ITAMP WORKSHOP

Computational Approaches to Time-Dependent Quantum Dynamics

May 9-11, 2002

Organizers: Charles Weatherford and Robert Wyatt


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 Abstracts 

  

Online Talks

Askar
audio

video

Banicescu

 Bittner

Burghardt 

Colgan 

 Collins

 Garashchuk

 Heller

 Kendrick

 Makri

 Martens

 Meier

 Meyer

 Micha

 Ohrn

 Parlant

 Prezhdo

 Rabitz

 Ritchie

 Schneider

 Schultz

 Weatherford

 Wyatt

Schedule

 Thursday, May 9, 2002

 Friday, May 10, 2002

Saturday, May 11, 2002

 Thursday, May 9, 2002

[All session in Pratt Conference Room]

8:30 a.m. Coffee
8:45 a.m.  INTRODUCTION: Kate Kirby

SESSION I: Charles Weatherford, Chair

 9:00-9:35 a.m. Barry Schneider: Computational Methods for Time Dependent Quantum Mechanics
 9:40-10:15 a.m. Eric Heller: New Approaches to Wavepacket Propagation
10:20-10:35 a.m. Coffee

 SESSION II: Brian Kendrick, Chair

10:35-11:10 a.m. Robert Wyatt: The Quantum Trajectory Method: Wavepacket Dynamics in Many Dimensions
11:15-11:50 a.m. Burke Ritchie: Three New Computational Methods for Solving the
Time-Dependent Schroedinger Equation
12:00-2:00 p.m. Lunch

SESSION III: Oleg Prezhdo, Chair

2:00-2:35 p.m. Attila Askar: Advances in Quantum Trajectory Approaches to Dynamics
2:40-3:15 p.m. Nancy Makri: Forward-Backward Semiclassical Dynamics
3:20-3:55 p.m. Charles Weatherford: Space-Time Basis Functions for the Time-Dependent Schrödinger Equation
4:00-4:15 p.m. Refreshments

SESSION IV: Irene Burghardt, Chair

4:15-4:50 p.m. Gérard Parlant: Semiclassical Nonadiabatic Dynamics with Quantum Trajectories
4:55-5:30 p.m. H.-D. Meyer: Multiconfiguration Time-Dependent Hartree (MCTDH): An Efficient Method for Propagating Wavepackets in Several Dimensions

5:45 p.m. Reception

 Friday, May 10, 2002

[All sessions in Phillips Auditorium]

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 SESSION V: Sophya Garashchuk, Chair

9:00-9:35 a.m. Eric Bittner: Quantum Trajectories in Liouville Space: Relaxation and Decoherence
9:40-10:15 a.m. David Micha: Eikonal Methods in Configuration and Phase Space for Quantum Molecular Dynamics
10:20-10:35 Coffee

SESSION VI: Attila Askar, Chair

10:35-11:10 a.m. Irene Burghardt: Hydrodynamic Methods for Mixed State Dynamics and Dissipation
11:15-11:50 a.m. Craig Martens: Simulation of Quantum Dynamics Using Entangled Classical Trajectory Ensembles
12:10-1:30 p.m. Lunch

SESSION VII: Eric Bittner, Chair

1:30-2:05 p.m. Ioana Banicescu: Parallelization Strategies for Wavepacket Dynamics Using the Quantum Trajectory Method
2:10-2:45 p.m. Yngve Ohrn: Direct, Nonadiabatic, Molecular Reaction Dynamics
2:50-3:25 p.m. Lee Collins:  Time-Dependent Simulations of Large-Scale Quantum Mechanical Processes
3:30-3:45 p.m. Refreshments

SESSION VIII: Ioana Banicescu, Chair

3:45-4:20 p.m. James Colgan: Time Dependent Studies of Atomic Ionization
4:25-5:00 p.m. Brian Kendrick: Quantum Wavepacket Dynamics Using the de Broglie-Bohm Formulation of Quantum Mechanics
5:05-5:40 p.m. Sophya Garashchuk: Semiclassical Implementation of the Moller Operators in Reactive Scattering; Simplified Calculation of the Stability Matrix

