The Breathing Orbital Valence Bond Method

The difference between the BOVB and VBSCF wave function can be illustrated on the simple example of the description of the A-B bond, where A and B are two polyelectronic fragments. While the VBSCF wave function reads like Equation 9.8, the BOVB wave function takes the following form  

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 importance and physical nature of dynamic correlation is even better appreciated in the case of 3e bonds, a type of bond in which the electron correlation is entirely dynamic, since there is no left-right correlation associated with odd-electron bonds. As noted earlier, the Hartree Fock and simple VB functions for 3e bonds (hence, GVB, SC, or VBSCF) are nearly equivalent and yield about similar bonding energies. Taking the F2 radical anion as an example, it turns out that, compared to the experimental bonding energy of 

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

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P. C. Hiberty, in Modern Electronic Structure Theory and Applications in Organic Chemistry, E. R. Davidson, Ed., World Scientific, River Edge, NJ, 1997, pp. 289-367. The Breathing Orbital Valence Bond Method. 

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) ...

P. C. Hiberty, S. Shaik, in Valence Bond Theory, D. L. Cooper, Ed., Elsevier, Amsterdam, The Netherlands, 2002, pp. 187-226. Breathing-Orbital Valence Bond—A Valence Bond Method Incorporating Static and Dynamic Electron Correlation Effects. 

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.)... 

The Netherlands, 2002, pp. 187-226. Breathing-Orbital Valence Bond—A Valence Bond Method Incorporating Static and Dynamic Electron Correlation Effects. 

P. C. Hiberty, S. Humbel, P. Archirel, J. Phys. Chem. 98, 11697 (1994). Nature of the Differential Electron Correlation in Three-Electron Bond Dissociation. Efficiency of a Simple Two-Configuration Valence Bond Method with Breathing Orbitals. 

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