Density functional theory (DFT) is a quantum mechanical theory used in physics and chemistry to investigate the electronic structure (principally the ground state) of many-body systems, in particular atoms, molecules and the condensed phases. DFT is among the most popular and versatile methods available in condensed matter physics, computational physics, and computational chemistry. In the tight binding model, electrons are treated as highly localised, and expanded as single electron wavefunctions in terms of atomic orbitals. ... 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. ... Møller-Plesset perturbation theory (MP) is one of several quantum chemistry post-Hartree-Fock ab initio quantum chemistry methods in the field of computational chemistry. ... 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. ... 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. ... This article or section is in need of attention from an expert on the subject. ... For a generally accessible and less technical introduction to the topic, see Introduction to quantum mechanics. ... A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... For other uses, see Chemistry (disambiguation). ... Electron configuration is the arrangement of electrons in an atom, molecule or other body. ... In physics, the ground state of a quantum mechanical system is its lowest-energy state. ... It has been suggested that Solid state physics be merged into this article or section. ... Computational physics is the study and implementation of numerical algorithms in order to solve problems in physics for which a quantitative theory already exists. ... 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. ...

Hohenberg-Kohn theorems

Although density functional theory has its conceptual roots in the Thomas-Fermi model described below, DFT was put on a firm theoretical footing by the Hohenberg-Kohn theorems (after Pierre Hohenberg and Walter Kohn) (H-K). The first of these demonstrates the existence of a one-to-one mapping between the ground state electron density and the ground state wavefunction of a many-particle system. Further, the second H-K theorem proves that the ground state density minimizes the total electronic energy of the system. The original H-K theorems held only for the ground state in the absence of magnetic field, although they have since been generalized.^[1] A banner on a light pole in the University of California, Santa Barbara, commemorating that Walter Kohn won the Nobel Prize in Chemistry in 1998. ... In mathematics and related technical fields, the term map or mapping is often a synonym for function. ... In physics, the ground state of a quantum mechanical system is its lowest-energy state. ...

The theorems can be extended to the time-dependent domain to derive time-dependent density functional theory (TDDFT), which can be also used to describe excited states. Time-dependent density functional theory (TDDFT) is a quantum mechanical method used in physics and chemistry to investigate the proprieties of many-body systems beyond the ground state structure. ...

The first Hohenberg-Kohn theorem is an existence theorem, stating that the mapping exists. That is, the H-K theorems tell us that the electron density that minimises the energy according to the true total energy functional describes all that can be known about the electronic structure. The H-K theorems do not tell us what the true total energy functional is, only that it exists. In mathematics, the term functional is applied to certain functions. ...

The most common implementation of density functional theory is through the Kohn-Sham method, which maps the properties of the system onto the properties of a system containing non-interacting electrons under a different potential. The kinetic energy functional of such a system of non-interacting electrons is known exactly. The exchange-correlation part of the total energy functional remains unknown, and must be approximated. Another approach, less popular than Kohn-Sham DFT (KS-DFT) but arguably more closely related to the spirit of the original H-K theorems, is orbital-free density functional theory (OFDFT), in which approximate functionals are also used for the kinetic energy of the interacting system. The Kohn-Sham equations are a set of eigenvalue equations within density functional theory (DFT). ...

Description of the theory

Traditional methods in electronic structure theory, in particular Hartree-Fock theory and its descendants, are based on the complicated many-electron wavefunction. The main objective of density functional theory is to replace the many-body electronic wavefunction with the electronic density as the basic quantity. Whereas the many-body wavefunction is dependent on 3N variables, three spatial variables for each of the N electrons, the density is only a function of three variables and is a simpler quantity to deal with both conceptually and practically. 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. ... This article discusses the concept of a wavefunction as it relates to quantum mechanics. ... 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...

