Craig C. Martens

Semiclassical-limit molecular dynamics on multiple electronic surfaces

In this paper, we present a new approach to treating many-body molecular dynamics on coupled electronic surfaces. The method is based on a semiclassical limit of the quantum Liouville equation. The formal result is a set of coupled classical-like partial differential equations for generalized distribution functions which describe both the nuclear probability densities on the coupled surfaces and the coherences between the electronic states. The Hamiltonian dynamics underlying the evolution of these distributions is augmented by nonclassical source and sink terms, which allow the flow of probability between the coupled surfaces and the corresponding formation and decay of electronic coherences. The formal results are shown analytically to reproduce the well-known Rabi and Landau–Zener results in appropriate limits. In addition, a direct numerical solution of the phase space partial differential equations is performed, and the results compared with exact quantum solutions for a model curve-crossing problem,...

The breaking and remaking of a bond: Caging of I2 in solid Kr

The caging of I2 in solid Kr is followed in real‐time following its dissociative excitation on the A(3Π1u) surface. The experiments involve pump–probe measurements with a time resolution of ≥150 fs. The experimental signals are reproduced using classical molecular dynamics simulations, and the classical Franck approximation. The comparison between experiment and simulation allows an unambiguous interpretation of features in the observed signal as being due to the initial impulsive stretch of the I–I bond, collision of the atoms with the cage wall, recoil and recombination, and the subsequent coherent oscillations of the nascent I2 molecule. These detailed observations are possible due to retention of coherence along the I–I coordinate throughout the caging process. The extent of coherence is dictated mainly by the initial impact parameters of the molecule‐cage collision, which in turn is controlled by the thermal and zero‐point amplitudes of lattice vibrations. The caging is well‐described as a sudden pro...

Quantum control of I2 in the gas phase and in condensed phase solid Kr matrix

We present experimental results and theoretical simulations for an example of quantum control in both gas and condensed phase environments. Specifically, we show that the natural spreading of vibrational wavepackets in anharmonic potentials can be counteracted when the wavepackets are prepared with properly tailored ultrafast light pulses, both for gas phase I2 and for I2 embedded in a cold Kr matrix. We use laser induced fluorescence to probe the evolution of the shaped wavepacket. In the gas phase, at 313 K, we show that molecular rotations play an important role in determining the localization of the prepared superposition. In the simulations, the role of rotations is taken into account using both exact quantum dynamics and nearly classical theory. For the condensed phase, since the dimensionality of the system precludes exact quantum simulations, nearly classical theory is used to model the process and to interpret the data. Both numerical simulations and experimental results indicate that a properly ...

Nanoprecipitation-assisted ion current oscillations

Nanoscale pores exhibit transport properties that are not seen in micrometre-scale pores, such as increased ionic concentrations inside the pore relative to the bulk solution, ionic selectivity and ionic rectification. These nanoscale effects are all caused by the presence of permanent surface charges on the walls of the pore. Here we report a new phenomenon in which the addition of small amounts of divalent cations to a buffered monovalent ionic solution results in an oscillating ionic current through a conical nanopore. This behaviour is caused by the transient formation and redissolution of nanoprecipitates, which temporarily block the ionic current through the pore. The frequency and character of ionic current instabilities are regulated by the potential across the membrane and the chemistry of the precipitate. We discuss how oscillating nanopores could be used as model systems for studying nonlinear electrochemical processes and the early stages of crystallization in sub-femtolitre volumes. Such nanopore systems might also form the basis for a stochastic sensor.

Femtosecond dynamics of coherent photodissociation—recombination of I2 isolated in matrix Ar

Abstract Pump—probe studies of I 2 in matrix Ar, with a time resolution of 180 fs, are reported. The experiments are simulated using classical molecular dynamics. Dissociative excitation of I 2 (A) results in coherent cage-induced recombination on the A/A′ surfaces. The recombinant molecule vibrates coherently even after extensive energy loss.

