Moving boundary truncated grid method for electronic nonadiabatic dynamics.

The moving boundary truncated grid method is developed to study the wave packet dynamics of electronic nonadiabatic transitions between a pair of diabatic potential energy surfaces. The coupled time-dependent Schrödinger equations (TDSEs) in the diabatic representation are integrated using adaptive truncated grids for both the surfaces. As time evolves, a variable number of grid points fixed in space are activated and deactivated without any advance information of the wave packet dynamics. Essential features of the truncated grid method are first illustrated through applications to three one-dimensional model problems, including the systems of single avoided crossing, dual avoided crossing, and extended coupling region with reflection. As a demonstration for chemical applications, the truncated grid method is then employed to study the dynamics of photoisomerization of retinal in rhodopsin described by a two-electronic-state two-dimensional model. To demonstrate the capability of the truncated grid method to deal with the electronic nonadiabatic problem in high dimensionality, we consider a multidimensional electronic nonadiabatic system in two, three, and four dimensions. The results indicate that the correct grid points are automatically activated to capture the growth and decay of the wave packets on both of the surfaces. Therefore, the truncated grid method greatly decreases the computational effort to integrate the coupled TDSEs for multidimensional electronic nonadiabatic systems.

Moving Boundary Truncated Grid Method: Application to the Time Evolution of Distribution Functions in Phase Space.

The moving boundary truncated grid (TG) method, previously developed to integrate the time-dependent Schrödinger equation and the imaginary time Schrödinger equation, is extended to the time evolution of distribution functions in phase space. A variable number of phase space grid points in the Eulerian representation are used to integrate the equation of motion for the distribution function, and the boundaries of the TG are adaptively determined as the distribution function evolves in time. Appropriate grid points are activated and deactivated for propagation of the distribution function, and no advance information concerning the dynamics in phase space is required. The TG method is used to integrate the equations of motion for phase space distribution functions, including the Klein-Kramers, Wigner-Moyal, and modified Caldeira-Leggett equations. Even though the initial distribution function is nonnegative, the solutions to the Wigner-Moyal and modified Caldeira-Leggett equations may develop negative basins in phase space originating from interference effects. Trajectory-based methods for propagation of the distribution function do not permit the formation of negative regions. However, the TG method can correctly capture the negative basins. Comparisons between the computational results obtained from the full grid and TG calculations demonstrate that the TG method not only significantly reduces the computational effort but also permits accurate propagation of various distribution functions in phase space.

Accelerating ring-polymer molecular dynamics with parallel-replica dynamics.

Nuclear quantum effects are important for systems containing light elements, and the effects are more prominent in the low temperature regime where the dynamics also becomes sluggish. We show that parallel replica (ParRep) dynamics, an accelerated molecular dynamics approach for infrequent-event systems, can be effectively combined with ring-polymer molecular dynamics, a semiclassical trajectory approach that gives a good approximation to zero-point and tunneling effects in activated escape processes. The resulting RP-ParRep method is a powerful tool for reaching long time scales in complex infrequent-event systems where quantum dynamics are important. Two illustrative examples, symmetric Eckart barrier crossing and interstitial helium diffusion in Fe and Fe-Cr alloy, are presented to demonstrate the accuracy and long-time scale capability of this approach.

Extending atomistic simulation timescale in solid/liquid systems: crystal growth from solution by a parallel-replica dynamics and continuum hybrid method.

Deposition of solid material from solution is ubiquitous in nature. However, due to the inherent complexity of such systems, this process is comparatively much less understood than deposition from a gas or vacuum. Further, the accurate atomistic modeling of such systems is computationally expensive, therefore leaving many intriguing long-timescale phenomena out of reach. We present an atomistic/continuum hybrid method for extending the simulation timescales of dynamics at solid/liquid interfaces. We demonstrate the method by simulating the deposition of Ag on Ag (001) from solution with a significant speedup over standard MD. The results reveal specific features of diffusive deposition dynamics, such as a dramatic increase in the roughness of the film.

Role of Geometric Relaxation in Oxygen Binding to Metal Nanoparticles.

Better oxygen reduction catalysts are needed to improve the efficiency and lower the cost of fuel cells. Metal nanoparticles are good candidates because their catalytic properties can differ from bulk metals. Using density functional theory calculations, we studied the geometric relaxation of metal nanoparticles upon oxygen binding. Because bound oxygen species are intermediates in the oxygen reduction reaction, the binding of oxygen can be correlated to catalytic activity. Our results show that Pt and Au are unique in that they exhibit a larger structural deformation than other metals, which is pronounced for particles with fewer than 100 atoms. The structural deformation induced by atomic oxygen binding stabilizes the oxidized state and thus reduces the catalytic activity of Pt-based random alloys. We show that the catalytic activity of Pt can be improved by forming alloys with less deformable metals.

Communication: κ-dynamics--an exact method for accelerating rare event classical molecular dynamics.

κ-dynamics is an accelerated molecular dynamics method for systems with slow transitions between stable states. Short trajectories are integrated from a transition state separating a reactant state from products. The first trajectory found that leads directly to a product without recrossing the transition state and starts in the reactant state is followed. The transition time is drawn from a distribution given by the transition state theory rate and the number of attempted trajectories. Repeating this procedure from each state visited gives a statistically exact state-to-state trajectory.

