Bond-centered orbitals

Antibonding Molecular Orbital. A Molecular Orbital that is andbonding between particular atomic centers. The opposite is a Bonding Molecular Orbital. 

Isolated F-atom Molecular orbitals Isolated P-atom orbitals of three-center bond p orbitals... 

Despite the precise knowledge of the muon hyperfine interaction and a wealth of other complementary information on Mu, no compelling theory emerged until 1986 when Cox and Symons proposed a molecular-orbital bond-center (BC) model to explain the muon hyperfine interaction (Symons, 1984 Cox and Symons, 1986). Since then it has been tested both theoretically (Van de Walle, 1991) and experimentally. 

The electronic states introduced by hydrogen in the band structure of Si are quite different depending upon the location of the impurity in the lattice. For H at the bond center we can, to a first approximation, treat the problem as involving only three states (Schaad, 1974 Fisch and Licciardello, 1978) the semiconductor bonding (b) and antibonding (a) states (which, in turn, are symmetric and antisymmetric combinations of hydrid orbitals on the two atoms) and the hydrogen Is orbital. The cor-... 

Fig. 5. (a) Schematic illustration of orbitals in the bond-center configuration. X and Y are the semiconductor atoms, (b) Corresponding energy levels obtained from simple molecular-bonding (or tight-binding) arguments for an elemental semiconductor... 

This simple treatment, formulated in a context of molecular bonding, was also what led Cox and Symons (1986) to propose the bond-center site as an explanation for anomalous muonium (Mu ). The location of the muon at the nodal plane of the nonbonding orbital explains the very small hyperfine coupling observed in pSR. Still, the muon is close to the electron, which occupies a nonbonding state on the neighboring semiconductor atoms. 

Results for hyperfine parameters for muonium at the bond-center site in Si are given in Table I. In elemental semiconductors, symmetry requires that the Is orbital does not couple to the antibonding combination of... 

Calculations of vibrational frequencies in a three-center bond as a function of Si—Si separation were performed by Zacher et al. (1986), using linear-combination-of-atomic-orbital/self-consistent field calculations on defect molecules (H3Si—H—SiH3). The value of Van de Walle et al. for H+ at a bond center in crystalline Si agrees well with the value predicted by Zacher et al. for a Si—H distance of 1.59 A. 

The NBO picture of 3c/2e T-bonding may be developed along lines parallel to those for 3c/4e tu-bonding in Eqs. (3.194) et seq. Let us first consider the special case of a homopolar two-center bond aAc = 2-1/2(hA + hB) interacting with a vacant one-center orbital nB = hB to form a three-center bond tABc of the form... 

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... 

Figure 4.104 Model MO diagrams for XeH2, XeH4, and PtH42. Light-gray coloration indicates atom-centered orbitals that are not involved in bonding.

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