January 12 - 16, 2009
Vibrational motion of ions in a linear trap can be efficiently controlled by creating small anharmonicity of the trapping potential and using optimally shaped MHz pulses to induce the desired states-to-state transitions. In this work the motional quantum states of ions in an anharmonic trap were calculated numerically using expansion over the basis set of Hermit polynomials. The Optimal Control Theory is employed in order to optimize shaped pulses for the major quantum gates, such as NOT, CNOT, Pi-rotation and the Hadamard transform.
On the dogmatic spirit we discuss the issue applicability of
adiabatic functional also in strong high frequency
laser-fields. On the pragmatic side we explain the necessity of
using a TUNED range-separated time-dependent and time
independent density functional theory for difficult systems.
For DFT we bring examples for symmetric cationic radicals, such
as H_{2}^{+}, He_{2}^{+},
Ne_{2}^{+},
(H_{2}O)_{2}^{+} and
(C_{6}H_{6})_{2}^{+} and for TDDFT we
discuss charge transfer excitations as examples. A tuned range
parameter theory is also capable of treating a variety of
solids.
Co-Authors in various parts of this work:
Dr. Helen Eisenberg, Dr. Ester Livshits, Tamar Stein (Institute
of Chemistry and the Fritz Haber Center for Molecular Dynamics,
The Hebrew University of Jerusalem)
Professor Leeor Kronik (Weizmann Institute of Science)
Professor Anna Krylov (University of California).
The time-dependent Schrödinger equation plays an essential role
to understand non-relativistic atomic and molecular processes.
This is a linear partial differential equation with a very
particular structure. A good model for a problem is usually
given by a Hamiltonian operator, which suffices to
describe the evolution of the system (for given initial conditions)
while preserving many qualitative properties (energy, unitarity, etc.).
Unfortunately, in general, analytical solutions for the equations
are unknown, even for most simple models, and numerical methods
are required.
Some techniques frequently used are spectral decomposition
or spatial discretisation. In general, one has to solve a system of
linear ordinary differential equations.
Standard numerical methods do not preserve the qualitative properties
mentioned and usually have a significant error propagation along
the integration. Then, to get accurate and reliable results can
be computationally very expensive. Geometric numerical integration has
been developed during the last years and it intends to build
numerical methods which preserve most qualitative properties
of the exact solution. Some of these methods are developed
for problems with similar structure to the Schrödinger equation leading
in many cases to improved qualitative and quantitative results.
In this talk we review two families of methods: Magnus integrators [1]
(for non-autonomous problems) and splitting methods [2] (for systems
which are separable in solvable parts).
[1] S. Blanes, F. Casas, J.A. Oteo and J. Ros, The Magnus and expansion
and some of its applications. Physics Reports. In Press.
[2] S. Blanes, F. Casas, and A. Murua, Splitting and composition methods in the
numerical integration of differential equations, (arXiv:0812.0377v1).
Joint work with Bastiaan J. Braams and Yimin Wang (Department of Chemistry and Cherry L. Emerson Center for Scientific Computation,
Emory University, Atlanta, GA 30322).
The currently exists a variety of methods to represent
potential energy surfaces for high dimensional systems, and
these will be reviewed after a short, selective, historical
introduction to the topic. I will describe the progress we have
made. The central aspect of progress is to perform standard least-squares fits of the order of 10^{4} "scattered" electronic energies using a polynomial basis that is invariant with respect to all permutations of like atoms. Some of the technical details of this approach will be given followed by several case studies with a focus on recent work on the water dimer and trimer.
I will conclude with a review of some related fitting strategies, which are quite different from full-dimensional fitting approaches, which are know as "n-mode representation of the potential," the "high dimensional model representation" and the "potfit."
Financial support from the National Science Foundation, the Department of
Energy, and the Office of Naval Research is gratefully acknowledged.
The photophysics of extended systems like conjugated polymers or molecular
aggregates is characterized on the one hand by the properties of the
molecular building blocks and on the other hand by the delocalized nature of
the electronic excitations, i.e., the formation of excitonic states. The
dynamical phenomena induced by photoexcitation therefore involve an interplay
of site-site interactions entailing excitation energy transfer, and vibronic
(electron-phonon) coupling which typically leads to ultrafast internal
conversion processes. We propose here a molecular-level, quantum-dynamical
approach as exemplified by our recent study of exciton dissociation at
interfaces of semiconducting polymer phases (so-called heterojunctions) [1].
This study combines a vibronic coupling model parametrized for the three
most relevant electronic states and 20-30 phonon modes, with accurate
multiconfigurational quantum dynamics calculations using the MCTDH method and
a Gaussian-based variant thereof (G-MCTDH) [2]. In addition, we employ
recently developed transformation techniques [1,3] by which a relevant set
of effective modes is constructed which account for the short-time dynamics
in high-dimensional systems involving conical intersection topologies. For
the semiconducting polymer systems under study, which typically involve high-
vs. low-frequency phonon bands, this analysis leads to a mechanistic picture
showing that the dynamical interplay between the two types of phonon modes
is crucial for the ultrafast dissociation of the photogenerated exciton
state. A perspective is given on the effect of averaging over ensembles of
interface structures, on the role of coherence, and on the extension of the
analysis to finite temperatures.
