Library

Notes: This is the second in a series on the ab initio calculation of the second, third, and fourth derivatives of the energy of a molecule with respect to nuclear coordinates. A knowledge of these derivatives yields, in particular, anharmonic spectroscopic constants. Here we discuss our implementation of the formula for the fourth derivative of the self-consistent-field energy and present full quartic force fields in internal coordinates for H2O and CO2.

Notes: Fluorescence upconversion was used to measure the time evolution of the fluorescence anisotropy of aniline in three hydrocarbon, alcohol, and aprotic polar solvents. The deconvoluted anisotropy decay time of 0.94±0.05 ps in aniline/isopentane solution is only 54% longer than calculated for free rotation of collision-free molecules, and increasing the solvent viscosity by a factor of 15 by going from isopentane to hexadecane increases the rotational relaxation time by only another 70% to 1.6 ps. The extended diffusion theory applied to the aniline/isopentane anisotropy decay resulted in a collisional time of 205±15 fs, implying that electronically excited aniline in this hydrocarbon rotates on average 19.5±1.5 deg between collisions. These results indicate that the orientational motion of electronically excited aniline in isopentane is significantly nondiffusive. The anisotropy decayed much more slowly in methanol and acetonitrile than in the hydrocarbons, presumably due to dipole–dipole interactions in acetonitrile and/or hydrogen bonding interactions in the hydroxylic solvent. The anisotropy decay in methanol presented double exponential behavior, probably due either to the coexistence of two slowly interconverting aniline species (hydrogen and nonhydrogen bonded) in solution or to a fast contribution from the hydrogen-bonded aniline molecules rotating around their long axes. Free rotation, hydrodynamic models, extended diffusion, and Langevin calculations were used to evaluate the results and comparisons were made among the various approaches.

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: The methodological dependence of observed ion–peptide associations in molecular dynamics simulations is investigated. We compare the results from several simulations of a pentapeptide in explicit solvent and salt ions which differ in the their treatment of the long ranged electrostatic interactions. Results for both the Ewald and switching function techniques are presented. It was found that there were important differences between the two methods for the water dipole–dipole temporal and spatial correlations, total dipole moment fluctuations, and self-diffusion constants. Electrostatic potentials calculated in the region of the peptide are also used to illustrate the large differences that can arise from different treatments of the electrostatic interactions. It appears that the switching function distorts the molecular electrostatic potential experienced by the salt ions to such a degree that their behaviour becomes highly dependent on the initial conditions. In summary, the use of a switching function is not recommended for the simulation of ions and their interactions with biomolecules.

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: A theory is developed to analyze the effects of noise on the dynamics of stable and bistable biochemical systems where a substrate, continuously provided by a constant external flow, is enzymatically converted into product. Analytical expressions for the ensemble average concentration of substrate at steady state, 〈x〉, are derived. It is found that noise induces a bias in 〈x〉. The bias is always positive in the case of noncooperative enzymatic catalysis, but it can be positive, negative, or zero in the case of cooperative enzymatic catalysis. In the case of bistable systems, 〈x〉 is dramatically affected by noise. A first-order phase transition between two concentration states is approached as the noise becomes asymptotically small. The transition occurs at a critical value of the flow that can be arrived at by means of an equal-area rule. This rule is a generalized form of the Maxwell rule for the van der Waals gas.

Notes: In this paper we present a derivation of time-dependent coupled Hartree–Fock (TDCHF) theory for the case of half-open shells. With this method frequency-dependent polarizabilities are calculated for the hydrogen and nitrogen atom, as well as for the diatomics CN, NH, and OH+. van der Waals coefficients of the half-open-shell systems with the H atom and the H2 molecule are computed. Other dispersion coefficients for dimers consisting of these monomers are available upon request.

Notes: Effective states arising from variational perturbation calculations in a full configuration interaction basis are used to calculate dynamic multipole polarizabilities for H2 at seven different bond lengths. These are combined with previously calculated dynamic polarizabilities for rare gas atoms to obtain the intramolecular bond length dependence of the anisotropic C6, C8, and C10 dispersion coefficients for H2–X (X=He, Ne, Ar, Kr, Xe) interactions. The results are generally in good agreement with previous semiempirical estimates where available.