Bio


Professor Thomas Markland focuses on problems at the interface of quantum mechanics and statistical mechanics, with applications ranging from chemistry and biology to geology and materials science. Markland Group research frequently explores theories of hydrogen bonding, the interplay between structure and dynamics, systems with multiple time and length-scales, and quantum mechanical effects. Particular current interests include proton and electron transfer in materials and enzymatic systems, atmospheric isotope separation, and the control of catalytic chemical reactivity in heterogeneous environments.

Thomas E. Markland studied chemistry at Balliol College, University of Oxford (MChem 2006), where as a Brackenbury Scholar he performed thesis work in the area of non-adiabatic dynamics. He continued at Oxford (D.Phil. 2009), working in quantum dynamics under the supervision of Professor David Manolopoulos. Together, the two developed an approach to allow quantum effects of nuclei to be included in condensed phase simulation at near classical computational cost, as well as elucidating isotope effects observed in liquids. Next, during postdoctoral work with Bruce Berne at Columbia University, Professor Markland focused on structure and dynamics in classical and quantum biophysical systems. He moved to Stanford in 2011 as an Assistant Professor in the Department of Chemistry. He has received recognition in a number of awards, including the Stanford Dean's Award for Distinguished Teaching, Cottrell Scholarship, ACS OpenEye Outstanding Junior Faculty Award, and Alfred P. Sloan Research Fellowship.

In broad terms, current research in the Markland Group lies in the application and development of theoretical methods to model condensed phase systems, with a particular emphasis on the role of quantum mechanical effects. Treatment of these problems requires a range of theoretical approaches as well as molecular mechanics and ab initio simulations. Lab members are particularly interested in developing and applying methods based on the path integral formulation of quantum mechanics to include quantum fluctuations such as zero-point energy and tunneling in the dynamics of reactive condensed phase systems. The group has also developed methods to treat non-equilibrium excited state dynamics by exploiting the combination of quantum-classical theory and quantum master equation approaches.

Work in the Markland Group has already provided insights into several systems, including reactions in liquids and enzymes, and the quantum liquid–glass transition. Group members have also introduced methods to perform path integral calculations at near classical computational cost, expanding our ability to treat large-scale condensed phase systems.

Please visit the Markland Group website to learn more.

Academic Appointments


Administrative Appointments


  • Member, Stanford PULSE Institute, SLAC National Accelerator Laboratory (2014 - Present)

Honors & Awards


  • Cottrell Scholar, Research Corporation for Science Advancement (2015)
  • Dean's Award for Distinguished Teaching, Stanford University School of Humanities & Sciences (2015)
  • Hellman Faculty Scholar, Stanford University (2014)
  • OpenEye Outstanding Junior Faculty Award, American Chemical Society (2014)
  • Sloan Research Fellowship, Alfred P. Sloan Foundation (2014)
  • Terman Fellow, Stanford University (2012)
  • Coulson Prize, Royal Society of Chemistry (2009)

Boards, Advisory Committees, Professional Organizations


  • General Member, Telluride Science Research Center (2015 - Present)

Professional Education


  • Postdoc, Columbia University, Theoretical Chemistry (2010)
  • DPhil, University of Oxford, Chemistry (2009)
  • MChem, University of Oxford, Chemistry (2006)

Current Research and Scholarly Interests


Our research centers on problems at the interface of quantum and statistical mechanics. Particular themes that occur frequently in our research are hydrogen bonding, the interplay between structure and dynamics, systems with multiple time and length-scales and quantum mechanical effects. The applications of our methods are diverse, ranging from chemistry to biology to geology and materials science. Particular current interests include proton and electron transfer in fuel cells and enzymatic systems, atmospheric isotope separation and the control of catalytic chemical reactivity using electric fields.

Treatment of these problems requires a range of analytic techniques as well as molecular mechanics and ab initio simulations. We are particularly interested in developing and applying methods based on the path integral formulation of quantum mechanics to include quantum fluctuations such as zero-point energy and tunneling in the dynamics of liquids and glasses. This formalism, in which a quantum mechanical particle is mapped onto a classical "ring polymer," provides an accurate and physically insightful way to calculate reaction rates, diffusion coefficients and spectra in systems containing light atoms. Our work has already provided intriguing insights in systems ranging from diffusion controlled reactions in liquids to the quantum liquid-glass transition as well as introducing methods to perform path integral calculations at near classical computational cost, expanding our ability to treat large-scale condensed phase systems.

