Restricted open shell Hartree-Fock Self-consistent

Hyperfine couplings, in particular the isotropic part which measures the spin density at the nuclei, puts special demands on spin-restricted wave-functions. For example, complete active space (CAS) approaches are designed for a correlated treatment of the valence orbitals, while the core orbitals are doubly occupied. This leaves little flexibility in the wave function for calculating properties of this kind that depend on the spin polarization near the nucleus. This is equally true for self-consistent field methods, like restricted open-shell Hartree-Fock (ROHF) or Kohn-Sham (ROKS) methods. On the other hand, unrestricted methods introduce spin contamination in the reference (ground) state resulting in overestimation of the spin-polarization. 

The restricted open-shell Hartree-Fock (ROHF) and the unrestricted Hartree Fock Method ( UHF) approximations permit, however, open-shell systems to be described, while maintaining the simplicity of the single-determinant approximation. This is made at the stage of self-consistent electronic-structure calculations. Afterwards, the obtained spin-orbitals can be used to get the correct total spin many-determinant wavefunction and to calculate the corresponding electron energy. 

Reaction coordinate, 296, 314, 365, 368 Reaction Path (RP) methods, 390 Reaction surface, 390 Reaction volume, 390 Redundant variables, 34, 327 Relaxation time, in simulations, 380 Renormalized Davidson correction, 137 Resonance, resonance structures, 200 Response, wave function, 242 Restricted Active Space Self-Consistent Field (RASSCF) method, 119 Restricted Hartree-Fock (RHF) method, 70 Restricted Open-shell Hartree-Fock (ROHF) method, 70... 

Calculations of core hole states and core electron binding energies have mostly concerned state-by-state optimization using open-shell Hartree-Fock, multiconfiguration self-consistent field, and configuration interaction techniques, while propagator techniques have been of restricted use owing to the relaxation problem ... 

In solving Eq. (2), an iterative process is used to adjust the until the best wavefunction is found [self-consistent field (SCF) theory]. For the open shell case where incompletely filled orbitals exist, spin-restricted Hartree-Fock (RHF) methods or unrestricted Hartree-Fock (UHF) methods may be used to calculate the energies.41 The extent of calculation, approximation, or neglect of the two-electron integral terms largely defines the computation method. 

J. D. Goddard, N. C. Handy, and H. F. Schaefer, Gradient techniques for open-shell restricted Hartree-Fock and multiconfiguration self-consistent-field methods, J. Chem. Phys. 71 1525 (1979). 

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