Within the framework of Kohn-Sham DFT, the intractable many-body problem of interacting electrons in a static external potential is reduced to a tractable problem of non-interacting electrons moving in an effective potential. The effective potential includes the external potential and the effects of the Coulomb interactions between the electrons, e.g. the exchange and correlation interactions. Modeling the latter two interactions becomes the difficulty within KS DFT. The simplest approximation is the local-density approximation (LDA), which is based upon exact exchange energy for a uniform electron gas, which can be obtained from the Thomas-Fermi model, and from fits to the correlation energy for a uniform electron gas. The Kohn-Sham equations are a set of eigenvalue equations within density functional theory (DFT). ... This article is about the many-body problem in quantum mechanics. ... In physics, a potential may refer to the scalar potential or to the vector potential. ... In physics, the exchange interaction is a quantum mechanical effect which increases or decreases the energy of two or more electrons when their wave functions overlap. ... This article needs to be wikified. ... In physics, the free electron model is a possible model for the behaviour of electrons in a crystal structure. ... Llewellyn Hilleth Thomas born in 1903 died in 1992. ... Fermi redirects here. ...

DFT has been very popular for calculations in solid state physics since the 1970s. In many cases DFT with the local-density approximation gives quite satisfactory results, for solid-state calculations, in comparison to experimental data at relatively low computational costs when compared to other ways of solving the quantum mechanical many-body problem. However, it was not considered accurate enough for calculations in quantum chemistry until the 1990s, when the approximations used in the theory were greatly refined to better model the exchange and correlation interactions. DFT is now a leading method for electronic structure calculations in both fields. Despite the improvements in DFT, there are still difficulties in using density functional theory to properly describe intermolecular interactions, especially van der Waals forces (dispersion); charge transfer excitations; transition states, global potential energy surfaces and some other strongly correlated systems; and in calculations of the band gap in semiconductors. Its poor treatment of dispersion renders DFT unsuitable (at least when used alone) for the treatment of systems which are dominated by dispersion (e.g. interacting noble gas atoms) or where dispersion competes significantly with other effects (e.g. in biomolecules). The development of new DFT methods designed to overcome this problem, by alterations to the functional or by the inclusion of additive terms, is a current research topic. Solid-state physics, the largest branch of condensed matter physics, is the study of rigid matter, or solids. ... Quantum chemistry is a branch of theoretical chemistry, which applies quantum mechanics and quantum field theory to address issues and problems in chemistry. ... In physics, chemistry, and biology, intermolecular forces are forces that act between stable molecules or between functional groups of macromolecules. ... In chemistry, the term van der Waals force originally referred to all forms of intermolecular forces; however, in modern usage it tends to refer to intermolecular forces that deal with forces due to the polarization of molecules. ... This article needs to be wikified. ... This article or section does not adequately cite its references or sources. ... A semiconductor is a material that is an insulator at very low temperature, but which has a sizable electrical conductivity at room temperature. ... This article is about the chemical series. ... A representation of the 3D structure of myoglobin, showing coloured alpha helices. ...

Derivation and formalism

As usual in many-body electronic structure calculations, the nuclei of the treated molecules or clusters are seen as fixed (the Born-Oppenheimer approximation), generating a static external potential V in which the electrons are moving. A stationary electronic state is then described by a wave function satisfying the many-electron Schrödinger equation 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. ... This box:      For a non-technical introduction to the topic, please see Introduction to quantum mechanics. ...

where H is the electronic molecular Hamiltonian, N is the number of electrons and U is the electron-electron interaction. The operators T and U are so-called universal operators as they are the same for any system, while V is system dependent or non-universal. As one can see, the actual difference between a single-particle problem and the much more complicated many-particle problem just arises from the interaction term U. There are many sophisticated methods for solving the many-body Schrödinger equation based on the expansion of the wave function in Slater determinants. While the simplest one is the Hartree-Fock method, more sophisticated approaches are usually categorized as post-Hartree-Fock methods. However, the problem with these methods is the huge computational effort, which makes it virtually impossible to apply them efficiently to larger, more complex systems. The electronic Hamiltonian for a multi-electron molecule in atomic units is: where is the vector position of electron with vector components in Bohr radii, is the charge of fixed nucleus a in units of the elementary charge, is the vector position of nucleus with vector components in Bohr radii. ... This box:      For a non-technical introduction to the topic, please see Introduction to quantum mechanics. ... In quantum mechanics, a Slater determinant (introduced by the American physicist John C. Slater[1]) is an expression describing the wavefunction of a many-fermion system which, by construction, satisfies the Pauli principle by being antisymmetric under an exchange of any pair of fermions. ... 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. ...