2016-17 Courses


Stanford Advisees


All Publications


  • Ab initio molecular dynamics with nuclear quantum effects at classical cost: Ring polymer contraction for density functional theory JOURNAL OF CHEMICAL PHYSICS Marsalek, O., Markland, T. E. 2016; 144 (5)

    Abstract

    Path integral molecular dynamics simulations, combined with an ab initio evaluation of interactions using electronic structure theory, incorporate the quantum mechanical nature of both the electrons and nuclei, which are essential to accurately describe systems containing light nuclei. However, path integral simulations have traditionally required a computational cost around two orders of magnitude greater than treating the nuclei classically, making them prohibitively costly for most applications. Here we show that the cost of path integral simulations can be dramatically reduced by extending our ring polymer contraction approach to ab initio molecular dynamics simulations. By using density functional tight binding as a reference system, we show that our ring polymer contraction scheme gives rapid and systematic convergence to the full path integral density functional theory result. We demonstrate the efficiency of this approach in ab initio simulations of liquid water and the reactive protonated and deprotonated water dimer systems. We find that the vast majority of the nuclear quantum effects are accurately captured using contraction to just the ring polymer centroid, which requires the same number of density functional theory calculations as a classical simulation. Combined with a multiple time step scheme using the same reference system, which allows the time step to be increased, this approach is as fast as a typical classical ab initio molecular dynamics simulation and 35× faster than a full path integral calculation, while still exactly including the quantum sampling of nuclei. This development thus offers a route to routinely include nuclear quantum effects in ab initio molecular dynamics simulations at negligible computational cost.

    View details for DOI 10.1063/1.4941093

    View details for Web of Science ID 000369893900014

    View details for PubMedID 26851913

  • Nonadiabatic Dynamics in Atomistic Environments: Harnessing Quantum-Classical Theory with Generalized Quantum Master Equations JOURNAL OF PHYSICAL CHEMISTRY LETTERS Pfalzgraff, W. C., Kelly, A., Markland, T. E. 2015; 6 (23): 4743-4748
  • Accurate nonadiabatic quantum dynamics on the cheap: Making the most of mean field theory with master equations JOURNAL OF CHEMICAL PHYSICS Kelly, A., Brackbill, N., Markland, T. E. 2015; 142 (9)

    View details for DOI 10.1063/1.4913686

    View details for Web of Science ID 000350973900015

  • Quantum delocalization of protons in the hydrogen-bond network of an enzyme active site PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Wang, L., Fried, S. D., Boxer, S. G., Markland, T. E. 2014; 111 (52): 18454-18459

    Abstract

    Enzymes use protein architectures to create highly specialized structural motifs that can greatly enhance the rates of complex chemical transformations. Here, we use experiments, combined with ab initio simulations that exactly include nuclear quantum effects, to show that a triad of strongly hydrogen-bonded tyrosine residues within the active site of the enzyme ketosteroid isomerase (KSI) facilitates quantum proton delocalization. This delocalization dramatically stabilizes the deprotonation of an active-site tyrosine residue, resulting in a very large isotope effect on its acidity. When an intermediate analog is docked, it is incorporated into the hydrogen-bond network, giving rise to extended quantum proton delocalization in the active site. These results shed light on the role of nuclear quantum effects in the hydrogen-bond network that stabilizes the reactive intermediate of KSI, and the behavior of protons in biological systems containing strong hydrogen bonds.

    View details for DOI 10.1073/pnas.1417923111

    View details for Web of Science ID 000347444400028

  • Quantum fluctuations and isotope effects in ab initio descriptions of water JOURNAL OF CHEMICAL PHYSICS Wang, L., Ceriotti, M., Markland, T. E. 2014; 141 (10)

    View details for DOI 10.1063/1.4894287

    View details for Web of Science ID 000342209400040

  • Multiple time step integrators in ab initio molecular dynamics. journal of chemical physics Luehr, N., Markland, T. E., Martínez, T. J. 2014; 140 (8): 084116-?