[1] H. Tamura, J. G. S. Ramon, E. R. Bittner, and I. Burghardt,
Phys. Rev. Lett. 100, 107402 (2008), J. Phys. Chem. B, 112, 495 (2008).
[2] G. A. Worth, H.-D. Meyer, H. Koeppel, L. S. Cederbaum, and I. Burghardt,
Int. Rev. Phys. Chem., 27, 569 (2008); I. Burghardt, K. Giri, and G. A. Worth,
J. Chem. Phys., 129, 174104 (2008).
[3] L. S. Cederbaum, E. Gindensperger and I. Burghardt, Phys. Rev. Lett.,
94, 113003 (2005).
Farmed and wild salmonid fish are subject to parasitism from a number of
copepod parasites of the family Caligidae. These sea lice are damaging,
causing reduced growth and appetite, wounding and susceptability to
secondary infections. Economic losses due to this type of parasites are
high, with a value in excess of US $100 million globally. The life history
of the parasite involves a succession of ten distinct developmental stages
from egg to adult. In the present talk I will focus on the mathematical
analysis of a nonlinear partial differential equation model with
distributed states-at-birth, which type of model is intended to desribe
the dynamics at the first chalimus stage of the parasite.
Molecular dynamics simulation has become a powerful tool for studying biochemical properties. At the heart of these calculations is the potential energy function that describes intermolecular interactions in the system, and often it is the accuracy of the potential energy surface that determines the reliability of simulation results. The current generation of force fields was essentially established in the 1960s; while the accuracy has been improved tremendously by systematic parameterization, little has changed in the formalism. The explicit polarization (X-Pol) potential is an electronic structure-based polarization force field, designed for molecular dynamics simulations and modeling of biopolymers. In this approach, molecular polarization and charge transfer effects are explicitly treated by a combined quantum mechanical and molecular mechanical (QM/MM) scheme, and the wave function of the entire system is variationally optimized by a double self-consistent field (DSCF) method. We illustrate the possibility of parametrizing the X-Pol potential to achieve the desired accuracy as that from MM force fields, and demonstrate the feasibility of carrying out molecular dynamics (MD) simulation of solvated proteins. We use a system consisting of 14281 atoms and about 30,000 basis functions, including the protein bovine pancreatic trypsin inhibitor (BPTI) in water with periodic boundary conditions, to show the efficiency of an electronic structure-based force field in atomistic simulations. In this model, an approximate electronic wave function for the entire system is variationally optimized to yield the minimum Born-Oppenheimer energy at every MD step; this allows the efficient evaluation of the required analytic forces for the dynamics. Intramolecular and intermolecular polarization and intramolecular charge transfer effects are examined and are found to be significant. The new-generation X-POL force field permits the inclusion of time-dependent quantum mechanical polarization and charge transfer effects in much larger systems than was previously possible.
Quantum-mechanical (QM) effects in molecular dynamics –
zero-point energy, tunneling and nonadiabatic dynamics –
are
essential for accurate description and understanding of
reactions in complex molecular systems.
Since the exact solution of the Schrödinger equation for such
systems in full dimension is neither feasible nor necessary,
the trajectory-based approaches have special appeal: classical
description is often appropriate for dynamics of heavy
particles such as nuclei, and cheap – methods of molecular
mechanics are routinely applied to high-dimensional systems of
hundreds of atoms. The challenge is to include quantum effects
on dynamics of the trajectories.
We use the de Broglie-Bohm formulation of the Schrodinger
equation to formulate a semiclassical trajectory method. QM
effects are included through the quantum force due to
localization of the trajectory ensemble, acting on the
trajectories in addition to the classical forces. A cheap
approximation to the quantum potential makes the method
practical in many dimensions and captures dominant quantum
effects in semiclassical systems.
The latest development is a description of the double well
dynamics – a prototype of the proton transfer
reactions – which exhibits "hard" quantum effect of tunneling. This is
achieved by combining the approximate quantum trajectory
dynamics with the population amplitudes in the reactant and
product wells. The trajectories are driven by the asymptotic
classical potentials, while the population amplitudes are
described in a small basis. The method is exact if these
reactant/product potentials are harmonic and the basis size is
sufficiently large. In the semiclassical regime trajectory
dynamics is approximate, and the basis size can be as small as
two functions. The approach is fully compatible with the
trajectory description of multidimensional systems capturing
quantum tunneling along the reactive coordinate and ZPE flow
among all degrees of freedom.
We apply a recently developed quantum version of Transition State Theory based on Quantum Normal Forms (QNF) to simple collinear reactions. We find that the normal form converges quickly for molecules which are not too light.
