Linear combinations of bond orbitals

Hiickel s calculations on planar conjugated systems were extensively exploited, and I refer you once again to Streitwieser s classic book. Molecular Orbital Theory for Organic Chemists. What few calculations that had been done at that time on the (T framework had used the method of linear combination of bond orbitals. 

A basic assumption made earlier in the discussion of diatomic molecules and crystalline CsCl is that electronic states can be written as linear combinations of atomic orbitals. We do not need to depart from that assumption now as we begin to describe electronic states in solids as linear combinations of bond orbitals, since bond orbitals can be written as linear combinations of atomic orbitals, and vice versa. Bond orbitals and atomic orbitals arc equivalent representations, but thinking in terms of bond and antibonding orbitals, which can be made to correspond with occupied and empty states of the covalent solid (as was shown in Fig. 2-3), is essential in making approximations. 

The kth valence band state is written as a linear combination of bond orbitals... 

Photoelectron spectra have been measured for other, more complex polyynes -The values obtained for a large number of polyynes can be correlated in a simple fashion in terms of a model based on linear combination of bonding orbitals -... 

The crystal structures of allyl-,25 cyclopent-2-enyl-,26 cyclohex-2-enyl-, and cyclo-hept-2-enyl-triphenyl-tin27 show that the Sn-allyl bond is oriented orthogonally to the plane of the C=C group with a Sn-C-C=C dihedral angle of 100 10°, and this is ascribed to a-n conjugation (carbon-metal hyperconjugation) (9-1) between the cj-Sn-C bond and the rT -C=C orbitals. This is supported by the photoelectron spectra, and by linear combination of bond orbitals calculations (see Section 3.1.2.3).28... 

Earlier attempts by molecular orbital (MO) methods, including db initio MO calculation, failed to reproduce the observed facts as reviewed by Abe and Mark in their paper. Recently, however, Brunck and Weinhold gave a qualitative explanation for the gauche preference in terms of the vicinal bond-antibond interaction by using INDO MO s expressed as a linear combination of bond orbitals, and Ohsaku and Imamura correctly predicted the preferred conformation of poly(oxyethylene) by the CNDO/2 MO method under the tight-binding approximation. The possibility... 

We place COT in the xy plane and allow it to relax to its stable tub conformation. Atoms 1, 2, 5 and 6 move to positive z and 3, 4, 7 and 8 to negative z, behind the plane of the diagram, but the four tt bonds can still be thought of essentially as being linear combinations of their Pz AOs. The four linear combinations of bond orbitals (LCBOs), labeled by their irreps in D2rf, are ... 

The characterization of the MOs of the interacting CBD molecules is straightforward. So is that of the two linear combinations of bond orbitals (LCBOs) of cubane, labeled and cr those labeled and (j+ are inter-... 

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... 

In bond orbital theory the wave functions of the molecule are derived from the wave functions associated with the different bonds of a molecule, i.e. from the bond orbitals. In the LCBO model the molecular orbitals are a linear combination of bond orbitals which in turn are a combination of the atomic orbitals or hybrids forming the bond in question [2b]. In the HLSP-method the many-electron wave functions are a sum of product functions which contain a Heitler and London type of factor (space function and spin function) for each bond of the molecule. 

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