    Abstract

    Multiple time-scale algorithms exploit the natural separation of time-scales in chemical systems to greatly accelerate the efficiency of molecular dynamics simulations. Although the utility of these methods in systems where the interactions are described by empirical potentials is now well established, their application to ab initio molecular dynamics calculations has been limited by difficulties associated with splitting the ab initio potential into fast and slowly varying components. Here we present two schemes that enable efficient time-scale separation in ab initio calculations: one based on fragment decomposition and the other on range separation of the Coulomb operator in the electronic Hamiltonian. We demonstrate for both water clusters and a solvated hydroxide ion that multiple time-scale molecular dynamics allows for outer time steps of 2.5 fs, which are as large as those obtained when such schemes are applied to empirical potentials, while still allowing for bonds to be broken and reformed throughout the dynamics. This permits computational speedups of up to 4.4x, compared to standard Born-Oppenheimer ab initio molecular dynamics with a 0.5 fs time step, while maintaining the same energy conservation and accuracy.

    View details for DOI 10.1063/1.4866176

    View details for PubMedID 24588157

  • Interface-Limited Growth of Heterogeneously Nucleated Ice in Supercooled Water JOURNAL OF PHYSICAL CHEMISTRY B Nistor, R. A., Markland, T. E., Berne, B. J. 2014; 118 (3): 752-760

    Abstract

    Heterogeneous ice growth exhibits a maximum in freezing rate arising from the competition between kinetics and the thermodynamic driving force between the solid and liquid states. Here, we use molecular dynamics simulations to elucidate the atomistic details of this competition, focusing on water properties in the interfacial region along the secondary prismatic direction. The crystal growth velocity is maximized when the efficiency of converting interfacial water molecules to ice, collectively known as the attachment kinetics, is greatest. We find water molecules that contact the intermediate ice layer in concave regions along the atomistically roughened surface are more likely to freeze directly. An increased roughening of the solid surface at large undercoolings consequently plays an important limiting role in the rate of ice growth, as water molecules are unable to integrate into increasingly deeper surface pockets. These results provide insight into the molecular mechanisms for self-assembly of solid phases that are important in many biological and atmospheric processes.

    View details for DOI 10.1021/jp408832b

    View details for Web of Science ID 000330252700012

    View details for PubMedID 24393086

  • Efficient and accurate surface hopping for long time nonadiabatic quantum dynamics JOURNAL OF CHEMICAL PHYSICS Kelly, A., Markland, T. E. 2013; 139 (1)

    Abstract

    The quantum-classical Liouville equation offers a rigorous approach to nonadiabatic quantum dynamics based on surface hopping type trajectories. However, in practice the applicability of this approach has been limited to short times owing to unfavorable numerical scaling. In this paper we show that this problem can be alleviated by combining it with a formally exact generalized quantum master equation treatment. This allows dramatic improvements in the efficiency of the approach in nonadiabatic regimes, making it computationally tractable to treat the quantum dynamics of complex systems for long times. We demonstrate our approach by applying it to a model of condensed phase charge transfer where our method is shown to be numerically exact in regimes where fewest-switches surface hopping and mean field approaches fail to obtain either the correct rates or long-time populations.

    View details for DOI 10.1063/1.4812355

    View details for Web of Science ID 000321716400006

    View details for PubMedID 23822290

  • Efficient methods and practical guidelines for simulating isotope effects JOURNAL OF CHEMICAL PHYSICS Ceriotti, M., Markland, T. E. 2013; 138 (1)

    Abstract

    The shift in chemical equilibria due to isotope substitution is frequently exploited to obtain insight into a wide variety of chemical and physical processes. It is a purely quantum mechanical effect, which can be computed exactly using simulations based on the path integral formalism. Here we discuss how these techniques can be made dramatically more efficient, and how they ultimately outperform quasi-harmonic approximations to treat quantum liquids not only in terms of accuracy, but also in terms of computational cost. To achieve this goal we introduce path integral quantum mechanics estimators based on free energy perturbation, which enable the evaluation of isotope effects using only a single path integral molecular dynamics trajectory of the naturally abundant isotope. We use as an example the calculation of the free energy change associated with H/D and (16)O/(18)O substitutions in liquid water, and of the fractionation of those isotopes between the liquid and the vapor phase. In doing so, we demonstrate and discuss quantitatively the relative benefits of each approach, thereby providing a set of guidelines that should facilitate the choice of the most appropriate method in different, commonly encountered scenarios. The efficiency of the estimators we introduce and the analysis that we perform should in particular facilitate accurate ab initio calculation of isotope effects in condensed phase systems.