 Saturday, May 11, 2002

[All sessions in Phillips Auditorium]

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 SESSION IX: Nancy Makri, Chair

9:00-9:35 a.m. Christoph Meier: Mixing Quantum and Classical Dynamics Using Bohmian Trajectories
9:40-10:15 a.m. Herschel Rabitz: Computational Issues in the Control of Quantum Dynamics Phenomena
10:20-10:35 a.m. Coffee

SESSION X: Lee Collins, Chair

10:35-11:10 a.m. Oleg Prezhdo: Incorporating Quantum Solvent Effects into Non-Adiabatic Molecular Dynamics
11:15-11:50 a.m. David Schultz: Time-Dependent, Lattice Approach for
Atomic and Molecular Collisions
12:00 noon Adjourn

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Participants

Prof. Attila Askar
Mathematics Department,
Koç University, Istinye, 80860 Istanbul, Turkey
aaskar@ku.edu.tr

Prof. Ioana Banicescu
Department of Computer Science,
Mississippi State University, P.O. Box 9637, Butler Hall
Mississippi State, MS 39762
ioana@cs.msstate.edu

Prof. Eric R. Bittner
Department of Chemistry,
University of Houston, Houston, TX 77204
bittner@uh.edu

Dr. Irene Burghardt
Departement de chimie ,
UMR 8642 du C.N.R.S. , Ecole Normale Superieure,
24, rue Lhomond , F-75231 Paris cedex 05, France
Irene.Burghardt@ens.fr

Dr. James Colgan
Dept. of Physics,
Auburn University, 206 Allison Labs., Auburn, AL 36830
jcolgan@physics.auburn.edu

Dr. Lee A. Collins,
Los Alamos National Laboratory, Group T-4, MS B-212, Los Alamos, NM 87545
lac@lanl.gov

Dr. Sophya Garashchuk
Department of Chemistry and Biochemistry,
University of South Carolina, 631 Sumter St., Columbia, SC 29208
garashchuk@mail.chem.sc.edu

Prof. Eric Heller
Physics Department, Harvard University, Cambridge, MA 02138
heller@physics.harvard.edu


Dr. Brian K. Kendrick
Theoretical Division,
Los Alamos National Laboratory, Group T12, Mail Stop B268,
Los Alamos, NM 87545
bkendric@lanl.gov

Professor Nancy Makri
Univ. of Illinois, A442 Chemical and Life Sciences Lab, University of Illinois, Urbana, IL 61801
nancy@makri.scs.uiuc.edu

Prof. Craig Martens
University of California,
Department of Chemistry, 574 Rowland Hall
Irvine, CA 92697-2025
cmartens@uci.edu

Dr. Christoph Meier
LCAR-IRSAMC, Université Paul Sabatier,
118, rte de Narbonne, F-31062 Toulose, France
chris@irsamc.ups-tlse.fr

Dr. Hans-Dieter Meyer
Theoretische Chemie,
Physikalisch-Chemisches Institut, Universitaet Heidelberg
Im Neuenheimer Feld 229 , D - 69120 Heidelberg, Germany
dieter@tc.pci.uni-heidelberg.de

Prof. David A. Micha
University of Florida , 2318 New Physics Bldg , P.O. Box 118435
Gainesville, FL 32611-8435
micha@qtp.ufl.edu

Prof. Nils Y. Ohrn,
University of Florida,
P.O. Box 118435, Gainesville, FL 32611-8435
ohrn@qtp.ufl.edu


Dr. Gérard Parlant
LSDMS UMR 5636, CC014, Université Montpellier II,
34095 Montpellier cedex 05 France
email:gerard.parlant@univ-montp2.fr

Prof. Oleg Prezhdo
Department of Chemistry,
University of Washington, Seattle, WA 98195
prezhdo@chem.washington.edu

Prof. Herschel Rabitz
Department of Chemsitry, Princeton University, Princeton, NJ 08544
hrabitz@princeton.edu

