Hartree-Fock method unrestricted

Pratt, G. W., Jr., Phys. Rev. 102, 1303, "Unrestricted Hartree-Fock method." The basis of the method with an example on the Li atom. 

Unrestricted Hartree-Fock method, 231 IJnsaturated hydrocarbons, polarizability, 76... 

In the unrestricted Hartree-Fock method, a single-determinant wave function is used with different molecular orbitals for a and jS spins, and the eigenvalue problem is solved with separate F and F matrices. With the zero differential overlap approximation, the F matrix elements (25) become... 

In this expression, the Fa operator is the usual Fock operator of the Unrestricted Hartree-Fock method [14] ... 

Spin-density distributions for the radical anions of several compounds including dibenzothiophene have been calculated using the unrestricted Hartree-Fock method. Calculated values were of the same order as observed values but close agreement was not obtained. Hjrperfine splitting constants were also calculated using both Model A and Model B as defined earlier results favored Model B. ... 

For open-shell systems, an extension of the Hartree-Fock method, called the unrestricted Hartree-Fock method, is sometimes used. For a closed-shell state, the lowest Hartree-Fock energy is generally obtained... 

The common way to treat free radicals is with the unrestricted Hartree-Fock method or UHF method. In this method, we employ separate spatial orbitals for the oc and the jl electrons, giving two sets of MO s, one for oc and one for fj electrons. Less commonly, free radicals are treated by the restricted open-shell Hartree-Fock or ROHF method, in which electrons occupy MO s in pairs as in the RHF method, except for the unpaired electron(s). The theoretical treatment of open-shell species is discussed in various places in references [1] and in [12]. 

Corrections for Improper HF Asymptotic Behaviour.—There are two techniques which may be used to obtain results at what is essentially the Hartree-Fock limit over the complete range of some dissociative co-ordinate in those cases where the single determinants] approximation goes to the incorrect asymptotic limit. These techniques are (i) to describe the system in terms of a linear combination of some minimal number of determinantal wavefunctions (as opposed to just one) 137 and (ii) to employ a single determinantal wavefunction to describe the system but to allow different spatial orbitals for electrons of different spins - the so-called unrestricted Hartree-Fock method. Both methods have been used to determine the potential surfaces for the reaction of an oxygen atom in its 3P and 1Z> states with a hydrogen molecule,138 and we illustrate them through a discussion of this work. 

It is generally found that if one increases the flexibility of a single-determinantal wavefunction by allowing each space orbital to assume an independent form (rather than insisting on double occupation by an and a (1 electron for those orbitals which would otherwise be so occupied as dictated by the electronic configuration) that the asymptotic difficulties of the wavefunction are removed. Thus, the unrestricted Hartree-Fock method usually predicts the correct dissociation products of a molecular system.140 The symmetrical (C2 ,) insertion of Of3P) into Ha yields the 33i state of the HaO system. The electronic configuration of this state expressed in terms of the unrestricted set of orbitals is... 

As the exact electronic eigenfunction is known to possess these properties it is clearly best to ensure that our approximate eigenfunction also possesses them. Most of the methods do this the exception being a variant of the Hartree-Fock method called the unrestricted Hartree-Fock method (UHF) which yields wavefu notions which are not eigenfunctions of S2 (see below). The Pauli principle is of central importance, and the problem of constructing approximate wavefunctions which obey it is considered below. 

Another example is provided by the EA of the state of the Na atom to generate the Na anion. Because the state is open shell, one would have to employ the unrestricted Hartree-Fock method to evaluate its orbitals and orbital energies to use in an EOM or GF EA calculation. However, one could, alternatively, compute the EA of Na by evaluating the IP of Na . The advantage would be that the Na is closed shell, so one could employ restricted Hartree-Fock methods to compute the requisite orbitals and orbital energies. 

UHE ultrahigh frequency unrestricted Hartree-Fock (method)... 

Kolos and Wolniewicz (130) published some very accurate absolute calculations on hydrogen. The SCF—M. O. method was used by Sahni, Sahwney and Hanley (131) to calculate coe, weXe, B , a , R and D of LiH. The unrestricted Hartree-Fock method as a tool for the computation of potential h 7persurfaces was investigated by Salotto and Burnelle (132). 

One may limit the GHF method by forcing some restrictions on the form of the GHF spinorbitals. A special case of the GHF method is known in textbooks as the unrestricted Hartree-Fock method (UHF). Despite its name. UHF is not a fully unrestricted method (as the GHF is). In the UHF. we assume that, [cf., Eq. (8.1)] ... 

Net atomic charges at P and H and the dipole moment p from an ab initio MO-SCF calculation (unrestricted Hartree-Fock method) are shown below [15] ... 

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