CASVB method

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. 

In the CASVB method of Thorsteinsson et al. (22,23), one transforms the canonical CASSCF orbitals so that the wave function (which we recall, is kept unchanged in this process) involves a dominant component of a VB-type wave function, TVb, which is chosen in advance and may be single- or multiconfiguration, as in Equation 9.5 ... 

Here TyB is the orthogonal complement of TVb to the CASSCF wave function, and SVb is the overlap between Tcas and Tv is- To ensure that the so-obtained VB function is as close as possible to the starting CASSCF wave function, the procedure transforms the orbitals in a manner that maximizes the overlap Svb- An alternative procedure is one that minimizes the energy of the VB function TVs- This latter procedure is, however, more expensive than the first one. As the two methods generally yield similar sets of orbitals, the method of Svb maximization is generally preferred (23). The 5Vb based CASVB method is implemented in the MOLPRO and MOLCAS packages. 

The CASVB method developed by Hirao et al. (24) differs from the previous one in the requirement that the final CASVB wave function, obtained after the... 

The CASVB method of Thorsteinsson et al. (22) is incorporated in the MOLPRO (67) and in the MOLCAS (68) packages. In addition to the features of the original CASVB method, the CASVB code also permits fully variational VB calculations, which can be single- or multiconfigura-tional in nature. 

MOPLRO A general-purpose package of programs. It contains the CASVB method. 

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. 

We have proposed two types of CASVB method. The first one is a method where the valence bond structures are constructed from orthogonal localized molecular orbitals (LMOs) [1], and the second is one from nonorthogonal localized molecular orbitals [2]. 

Canonical momentum operator, 248 Car and Parrinello (CP) method, 388 CASMP2, CASPT2 methods, 132 CASVB method, 202 Cavity, in reaction field models, 393 CBS-4, CBS-q, CBS-Q and CBS-APNO methods, 167... 

The CASVB functions [50,51] can be obtained by transforming the canonical CASSCF functions without loss of energy. First we transform the CASSCF delocalized MO to localized MO using the arbitrariness in the definition of the active orbitals. Then we perform a full Cl again in the active space. The CASVB method provides an alternative tool for describing the correlated wave functions. 

One may re-define the active orbitals utilizing the invariance of the active orbital space. In the orthogonal CASVB method, the LMOs constructed by Boys localization procedure are used that is, active orbitals are transformed so as to have the minimum sum of expectation values. If the active orbitals are defined appropriately, the LMOs obtained nearly always turn out to be localized on a single atomic center with small localization tails on to neighboring atoms. In the non-orthogonal CASVB case, the atomic-like orbitals are constructed by Ruedenberg s projected localization procedure. 

The reaction for fluorine (Rl) is highly exothermic, while the reactions for chlorine (R2), bromine (R3), and iodine (R4) are endothermic. The heats of these reactions are 30.8, — 1.2, — 16.7, and — 32.7 kcal/mol for reactions (Rl), (R2), (R3), and (R4), respectively. According to Hammond s postulate, reaction (Rl) should have an early TS, and reactions (R2) and (R3) should have late TSs. What the electronic states are during these reactions, and how the CASVB method describes the electronic structure, are our interests in this section. 

If we re-take the TS of chemical bonds as the origin, these facts well explain the shift of TS (from the early TS side to the late TS side) that Hammond s postulate predicts, indicating that the CASVB method is a powerful tool for describing the electronic structure and chemical bond during chemical reactions. 

Valence-bond methods have increased its applicability recently. One example is the CASVB (complete active space valence bond) method. A CASVB wave function can be obtained simply by transforming a canonical CASSCF function and readily interpreted in terms of the well-known classical VB resonance structures. The total CASVB wave function is identical to the canonical CASSCF wave function. In other words, the MO description and the VB description are equivalent, at least at the level of CASSCF. The CASVB method provides an alternative tool for describing the correlated wave functions. 

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