Dr. A. Burke Ritchie
University of California,
L-018 Lawrence Livermore National Laboratory
Livermore, CA 94550-9234
ritchie1@llnl.gov

Dr. Barry I. Schneider
National Science Foundation,
Theoretical Atomic, Molecular and Optical Physics
4201 Wilson Blvd., Arlington, VA 22230
bis@bohr.mps.nsf.gov

Dr. David R. Schultz
Physics Division, Oak Ridge National Laboratory, M.S. 6373, Bldg. 6003, P.O. Box 2008
Oak Ridge, TN 37831-6373
schultzd@ornl.gov

Prof. Charles Weatherford,
Physics Department, Florida A&M University, 205 Jones Hall, Tallahassee, FL 32307
weatherf@cennas.nhmfl.gov

Prof. Robert Wyatt
Department of Chemistry, University of Texas, Austin, TX 78712
cman041@aurora.hpc.utexas.edu

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Abstracts

Askar

Banicescu

 Bittner

Burghardt 

Colgan 

 Collins

 Garashchuk

 Heller

 Kendrick

 Makri

 Martens

 Meier

 Meyer

 Micha

 Ohrn

 Parlant

 Prezhdo

 Rabitz

 Ritchie

 Schneider

 Schultz

 Weatherford

 Wyatt

 

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 Advances in Quantum Trajectory Approaches to Dynamics

Attila Askar

Koç University,
Saryer, Istanbul 89010, Turkey

The quantum fluid dynamics (QFD) formulation is based on the separation of the amplitude and phase of the complex wave function in Schrodinger's equation. The approach leads to conservation laws for an equivalent "gas continuum". The Lagrangian [1] representation corresponds to following the particles of the fluid continuum, i. e. calculating "quantum trajectories". The Eulerian [2] representation on the other hand, amounts to observing the dynamics of the gas continuum at the points of a fixed coordinate frame. The combination of several factors leads to a most encouraging computational efficiency. QFD enables the numerical analysis to deal with near monotonic amplitude and phase functions. The Lagrangian description concentrates the computation effort to regions of highest probability as an optimal adaptive grid. The Eulerian representation allows the study of multi-coordinate problems as a set of one-dimensional problems within an alternating direction methodology. An explicit time integrator limits the increase in computational effort with the number of discrete points to linear. Discretization of the space via local finite elements [1,2] and global radial functions [3] will be discussed. Applications include wave packets in four-dimensional quadratic potentials and two coordinate photo-dissociation problems for NOCl and NO2.

[1] "Quantum fluid dynamics (QFD) in the Lagrangian representation with applications to photo-dissociation problems", F. Sales, A. Askar and H. A. Rabitz, J. Chem. Phys. 11, 2423 (1999)

[2] "Multidimensional wave-packet dynamics within the fluid dynamical formulation of the Schrodinger equation", B. Dey, A. Askar and H. A. Rabitz, J. Chem. Phys. 109, 8770 (1998)

[3] "Solution of the quantum fluid dynamics equations with radial basis function interpolation", Xu-Guang Hu, Tak-San Ho, H. A. Rabitz and A. Askar, Phys. Rev. E. 61, 5967 (2000)

 Parallelization Strategies for Wavepacket Dynamics Using the Quantum Trajectory Method*

Ioana Banicescu

Department of Computer Science and Engineering Research Center
Mississippi State University
Mississippi State, MS 39762

Abstract PDF

The study of quantum mechanics is based on finding the solution to the time-dependent Schroedinger equation (TDSE). One approach to solving the TDSE is the Quantum Fluid Dynamics (QFD) formulation, where wavepacket dynamics are based on the Bohmian formalism [1]. One of several computational approaches for simulating wavepacket dynamics is the algorithm introduced by Lopreore and Wyatt [2]. The algorithm solves the one-dimensional Lagrangian QFD equations of motion using a moving least square (MLS) method. This quantum trajectory method (QTM) is particularly attractive, given its simplicity without sacrifice of accuracy. However, its implementation is computationally-intensive, mainly due to frequent use of the MLS method. Therefore, parallel algorithms are necessary for simulating realistic applications within reasonable amount of time.

