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95 relations: Ab initio quantum chemistry methods, Ansatz, Atom, Atomic orbital, Basis set (chemistry), Bogoliubov transformation, Bohr model, Born–Oppenheimer approximation, Boson, Calculus of variations, Central field approximation, Clemens C. J. Roothaan, Computational chemistry, Computational physics, Configuration interaction, Configuration state function, Coulomb operator, Coulomb's law, Density functional theory, Determinant, DIIS, Douglas Hartree, Eigendecomposition of a matrix, Electronic correlation, Exchange operator, Expected value, Fermion, Fixed-point iteration, Fock matrix, Gaussian orbital, George G. Hall, Gram–Schmidt process, Ground state, Group theory, Hamiltonian (quantum mechanics), Hartree equation, Hartree product, Hybrid functional, Hydrogen atom, Identical particles, Identity matrix, Iteration, Iterative method, John C. Slater, John Pople, Journal of Applied Physics, Koopmans' theorem, Linear combination, Linear combination of atomic orbitals, List of quantum chemistry and solid-state physics software, ..., London dispersion force, Many-body problem, Møller–Plesset perturbation theory, Mean field theory, Modern valence bond theory, Molecular Hamiltonian, Molecular orbital, Molecular physics, Momentum, Moseley's law, Multi-configurational self-consistent field, Nuclear physics, Numerical stability, Old quantum theory, Open shell, Orbital overlap, Orthogonality, Particle statistics, Pauli exclusion principle, Permanent (mathematics), Perturbation theory, Post-Hartree–Fock, Principal quantum number, Quadratic configuration interaction, Quantum chemistry, Quantum defect, Quantum number, Reinhart Ahlrichs, Restricted open-shell Hartree–Fock, Robert Bruce Lindsay, Roothaan equations, Schrödinger equation, Screening effect, Slater determinant, Slater-type orbital, Special relativity, Stationary state, Unitary transformation, Unrestricted Hartree–Fock, Variational method (quantum mechanics), Variational Monte Carlo, Variational principle, Vladimir Fock, Wave function, X-ray. Expand index (45 more) »
Ab initio quantum chemistry methods
Ab initio quantum chemistry methods are computational chemistry methods based on quantum chemistry.
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Ansatz
In physics and mathematics, an ansatz (meaning: "initial placement of a tool at a work piece", plural ansätze; or ansatzes) is an educated guessIn his book on "The Nature of Mathematical Modelling", Neil Gershenfeld introduces ansatz, with interpretation "a trial answer", to be an important technique for solving differential equations.
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Atom
An atom is the smallest constituent unit of ordinary matter that has the properties of a chemical element.
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Atomic orbital
In quantum mechanics, an atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom.
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Basis set (chemistry)
A basis set in theoretical and computational chemistry is a set of functions (called basis functions) that is used to represent the electronic wave function in the Hartree–Fock method or density-functional theory in order to turn the partial differential equations of the model into algebraic equations suitable for efficient implementation on a computer.
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Bogoliubov transformation
In theoretical physics, the Bogoliubov transformation, also known as Bogoliubov-Valatin transformation, were independently developed in 1958 by Nikolay Bogolyubov and John George Valatin for finding solutions of BCS theory in a homogeneous system.
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Bohr model
In atomic physics, the Rutherford–Bohr model or Bohr model or Bohr diagram, introduced by Niels Bohr and Ernest Rutherford in 1913, depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus—similar to the structure of the Solar System, but with attraction provided by electrostatic forces rather than gravity.
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Born–Oppenheimer approximation
In quantum chemistry and molecular physics, the Born–Oppenheimer (BO) approximation is the assumption that the motion of atomic nuclei and electrons in a molecule can be separated.
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Boson
In quantum mechanics, a boson is a particle that follows Bose–Einstein statistics.
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Calculus of variations
Calculus of variations is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers.
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Central field approximation
In atomic physics, the central field approximation for many-electron atoms takes the combined electric fields of the nucleus and all the electrons acting on any of the electrons to be radial and to be the same for all the electrons in the atom.