Here DFT provides an appealing alternative, being much more versatile as it provides a way to systematically map the many-body problem, with U, onto a single-body problem without U. In DFT the key variable is the particle density which is given by

Hohenberg and Kohn proved in 1964 that the relation expressed above can be reversed, i.e. to a given ground state density it is in principle possible to calculate the corresponding ground state wavefunction . In other words, is a unique functional of , i.e. A banner on a light pole in the University of California, Santa Barbara, commemorating that Walter Kohn won the Nobel Prize in Chemistry in 1998. ... In mathematics, the term functional is applied to certain functions. ...

and consequently all other ground state observables are also functionals of

From this follows, in particular, that also the ground state energy is a functional of

,

where the contribution of the external potential can be written explicitly in terms of the density

The functionals and are called universal functionals while is obviously non-universal, as it depends on the system under study. Having specified a system, i.e. is known, one then has to minimize the functional

with respect to , assuming one has got reliable expressions for and . A successful minimization of the energy functional will yield the ground state density and thus all other ground state observables.

The variational problem of minimizing the energy functional can be solved by applying the Lagrangian method of undetermined multipliers, which was done by Kohn and Sham in 1965. Hereby, one uses the fact that the functional in the equation above can be written as a fictitious density functional of a non-interacting system

where denotes the non-interacting kinetic energy and is an external effective potential in which the particles are moving. Obviously, if is chosen to be

Thus, one can solve the so-called Kohn-Sham equations of this auxiliary non-interacting system

which yields the orbitals that reproduce the density of the original many-body system In chemistry, a molecular orbital is a region in which an electron may be found in a molecule. ...

The effective single-particle potential can be written in more detail as

where the second term denotes the so-called Hartree term describing the electron-electron Coulomb repulsion, while the last term is called the exchange correlation potential. Here, includes all the many-particle interactions. Since the Hartree term and depend on , which depends on the , which in turn depend on , the problem of solving the Kohn-Sham equation has to be done in a self-consistent (i.e. iterative) way. Usually one starts with an initial guess for , then calculates the corresponding and solves the Kohn-Sham equations for the . From these one calculates a new density and starts again. This procedure is then repeated until convergence is reached. The word iteration is sometimes used in everyday English with a meaning virtually identical to repetition. ...

Approximations (Exchange-Correlation functionals)

The major problem with DFT is that the exact functionals for exchange and correlation are not known except for the free electron gas. However, approximations exist which permit the calculation of certain physical quantities quite accurately. In physics the most widely used approximation is the local-density approximation (LDA), where the functional depends only on the density at the coordinate where the functional is evaluated: The local-density approximation, (LDA), is a density functional model in physics, which approximates the exchange and correlation (XC) energy. ...

The local spin-density approximation (LSDA) is a straightforward generalization of the LDA to include electron spin: In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is the motion of its center of mass about an external point. ...

Highly accurate formulae for the exchange-correlation energy density have been constructed from quantum Monte Carlo simulations of a free electron model.^[2] This article or section is in need of attention from an expert on the subject. ... In solid-state physics, the free electron model is a simple model for the behaviour of valence electrons in a crystal structure of a metallic solid. ...

Generalized gradient approximations (GGA) are still local but also take into account the gradient of the density at the same coordinate: For other uses, see Gradient (disambiguation). ...