This talk will describe our multidisciplinary collaborative research project on the development of parallel versions of the algorithm by Lopreore and Wyatt [2] for shared and distributed memory architectures. Preliminary experiments indicate that the parallel algorithm achieves efficiency values of up to 65% on a 8-processor shared memory machine, and up to 82% on a 32-processor cluster. Further optimization of this algorithm's implementation is expected to result in even higher efficiency values. Adapting the algorithm for two- and three-dimensional problems is expected to lead to load imbalance among processors, and therefore result in performance degradation. In that case, to adequately address this problem, novel loop scheduling techniques will be incorporated in the parallel implementation of the algorithm. The talk will conclude with insights we have gained from this work and future directions of our collaborative research.

References

[1] D. Bohm, Phys. Rev. 85, 166 (1952); 85, 180 (1952)
[2] C. L. Lopreore and R. W. Wyatt, Phys. Rev. Lett. 82, 5190 (1999)
[3] R. G. Brook, P. E. Oppenheimer, C. A. Weatherford, I. Banicescu and J. Zhu, Int. J. Quant. Chem.,
00, 1 (2001).

________________________
*This work was supported by the National Science Foundation Grants NSF ITR/ACS Award # ACI0081303, NSF CA-REER Award # ACI9984465, and Award # EEC-9730381

 Quantum Trajectories in Liouville Space: Relaxation and Decoherence

Eric R. Bittner and Jeremy B. Maddox

Department of Chemistry
University of Houston
Houston, TX 77204

In recent years trajectory based methodologies have become increasingly popular for evaluating the time evolution of quantum systems. A revival of the de Broglie­Bohm interpretation of quantum mechanics has spawned several such techniques for examining quantum dynamics from a hydrodynamic perspective. Using techniques similar to those found in computational fluid dynamics one can construct the wave function of a quantum system at any time from the trajectories of a discrete ensemble of hydrodynamic fluid elements (Bohm particles) which evolve according to nonclassical equations of motion. Until very recently these schemes have been limited to conservative systems. In this talk, we present our methodology for including the effects of a thermal environment into the hydrodynamic formulation of quantum dynamics. We derive hydrodynamic equations of motion from the Caldeira-Leggett master equation for the reduced density matrix and give a brief overview of our computational scheme that incorporates an adaptive Lagrangian mesh. Our applications focus upon the dissipative dynamics of open unbounded quantum systems. Using both the Wigner phase space representation and the linear entropy, we probe the breakdown of the Markov approximation of the bath dynamics at low temperatures. We suggest a criteria for rationalizing the validity of the Markov approximation in open unbound systems and discuss decoherence, energy relaxation, and quantum/classical correspondence in the context of the Bohmian paths.

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 Hydrodynamic Methods for Mixed State Dynamics and Dissipation


Irene Burghardt[1]; Lorenz S. Cederbaum[2], Klaus B. Moller[1]


[1]Département de Chimie, UMR 8642, Ecole Normale Supérieure, rue Lhomond,
F-75231 Paris cedex 05, France
[2]Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im
Neuenheimer Feld 229, Germany

Abstract PDF

 Time Dependent Studies of Atomic Ionization

J. Colgan, M.S. Pindzola, and F. Robicheaux

Auburn University
Auburn, AL 36849

Abstract PDF

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 Time-Dependent Simulations of Large-Scale Quantum Mechanical Processes

L.A. Collins

Los Alamos National Laboratory
Group T-4, MS B-212
Los Alamos, NM 87545

The need to model more accurately and intricately the basic quantum mechanical processes that govern the temporal evolution of large assemblies of particles grows daily, requiring concomitant advances in computational procedures and algorithms. Such systems cover a wide variety of phenomena including shock-compressed materials, dense plasmas, Rydberg gases, atoms in fields, and Bose-Einstein condensates. While seemingly unrelated, the techniques employed to model these conditions involve some rather close associations and concepts. We consider two specific examples: 1) Molecular Dynamics (MD) simulations of N-atom systems, and 2) solutions of the time-dependent Schrödinger equation for ultracold media.

