Chemical Physics

We show how the dynamically nonlocal formulation of classical nuclear motion in the presence of quantal electronic transitions presented many years ago by Pechukas can be localized in time using time dependent perturbation theory to give an impulsive force which acts when trajectories hop between electronic surfaces. The action of this impulsive force is completely equivalent to adjusting the nuclear velocities in the direction of the nonadiabatic coupling vector so as to conserve energy, a procedure which is widely used in surface hopping trajectory methods. This is the first time the precise connection between these two formulations of the nonadiabatic dynamics problem has been considered. We also demonstrate that the stationary phase approximation to the reduced propagator at the heart of Pechukas' theory is not unitary due to its neglect of nonstationary paths. As such mixed quantum-classical evolution schemes based on this approximation are not norm conserving and in general must fail to give the correct branching between different competing electronic states. Tully's phase coherent, fewest switches branching algorithm is guaranteed to conserve the norm. The branching between different alternatives predicted by this approach, however, may be inaccurate, due to use of the approximate local dynamics. We explore the relative merits of these different approximations using Tully's 1D two state example scattering problems for which numerically exact results are easily obtained.

Microwave detected, microwave-optical double resonance was used to record the A state electronic spectrum of NH3, NH2D, and NHD2 with both vibrational and rotational resolution. To investigate ND3 with the same resolution as we had with our hydrogen containing isotopomers, a strip-line cell was constructed allowing the simultaneous passage of radio-frequency and ultraviolet radiation. Rotational constants were obtained as a function of nu2 excitation and an A state equilibrium bond length was estimated at 1.055(8) angstroms. In addition, the harmonic force field for the A state has been experimentally determined. fhh, falpha,alpha-falpha,alpha', and frr were found to be 1.06(4)aJ/angstrom2, 0.25(2)aJ, and 4.9aJ/angstrom^2 respectively. This calculated harmonic force field predicts that the asymmetry observed in the NH3 2(4) band is due to a strong anharmonic interaction with the 4(3) level and the broad feature observed in the dispersed fluorescence spectrum previously assigned to the 1(1) band is more likely attributable to the 4(2) level.

Using microwave detected, microwave-optical double resonance, we have measured the homogeneous linewidths of individual rovibrational transitions in the à state of NH3, NH2D, NHD2, and ND3. We have used this excited state spectroscopic data to characterize the height of the dissociation barrier and the mechanisms by which the molecule uses its excess vibrational and rotational energies to help overcome this barrier. To interpret the observed vibronic widths, a one dimensional, local mode potential has been developed along a N-H(D) bond. These calculations suggest the barrier height is roughly 2100cm-1, approximately 1000cm-1 below the ab initio prediction. The observed vibronic dependence of levels containing two or more quanta in nu2 is explained by a Fermi resonance between nu2 and the N-H(D) stretch. This interaction also explains the observed trends due to isotopic substitution. The rotational enhancement of the predissociation rates in the NH3 2(1) level is dominated by Coriolis coupling while for the same level in ND3, centrifugal effects dominate.

This paper describes a mixed direct-iterative method for boundary integral formulations of dielectric solvation models. We give an example for which a direct solution at thermal accuracy is nontrivial and for which Gauss-Seidel iteration diverges in rare but reproducible cases. This difficulty is analyzed by obtaining the eigenvalues and the spectral radius of the iteration matrix. This establishes that the nonconvergence is due to inaccuracies of the asymptotic approximations for the matrix elements for accidentally close boundary element pairs on different spheres. This difficulty is cured by checking for boundary element pairs closer than the typical spatial extent of the boundary elements and for those pairs performing an `in-line' Monte Carlo integration to evaluate the required matrix elements. This difficulty are not expected and have not been observed when only a direct solution is sought. Finally, we give an example application of these methods to deprotonation of monosilicic acid in water.

