Natural hybrid orbital

The N/2 Lewis-type NBOs of highest occupancy ( /AB) 2) can be directly associated with the localized electron pairs of the chemist s Lewis-structure diagram.46 Each Lewis-type NBO f2AB can be decomposed into constituent natural hybrid orbitals (NHOs) hA and hB on atoms A and B,... 

One way in which the n bonds in these compounds may be examined is by calculating natural bond orbitals (NBO) from the molecular wave function." Here, the MOs are localized, and the nature of the localized orbitals may be examined. The p-n localized orbital is found to have decreased occupation as the carbon-carbon bond is distorted, indicating that the p orbitals are being used in part in forming other localized orbitals (i.e., rehybridized). It is also possible to calculate natural hybrid orbitals, and their deviation from the line of centers between the atoms involved. The deviations are included in Table 15.2, and are seen to increase markedly with increased twisting. 

The third step of the NBO algorithm is the calculation of the natural hybrid orbitals (NHOs), which form the two-center (sometimes three-center) NBOs. The density matrix in the NAO basis is first partitioned into one-center and two-center subblocks. Each one-center block is searched for NAOs, which have an occupancy >1.90e. These one-center orbitals... 

The Natural Bond Orbital analysis of Weinhold [Foster and Weinhold, 1980 Reed, Weinstock etal., 1985 Reed, Curtiss etal., 1988] generates, departing from canonical MOs, a set of localized one center (core, lone pairs) and two center (jt and a bonds) strongly occupied orbitals, and a set of one center (Rydberg) and two center (a, Jt ) weakly occupied orbitals the NBOs. The Natural Bond Orbitals (NBOs) are obtained by a sequence of transformations from the input basis to give, first, the Natural Atomic Orbitals (NAOs), then the Natural Hybrid Orbitals (NHOs), and finally the Natural Bond Orbitals (NBOs). For NAOs, atomic charges can be calculated as a summation of contributions given by orbitals localized on each atom moreover, from NBOs, bond order can be also calculated. 

Figure 7.1 presents contour diagrams for the Lewis-type NBOs of formaldehyde (panels a, c, e, g, h), calculated at the B3LYP/6-311-H-G""" level of hybrid density functional theory (DFT). As is immediately apparent, the bonding Gch, and Kcq NBOs exhibit the familiar sigma and pi shapes of idealized textbook depictions. The resemblance to expected textbook forms is further emphasized when each A-B bond is written as a linear combination (LC) of its constituent natural hybrid orbitals (NHOs) and with polarization coefficients and Cg, namely. 

Foster JP, Weinhold F (1980) Natural hybrid orbitals. J Am Chem Soc 102 7211-7218... 

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... 

Natural Hybrid Orbitals and Natural Bond Orbitals... 

CCSD(T) = coupled cluster configuration interaction including all singly and doubly excited configurations with perturbative inclusion of triples CISD = configuration interaction all singly and doubly excited configurations included DME = dimethyl ether NHO = natural hybrid orbital PDME = proto-nated dimethyl ether. 

The extracted Natural Hybrid Orbitals (NHOs) are therefore not simply encoded forms of the molecular shape, as envisioned in valence shell electron pair repulsions (VSEPR)-type caricatures of hybridization theory. Instead, the NHOs represent optimal fits to the ESS-provided electronic occupancies (first-order density matrix elements cf. V B, p. 21ff) in terms of known angular properties of basis AOs. Thus, the NHOs predict preferred directional characteristics of bonding from angular patterns of electronic occupancy, and the deviations (if any) between NHO directions and the actual directions of bonded nuclei give important clues to bond strain or bending that are important descriptors of molecular stability and function. 

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... 

Figure 4. Orientation of the natural hybrid orbital of the lone electron pair at the phosphorus atom in 10 (Pn = P, R = Cl) as found by the RffF/6-31G calculations. ...

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