We have employed MD methods to investigate a large range of strongly-interacting systems [1], including shock-compressed fluids, dense plasmas, phase transitions from solid to liquid and from liquid to vapor, dislocations in solids, and ultracold Rydberg gases and plasmas. In all cases, a representative cell of N atoms models the extended medium. Within the cell, all interactions and motions are treated at the highest possible level. Since for most applications, the nuclei move far more slowly than the electrons, a Born-Oppenheimer separation applies in which the nuclei receive a classical and the electrons, a quantum mechanical treatment. The evolution of the system occurs in time by the application of a simple two-step process: 1) for a given configuration of the atoms, determine the forces, and 2) from these forces, apply the basic equations-of-motion to advance the particles in time. The calculation of the forces marks the time delimiting step and involves three areas. The first concerns short-range interactions, involving direct, exchange, and correlation effects among the quantal, active electrons. This we handle with Density Functional approaches, usually in the generalized gradient approximation. The second area involves long-range effects, which are basically classical, due to the interacting nuclear charges. These require Ewald or more usually tree techniques for efficient solution. Finally, further efficiency arises from recognizing the different time scales of the simulation. The forces change most radically for neighboring particles; therefore, considerable economy results from calculating only the local forces at each time step and updating the average far-field effects only after many steps. This
strategy encompasses a variety of reference system propagator algorithms (RESPA). Current simulations can effectively handle on the order of a few hundred particles for the long temporal propagations (~1000 steps) required to converge the salient system properties. Remarkably, this gives sufficient information on the static and dynamical behavior for many extended systems. However, to treat cases as mixtures and phase transitions requires larger samples and longer times and further developments.

A related endeavor has focused on the development of efficient techniques for solving the multi-dimensional, time-dependent linear and nonlinear Schrödinger equation [2]. Applications have included atoms in intense fields, quantum control of molecular systems by short-pulsed lasers, and, most recently, Bose-Einstein condensates. The range and efficacy of the method have facilitated the investigation of such phenomena as solitons, vortices, and trapping in optical lattices. Two approaches have proven particularly powerful: the real space product formulae (RSPF) and the discrete variable representation (DVR). The former derives from the partitioning of the hamiltonian into simple terms based on a Lie-Trotter algebra. The latter utilizes the special relationships involving orthogonal special functions and their zeros and weights. We discuss various implementations of these approaches for general spatial and temporal expansions as well as in the finite element scheme. We shall discuss the relative merits of the various approaches as well as show connections to the MD simulation techniques.

In collaboration with Joel Kress (LANL) and Stephane Mazevet (LANL) on the MD simulations and Barry Schneider (NSF) and David Feder (NIST) on the time-dependent Schrödinger equation.

[1] J. Kress et. al. Phys. Rev. Lett. 83, 3896 (1999); L. Collins et. al. Phys. Rev. B 63, 184110 (2001); and S. Mazevet et. al. Phys. Rev. Lett. 055001 (2002).

[2] J. Denschlag et. al. Science 287, 97 (2000); B. Andersen et. al. Phys. Rev. Lett. 86, 2926 (2001).

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 Semiclassical Implementation of the Moller Operators in Reactive Scattering; Simplified Calculation of the Stability Matrix

Sophya Garashchuk

Department of Chemistry & Biochemistry
University of South Carolina
Columbia, SC 29208
 

Talk PDF

 New Approaches to Wavepacket Propagation

Eric J. Heller

Physics Department and Chemistry Department
Harvard University
Cambridge, MA 02138

Wavepacket propagation, implemented numerically but motivated semiclassically, is receiving wide attention. I will review some issues facing some of these methods as they push into many dimensions, and focus on a particular approach involving generalized gaussian wavepacket dynamics, (GGWD) as recently pioneered by Troy Van Voorhis in our group at Harvard. GGWD is the full semiclassical version of state to state amplitudes between
coherent states, and it involves complex trajectories in real time. Van Voorhis has recently shown that the approach is quite tractable and stable for computation of complex spectra from autocorrelation functions, in the presence of multiple periodic orbits and nonlinear structure in phase space. The results for CO2 photodissociation and the prospects for scaling up to many degrees of freedom will be discussed.

