vibrational frequencies , reactivity , or other spectroscopicquantities, and cross sections for collision with other particles.

The methods used both static and dynamic situations. In all cases, the computer time and other resources (such as the memory and the disk space) increase rapidly with the size of the system being studied. That system can be a molecule, a group of molecules, or a solid. Computational chemistry methods range from very close to highly accurate; the latter are usually possible for small systems only. Ab initio methods are based entirely on quantum mechanics and basic physical constants . Other methods are called empirical or semi-empirical because they use additional empirical parameters.

Both ab initio and semi-empirical approaches involve approximations. These methods are easier to overcome, to approximate the limitations of the system (for example, periodic boundary conditions ), to the 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 assuming that the nuclei remain in place during the calculation. In principle, ab initio methodseventually converges 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.

In some cases, the details of electronic structure are less important than the long-time phase space behavior of molecules. This is the case in conformational studies of proteins and protein-ligand binding thermodynamics. Classical approximations to the energy field are used, they are computationally less intensive than electronic calculations, to enable longer simulations of molecular dynamics . Furthermore, pathformatics uses even more empirical (and computationally cheaper) methods like machine learning based on physicochemical properties. A typical problem in pathology is to predict the binding affinity of drug molecules to a given target.

    • 4.4Molecular mechanics
    • 4.5Methods for solids
    • 4.6Chemical dynamics
    • 4.7Molecular dynamics
    • 4.8Quantum Mechanics / Molecular Mechanics (QM / MM)
  • 5Interpreting molecular wave functions
  • 6Software packages
  • 7See also
  • 8Notes and references
  • 9Bibliography
  • 10Specialized journals on computational chemistry
  • 11External links

History

Building on the founding and theories in the history of quantum mechanics , the first theoretical calculations in chemistry were those of Walter Heitler and Fritz London in 1927. The books that were influential 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 textbookValencia , each of which served as primary references for chemists in the decades to follow.

With the development of efficient computer technology in the 1940s, the solutions of elaborate wave equations for complex atomic systems In the early 1950s, the first semi-empirical atomic orbital calculations were performed. Theoretical chemists have become extensive users of the early digital computers. One major advance came with the 1951 paper in Modern Physics by Clemens Roothaan CJ in 1951, largely on the “LCAO MO” approach (Linear Combination of Atomic Orbitals Molecular Orbitals), for many years the second-most cited paper in that journal . A very detailed account of such use in the United Kingdom is given by Smith and Sutcliffe. [1] The first ab initioHartree-Fock method calculations on diatomic molecules were performed 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 respectivement in 1960. [2] The first polyatomic calculations using Gaussian orbitals Were Performed in the late 1950s. The first configuration interaction interactions were performed in Cambridge on the EDSAC in the 1950s using Gaussian orbitals by Boys and coworkers. [3] By 1971, when a bibliography of ab initioWas published calculations, [4] the Largest molecules included Were naphthaleneand azulene . [5] [6] Abstracts of many earlier developments in ab initio theory by Schaefer. [7]

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

In the early 1970s, effective ab initio computer programs such as ATMOL, Gaussian , IBMOL, and POLYAYTOM, began to be used to speed ab initio calculations of molecular orbitals. 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 . [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, widely different methods were introduced as part of a new emerging discipline of computational chemistry . [12] The Journal of Computational Chemistry was first published in 1980.

Compoundational chemistry has featured in several Nobel Prize awards, most notably in 1998 and 2013. Walter Kohn , “for his development of density-functional theory,” and John Pople , “for his development of computational methods in quantum chemistry,” received the 1998 Nobel Prize in Chemistry. [13] Martin Karplus , Michael Levitt and Arieh Warshel received the 2013 Nobel Prize in Chemistry for “the development of multiscale models for complex chemical systems”. [14]

Fields of application

The term theoretical chemistry can be defined as a mathematical description of chemistry, whereas computational chemistry is usually used when it is possible for it to 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.

Computational chemistry has two different aspects:

  • Computational studies, used to find a starting point for a study of spectroscopic peaks.
  • Computational studies, used to predict the possibility of being investigated by experiments.

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

Several major areas can be distinguished within computational chemistry:

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

Accuracy

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. Computational chemists often attempt to solve the non-relativistic Schrödinger equation , with relativistic corrections added, une actual progress has been made in solving the fully relativistic Dirac equation . In principle, it is possible to solve the Schrödinger equation in its time-dependent or time-independent form, as appropriate for the problem in hand; in practice, this is not possible except for very small systems. Therefore, a great number of methods 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 of many electrons, due to the computational cost of full relativistic-inclusive methods. This complicates the study of molecules interacting with high atomic mass units, such as transitional metals and their catalytic properties. Present algorithms in computational chemistry with the ability to calculate electrons with sufficient accuracy. Errors for energies can be less than a few kJ / mol. For geometries, bound lengths can be predicted within a few picometers and bound angles within 0.5 degrees. The treatment of larger molecules than a few electron donations is computationally tractabledensity functional theory (DFT).

