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Abstracts and Talk Materials
Chemical Dynamics: Challenges and Approaches
January 12-16, 2009


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Single-sweep methods for free energy calculations
January 13, 2009 3:00 pm - 3:30 pm

Free energy (or potential of mean force) calculations are a central issue in biophysics. Molecular dynamics (MD) simulations provide a tool for performing such calculations on a computer in a way which is potentially both precise and inexpensive. Since a free energy associated with some collective variables is proportional to the logarithm of the probability density function of these variables, it can in principle be calculated by histogram methods based on the binning of an MD trajectory. This direct approach, however, turns out to be unpractical in general because the time scale required for the trajectory to explore all the relevant regions of configuration space is prohibitively long. The standard way around this difficulty is to use umbrella sampling methods such as the weighted histogram analysis method (WHAM), but this technique is restricted to calculations of free energies in low dimension, i.e. when the number of collective variables is small (typically, 1 or 2). An alternative approach, however, is to calculate the gradient of the free energy (i.e. the mean force) locally, and use these data to reconstruct the free energy globally. In this talk, I will present a new method based on this idea which can be used to map free energy landscapes in multidimensions. The method uses radial-basis functions to represent the free energy and a variational approach to reconstruct the free energy globally from the local data on the mean force. The method will be illustrated on the several examples and compared with existing techniques based on histogram methods such as WHAM or metadynamics.

Millard Alexander - University of Maryland
http://www.chem.umd.edu/groups/alexander/

Concluding discussion
January 14, 2009 11:40 am - 12:15 pm


Dmitri Babikov - Marquette University
http://www.marquette.edu/chem/faculty/Babikov.shtml

Coherent and optimal control of adiabatic motion of ions in a trap
January 12, 2009 5:40 pm - 7:00 pm

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.

 

Concluding discussion
January 13, 2009 11:20 am - 12:20 pm


Roi Baer - Hebrew University
http://www.fh.huji.ac.il/~roib/index.html

Dogmatic and pragmatic spirits in time-dependent density functional theory
January 15, 2009 11:40 am - 12:10 pm

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 H2+, He2+, Ne2+, (H2O)2+ and (C6H6)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).

Sergio Blanes - Polytechnical University of Valencia
http://personales.upv.es/~serblaza/

Geometric integrators for the Schrödinger equation: Splitting and Magnus integrators
January 12, 2009 4:20 pm - 4:50 pm

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).

Joel Bowman - Emory University
http://www.chemistry.emory.edu/faculty/bowman.html

Overview talk on potential energy surfaces
January 12, 2009 9:00 am - 9:45 am

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 104 "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.

Irene Burghardt - École Normale Supérieure
http://www.chimie.ens.fr/UMR8642/Quantique/

Quantum dynamics of photoinduced processes in extended molecular systems
January 15, 2009 2:40 pm - 3:10 pm

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).

David Coker - Boston University
http://www.bu.edu/chemistry/faculty/profile/coker.html

Concluding discussion
January 16, 2009 12:20 pm - 1:20 pm


József Farkas - University of Stirling
http://www.cs.stir.ac.uk/~jzf/

Analysis of structured populations in aquaculture
January 12, 2009 5:40 pm - 7:00 pm

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.

Jiali Gao - University of Minnesota, Twin Cities
http://jialigao.org/

The X-Pol potential: an explicit polarization quantum mechanical force field for condensed phase and protein dynamics
January 15, 2009 2:00 pm - 2:30 pm

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.

Sophya Garashchuk - University of South Carolina

Tunneling dynamics in a double well within the approximate quantum trajectories framework
January 12, 2009 5:40 pm - 7:00 pm

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.

Arseni Goussev - University of Bristol
http://www.maths.bris.ac.uk/~maaog/
Roman Schubert - University of Bristol

Quantum transition state theory applied to collinear reactions
January 12, 2009 5:40 pm - 7:00 pm

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.

Hua Guo - University of New Mexico
http://www.unm.edu/~hguo/

Quantum dynamics of complex-forming reactions
January 13, 2009 8:30 am - 9:00 am

We will discuss some recent advances in quantum dynamic studies of several complex-forming reactions, such as H + O2 → OH + O and O + H2 → 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.

George Hagedorn - Virginia Polytechnic Institute and State University
http://www.math.vt.edu/people/hagedorn/

Non–adiabatic scattering wave functions in a simple Born–Oppenheimer model
January 12, 2009 5:40 pm - 7:00 pm


 

The time-dependent Born-Oppenheimer approximation, crossings, and avoided crossings
January 16, 2009 11:00 am - 11:30 am

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.

