Multi-reference self-consistent field

Werner and co-workers [2, 21, 34] used internally-contracted multi-reference configuration-interaction (IC-MRCI) calculations, based on state-averaged (three-state) multi-configuration, self-consistent-field (MCSCF) calculations with large atomic orbital basis sets, to determine the three electronically adiabatic C1(F)+H2 PESs in the reactant arrangement L4, 2A, and lA. These all correlate with X( P) + H2. These three adiabatic electronic states are the IC-MRCI approximations to the three lowest eigenfunctions of Hgi, namely... 

For variational methods, such as Hartree-Fock (HF), multi-configurational self-consistent field (MCSCF), and Kohn-Sham density functional theory (KS-DFT), the initial values of the parameters are equal to zero and 0) thus corresponds to the reference state in the absence of the perturbation. The A operators are the non-redundant state-transfer or orbital-transfer operators, and carries no time-dependence (the sole time-dependence lies in the complex A parameters). Furthermore, the operator A (t)A is anti-Hermitian, and tlie exponential operator is thus explicitly unitary so that the norm of the reference state is preserved. Perturbation theory is invoked in order to solve for the time-dependence of the parameters, and we expand the parameters in orders of the perturbation... 

Shortly after the above was written, a paper by Jaszuhski et al. [47] on FH appeared. They used the polarization propagator technique (a Danish tradition ) and calculated the QRF using a multi-configurational-self-consistent-field reference state (the previously unimplemented formalism had been developed by Olsen and Jprgensen [48]). They also took into account zero-point-vibrational averaging. For p(SHG) at X = 6943 A, and using CAS 4220 functions (more than 125000 determinants), their final value was (in the Ward convention) -7.8 a.u. or 71% of the experimental value they considered that Sekino and Bartlett s [38] estimate to be an exaggeration of "how close to experiment theory can get". However, their own value is, in fact, within the limits that Sekino and Bartlett proposed. 

However, although, starting from this point, many sophisticated methods for wave function expansion, for example, the coupled cluster approach, multi-configuration self-consistent-field method or multi-reference Cl methods, have been developed, the correlation problem faced many computational limitation, some of them almost insurmountable, due to the immense number of integrals to be evaluated. 

PHF methods can, in turn, be classified as the variational and nonvariational ones. In the former gronp of methods the coefficients in linear combination of Slater determinants and in some cases LCAO coefficients in HF MOs are optimized in the PHF calculations, in the latter such an optimization is absent. To the former group of PHF methods one refers different versions of the configuration interaction (Cl) method, the multi-configuration self-consistent field (MCSCF) method, the variational coupled cluster (CC) approach and the rarely used valence bond (VB) and generaUzed VB methods. The nonvariational PHF methods inclnde the majority of CC reaUza-tions and many-body perturbation theory (MBPT), called in its molecular realization the MoUer-Plessett (MP) method. In MP calculations not only RHF but UHF MOs are also used [107]. 

AIMD = ab initio molecular dynamics B-LYP = Becke-Lee-Yang-Parr CVC = core-valence correlation DF = density functional LDA = local density approximation MCLR = multi-configurational linear response MP2 = Mpller-Plesset second order (MRD)CI = multi-reference double-excitation configuration interaction RPA = random phase approximation TD-MCSCF = time-dependent multi-configurational self-consistent field TD-SCF = time-depen-dent self-consistent field. 

Mulliken population analysis, 218 Multi-Configuration Self Consistent Field (MCSCF) methods, 117 Multi-Reference Configuration Interaction (MRCI) methods, 122 Multiple minima, 339... 

A number of types of calculations begin with a HF calculation and then correct for correlation. Some of these methods are Moller-Plesset perturbation theory (MPn, where n is the order of correction), the generalized valence bond (GVB) method, multi-configurational self-consistent field (MCSCF), configuration interaction (Cl), and coupled cluster theory (CC). As a group, these methods are referred to as correlated calculations. 

Werner H-J 1987 Matrix-formulated direct multiconfigurational self-consistent field and multi reference configuration interaction methods Adv. Chem. Phys. 69 1... 

Density Functional Theory, DFT (B3LYP), CASSCF (Complete Active-State Self-Consistent Field) and MRSD-CI (Multi-Reference Single-Double Correlation Interaction) calculations on the diatomic units AuO, AuO", AuO " and AuO " clearly show that stability of Au-0 bond reduces in this order. This trend is consistent with the molecular orbital diagram of AuO molecule presented in Fig. 10. 

They showed that the dimerized bond should be considered as a singlet diradical. Therefore, a qualitatively correct description of the dimer requires at least a generalized valence bond, GVB-PP132, or a two configuration self-consistent field (TCSCF)33 wave function. More recently, Paulus29 performed a more exhaustive multi-reference analysis of silicon clusters and reconfirmed this conclusion. 

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