Valence antibond

Table 3.29. The NBO descriptors of XYZ triatomic anions (see Table 3.28), showing natural atomic charges (Q), percentage polarization of oxy and ayz NBOs toward terminal atoms, second-order nz— oxy and nx->OYZ stabilizations (A/s(2)), and occupancies of valence antibonds (oxy and ayz ) and extra-valent Rydberg orbitals (ry ) parenthesized values refer to Lewis structure of lower accuracy...

The importance of n-7t CT delocalization can also be assessed by deleting these interactions (with the DEL option) and reoptimizing the structure, as shown in Fig. 5.43. For this purpose we deleted all three valence antibonds of NO+(ono and two 7Tno NBOs) to suppress the leading possible valence CT delocalizations from Fewis base to Fewis acid. Note that these three NBOs have zero occupancy... 

Figure 5.43 The optimized structure of CT-deleted H3N- NO+ (with valence antibonds of NO+ deleted to suppress intermolecular nN-7tNO delocalization). The shortest intermolecular N- O and N- -N distances are 2.99 and 3.11 A, respectively, and the net binding energy is 20.4 kcal mol-1 (cf. Fig. 5.42 and Table 5.23).

Delocalization effects are represented in NBO theory by partial occupancy of non-Lewis-type NBOs, corresponding to departiu-es from a perfectly localized Lewis structure description. Non-Lewis NBOs include the valence antibonds, that is, the out-of-phase combinations accompany each in-... 

The non-Lewis /I-NBOs of vinoxy consist of the 1-c ric, hole (labeled LP in NBO output) as well as the usual valence antibonds ( ch> co co> co)and Rydberg orbitals. Figure 7.4d depicts the form of the most important /1-acceptor he, whose orbital energy (0.0874 a.u.) lies significantly below that of other non-Lewis NBOs (e.g., 0.0046 a.u. for the next-lowest Pco ) According to the second-order estimates... 

Table 7.17 exhibits NBOs of the equilibrium A-state vinoxy water complex in a form directly comparable with the isolated vinoxy radical of Table 7.14. Subtle changes of Lewis structure are seen throughout but most notably in the 71 0 bond repolarization (from 50.9 to 54.0% on O) and occupancy increase (by 0.0068e). More significant population shifts are found in the valence antibond occupancies (not shown) and net atomic and molecular unit charges (not shown), which correspond to an overall transfer of 0.01836e from the vinoxy to the water moiety. As suggested by Equation 7.9, population shifts Aq of this magnitude are expected to correspond to stabilization energies of the order of 0.02 a.u. (-12 kcal/mol).

The bonds vary smoothly from covalent (ca=Cb) to ionic (ca Cb) limit. Each valence bonding NBO o must be paired with a corresponding valence antibonding NBO o (the acceptor) to complete the span of the valence space ... 

As noted above (equations 9 and 10), each pair of valence NHOs /ia, /ib leads to a complementary pair of valence bond (/)ab) and antibond ( ab) orbitals. Although the latter orbitals play no role in the elementary Lewis picture, their importance was emphasized by Lennard-Jones and Mulliken in the treatment of homonuclear diatomic molecules. Since valence antibonds represent the residual atomic valence-shell capacity that is not saturated by covalent bond formation, they are generally found to play the leading role in noncovalent interactions and delocalization effects beyond the Lewis structure picture. Indeed, it may be said that the NBO treatment of bond-antibond interactions constitutes its most unique and characteristic contribution toward extending the Lewis structure concepts of valence theory. Although the NBO hybrids and polarization coefficients are chosen to minimize the role of antibonds, the final non-zero weighting of non-Lewis orbitals reflects their essential contribution to wavefunction delocalization. 

Confusion often arises between the virtual orbitals 0, of SCF-MO theory and the localized valence antibonds Xb)-Although the spaces spanned by these sets overlap to a considerable extent, expansion of one set in terms of the other (e.g., in LCNBO-MO form) shows that they are far from identical. Indeed, the virtual orbitals are by their nature completely unoccupied, making no physical contribution to the SCF wavefunction or measurable properties. In contrast, the valence antibonds contribute irreducibly to the energy lowering and density shifts associated with electron delocalization, and their non-zero occupancies reflect the important physical effects of delocalization on the wavefunction and molecular properties. 

To see how valence antibonds contribute to the occupied molecular orbitals [orbital energies e, in Hartree-Fock... 

As shown in the output, the five leading L-type NBOs 1-5, of near-double occupancy, are followed by the 24 remaining NL-type (starred) NBOs of Rydberg (RY ) or valence antibond (BD ) type, all of negligible occupancy (and safely ignorable for all practical purposes). The core (CR) NBO 2 is essentially identical to the F IsNAO exhibited previously (Fig. 3.1). Profile, contour, and surface plots for the remaining valence NBOs of BD, LP type are shown in Fig. 4.1. 

Each Lewis-type Tabc must therefore be complemented by two remaining three-center awttbond NBOs (labeled 3C in NBO output) to conserve basis completeness and orthonormality. In many cases, these valence antibond NBOs (as optimally chosen by the NBO program) correspond to two-center re-type Tabc " and three-center A-type Tabc linear combinations (cf. W B, p. 306ff),... 

Even without consulting the numerical entries of the E(2) table, an alert chemistry student will generally look first for antibonds in the vicinal anfr-positions around each lone pair (or other strong donor NBO) as principal sites for resonance delocalizations, based on general considerations discussed above. In order to go beyond the elementary Lewis structure picture, the first step is to identify details (occupancy, shape, and location) of the important valence antibonds. 

As expected, the largest NLMO tail coefficients are usually associated with the valence antibonds (if any such exist) at vicinal awti-positions relative to the parent NBO, such as the cr()jj tail of in NLMO 2 (5.42). (Note that the order of... 

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