Natural bond orbital concepts

The concept of natural orbitals may be used for distributing electrons into atomic and molecular orbitals, and thereby for deriving atomic charges and molecular bonds. The idea in the Natural Atomic Orbital (NAO) and Natural Bond Orbital (NBO) analysis developed by F. Weinholt and co-workers " is to use the one-electron density matrix for defining the shape of the atomic orbitals in the molecular environment, and derive molecular bonds from electron density between atoms. 

NBO Natural Bond Orbital. Orbitals resulting from a sort of localization scheme that resembles the traditional concepts of 2-center bonds and lone electron pairs. 

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... 

All calculations in Ref. [22] were performed utilizing the Gaussian-98 code [30]. The potential energy scan was performed by means of the Mqller-Plesset perturbation theory up to the fourth order (MP4) in the frozen core approximation. The electronic density distribution was studied within the population analysis scheme based on the natural bond orbitals [31,32], A population analysis was performed for the SCF density and MP4(SDQ) generalized density determined applying the Z-vector concept [33]. 

Carpenter, J.E. and Weinhold, F., J. Mol. Struct. (Theochem.), 169, 41-62, 1988 Weinhold, F. and Carpenter, J.E., The natural bond orbital lewis structure concept for molecules, radicals, and radical ions, in Proceedings of the International Workshop on the Structure of Small Molecules and Ions, Naaman, R. and Vager, Z., Eds., Plenum, New York, 1988, pp. 227-236. 

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]. 

The concept of hyperconjugation relies on a local orbital picture of quantum chemistry that is consistent with the common chemist s view of Lewis structures. Natural bond orbital (NBO) analysis [30] has been used to explain the anomeric effect by showing a favorable interaction between the heteroatom lone pair and the ct orbital of the substituent bonded to the anomeric carbon [16, 31, 32]. This was done most recently by Freitas [33] for a series of 2-substituted tetrahydropyrans, who found that NBO analysis provides a coherent framework in which to analyze the results, as we do in this report. Freitas points out that steric, electrostatic, and hyperconjugative effects play a role whether or not the anomeric effect is observed in his calculations, and sometimes the hypercongjugative effect is not the dominate factor in the preference of one isomer over the other. 

Weinhold F, Landis CR (2001) Natural bond orbitals and extensions of localized bonding concepts. Chem Educ Res Pract 2 91-104... 

Furthermore, natural bond orbital (NBO) analysis of the first-order density has also been used to quantify aromaticity [73,74]. More recently Boldyrev and Zubarev [75] developed the adaptive natural density partitioning (AdNDP) algorithm attempting to combine the ideas of Lewis theory and aromaticity. The results obtained by the application of the AdNDP algorithm to the systems with non-classical bonding can be readily interpreted from the point of view of aromatic-ity/antiaromaticity concepts. 

Keywords Bond path Bond critical point Laplacian of the electron density Hydrogen bond Halogen bond Pnicogen bond Lewis acid-Lewis base interaction Quantum Theory of Atoms in Molecules (QTAIM) Natural Bond Orbitals (NBO) method o-hole concept Electrostatic potential... 

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. 

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