There is some dispute in the field of whether or not these 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 that are called molecular mechanics (MM). In QM-MM methods, small parts of large complexes are treated quantum mechanically (QM), and the remainder is treated approximately (MM).

Methods

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 area ) created from the total energy (ie, the electronic energy, plus the repulsion energy between the nuclei) as a function of the coordinates of all 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 is called the global minimum and corresponds to the most stable isomer. If there is one particular co-ordinate, the stationary point is atransition 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 has become routine only after efficient methods for calculating the first derivative of the energy with respect to all atomic coordinates becomes available. The 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 is negative (ie, 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. When one of these is found, it is necessary to move from one to the next, and to experiment with it.

The total energy is determined by approximate solutions of the time-dependent Schrödinger equation, usually with no relativistic terms included, and by making use of the Born-Oppenheimer approximation , which allows for the separation of electronic and nuclear motions, thus simplifying the Schrödinger equation . 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 deals with electrons and nuclei on a common jog. 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:

Ab initio methods

Main article: Ab initio quantum chemistry methods

The programs used in computational chemistry are based on many different quantum-chemical methods that solve the molecular Schrödinger equation associated with the Hamiltonian molecular . Methods that do not include any empirical or semi-empirical parameters in their equations – being derived from the principles of 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 the first principles (quantum theory) and then is solved within an error margin that is qualitatively known beforehand. If numerical iterative methods must be used, the aim is to iterate up to full Machine accuracy is Obtained (the best That Is as possible with a finite word length on the computer, and dans le mathematical and / or physical approximations made).

Diagram illustrating various ab initio electronic structure methods in terms of energy. Spacings are not to scale.

The first type of ab initio electronic structure 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 of size is increased, the energy and wave function tends towards a limit called the Hartree-Fock limit. Many types of calculations (termed post-Hartree-Fock methods) and a correct calculation for the 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. To obtain exact agreement with experiment, it is necessary to include relativistic and spin orbit terms, both of which are more important for heavy atoms. In all of these approaches, 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 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 configurationsmust be used. 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 leads 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. Kcal / mol or 4 kJ / mol. To reach a degree of accuracy in a post-Haringe-Fock methods and combines the results. These methods are called quantum chemistry composite methods .

Density functional methods

Main article: Density functional theory

Density functional theory (DFT) methods are often considered to be the first methods for determining the molecular electronic structure, even though many of the most common functions are derived from empirical data, or from more complex calculations. In DFT, the total energy is expressed in terms of the total one- 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. Some methods combine the functional exchange function with the Hybrid exchange method .

Semi-empirical and empirical methods

Main article: Semi-empirical quantum chemistry methods

Semi-empirical quantum chemistry methods are based on the Hartree-Fock methodformalism , but make many approximations and obtain some parameters from empirical data. They are very important in computational chemistry for large molecules where the full Hartree-Fock method without approximations is too costly. The use of empirical parameters appears to allow some inclusion of correlation effects into the methods.

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 .

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, a 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, ie, 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 be relevant when describing other molecules of the same class.

These methods can be applied to a wide range of biological molecules and allow studies of the approach and interaction of potential drug molecules. [15] [16]

Methods for solids

Main article: 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 the 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 the area in the Brillouin zone.

Chemical dynamics

Once the electronic and nuclear variables are separated (dans le 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 Hamiltonian full molecular ). In the complementary energy-dependent approach, the time-independent Schrödinger equation is solved using scattering theory theory . The potential of the interatomic interaction is given by the potential energy surfaces. In general, the potential energy surfaces are coupled via the vibronic coupling terms.

The most popular methods for propagating the wave packet associated with molecular geometry are:

  • the technical split operator ,
  • the Chebyshev (real) polynomial ,
  • the multi-configuration time-dependent Hartree method (MCTDH),
  • the semiclassical method.

Molecular dynamics

Main article: Molecular dynamics

Molecular dynamics (MD) uses either quantum mechanics , Newton’s laws of motion or a mixed model to examine the time-dependent behavior of systems, including vibrations or Brownian motion and reactions. MD combined with density functional theory leads to hybrid models .

Quantum Mechanics / Molecular Mechanics (QM / MM)

Main article: QM / MM

QM / MM is a hybrid method that attempts to combine the accuracy of quantum mechanics with the speed of molecular mechanics. It is useful for simulating very large molecules such as enzymes .

