Non-Lewis type NBO

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... 

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. 

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... 

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),... 

Resonance such as (5.28a)-(5.28c) is inherently a quantal phenomenon, with no classical counterpart. In NBO language, each of the resonance interactions (5.28a)-(5.28c) corresponds to a donor-acceptor interaction between a nominally filled (donor Lewis-type) and unfilled (acceptor non-Lewis-type) orbital, the orbital counterpart of G. N. Lewis s general acid-base concept. As mentioned above, Lewis and Werner (among others) had well recognized the presence of such valence-like forces in the dative or coordinative binding of free molecular species. Thus, the advent of quantum mechanics and Pauling s resonance theory served to secure and justify chemical concepts that had previously been established on the basis of compelling chemical evidence. 

Figure 7.1 NBOView two-dimensional contour images of formaldehyde valence-shell NBOs of Lewis type (a,c,e,g,h) and non-Lewis type (b,d,f).

Simple second-order perturbation theory is well adapted to describe the energy lowering and occupancy shifts associated with delocalizing interactions between specific Lewis and non-Lewis NBOs. The unperturbed wave function /l corresponds to the perfectly localized Lewis structure limit, with all Lewis-type (electron donor) NBOs fully occupied and all non-Lewis-type (electron acceptor) NBOs completely vacant. The perturbative interaction of donor NBO a B with acceptor NBO CD leads to the approximate second-order energy lowering... 

The occupied orbitals on the left in Equation 7.13 are both Lewis-type (unstarred), but on the right is non-Lewis-type, and its occupancy is not accoimted to PLe. In rare cases where the standard NBO search leads to such a hinh-occupancy and pair, the error associated with occupancy is not properly taken into account, and the search may return a structure that is not the best possible in the maximum-occupancy sense (as can be checked with a CHOOSE keylist). This type of anomaly cannot occur when (rather than PLewis) is chosen as the variational objective function. For this reason we recommend that the generalized EXCITE search in NBO 5.X be used in all cases, including ground states, even though it requires additional computation time and usually gives the same result as NBO 5.0. 

HONDO = bond orbital - neglect of differential overlap (SCF-MO) GIAO = gauge-including atomic orbital L = Lewis-type (or localized) LC-BO = linear combination of bond orbitals LCNBO = linear combination of NBOs LMO = localized molecular orbital MSPNBO = maximum spin-paired NBO NBBP = natural bond-bond polarizability NBO = natural bond orbital NCS = natural chemical shielding NEDA = natural energy decomposition analysis NHO = natural hybrid orbital NL = non-Lewis-type (or... 

The chemist s idealized Lewis structure picture describes the N/2 electron pairs as localized in one-center ( lone pair ) or two-center ( bond ) regions of the molecule. The natural bond orbital (NBO) algorithm leads to an optimal set of one- and two-center orbitals that are in close correspondence with this picture. In effect, the algorithm searches the density matrix for the set of N/2 localized Lewis-type lone pair and bond orbitals of near-double occupancy that best describe the given wave-function, with the residual weakly occupied non-Lewis-type... 

Figure 4 Valence-shell NBOs of formaldehyde (RHF/6-311 level), showing (a) Lewis-type ( donor ) and (b) non-Lewis-type ( acceptor ) orbital shapes and nodal patterns...

As shown in the output, this particular NBO search terminated successfully after only a single cycle, which satisfied the default search criteria. The search yielded a Lewis structure with one core (CR), one bond (BD), and three lone pair (LP) Lewis-type (L) NBOs, which described about 99.95% of the total electron density (i.e., 9.995 of the 10 electrons). These five L-type NBOs easily satisfied the default threshold (1.90e) for pair occupancy [the 0 under Low occ (L) ] and the remaining 17 non-Lewis (NL) NBOs were all well below the O.le occupancy threshold [ High occ (NL) ] to be considered a satisfactory Lewis structure. [The Dev entry refers to deviations from the initial guess that steers multiple cycles of the search algorithm (if required), beyond the scope of this book consult the NBO... 

SlTn, SITa = normalization constants). A portion of the NBO listing for the three-center Bi—Hg-B2 NBOs of B2H6 is displayed in FO-4.14, showing the Lewis-type tBHB bond (NBO 2) and non-Lewis-type Tbhb (NBO 25) and Tbhb (NBO 26) antibonds for this case. 

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,... 

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... 

Table 3.41. NBO/NRT descriptors for B4H10 (see Fig. 3.103(a)), showing (a) alternative styx codes (with specific bond types) and associated non-Lewis density error (b) NHO hu and percentage polarization for NBOs of the...

A similar conclusion was drawn based on nucleus-independent chemical shift (NICS) calculations, that is, there is no significant aromatic character to a 1,2-dihydrodiazete. Natural bond orbital (NBO) analysis provides the means of investigating the extent of electron delocalization within a given structure and also indicates the bond order. In Lewis-type bonding orbitals electron density is depleted with increase in the occupancy in antibonding or non-Lewis orbitals. In the case of cis-14 or trans-14, there is less occupancy in non-Lewis orbitals and the bond order is more like localized bonds N-N (1.01), C-N (1.06) and C=C (1.76), which are similar to the nonaromatic substances. 

Rydberg orbitals. The contribution to the total density matrix from unoccupied orbitals is generally small however, antibonds play an important role since they represent unused valence-shell capacity. The energy of a molecule can be decomposed into two components associated with covalent and noncovalent structures the former corresponds to the ideal Lewis contributions, and the latter is associated with non-Lewis contributions. The nondiagonal elements of the Fock matrix in the NBO basis are interpreted as the stabilizing interaction between occupied orbitals of the formal Lewis structure and unoccupied ones. Since the corrections to the energy of the Lewis-type picture are usually small, they can be approximated by second-order perturbation theory, Eq. (78),... 

Bonding NBOs of the Lewis orbital -type have occupation numbers near 2, and antibonding NBOs are of the non-Lewis orbital -type (occupation numbers near... 

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