NLMO hybridizations

Fig. 19. Relationship between computed activation energies (B3LYP/6-311+G ) and p-orbital contribution in the NLMO hybridization of the lone pairs on the coordinating atoms (156).

Formally, the lone pairs on molecular nitrogen, hydrogen cyanide, and carbon monoxide are sp hybrid orbitals, whereas NLMO hybridizations calculated even lower p contributions. Hence, these lone pairs have low directionality, the electron density remains close to the coordinating atom and interaction between the lone pair and the Be2+ is comparatively weak. The Be-L bonds are easily disrupted and ligand exchange consequently can proceed with a low activation barrier. A high degree of p character, on the other hand, means that the lone pair is directed toward beryllium, with electron density close to the metal center, and thus well suited for coordination. 

Figure 7. Average NPA p/s hybridization ratio [97] on carbon and corresponding NPA-NLMO hybridization ratio [98] of C-I bonds in the CUt.Jn and CBr4.oIn series.

Table 1.1 Central-atom NPA charges Q(E) and NAO/NLMO hybridization ratios of bonds (BD) and lone pairs for minima and inversion transition states of ammonia homologues .

These considerations are supported by the NAO/NLMO hybridization ratios of NHj versus PHj at both iriinitnurn and transition-state structures (Table 1.1). 

Figure 4.107 Perturbative interaction diagrams (on a common vertical energy scale cf. Fig. 4.106) depicting significant localized bonding interactions for PtH42 (a) metal hybrid formation (NAO NHO), (b) interaction of bonding hybrids to form bonding (a) and antibonding (a ) NBOs (NHO- NBO), and (c) nH

Figure 1.2 NAO/NLMO p/s hybridization ratios for hydrides and fluorides of second and third period elements in their maximum oxidation state (B3LYP/def2-TZVP resuits).

Using time-dependent density functional cubic response theory, a scheme has been designed to analyze the static and dynamic second hyperpolarizabilities in terms of y densities as well as in terms of contributions from natural bond orbitals (NBOs) and natural localized molecular orbitals (NLMOs). This approach, which has been implemented for both hybrid and nonhybrid TDDFT schemes and which is based on Slater-type basis functions, constitutes an extension of previously proposed schemes limited to the static responses. 

AO = basis functions ( atomic orbitals ) of the wavefunction NAO = natural atomic orbitals NHO = natural hybrid orbitals NBO = natural bond orbitals NLMO = natural localized molecular orbitals... 

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