Natural hybrid orbitals, NHO

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,... 

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. 

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. 

Natural bond orbital (NBO) analysis The NBO analysis transforms the canonical delocalized Hartree-Fock (HF) MOs and non-orthogonal atomic orbitals (AOs) into the sets of localized natural atomic orbitals (NAOs), hybrid orbitals (NHOs), and bond orbital (NBOs). Each of these localized basis sets is complete, orthonormal, and describes the wavefunction with the minimal amount of filled orbitals in the most rapidly convergent fashion. Filled NBOs describe the hypothetical, strictly localized Lewis structure. NPA charge assignments based on NBO analysis correlate well with empirical charge measures. ... 

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... 

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. 

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... 

The analysis of results of delocalised molecular orbital calculations for more complex molecules is problematic because there is no longer a simple relationship with the Lewis-localised bond representations. The use of fragment analyses and overlap populations has been helpful, but requires some knowledge of perturbation theory. Several methods have been developed to attempt to bridge the gap between the molecular orbital calculations and Lewis structures - one that is widely used is natural bonding orbitals (NBOs). Each bonding NBO Oab (the donor) can be written in terms of two directed valence hybrids (NHOs) h, hs on atoms A and B, with corresponding polarisation coefficients Ca, Cb ... 

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