Method valence bond, complete

An MCSCF calculation in which all combinations of the active space orbitals are included is called a complete active space self-consistent held (CASSCF) calculation. This type of calculation is popular because it gives the maximum correlation in the valence region. The smallest MCSCF calculations are two-conhguration SCF (TCSCF) calculations. The generalized valence bond (GVB) method is a small MCSCF including a pair of orbitals for each molecular bond. 

Amovilli et al. [20] presented a method to carry out VB analysis of complete active space-self consistent field wave functions in aqueous solution by using the DPCM approach [3], A Generalized Valence Bond perfect pairing (GVB-PP) level... 

I think that the theory of resonance is independent of the valence-bond method of approximate solution of the Schrodinger wave equation for molecules. I think that it was an accident in the development of the sciences of physics and chemistry that resonance theory was not completely formulated before quantum mechanics. It was, of course, partially formulated before quantum mechanics was discovered and the aspects of resonance theory that were introduced after quantum mechanics, and as a result of quantum mechanical argument, might well have been induced from chemical facts a number of years earlier. [25]... 

H. Nakano, K. Sorakubo, K. Nakayama, K. Hirao, in Valence Bond Theory, D. L. Cooper, Ed. Elsevier, Amsterdam, The Netherlands, 2002, pp. 55-77. Complete Active Space Valence Bond (CASVB) Method and its Application in Chemical Reactions. 

Complete active space valence bond (CASVB) method and its application to chemical reactions... 

The complete active space valence bond (CASVB) method is an approach for interpreting complete active space self-consistent field (CASSCF) wave functions by means of valence bond resonance structures built on atom-like localized orbitals. The transformation from CASSCF to CASVB wave functions does not change the variational space, and thus it is done without loss of information on the total energy and wave function. In the present article, some applications of the CASVB method to chemical reactions are reviewed following a brief introduction to this method unimolecular dissociation reaction of formaldehyde, H2CO — H2+CO, and hydrogen exchange reactions, H2+X — H+HX (X=F, Cl, Br, and I). 

The complete active space valence bond (CASVB) method [1,2] is a solution to this problem. Classical valence bond (VB) theory is very successful in providing a qualitative explanation for many aspects. Chemists are familiar with the localized molecular orbitals (LMO) and the classical VB resonance concepts. 

Therefore, the dependence on the coefficients does not enter the gradient expression not for fixed orbitals, which is the classical Valence Bond approach and not for optimised orbitals, irrespective of whether they are completely optimised or if they are restricted to extend only over the atomic orbitals of one atom. If the wavefimction used in the orbital optimisation differs, additional work is required. This would apply to a multi-reference singles and doubles VB (cf. [20,21]). Then we would require a yet unimplemented coupled-VBSCF procedure. Note that the option to fix the orbitals is not available in orthogonal (MO) methods, due to the orthonormality restriction. 

Curves that go beyond the Flartree-Fock method have been calculated for certain systems, and the list grows monthly. Of special interest is the series on ground [62-64] and excited states [63, 64] of CO, on NaLi and NaLi+ using an extended Flartree-Fock method with optimized double-valence configurations [65], HeLi by a valence-bond method [66], and so on. A quite complete listing of all nonempirical potential-energy curves calculated through 1967 is included in the NBS report [33]. 

Fock molecular orbital (HF-MO), Generalized Valence Bond (GVB) [49,50] and the Complete Active Space Self-consistent Filed (CASSCF) [50,51], and full Cl methods. [51] Density Functional Theory (DFT) calculations [52-54] are also incorporated into AIMD. One way to perform liquid-state AIMD simulations, is presented in the paper by Hedman and Laaksonen, [55], who simulated liquid water using a parallel computer. Each molecule and its neighbors, kept in the Verlet neighborlists, were treated as clusters and calculated simultaneously on different processors by invoking the standard periodic boundary conditions and minimum image convention. 

QM/MM (AM1/CHARMM) or empirical valence bond methods, respectively164 168), for forcing the conformation of chorismate in solution into the more restricted conformation found in the enzyme. This equates to a catalytic benefit of only around 40-55% of the total AA G between enzyme and solvent. The good agreement between these findings, which applied completely different theoretical methods, is striking and suggests that this is a reliable result. 

The choice of reference space for MRCI calculations is a complex problem. First, a multieonfigurational Hartree-Fock (MCSCF) approach must be chosen. Common among these are the generalized valence-bond method (GVB) and the complete active space SCF (CASSCF) method. The latter actually involves a full Cl calculation in a subspace of the MO space—the active space. As a consequence of this full Cl, the number of CSFs can become large, and this can create very long Cl expansions if all the CASSCF CSFs are used as reference CSFs. This problem is exacerbated when it becomes necessary to correlate valence electrons in the Cl that were excluded from the CASSCF active space. It is very common to select reference CSFs, usually by their weight in the CASSCF wave function. Even more elaborate than the use of a CASSCF wave function as the reference space is the seeond-order Cl, in which the only restriction on the CSFs is that no more than two electrons occupy orbitals empty in the CASSCF wave function. Such expansions are usually too long for practical calculations, and they seldom produce results different from a CAS reference space MRCI. 

In the preceding discussion, the creation and annihilation operators always referred to a set of orthonormal spin-orbitals. We can ask how much of the formalism holds in cases where complete orthonormality can no longer be assumed, for example, in valence-bond calculations or in the generalized Sturmian method. 

It has frequently been the custom for supporters of one or the other of these theories to claim a measure of chemical insight and quantitative reliability for the method of their choice. This is a pity because neither method is complete or fully satisfactory. Fortunately in most of their conclusions the two theories agree, although they reach their conclusions in quite distinct ways. This means that we must not arbitrarily reject one or the other.. . . There is little doubt but that the molecular-orbital theory is conceptually the simplest. Historically it was developed after the other theory was already established, and for that reason has been a little slower in gaining acceptance. Its present status, however, in dealing with excited states, is fully equal to that of the valence-bond theory."... 

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