We will discuss some recent advances in quantum dynamic
studies of several complex-forming reactions, such as H +
O_{2} → OH + O and O + H_{2} → OH + H.
Calculated differential and
integral cross sections shed much light on mechanisms of these
reactions. We will address important dynamic issues such as
non-adiabatic transitions and statistical nature of the
reactions.
We review mathematical results concerning the time-dependent
Born-Oppenheimer approximation. We then turn attention to some results
concerning molecular propagation through level crossings and avoided
crossings with small gaps.
Recent advances in the development of the nuclear-electronic orbital (NEO) approach will be presented. In the NEO approach, selected nuclei are treated quantum mechanically on the same level as the electrons with molecular orbital techniques. For hydrogen transfer and hydrogen bonding systems, typically the hydrogen nuclei and all electrons are treated quantum mechanically. Electron-proton dynamical correlation is highly significant because of the attractive electrostatic interaction between the electron and the proton. An explicitly correlated Hartree-Fock scheme has been formulated to include explicit electron-proton correlation directly into the nuclear-electronic orbital self-consistent-field framework with Gaussian-type geminal functions. A multicomponent density functional theory has also been formulated, and electron-proton functionals have been developed based on the explicitly correlated electron-proton pair density. Initial applications illustrate that these new methods provide accurate nuclear densities, thereby enabling calculations of a wide range of molecular properties. Recently the NEO method has been combined with vibronic coupling theory to calculate hydrogen tunneling splittings in polyatomic molecules. In this NEO-vibronic coupling approach, the transferring proton and all electrons are treated quantum mechanically at the NEO level, and the other nuclei are treated quantum mechanically using vibronic coupling theory. This approach is computationally practical and efficient for relatively large molecules. The calculated tunneling splitting for malonaldehyde is in excellent agreement with the experimental value. Furthermore, this approach enables the identification of the dominant modes coupled to the transferring hydrogen motion and provides insight into their roles in the hydrogen tunneling process.
This talk will discuss recent developments in one-electron model Hamiltonians for the hydrated electron, and their application to both anionic water clusters and bulk aqueous electrons. Our group has recently developed a new hydrated-electron model that combines the polarizable AMOEBA water model with a "static exchange" treatment of the electron-water interaction, parameterized from electronic structure calculations. Efficient, grid-based QM/MM algorithms have also been developed, in which the QM wave function and the MM water molecules polarize one another in a fully self-consistent fashion. Comparison to electronic structure benchmarks indicates that the new model is substantially more accurate than existing models based on non-polarizable water potentials. What role, if any, the polarization plays in establishing the structure of anionic water clusters will be discussed, along with preliminary results from bulk simulations.
We perform a rigorous mathematical analysis of the bending modes of
a linear triatomic molecule that exhibits the Renner-Teller effect.
Assuming the potentials are smooth, we prove that the wave functions
and energy levels have asymptotic expansions in powers of epsilon,
where the fourth power of epsilon is the ratio of an electron mass to the mass of a
nucleus. To prove the validity of the expansion, we must prove
various properties of the leading order equations and their
solutions. The leading order eigenvalue problem is analyzed in
terms of a parameter b, which is equivalent to the parameter
originally used by Renner. Perturbation theory and finite
difference calculations suggest that there is a crossing involving the ground bending vibrational
state near b=0.925. The crossing involves two states with
different degeneracy.
The form of accurate semiclassical surface hopping propagators and wave
functions for processes involving more than one electronic quantum state
is discussed. It is shown that conditions, which define the required
non-classical events along trajectories, can be derived from the
Schrödinger equation. These conditions also uniquely specify the
direction of the momentum change accompanying the energy conserving hops
between electronic energy surfaces and the amplitudes associated with
these hops. Transition probabilities obtained from surface hopping
calculations on model systems are presented for classically allowed and
classically forbidden transitions, and these results are compared with
exact quantum calculations.
We studied the detailed reaction mechanism of autocatalytic intramolecular isopeptide bond formations in pili of Gram-negative bacteria with the recently developed QM/MM minimum free-energy path (QM/MM-MFEP) method. The scrutinized reaction mechanism consists of at least three steps in which proton transfers occur prior to and after the formation of the intramolecular isopeptide bond. Preliminary results revealed crucial roles of an active-site Glu residue in both the proton transfer reactions and the formation of the intramolecular isopeptide bond. Our results will provide important information for identifying and designing new vaccine candidates that can be applied to the bacterial
pilus.
