Quasi-restricted orbitals

In this equation, there enters a set of quasi-restricted orbitals (QROs) that are explained in detail in [84], It may be appreciated that both formulations involve the terms that are already apparent in the general treatment (Eqs. (39)-(41)). Namely, the first two terms correspond to the contributions from the spin-conserving excitations, while the third and fourth terms correspond to the contributions from the excited states of lower and higher multiplicity than the ground state, respectively. However, this QRO formalism is now superseded by the more general development in Eqs. (72)-(74). More information on the relative importance of the individual terms can be found below ( 3.5, 3.6). 

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. 

It is well known that in an ideal one-dimensional conductor the transverse orbital motion is restricted thus, the carriers cannot make circular motions in the presence of a magnetic field. Hence, one could hardly e qrect any MC in an ideal one-dimensional conductor. However, in the presence of any finite interchain transfer integral, as in several quasi-one-dimensional conductors, the MC can be used as a powerfiil tool to investigate the intra-versus interchain transport. Nevertheless, the fine features in anisotropic MC can be easify smeared in the presence of disorder. 

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