哈特里-福克方法Hartree–Fock method

对每个电子求解单电子福克方程 F̂φᵢ = εᵢφᵢ，福克算符包含动能、核吸引、库仑排斥（平均场）和交换项（来自波函数的反对称性）。由于福克算符依赖于待求的轨道，需要先猜测初始轨道，反复计算直到轨道和能量不再变化（自洽场，SCF）。1951 年罗特汉和霍尔把分子轨道展开为原子基函数的线性组合，得到矩阵方程 FC = SCε，便于计算机求解。

Each electron obeys a one-electron Fock equation F̂φᵢ = εᵢφᵢ, where the Fock operator contains kinetic energy, nuclear attraction, Coulomb repulsion (the mean field) and an exchange term arising from antisymmetry. Because the Fock operator depends on the orbitals being sought, one guesses initial orbitals and iterates until orbitals and energy stop changing (the self-consistent field, SCF). In 1951 Roothaan and Hall expanded molecular orbitals in atomic basis functions, giving the matrix equation FC = SCε suitable for computers.

1928 年英国物理学家道格拉斯·哈特里提出自洽场方法，用乘积波函数计算原子。1930 年苏联物理学家弗拉基米尔·福克和斯莱特分别指出必须使用反对称波函数，引入交换项，形成哈特里-福克方法。早期计算靠手摇计算器完成，哈特里父子曾计算了许多原子的波函数。

In 1928 the British physicist Douglas Hartree proposed the self-consistent field method using product wavefunctions for atoms. In 1930 the Soviet physicist Vladimir Fock, and Slater independently, showed an antisymmetric wavefunction was needed, adding the exchange term and creating the Hartree–Fock method. Early calculations were done on hand calculators, and Hartree and his father computed wavefunctions for many atoms.

哈特里-福克方法忽略了电子之间的瞬时相关运动（电子相关），通常能得到总能量的约 99%，但剩余的相关能（约 1%）往往与化学反应能量同一量级，因此对键解离能、反应热和弱相互作用描述不准。后哈特里-福克方法（MP2、CI、CCSD(T)）在此基础上加入电子相关校正。库普曼斯定理指出 HF 轨道能量的负值近似等于电离能。

Hartree–Fock neglects the instantaneous correlated motion of electrons (electron correlation). It typically captures about 99% of the total energy, but the missing correlation energy, about 1%, is often comparable to reaction energies, so it describes bond dissociation, reaction heats and weak interactions poorly. Post-Hartree–Fock methods (MP2, CI, CCSD(T)) add correlation corrections. Koopmans' theorem states that the negative of an HF orbital energy approximates an ionisation energy.