Restricted Hartree-Fock calculations

We ve chosen a restricted (R) Hartree-Fock (HF) calculation using the 6-31G(d) basis set(6-31G(d)). 

In contrast to the semiempirical results, full optimization of the molecular geometry of 1-fluorosilatrane by restricted Hartree-Fock (RHF) calculations using the 3-21G, 3-21G and 6-31G basis sets did not find evidence for the existence of an endo minimum on the energy hypersurface193. Since the exo form was never found experimentally, the ab initio results support the view of the exclusive existence of silatranes in the endo form. As for the equilibrium Sk—N distance, the ab initio calculations using polarized basis sets overestimated its value (2.556 A) even more than the AMI and PM3 methods. 

Computational Details. Restricted Hartree-Fock (RHF) calculations were carried out using Gaussian 94 (45) and ACES II (46) on an IBM RISC/6000 computer. The gauge independent atomic orbitals (GIAO) method was used for the shielding calculations (47). All second-order many-body perturbation theory (MBPT2, also referred to as MP2) calculations were performed with ACES II (46). 

Closed-shell (diamagnetic) systems can be investigated using a restricted Hartree-Fock (RHF) calculation, while unrestricted Hartree-Fock (UHF) calculations are able to accommodate open-shell (paramagnetic) systems as well. The Hartree-Fock approximation is also important in serving as a foundation for a variety of more accurate quantum chemical calculations that account for electron correlation. 

Hartree Fock calculations carried out without restrictions on the spatial parts of the alpha and beta spin orbitals are referred to as unrestricted Hartree-Fock (UHF) calculations. Often, it is useful to impose the condition that the alpha and beta spin... 

Calculations such as the one discussed above do not involve imposed symmetry restrictions on the reference wavefunction. Hence this approach is referred to as the unrestricted Hartree-Fock (UHF) method. When symmetry restrictions are imposed upon the reference wavefunction the resulting calculation is denoted a restricted Hartree-Fock (RHF) calculation. When the simplest RHF type calculation is carried out for a closed-shell reference state (i.e., one having doubly occupied orbitals), the nondehned part of the Fock potential (the occupied-occupied) and (empty-empty) part is often chosen to have the same form as the (occupied-empty) part defined from the BT. We then would obtain for the entire Fock potential... 

A restricted Hartree-Fock SCF calculation will be performed using Pulay DIPS + Geometric Direct Minimization Optimization ... 

Chang et al. (1991) performed ab initio restricted Hartree-Fock (RHF) calculations on Cgo cages with several metal atoms inside. They used a Gaussian basis set containing up to 556 basis functions and 257 valence electrons. All calculations of Chang et al. (1991) took full advantage of the icosahedral symmetry (IJ. In the 1 point group, the central atoms, s, p, d and f orbitals correlate into a, tj , h and t2 + gu representations, respectively. 

Sometimes the term restricted Hartree-Fock (RHF) is used to emphasize that the wavefunction is restricted to be a single determinantal function for a configuration wherein electrons of a spin occupy the same space orbitals as do the electrons of P spin. When this restriction is relaxed, and different orbitals are allowed for electrons with different spins, we have an unrestricted Hartree-Fock (UHF) calculation. This refinement is most likely to be important when the numbers of a- and -spin electrons differ. We encountered this concept in Section 8-13, where we noted that the unpaired electron in a radical causes spin polarization of other electrons, possibly leading to negative spin density. 

For the simulation of amorphous polymers in the solid state, these limitations are not very restrictive, as most commercially important polymers display a simple bonding situation that is well parametrized by modern force fields. They contain mostly atoms of the first two rows of the periodic system and can be mostly treated by non-relativistic Hartree-Fock level calculations. It is emphasized, however, that the above requirements should be checked for any system in advance. 

Briefly, the starting point for M ller-Plesset calculations is either an unrestricted Hartree-Fock (UHF) calculation or a closed-shell restricted Hartree-Fock (RHF) calculation. The zero order Hamiltonian, Hq, is then taken to be the sum of the one-electron Fock operators, Fp, and the perturbation, V, is defined as the difference between Hq and the full, many-electron Hamiltonian, ducing an expansion parameter, X, then gives. 

Choose LHH(spin Unrestricted Hartree-Fock) or RHF (spin Restricted Ilartree-Fock) calculations according to your molecular system. HyperChem supports UHF for both open-sh el I and closed-shell calcii lation s an d RHF for cUised-shell calculation s on ly, Th e closed-shell LHFcalculation may be useful for studyin g dissociation of m olectilar system s. ROHF(spin Restricted Open-shell Hartree-Fock) is not supported in the current version of HyperChem (for ah initio calculations). 

Introductory descriptions of Hartree-Fock calculations [often using Rootaan s self-consistent field (SCF) method] focus on singlet systems for which all electron spins are paired. By assuming that the calculation is restricted to two electrons per occupied orbital, the computation can be done more efficiently. This is often referred to as a spin-restricted Hartree-Fock calculation or RHF. 

Quantum mechanics calculations use either of two forms of the wave function Restricted Hartree-Fock (RHF) or Unrestricted Hartree-Fock (UHF). Use the RHF wave function for singlet electronic states, such as the ground states of stable organic molecules. 

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