Chemical Physics

Molecular exciton effects in the neutral and maximally doped C60 (C70) are considered using a tight binding model with long-range Coulomb interactions and bond disorder. By comparing calculated and observed optical spectra, we conclude that relevant Coulomb parameters for the doped cases are about half of those of the neutral systems. The broadening of absorption peaks is well simulated by the bond disorder model.

Packing transitions in the lowest energy structures of Li clusters as a function of size have been identified via simulated annealing. For N>21, the large p character of Li leads to unexpected ionic structures. At N~25, a packing pattern based on interpenetrating 13-atom icosahedra and similar to that of Na and K appears. This pattern persists until at N=55, where another transition to a structure based on a Mackay icosahedron occurs. For clusters of size 55 and 147, the optimized FCC structure representative of the bulk is still slightly higher in energy than the optimal MIC. (RK-94-03)

A Monte Carlo method for dynamics simulation of all-atom protein models is introduced, to reach long times not accessible to conventional molecular dynamics. The considered degrees of freedom are the dihedrals at C α -atoms. Two Monte Carlo moves are used: single rotations about torsion axes, and cooperative rotations in windows of amide planes, changing the conformation globally and locally, respectively. For local moves Jacobians are used to obtain an unbiased distribution of dihedrals. A molecular dynamics energy function adapted to the protein model is employed. A polypeptide is folded into native-like structures by local but not by global moves.

Quantum annealing is a new method for finding extrema of multidimensional functions. Based on an extension of classical, simulated annealing, this approach appears robust with respect to avoiding local minima. Further, unlike some of its predecessors, it does not require an approximation to a wavefunction. In this paper, we apply the technique to the problem of finding the lowest energy configurations of Lennard-Jones clusters of up to 19 particles (roughly 10 5 local minima). This early success suggests that this method may complement the widely implemented technique of simulated annealing.

The band gaps and spectral shifts of CdS, CdSe, CdTe, AlP, GaP, GaAs, and InP semiconductor clusters are calculated from band structure calculations using accurate local and non-local empirical pseudopotentials. The effect of spin-orbit coupling on the band structures is included in the calculations when they are important. The complete set of pseudopotential parameters and full computational details are reported for all these semiconductors. The calculated spectral shifts of zinc-blende and wurtzite CdS, wurtzite CdSe, and zinc-blende InP clusters are in good agreement with experiments over a range of cluster sizes. The effect of crystal structure on the band gaps is small in large clusters but becomes important in small clusters. In the absence of experimental data, our calculations provide reasonable estimates of expected spectral shifts for the other clusters. These results demonstrate that the empirical pseudopotential method yields unique insights into the quantum confinement effects and is a powerful tool for calculating the spectral shifts of semiconductor clusters.

The dynamics near the top of a potential barrier is studied in the temperature region where quantum effects become important. The time evolution of the density matrix of a system that deviates initially from equilibrium in the vicinity of the barrier top but is in local equilibrium away from the barrier top is determined. Explicit results are given for a range of parameters where the nonequilibrium state is not affected by anharmonicities of the barrier potential except for the barrier height. In particular, for a system confined initially to one side of the barrier the relaxation to a quasi--stationary flux state is determined. The associated rate constant is evaluated and the relation to other rate formulas is discussed in detail.

The formation of O 2 by radiative association and by inverse predissociation of ground state oxygen atoms is studied using quantum-mechanical methods. Cross sections, emission spectra, and rate coefficients are presented and compared with prior experimental and theoretical results. At temperatures below 1000~K radiative association occurs by approach along the 1 3 Π u state of O 2 and above 1000~K inverse predissociation through the B 3 Σ − u state is the dominant mechanism. This conclusion is supported by a quantitative comparison between the calculations and data obtained from hot oxygen plasma spectroscopy.

There exists a generic relationship between the thermodynamics of a continuous polymer with a generic self-interaction and the two-point function of an interacting field-theory. In addition, the (2N)-point function of the resulting field theory is similarly related to a system of N interacting polymers. In the present paper, this relation is explored for the special case of a polyelectrolyte, characterized by a screened Coulomb pair potential. The corresponding field theory can be recast in a particularly simple form, corresponding to a quantum-mechanical particle, self-interacting via the emission and absorption of a massive scalar field. This is particularly useful in a perturbative treatment: perturbative expansions for the polyelectrolyte can be simply derived from the loop expansion for the related field-theoretical two-point function, for which established computational methods exist.

A practical method for finding free energy barriers for transitions in high-dimensional classical and quantum systems is presented and used to calculate the dissociative sticking probability of H2 on a metal surface within transition state theory (TST). The reversible work involved in shifting the system confined to a hyperplane from the reactant region towards products is evaluated directly. Quantum mechanical degrees of freedom are included by using Feynman Path Integrals with the hyperplane constraint applied to the centroid of the cyclic paths. An optimal dividing surface for the rate estimated by TST is identified naturally in the course of the reversible work evaluation. The free energy barrier is determined relative to the reactant state directly, so an estimate of the transition rate can be obtained without requiring a solvable reference model for the transition state. The method has been applied to calculations of the sticking probability of a thermalized hydrogen gas on a Cu(110) surface. The two hydrogen atoms were included quantum mechanically, and over two hundred atoms in the Cu crystal where included classically. The activation energy for adsorption and desorption was determined and found to be significantly lowered by tunneling at low temperature. The calculated values agree quite well with experimental estimates. Dynamical corrections to the classical TST rate estimate were evaluated and found to be small.

We consider the thermodynamics of a uniformly charged polyelectrolyte with harmonic bonds. For such a system there is at high temperatures an approximate scaling of global properties like the end-to-end distance and the interaction energy with the chain-length divided by the temperature. This scaling is broken at low temperatures by the ultraviolet divergence of the Coulomb potential. By introducing a renormalization of the strength of the nearest- neighbour interaction the scaling is restored, making possible an efficient blocking method for emulating very large polyelectrolytes using small systems. The high temperature behaviour is well reproduced by the analytical high- T expansions even for fairly low temperatures and system sizes. In addition, results from low- T expansions, where the coefficients have been computed numerically, are presented. These results approximate well the corresponding Monte Carlo results at realistic temperatures. A corresponding analysis of screened chains is performed. The situation here is complicated by the appearance of an additional parameter, the screening length. A window is found in parameter space, where scaling holds for the end-to-end distance. This window corresponds to situations where the range of the potential interpolates between the bond length and the size of the chain. This scaling behaviour, which is verified by Monte Carlo results, is consistent with Flory scaling. Also for the screened chain a blocking approach can be devised, that performs well for low temperatures, whereas the low- T expansion is inaccurate at realistic temperatures.