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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 = (/) (,).
The Hartree–Fock method finds its typical application in the solution of the Schrödinger equation for atoms, molecules, nanostructures [3] and solids but it has also found widespread use in nuclear physics. (See Hartree–Fock–Bogoliubov method for a discussion of its application in nuclear structure theory).
Hartree's expressions that contain differ from the modern form due to a change in the definition of , as explained below. In 1957, Bethe and Salpeter's book Quantum mechanics of one-and two-electron atoms [ 3 ] built on Hartree's units, which they called atomic units abbreviated "a.u.".
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 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.
Douglas Hartree introduced the Hartree equation for atoms. [56] 1928–1930 – John Hasbrouck Van Vleck formalizes the quantum theory of magnetism and formulates Van Vleck paramagnetism. 1928 – Linus Pauling outlines the quantum nature of the chemical bonds. 1928 – Friedrich Hund and Robert S. Mulliken introduce the concept of molecular ...
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. It applies to closed-shell molecules or atoms where all molecular orbitals or atomic orbitals, respectively, are doubly occupied. This is generally called Restricted Hartree–Fock theory.
Electron correlation energy in terms of various levels of theory of solutions for the Schrödinger equation. Within the Hartree–Fock method of quantum chemistry, the antisymmetric wave function is approximated by a single Slater determinant. Exact wave functions, however, cannot generally be expressed as single determinants.