    View details for DOI 10.1063/1.4772676

    View details for Web of Science ID 000313330000013

    View details for PubMedID 23298033

  • Ring-Polymer Molecular Dynamics: Quantum Effects in Chemical Dynamics from Classical Trajectories in an Extended Phase Space ANNUAL REVIEW OF PHYSICAL CHEMISTRY, VOL 64 Habershon, S., Manolopoulos, D. E., Markland, T. E., Miller, T. F. 2013; 64: 387-413

    Abstract

    This article reviews the ring-polymer molecular dynamics model for condensed-phase quantum dynamics. This model, which involves classical evolution in an extended ring-polymer phase space, provides a practical approach to approximating the effects of quantum fluctuations on the dynamics of condensed-phase systems. The review covers the theory, implementation, applications, and limitations of the approximation.

    View details for DOI 10.1146/annurev-physchem-040412-110122

    View details for Web of Science ID 000321771600018

    View details for PubMedID 23298242

  • Isotope effects in water as investigated by neutron diffraction and path integral molecular dynamics JOURNAL OF PHYSICS-CONDENSED MATTER Zeidler, A., Salmon, P. S., Fischer, H. E., Neuefeind, J. C., Simonson, J. M., Markland, T. E. 2012; 24 (28)

    Abstract

    The structures of heavy and light water at 300 K were investigated by using a joint approach in which the method of neutron diffraction with oxygen isotope substitution was complemented by path integral molecular dynamics simulations. The diffraction results, which give intra-molecular O-D and O-H bond distances of 0.985(5) and 0.990(5) ?, were found to be in best agreement with those obtained by using the flexible anharmonic TTM3-F water model. Both techniques show a difference of  ? 0.5% between the O-D and O-H intra-molecular bond lengths, and the results support a competing quantum effects model for water in which its structural and dynamical properties are governed by an offset between intra-molecular and inter-molecular quantum contributions. Further consideration of the O-O correlations is needed in order to improve agreement with experiment.

    View details for DOI 10.1088/0953-8984/24/28/284126

    View details for Web of Science ID 000305786400028

    View details for PubMedID 22738936

  • Zeidler et al. Reply PHYSICAL REVIEW LETTERS Zeidler, A., Salmon, P. S., Fischer, H. E., Neuefeind, J. C., Simonson, J. M., Lemmel, H., Rauch, H., Markland, T. E. 2012; 108 (25)
  • Growing Point-to-Set Length Scale Correlates with Growing Relaxation Times in Model Supercooled Liquids PHYSICAL REVIEW LETTERS Hocky, G. M., Markland, T. E., Reichman, D. R. 2012; 108 (22)

    Abstract

    It has been demonstrated recently that supercooled liquids sharing simple structural features (e.g. pair distribution functions) may exhibit strikingly distinct dynamical behavior. Here we show that a more subtle structural feature correlates with relaxation times in three simulated systems that have nearly identical radial distribution functions but starkly different dynamical behavior. In particular, for the first time we determine the thermodynamic "point-to-set" length scale in several canonical model systems and demonstrate the quantitative connection between this length scale and the growth of relaxation times. Our results provide clues necessary for distinguishing competing theories of the glass transition.

    View details for DOI 10.1103/PhysRevLett.108.225506

    View details for Web of Science ID 000304695900010

    View details for PubMedID 23003622

  • Unraveling quantum mechanical effects in water using isotopic fractionation PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Markland, T. E., Berne, B. J. 2012; 109 (21): 7988-7991

    Abstract

    When two phases of water are at equilibrium, the ratio of hydrogen isotopes in each is slightly altered because of their different phase affinities. This isotopic fractionation process can be utilized to analyze water's movement in the world's climate. Here we show that equilibrium fractionation ratios, an entirely quantum mechanical property, also provide a sensitive probe to assess the magnitude of nuclear quantum fluctuations in water. By comparing the predictions of a series of water models, we show that those describing the OH chemical bond as rigid or harmonic greatly overpredict the magnitude of isotope fractionation. Models that account for anharmonicity in this coordinate are shown to provide much more accurate results because of their ability to give partial cancellation between inter- and intramolecular quantum effects. These results give evidence of the existence of competing quantum effects in water and allow us to identify how this cancellation varies across a wide-range of temperatures. In addition, this work demonstrates that simulation can provide accurate predictions and insights into hydrogen fractionation.

