Lewis- type NBO

The N/2 Lewis-type NBOs of highest occupancy ( /AB) 2) can be directly associated with the localized electron pairs of the chemist s Lewis-structure diagram.46 Each Lewis-type NBO f2AB can be decomposed into constituent natural hybrid orbitals (NHOs) hA and hB on atoms A and B,... 

The localized wavefunction EL formed from N/2 doubly occupied Lewis-type NBOs,... 

How do LMOs differ from NBOs Each occupied LMO (Ua) can be written in terms of a parent Lewis-type NBO (Ua) with a weak delocalization tail from other non-Lewis NBOs (fV),... 

Figure 7.1 presents contour diagrams for the Lewis-type NBOs of formaldehyde (panels a, c, e, g, h), calculated at the B3LYP/6-311-H-G""" level of hybrid density functional theory (DFT). As is immediately apparent, the bonding Gch, and Kcq NBOs exhibit the familiar sigma and pi shapes of idealized textbook depictions. The resemblance to expected textbook forms is further emphasized when each A-B bond is written as a linear combination (LC) of its constituent natural hybrid orbitals (NHOs) and with polarization coefficients and Cg, namely. 

The upper entries in Table 7.1 summarize details of the LC-NHO expansions for valence Lewis-type NBOs of formaldehyde at the B3LYP/6-311-H-G""" level. The carbon and oxygen hybrids of a o and Gch have the expected sp -like composition, and the polarization coefficients vary in the expected way with elec-... 

Table 7.1 Occupancies and Compositions of Lewis-Type NBOs of Formaldehyde at Various Theoretical Levels ...

Table 7.2 Occupancies and Compositions of Acyl Group Lewis-Type NBOs of Acetaldehyde 2 at the B3LYP/6-311-M-G Level (cf formaldehyde NBOs of Table 7.1)...

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 standard NBO algorithm attempts to maximize the total occupancy PLewis of Lewis-type (unstarred) NBOs, under the assumption that Lewis-type orbitals are formally occupied and non-Lewis-type (starred) orbitals are formally vacant in the best single NBO configuration. This assumption is obviously untenable for excited states, where promotions from Lewis-type to non-Lewis-type NBOs should be a common feature. We therefore define to be the total occupancy of the N most highly occupied spin-NBOs (whether of Lewis- or non-Lewis-type) and Poco the... 

Table 7.4 exhibits some details of a and (i Lewis-type NBOs for the ground-state vinoxy radical. These can be... 

Table 7.5 exhibits details of a and fi Lewis-type NBOs for vinoxy A A, corresponding to the Lewis structure representations 8a and 8b. 

The greater delocalization in the / manifold is manifested in the lower overall percent Pl values (97.87% [a] vs. 97.30% [p ) as well the individual NBO occupancies. In the a manifold, the only significantly depopulated Lewis-type NBOs are Uq (due to the usual ric i =co delocalization) and Hq (dne to Hq ch o cc ) However, in the ji manifold, only the two methylenic C-H bonds are well localized (occnpancies > 0.99e), whereas other Lewis NBOs exhibit losses np to 10%. The forms of the B -state NBOs closely resemble their counterparts in other states, and the interhybrid angles of the planar bonding skeleton show negligible bond bending in this state. 

Since Lewis-type NBOs typically have (slightly) less than double occupancy, they are not yet true molecular orbitals in the Hartree-Fock sense. Equivalently, one may say that a determinant of doubly-occupied NBOs, the natural Lewis structure wavefunction "Pl = det (cTAB) (crcD) I must have higher energy than the Hartree-Fock MO wavefunction... 

From the mode of construction, it is evident that each NLMO will have a dominant contribution from a parent Lewis-type NBO delocalization tails) from non-Lewis-type NBOs leading to expressions of the form... 

Figure 4.7 shows the Lewis-type NBO (4.43) in contour diagrams of overlapping NHOs (left) and final NBO (center), or as a surface plot (right). Figure 4.8 similarly shows the non-Lewis-type NBOs (4.44), (4.45) in contour and surface plots. 

NBO delocalizations (e.g., of o —> rtoo type cf. Chapter 5) that significantly affect ozone structure and reactivity. Further aspects of the interplay between spin hybridization (involving Lewis-type NBOs) and resonance hybridization (involving non-Lewis NBOs) will be discussed in Chapter 5. 

The previous chapter has given considerable evidence for the accuracy of the -based picture in a variety of open- and closed-shell species, based on the high percentage of electron density that is accounted for in Lewis-type NBOs alone. The complete NBO basis set Q, naturally separates into Lewis and non-Lewis components,... 

The unperturbed Lewis-type description (5.9 and 5.10) neglects the real-world interactions (5.12) between donor (Lewis-type) and acceptor (non-Lewis-type) NBOs of a parent Lewis structure However, the typical high accuracy of this... 

Instead of a single deletion, let us now consider NOSTAR deletion of all interactions with non-Lewis NBOs. In this case, we obtain the occupancy and energy changes shown in 1/0-5.6, in which all Lewis-type NBOs are restored to exact double occupancy and all non-Lewis NBOs are completely vacant, corresponding to the idealized NLS limit... 

Lewis-type NBO with a weak non-Lewis tail from whereas the out-of-phase (vacant, higher-energy) (Eq. 5.36) is predominantly the non-Lewis... 

A multiconfigurational wavefunction leads to an additional NLMO coupling contribution that appears near the end of DIPOLE output.) Each occupied (NLMO) expanded in terms of its parent Lewis-type NBO (pf and... 

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