 Quantum Wavepacket Dynamics Using the de Broglie-Bohm Formulation of Quantum Mechanics

Brian K. Kendrick

Theoretical Division (T-12, MS-B268)
Los Alamos National Laboratory
Los Alamos, NM 87545

Abstract PDF

Forward-Backward Semiclassical Dynamics

Nancy Makri

Departments of Chemistry and Physics
University of Illinois
Urbana, Illinois 61801

Forward-backward semiclassical dynamics (FBSD) provides a practical methodology for including quantum mechanical effects in classical trajectory simulations of polyatomic systems. FBSD expressions for time-dependent expectation values or correlation functions take the form of phase space integrals with respect to trajectory initial conditions, weighted by the coherent state transform of a corrected density operator. It is shown that the initial density in finite temperature expressions can be fully quantized by employing the discretized path integral representation of statistical mechanics, thus ensuring a proper treatment of zero point effects and capturing important imaginary components that are absent from purely classical trajectory methods. Optimal sampling is achieved through Monte Carlo or molecular dynamics techniques. Applications to polyatomic clusters and condensed phase processes are presented.

 Simulation of Quantum Dynamics Using Entangled Classical Trajectory Ensembles

Craig C. Martens

Department of Chemistry
University of California, Irvine
Irvine, CA 92697-2025

The time-dependent quantum mechanics of heavy particles moving on a single potential energy surface can often be represented surprisingly well by the evolution of classical trajectory ensembles. However, manifestly quantum mechanical phenomena such as transitions between coupled electronic states, electronic coherence and its decay, or quantum mechanical tunneling require fundamental modification of the purely classical equations of motion. In this talk, I describe a general approach to simulating molecular dynamics with intrinsic quantum effects using classical trajectories and its application to the problems of nonadiabatic dynamics, coherent multistate electronic-nuclear dynamics, and tunneling through potential barriers. When viewed from the trajectory ensemble perspective, quantum effects arise as a breakdown of the statistical independence of the trajectories in the ensemble and a nonlocal entanglement of their collective evolution.

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 Mixing Quantum and Classical Dynamics Using Bohmian Trajectories

E. Gindensperger, C. Meier and J. A. Beswick

LCAR-IRSAMC
Université Paul Sabatier
31062 Toulouse, France

A novel time-dependent hybrid quantum/classical propagation scheme based on Bohmian quantum trajectories is presented . The quantum subsystem is described by a wave packet depending on the quantum coordinates x and parametrically on the classical trajectories X(t).

The wave packet is used to calculate de Broglie-Bohm quantum trajectories x(t) which are used to calculate the force acting on the classical variables. Quantum corrections of the classical equation of motion are also included.

A detailed, rigorous derivation of the working equations starting from the full-dimensional quantum Hamiltonian will be given. Subsequently, the method is applied to simple test cases where a comparison with full-dimensional quantum calculations is still possible. Among other examples, results of rotational diffractive scattering of a diatomic molecule from a two-dimensional corrugated surface will be presented.

Since a large number of classical degrees of freedom can be taken into account, the proposed mixing scheme might successfully describe the dissipative dynamics of a quantum subsystem interacting with femtosecond laser pulses while being coupled to a classical bath. First results on the vibrational decoherence of iodine in a high pressure rare gas environment after femtosecond excitation will be presented.