    View details for DOI 10.1073/pnas.1203365109

    View details for Web of Science ID 000304445800021

    View details for PubMedID 22566650

  • Reduced density matrix hybrid approach: Application to electronic energy transfer JOURNAL OF CHEMICAL PHYSICS Berkelbach, T. C., Markland, T. E., Reichman, D. R. 2012; 136 (8)

    Abstract

    Electronic energy transfer in the condensed phase, such as that occurring in photosynthetic complexes, frequently occurs in regimes where the energy scales of the system and environment are similar. This situation provides a challenge to theoretical investigation since most approaches are accurate only when a certain energetic parameter is small compared to others in the problem. Here we show that in these difficult regimes, the Ehrenfest approach provides a good starting point for a dynamical description of the energy transfer process due to its ability to accurately treat coupling to slow environmental modes. To further improve on the accuracy of the Ehrenfest approach, we use our reduced density matrix hybrid framework to treat the faster environmental modes quantum mechanically, at the level of a perturbative master equation. This combined approach is shown to provide an efficient and quantitative description of electronic energy transfer in a model dimer and the Fenna-Matthews-Olson complex and is used to investigate the effect of environmental preparation on the resulting dynamics.

    View details for DOI 10.1063/1.3687342

    View details for Web of Science ID 000300944000006

    View details for PubMedID 22380029

  • Theory and simulations of quantum glass forming liquids JOURNAL OF CHEMICAL PHYSICS Markland, T. E., Morrone, J. A., Miyazaki, K., Berne, B. J., Reichman, D. R., Rabani, E. 2012; 136 (7)

    Abstract

    A comprehensive microscopic dynamical theory is presented for the description of quantum fluids as they transform into glasses. The theory is based on a quantum extension of mode-coupling theory. Novel effects are predicted, such as reentrant behavior of dynamical relaxation times. These predictions are supported by path integral ring polymer molecular dynamics simulations. The simulations provide detailed insight into the factors that govern slow dynamics in glassy quantum fluids. Connection to other recent work on both quantum glasses as well as quantum optimization problems is presented.

    View details for DOI 10.1063/1.3684881

    View details for Web of Science ID 000300551000025

    View details for PubMedID 22360252

  • Reduced density matrix hybrid approach: An efficient and accurate method for adiabatic and non-adiabatic quantum dynamics JOURNAL OF CHEMICAL PHYSICS Berkelbach, T. C., Reichman, D. R., Markland, T. E. 2012; 136 (3)

    Abstract

    We present a new approach to calculate real-time quantum dynamics in complex systems. The formalism is based on the partitioning of a system's environment into "core" and "reservoir" modes with the former to be treated quantum mechanically and the latter classically. The presented method only requires the calculation of the system's reduced density matrix averaged over the quantum core degrees of freedom which is then coupled to a classically evolved reservoir to treat the remaining modes. We demonstrate our approach by applying it to the spin-boson problem using the noninteracting blip approximation to treat the system and core, and Ehrenfest dynamics to treat the reservoir. The resulting hybrid methodology is accurate for both fast and slow baths, since it naturally reduces to its composite methods in their respective regimes of validity. In addition, our combined method is shown to yield good results in intermediate regimes where neither approximation alone is accurate and to perform equally well for both strong and weak system-bath coupling. Our approach therefore provides an accurate and efficient methodology for calculating quantum dynamics in complex systems.