Sharon Hammes-Schiffer - The Pennsylvania State University
http://www.scs.illinois.edu/schiffer/index.html

Nuclear-electronic orbital approach: Electron-proton correlation, multicomponent density functional theory, and tunneling splittings
January 14, 2009 9:30 am - 10:00 am

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.

John Herbert - The Ohio State University
http://www.chemistry.ohio-state.edu/~herbert/

Fourier grid QM/MM simulations of the hydrated electron
January 12, 2009 10:00 am - 10:30 am

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.

Mark Herman - University of Minnesota, Twin Cities
http://www.math.rochester.edu/people/faculty/herman

Born-Oppenheimer corrections near a Renner-Teller intersection
January 12, 2009 5:40 pm - 7:00 pm

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.

Michael Herman - Tulane University

Well defined and accurate semiclassical surface hopping propagators and wave functions
January 16, 2009 11:40 am - 12:10 pm

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.

Xiangqian Hu - Duke University

Mechanistic simulation of the autocatalytic isopeptide bond formation in pili with QM/MM minimum free energy path method
January 12, 2009 5:40 pm - 7:00 pm

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.

Francesca Ingrosso - Université de Nancy I (Henri Poincaré)

Solvation dynamics in supercritical fluoroform
January 12, 2009 5:40 pm - 7:00 pm

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.

Leif Jacobson - The Ohio State University

A self-consistent, polarizable, electron-water potential for use in hydrated-electron simulations
January 12, 2009 5:40 pm - 7:00 pm

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.

Nancy Makri - University of Illinois at Urbana-Champaign
http://www.scs.uiuc.edu/chem/faculty/Nancy_Makri.html

Path integral and semiclassical methods for quantum dynamics
January 14, 2009 11:00 am - 11:30 am

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.

David Manolopoulos - University of Oxford
http://www.chem.ox.ac.uk/researchguide/demanolopoulos.html

A fast path integral method for liquid water
January 12, 2009 5:00 pm - 5:30 pm

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).

David Masiello - Northwestern University
http://faculty.wcas.northwestern.edu/~djm269/

Many-body theory of surface-enhanced Raman scattering
January 12, 2009 5:40 pm - 7:00 pm

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.

Anne McCoy - The Ohio State University
http://www.chemistry.ohio-state.edu/~mccoy/research

Using Diffusion Monte Carlo to investigate molecules that undergo large amplitude vibrational motions
January 12, 2009 2:00 pm - 2:45 pm

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.

Hans-Dieter Meyer - Ruprecht-Karls-Universität Heidelberg
http://www.pci.uni-heidelberg.de/tc/usr/dieter/

Quantum molecular dynamics of complex systems studied with MCTDH: Dynamics and IR-spectroscopy of the protonated water dimer H5O2+ and its isotopologues
January 13, 2009 9:10 am - 9:40 am

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.

Craig Michoski - University of Texas, Austin
https://webspace.utexas.edu/michoski/Michoski.html

Partial differential equations in chemical dynamics with finite elements
January 12, 2009 5:40 pm - 7:00 pm

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.

Isamu Ohnishi - Hiroshima University

Memory, hysteresis and oscillation induced by multiple covalent modifications and its application to circadian rhythm of Cyanobacteria
January 12, 2009 5:40 pm - 7:00 pm

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.

Maurizio Persico - Università di Pisa
http://perseo.dcci.unipi.it/

Azobenzene in solution: excited state dynamics simulation
January 12, 2009 5:40 pm - 7:00 pm

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.

 

A model for the photo-orientation of a molecular sample irradiated with polarized light
January 12, 2009 5:40 pm - 7:00 pm

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.

 

Surface hopping dynamics with direct semiempirical solution of the electronic problem
January 14, 2009 3:00 pm - 3:30 pm

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.

Gilles Peslherbe - Concordia University
http://faculty.concordia.ca/peslherbe/

Concluding discussion
January 14, 2009 5:10 pm - 6:10 pm


Bill Poirier - Texas Tech University
http://www.depts.ttu.edu/chemistry/faculty/poirier/poirier.html

Concluding discussion
January 12, 2009 11:50 am - 12:30 pm


Oleg Prezhdo - University of Washington
http://www.chem.rochester.edu/faculty/faculty.php?name=prezhdo

Dynamics on the nanoscale: Time-domain ab initio studies of quantum dots and carbon nanotubes
January 15, 2009 8:30 am - 9:15 am

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).

Vitaly Rassolov - University of South Carolina
http://www.chem.sc.edu/people/facultyStaffDetails.asp?SID=19

Stable long-time semiclassical description of zero-point energy in high-dimensional molecular systems
January 16, 2009 9:30 am - 10:00 am

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.

