This chapter gives a detailed description of the Hartree–Fock method, which is the fundamental method of quantum chemistry, and the computational tools for efficiently solving this method. First, the Hartree method for solving the three-body problem, in order to calculate multi-electron systems, is explained in Sect. 2.1, and the molecular orbital theory, which uses the LCAO–MO approximation, is presented in Sect. 2.2. After introducing the Slater determinant in Sect. 2.3, the Hartree–Fock method is described, including the formulation of the equation and the SCF process to solve this equation, in Sect. 2.4. Then, the Roothaan method for casting the Hartree–Fock equation as a matrix equation and the basis functions used in this method are surveyed in Sect. 2.5 and Sect. 2.6, respectively. The methods used for the efficient two-electron integral calculation, which is the bottleneck in the Hartree–Fock calculation, are concretely explained in Sect. 2.7. As an extension of the Hartree–Fock method to the open-shell case, the unrestricted Hartree–Fock (UHF) method is reviewed in Sect. 2.8. The electronic states of atoms are finally discussed as an achievement of the Hatree–Fock method, with reference to the periodical table, in Sect. 2.9.
Atomic Orbital Orbital Energy Hamiltonian Operator Fast Multipole Method Core Orbital
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