Semiclassical multistate Liouville dynamics in the adiabatic representation

In this paper, we describe implementation of the semiclassical Liouville method for simulating molecular dynamics on coupled electronic surfaces in the electronic adiabatic representation. We cast the formalism in terms of semiclassical motion on Born–Oppenheimer potential energy surfaces with nonadiabatic coupling arising from the coordinate dependence of the adiabatic electronic eigenstates. Using perturbation theory and asymptotic evaluation of the resulting time integrals, we derive an expression for the probability of transition between adiabatic states which agrees with the result given previously by Miller and George [W. H. Miller and T. F. George, J. Chem. Phys. 56, 5637 (1972)]. We also demonstrate numerically the equivalence of semiclassical trajectory-based calculations in the adiabatic and diabatic representations by performing molecular dynamics simulations on a model two-state system and comparing with exact quantum mechanical results. Excellent agreement between the exact and semiclassical ...

Simulation of ultrafast dynamics and pump–probe spectroscopy using classical trajectories

In this paper, we develop a method for accurately modeling ultrafast molecular dynamics and pump–probe spectroscopy using classical trajectory simulations. The approach is based on a semiclassical limit of the Liouville formulation of quantum mechanics. Expressions for the nonstationary classical phase space probability density created by an ultrashort laser pulse on an excited electronic state, and the observable fluorescence signal resulting from a pump–probe experiment, are derived in the weak‐field limit using perturbation theory. By introducing additional approximations, these expressions are cast in a form that can be directly implemented using classical trajectory integration and ensemble averaging. The method is tested against multisurface time‐dependent quantum mechanical wave packet calculations for a one‐dimensional model system representing I2 photodissociation‐recombination in a static Ar lattice. Nearly quantitative agreement between the exact calculations and the trajectory‐based method is ...

One‐atom cage effect in collinear I2(B)–Ar complexes: A time‐dependent wave packet study

Two‐dimensional time‐dependent wave packet calculations are carried out on a collinear model of the I2(B)–Ar complex to investigate the possible kinematic origin of the one‐atom cage effect in small van der Waals molecules. Three different excitation wavelengths are considered (496.5, 488, and 476.5 nm), and the dynamics are assumed to be restricted to the I2 B state electronic surface, with no nonadiabatic transitions following the pump excitation. Good agreement with experiment is obtained. To investigate the sensitivity of observable final state distributions on the weak intermolecular potential between I2 and Ar, three slightly different B state I–Ar interactions are employed for the case of 488 nm excitation. It is found that relatively small changes in the form and magnitude of the weak van der Waals interactions can have a large effect on the final state distributions. These results suggest that the experimental data on I2–Ar photodissociation–recombination can be explained by a purely kinematic on...

Simulation of quantum processes using entangled trajectory molecular dynamics

In this paper, we describe a new method for simulating quantum processes using classical-like molecular dynamics. The approach is based on solving the quantum Liouville equation in the Wigner representation using ensembles of classical trajectories in phase space. The nonlocality of quantum mechanics is incorporated in the trajectory representation as nonclassical interactions between the members of the ensemble, leading to an entanglement of their evolution. The statistical independence of the individual trajectories making up an ensemble in the classical limit is lost when quantum effects are included, and the entire state of the system must be propagated as a unified whole. We develop the formalism and its numerical implementation, and illustrate its application on two model problems of quantum mechanical tunneling: escape from a metastable well and wave packet penetration of the Eckhart barrier.

Nonlinear dynamics of methyl rotation and intramolecular energy diffusion in p‐fluorotoluene

This paper examines the effect of large amplitude internal rotation on the rate and extent of intramolecular vibrational energy redistribution (IVR). We study a classical Hamiltonian modeling the vibrations of p‐fluorotoluene in its first excited singlet (S1) electronic state. We find that the full many‐dimensional vibrational phase space of this system can be approximately decomposed into two subsystems. The first consists of the methyl rotor and the lowest‐frequency ring modes, which interest strongly and chaotically with the methyl rotor. Within this subsystem, energy is rapidly exchanged. The second subsystem consists of the remaining high‐frequency modes, which do not strongly couple to the methyl rotor directly. The chaotic low‐frequency ring–rotor dynamics generate an effectively random force on the remaining degrees of freedom. This intrinsically stochastic perturbation induces slower intramolecular energy diffusion and relaxation of nonequilibrium initial distributions in the higher‐frequency rin...