Using the latter (GGA) very good results for molecular geometries and ground state energies have been achieved.

Potentially more accurate than the GGA functionals are meta-GGA functions. These functionals include a further term in the expansion, depending on the density, the gradient of the density and the Laplacian (second derivative) of the density. In vector calculus, the Laplace operator or Laplacian is a differential operator equal to the sum of all the unmixed second partial derivatives of a dependent variable. ... In mathematics, the derivative is one of the two central concepts of calculus. ...

Difficulties in expressing the exchange part of the energy can be relieved by including a component of the exact exchange energy calculated from Hartree-Fock theory. Functionals of this type are known as hybrid functionals. 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. ...

Generalizations to include magnetic fields

The DFT formalism above breaks down in the presence of a vector potential, i.e. a magnetic field. In such a case, the one-to-one mapping between electron density and external potential breaks down. Generalizations to include the effects of magnetic fields have led to two different theories: current density functional theory and magnetic field functional theory. In both these theories, the functional used for the exchange and correlation must be generalized to include more than just the electron density. In current density functional theory, developed by Vignale and Rasolt, the functionals become dependent on both the electron density and the current density. In magnetic field density functional theory, developed by Salsbury, Grayce and Harris, the functionals depend on the electron density and the magnetic field, and the functional form can depend on the form of the magnetic field. In both of these theories it has been difficult to develop functionals beyond their equivalent to LDA, which are also readily implementable computationally. For the indie-pop band, see The Magnetic Fields. ...

Applications

C₆₀ with isosurface of ground state electron density as calculated with DFT

In practice, Kohn-Sham theory can be applied in several distinct ways depending on what is being investigated. In solid state calculations, the local density approximations are still commonly used along with plane wave basis sets, as an electron gas approach is more appropriate electrons delocalised through an infinite solid. In molecular calculations, however, more sophisticated functionals are needed, and a huge variety of exchange-correlation functionals have been developed for chemical applications. Some of these are inconsistent with the uniform electron gas approximation, however, they must reduce to LDA in the electron gas limit. Among physicists, probably the most widely used functional is the revised Perdew-Burke-Ernzerhof exchange model (a direct generalized-gradient parametrization of the free electron gas with no free parameters); however, this is not sufficiently calorimetrically accurate for gas-phase molecular calculations. In the chemistry community, one popular functional is known as BLYP (from the name Becke for the exchange part and Lee, Yang and Parr for the correlation part). Even more widely used is B3LYP [3-5] which is a hybrid functional in which the exchange energy, in this case from Becke's exchange functional, is combined with the exact energy from Hartree-Fock theory. Along with the component exchange and correlation funсtionals, three parameters define the hybrid functional, specifying how much of the exact exchange is mixed in. The adjustable parameters in hybrid functionals are generally fitted to a 'training set' of molecules. Unfortunately, although the results obtained with these functionals are usually sufficiently accurate for most applications, there is no systematic way of improving them (in contrast to some of the traditional wavefunction-based methods like configuration interaction or coupled cluster theory). Hence in the current DFT approach it is not possible to estimate the error of the calculations without comparing them to other methods or experiments. Zirconocene with an isosurface showing areas of the molecule susceptible to electrophilic attack. ... In the physics of wave propagation (especially electromagnetic waves), a plane wave (also spelled planewave) is a constant-frequency wave whose wavefronts (surfaces of constant amplitude and phase) are infinite parallel planes normal to the propagation direction. ... In physics, the free electron model is a possible model for the behaviour of electrons in a crystal structure. ... This article discusses the concept of a wavefunction as it relates to quantum mechanics. ... 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. ...

For molecular applications, in particular for hybrid functionals, Kohn-Sham DFT methods are usually implemented just like Hartree-Fock itself, 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. ...