Interpreting molecular wave functions

The atoms in molecules (QTAIM) model of Richard Bader was developed to effectively link the quantum mechanical model of a molecule, as an electronic wavefunction, to chemically useful concepts such as atoms in molecules, functional groups, bonding, the theory of Lewis peers , and the valence bond model . Bader HAS Demonstrated That thesis empirically Useful chemistry concepts can be related to the topology of the observable load density distribution, whether gold Measured Calculated from a quantum mechanical wavefunction. QTAIM analysis of molecular wavefunctions is implemented, for example, in the AIMAll software package.

Software packages

Many self-sufficient computational chemistry software packages exist. Some include many methods covering a wide range, while others Details of most of them can be found in:

  • Biomolecular modeling programs: proteins , nucleic acid .
  • Molecular mechanics programs.
  • Quantum chemistry and solid state physics software supporting several methods.
  • Molecular software design
  • Semi-empirical programs.
  • Valencia bond programs .

See also

  • List of computational chemists
  • Bioinformatics
  • Computational biology
  • Computational Chemistry List
  • Efficient code generation by computer algebra
  • Comparison of force field implementations
  • Important publications in computational chemistry
  • In silico
  • International Academy of Quantum Molecular Science
  • Mathematical Chemistry
  • Molecular graphics
  • Molecular modeling
  • Molecular modeling on GPUs
  • Monte Carlo molecular modeling
  • Protein dynamics
  • Scientific computing
  • Statistical mechanics
  • Solvent models

Notes and references

  1. Jump up^ Smith, SJ; Sutcliffe, BT (1997). “The development of Computational Chemistry in the United Kingdom”. Reviews in Computational Chemistry . 10 : 271-316.
  2. Jump up^ Schaefer, Henry F. III (1972). The electronic structure of atoms and molecules . Reading, Massachusetts: Addison-Wesley Publishing Co. p. 146.
  3. Jump up^ Boys, SF; Cook, GB; Reeves, CM; Shavitt, I. (1956). “Automatic fundamental calculations of molecular structure”. Nature . 178 (2): 1207.Bibcode : 1956Natur.178.1207B . doi : 10.1038 / 1781207a0 .
  4. Jump up^ Richards, WG; Walker, TEH; Hinkley RK (1971). A bibliography of ab initio molecular wave functions . Oxford: Clarendon Press.
  5. Jump up^ Preuss, H. (1968). “DasSCF-MO-P (LCGO) -Verfahren und seine Varianten”. International Journal of Quantum Chemistry . 2 (5): 651.Bibcode : 1968IJQC …. 2.651P . doi : 10.1002 / qua.560020506 .
  6. Jump up^ Buenker, RJ; Peyerimhoff, SD (1969). “Ab initio SCF calculations for azulene and naphthalene”. Chemical Physics Letters . 3 : 37. Bibcode :1969CPL ….. 3 … 37B . doi : 10.1016 / 0009-2614 (69) 80014-X .
  7. Jump up^ Schaefer, Henry F. III (1984). Quantum Chemistry . Oxford: Clarendon Press.
  8. Jump up^ Streitwieser, A .; Brauman, JI; Coulson, CA (1965). Supplementary Tables of Molecular Orbital Calculations . Oxford: Pergamon Press.
  9. Jump up^ Pople, John A .; Beveridge, David L. (1970). Approximate Molecular Orbital Theory . New York: McGraw Hill.
  10. Jump up^ Allinger, Norman (1977). 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. Jump up^ Fernbach, Sidney; Taub, Abraham Haskell (1970). Computers and Their Role in the Physical Sciences . Routledge. ISBN  0-677-14030-4 .
  12. Jump up^ “vol 1, preface”. Reviews in Computational Chemistry . doi : 10.1002 / 9780470125786 .
  13. Jump up^ “The Nobel Prize in Chemistry 1998” .
  14. Jump up^ “The Nobel Prize in Chemistry 2013” (Press release). Royal Swedish Academy of Sciences. October 9, 2013 . Retrieved October 9, 2013 .
  15. Jump up^ Rubenstein, Lester A .; Zauhar, Randy J .; Lanzara, Richard G. (2006). “Molecular dynamics of a biophysical model for β2-adrenergic and G protein-coupled receptor activation” (PDF) . Journal of Molecular Graphics and Modeling . 25 (4): 396. doi : 10.1016 / j.jmgm.2006.02.008. PMID  16574446 .
  16. Jump up^ Rubenstein, Lester A .; Lanzara, Richard G. (1998). “Activation of G protein-coupled receptors entails cysteine ​​modulation of agonist binding”(PDF) . Journal of Molecular Structure: THEOCHEM . 430 : 57. doi :10.1016 / S0166-1280 (98) 90217-2 .