Restricted Hartree-Fock theory

An initial equilibrium structure is obtained at the Hartree-Fock (HF) level with the 6-31G(d) basis [47]. Spin-restricted (RHF) theory is used for singlet states and spin-unrestricted Hartree-Fock theory (UHF) for others. The HF/6-31G(d) equilibrium structure is used to calculate harmonic frequencies, which are then scaled by a factor of 0.8929 to take account of known deficiencies at this level [48], These frequencies are used to evaluate the zero-point energy Ezpe and thermal effects. 

An initial equilibrium structure is obtained by geometry optimization at the Hartree-Fock (HF) level with the 6-31G(d) basis.68 69 Spin-restricted Hartree-Fock (RHF) theory is used for singlet states and spin-unrestricted Hartree-Fock theory (UHF) for others. 

Ab initio Hartree-Fock theory is based on one single approximation, namely, the N-dectron wavefunction, F is restricted to an antisymmetrized product, a Slater determinant, of one-electron wavefunction, so called spin orbitals,... 

The equations require to be modified for open-shell systems, in which some orbitals are doubly occupied and some singly (this is called spin-restricted Hartree-Fock theory). A further extension to the theory involves electrons of a and /3 spin being assigned to different molecular orbitals, type equations are described as unrestricted Hartree-Fock [31]. 

Hartree-Fock (theory) (FIF) (restricted HF, RFIF for closed shells unrestricted HF, UHF for open shells)... 

Hartree-Fock theory, 20-32, 218-231 approximation, 222 energy, 222-226 restricted (RHF), 234-236 successes and failures, 29-30 imrestricted (UHF), 222-234 wave function, 223... 

For most applications, the external potential operator v reduces to a local potential v(r), and the Hohenberg-Kohn theory is valid for the ground state. The present derivation follows exactly the logic of standard Hartree-Fock theory. It is not restricted to ground states and remains valid for fractional occupation numbers. 

In the 0PM schemes one starts from a Hartree-Fock like exchange energy, but the energy is optimized under the restriction that the effective potential is local. So exchange only 0PM is as close to Hartree-Fock theory as a scheme with a local potential can be. 

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