Thomas-Fermi model

The predecessor to density functional theory was the Thomas-Fermi model, developed by Thomas and Fermi in 1927. They used a statistical model to approximate the distribution of electrons in an atom. The mathematical basis postulated that electrons are distributed uniformly in phase space with two electrons in every h³ of volume^[3]. For each element of coordinate space volume d³r we can fill out a sphere of momentum space up to the fermi momentum p_f^[4] Llewellyn Hilleth Thomas born in 1903 died in 1992. ... Fermi redirects here. ...

equating the number of electrons in coordinate space to that in phase space gives:

solving for p_f and substituting in the classical kinetic energy formula then leads directly to a kinetic energy represented as a functional of the electron density: The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. ... In mathematics, the term functional is applied to certain functions. ...

As such, they were able to calculate the energy of an atom using this kinetic energy functional combined with the classical expressions for the nuclear-electron and electron-electron interactions (which can both also be represented in terms of the electron density).

Although this was an important first step, the Thomas-Fermi equation's accuracy is limited because the resulting kinetic energy functional is only approximate, and because the method does not attempt to represent the exchange energy of an atom as a conclusion of the Pauli principle. An exchange energy functional was added by Dirac in 1928. Exchange interaction is the quantum mechanical effect of increasing or decreasing the energy of two or more fermions when their wave functions overlap. ... The Pauli exclusion principle, commonly referred to simply as the exclusion principle, is a quantum mechanical principle formulated by Wolfgang Pauli in 1925, which states that no two identical fermions may occupy the same quantum state. ... Paul Adrien Maurice Dirac, OM, FRS (IPA: [dɪræk]) (August 8, 1902 – October 20, 1984) was a British theoretical physicist and a founder of the field of quantum physics. ...

However, the Thomas-Fermi-Dirac theory remained rather inaccurate for most applications. The largest source of error was in the representation of the kinetic energy, followed by the errors in the exchange energy, and due to the complete neglect of electron correlation. Electronic correlation refers to the interaction between electrons in a quantum system whose electronic structure is being considered. ...

Teller (1962) showed that Thomas-Fermi theory cannot describe molecular bonding. This can be overcome by improving the kinetic energy functional. Edward Teller (original Hungarian name Teller Ede) (January 15, 1908 – September 9, 2003) was a Hungarian-born American theoretical physicist, known colloquially as the father of the hydrogen bomb, even though he did not care for the title. ...

The kinetic energy functional can be improved by adding the Weizsäcker (1935) correction: Carl Friedrich von Weizsäcker, 1993 Carl Friedrich Freiherr (Baron) von Weizsäcker (28 June 1912, Kiel – 28 April 2007, Söcking near Starnberg) was a German physicist and philosopher. ...

Software supporting DFT

What is ABINIT ? ABINIT is a package whose main program allows one to find the total energy, charge density and electronic structure of systems made of electrons and nuclei (molecules and periodic solids) within Density Functional Theory (DFT), using pseudopotentials and a planewave basis. ... The Amsterdam Density Functional program (ADF) is software for first-principles electronic structure calculations making use of Density functional theory. ... Atomistix Virtual NanoLab is a user-friendly software package for simulating and analysing the properties of nanoscale devices. ... CADPAC, the Cambridge Analytic Derivatives Package, is a suite of programs for ab initio computational chemistry calculations. ... CASTEP is a commercial software package which uses density functional theory with a plane wave basis set to calculate electronic properties of solids from first principles. ... Da Capo is a musical term in Italian, meaning from the beginning. ... 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. ... EXCITING is a state-of-the-art full-potential linearized augmented plane wave (FP-LAPW) code which uses quantum mechanics, specifically density functional theory (DFT), to determine the physical properties of solids and molecules. ... 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. ... GAUSSIAN is a computational chemistry software program, first written by John Pople. ... keels is bent and she has a big nose which she picks every day. ... 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. ... A parsec is the distance from the Earth to an astronomical object which has a parallax angle of one arcsecond. ... PC GAMESS is a quantum computational chemistry program for Intel-compatible x86, AMD64/EM64T processors based on GAMESS (US) sources. ... 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. ... PWscf (Plane-Wave Self-Consistent Field) is a set of programs for electronic structure calculations within density functional theory and density functional perturbation theory, using plane wave basis sets and pseudopotentials. ... Q-Chem is a computational chemistry software program. ... SIESTA (Spanish Initiative for Electronic Simulations with Thousands of Atoms) is an original method and a software implementation for performing electronic structure calculations and ab initio molecular dynamics simulations of molecules and solids. ... Socorro is a Spanish word that means aid, by providing help or relief. ... Spartan is a molecular modelling application from Wavefunction, Inc. ... TURBOMOLE is a Quantum chemistry ab initio program package, developed at the group of Prof. ... The Vienna Ab-initio Simulation Package, better known as VASP (or alternatively VAMP), is a package for performing ab-initio quantum mechanical molecular dynamics (MD) using pseudopotentials and a plane wave basis set. ...