We present a molecular dynamics simulation study of solvation and collective polarizability dynamics supercritical fluoroform at a series of densities at constant temperature, slightly above the critical temperature, T_c. Our solvation dynamics studies were designed to represent the time-dependent frourescence Stokes shift for the chromophore coumarin 153. The equilibrium and nonequilibrium solvation responses were calculated. We found strong density dependence of solvation time correlations, with slower decay at lower densities and more pronounced for the excited-state than for the ground-state response. As for the nonequilibrium response, we showed that the inclusion of the interaction between the solute charge density and solvent induced dipoles improves the agreement with available experimental data. Preliminary results of an investigation of collective polarizability anisotropy relaxation in pure supercritical fluoroform are also presented. We focus on the nuclear response observable in optical Kerr effect and show that the results at higher densities are sensitive to the model used for the interaction-induced polarizability.
Previously Turi and Borgis have parameterized an electron-water interaction potential in the static exchange approximation to yield a one-electron pseudopotential that has been applied to the study of anionic water clusters and the bulk hydrated electron. This potential has been used solely in conjunction with the Simple Point Charge (SPC) water model which is known to yield poor results for neutral water clusters. We re-parameterize the pseudopotential to be used with the polarizable AMOEBA water model to yield a potential in which the one-electron density polarizes the water molecules and vice versa in a fully self-consistent manner. The resulting model Hamiltonian is considerably more accurate for reproducing vertical electron binding energies (VEBEs), cluster geometries, and relative isomer energies when compared to ab initio results. The role of self-consistent polarization is particularly pronounced in clusters where the excess electron is bound in the interior of the cluster.
Recent developments in semiclassical and path integral methods for quantum dynamics will be presented.
Forward-backward semiclassical dynamics (FBSD) is a rigorous and efficient methodology for capturing quantum mechanical effects in the time evolution of condensed phase systems through classical trajectory information. Combined with a discretized path integral representation of the Boltzmann operator, this methodology has enabled the simulation of the dynamics of such fluids as para-hydrogen and helium across the normal-to-superfluid transition. The results of these calculations are in very good agreement with experimental results on diffusion coefficients and dynamic structure factors probed by neutron scattering. The FBSD simulations provide novel insights into the separate roles of quantum mechanical and quantum statistical effects on the dynamics of these fluids.
Accurate, fully quantum mechanical results for the short-time behavior of complex-time correlation functions of low-temperature fluids have been obtained using the pair product approximation to evaluate the complex-time propagator in a single step. These results provide useful benchmarks for assessing the accuracy of approximate propagation methods.
Finally, an iterative Monte Carlo (IMC) methodology appears to overcome the sign problem associated with path integral calculations. By evaluating the discretized path integral expression iteratively on a grid selected by a Monte Carlo procedure. Both the grid points and the summations performed in each iteration utilize importance sampling, leading to favorable scaling with the number of particles, while the stepwise evaluation of the integrals circumvents the exponential growth of statistical error with time.
We have recently shown how path integral simulations can be
streamlined by decomposing the potential into a sum of rapidly
varying short-range and slowly varying long-range contributions.
In this talk, I will describe an efficient way to perform this
decomposition for systems with electrostatic interactions, and
illustrate the method with an application to a flexible water
model. In the limit of large system size, where the calculation
of long-range forces dominates, the present method enables path
integral (and ring polymer molecular dynamics) simulations of
liquid water to be performed with less than twice the computational
effort of classical molecular dynamics simulations [1,2].
[1] T. E. Markland and D. E. Manolopoulos, J. Chem. Phys.129, 024105 (2008).
[2] T. E. Markland and D. E. Manolopoulos, Chem. Phys. Lett. 464, 256 (2008).
Joint work with George C. Schatz.
A many-body Green's function approach to the microscopic theory
of surface-enhanced Raman
scattering is presented. Interaction ects between a general
molecular system and a spatially
anisotropic metal particle supporting plasmon excitations in
the presence of an external radiation
field are systematically included through many-body
perturbation theory. Reduction of the
exact ects of molecular-electronic correlation to the level of
Hartree-Fock mean-field theory is
made for practical initial implementation, while description of
collective oscillations of conduction
electrons in the metal is reduced to that of a classical plasma
density; extension of the former to
a Kohn-Sham density-functional or second-order Møller-Plesset
perturbation theory is discussed;
further specialization of the latter to the random-phase
approximation allows for several salient
features of the formalism to be highlighted without need for
numerical computation. Scattering and
linear-response properties of the coupled system subjected to
an external perturbing electric field
in the electric-dipole interaction approximation are
investigated. Both damping and finite-lifetime
ects of molecular-electronic excitations as well as the
characteristic fourth-power enhancement
of the molecular Raman scattering intensity are elucidated from
first principles. It is demonstrated
that the presented theory reduces to previous models of
surface-enhanced Raman scattering and
leads naturally to a semiclassical picture of the response of a
quantum-mechanical molecular system
interacting with a spatially anisotropic classical metal
particle with electronic polarization
approximated by a discretized collection of electric dipoles.
