Natural Bond Orbitals approach

In this section, we present a unified picture of the different electronic effects that combine to determine methyl rotor potentials in the S0, Sp and D0 electronic states of different substituted toluenes. Our approach is based on analysis of ab initio wavefunctions using the natural bond orbitals (NBOs)33 of Weinhold and cowork-ers. We will attempt to decompose the methyl torsional potential into two dominant contributions. The first is repulsive steric interactions, which are important only when an ortho substituent is present. The second is attractive donor-acceptor interactions between CH bond pairs and empty antibonding orbitals vicinal to the CH bonds. In the NBO basis, these attractive interactions dominate the barrier in ethane (1025 cm-1) and in 2-methylpropene (1010 cm-1) see Figure 3. By analogy, donor-acceptor attractions are important in toluenes whenever there is a substantial difference in bond order between the two ring CC bonds adjacent to the C-CH3 bond. Viewed the other way around, we can use the measured methyl rotor potential as a sensitive probe of local ring geometry. 

Table 7.6 Comparison of Mulliken and natural bond orbital (NBO)/natural population analysis (NPA) charges in LiH and LiF using different basis sets and computational approaches. ...

The experimentally measured coupling constant J(HaHy)exp. = 5.5 Hz is reproduced by calculations for the endo-si y substituted model structure 44 using a finite perturbation level (FPT) 26) (Perdew/IGLO-III) approach J(HaHy)caic. = 5.9 Hz, whereas only 1.2 Hz is calculated for the HaHy-coupling constant in the exo-si y substituted model structure 45. Finally the bonding orbital of the bridging C-C-bond between Cq and Cy in these type of bicyclobutonium ions can be visualized by calculations of the natural bond orbitals (NBO s) (Figure 13). 

At the same time, the formally independent particle nature of DFT allows the application of standard interpretative tools developed for the HF approach. This is true not only for the standard MuUiken population analysis, but also for more sophisticated schemes, like the Natural Bond Orbital (NBO) analysis [9], the Atomic Polarizable Tensor population [10], or the Atom in Molecule (AIM) approach [11]. These tools allow the use of familiar and well known models to analyze the molecular wave function and to rationalize it in terms of classical chemical concepts. In short, DFT is providing very effective quantum... 

The tt-overlap populations between both phenyl and amino moieties are in line with a shorter C—N bond distance. Figure 5 gives a summary of the atomic natural charges and bond indices, computed using the natural bond orbital (NBO) approach. The following bond indices, C1-N7 1.11, C1-C2 1.35, C2-C3 1.45 and C3-C4 1.42, indicate that the CN bond is slightly more than a single bond and the CC bonds are less than... 

Decomposition of interaction energies is desired for qualitative chemical analyses of complicated multi-valent interactions in supramolecular aggregates but such a decomposition cannot be uniquely defined within fundamental physical theory. A popular semi-quantitative decomposition method with nice formal features to be mentioned in this context is Weinhold s natural bond orbital (NBO) approach to intermolecular interactions [232, 233]. Comparable is the recently proposed energy decomposition analysis by Mo, Gao and Peyerimhoff [234, 235] which is based on a block-localized wave function. Other energy decomposition schemes proposed are the energy decomposition analysis (EDA) by Kitaura and Morokuma [236] and a similar scheme by Ziegler and Rauk [237]. 

So far we have presented cDFT as a means to impose a charge or a spin density on a group of atoms. However, we have not specified how such charges are calculated in practice. It is well known that atomic charges cannot be strictly defined in quantum mechanics and, as a corollary, that multiple population analysis (PA) approaches can be developed to reach this goal. A central point PAs have to address is to define a criterion for assigning each fraction of the electronic density of every point in space to the individual atoms. Some PAs realize this partition with criteria relying on the KS molecular orbital coefficients. The MuUiken [227], Lowdin [228], and the more sophisticated Natural Bond Orbital [229,230] approaches are examples of... 

Finally, in order to give a chemical sounding description of the electronic structure of these molecules the natural bond orbital (NBO) approach and the related natural population analysis (NPA) - have been computed and discussed. The NPA approach is particularly effective in the case of inorganic complexes, since it gives a description of the electronic distribution less sensitive to the computational parameters (e.g. basis set) with respect to other more commonly used population analysis such as the Mulliken one [70]. 

Verkade JG (1986) A pictorial approach to molecular bonding. Springer, New York Giendening ED, Landis CR, Weinhold F (2012) Natural bond orbital methods. Wiley Interdiscip Rev Comput Mol Sci 2 1-42. doi 10.1002/wcms.51... 

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. 

Carbocation Force Fields Carbocation Stabilities Comparison of Theory and Experiment Carbohydrate Force Fields Carbohydrates Conformational Analysis 1 Conformational Analysis 2 Conformational Analysis 3 Force Fields A Brief Introduction Force Fields A General Discussion Infrared Spectra Interpretation by the Characteristic Frequency Approach Natural Bond Orbital Methods Solvation Carbohydrates Transition States in Organic Chemistry Ab Initio. 

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