Detailed single-molecule spectroelectrochemical studies of the oxidation of conjugated polymers.

Single-particle fluorescence spectroelectrochemistry was used to investigate the electrochemical oxidation of isolated, immobilized particles of the conjugated polymers BEH-PPV and MEH-PPV at an indium tin oxide (ITO) electrode immersed in an electrolyte solution. Two types of particles were investigated: (i) polymer single molecules (SM) and (ii) nanoparticle (NP) aggregates of multiple polymer single molecules. For the BEH-PPV polymer, the observation of nearly identical lowest oxidation potentials for different SM in the ensemble is evidence for effective electrostatic screening by the surrounding electrolyte solution. A combination of Monte Carlo simulations and application of Poisson-Boltzmann solvers were used to model the charging of polymer single molecules and nanoparticles in the electrochemical environment. The results indicate that the penetration of electrolyte anions into the polymer nanoparticles is necessary to produce the observed narrow fluorescence quenching vs oxidation potential curves. Finally, fluorescence-lifetime single-molecule spectroelectrochemical (SMS-EC) data revealed that at low potential an excited state reduction process (i.e., electron transfer from ITO to the polymer) is probably the dominant fluorescence quenching process.

Analysis of orientational dynamics of single fluorophore trajectories from three-angle polarization experiments.

An algorithm of single fluorophore orientation reconstruction based on a recently proposed method [J. T. Fourkas, Opt. Lett. 26, 211 (2001)] is studied, which converts three measured intensities {I(0),I(45),I(90)} to the dipole orientation {I(T),theta,phi}. Fluctuations in the detected signals {deltaI(0),deltaI(45),deltaI(90)} caused by the shot noise results in different profiles in deltatheta and deltaphi, causing the originally equivalent coordinates (X,Y,Z) to separate into in-plane (X,Y) and out-of-plane (Z) components. The overall fluctuation in deltatheta turns out to be higher than deltaphi, and thus noise has a greater effect on the Z component of the signal than on the X and Y components. Therefore, care should be taken not to interpret differences in the in-plane and out-of-plane dynamics as being evidence of nonisotropic rotational motion. For some molecular orientations around Theta=pi2, the total signal intensity cannot be inverted directly to angular coordinates. An optimization method is proposed that calculates the corrected angular coordinates for the points in the trajectory. To test the effects of this recovery scheme, the covariance/correlation functions for reconstructed angular trajectories were calculated for the case of isotropic rotational diffusion. Rotational correlation functions of rank [script-l] were found to deviate from the ideal single exponential decay as a result of the noise. This effect becomes more significant for large [script-l] cases. The correlation functions were fitted to a stretch exponential to characterize their deviation from the true single exponential decay. Correlation functions of Z have larger deviations from the true correlation function due to the larger noise in the Z component. The trends and the distributions of stretched exponential parameters {tau(F)} and {beta(F)} fitted from trajectories of a given size T also exhibit the influences from noise. Again, large [script-l] cases show a greater effect from the noise which eliminates the benefit of calculating higher rank correlation functions because of the smaller time constants. Due to the errors in estimating the correlation functions, significant differences between correlation functions of different orders can result from the statistics rather than being an indication of a nondiffusive behavior.

Determining if a system is heterogeneous: the analysis of single molecule rotational correlation functions and their limitations.

Single molecule spectroscopy can be utilized to measure distributions of individual molecular properties that may be averaged out in the ensemble measurement. For example, complex dynamics in disordered systems can be investigated by observing single molecule rotations via fluorescence spectroscopy. The rotational time of a single transient can be calculated from the correlation function of the reduced linear dichroism signal which fluctuates over time as the molecule reorients in its surroundings. Distributions of rotational time constants can be used to characterize the heterogeneity of molecular environments in the material. This paper reviews some theoretical studies on (1) the high numerical aperture effects on the final correlation function, and how it can be related to optical anisotropy decays in a bulk measurement; (2) the statistical errors resulting from the finite observation length that will propagate into distributions of rotational times. These lead to the discussions on how to interpret correctly the distribution of properties measured from a set of single molecule data, and to determine if in fact the system is heterogeneous.

Effect of finite trajectory length on the correlation function analysis of single molecule data.

The effect of finite trajectory length on single molecule rotational correlation functions has been studied by utilizing time series analysis and numerical simulations. Correlation functions obtained from the trajectories of length less than 100 times the correlation time constant (tau([script-l])) exhibit significant deviations from the true correlation function. The distributions of sample time constants (tau(F)) and stretching exponents (Beta(F)) are mapped by fitting a large number of rotational trajectories to stretched exponentials. As the trajectory length gets smaller, the distributions become broader and asymmetric and their mean values deviate from the true value predicted by pure rotational diffusion. Analysis based on higher order spherical harmonics is suggested as a method for minimizing the effect of the trajectory length. The distributions of time constants for different higher order spherical harmonics are also compared. While the focus of the paper is on rotational correlation functions, the general conclusions apply to any dynamical process that yields an exponentially decaying correlation function.