Breathing orbital effect

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... 

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. 

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. 

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. 

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

As discussed in greater detail in the following section, the conceptual confusion over DODS-type splitting and orbital breathing effects often stems from mistaken attribution of physical significance to the numerical basis functions that are employed... 

As before, the Natural Atomic Orbitals (NAOs) serve as the optimal effective atom-like orbitals for describing the overall electron density distribution of the molecular wavefunction, so that finding the atomic electrons in NBO output is not more difficult than in Chapter 2. We shall first examine how the NAOs within the molecular environment differ from the free-space forms encountered in Chapter 2. We use the experience gained there to anticipate the breathing ... 

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