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Clemens C. J. Roothaan
Clemens C.J. Roothaan (born in August 29, 1918 in Nijmegen) is a Dutch physicist.
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Computational chemistry
Computational chemistry is a branch of chemistry that uses computer simulation to assist in solving chemical problems.
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Computational physics
Computational physics is the study and implementation of numerical analysis to solve problems in physics for which a quantitative theory already exists.
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Configuration interaction
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.
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Configuration state function
In quantum chemistry, a configuration state function (CSF), is a symmetry-adapted linear combination of Slater determinants.
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Coulomb operator
The Coulomb operator, named after Charles-Augustin de Coulomb, is a quantum mechanical operator used in the field of quantum chemistry.
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Coulomb's law
Coulomb's law, or Coulomb's inverse-square law, is a law of physics for quantifying the amount of force with which stationary electrically charged particles repel or attract each other.
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Density functional theory
Density functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (principally the ground state) of many-body systems, in particular atoms, molecules, and the condensed phases.
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Determinant
In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.
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DIIS
DIIS (direct inversion in the iterative subspace or direct inversion of the iterative subspace), also known as Pulay mixing, is an extrapolation technique.
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Douglas Hartree
Douglas Rayner Hartree PhD, FRS (27 March 1897 – 12 February 1958) was an English mathematician and physicist most famous for the development of numerical analysis and its application to the Hartree–Fock equations of atomic physics and the construction of a differential analyser using Meccano.
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Eigendecomposition of a matrix
In linear algebra, eigendecomposition or sometimes spectral decomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors.
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Electronic correlation
Electronic correlation is the interaction between electrons in the electronic structure of a quantum system.
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Exchange operator
In quantum mechanics, the exchange operator \hat, also known as permutation operator, is a quantum mechanical operator that acts on states in Fock space.
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Expected value
In probability theory, the expected value of a random variable, intuitively, is the long-run average value of repetitions of the experiment it represents.
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Fermion
In particle physics, a fermion is a particle that follows Fermi–Dirac statistics.
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Fixed-point iteration
In numerical analysis, fixed-point iteration is a method of computing fixed points of iterated functions.
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Fock matrix
In the Hartree–Fock method of quantum mechanics, the Fock matrix is a matrix approximating the single-electron energy operator of a given quantum system in a given set of basis vectors.
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Gaussian orbital
In computational chemistry and molecular physics, Gaussian orbitals (also known as Gaussian type orbitals, GTOs or Gaussians) are functions used as atomic orbitals in the LCAO method for the representation of electron orbitals in molecules and numerous properties that depend on these.
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George G. Hall
George Garfield Hall (born 5 March 1925-6th May 2018), is a Northern Irish applied mathematician known for original work and contributions to the field of Quantum chemistry.
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Gram–Schmidt process
In mathematics, particularly linear algebra and numerical analysis, the Gram–Schmidt process is a method for orthonormalising a set of vectors in an inner product space, most commonly the Euclidean space Rn equipped with the standard inner product.
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Ground state
The ground state of a quantum mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system.
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Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.
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Hamiltonian (quantum mechanics)
In quantum mechanics, a Hamiltonian is an operator corresponding to the total energy of the system in most of the cases.
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Hartree equation
In 1927, a year after the publication of the Schrödinger equation, Hartree formulated what are now known as the Hartree equations for atoms, using the concept of self-consistency that Lindsay had introduced in his study of many electron systems in the context of Bohr theory.
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Hartree product
The Hartree product is a system (many-particle) wavefunction, given as a combination of wavefunctions of the individual particle wavefunctions.
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Hybrid functional
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 (ab initio or empirical).
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Hydrogen atom
A hydrogen atom is an atom of the chemical element hydrogen.
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Identical particles
Identical particles, also called indistinguishable or indiscernible particles, are particles that cannot be distinguished from one another, even in principle.
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Identity matrix
In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere.
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Iteration
Iteration is the act of repeating a process, to generate a (possibly unbounded) sequence of outcomes, with the aim of approaching a desired goal, target or result.
