BOVB method

The BOVB method has several levels of accuracy. At the most basic level, referred to as L-BOVB, all orbitals are strictly localized on their respective fragments. One way of improving the energetics is to increase the number of degrees of freedom by permitting the inactive orbitals to be delocalized. This option, which does not alter the interpretability of the wave function, accounts better for the nonbonding interactions between the fragments and is referred to... 

The BOVB method has been successfully tested for its ability to reproduce dissociation energies and/or dissociation energy curves, close to the results (or estimated ones) of full Cl or to other highly accurate calculations performed with the same basis sets. A variety of two-electron and odd-electron bonds, including difficult test cases as F2, FH, and F2 (38,42), and the H3M-C1 series (M = C, Si, Ge, Sn, Pb) (39,43,44) were investigated. 

The BOVB method is implemented in the XMVB package and also in the TURTLE module in GAMESS UK. 

To run a BOVB calculation smoothly, it is advisable to start from an appropriate guess function, which may be, for example, a preliminary VBSCF wave function. In the XMVB program, the BOVB procedure sets up automatically by coding the keyword bovb in the input. As with the VBSCF method, the spectator orbitals in the BOVB method may be defined as either localized or delocalized, resulting in the L- and D-BOVB methods, respectively. 

D-BOVB and SD-BOVB Calculations ofF2 Like VBSCF, the BOVB method is improved by allowing the spectator orbitals to be delocalized in the so-called D-BOVB or SD-BOVB levels. As long as the spectator orbitals can be distinguished from the active ones by symmetry, which is the case of the lone pairs of tt symmetry in the F2 molecule, delocalizing these orbitals is easily done The user has only to specify which basis functions the spectator orbitals are allowed to be made of, much the same as in VBSCF. This is shown in Input 10.6 for a calculation of D-BOVB type, in which the tt spectator orbitals are allowed to delocalize. 

As discussed in Chapter 9, the VBCI method provides results that are at par with the BOVB method, the difference being that the electrons of the spectator orbitals are correlated too in the VBCI method. The wave function starts from a VBSCF wave function and augments it with subsequent local configuration interaction that can be restricted to single excitations (VBCIS level), or single and double excitations (VBCISD), or higher excitations. Here, we will consider only the VBCISD level, which is a good compromise between accuracy and cost efficiency. 

Delocalization of the inactive orbitals (D-BOVB or SD-BOVB) is important for getting accurate energetics. Once again, it is important to make sure that the orbitals that are delocalized are the inactive ones, while the active set remains purely localized, which is the basic tenet of the BOVB method. To avoid a spurious exchange between the active and inactive spaces during the... 

BOVB Breathing orbital valence bond. A VB computational method. The BOVB wave function is a linear combination of VB structures that simultaneously optimizes the structural coefficients and the orbitals of the structures and allows different orbitals for different structures. The BOVB method must be used with strictly localized active orbitals (see HAOs). When all the orbitals are localized, the method is referred to as L-BOVB. There are other BOVB levels, which use delocalized MO-type inactive orbitals, if the latter have different symmetry than the active orbitals. (See Chapters 9 and 10.)... 

More recently Hiberty et ol[26] proposed the breathing orbital valence bond (BOVB) method, which can perhaps be described as a combination of the Coulson-Fisher method and techniques used in the early calculations of the Weinbaum.[7] The latter are characterized by using differently scaled orbitals in different VB structures. The BOVB does not use direct orbital scaling, of course, but forms linear combinations of AOs to attain the same end. Any desired combination of orbitals restricted to one center or allowed to cover more than one is provided for. These workers suggest that this gives a simple wave function with a simultaneous effective relative accuracy. 

Among the VB related methods existent in the literature, besides GVB and SCVB, it is worth mentioning the VB-SCF and the BOVB (breathing orbital valence bond) methods [3]. The VB-SCF method incorporates orbital optimization to the classical VB scheme. When one has more than one important perfect pairing scheme (or resonance , but see the next Section) the BOVB method can be utilised. More recently McWeeny also presented his version of the classical VB method including orbital optimization and multistructural capabilities [20]. 

The BOVB method is aimed at combining the qualities of interpretability and compactness of valence bond wave functions with a quantitative accuracy of the energetics. The fundamental feature of the method is the freedom of the orbitals to be different for each VB structure during the optimization process. In this manner, the orbitals respond to the instantaneous field of the individual VB structure rather than to an average field of all the structures. As such, the BOVB method accounts for the differential dynamic correlation that is associated with elementary processes like bond forming/breaking, while leaving the wave function compact. The use of strictly localized orbitals ensures a maximum correspondence between the wave function and the concept of Lewis structure, and makes the method suitable for calculation of diabatic states. 

