CASVB bonds

We discuss all of the key features of our current CASVB methodology for modem valence bond calculations on ground and excited states. The CASVB strategy may be used to generate compact representations of CASSCF wavefunctions or, alternatively, to perform the fully-variational optimization of various general types ofVB wavefunction. We report also a new application, namely to the fourteen % electrons of a planar dimethylenecyclobu-tadiene chain with three rings. 

In an early application to butadiene [16], and later to the ground and excited states of benzene [17], Berry analyzed MO-based wavefunctions using valence bond concepts, simply by considering the overlaps with nonorthogonal VB structures. Somewhat closer than this to a CASVB type of approach, are the procedures employed by Linnett and coworkers, in which small Cl wavefunctions were transformed (exactly) to nonorthogonal representations [18-20]. The main limitation in their case was on the size of systems that may be treated (the authors considered no more than four-electron systems), both because this non-linear transformation must exist, and because it must be possible to obtain it with reasonable effort. 

Hirao has also recently considered the transformation of CASSCF wavefrmctions to valence bond form [24, 25]. An orthogonal VB orbital basis was first considered, in which case the CASSCF Cl vector may be found by re-solving the Cl problem. Later he considered also the transformation to a classical VB representation. The transformation of the CASSCF space was achieved by calculating all overlap terms, (oCASscFj cASVB gjjjj golving the subsequent linear problem, using a Davidson-like iterative scheme. 

An Overview of the CASVB Approach to Modem Valence Bond Calculations... 

As is the case for standard orthogonal-orbital MCSCF calculations, the optimization of VB wavefimctions can be a complicated task, and a program such as CASVB should therefore not be treated as a black box . This is true, to a greater or lesser extent, for most procedures that involve orbital optimization (and, hence, non-linear optimization problems), but these difficulties are compounded in valence bond theory by the... 

For the valence bond orbitals themselves, it is generally natural to specify a starting guess in the AO basis. Such a guess might, of course, not lie entirely inside the space spanned by the active space, and it must therefore be projected onto the space of the active MOs. This is achieved trivially in CASVB, by multiplication by the inverse of the matrix of MO coefficients. 

T. Thorsteinsson, D.L. Cooper, J. Gerratt and M. Raimondi A New Approach to Valence Bond Calculations CASVB, in R. McWeeny, J. Mamani, Y.G. Smeyers and S. Wilson (Eds.), Quantum Systems in Chemistry and Physics Trends in Methods and Applications, Kluwer Academic Publishers, Dordrecht (1997). 

An overview of the CASVB approach to modern valence bond calculations 303... 

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. 

The combination of the spin-coupled formulation of modem valence bond theory with intrinsic reaction coordinate calculations provides easy-to-interpret models for the electronic rearrangements that occur along reaction pathways. We survey here the information revealed by such studies of the mechanisms of various gas-phase six-electron pericyclic reactions the Diels-Alder reaction between butadiene and ethene, the electrocyclization of cis-l,3,5-hexatriene, the 1,3-dipolar cycloaddition between fulminic acid and ethyne, and the 1,3-dipolar cycloaddition of diazomethane. The fully-variational CASVB strategy proves particularly efficient for such studies. 

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. 

In this article, we present applications of CASVB to chemical reactions the unimolecular dissociation reaction of formaldehyde, H2CO — H2+CO [5], and a series of hydrogen exchange reactions, H2+X — H+HX (X-F, Cl, Br, and I). The method in this article is based on the occupation numbers of VB structures that are defined by the weights of the spin-paired functions in the CASVB functions, so that we could obtain a quantitative description of the nature of electronic structures and chemical bonds even during reactions. 

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