NBO analysis

The concept of natural orbitals may be used for distributing electrons into atomic and molecular orbitals, and thereby for deriving atomic charges and molecular bonds. The idea in the Natural Atomic Orbital (NAO) and Natural Bond Orbital (NBO) analysis developed by F. Weinholt and co-workers " is to use the one-electron density matrix for defining the shape of the atomic orbitals in the molecular environment, and derive molecular bonds from electron density between atoms. 

As a result of these substituent-induced polarizations, the complementary conjugative interactions at each ring site become somewhat imbalanced (so that, e.g., the donor-acceptor interaction from C3—C4 to C5—C(, is 23.1 kcal mol-1, but that in the opposite direction is only 16.4 kcal mol-1). From the polarization pattern in (3.133) one can recognize that excess pi density is accumulated at the ortho (C2, C6) and para (C4) positions, and thus that the reactivity of these sites should increase with respect to electrophilic attack. This is in accord with the well-known o, /(-directing effect of amino substitution in electrophilic aromatic substitution reactions. Although the localized NBO analysis has been carried out for the specific Kckule structure of aniline shown in Fig. 3.40, it is easy to verify that exactly the same physical conclusions are drawn if one starts from the alternative Kekule structure. 

Comparison with (3.156) shows that F(NBO) is intrinsically of significantly higher accuracy than h(HMO) for describing the actual pi interactions of benzene. Because F(nbo) js tjje fundamental starting point for localized NBO analysis of conjugafive interactions, we can conclude that the NBO donor-acceptor picture is inherently more accurate than that based on the Hiickel tight-binding approximation. 

At a more quantitative level, NBO analysis has been employed in a variety of investigations102 to dissect the detailed pathways of TB interactions. Quantitative theoretical and experimental studies have shown the general unreliability of the older AO-based superexchange model103 as a guide to TB pathways. The modem NBO-based picture of TB/TS interactions is authoritatively described elsewhere104 and need not be elaborated here. 

The NBO donor acceptor picture of hypervalency hyperbonds Let us re-examine the 3c/4e MO description from the localized NBO perspective. NBO analysis of the MO wavefunction (3.193) may lead to the Lewis structure A + B—C, with NBOs... 

However, the relative accuracies of the two possible structural bond patterns can be assessed more quantitatively with NBO analysis. The NBO procedure allows one to specify alternative Lewis structure patterns of two- and three-center bonds158 and determine the non-Lewis density error pni, of each such structure. As shown in Table 3.41(a), the non-Lewis density of the 4012 structure (0.6072c) is smaller than that of the 3103 structure (0.8760c), which confirms that the 4012 structure (3.248) is indeed the superior bonding description in this case. 

The NBO analysis reveals the strong electronic similarities between C2B9H112-and C5H5-. The optimal NBO Lewis structure representations, (3.268a)-(3.268c), all have two-center single bonds connecting the B7, Bg, B9, C10, and Cn rim atoms, with the familiar motif of a two-center B—B bond flanked by four... 

The NBO analysis characterizes the 7tcc— nnf interaction as relatively modest (25.0kcal mol-1), with 0.09e charge transfer from ethylene to HfH4. Accordingly, the coordinated alkene is somewhat activated toward nucleophilic attack, but the chemical effects are minor compared with those for other donor-acceptor motifs to be discussed below. 

Recently, we analyzed the role of electron repulsion relative to bond breaking and antiaromaticity effects on a quantitative basis using Natural Bond Orbital (NBO) analysis.24 Two other destabilizing factors were considered at the initial stage of the cyclization in addition to four-electron repulsion between the filled in-plane acetylenic re-orbitals - distortion/breaking of the acetylenic bonds as a result of their bending, and the fact that, at a distance of ca. 3 A, the in-plane re-orbitals become parallel and reach a geometry that resembles the antiaromatic TS of the symmetry forbidden [2S + 2S] cycloaddition (vide infra). 

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