Library

Notes: Correlation contributions to the multipole moments and frequency dependent polarizabilities of molecules are described within the framework of time-dependent coupled Hartree–Fock and many-body perturbation theory. Computationally feasible expressions are given for the "true'' correlation contributions to the multipole moments and frequency dependent polarizabilities. The polarizabilities of argon, ammonia and water and the van der Waals induction and dispersion coefficients of H2O–H2O and Ar–NH3 are presented.

Notes: This is the fourth in a series of papers on the ab initio calculation of the third and fourth derivatives of the energy of a molecule. In this paper we examine anharmonic effects in the infrared and Raman spectra of benzene. The following spectroscopic properties have been calculated; ab initio anharmonic corrections (ω−ν) and estimates of the harmonic frequencies ω for all 30 vibrational modes of C6H6 and C6D6, a complete set of anharmonic constants x and g for C6H6, intensities for the infrared spectrum of C6H6 up to 6148 cm−1, and anharmonic corrections to the Raman scattering factors for the fundamental modes of C6H6. In addition, we have improved on previous calculations of the equilibrium geometry of benzene, using Møller–Plesset perturbation theory and a triple zeta plus double polarization (TZ2P) basis. We have also calculated a zero-point vibrationally averaged geometry which is in good agreement with the experimental R0 value. All these calculations are based on a Hartree–Fock quartic potential, cubic dipole surface, and quadratic polarizability surface, using a double-zeta plus polarization (DZP) basis. This is the first time a complete anharmonic potential has been obtained for a molecule of this size; the computer time required was minimized by the use of analytic derivative programs in favor of finite-difference programs. The quartic potential is presented in three coordinate systems.We discuss efficient algorithms for the nonlinear transformation of the potential from normal coordinates to valence coordinates and for symmetry checking the potential. The approximations used in our calculations have been examined and we find that the use of a Hartree–Fock DZP potential together with a perturbative treatment of the vibrational Hamiltonian is just as accurate for D6h benzene as for smaller molecules. In order to examine correlation effects in the B2u modes 14 and 15, basis-set limit second-order Møller–Plesset TZ2P+f harmonic frequencies have been calculated for these modes. It is suggested that, while these modes are very sensitive to correlation, anharmonicity has only a small effect, so a Hartree–Fock DZP anharmonic potential is adequate. Furthermore, experimental determination of anharmonic corrections to frequencies is very difficult for a molecule of this size so we hope our calculations will fill this gap.

Notes: Calculations of the dynamic dipole, quadrupole, and octopole polarizabilities of Ne, Ar, Kr, and Xe are carried out using both time-dependent coupled Hartree–Fock and many-body perturbation theory methods. Dispersion coefficients are calculated for interactions involving these species. The dynamic polarizabilities are combined with previously published dynamic polarizabilities of H, He, H2, N2, HF, and CO to obtain dispersion coefficients for the interactions involving one of these species and one of Ne, Ar, Kr, or Xe. The dipole–dipole dispersion coefficients agree quite well with the best available semiempirical estimates. The isotropic higher multipole coefficients are in reasonable agreement with previous semiempirical estimates where available, and the anisotropic ones are, in most cases, the first reliable ones to appear in the literature. Nonadditive three-body dispersion coefficients for the Ne3, Ar3, Kr3, and Xe3 interactions are also calculated.

Notes: Abstract: To model the possible involvement of sulfated proteoglycans in amyloidogenesis, we examined the influence of sulfate ions, heparan, and Congo red on the conformation and morphology of peptides derived from the Alzheimer β/A4 amyloid protein. The peptides included residues 11–28, 13–28, 15–28, and 11–25 of β/A4. Negative-stain electron microscopy revealed a sulfate-specific tendency of the preformed peptide fibrillar assemblies of β(11–28), β(13–28), and β(11–25), but not β(15–28), to undergo extensive lateral aggregation and axial growth into “macrofibers” that were ∼0.1–0.2 μm wide by ∼20–30 μm long. Such effects were observed at low sulfate concentrations (e.g., 5–50 mM) and could not be reproduced under comparable conditions with Na2HPO4, Na2SeO4, or NaCl. Macrofibers in NaCl were only observed at 1,000 mM. At physiological ionic strength of NaCl, fibril aggregation was observed only with addition of sulfate ions at 5–50 mM. Selenate ions, by contrast with sulfate ions, induced only axial and not substantial lateral aggregation of fibrils. X-ray diffraction indicated that the original cross-β peptide conformation remained unchanged; however, sulfate binding did produce an intense ∼65 Å meridional reflection not recorded with control peptides. This new reflection probably arises from the periodic deposition of the electron-dense sulfate along the (long) axis of the fibril. The sulfate binding could provide sites for the binding of additional fibrils that generate the observed lateral and axial aggregation. The binding of heparan to β(11–28) also produced extensive aggregation, suggesting that in vivo sulfated compounds can promote macrofibers. The amyloid-specific, sulfonated dye Congo red, even in the presence of sulfate ions, produced limited aggregation and reduced axial growth of the fibrils. Therefore, electrostatic interactions are important in the binding of exogenous compounds to amyloid fibrils. Our findings suggest that the sulfate moieties of certain molecules, such as glycosaminoglycans, may affect the aggregation and deposition of amyloid fibrils that are observed as extensive deposits in senile plaques and cerebrovascular amyloid.

Notes: Two related problems are considered: (i) the inverse scattering problem for a potential V(x) supported on the half-line {x≥0}, when the given data is ||R−(k)||, the amplitude of the reflection coefficient and (ii) determination of a function g(t) supported on the half-line {t≥0} when the given data is ||gˆ(k)||, the amplitude of the Fourier transform of g. Under certain conditions on V or g, uniqueness theorems are proved and computational methods are developed. A numerical example of recovery of V(x) from ||R−(k)|| is given.