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In order to solve the equation of an electron in a spherical potential, Hartree first introduced atomic units to eliminate physical constants. Then he converted the Laplacian from Cartesian to spherical coordinates to show that the solution was a product of a radial function () / and a spherical harmonic with an angular quantum number , namely = (/) (,).
A solution of these equations yields the Hartree–Fock wave function and energy of the system. Hartree–Fock approximation is an instance of mean-field theory, [1] where neglecting higher-order fluctuations in order parameter allows interaction terms to be replaced with quadratic terms, obtaining exactly solvable Hamiltonians.
In theoretical and computational chemistry, a basis set 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.
The Appleton–Hartree equation, sometimes also referred to as the Appleton–Lassen equation, is a mathematical expression that describes the refractive index for electromagnetic wave propagation in a cold magnetized plasma.
The Hartree–Fock method is also used in atomic physics and condensed matter physics as Density Functional Theory, DFT. The process of solving the Hartree–Fock equations can only be iterative, since these are in fact a Schrödinger equation in which the potential depends on the density, that is, precisely on the wavefunctions to be
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. While restricted Hartree–Fock theory uses a single molecular orbital twice, one multiplied by the α spin function and the other multiplied by the β spin function in the Slater determinant, unrestricted Hartree–Fock theory ...
The hartree (symbol: E h), also known as the Hartree energy, is the unit of energy in the atomic units system, named after the British physicist Douglas Hartree. Its CODATA recommended value is E h = 4.359 744 722 2060 (48) × 10 −18 J [ 1 ] = 27.211 386 245 981 (30) eV .
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. [1] It is most often formed in computational chemistry when attempting to solve the Roothaan equations for an atomic or molecular system.