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Iterative method
In computational mathematics, an iterative method is a mathematical procedure that uses an initial guess to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones.
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John C. Slater
John Clarke Slater (December 22, 1900 – July 25, 1976) was a noted American physicist who made major contributions to the theory of the electronic structure of atoms, molecules and solids.
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John Pople
Sir John Anthony Pople, (31 October 1925 – 15 March 2004) was a British theoretical chemist who was awarded the Nobel Prize in Chemistry with Walter Kohn in 1998 for his development of computational methods in quantum chemistry.
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Journal of Applied Physics
The Journal of Applied Physics is a peer-reviewed scientific journal with a focus on the physics of modern technology.
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Koopmans' theorem
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).
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Linear combination
In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants).
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Linear combination of atomic orbitals
A linear combination of atomic orbitals or LCAO is a quantum superposition of atomic orbitals and a technique for calculating molecular orbitals in quantum chemistry.
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List of quantum chemistry and solid-state physics software
Quantum chemistry computer programs are used in computational chemistry to implement the methods of quantum chemistry.
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London dispersion force
London dispersion forces (LDF, also known as dispersion forces, London forces, instantaneous dipole–induced dipole forces, or loosely van der Waals forces) are a type of force acting between atoms and molecules.
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Many-body problem
The many-body problem is a general name for a vast category of physical problems pertaining to the properties of microscopic systems made of a large number of interacting particles.
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Møller–Plesset perturbation theory
Møller–Plesset perturbation theory (MP) is one of several quantum chemistry post-Hartree–Fock ab initio methods in the field of computational chemistry.
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Mean field theory
In physics and probability theory, mean field theory (MFT also known as self-consistent field theory) studies the behavior of large and complex stochastic models by studying a simpler model.
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Modern valence bond theory
Modern valence bond theory is the application of valence bond theory, with computer programs that are competitive in accuracy and economy with programs for the Hartree–Fock method and other molecular orbital based methods.
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Molecular Hamiltonian
In atomic, molecular, and optical physics and quantum chemistry, the molecular Hamiltonian is the Hamiltonian operator representing the energy of the electrons and nuclei in a molecule.
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Molecular orbital
In chemistry, a molecular orbital (MO) is a mathematical function describing the wave-like behavior of an electron in a molecule.
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Molecular physics
Molecular physics is the study of the physical properties of molecules, the chemical bonds between atoms as well as the molecular dynamics.
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Momentum
In Newtonian mechanics, linear momentum, translational momentum, or simply momentum (pl. momenta) is the product of the mass and velocity of an object.
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Moseley's law
Moseley's law is an empirical law concerning the characteristic x-rays that are emitted by atoms.
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Multi-configurational self-consistent field
Multi-configurational self-consistent field (MCSCF) is a method in quantum chemistry used to generate qualitatively correct reference states of molecules in cases where Hartree–Fock and density functional theory are not adequate (e.g., for molecular ground states which are quasi-degenerate with low-lying excited states or in bond breaking situations).
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Nuclear physics
Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions.
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Numerical stability
In the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms.
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Old quantum theory
The old quantum theory is a collection of results from the years 1900–1925 which predate modern quantum mechanics.
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Open shell
In the context of atomic orbitals, an open shell is a valence shell which is not completely filled with electrons or that has not given all of its valence electrons through chemical bonds with other atoms or molecules during a chemical reaction.
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Orbital overlap
In chemical bonds, an orbital overlap is the concentration of orbitals on adjacent atoms in the same regions of space.
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Orthogonality
In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms.
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Particle statistics
Particle statistics is a particular description of multiple particles in statistical mechanics.
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Pauli exclusion principle
The Pauli exclusion principle is the quantum mechanical principle which states that two or more identical fermions (particles with half-integer spin) cannot occupy the same quantum state within a quantum system simultaneously.
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Permanent (mathematics)
In linear algebra, the permanent of a square matrix is a function of the matrix similar to the determinant.
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Perturbation theory
Perturbation theory comprises mathematical methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem.
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Post-Hartree–Fock
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.
