Neil Shenvi

Quantum random-walk search algorithm

Quantum random walks on graphs have been shown to display many interesting properties, including exponentially fast hitting times when compared with their classical counterparts. However, it is still unclear how to use these novel properties to gain an algorithmic speedup over classical algorithms. In this paper, we present a quantum search algorithm based on the quantum random-walk architecture that provides such a speedup. It will be shown that this algorithm performs an oracle search on a database of N items with

A new approach to decoherence and momentum rescaling in the surface hopping algorithm.

O(\sqrt{N})

Dynamical Steering and Electronic Excitation in NO Scattering from a Gold Surface

calls to the oracle, yielding a speedup similar to other quantum search algorithms. It appears that the quantum random-walk formulation has considerable flexibility, presenting interesting opportunities for development of other, possibly novel quantum algorithms.

The initial and final states of electron and energy transfer processes: diabatization as motivated by system-solvent interactions.

As originally proposed, the fewest switches surface hopping (FSSH) algorithm does not allow for decoherence between wavefunction amplitudes on different adiabatic surfaces. In this paper, we propose an inexpensive correction to standard FSSH dynamics wherein we explicitly model the decoherence of nuclear wave packets on distinct electronic surfaces. Our augmented fewest switches surface hopping approach is conceptually simple and, thus far, it has allowed us to capture several key features of the exact quantum results. Two points in particular merit attention. First, we obtain the correct branching ratios when a quantum particle passes through more than one region of nonadiabatic coupling. Second, our formalism provides a new and natural approach for rescaling nuclear momenta after a surface hop. Both of these features should become increasingly important as surface hopping schemes are applied to higher-dimensional problems.

Nonadiabatic dynamics at metal surfaces: independent-electron surface hopping.

Simulating Surfaces Although modern computational chemistry can often match or even exceed experimental accuracy in modeling gas phase reactions, the surface-bound processes involved in most practical catalysis pose a substantially greater challenge to theory (see the Perspective by Hasselbrink). Díaz et al. (p. 832) show that a modification to standard density functional methods can predict reaction barrier heights to within 1 kilocalorie per mole for the widely studied dissociative adsorption of dihydrogen on copper. In a complementary study, Shenvi et al. (p. 829) apply an efficient algorithmic framework to model transitions among multiple electronic states at a metal surface and successfully account for the complex dependence of nitric oxide scattering on the small molecules vibrations and rotations. Theory accounts for the complex ways in which vibrations and rotations of nitric oxide molecules affect scattering from a surface. Nonadiabatic coupling of nuclear motion to electronic excitations at metal surfaces is believed to influence a host of important chemical processes and has generated a great deal of experimental and theoretical interest. We applied a recently developed theoretical framework to examine the nature and importance of nonadiabatic behavior in a system that has been extensively studied experimentally: the scattering of vibrationally excited nitric oxide molecules from a Au(111) surface. We conclude that the nonadiabatic transition rate depends strongly on both the N-O internuclear separation and the molecular orientation and, furthermore, that molecule-surface forces can steer the molecule into strong-coupling configurations. This mechanism elucidates key features of the experiments and provides several testable predictions regarding the dependence of vibrational energy transfer on the initial vibrational energy, molecular orientation, and incident angle.

Simultaneous-trajectory surface hopping: A parameter-free algorithm for implementing decoherence in nonadiabatic dynamics

For a system which undergoes electron or energy transfer in a polar solvent, we define the diabatic states to be the initial and final states of the system, before and after the nonequilibrium transfer process. We consider two models for the system-solvent interactions: A solvent which is linearly polarized in space and a solvent which responds linearly to the system. From these models, we derive two new schemes for obtaining diabatic states from ab initio calculations of the isolated system in the absence of solvent. These algorithms resemble standard approaches for orbital localization, namely, the Boys and Edmiston-Ruedenberg (ER) formalisms. We show that Boys localization is appropriate for describing electron transfer [Subotnik et al., J. Chem. Phys. 129, 244101 (2008)] while ER describes both electron and energy transfer. Neither the Boys nor the ER methods require definitions of donor or acceptor fragments and both are computationally inexpensive. We investigate one chemical example, the case of oligomethylphenyl-3, and we provide attachment/detachment plots whereby the ER diabatic states are seen to have localized electron-hole pairs.

Phase-corrected surface hopping: correcting the phase evolution of the electronic wavefunction.

Recent experiments have shown convincing evidence for nonadiabatic energy transfer from adsorbate degrees of freedom to surface electrons during the interaction of molecules with metal surfaces. In this paper, we propose an independent-electron surface hopping algorithm for the simulation of nonadiabatic gas-surface dynamics. The transfer of energy to electron-hole pair excitations of the metal is successfully captured by hops between electronic adiabats. The algorithm is able to account for the creation of multiple electron-hole pairs in the metal due to nonadiabatic transitions. Detailed simulations of the vibrational relaxation of nitric oxide on a gold surface, employing a multistate potential energy surface fit to density functional theory calculations, confirm that our algorithm can capture the underlying physics of the inelastic scattering process.

Decoherence and surface hopping: When can averaging over initial conditions help capture the effects of wave packet separation?

In this paper, we introduce a trajectory-based nonadiabatic dynamics algorithm which aims to correct the well-known overcoherence problem in Tullys popular fewest-switches surface hopping algorithm. Our simultaneous-trajectory surface hopping algorithm propagates a separate classical trajectory on each energetically accessible adiabatic surface. The divergence of these trajectories generates decoherence, which collapses the particle wavefunction onto a single adiabatic state. Decoherence is implemented without the need for any parameters, either empirical or adjustable. We apply our algorithm to several model problems and find a significant improvement over the traditional algorithm.

Effects of a random noisy oracle on search algorithm complexity

In this paper, we show that a remarkably simple correction can be made to the equation of motion which governs the evolution of the electronic wavefunction over some prescribed nuclear trajectory in the fewest-switches surface hopping algorithm. This corrected electronic equation of motion can then be used in conjunction with traditional or modified surface hopping methods to calculate nonadiabatic effects in large systems. Although the correction adds no computational cost to the algorithm, it leads to a dramatic improvement in scattering probabilities for all model problems studied thus far. We show that this correction can be applied to one of Tullys original one-dimensional model problems or to a more sophisticated two-dimensional example and yields substantially greater accuracy than the traditional approach.

Model Hamiltonian for the interaction of NO with the Au(111) surface

Fewest-switches surface hopping (FSSH) is a popular nonadiabatic dynamics method which treats nuclei with classical mechanics and electrons with quantum mechanics. In order to simulate the motion of a wave packet as accurately as possible, standard FSSH requires a stochastic sampling of the trajectories over a distribution of initial conditions corresponding, e.g., to the Wigner distribution of the initial quantum wave packet. Although it is well-known that FSSH does not properly account for decoherence effects, there is some confusion in the literature about whether or not this averaging over a distribution of initial conditions can approximate some of the effects of decoherence. In this paper, we not only show that averaging over initial conditions does not generally account for decoherence, but also why it fails to do so. We also show how an apparent improvement in accuracy can be obtained for a fortuitous choice of model problems, even though this improvement is not possible, in general. For a basic set of one-dimensional and two-dimensional examples, we find significantly improved results using our recently introduced augmented FSSH algorithm.