Unrestricted Hartree-Fock method configuration interaction

Ellis has recently shown how this procedure can be applied effectively for evaluating the matrix components needed in unrestricted Hartree-Fock and configuration interaction calculations, while Boys and Handy- have employed a similar method in the application of the transcorrelated method to lithium hydride. 

If we except the Density Functional Theory and Coupled Clusters treatments (see, for example, reference [1] and references therein), the Configuration Interaction (Cl) and the Many-Body-Perturbation-Theory (MBPT) [2] approaches are the most widely-used methods to deal with the correlation problem in computational chemistry. The MBPT approach based on an HF-SCF (Hartree-Fock Self-Consistent Field) single reference taking RHF (Restricted Hartree-Fock) [3] or UHF (Unrestricted Hartree-Fock ) orbitals [4-6] has been particularly developed, at various order of perturbation n, leading to the widespread MPw or UMPw treatments when a Moller-Plesset (MP) partition of the electronic Hamiltonian is considered [7]. The implementation of such methods in various codes and the large distribution of some of them as black boxes make the MPn theories a common way for the non-specialist to tentatively include, with more or less relevancy, correlation effects in the calculations. 

QDMBPT = quasi-degenerate many-body perturbation theory, (POL-) Cl = (polarization-) configuration interaction, MC SCF = multiconfiguration SCF, CAS SCF = complete active space SCF, MRD Cl = multireference double-excitation Cl, UHF = unrestricted Hartree-Fock, UMP2 = unrestricted Moller-Plesset perturbation method of second order. - An analytical, combined polynomial-exponential form for E(x) with x = (r-rg)/r and a figure for x= —0.98 to +0.04. 

Beyond Hartree-Fock, the energies (and wavefunctions) may be improved at several levels various orders of the perturbation method at the Moller-Plesset level (1934) (MP2, MP3, MP4) for open-shell systems we could use either unrestricted MP2 (Pople et al. 1976) or one of several variants of the perturbation method based on the ROHF wavefunction the Z-averaged perturbation theory (ZAPT) (Lee and Jayatilaka 1993 Lee et al. 1994) and RMP (Knowles et al. 1980 Lauderdale et al. 1991) configuration interaction (Cl) method (Brooks and Schaefer 1979 Ivanic and Ruedenberg 2001). 

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