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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: The potential energy function about the C–C single bond for the ground state 1,3-butadiene has been derived from ab initio calculations at both the Hartree–Fock (HF) level with 6-31G, 6-31G*, and 6-311G** basis sets and the second-order Møller–Plesset perturbation (MP2) level with 6-31G* basis set with the complete geometry optimizations at each of 15 fixed CCCC dihedral angles; the total energies and optimized geometries for the s-trans, gauche, and s-cis conformers were also determined at MP2 level with 6-311G* basis set and the third-order Møller–Plesset perturbation (MP3) level with 6-31G* basis set. The second stable conformer of the butadiene is predicted to be a gauche structure from all the calculations with a CCCC dihedral angle between 35° and 40° and a barrier of 0.5–1.0 kcal/mol to the s-cis transition state, and the theoretical torsional potentials are in good agreement with the experimental potential function of trans–gauche–gauche case derived by Durig et al.; by contrast, the theoretical torsional components differ significantly from the experimental results obtained from a trans–cis model. Vibrational frequencies and force field for s-trans and gauche conformers of 1,3-butadiene are determined at the Hartree–Fock and MP2 levels with 6-31G, 6-31G*, 6-311G, and 6-311G* basis sets. The mean absolute percentage deviations of the calculated frequencies from the experimental values (not corrected for anharmonicity) are ∼10%–13% and 3%–6% for the Hartree–Fock and MP2 methods, respectively. The effects of polarization functions and electron correlation on the force fields are studied, and the additivity of correlation and d function effects are discussed. Comparisons are made with other force fields, including experimental and previous ab initio results.

Notes: In the classical time-dependent Hartree approximation (TDH), the dynamics of a single molecule is approximated by that of a "field'' (each field being N "copies'' of the molecule which are transparent to one another while interacting with the system via a scaled force). It is shown that when some molecules are represented by a field of copies, while other molecules are represented normally, the average kinetic energy of the system increases linearly with the number of copies and diverges in the limit of large N. Nevertheless, the TDH method with appropriate energy scaling can serve as a useful means of enhancing the configurational sampling for problems involving coupled systems with disparate numbers of degrees of freedom.

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: The effective electronic donor/acceptor coupling (HDA) for a bridged electron transfer system is defined. An expression for HDA in terms of the bridge Green's function is developed for systems represented by a tight-binding Hamiltonian. HDA is computed exactly for two systems and the existence of a dimensionless parameter which determines whether the effective coupling oscillates or decays with increasing donor/acceptor distance is demonstrated. A numerical technique for computing HDA is developed and shown to be significantly more powerful than conventional techniques.