Density functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure of many-body systems, in particular atoms, molecules, and the condensed phases. Using this theory, the properties of a many-electron system can be determined by using functionals, i.e. functions of another function. In the case of DFT, these are functionals of the spatially dependent electron density. DFT is among the most popular and versatile methods available in condensed-matter physics, computational physics, and computational chemistry.
In solid-state physics, the electronic band structure of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have.
PLATO is a suite of programs for electronic structure calculations. It receives its name from the choice of basis set used to expand the electronic wavefunctions.
Electronic correlation is the interaction between electrons in the electronic structure of a quantum system. The correlation energy is a measure of how much the movement of one electron is influenced by the presence of all other electrons.
Koopmans' theorem states that in closed-shell Hartree–Fock theory (HF), the first ionization energy of a molecular system is equal to the negative of the orbital energy of the highest occupied molecular orbital (HOMO). This theorem is named after Tjalling Koopmans, who published this result in 1934.
SIESTA is an original method and its computer program implementation, to efficiently perform electronic structure calculations and ab initio molecular dynamics simulations of molecules and solids. SIESTA uses strictly localized basis sets and the implementation of linear-scaling algorithms. Accuracy and speed can be set in a wide range, from quick exploratory calculations to highly accurate simulations matching the quality of other approaches, such as the plane-wave and all-electron methods.
Octopus is a software package for performing Kohn–Sham density functional theory (DFT) and time-dependent density functional theory (TDDFT) calculations.
The Kohn-Sham equations are a set of mathematical equations used in quantum mechanics to simplify the complex problem of understanding how electrons behave in atoms and molecules. They introduce fictitious non-interacting electrons and use them to find the most stable arrangement of electrons, which helps scientists understand and predict the properties of matter at the atomic and molecular scale.
Spartan is a molecular modelling and computational chemistry application from Wavefunction. It contains code for molecular mechanics, semi-empirical methods, ab initio models, density functional models, post-Hartree–Fock models, and thermochemical recipes including G3(MP2) and T1. Quantum chemistry calculations in Spartan are powered by Q-Chem.
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 electron correlation effects into the methods.
Car–Parrinello molecular dynamics or CPMD refers to either a method used in molecular dynamics or the computational chemistry software package used to implement this method.
Hybrid functionals are a class of approximations to the exchange–correlation energy functional in density functional theory (DFT) that incorporate a portion of exact exchange from Hartree–Fock theory with the rest of the exchange–correlation energy from other sources. The exact exchange energy functional is expressed in terms of the Kohn–Sham orbitals rather than the density, so is termed an implicit density functional. One of the most commonly used versions is B3LYP, which stands for "Becke, 3-parameter, Lee–Yang–Parr".
In density functional theory (DFT), the Harris energy functional is a non-self-consistent approximation to the Kohn–Sham density functional theory. It gives the energy of a combined system as a function of the electronic densities of the isolated parts. The energy of the Harris functional varies much less than the energy of the Kohn–Sham functional as the density moves away from the converged density.
CONQUEST is a linear scaling, or O(N), density functional theory (DFT) electronic structure open-source code. The code is designed to perform DFT calculations on very large systems containing many thousands of atoms. It can be run at different levels of precision ranging from ab initio tight binding up to full DFT with plane wave accuracy. It has been applied to the study of three-dimensional reconstructions formed by Ge on Si(001), containing over 20,000 atoms. Tests on the UK's national supercomputer HECToR in 2009 demonstrated the capability of the code to perform ground-state calculations on systems of over 1,000,000 atoms.
Minnesota Functionals (Myz) are a group of highly parameterized approximate exchange-correlation energy functionals in density functional theory (DFT). They are developed by the group of Prof. Donald Truhlar at the University of Minnesota. These functionals are based on the meta-GGA approximation, i.e. they include terms that depend on the kinetic energy density, and are all based on complicated functional forms parametrized on high-quality benchmark databases. These functionals can be used for traditional quantum chemistry and solid-state physics calculations. The Myz functionals are widely used and tested in the quantum chemistry community.
In computational chemistry, a solvent model is a computational method that accounts for the behavior of solvated condensed phases. Solvent models enable simulations and thermodynamic calculations applicable to reactions and processes which take place in solution. These include biological, chemical and environmental processes. Such calculations can lead to new predictions about the physical processes occurring by improved understanding.
The Strictly-Correlated-Electrons (SCE) density functional theory approach, originally proposed by Michael Seidl, is a formulation of density functional theory, alternative to the widely used Kohn-Sham DFT, especially aimed at the study of strongly-correlated systems. The essential difference between the two approaches is the choice of the auxiliary system. In Kohn-Sham DFT this system is composed by non-interacting electrons, for which the kinetic energy can be calculated exactly and the interaction term has to be approximated. In SCE DFT, instead, the starting point is totally the opposite one: the auxiliary system has infinite electronic correlation and zero kinetic energy.
In mathematics, the Rayleigh theorem for eigenvalues pertains to the behavior of the solutions of an eigenvalue equation as the number of basis functions employed in its resolution increases. Rayleigh, Lord Rayleigh, and 3rd Baron Rayleigh are the titles of John William Strutt, after the death of his father, the 2nd Baron Rayleigh. Lord Rayleigh made contributions not just to both theoretical and experimental physics, but also to applied mathematics. The Rayleigh theorem for eigenvalues, as discussed below, enables the energy minimization that is required in many self-consistent calculations of electronic and related properties of materials, from atoms, molecules, and nanostructures to semiconductors, insulators, and metals. Except for metals, most of these other materials have an energy or a band gap, i.e., the difference between the lowest, unoccupied energy and the highest, occupied energy. For crystals, the energy spectrum is in bands and there is a band gap, if any, as opposed to energy gap. Given the diverse contributions of Lord Rayleigh, his name is associated with other theorems, including Parseval's theorem. For this reason, keeping the full name of "Rayleigh Theorem for Eigenvalues" avoids confusions.
The linearized augmented-plane-wave method (LAPW) is an implementation of Kohn-Sham density functional theory (DFT) adapted to periodic materials. It typically goes along with the treatment of both valence and core electrons on the same footing in the context of DFT and the treatment of the full potential and charge density without any shape approximation. This is often referred to as the all-electron full-potential linearized augmented-plane-wave method (FLAPW). It does not rely on the pseudopotential approximation and employs a systematically extendable basis set. These features make it one of the most precise implementations of DFT, applicable to all crystalline materials, regardless of their chemical composition. It can be used as a reference for evaluating other approaches.
The FLEUR code is an open-source scientific software package for the simulation of material properties of crystalline solids, thin films, and surfaces. It implements Kohn-Sham density functional theory (DFT) in terms of the all-electron full-potential linearized augmented-plane-wave method. With this, it is a realization of one of the most precise DFT methodologies. The code has the common features of a modern DFT simulation package. In the past, major applications have been in the field of magnetism, spintronics, quantum materials, e.g. in ultrathin films, complex magnetism like in spin spirals or magnetic Skyrmion lattices, and in spin-orbit related physics, e.g. in graphene and topological insulators.