We simulate the compression of a two-component Lennard-Jones liquid at a variety of constant temperatures using a molecular dynamics algorithm in an isobaric-isothermal ensemble. The viscosity of the liquid increases with pressure, undergoing a broadened transition into a structurally arrested, amorphous state. This transition, like the more familiar one induced by cooling, is correlated with a significant increase in icosahedral ordering. In fact, the structure of the final state, as measured by an analysis of the bonding, is essentially the same in the glassy, frozen state whether produced by squeezing or by cooling under pressure. We have computed an effective hard-sphere packing fraction at the transition, defining the transition pressure or temperature by a cutoff in the diffusion constant, analogous to the traditional laboratory definition of the glass transition by an arbitrary, low cutoff in viscosity. The packing fraction at this transition point is not constant, but is consistently higher for runs compressed at higher temperature. We show that this is because the transition point defined by a constant cutoff in the diffusion constant is not the same as the point of structural arrest, at which further changes in pressure induce no further structural changes, but that the two alternate descriptions may be reconciled by using a thermally activated cutoff for the diffusion constant. This enables estimation of the characteristic activation energy for diffusion at the point of structural arrest.

Acid ionization in aprotic media is studied using Molecular Dynamics techniques. In particular, models for HCl ionization in acetonitrile and dimethylsulfoxide are investigated. The proton is treated quantum mechanically using Feynman path integral methods and the remaining molecules are treated classically. Quantum effects are shown to be essential for the proper treatment of the ionization. The potential of mean force is computed as a function of the ion pair separation and the local solvent structure is examined. The computed dissociation constants in both solvents differ by several orders of magnitude which are in reasonable agreement with experimental results. Solvent separated ion pairs are found to exist in dimethylsulfoxide but not in acetonitrile. Dissociation mechanisms in small clusters are also investigated. Solvent separated ion pairs persist even in aggregates composed of rather few molecules, for instance, as few as thirty molecules. For smaller clusters or for large ion pair separations cluster finite-size effects come into play in a significant fashion.

This review covers applications of quantum Monte Carlo methods to quantum mechanical problems in the study of electronic and atomic structure, as well as applications to statistical mechanical problems both of static and dynamic nature. The common thread in all these applications is optimization of many-parameter trial states, which is done by minimization of the variance of the local or, more generally for arbitrary eigenvalue problems, minimization of the variance of the configurational eigenvalue.

Monte Carlo methods are used to study the phase transition in ammonium chloride from the orientationally ordered δ phase to the orientationally disordered γ phase. An effective pair potential is used to model the interaction between ions. Thermodynamic properties are computed in the canonical and isothermal-isobaric ensembles. Each ammonium ion is treated as a rigidly rotating body and the lattice is fixed in the low-temperature CsCl geometry. A simple extension of the Metropolis Monte Carlo method is used to overcome quasiergodicity in the rotational sampling. In the constant- NVT calculations the lattice is held rigid; in the constant- NpT calculations the lattice parameter is allowed to fluctuate. In both ensembles the order parameter rapidly falls to zero in the range (200 - 250)K, suggesting that the model disorders at a temperature in fair agreement with the experimental disordering temperature (243K). Peaks in the heat capacity and thermal expansivity curves are also found in the same temperature range.

In a previous paper (this http URL, chem-ph/9406003) we developed a form of variational trial wave function and applied it to van der Waals clusters: five or less atoms of Ar and Ne modeled by the Lennard-Jones potential. In addition, we tested the trial functions for a hypothetical, light atom resembling Ne but with only half its mass. We did not study atoms such as He with larger de Boer parameters, i.e., systems in which the zero point energy plays a more important role relative to the potential energy. This is the main purpose of the present paper. In fact, we study clusters to the very limit where the zero-point energy destroys the ground state as a bound state. A simple picture of this un-binding transition predicts the power law with which the energy vanishes as the de Boer parameter approaches its critical value and the power of the divergence of the the size of the clusters in this limit. Our numerical results are in agreement with these predictions.

Molecular dynamics calculations and optical spectroscopy measurements of weakly active infrared modes are reported. The results are qualitatively understood in terms of the "motional diminishing" of IR lines, a process analogous to the motional narrowing of a nuclear magnetic resonance (NMR) signal. In molecular solids or liquids where the appropriate intramolecular resonances are observable, motional diminishing can be used to study the fluctuations of the intermolecular interactions having time scales of 1psec to 100psec.