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Principal quantum number
In quantum mechanics, the principal quantum number (symbolized n) is one of four quantum numbers which are assigned to all electrons in an atom to describe that electron's state.
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Quadratic configuration interaction
Quadratic configuration interaction (QCI) is an extension of configuration interaction that corrects for size-consistency errors in single and double excitation CI methods (CISD).
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Quantum chemistry
Quantum chemistry is a branch of chemistry whose primary focus is the application of quantum mechanics in physical models and experiments of chemical systems.
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Quantum defect
The term quantum defect is ambiguous.
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Quantum number
Quantum numbers describe values of conserved quantities in the dynamics of a quantum system.
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Reinhart Ahlrichs
Reinhart Ahlrichs (16 January 1940 – 12 October 2016) was a German theoretical chemist.
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Restricted open-shell Hartree–Fock
Restricted open-shell Hartree–Fock (ROHF) is a variant of Hartree–Fock method for open shell molecules.
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Robert Bruce Lindsay
Robert Bruce Lindsay (1 January 1900 – 2 March 1985) was an American physicist and physics professor, known for his prolific authorship of physics books in acoustics, and historical and philosophical analyses of physics.
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Roothaan equations
The Roothaan equations are a representation of the Hartree–Fock equation in a non orthonormal basis set which can be of Gaussian-type or Slater-type.
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Schrödinger equation
In quantum mechanics, the Schrödinger equation is a mathematical equation that describes the changes over time of a physical system in which quantum effects, such as wave–particle duality, are significant.
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Screening effect
In solids, especially in metals and semiconductors, the electrostatic screening or screening effect reduces the electrostatic field and Coulomb potential of an ion inside the solid.
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Slater determinant
In quantum mechanics, a Slater determinant is an expression that describes the wave function of a multi-fermionic system that satisfies anti-symmetry requirements, and consequently the Pauli principle, by changing sign upon exchange of two electrons (or other fermions).
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Slater-type orbital
Slater-type orbitals (STOs) are functions used as atomic orbitals in the linear combination of atomic orbitals molecular orbital method.
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Special relativity
In physics, special relativity (SR, also known as the special theory of relativity or STR) is the generally accepted and experimentally well-confirmed physical theory regarding the relationship between space and time.
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Stationary state
A stationary state is a quantum state with all observables independent of time.
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Unitary transformation
In mathematics, a unitary transformation is a transformation that preserves the inner product: the inner product of two vectors before the transformation is equal to their inner product after the transformation.
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Unrestricted Hartree–Fock
Unrestricted Hartree–Fock (UHF) theory is the most common molecular orbital method for open shell molecules where the number of electrons of each spin are not equal.
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Variational method (quantum mechanics)
In quantum mechanics, the variational method is one way of finding approximations to the lowest energy eigenstate or ground state, and some excited states.
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Variational Monte Carlo
In computational physics, variational Monte Carlo (VMC) is a quantum Monte Carlo method that applies the variational method to approximate the ground state of a quantum system.
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Variational principle
A variational principle is a scientific principle used within the calculus of variations, which develops general methods for finding functions which extremize the value of quantities that depend upon those functions.
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Vladimir Fock
Vladimir Aleksandrovich Fock (or Fok; Влади́мир Алекса́ндрович Фок) (December 22, 1898 – December 27, 1974) was a Soviet physicist, who did foundational work on quantum mechanics and quantum electrodynamics.
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Wave function
A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system.
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X-ray
X-rays make up X-radiation, a form of electromagnetic radiation.
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HF theory, Hartree-Fock, Hartree-Fock Theory, Hartree-Fock approximation, Hartree-Fock energy, Hartree-Fock equation, Hartree-Fock equations, Hartree-Fock method, Hartree-Fock theory, Hartree–Fock, Hartree–Fock equation, Hartree–Fock equations, Hartree–Fock theory, Restricted Hartree-Fock, SCF theory, Self consistent field, Self consistent field method, Self-consistent field, Self-consistent field method.
References
[1] https://en.wikipedia.org/wiki/Hartree–Fock_method
