Unrestricted Hartree-Fock model

Here, occ means occupied and virt means virtual. In the restricted Hartree-Fock model, each orbital can be occupied by at most one a spin and one (i spin electron. That is the meaning of the (redundant) Alpha in the output. In the unrestricted Hartree-Fock model, the a spin electrons have a different spatial part to the spin electrons and the output consists of the HF-LCAO coefficients for both the a spin and the spin electrons. 

In addition, since the HPHF wavefunction exhibits a two-determinantal form, this model can be used to describe singlet excited states or triplet excited states in which the projection of the spin momentum Ms=0. The HPHF approximation appears thus as a simple method for the direct determination of excited states (with Afs=0)such as the usual Unrestricted Hartree Fock model does for determining triplet excited states with Ms = 1. 

Table A5-50 Structures of Diatomic and Small Polyatomic Radicals. Unrestricted Hartree-Fock Models... 

One way to overcome this difficulty is to use different orbitals for different spins (DODS model). This technique introduced, into the Hartree-Fock scheme, gave rise to the unrestricted Hartree-Fock model (UHF), the wave-function being written as an open shell single Slater determinant[2) ... 

The field of expansion coefficients is constrained to be the real numbers while retaining the possibility that each MO has an a and spin component. This is the Real General Unrestricted Hartree-Fock model (R)GUHF. The use of complex coefficients is sufficiently rare that this model is often called simply GUHF. 

The field of real numbers is retained for the coefficients, but now each MO is formed by linear combinations of basis functions having either an a spin factor or a. P spin factor. The most graphic name of this model is Different Orbitals for Different Spins (DODS). However, historically, this was the first Hartree-Fbck method to be used which had any of the common constraints removed and so has also come to be known as simply the Unrestricted Hartree Fock model (UHF). Obviously this name should really be used for CGUHF. 

Minimal END has also been applied to a model system for intramolecular electron transfer. The small triatomic system LiHLi is bent C2V structure. But the linear structure presents an unrestricted Hartree-Fock (UHF) broken symmetry solution with the two charge localized structures... 

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. ... 

Unrestricted models, for example, the unrestricted Hartree-Fock (or UHF) model, are actually simpler and generally less costly than the corresponding restricted models, and because of this are much more widely used. Results for open-shell molecules provided in this book will make use of unrestricted models. 

Pople refers to a specific set of approximations as defining a theoretical model. Hence the ab initio or Hartree-Fock models employ the Born-Oppenheimer, LCAO and SCF approximations. If the system under study is a closed-shell system (even number of electrons, singlet state), the constraint that each spatial orbital should contain two electrons, one with a and one with P spin, is normally made. Such wavefunctions are known as restricted Hartree-Fock (RHF). Open-shell systems are better described by unrestricted Hartree-Fock (UHF) wavefunctions, where a and P electrons occupy different spatial orbitals. We have seen that Hartree-Fock (HF) models give rather unreliable energies. 

We adopt the same chemisorption model as in our previous work [3], which within the unrestricted Hartree-Fock approximation involves a self-consistent calculation of the electronic charge on the adatom. The basis elements needed for the calculation are the... 

The group of Zhao is studying a broad spectrum of clusters with a fixed set of methods. They use EA approaches on TB and empirical potentials, sometimes followed by GGA-DFT refinements electronic and magnetic properties are studied with an spd-band model Hamiltonian in the unrestricted Hartree-Fock (UHF) approximation. Among other systems, they have studied pure clusters of Ag [86],Rh [87],V [88] andCr [89], and mixed clusters of similar atom types, for example, Co/Cu [90] or V/Rh [91], for cluster sizes up to n=13-18. 

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