Breathing orbital

P. C. Hiberty, S. Humbel, C. P. Byrman, J. H. van Lenthe, J. Chem. Phys. 101, 5969 (1994). Compact Valence Bond Functions with Breathing Orbitals Application to the Bond Dissociation Energies of F2 and FH. 

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. 

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. 

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.)... 

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]. 

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 computed equilibrium distance and bonding energy of F2- are displayed in Table 5. To appreciate better the sensitivity of active vs inactive orbitals to the breathing orbital effect, the latter has been introduced by steps In the first step no breathing orbitals are used (La = Lr, Ra = Rr, (Pi = cpf) this VBSCF calculation is nearly equivalent to the ROHF level. In the second step, only active orbitals are included in the breathing set (La 1- Lr, Ra Rr), while in the next step full breathing is permitted (La Lr, Ra Rr, cpi cpi ). The latter wave function, at the L-BOVB level, can be represented as in 26, 27 below. 

The breathing orbital effect, restricted to the active orbitals that are directly involved in the three-electron bond, already improves the bonding energy by some 17 kcal/mol relative to the ROHF value (Table 5). Extension of the... 

G basis set). BOVB calculations are performed with all valence orbitals being included in the set of breathing orbitals (fully-breathing option) unless otherwise specified (entry 2). 

The Hartree-Fock error is thus completely corrected by the breathing orbital effect. On a per orbital basis, each active AO contributes for 8.6 kcal/mol to the overall BO stabilization, while the inactive lone pairs have a lesser influence, about 2.8 kcal/mol each. 

The valence orbitals of Cl2 are spatially larger than those of F2 . Accordingly, the breathing orbital effect is expected to be less important in CI2 than in F2, since two electrons occupying the same orbital are now less confined than in the compact orbitals of F2. ... 

As shown by Clark [38] in a comprehensive computational study of (HnX XHn)+ radical cations (X= Li to C, Na to Si), one-electron bonds are already rather well described by simple Hartree-Fock theory. This is because the active system contains a single electron, so that the breathing orbital effect is ineffective in the active subspace, where each orbital is either empty or singly occupied as illustrated in 32, 33 for the OC bond. 

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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