MC SCF

Lengsfield B H III 1980 General second-order MC-SCF theory a density matrix directed algorithm J. Chem. Phys. 73 382... 

Drukker, K., Hammes-Schiffer, S. An analytical derivation of MC-SCF vibrational wave functions for the quantum dynamical simulation of multiple proton transfer reactions Initial application to protonated water chains. J. Chem. Phys. 107 (1997) 363-374. 

When the symmetry breaking of the wave function represents a biased procedure to decrease the weights of high energy VB stmctures which were fixed to umealistic values the tymmetry and single determinant constraints, one may expect that the valence CASSCF wave function will be symmetry-adapted, since this function optimizes the coefficients of all VB forms (the valence CASSCF is variational determination of the best valence space and of the best valence function, i.e. an optimal valence VB picture). In most problems the symmetry breaking should disappear when going to the appropriate MC SCF level. This is not always the case, as shown below. 

MC-SCF treatments written in terms of coupled Fock equations [44], The simplest examples are the two-configuration SCF theory [45] used in and pi+2 atomic mixing [46], or bonding-antibonding molecular problems [47], and more generally the Clementi-Veillard electron-pair MC-SCF theory [48],... 

In the recent past, we have investigated and published examples illustrating the different cases. For instance in Ref [17] a Roothaan open-shell system, H3, has been detailed, in Refs. [18, 19] a SCF treatment for infinite chains and finally in Ref [16] a MC-SCF treatment were proposed. 

Table 2. The Relative Energies of Various Electronic States of 1 a at the CISD + Q/6-31 G(d)//(MC)SCF/6-31 G(d) and B3LYP/6-31 G(d) Levels of Theory...

Density functional theory and MC-SCF calculations have been applied to competing concerted and stepwise mechanisms of cycloaddition reactions. ... 

Density functional theory and MC-SCF calculations have been applied to a number of pericyclic reactions including cycloadditions and electrocyclizations. It has been established that the transition states of thermally allowed electrocyclic reactions are aromatic. Apparently they not only have highly delocalized structures and large resonance stabilizations, but also strongly enhanced magnetic susceptibilities and show appreciable nucleus-independent chemical-shift values. 

While the (one-particle) Brillouin condition BCi has been known for a long time, and has played a central role in Hartree-Fock theory and in MC-SCF theory, the generalizations for higher particle rank were only proposed in 1979 [38], although a time-dependent formulation by Thouless [39] from 1961 can be regarded as a precursor. 

This is nothing but the Brillouin condition of MC-SCF theory. Explicitly, in an... 

For the sake of completeness, we recall that the idea of the single-root formalism exploiting the Hilbert space approach was also proposed by Banerjee and Simons [31] and Laidig and Bartlett [34,35]. In both approaches they start from the complete active space MC SCF wave function, however, in order to eliminate redundant cluster amplitudes they approximate the wave operator by... 

The four steps outlined above appear to be a good general approach to diatomic potentials, as can be seen from the F2 results shown in Fig. 11. The first two steps are essential to obtain a physically acceptable surface the third step may add appreciably to the binding energy particularly for weak bonds, and the last step, which is the most tedious, is hopefully not essential for many molecules. It has however still to be established that good MC SCF wavefunctions for polyatomic molecules may be constructed by similar arguments. 

The standard method for selecting the 4>j is to ask for the <)>i which maximize the importance of one or more terms in the sum. This gives the self-consistent-field (SCF) or multiconfiguration SCF (MC-SCF) equations. If each < >. is expanded as a linear combination of some fixed set of basis functions f - the coefficients can be found by an extension of the Roothaan SCF equations. 

J. Olsen, D.L.Yeager, and P. Jorgensen, Optimization and characterization of a Multiconfigurational Self-Consistent Field (MC-SCF) State", in Adv. Chem. Phys. 54,1 (1983). 

B.O.Roos, The Multiconfigurational (MC) SCF Method, in Methods in Computational Physics (G.H.F Diercksen and S.Wilson, eds), D.Reidel Publishing Company, Dordrecht (1983). 

P. Pulay and T.P. Hamilton, UHF Natural Orbitals for Defining and Starting MC-SCF Calculations, J.Chem. Phys. 88, 4926 (1988). 

A more recent and much more complete calculation at the MC-SCF-CI level by Blomberg and Wahlgren134 on the dianion of Ni(edt)2 produced the wrong ground state configuration (tetrahedral), and an estimate of d-d excitation energies, while made, lacked significance. 

MC-SCF calculations on polyatomic molecules are still rather rare, although there have been many such calculations on triatomic and diatomic molecules. Levy45 has described the results of such calculations using a minimal STO basis set for CH4, C2H4, and CjjHa. A quadratically convergent method was described and the results of localizing the orbitals were investigated. 

N. Yamamoto, F. Bernardi, A. Bottoni, M. Olivucci, M. A. Robb, and S. Wilsey,J. Am. Cbem. Soc., 116, 2064 (1994), and references cited therein. Mechanism of Carbene Formation from the Excited States of Diazirine and Diazomethane An MC-SCF Study. 

I. N. Ragazos, M. A. Robb, F. Bernardi, and M. Olivucci, Chem. Phys. Lett., 197, 217 (1992). Optimization and Characterisation of the Lowest Energy Point on a Conical Intersection Using an MC-SCF Lagrangian. 

MC-SCF Perturbation Theory Orthogonal Valence Bond Moller-Plesset 2 (OVB-MP2). 

F. Bernardi, M. Olivucci, and M. A. Robb,/. Am. Chem. Soc., 114,1606 (1992). Simulation of MC-SCF Results on Covalent Organic Multi-bond Reactions Molecular Mechanics with Valence Bond (MM-VB). 

Palmer, I.J., Ragazos, I.N., Bernardi, F., Olivucci, M., and Robb, M.A. (1994) An MC-SCF study of the photochemical Paternd-Buchi reaction. Journal of the American Chemical Society, 116, 2121-2132. 

In order to make up for those imperfections one needs to turn to post-Hartree-Fock methods. Two variational techniques are worth discussing due to their popularity the configuration-interaction (SCF Cl) method and the multiconfiguration self-consistent-field (MC SCF) method. 

The MC SCF method usually takes into account a minimum number of configurations capable of assuring some fundamental requirements, this step being followed by the optimization of the basis functions using the self-consistent-field method. For example, in order to describe accurately the dissociation of ground-state H2 it is only necessary to consider the two-configuration wave function... 

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