This talk will highlight recent work in our group in which we use Diffusion Monte Carlo approaches to study molecular vibrations of several fluxional systems. The molecular systems that will be the focus of the talk will be CH5+ and ion-water complexes. For these studies, we focus on two approaches. The first involves a fixed-node treatment of rotationally and vibrationally excited states. This approach enables us to evaluate the "zero-order bright state" associated with a particular molecular vibration. The results of these calculations include the frequency of the state of interest as well as the associated probability amplitude. A second approach will be described in which we re-express the excited state energy as an expectation value over the ground-state wave function. The results of these approaches are promising.
In this presentation we discuss a full (15D) quantum simulation of the
infrared absorption spectrum and dynamics of the protonated water dimer
(H5O2+) by the multiconfiguration time-dependent Hartree (MCTDH) method.
The main features of the IR spectrum are explained an assigned, in
particular a complicated doublet structure at about 1000 cm-1 related
to the proton transfer motion, which was not understood. Also the
couplings of various fundamental motions which shape the spectrum
between 800 and 2000 cm-1 are explained and assigned. A picture of the
cation arises in which the central proton motion determines the dynamics
of various other modes, mostly water bending and water pyramidalization.
We show that a full quantum-dynamical description of such a complex
molecular system can be achieved, providing explicative and predictive
power and a very good agreement to available experimental data.
This success is largely due to the use of the MCTDH method, a powerful
algorithm for propagating wavepackets. The basics of the MCTDH algorithm
are briefly discussed.
To account for the interatomic potential and the interaction with the
radiation we make use of the potential energy surface and dipole-moment
surfaces recently developed by Bowman and collaborators, which constitute
the most accurate ab initio surfaces available to date for this system.
We introduce some mathematical analysis in the form of existence and uniqueness results for chemically miscible compressible classical systems of equations. Then we show some extensions to chemical reactor systems, where chemical kinetics and intermolecular diffusion is taken into consideration, and applied to atmospheric chemistry. Finally we show an extension to quantum hydrodynamic systems of equations, used to model chemical reactions.
No transcription-translation feedback system of circadian clock by
KaiC protein's
phosphorylation is very interesting and also significant as a kind of
core cycle of the
circadian rhythm in Cyanobacteria. In order to understand the
oscillation phenomena,
we pay attention to a function of memory in a cell level. A standard
structure of such a
binary digit of memory is presented by use of multiple covalent
modifications in this
presentation. A key idea is bistability of covalent modification
states which creates
hysterecally and digitally switching mechanism between them. By use of
this kind of
memory, we see the circadian oscillation be realized. In fact, by deterministic
simulations as well as by stochastic simulation, it is shown that the
system obtains
stable circadian oscillations, and shown that multiplicity of
modification sites reinforces
the stability of memory in several senses. Moreover, it is reported
that this model
explains well several molecular biologically experimental facts about
period's change by
use of mutants of Kai proteins in the circadian rhythm of Cyanobacteria.
We present a strategy for the simulation of nonadiabatic excited state
dynamics by surface hopping, with direct calculation of the electronic
wavefunctions and energies. The electronic problem is solved by a
semiempirical NDO method, especially modified to deal with excited
states, bond breaking and orbital degeneracies. A reparameterization of
the semiempirical hamiltonian is needed to obtain accurate PESs.
For large systems, a QM/MM variant is available.
The focus of the talk will be on open problems and future perspectives.
We present a set of surface hopping simulations of the excited state
decay and photoisomerization of azobenzene, in vacuo and in two solvents
of different viscosity, methanol and ethylene glycol. We are able to
reproduce the experimental quantum yields and the fluorescence
transients (both intensity and anisotropy). We bring out the effects of
solvation on the photodynamics and propose a new interpretation of
recent experiments.
Molecules irradiated by polarized light have a maximum excitation
probability when their transition dipole vector is parallel to the light
polarization. An excited molecule, because of its internal motions and
of the interactions with the chemical environment, will change its
orientation. As a consequence, a molecular sample gets oriented when
irradiated, but the spontaneous rotational diffusion tends to restore the
isotropic conditions. We have set up a stochastic model to represent
the photo-induced anisotropy and its development in time. The
calculation uses as input the results of single chromophore surface
hopping simulations. The method is tested on azobenzene and shows the
interplay of photo-orientation, rotational diffusion, and
photoisomerization.
Device miniaturization requires an understanding of the dynamical response of materials on the nanometer scale. A great deal of experimental and theoretical work has been devoted to characterizing the excitation, charge, spin, and vibrational dynamics in a variety of novel materials, including carbon nanotubes, quantum dots, conducting polymers, inorganic semiconductors and molecular chromophores. We have developed state-of-the-art non-adiabatic molecular dynamics techniques and implemented them within time-dependent density functional theory in order to model the ultrafast photoinduced processes in these materials at the atomistic level, and in real time.
Quantum dots (QD) are quasi-zero dimensional structures with a unique combination of molecular and bulk properties. As a result, QDs exhibit new physical properties such as carrier multiplication, which has the potential to greatly increase the efficiency of solar cells. The electron-phonon and Auger relaxation in QDs compete with carrier multiplication. Our detailed studies of the competing processes in PbSe QDs rationalize why carrier multiplication was first observed in this material.
