BOVB Wavefunctions

With the orbitals numbered as shown above, two linearly independent spin-couplings would be 

Another set of configurations which it is sometimes useful to add to each spincoupling is based on the restricted Cl (RCI) ideas of Goddard and coworkers (e.g. see [21]). We have found that on some problems the variational bound is 

The total wavefunction is then obtained by taking the direct product of all such structures. This leads, for P pairs, to a total of 3P spatial configurations 

The RCI expansion produces a relatively small number of additional terms and can be used for problematic cases to stabilize the energy obtained from Eq. (10). A wavefunction including these additional configurations for the example above would be denoted BOVB(41+S+RCI). 

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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. 

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... 

Given that we intend to employ a wide range of different expansions in our BOVB calculations it is important to know which types of configurations dominate the wavefunction and which simply serve to condition Eq. (10). The usual way to analyze a wavefunction is to calculate the weight of each configuration within the total wavefunction. The most widely used definition of weight is that of Chirgwin and Coulson [26]... 

C2nH2n+2 systems there are 2n tt-electrons and we include all of these in our calculations. The wavefunction used may be denoted BOVB(2 ,7+5) in the notation of Eq. (14). As may be anticipated the outcome of the BOVB... 

Overlap integrals obtained from BOVB(6,1+S+RCI) wavefunction for dioxirane in a cc-pVDZ basis ... 

Fig. 5. Symmetry unique orbitals of methane obtained with BOVB(8,l+S+RCI) wavefunction using a cc-pVDZ basis.

We have shown the BOVB description of n and a bonds in the previous examples. We conclude this section with the BOVB description of the water molecule in which we allow both the bonding and lone-pair electrons to be described in nonorthogonal orbitals. This leads to an eight electron problem which we describe with a BOVB(S, 1+S+RC1)/cc-pVDZ wavefunction. Again the geometry is HF/cc-pVDZ. The BOVB(8,1+S+RCT) energy lies approximately 0.008 au above the BOVB(S, V) energy. 

One solution to this basis set problem in more recent classical VB-style approaches, such as some types of VBSCF (VB self-consistent-field) wavefunctions and the BOVB ( breathing orbital VB) method,is to use variational hybrid atomic orbitals (HAOs) expanded in terms of the basis functions on a single centre only. 

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