Natural bond orbital description

The EBO concept rehes on a multi-configurational wavefunction and takes into account the effect of electron correlation involving the antibonding orbitals. There are various ways of quantifying bond orders [12-14]. The Natural Bond Orbital (NBO) valence and bonding concepts are also extensively used in the analysis of multiple bonds. NBO, like EBO, is based on a quantum mechanical wavefunction. The NBO description of a bond can be derived by variational, perturbative, or density functional theory (DFT) approximations of arbitrary form and accuracy [15]. 

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]. 

An alternative description of the chemical bonding between a transition metal atom and its surrounding atoms is provided by the natural bond orbital analysis (NBO). This method developed by Weinhold et al. [23] uses the one-electron matrix as starting point to find the... 

However, a localized adaptation of the natural orbital algorithm allows one to similarly describe/civ-center molecular subregions in optimal fashion, corresponding to the localized lone pairs (one-center) and bonds (two-center) of the chemist s Lewis structure picture. The Natural Bond Orbitals (NBOs) that emerge from this algorithm are intrinsic to, uniquely determined by, and optimally adapted to localized description of, the system wavefunction. The compositional descriptors of NBOs map directly onto bond hybridization, polarization, and other freshman-level bonding concepts that underlie the modem electronic theory of valency and bonding. 

The naive concept that a fixed set of valence AOs suffices for all charge states and bonding environments is equivalent to the use of a minimum basis set (e.g., STO-3G), which is known to be quite inadequate for quantitative purposes. Nevertheless, if the AOs are properly allowed to adjust dynamically in the molecular environment, one recovers a minimal-basis description that is surprisingly accurate the natural minimal basis. In the NBO framework the effective natural atomic orbitals are continually optimized in the molecular environment, and the number of important NAOs therefore remains close to minimal, greatly simplifying the description of bonding. 

It must be emphasized that the formulation of three-center T-bonds provides a qualitative (not merely incremental) improvement in the accuracy of the natural Lewis-structure description of diborane. Because a three-center orbital is intrinsically more mathematically flexible than a two-center orbital, the description of any molecule is seemingly improved by employing three-center in place of two-center NBOs. However, for most non-boron molecules this improvement would be quite negligible (e.g., less than 0.1% for ethane, whose two-center Lewis-structure... 

If experimental data is used to parameterize a semi-empirical model, then the model should not be extended beyond the level at which it has been parameterized. For example, experimental bond energies, excitation energies, and ionization energies may be used to determine molecular orbital energies which, in turn, are summed to compute total energies. In such a parameterization it would be incorrect to subsequently use these mos to form a wavefunction, as in Sections 3 and 6, that goes beyond the simple product of orbitals description. To do so would be inconsistent because the more sophisticated wavefunction would duplicate what using the experimental data (which already contains mother nature s electronic correlations) to determine the parameters had accomplished. 

---