Bond-centered functions

Wu et al. calculated the interaction-induced electric properties of the FH-NH3 hydrogen-bonded complex. The authors relied on second-order Moller-Plesset perturbation theory with large standard basis sets. Their best values were obtained with a aug-cc-pVTZ basis augmented with bond-centered functions. The results were suitable corrected for basis set superposition errors (BSSE) with the counterpoise (CP) method. The reported values are p = 0.4762 for the dipole moment, amt= 0.8057 e ao Eh for the mean polarizability and = 3.31 e ao Eh for the mean first hyperpolarizability. It is worth noticing that without the BSSE corrections the values for the above properties are p = 0.4757 for the dipole moment, aj ,= 0.7235 e ao Eh for the mean polarizability and ) ( = 3.66... 

The charge density in a (110) plane for neutral H at the bond-center site in Si, as obtained from pseudopotential-density-functional calculations by Van de Walle et al. (1989), is shown in Fig. 7a. In the bond region most of the H-related charge is derived from levels buried in the valence band. It is also interesting to examine the spin density that results from a spin-polarized calculation, as described in Section II.2.d. The difference between spin-up and spin-down densities is displayed in Fig. 7b. It is clear... 

An unambiguous identification of anomalous muonium with the bond-center site became possible based on pseudopotential-spin-density-functional calculations (Van de Walle, 1990). For an axially symmetric defect such as anomalous muonium the hyperfine tensor can be written in terms of an isotropic and an anisotropic hyperfine interaction. The isotropic part (labeled a) is related to the spin density at the nucleus, ip(0) [2 it is often compared to the corresponding value in vacuum, leading to the ratio i7s = a/Afee = j i (O) Hi/) / (O) vac- The anisotropic part (labeled b) describes the p-like contribution to the defect wave function. 

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 Hy-CI function used for molecular systems is based on the MO theory, in which molecular orbitals are many-center linear combinations of one-center Cartesian Gaussians. These combinations are the solutions of Hartree-Fock equations. An alternative way is to employ directly in Cl and Hylleraas-CI expansions simple one-center basis functions instead of producing first the molecular orbitals. This is a subject of the valence bond theory (VB). This type of approach, called Hy-CIVB, has been proposed by Cencek et al. (Cencek et.al. 1991). In the full-CI or full-Hy-CI limit (all possible CSF-s generated from the given one-center basis set), MO and VB wave functions become identical each term in a MO-expansion is simply a linear combination of all terms from a VB-expansion. Due to the non-orthogonality of one-center functions the mathematical formalism of the VB theory for many-electron systems is rather cumbersome. However, for two-electron systems this drawback is not important and, moreover, the VB function seems in this case more natural. 

It does not seem practical to use bond-centered fitting functions in chemical dynamics calculations in which bonds are being broken and reformed. Thus our fitting functions are uncontracted and scaled from the 6-311G orbital sets in the s manifold. The atomic L > 0 fitting functions are unsealed and contracted exactly as optimized for Turbomole calculations [14] except that the silicon basis is uncontracted. The calculations are performed in Cs symmetry. 

For convenience and to avoid confusion, we will symbolize a purely covalent bond between A and B centers as A — B, while the notation A—B will be employed for a composite bond wave function like the one displayed in Equation 3.4. In other words, A—B refers to the real bond while A — B designates its covalent component. 

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