Adrian Roitberg - University of Florida
http://www.qtp.ufl.edu/~roitberg/people.htm

Optimizing efficiency in replica-exchange molecular dynamics and avoiding the traps of Langevin dynamics
January 15, 2009 9:30 am - 10:00 am

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.

Peter Saalfrank - Universität Potsdam
http://tcb16.chem.uni-potsdam.de/saalfrank/curric_saal.html

Reduced vs. full system-bath quantum dynamics: Vibrational excitation and relaxation of adsorbates at surfaces
January 13, 2009 10:40 am - 11:10 am

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.

George Schatz - Northwestern University
http://www.theory.northwestern.edu/schatz/

Trajectory studies of gas/liquid reactions
January 14, 2009 8:30 am - 9:15 am

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.

Gregory Schenter - Pacific Northwest National Laboratory
http://www.pnl.gov/science/staff/staff_info.asp?staff_num=5615

Self consistent polarization electronic structure
January 14, 2009 4:30 pm - 5:00 pm

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.

Tamar Schlick - New York University
http://www.math.nyu.edu/faculty/schlick/

Overview talk: Advanced computing platforms offer a "microscope" for [simulating] conformational changes
January 13, 2009 2:00 pm - 2:45 pm

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.

Greg Scholes - University of Toronto
http://www.chem.utoronto.ca/staff/SCHOLES/scholes_home.html

Concluding discussion
January 15, 2009 4:50 pm - 5:50 pm


Igor Schweigert - Naval Research Laboratory
http://www.qtp.ufl.edu/~igor

Symmetry-broken independent-particle models in Born-Oppenheimer molecular dynamics of chemical bond dissociation
January 12, 2009 5:40 pm - 7:00 pm

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.

Christof Schütte - Freie Universität Berlin
http://www.biocomputing-berlin.de/biocomputing/en/prof_christof_schuette/

Rare event statistics in molecular dynamics
January 13, 2009 4:30 pm - 5:00 pm

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.

Avital Shurki - Hebrew University
http://pharmacy.huji.ac.il/avital/

Hybrid ab initio valence bond / molecular mechanics (VB/MM), a new method for calculating biochemical systems
January 15, 2009 4:10 pm - 4:40 pm

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.

Joseph Subotnik - Tel Aviv University
http://www.joesubotnik.com/

A quantum chemist’s view of molecular conduction via the reduced density matrix
January 12, 2009 5:40 pm - 7:00 pm

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.

David Tannor - Weizmann Institute of Science
http://www.weizmann.ac.il/chemphys/tannor/

Bohmian mechanics with complex action: An exact formulation of quantum mechanics with complex trajectories
January 12, 2009 3:00 pm - 3:30 pm

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.

Stefan Teufel - Eberhard-Karls-Universität Tübingen
http://www.maphy.uni-tuebingen.de/members/stte

Adiabatic perturbation theory and the time-dependent Born-Oppenheimer approximation
January 16, 2009 8:30 am - 9:15 am

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.

Donald Thompson - University of Missouri
http://www.chem.missouri.edu/Thompson/

Automatic construction of ab initio potential energy surfaces
January 12, 2009 11:10 am - 11:40 am

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.

Mark Tuckerman - New York University
http://homepages.nyu.edu/~mt33/

Concluding discussion
January 13, 2009 5:50 pm - 6:15 pm


Oriol Vendrell-Romagosa - Ruprecht-Karls-Universität Heidelberg
http://www.pci.uni-heidelberg.de/tc/usr/oriol/

Infrared spectroscopy and dynamics of the Zundel cation
January 12, 2009 5:40 pm - 7:00 pm

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.

Saulo Vázquez -

Improved united-atom models for perfluorinated self-assembled monolayers
January 12, 2009 5:40 pm - 7:00 pm

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.

Haobin Wang - New Mexico State University
http://www.chemistry.nmsu.edu/Faculty/WANG.htm

Multilayer multiconfiguration time-dependent Hartree theory
January 15, 2009 11:00 am - 11:30 am

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.

Marcus Weber - Konrad-Zuse-Zentrum für Informationstechnik (ZIB)
http://www.zib.de/weber/

Recent progress in conformational analysis
January 13, 2009 5:10 pm - 5:40 pm

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.

Weitao Yang - Duke University
http://fds.duke.edu/db/aas/Chemistry/faculty/weitao.yang

Overview talk: Free energies of chemical reactions in solution and in enzymes with Ab initio quantum mechanics/molecular mechanics methods
January 14, 2009 2:00 pm - 2:45 pm

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).

Xiancheng Zeng - Duke University

Calculating solution redox free energies with Ab initio QM/MM minimum free energy path method
January 12, 2009 5:40 pm - 7:00 pm

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.

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