The requirement that all Lewis structures be generated requires in turn that both covalent and ionic components of the chemical bonds have to be considered. As the number of VB structures grows exponentially with the number of electrons, it is already apparent that the BOVB method will not be... 

An important feature of the BOVB method is that the active orbitals are chosen to be strictly localized on a single atom or fragment, without any delocalization tails. If this were not the case, a so-called "covalent" structure, defined with more or less delocalized orbitals like, e.g., Coulson-Fischer orbitals, would implicitly contain some ionic contributions, which would make the interpretation of the wave function questionable [27]. The use of pure AOs is therefore a way to ensure an unambiguous correspondence between the concept of Lewis structural scheme and its mathematical formulation. Another reason for the choice of local orbitals is that the breathing orbital effect is... 

The above best calculation [11] corresponds to the simplest level of the BOVB method, referred to as L-BOVB. All orbitals, active and inactive, are strictly local, and the ionic structures are of closed-shell type, as represented in 10 and 11. However the theory can be further improved, and the corresponding levels are displayed in Table 2. It appears that the L-BOVB/6-31+G level, yields a fair bonding energy, but an equilibrium distance that is rather too long compared to sophisticated estimations. This is the sign of an incomplete description of the bond. Indeed this simpler level does not fully account for the... 

By nature, the BOVB method describes properly the dissociation process. As a test case, the dissociation curve of the FH molecule was calculated at the highest BOVB level (extended SD-BOVB), and compared with a reference full Cl dissociation curve calculated by Bauschlicher et al. [33] with the same basis set. The two curves, that were compared in Ref. 12, were found to be practically indistinguishable within an error margin of 0.8 kcal/mol, showing the ability of the BOVB method to describe the bonding interaction equally well at any interatomic distance from equilibrium all the way to infinite separation [12]. 

The (H3C CH3)+ radical cation was selected, to test the ability of the BOVB method to describe one-electron bonds, since this bond exhibits the largest correlation effect in the series. The bonding energy, calculated at the D-BOVB level, amounts to 48.7 kcal/mol, in fair agreement with the MP4 value. 

The BOVB method does not of course aim to compete with the standard ab initio methods. BOVB has its specific domain. It serves as an interface between the quantitative rigor of today s capabilities and the traditional qualitative matrix of concepts of chemistry. As such, it has been mainly devised as a tool for computing diabatic states, with applications to chemical dynamics, chemical reactivity with the VB correlation diagrams, photochemistry, resonance concepts in organic chemistry, reaction mechanisms, and more generally all cases where a valence bond reading of the wave function or the properties of one particular VB structure are desirable in order to understand better the nature of an electronic state. The method has passed its first tests of credibility and is now facing a wide field of future applications. 

In the next section we review some of the theoretical and practical details of the BOVB method. In particular we consider means by which much larger calculations may be attempted. In section 3, we present some illustrative calculations to expose the properties of BOVB wavefunctions and familiarize the reader with the BOVB description of electronic structure. This is followed by a description of some recent calculations on the pseudohalide acid HCS2N3 and a large diphosphaallene radical anion. We conclude by summarizing the strengths and weaknesses of the BOVB method as a general quantum chemical tool and suggest areas for future development. 

In this section we outline some simple calculations which illustrate the nature of the results we can expect from the BOVB method we have described. Our purpose here is not to report new applications, those will be given in the next section, but rather to illustrate the utility of what we have proposed and enable a comparison to be made with other valence bond schemes. 

The model system we have treated with the BOVB method and the full system with the PM3 semiempirical method. The total energy is evaluated as... 

It is appropriate to conclude by asking what the BOVB method has to offer valence bond theory in general and, perhaps more importantly, what it may offer the larger area of quantum chemistry as a whole. 

The BOVB method suggested by Hiberty et employs a multi-configuration... 

A number of computational studies performed using the BOVB method (see e.g. ref. 12 and references therein) indicate that this method includes some of the dynamic correlation energy which is missing in approaches such as GVB-PP-SO and SC. This d5mamic correlation energy comes from the fact that BOVB allows the orbitals in different structures to become different which, for a wavefunction with N active electrons and L structures leads to an V electrons in LN orbitals construction. A BOVB wavefunction of this type can perform better than its GVB-PP-SO and SC counterparts which represent V electrons in N orbitals constructions. In certain circumstances, it can even perform better than an V in N CASSCF wavefunction. However, it is not fair to compare a BOVB wavefunction with N active electrons and L structures to an V in Af CASSCF wavefunction as its direct... 

Another VB study of S 2 identity reactions has been reported by Song, Wu, Hiberty and Shaik. These authors applied the BOVB method on its own and within the VBPCM framework (VB coupled with a polarised continuum model) to the reactions... 

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