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Notes: The McLachlan variational principle for the time-dependent Schrödinger equation is utilized in conjunction with extant localized Guassian wave packet technology to deduce equations of motion for general multidimensional Gaussians. These equations of motion are characterized by the same simplicity as the local quadratic expansion results of Heller [J. Chem. Phys. 62, 1544 (1975)]. However, the resultant variational wave packet evolution is shown to be an improvement over its local quadratic analog as a tool for computing certain photodissociation spectra. Numerical examples drawn from the Beswick–Jortner model of ICN photodissociation [Chem. Phys. 24, 1 (1977)] are presented.

Notes: A method is presented that uses integral equation theory to determine analytic temperature derivatives of the radial distribution functions. It is illustrated by studying the solvation thermodynamics of monatomic solutes in aqueous solution. The results agree well with the density derivative method developed previously [Yu and Karplus, J. Chem. Phys. 89, 2366 (1988)]. An expression for the solvation enthalpy is derived which allows direct comparison with experimental and isobaric–isothermal (NPT) ensemble simulation data. Satisfactory agreement with experiment is found for pure water and for the aqueous solvation of monovalent ions. Simple equations that exploit the site–site HNC closures are given for the decomposition of the potential of mean force into its enthalpic (or energetic) and entropic components. Since the extended RISM (HNC-RISM) theory yields an incorrect (trivial) value of the dielectric constant, two different ways to correct for the asymptotic behavior of the solute–solute potential of mean force are compared. They lead to similar results but the method in which the solvent dielectric constant is modified from the outset can be applied more generally.The interactions between nonpolar and between polar solutes in water are decomposed into enthalpic and entropic contributions. This is difficult to do by computer simulations because of the lack of precision in such calculations. The association of nonpolar solutes in water is found to have comparable enthalpic and entropic contributions; this result disagrees with the usual description of an entropy-dominated hydrophobic interaction. For ions, the somewhat surprising result is that the association of like-charged species is enthalpy driven while for oppositely charged ions entropic effects are dominant. The process of bringing two like-charged ions together leads to higher local charge density; the more favorable solvation enthalpy arising from this increase in charge density (q2 dependence) more than compensates for the Coulombic repulsion. For oppositely charged ions, association leads to a partial charge neutralization in which the favorable Coulombic attraction is overwhelmed by the loss of stabilizing solvation enthalpy. The entropic increase is due to the greater freedom of the surrounding water molecules resulting from the partial charge neutralization.

Notes: Inelastic neutron scattering spectra are calculated from harmonic and damped harmonic models of the internal dynamics of a small protein, the bovine pancreatic trypsin inhibitor (BPTI). Numerical Fourier transformation of the intermediate scattering function Fvibinc (q, t) is used to calculate the inelastic scattering. This permits the inclusion of multiphonon scattering and frictional damping effects. Although for a typical experimental configuration, the multiphonon contribution does not significantly alter the form of the scattering at frequencies below about 30 cm−1, it does have a significant effect on the scattering intensity at higher frequencies. Frictional damping is introduced into the harmonic model by assuming that each mode acts as an independent damped Langevin oscillator. With this model and the assumption that the lowest frequency modes are overdamped while the higher frequency modes are underdamped, improved agreement with the experimental BPTI powder results is obtained. The measured scattering from BPTI in solution shows increased intensity at frequencies below 50 cm−1 relative to the powder results. The solution scattering profile can be reproduced approximately by the addition of overdamped Langevin oscillator normal modes to the dynamic model in best agreement with the powder data. Several other aspects of neutron scattering from proteins are examined. Anisotropy in the harmonic resolution broadened scattering is demonstrated. Spectra calculated assuming classical equations of motion are shown to agree with those calculated with the full quantum-mechanical dynamical model. Translational diffusion broadening is found to be small compared to the instrumental resolution broadening for the range of scattering wave vectors of interest. The contribution of the coherent scattering to the measured intensity is calculated for the case of a partially hydrated protein. Under typical experimental conditions, the measured cross sections are dominated by the incoherent scattering and the self part of the coherent scattering, a result that justifies the comparison of experimental data with calculated incoherent scattering spectra.