The electron-phonon interactions in carbon nanotubes (CNT) determine the response times of optical switches and logic gates, the extent of heating and energy loss in CNT wires and field-effect transistors, and even a superconductivity mechanism. Our ab initio studies of CNTs directly mimic the experimental data and reveal a number of unexpected features, including the fast intrinsic intraband relaxation and electron-hole recombination, the importance of defects, the dependence of the relaxation rate on the excitation energy and intensity, and a detailed understanding of the role of active phonon modes.
O. V. Prezhdo, W. R. Duncan, V. V. Prezhdo, “Dynamics of the photoexcited electron at the chromophore-semiconductor interface”, Acc. Chem. Res., 41, 339 (2008).
O. V. Prezhdo, “Multiple excitons and electron-phonon bottleneck in semiconductor quantum dots: Insights from ab initio studies”, Chem. Phys. Lett. – Frontier Article, 460, 1-9, (2008)
B. F. Habenicht, O. V. Prezhdo, “Nonradiative quenching of fluorescence in a semiconducting carbon nanotube: a time-domain ab initio study”, Phys. Rev. Lett., 100, 197402 (2008).
Joint work with Sophya Garashchuk (Universit of South Carolina).
Semiclassical implementation of the quantum trajectory formalism [J. Chem. Phys. 120, 1181 (2004)] is further developed to give stable long-time description of zero-point energy in anharmonic systems of high dimensionality. The method is based on a numerically cheap linearized quantum force approach; stabilizing terms compensating for the linearization errors are added into the time evolution equations for the classical and nonclassical components of the momentum operator. The wavefunction normalization and energy are rigorously conserved. Numerical tests are performed for model systems of up to 40 degrees of freedom.
I will present two different half-talks. In the first section, I will focus on the ideas behind replica exchange molecular dynamics, with an emphasis on improving efficiency by optimizing the time between attempted exchanges in Monte Carlo. In the second half, I will present a peculiarity of Langevin thermostats, which could cause substantially wrong dynamical behavior if care is not taken in the choice of random seeds.
Vibrationally excited adsorbates at surfaces have been suggested to be
useful precursors in a number of applications, ranging from spectroscopy
over quantum computing, to vibrationally mediated, bond-selective
chemistry. To selectively excite adsorbate vibrations, tailored infrared laser
pulses can be used, which are, however, perturbed by ultrafast vibrational
relaxation.
In this talk we shall present approaches of how to calculate vibrational
lifetimes, and the laser-driven excitation and quantum dynamics of
adsorbates at semiconductor (H/Si(100)) or at metal surfaces (CO/Cu(100) and
H/Ru(0001)). For this purpose a reduced description of this system
(molecule) / bath (surface) problem is chosen by applying
Markovian or non-Markovian open-system density matrix theory, often with
relaxation rates determined from perturbation theory. For H/Si, where vibrational
relaxation is due to vibration-phonon coupling, in addition a `full' approach is
adopted in which a multi-dimensional nuclear Schrödinger equation of the
system-bath type is solved by using efficient schemes based on single- or
multi-configurational time-dependent Hartree methods.
This talk will describe recent work in my group by Brian Radak, Scott Yockel and Dongwook Kim concerned with modeling the dynamics of reactions at the gas/liquid interface using a QM/MM approach. The reactions involve atomic oxygen and atomic fluorine collisions with liquid squalane, which is a hydrocarbon polymer, at hyperthermal energies (0.5-5.0 eV). The QM/MM model involves use of the MSINDO semiempirical Hamiltonian for the QM part, and the OPLS empirical force field for the MM part, with QM/MM calculations being done within the framework of the ONIOM model. In all studies, we have calibrated the accuracy of the electronic structure model by comparison with coupled-cluster results for similar gas phase reactions, and we have in some cases done direct dynamics studies of the gas phase reaction dynamics for reference. Detailed comparison with beam/surface measurements are provided. These studies provide new insights about the role of liquid interfaces in governing reactive collisions. They also demonstrate how dynamical processes may be described for condensed phase systems in which several bonds may be broken or formed in a series of chemical reactions all within a single simulation.
I will describe our efforts to enhance efficient electronic structure methods such as NDDO semiempirical theory and density functional theory (DFT) by adding self consistent polarization (SCP). This approach enhances the polarization response of an efficient electronic structure method while providing a consistent representation of the dispersive interaction that is based on second-order perturbation theory. The first application of this method resulted in the effective parameterization of the interaction of water clusters to reproduce the accurate MP2/CBS estimates of small water cluster binding energies as well as the intramolecular frequency shifts as a function of cluster size. Preliminary efforts to extend this approach to DFT electronic structure will be described in terms of Argon and water systems.