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 Multiconfiguration Tilme-Dependent Hartree (MCTDH): An Efficient Method for Propagating Wavepackets in Several Dimensions

H.-D. Meyer

Theoretische Chemie
Physikalisch-Chemisches Institut
Universität Heidelberg
Im Neuenheimer Feld 229
D-69120 Heidelberg, Germany
 

Abstract PDF

 Eikonal Methods in Configuration and Phase Space for Quantum Molecular Dynamics

David A. Micha

Departments of Chemistry and Physics
University of Florida
Gainesville, FL 32611
 

Abstract PDF

 Direct, Nonadiabatic, Molecular Reaction Dynamics

Nils Y. Ohrn


University of Florida
P.O. Box 118435
Gainesville, FL 32611-8435

Abstract PDF

 Semiclassical Nonadiabatic Dynamics with Quantum Trajectories


Gérard Parlant


LSDSMS, CNRS & Université Montpellier II CC 014,
Place Eugène Bataillon, 34095 Montpellier Cedex 5, France E-mail: gerard.parlant@univ-montp2.fr

Abstract PDF

 Incorporating Quantum Solvent Effects into Non-Adiabatic
Molecular Dynamics

Oleg Prezhdo

Department of Chemistry
University of Washington
Seattle, WA 98195-1700

Recent approaches dealing with quantum effects in condensed phase environments will be discussed. Standard non-adiabatic molecular dynamics (NA MD) treats NA transitions in a small subsystem quantum mechanically and the majority of the degrees of freedom classically. The techniques developed in our group modify NA MD to include quantum effects for all degrees of freedom, while still allowing for application of the modified NA MD to condensed phase systems.

The following approaches will be discussed:

1. The stochastic mean-field approximation [1,2] incorporates quantum decoherence into the quantum-classical mean-field and disposes of the ad hoc surface hopping ansatz.

2. NA MD based on Bohmian formulation of quantum mechanics [3] resolves the quantum backreaction branching problem and provides a greater flexibility in the coupling of quantum and classical subsystems.

3. Quantized Hamilton dynamics [4-8], including the quantized mean-field approach [5] incorporates zero point energy and tunneling effects by a straightforward extension of classical mechanics into quantum dimensions.

Application of NA MD in combination with density functional theory to ultrafast photo-induced electron transfer from a molecular donor to TiO2 acceptor will be presented [9]. The transfer process forms the foundation for solar cells of the Graetzel type and is typical of the dye sensitized semiconductor nano-materials used in photocatalysis and photoelectrolysis.

1. O. V. Prezhdo "Mean-field approximation for the stochastic Schroedinger equation", J. Chem. Phys. 111, p.8366 (1999)

2. O. V. Prezhdo "Quantum anti-Zeno acceleration of a chemical reaction", Phys. Rev. Lett. 85, p.4413 (2000)

3. O. V. Prezhdo, C. Brooksby "Quantum backreaction through the Bohmian particle", Phys. Rev. Lett. 86, p.3215 (2001)

4. O. V. Prezhdo, Yu. V. Pereverzev "Quantized Hamilton dynamics", J. Chem. Phys. 113, p.6557 (2000)

5. C. Brooksby, O. V. Prezhdo "Quantized mean-field approximation", Chem. Phys. Lett. 346, p.463 (2001)

6. O. V. Prezhdo, Yu. V. Pereverzev "Quantized Hamilton dynamics for a general potential", J. Chem. Phys., in press

7. E. Pahl, O. V. Prezhdo "Extension of quantized Hamilton dynamics to higher orders", J. Chem. Phys., in press

8. O. V. Prezhdo "Classical mapping for the second order quantized Hamilton dynamics", J. Chem. Phys., in review

9. W. Stier, O. V. Prezhdo "Non-adiabatic molecular dynamics simulation of light-induced electron transfer from an anchored molecular electron donor to a semiconductor acceptor", J. Phys. Chem. B, in press

 Computational Issues in the Control of Quantum Dynamics Phenomena

Herschel Rabitz

Department of Chemistry
Princeton University
Princeton, NJ 08544

The control of quantum phenomena embraces a variety of applications, with the most common implementation involving tailored laser pulses to steer the dynamics of a quantum system towards some specified observable outcome. The theoretical and computational aspects of this subject are intimately tied to the growing experimental capabilities, especially the ability to perform massive numbers of high throughput experiments. Computational studies in this context have special roles. Especially important is the use of computational techniques to develop new control algorithms, which ultimately would be implemented in the laboratory to guide the control of complex quantum systems. Beyond control alone, many of the same concepts can be exploited for the performance of experiments optimally tuned for inversion, to extract Hamiltonian information. The latter scenario poses very high demands on the efficiency of solving the quantum dynamics equations to extract the information content from the experimental data. The concept of exploiting a computational quantum control tool kit will be introduced as a means for addressing many of these challenges.

