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 efficient computer programs to calculate the structures and properties of molecules and solids it is necessary because apart from relatively recent results concerning the hydrogen molecular ion dihydrogen cation see references therein for more details the quantum manybody problem cannot be solved analytically much less in closed form while computational results normally complement the information obtained by chemical experiments it can in some cases predict hitherto unobserved chemical phenomena it is widely used in the design of new drugs and materials examples of such properties are structure ie the expected positions of the constituent atoms absolute and relative interaction energies electronic charge density distributions dipoles and higher multipole moments vibrational frequencies reactivity or other spectroscopic quantities and cross sections for collision with other particles the methods used cover both static and dynamic situations in all cases the computer time and other resources such as memory and disk space increase rapidly with the size of the system being studied that system can be one molecule a group of molecules or a solid computational chemistry methods range from very approximate to highly accurate the latter are usually feasible for small systems only ab initio methods are based entirely on quantum mechanics and basic physical constants other methods are called empirical or semiempirical because they use additional empirical parameters both ab initio and semiempirical approaches involve approximations these range from simplified forms of the firstprinciples 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 bornoppenheimer approximation which greatly simplifies the underlying schrdinger equation by assuming that the nuclei remain 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 tractable in some cases the details of electronic structure are less important than the longtime phase space behavior of molecules this is the case in conformational studies of proteins and proteinligand binding thermodynamics classical approximations to the potential energy surface are used as they are computationally less intensive than electronic calculations to enable longer simulations of molecular dynamics furthermore cheminformatics uses even more empirical and computationally cheaper methods like machine learning based on physicochemical properties one typical problem in cheminformatics is to predict the binding affinity of drug molecules to a given target 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 the books that were influential in the early development of computational quantum chemistry include linus pauling and e bright wilsons 1935 introduction to quantum mechanics with applications to chemistry eyring walter and kimballs 1944 quantum chemistry heitlers 1945 elementary wave mechanics with applications to quantum chemistry and later coulsons 1952 textbook valence 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 began to be a realizable objective in the early 1950s the first semiempirical atomic orbital calculations were performed theoretical chemists became extensive users of the early digital computers one major advance came with the 1951 paper in reviews of modern physics by clemens c j roothaan in 1951 largely on the lcao mo approach linear combination of atomic orbitals molecular orbitals for many years the secondmost cited paper in that journal a very detailed account of such use in the united kingdom is given by smith and sutcliffe in 1964 hckel method calculations using a simple linear combination of atomic orbitals lcao method to determine electron energies of molecular orbitals of electrons in conjugated hydrocarbon systems of molecules ranging in complexity from butadiene and benzene to ovalene were generated on computers at berkeley and oxford in the early 1970s efficient 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 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 the journal of computational chemistry was first published in 1980 computational chemistry has featured in several nobel prize awards most notably in 1998 and 2013 walter kohn for his development of the densityfunctional theory and john pople for his development of computational methods in quantum chemistry received the 1998 nobel prize in chemistry fields of application 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 computational chemistry has two different aspects computational studies used 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 used to predict the possibility of so far entirely unknown molecules or to explore reaction mechanisms not readily studied via experiments 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 or more accurate quantum chemical methods to find stationary points on the energy surface 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 quantitative structureproperty relationship qspr and quantitative structureactivity 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 nonrelativistic schrdinger equation with relativistic corrections added although some progress has been made in solving the fully relativistic dirac equation in principle it is possible to solve the schrdinger equation in either its timedependent or timeindependent form as appropriate for the problem in hand in practice this is not possible except for very small systems therefore a great number of approximate methods strive to achieve the best tradeoff 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 relativisticinclusive methods this complicates the study of molecules interacting with high atomic mass unit atoms such as transitional metals and their catalytic properties present algorithms in computational chemistry can routinely calculate the properties of small molecules that contain up to about 40 electrons with errors for energies less than a few kjmol for geometries bond lengths can be predicted within a few picometres and bond angles within 05 degrees 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 semiempirical approximate methods even larger molecules are treated by classical mechanics methods that use what are called molecular mechanics mm in qmmm 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 surface created from the total energy ie the electronic energy plus the 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 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 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 the search away from it if the experimenter is looking solely for local minima and transition structures the total energy is determined by approximate solutions of the timedependent schrdinger equation usually with no relativistic terms included and by making use of the bornoppenheimer approximation which allows for the separation of electronic and nuclear motions thereby simplifying the schrdinger 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 treat electrons and nuclei on a common footing density functional methods and semiempirical 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 ab initio quantum chemistry methods the programs used in computational chemistry are based on many different quantumchemical methods that solve the molecular schrdinger equation associated with the molecular hamiltonian methods that do not include any empirical or semiempirical 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 must be used 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 within the mathematical andor physical approximations made diagram illustrating various ab initio electronic structure methods in terms of energy spacings are not to scale