Quasi-restricted Hartree-Fock

J. Gauss, J. F. Stanton, and R. J. Bartlett,/. Chem. Phys., 95,2639 (1991). Analytic Evaluation of Energy Gradients at the Coupled-Cluster Singles and Doubles Level Using Quasi-Restricted Hartree-Fock Open-Shell Reference Functions. 

Correlation methods that can use quasi-restricted Hartree-Fock (QRHF) or Brueckner orbital reference determinants include CCSD, CCSDT, CCSD(T), CCSDT-1, CCSDT-2, and CCSDT-3. 

CIS = configuration interaction with single excitations EA = electron attachment EE = electron excitation EOM = equation of motion GIAO = gauge-independent atomic orbital QRHF = quasi-restricted Hartree-Fock TDHF = time-dependent Hartree - Fock. 

One of the strengths of CC theory is its ability to handle orbitals that are not variationally optimum for the problem of interest. In Cl methods, if one uses a set of orbitals that is not optimum, one usually introduces significant contributions from other references, i.e., making the problem a multireference problem. In CC theory this is not the case, as the exponential wave operator effectively rotates the orbitals, and the results from a nonoptimum set of orbitals are usually very good. This feature has several practical implications. For several years, a procedure termed quasi-restricted Hartree-Fock... 

Another category of approaches that avoids the symmetry breaking problem of the orbitals for the target state is based on using a related, well-behaved HF reference instead. Examples of such techniques include quasi-restricted Hartree-Fock coupled-cluster (QRHF CC) (11,19), symmetry adapted cluster configuration interaction (SAC-CI) (22,23), coupled-cluster linear response theory (CCLRT) (24-26) or equivalently equation-of-motion coupled-cluster (EOM-CC) (27-32), Fock space multi-reference coupled-cluster (FSMRCC) (33-37), and similarity transformed equation-of-motion coupled-cluster (STEOM-CC) (38-40). In the case of NO3 and N03, the restricted Hartree-Fock (RHF) orbitals of the closed-shell N03 anion system can be used as the reference. The anion orbitals are stable with respect to symmetry perturbations, and the system does not suffer from the artifactual symmetry breaking of the neutral and cation. 

Kobayashi, Sasagane and Yamaguchi" have developed the theory of the time-dependent spin-restricted Hartree-Fock method for application to open shell systems (TDROHF). The expression for the cubic hyperpolarizability is obtained from the quasi-energy derivative (QED) method. The theory is applied to the investigation of the frequency-dependent y susceptibility of the Li, Na, K and N atoms. 

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