### Session W18: Theoretical Methods and Algorithms

 Thursday, March 8, 2007 2:30PM - 2:42PM W18.00001: Quantum Entanglement and Electron Correlation in Molecular Systems Hefeng Wang , Sabre Kais We study the relation between quantum entanglement and electron correlation in quantum chemistry calculations. We prove that the Hartree-Fock (HF) wave function does not violate Bell's inequality, thus is not entangled while the configuration interaction (CI) wave function is entangled since it violates Bell's inequality. Entanglement is related to electron correlation and might be used as an alternative measure of the electron correlation in quantum chemistry calculations. As an example we show the calculations of entanglement for the H$_2$ molecule and how it correlates with the traditional electron correlation, which is the difference between the exact and the HF energies. Thursday, March 8, 2007 2:42PM - 2:54PM W18.00002: Infinite, periodic systems in external fields -- an efficient, theoretical method Michael Springborg The response of periodic systems to external electric fields is a challenging theoretical problem. We show how the vector potential approach yields a numerically efficient treatment of the combined electronic and nuclear response to a finite static field. Our method is based on a self-consistent reformulation of the charge flow term in the single particle Hamiltonian. Careful numerical implementation yields a treatment whose computational needs are only marginally larger than those of a conventional field-free calculation. To prove the method we have performed model calculations for a qusi-one-dimensional (polymeric) system. The model contains all essential elements of an ab initio Kohn-Sham or Hartree-Fock Hamiltonian but allows for extensive testing. Thursday, March 8, 2007 2:54PM - 3:06PM W18.00003: Quantum master equation in phase space: Application to the Brownian motion in a periodic potential William Coffey , Yuri Kalmykov , Sergey Titov , Bernard Mulligan The quantum Brownian motion of a particle in a periodic potential $V(x)=-V_0 \cos (x/x_0 )$ is treated using the master equation for the time evolution of the Wigner distribution function $W(x,p,t)$ in phase space $(x,p)$. Explicit equations for the diffusion coefficients of the master equation for this dissipative quantum system are derived. The dynamic structure factor and longest relaxation time are evaluated by using matrix continued fractions. The longest relaxation time so obtained is compared with the quantum-mechanical escape rate formula. The matrix continued fraction solution agrees well with the analytical solution of the corresponding Kramers turnover problem. Thursday, March 8, 2007 3:06PM - 3:18PM W18.00004: Scrutinizing concepts in chemical kinetics: Sensitivity analysis and mean-field approximation Hakim Meskine , Karsten Reuter , Matthias Scheffler , Horia Metiu We present kinetic Monte Carlo (kMC) simulations for the CO oxidation reaction at RuO$_{2}$(110), based on rate constants determined by density-functional theory and transition-state theory. The composition and structure of the catalyst surface are computed in reactive environments ranging from ultra-high vacuum (UHV) to technologically relevant conditions (pressures of several atmospheres and elevated temperatures). This setup enables us to scrutinize frequently employed concepts in the modeling of chemical kinetics: Sensitivity analyses are performed to identify the rate determining steps under the different environmental conditions. While helpful under UHV conditions, this analysis proves to be of little use for catalytically relevant environments, since then a larger number of elementary processes contributes equally to the total rate of product formation. We also check on the mean-field approximation employed in phenomenological microkinetics by comparing rate equations based on the same first-principles rate constants to the kMC simulations, where the spatial distribution of the chemicals at the catalyst surface is explicitly considered. The rate equation activities are found to be in serious error, even failing to identify the correct dominant reaction mechanism. Thursday, March 8, 2007 3:18PM - 3:30PM W18.00005: A new mixed quantum/semiclassical propagation methodology Steven Schwartz We present a new propagation algorithm for the evolution of a highly quantum subsystem coupled to a more classical like bath. The quantum system is treated exactly, while the bath is evolved with a frozen Gaussian evolution. An evolution operator correction scheme we recently developed is then applied to compute the coupling between the quantum systems and the semiclassical bath. The scheme is applied to test problems and found to be accurate and not significantly more difficult to implement than standard classical molecular dynamics. The approach also admits the possibility of higher order correction to obtain exact quantum results. Thursday, March 8, 2007 3:30PM - 3:42PM W18.00006: Improved Polarizabilities and Dissociation in DFT: Vignale-Kohn Revisited Neepa Maitra , Meta van Faassen We develop a novel approach to the problem of polarizabilities and dissociation in electric fields from the static limit of the Vignale-Kohn (VK) functional. The VK response potential, extracted from the longitudinal component of the VK vector potential has ground-state properties that notably improve over VK response and over usual (semi-)local functionals. The VK density response is not the ground-state response in the corresponding field. Cases where VK density response yields poor polarizabilities, eg the H2 chain, work well in our approach. This is the first density functional method that correctly dissociates open-shell fragments in a field. Thursday, March 8, 2007 3:42PM - 3:54PM W18.00007: What decides if a smarter army can win a battle? Linda Shanahan , Surajit Sen We study the kinetics associated with a war'' in which an attacking army attempts to win over a spatially dispersed defender on a 2D lattice. The levels of engagement are comparable in our study. The conflicting parties can annihilate, win or lose at any given site depending upon certain preselected rules of