 

Three New Computational Methods for Solving the
Time-Dependent Schroedinger Equation

Burke Ritchie

University of California
Lawrence Livermore National Laboratory
Livermore, CA 94550

and

Livermore Software Technology Corporation
7374 Las Positas Road
Livermore, CA 94550

First I review a pair of time-dependent 3D Schroedinger-equation solvers which collaborators and I have developed over the last few years with applications to ion-atom charge-exchange collisions and electron-molecule elastic scattering. The first is an implicit variation (ISOP) on the Fast Fourier Transform (FFT) explicit split-operator (ESOP) method of Feit and Fleck, applied to ion-atom charge exchange. The second is the use of FFT methods to evaluate the propagator for the time-dependent integral Schroedinger equation, applied to electron scattering. The second method was developed to avoid the use of a wave packet, whose spreading with time tends to restrict the electron momentum to values larger than 1 atomic unit. Finally I describe preliminary results for the solution of the "fluid" equations of the 3D phase-amplitude Schroedinger-equation solution, i. e. of the "fluid" equations of Bohm, applied to electron scattering.

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 Computational Methods for Time Dependent Quantum Mechanics

B.I. Schneider

Physics Division
National Science Foundation
Arlington, VA 22230

and

Optical Physics Division
National Institute of Standards and Technology
Gaithersburg, MD 20899
 

Talk PDF

 Time-Dependent, Lattice Approach for
Atomic and Molecular Collisions

David R. Schultz

Physics Division
Oak Ridge National Laboratory
Oak Ridge, TN 37831-6373

After briefly reviewing general progress in applying a direct, lattice solution of the time-dependent Schrödinger equation (LTDSE) to study ion-atom collisions, two recent works will be described in more detail. In one, the LTDSE approach has been used to aid in elucidating the underlying collision dynamics applicable to interpreting recent momentum imaging experiments examining the ejected electron spectrum. In the other, the method has been applied to study the fully correlated antiproton-helium ionization problem in reduced electronic dimensions in order to advance the technique towards treatment of multiple-electron systems. Finally, new, potential applications will be outlined to stimulate discussion of the applicability and utility of the approach to wider classes of problems.

Space-Time Basis Functions for the Time-Dependent Schrödinger Equation


Charles Weatherford


Physics Department
Florida A&M University
Tallahassee, FL 32307

Abstract PDF

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 The Quantum Trajectory Method: Wavepacket Dynamics in Many Dimensions

Robert E. Wyatt

Institute for Theoretical Chemistry and
Department of Chemistry and Biochemistry
The University of Texas at Austin
Austin, Texas

In quantum dynamics, the goal is to solve the Schrodinger time-dependent wave equation to find the time evolution of the wavefunction describing the system. A new approach will be described for solving the Schrodinger equation in which the computational tool is a set of quantum trajectories. This method, referred to as the quantum trajectory method (QTM), is based upon the equations of quantum hydrodynamics that were developed by de Broglie, Madelung, Bohm and others. The QTM develops trajectories for elements of the probability fluid. These fluid elements evolve under the influence of both the 'classical' force and quantum force (related to the gradient of the nonlocal quantum potential). The computational method will be described, and applications will be made to electronic nonadiabiatic dynamics, including an example involving two electronic states interacting with a number of 'bath' modes. In this problem, a very small number of quantum trajectories are computed (about 200), even though the dimensionality is high (>20). For this example, the least squares fitting techniques will be described (this algorithm is needed to compute derivatives required for the equations of motion) and the use of adaptive remeshing will be illustrated (this improves the stability and permits integration to longer times).

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