Breathing orbital VB

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. 

The breathing-orbital VB (BOVB) method [P. C. Hiberty and S. Shaik, Theor. Chem. Acc., 108, 255 (2002) and references cited therein] differs in two ways from the VBSCF method. Each orbital in the BOVB method is always taken to be localized on an individual atom. The orbitals used in different structures are free to differ, so that each VB structure has its own set of optimized orbitals. 

BEP = Bell-Evans-Polanyi BOVB = breathing orbital VB FMVB = fragments in molecules based VB HL structure = Heitler-London structure PRS = perfectly resonating state VBCM = VB configuration mixing VBSCD = VB state correlation diagram VBSCF = self-consistent field VB. 

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]. 

Figure 6.5b shows the breathing orbital valence bond (BOVB) computed energy curves of various state wave functions. The first one on the left-hand side shows the energy of the fundamental structure 55 plotted along the Li- -Li distance. It is seen that this structure is repulsive, much like the corresponding structure for the FM state of H2 (Figure 6.2). The second plot shows a Hnear combination of the fundamental structure with the two triplet ionic structures. It is seen that the addition of 3>j (ion) results in an incipient FMNP bond. Adding the other structures in the third and fourth plots deepens the energy well to its final BOVB value, which is D = 0.639 with a cc-pVDZ basis set and 0.888 kcal mol for cc-pCVTZ [2a] the CCSD values for the two basis sets are 0 =0.738 and 0.902 kcal mol h The agreement of VB with the standard coupled cluster method is satisfactory. The final VB wave function is shown in Eq. (6.1) ...

As a consequence of the BOVB procedure, the active orbitals (those involved in the bond) can use this extra degree of freedom to adapt themselves to their instantaneous occupancies. The spectator orbitals (not involved in the bond) can fit the instantaneous charges of the atoms to which they belong. Thus, all the orbitals follow the charge fluctuation that is inherent to any bond by undergoing instantaneous changes in size and shape, hence the name breathing orbitals . The same philosophy imderlies the description of odd-electron bonds, in terms of two VB structures. 

---