engagement. The attacker possesses higher intelligence, which is manifested through the moves of the attackers. We show that an intelligent'' attacker with subcritical number of attackers cannot win in the engagement. Thursday, March 8, 2007 3:54PM - 4:06PM W18.00008: Foundations for Cooperating with Control Noise in the Manipulation of Quantum Dynamics Feng Shuang , Herschel Rabitz , Mark Dykman This work develops the theoretical foundations for the ability of a control field to cooperate with noise in the manipulation of quantum dynamics. The noise enters as run-to-run variations in the control amplitudes, phases and frequencies with the observation being an ensemble average over many runs as is commonly done in the laboratory. Weak field perturbation theory is developed to show that noise in the amplitude and frequency components of the control field can enhance the process of population transfer in a multilevel ladder system. The analytical results in this paper support the point that under suitable conditions an optimal field can cooperate with noise to improve the control outcome. Thursday, March 8, 2007 4:06PM - 4:18PM W18.00009: Enthalpy of molecular solids beyond the harmonic approximation: application to hydrogen storage Nikolai Zarkevich , D.D. Johnson With low potential energy barriers, the harmonic approximation for phonon modes can be invalid [1]. Molecular solids are composed of strongly-bonded molecules held together by relatively weak intermolecular forces. As intermolecular interactions are usually not harmonic, a new theoretical approach is needed to obtain enthalpies of molecular solids at finite temperature. We develop such a theory for molecular solids and liquids, and apply it to obtain enthalpy differences between various phases from the first principles. We also calculate Gibbs free energy, and show that a phase diagram (e.g., a van't Hoff plot) can be constructed as a graphical solution of the Gibbs equation. To exemplify important applications, we consider materials and reactions for the high-capacity hydrogen storage. [1] Phys.Rev.Lett.97, 119601 (2006). Thursday, March 8, 2007 4:18PM - 4:30PM W18.00010: Realistic simulations of low temperature Cu(100) growth: extending time and length scales by parallel temperature-accelerated dynamics Y. Shim , J.G. Amar , A.F. Voter , B.P. Uberuaga The temperature-accelerated dynamics (TAD) method is a powerful tool for carrying out non-equilibrium simulations of systems with infrequent events over extended time-scales. However, due to the serial nature of the method the computation time scales as $N^2 - N^3$, where $N$ is the number of atoms. As a result, TAD simulations have been limited to relatively small system sizes. By combining temperature-accelerated dynamics with a recently proposed parallel synchronous sublattice algorithm, we are able to simulate the dynamic evolution of systems over much larger length as well as longer time scales. In particular, we find that the computational time using our parallel accelerated dynamics method scales as $log(N)$ or better. Preliminary results for the growing film morphology in low-temperature Cu(100) growth will also be presented. These include the observation of a wide variety of defect configurations. Thursday, March 8, 2007 4:30PM - 4:42PM W18.00011: Electrostatics in Periodic-boundary Conditions and Real-space Corrections Ismaila Dabo , nicola Marzari We address periodic-image errors arising from the use of periodic-boundary conditions to describe systems that do not exhibit full three-dimensional periodicity. We show that the difference between the Coulomb potential calculated by Fourier transforms and the exact potential can be characterized analytically. Based on this observation, we present an efficient real-space method to correct periodic-image errors in plane-wave calculations. Comparing the method with existing schemes, we show that it is particularly advantageous for studying systems exhibiting one- or two-dimensional periodicity. As an application, we consider the vibrational properties of CO adsorbed on charged platinum surfaces. Thursday, March 8, 2007 4:42PM - 4:54PM W18.00012: Quantum instanton evaluation of the kinetic isotope effects Jiri Vanicek , William H. Miller The quantum instanton approximation is used to compute kinetic isotope effects for intramolecular hydrogen transfer in \textit{cis}-1,3-pentadiene. Due to the importance of skeleton motions, this system with 13 atoms is a simple prototype for hydrogen transfer in enzymatic reactions. The calculation is carried out using thermodynamic integration with respect to the mass of the isotopes and a path integral Monte Carlo evaluation of relevant thermodynamic quantities. Efficient virial'' estimators are derived for the logarithmic derivatives of the partition function and the delta-delta correlation functions. These estimators require significantly fewer Monte Carlo samples since their statistical error does not increase with the number of discrete time slices in the path integral. The calculation treats all 39 degrees of freedom quantum-mechanically and uses an empirical valence bond potential based on a modified general AMBER force field. The importance of quantum effects due to the skeleton motion is demonstrated by comparison with a mixed quantum-classical calculation. Thursday, March 8, 2007 4:54PM - 5:06PM W18.00013: ABSTRACT WITHDRAWN Thursday, March 8, 2007 5:06PM - 5:18PM W18.00014: Novel mechanism of dissipation in synthetic rotary motors Corina Barbu , Vincent Crespi We study novel mechanisms of dissipation in nanoscale and molecular-scale motors. In traditional treatments of such systems, the background degrees of freedom are integrated out into a thermal bath, and the rotator is coupled directly to this bath via phenomenological terms such as viscous damping or Langevin forces. We have investigated a situation in which one degree of freedom is pulled out from the thermal bath and into the explicit equations of motion, interposed between the bath and the motor. We describe a regime in which the deceleration of an unpowered rotor follows a universal \textit{power law}, rather than a standard exponential decay.