hartree

Hartree refers to a unit of energy used primarily in atomic physics and quantum chemistry, and to the family of methods associated with its name. The Hartree energy, denoted Eh, is the atomic unit of energy equal to about 4.35974417 × 10^-18 joules, or 27.211386 eV. It is twice the Rydberg energy, and in atomic units many fundamental constants (electron mass, elementary charge, reduced Planck constant, and vacuum permittivity) are set to 1, making Eh a natural energy scale for electronic structure calculations.

In the atomic unit system, the Hartree energy serves as a convenient reference for comparing electronic energies and reaction barriers. It also relates to the Bohr model via the Bohr radius and Coulomb interactions, with Eh often used to express energies of molecular orbitals and chemical bonds.

Hartree method refers to an early self-consistent-field approach to solving the many-electron Schrödinger equation. Introduced by Douglas Hartree, it replaces the complex many-electron wavefunction with a product of single-electron orbitals and solves a set of coupled, one-electron equations iteratively until self-consistency is achieved. While computationally simple, the Hartree method neglects exchange and correlation effects between electrons, limiting accuracy.

Hartree-Fock, developed subsequently by Vladimir Fock and others, improves on the Hartree approach by enforcing antisymmetry of the total wavefunction through a Slater determinant, thereby incorporating exchange interactions. Today, Hartree and Hartree-Fock form foundational concepts in quantum chemistry and solid-state physics, with Eh remaining the standard energy unit in many calculations and in discussions of electronic structure. The term Hartree honors Douglas Hartree, whose work helped establish self-consistent field methods widely used in theory and computation.