Solving challenging conformational dynamics problems requires advanced tools from chemistry, mathematics, physics, biology, engineering and scientific computing. In recent years, an enormous range of methods has been proposed for exploring conformational space, deducing mechanistic information, computing free energy profiles, and estimating reaction rates. Methods range from simple stochastic approaches to various spectral-based methods, to coarse-graining approaches, to rigorous mathematical approaches that manipulate by divide and conquer strategies the energy function an simulation protocol. A flavor of this enormous range of innovative approaches will be presented through selected examples and applications. Applications to DNA polymerases fidelity mechanisms by transition path sampling, molecular dynamics, and quantum/classical hybrid simulations will also be described.
The efficient determination of reliable rare event statistics is one of the grand challenges in molecular dynamics. For example, direct accurate computation of folding rates requires very long simulations, in many cases infeasibly long ones. The question of how the exploration of such transition statistics can be sped up has attracted much attention recently. The talk will
present some new approaches to this problem. In these approaches the energy landscape of
a molecular system is appropriately coarse grained into a discrete transition network. Simultaneously, the associated transition rates are computed from parallel molecular dynamics simulations until accuracy requirements are met.
Total simulation lengths will be shown to be much shorter than those required by direct simulation approaches.
Joint work with Brett I. Dunlap.
Simulating chemical bond dissociation dynamics requires
electronic
structure methods to seamlessly describe the transition
from the initial closed-shell configuration to an open-shell
intermediate.
Direct-dynamic simulations of the RO-NO2 bond dissociation
in nitric
esters are presented to demonstrate the importance of using
unrestricted single-determinant methods and
spin-symmetry-broken orbitals. Challenges in locating the symmetry-broken
electronic potential energy surface in the course of a reactive
trajectory are discussed. The second derivative of the unrestricted energy
with respect to nuclear displacement is shown to be
discontinuous at the onset of symmetry breaking, in analogy with the
discontinuous specific heat in the Landau theory of second-order phase
transitions.
The growing demand for realistic methods that would calculate
chemical reactions in biological systems resulted with the
development of hybrid quantum mechanical (QM) molecular
mechanical (MM) schemes. Recent years have proven schemes that
are based on concepts from valence bond (VB) methodology, to be
beneficial for the description of enzyme catalysis and
reactivity. The development of a new hybrid (QM/MM) method
where the QM part is treated by ab-initio Valence Bond (VB)
theory will be presented. This VB/MM method has the advantages
of Empirical VB (EVB) methodology but does not rely on
empirical parameterization for the quantum part. The method
utilizes various approximations that will be explained.
Furthermore, examination of these approximations which was
based on a recent extension of the method justifies their use.
The validity of the method will be shown to be successful in
several examples.
We present a very simple model for numerically describing the steady state dynamics of a system interacting with continua of states representing a bath. Our model can be applied to equilibrium and non-equilibrium problems. For a one-state system coupled to two free electron reservoirs, our results match the Landauer formula for current traveling through a molecule. More significantly, we can also predict the non- equilibrium steady state population on a molecule between two out-of-equilibrium contacts. While the method presented here is for one-electron Hamiltonians, we outline how this model may be extended to include electron-electron interactions and correlations, an approach which suggests a connection between the conduction problem and the electronic structure problem.
Ever since the advent of Quantum Mechanics, there has been a quest for a trajectory based formulation of quantum theory that is exact. In the 1950’s, David Bohm, building on earlier work of Madelung and de Broglie, developed an exact formulation of quantum mechanics in which trajectories evolve in the presence of the usual Newtonian force plus an additional quantum force. In recent years, there has been a resurgence of interest in Bohmian Mechanics (BM) as a numerical tool because of its apparently local dynamics, which could lead to significant computational advantages for the simulation of large quantum systems. However, closer inspection of the Bohmian formulation reveals that the nonlocality of quantum mechanics has not disappeared — it has simply been swept under the rug into the quantum force. In this work, we present a new formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex. This requires the propagation of complex trajectories, but with the reward of a significantly higher degree of localization. For example, using strictly localized trajectories (no communication with their neighbors) we obtain extremely accurate quantum mechanical tunneling probabilities down to 10-7. We have recently extended the formulation to include interference effects, which has been one of the major obstacles in conventional Bohmian mechanics. Applications to one- and two-dimensional tunneling, thermal rate constants in one and two dimensions, and the calculation of eigenvalues will be provided. A variation on the method allows for the calculation of thermal rate constants and eigenvalues using just one or two zero-velocity trajectories. On the formal side, the approach is shown to be a rigorous extension of generalized Gaussian wavepacket methods to give exact quantum mechanics, and has intriguing implications for fundamental quantum mechanics.
Adiabatic perturbation theory is a general scheme that allows for the mathematically rigorous derivation
of effective equations in quantum mechanical slow-fast systems. In this lecture I explain how to justify and
compute corrections to the time-dependent Born-Oppenheimer approximation. In the second part I present
some recent results (jointly with Volker Betz) on computing the dynamics of exponentially small non-adiabatic transitions between
different electronic energy surfaces.