See also

• Molecule
• Molecular modeling
• Basis set (chemistry)
• Quantum chemistry
• Software for molecular mechanics modeling
• Kohn-Sham equations

3D (left and center) and 2D (right) representations of the terpenoid molecule atisane. ... The backbone dihedral angles are included in the molecular model of a protein. ... In modern computational chemistry, quantum chemical calculations are typically performed within a finite set of basis functions. ... Quantum chemistry is a branch of theoretical chemistry, which applies quantum mechanics and quantum field theory to address issues and problems in chemistry. ... Min - Optimization, MD - Molecular Dynamics, MC - Monte Carlo, QM - Quantum mechanics. ... The Kohn-Sham equations are a set of eigenvalue equations within density functional theory (DFT). ...

Books on DFT

• R. Dreizler, E. Gross, Density Functional Theory (Plenum Press, New York, 1995).
• C. Fiolhais, F. Nogueira, M. Marques (eds.), A Primer in Density Functional Theory (Springer-Verlag, 2003). [3]
• Kohanoff, J., Electronic Structure Calculations for Solids and Molecules: Theory and Computational Methods (Cambridge University Press, 2006).
• W. Koch, M. C. Holthausen, A Chemist's Guide to Density Functional Theory (Wiley-VCH, Weinheim, ed. 2, 2002).
• R. G. Parr, W. Yang, Density-Functional Theory of Atoms and Molecules (Oxford University Press, New York, 1989).
• N.H. March, Electron density theory of atomes and molectules, Academic Press, ISBN 0-12-470525-1

Key papers

• L.H. Thomas, The calculation of atomic fields, Proc. Camb. Phil. Soc, 23 542-548
• P. Hohenberg and W. Kohn, Phys. Rev. 136 (1964) B864
• W. Kohn and L. J. Sham, Phys. Rev. 140 (1965) A1133
• A. D. Becke, J. Chem. Phys. 98 (1993) 5648
• C. Lee, W. Yang, and R. G. Parr, Phys. Rev. B 37 (1988) 785
• P. J. Stephens, F. J. Devlin, C. F. Chabalowski, and M. J. Frisch, J. Phys. Chem. 98 (1994) 11623
• K. Burke, J. Werschnik, and E. K. U. Gross, Time-dependent density functional theory: Past, present, and future. J. Chem. Phys. 123, 062206 (2005). OAI: arXiv.org:cond-mat/0410362.

References

The American Physical Society was founded in 1899 and is the worlds second largest organization of physicists. ... A digital object identifier (or DOI) is a standard for persistently identifying a piece of intellectual property on a digital network and associating it with related data, the metadata, in a structured extensible way. ... A digital object identifier (or DOI) is a standard for persistently identifying a piece of intellectual property on a digital network and associating it with related data, the metadata, in a structured extensible way. ...

External links

• Walter Kohn, Nobel Laureate Freeview video interview with Walter on his work developing density functional theory by the Vega Science Trust.
• Klaus Capelle, A bird's-eye view of density-functional theory
• Walter Kohn, Nobel Lecture