the simplest type of ab initio electronic structure calculation is the hartreefock method hf an extension of molecular orbital theory in which the correlated electronelectron 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 hartreefock limit many types of calculations termed posthartreefock methods begin with a hartreefock calculation and subsequently correct for electronelectron repulsion referred to also as electronic correlation as these methods are pushed to the limit they approach the exact solution of the nonrelativistic schrdinger equation 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 hartreefock 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 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 chemical accuracy is the accuracy required to make realistic chemical predictions and is generally considered to be 1kcalmol or 4kjmol to reach that accuracy in an economic way it is necessary to use a series of posthartreefock methods and combine the results these methods are called quantum chemistry composite methods density functional methods density functional theory 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 in dft the total energy is expressed in terms of the total oneelectron 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 density functional exchange functional with the hartreefock exchange term and are termed hybrid functional methods semiempirical methods semiempirical quantum chemistry methods semiempirical quantum chemistry methods are based on the hartreefock method formalism but make many approximations and obtain some parameters from empirical data they were very important in computational chemistry from the 60s to the 90s especially for treating large molecules where the full hartreefock method without the approximations were too costly the use of empirical parameters appears to allow some inclusion of correlation effects into the methods primitive semiempirical methods were designed even before where the twoelectron part of the hamiltonian is not explicitly included for electron systems this was the hckel method proposed by erich hckel and for all valence electron systems the extended hckel method proposed by roald hoffmann sometimes hckel methods are referred to as completely emprirical because they do not derive from a hamiltonian molecular mechanics molecular mechanics in many cases large molecular systems can be modeled successfully while avoiding quantum mechanical calculations entirely molecular mechanics simulations for example use one 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 have any relevance when describing other molecules of the same class these methods can be applied to proteins and other large biological molecules and allow studies of the approach and interaction docking of potential drug molecules methods for solids 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 semiempirical calculations yield orbital energies therefore they can be applied to band structure calculations since it is timeconsuming to calculate the energy for a molecule it is even more timeconsuming to calculate them for the entire list of points in the brillouin zone chemical dynamics once the electronic and nuclear variables are separated within the bornoppenheimer representation in the timedependent approach the wave packet corresponding to the nuclear degrees of freedom is propagated via the time evolution operator physics associated to the timedependent schrdinger equation for the full molecular hamiltonian in the complementary energydependent approach the timeindependent schrdinger equation is solved using the scattering theory formalism the potential representing 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 to the molecular geometry are the split operator technique the chebyshev real polynomial the multiconfiguration timedependent hartree method mctdh the semiclassical method molecular dynamics molecular dynamics molecular dynamics md use either quantum mechanics molecular mechanics or a mixture of both to calculate forces which are then used to solve newtons laws of motion to examine the timedependent behaviour of systems the result of a molecular dynamics simulation is a trajectory that describes how the position and velocity of particles varies with time quantum mechanicsmolecular mechanics qmmm qmmm qmmm 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 pairs and the valence bond model bader has demonstrated that these empirically useful chemistry concepts can be related to the topology of the observable charge density distribution whether measured or calculated from a quantum mechanical wavefunction qtaim analysis of molecular wavefunctions is implemented for example in the aimall software package software packages many selfsufficient computational chemistry software packages exist some include many methods covering a wide range while others concentrate on a very specific range or even on one method details of most of them can be found in biomolecular modelling programs proteins nucleic acid molecular mechanics programs quantum chemistry and solid state physics software supporting several methods molecular design software semiempirical programs valence bond programs chemistry portal physics portal 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 modelling molecular modeling on gpus monte carlo molecular modeling protein dynamics scientific computing statistical mechanics solvent models notes and references bibliography c j cramer essentials of computational chemistry john wiley sons 2002 t clark a handbook of computational chemistry wiley new york 1985 r dronskowski computational chemistry of solid state materials wileyvch 2005 ak hartmann practical guide to computer simulations world scientific 2009 f jensen introduction to computational chemistry john wiley sons 1999 ki ramachandran g deepa and krishnan namboori pk computational chemistry and molecular modeling principles and applications springerverlag gmbh isbn9783540773023 d rogers computational chemistry using the pc 3rd edition john wiley sons 2003 p v r schleyer editorinchief encyclopedia of computational chemistry wiley 1998 isbn047196588x d sherrill notes on quantum mechanics and computational chemistry j simons an introduction to theoretical chemistry cambridge 2003 isbn9780521530477 a szabo ns ostlund modern quantum chemistry mcgrawhill 1982 d young computational chemistry a practical guide for applying techniques to real world problems john wiley sons 2001 d youngs introduction to computational chemistry lewars errol g 2011 computational chemistry heidelberg springer doi1010079789048138623 isbn9789048138609 specialized journals on computational chemistry reviews in computational chemistry journal of computational chemistry journal of chemical information and modeling journal of computeraided molecular design journal of chemical information and modeling journal of chemical theory and computation computational and theoretical polymer science computational and theoretical chemistry journal of theoretical and computational chemistry journal of cheminformatics journal of computer chemistry japan annual reports in computational chemistry computers chemical engineering journal of chemical software molecular informatics journal of computer aided chemistry theoretical chemistry accounts wikimedia commons has media related to computational chemistry nist computational chemistry comparison and benchmark database contains a database of thousands of computational and experimental results for hundreds of systems american chemical society division of computers in chemistry american chemical society 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