A highly accurate and efficient method for molecular global
potential energy surface (PES) construction and fitting is
demonstrated. An interpolating moving least-squares (IMLS)
method using low-density ab initio potential, gradient, or
Hessian values to compute PES parameters is shown to lead to an
accurate and efficient PES representation. The method is
automated and flexible so that a PES can be optimally generated
for classical trajectories, spectroscopy, or other
applications. Two main drivers for the fitting method have
been developed thus far. The first is a PES generator designed
primarily for spectroscopy applications. Using this method,
the configuration space defined by a specified energy range is
automatically fit to a predefined accuracy. A second approach
is based on trajectory methods for computing reaction rates.
In this approach, the configuration space that is dynamically
accessible to a particular ensemble of trajectories is fit "on
the fly." Results that are indicative of the accuracy,
efficiency, and scalability will be presented.
Several united-atom (UA) force fields for perfluorinated self-assembled monolayer (FSAM) surfaces are proposed. These UA models of FSAM are based on a preceding force field, and the modifications done in this work involved the type of potential function and parameters used to represent the nonbonded interactions among the united atoms of the FSAM chains, which have been shown to play a key role in the energy transfer that takes place in collisions of gases with self-assembled monolayers.
Results are presented on the dynamics and IR spectroscopy of the Zundel
(H5O2+) cation. The full-dimensional (15D) quantum simulations are
performed with the multiconfiguration time-dependent Hartree (MCTDH)
method.
We investigate the IR spectroscopy of H5O2+ and various of its
isotopomers, namely D5O2+, HD4O2+ and DH4O2+ isotopomers, and provide a
comparison to recent experiments on these systems. Dramatic changes in the
dynamics and spectroscopy of the clusters are observed upon isotopic
substitution.
Accurate measurements of IR spectra of protonated water clusters prepared
in the gas phase has become possible in recent years. The aim of our
theoretical studies is to sheed light on interpretation of these complex
spectra, provide useful physical insight in the dynamics of the hydrated
proton, and last but not least, to advance in the description of complex
molecular systems and clusters by full quantum methods.
The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) theory
is a rigorous and powerful method to simulate quantum dynamics in complex
many-body problems. This approach extends the regular MCTDH theory of
Meyer, Manthe, and Cederbaum to include several dynamically contracted
layers whose equations of motion are determined from variational principle.
In this talk I will discuss the general derivation of the theory,
the scaling of the method, and the application of the theory to simulate
dynamics of electron transfer reactions in the condensed phase.
Furthermore, a new generalization of the theory, the ML-MCTDH theory with
second quantization (ML-MCTDH/SQ) will be presented to treat many-body
identical particle (fermion or boson) systems.
Conformation dynamics aims at an identification of dynamically metastable subsets of the position space of molecular systems.
A time-discretized molecular simulation of such a system leads to a Markov operator. A space discretization of this operator leads to a
stochastic transition matrix. In the talk, a cluster algorithm is presented which identifies metastable subsets of the position space by
a spectral analysis of the transition matrix. This analysis was originally valid for reversible Markov chains, but can be extended to the
non-reversible case.
Combined quantum mechanics/molecular mechanics (QM/MM) methods
provide an accurate and efficient energetic description of
complex chemical and biological systems, leading to significant
advances in the understanding of chemical reactions in solution
and in enzymes. Here we review progress in QM/MM methodology
and applications, focusing on ab initio QM-based approaches. Ab
initio QM/MM methods capitalize on the accuracy and reliability
of the associated quantum-mechanical approaches, however, at a
much higher computational cost compared with semiempirical
quantum-mechanical approaches. Thus reaction-path and
activation free-energy calculations based on ab initio QM/MM
methods encounter unique challenges in simulation timescales
and phase-space sampling. This review features recent
developments overcoming these challenges and enabling accurate
free-energy determination for reaction processes in solution
and in enzymes, along with applications. (Reference: Hao. Hu
and Weitao Yang, Annual Review of Physical Chemistry, 59,.
573–601, 2008).
A quantum mechanical/molecularmechanical minimum free energy path
(QM/MM-MFEP) method was developed to calculate the redox free energies
of large systems in solution with greatly enhanced efficiency for
conformation sampling. The QM/MM-MFEP method describes the
thermodynamics of a system on the potential of mean force (PMF)
surface of the solute degrees of freedom. The MD sampling is only
carried out with the QM subsystem fixed. It thus avoids "on-the-fly"
QM calculations and overcomes the high computational cost of the
direct ab initio QM/MM molecular dynamics (MD) needed for sampling.
The enhanced efficiency and uncompromised accuracy of this approach
are especially significant for biochemical systems. The QM/MM-MFEP
method thus provides an efficient approach to free energy simulation
of complex electron transfer reactions.