RHF

The UIIF wnive fimction can also apply to singlet molecules. F sn-ally, the results are the same as for the faster RHF method. That is, electron s prefer to pair, with an alpha electron sh arin g a m olecu lar space orbital with a beta electron. L se the L lIF method for singlet states only to avoid potential energy discontinuities when a covalent bond Is broken and electron s can impair (see Bond Breaking on page 46). 

Although LHF is often a better theoretical treatment of open-shell systems than the RHF (half-electron) methods, it takes longer to compute. Separate matrices for electrons of each spin roughly double the length of the calculation. ... 

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). 

On e would ii ormally choose RHF for closed-sh ell sin gleis an d I. IIF for open-shell doublets and triplets. 

UHF and RHF dissociation curves for H2. (Figure adapted from Szabo A,NS Ostlund 1982. Modem antum Chemistry. Introduction to Advanced Electronic Structure Theory. New York, McGraw-Hill.)... 

Within the periodic Hartree-Fock approach it is possible to incorporate many of the variants that we have discussed, such as LFHF or RHF. Density functional theory can also be used. I his makes it possible to compare the results obtained from these variants. Whilst density functional theory is more widely used for solid-state applications, there are certain types of problem that are currently more amenable to the Hartree-Fock method. Of particular ii. Icvance here are systems containing unpaired electrons, two recent examples being the clci tronic and magnetic properties of nickel oxide and alkaline earth oxides doped with alkali metal ions (Li in CaO) [Dovesi et al. 2000]. 

CONTRL SCFTYP = RHF COORD = ZMT END BASIS GBASIS = STO NGAUSS = 3 END DATA... 

A variation on the HF procedure is the way that orbitals are constructed to reflect paired or unpaired electrons. If the molecule has a singlet spin, then the same orbital spatial function can be used for both the a and P spin electrons in each pair. This is called the restricted Hartree-Fock method (RHF). 

For singlet spin molecules at the equilibrium geometry, RHF and UHF wave functions are almost always identical. RHF wave functions are used for singlets because the calculation takes less CPU time. In a few rare cases, a singlet molecule has biradical resonance structures and UHF will give a better description of the molecule (i.e., ozone). 

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. 

For systems with unpaired electrons, it is not possible to use the RHF method as is. Often, an unrestricted SCF calculation (UHF) is performed. In an unrestricted calculation, there are two complete sets of orbitals one for the alpha electrons and one for the beta electrons. These two sets of orbitals use the same set of basis functions but different molecular orbital coefficients. 

Semiempirical programs often use the half-electron approximation for radical calculations. The half-electron method is a mathematical technique for treating a singly occupied orbital in an RHF calculation. This results in consistent total energy at the expense of having an approximate wave function and orbital energies. Since a single-determinant calculation is used, there is no spin contamination. 

The consistent total energy makes it possible to compute singlet-triplet gaps using RHF for the singlet and the half-electron calculation for the triplet. Koopman s theorem is not followed for half-electron calculations. Also, no spin densities can be obtained. The Mulliken population analysis is usually fairly reasonable. 

The ah initio methods available are RHF, UHF, ROHE, GVB, MCSCF along with MP2 and Cl corrections to those wave functions. The MNDO, AMI, and PM3 semiempirical Hamiltonians are also available. Several methods for creating localized orbitals are available. 

RHF (restricted Hartree-Fock) ah initio method for singlet systems ROHF (restricted open-shell Hartree-Fock) ah initio method for open-shell systems... 

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. 

Spin orbitals are grouped in pairs for an RHF calculation. Each member of the pair differs in its spin function (one alpha and one beta), but both must share the same space function. For N electrons, N/2 different molecular orbitals (space functions) are doubly occupied, with one alpha (spin up) and one beta (spin down) electron forming a pair. 

You can also use a RHF wave function with Cl for calculations involving bond breaking, instead of using a UHF wave function (see also Bond Breaking on page 46). 

Be careful when you use the Orbital Criterion for symmetrical systems. To get correct results, you must include all or none of any set of degenerate orbitals in the Cl, not just some of them. Carrying out an RHF calculation first and studying the Orbitals dialog box will help you to spot degenerate orbitals and avoid this pitfall. 

In large systems there can be many orbitals in a small energy range, and the size of the Cl matrix can be very sensitive to the value of the maximum excitation if you use Biergy Criterion. Since calculation time depends heavily on the size of the Cl matrix, you can end up with very long calculations, especially if you use the ab initio methods or the MNDO, AMI, or PM3 semi-empirical methods. This could exhaust the memory of your system. Again, inspecting the results of an RHF (no Cl) calculation will help you avoid these pitfalls. 

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