Hartree-Fock, grand canonical

Abbreviations MD, molecular dynamics TST, transition state theory EM, energy minimization MSD, mean square displacement PFG-NMR, pulsed field gradient nuclear magnetic resonance VAF, velocity autocorrelation function RDF, radial distribution function MEP, minimum energy path MC, Monte Carlo GC-MC, grand canonical Monte Carlo CB-MC, configurational-bias Monte Carlo MM, molecular mechanics QM, quantum mechanics FLF, Hartree-Fock DFT, density functional theory BSSE, basis set superposition error DME, dimethyl ether MTG, methanol to gasoline. 

Instead of the standard Hartree-Fock reference calculation, a grand-canonical Hartree-Fock calculation [35] is used with the occupation number of a single spin-orbital (i.e., the transition spin-orbital) set to 0.5. Upon convergence, appreciable corrections to the relaxation energy are included in the transition spin-orbital s energy [23, 24], Usually a very close agreement with the ASCF method [36] is obtained [26], The second order electron propagator is applied to the ensemble... 

Electron-electron interactions determine the detailed state formation for a partially filled shell from nearly degenerate atomic d-orbitals. The emphasis here is to demonstrate the nature of the grand canonical ensemble Hartree-Fock which allows partial occupancy of spin orbitals while maintaining point group or spherical symmetry. The analysis is set in the proper spin orbital basis with spin-orbit coupling as well as octahedral symmetry accounted for in the canonical Hartree-Fock solutions. Explicit expressions for the separable representation of the electron interaction are offered to exemplify the available reductions. 

Table 4.2 Multiplet separations from Grand Canonical Hartree-Fock central field calculations and experiment for some atomic systems in units of cm. ...

Polarization propagator calculations based on the grand canonical Hartree-Fock orbitals have been performed by P. Jorgensen and Y. Ohm, in Chem. Phys. Lett. 18, 261 (1973) for triplet-triplet absorption spectra of hydrocarbons. 

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