    View details for DOI 10.1063/1.3671372

    View details for Web of Science ID 000299387700015

    View details for PubMedID 22280750

  • Oxygen as a Site Specific Probe of the Structure of Water and Oxide Materials PHYSICAL REVIEW LETTERS Zeidler, A., Salmon, P. S., Fischer, H. E., Neuefeind, J. C., Simonson, J. M., Lemmel, H., Rauch, H., Markland, T. E. 2011; 107 (14)

    Abstract

    The method of oxygen isotope substitution in neutron diffraction is introduced as a site specific structural probe. It is employed to measure the structure of light versus heavy water, thus circumventing the assumption of isomorphism between H and D as used in more traditional neutron diffraction methods. The intramolecular and intermolecular O-H and O-D pair correlations are in excellent agreement with path integral molecular dynamics simulations, both techniques showing a difference of ?0.5% between the O-H and O-D intramolecular bond distances. The results support the validity of a competing quantum effects model for water in which its structural and dynamical properties are governed by an offset between intramolecular and intermolecular quantum contributions.

    View details for DOI 10.1103/PhysRevLett.107.145501

    View details for Web of Science ID 000296285800014

    View details for PubMedID 22107211

  • Quantum fluctuations can promote or inhibit glass formation NATURE PHYSICS Markland, T. E., Morrone, J. A., Berne, B. J., Miyazaki, K., Rabani, E., Reichman, D. R. 2011; 7 (2): 134-137

    View details for DOI 10.1038/NPHYS1865

    View details for Web of Science ID 000286807000015

  • Efficient multiple time scale molecular dynamics: Using colored noise thermostats to stabilize resonances JOURNAL OF CHEMICAL PHYSICS Morrone, J. A., Markland, T. E., Ceriotti, M., Berne, B. J. 2011; 134 (1)

    Abstract

    Multiple time scale molecular dynamics enhances computational efficiency by updating slow motions less frequently than fast motions. However, in practice, the largest outer time step possible is limited not by the physical forces but by resonances between the fast and slow modes. In this paper we show that this problem can be alleviated by using a simple colored noise thermostatting scheme which selectively targets the high frequency modes in the system. For two sample problems, flexible water and solvated alanine dipeptide, we demonstrate that this allows the use of large outer time steps while still obtaining accurate sampling and minimizing the perturbation of the dynamics. Furthermore, this approach is shown to be comparable to constraining fast motions, thus providing an alternative to molecular dynamics with constraints.

    View details for DOI 10.1063/1.3518369

    View details for Web of Science ID 000286010600006

    View details for PubMedID 21218993

  • Efficient stochastic thermostatting of path integral molecular dynamics JOURNAL OF CHEMICAL PHYSICS Ceriotti, M., Parrinello, M., Markland, T. E., Manolopoulos, D. E. 2010; 133 (12)

    Abstract

    The path integral molecular dynamics (PIMD) method provides a convenient way to compute the quantum mechanical structural and thermodynamic properties of condensed phase systems at the expense of introducing an additional set of high frequency normal modes on top of the physical vibrations of the system. Efficiently sampling such a wide range of frequencies provides a considerable thermostatting challenge. Here we introduce a simple stochastic path integral Langevin equation (PILE) thermostat which exploits an analytic knowledge of the free path integral normal mode frequencies. We also apply a recently developed colored noise thermostat based on a generalized Langevin equation (GLE), which automatically achieves a similar, frequency-optimized sampling. The sampling efficiencies of these thermostats are compared with that of the more conventional Nosé-Hoover chain (NHC) thermostat for a number of physically relevant properties of the liquid water and hydrogen-in-palladium systems. In nearly every case, the new PILE thermostat is found to perform just as well as the NHC thermostat while allowing for a computationally more efficient implementation. The GLE thermostat also proves to be very robust delivering a near-optimum sampling efficiency in all of the cases considered. We suspect that these simple stochastic thermostats will therefore find useful application in many future PIMD simulations.

    View details for DOI 10.1063/1.3489925

    View details for Web of Science ID 000282648000007

    View details for PubMedID 20886921

  • A fast path integral method for polarizable force fields JOURNAL OF CHEMICAL PHYSICS Fanourgakis, G. S., Markland, T. E., Manolopoulos, D. E. 2009; 131 (9)

    Abstract

    A quantum simulation of an imaginary time path integral typically requires around n times more computational effort than the corresponding classical simulation, where n is the number of ring polymer beads (or imaginary time slices) used in the calculation. It is however possible to improve on this estimate by decomposing the potential into a sum of slowly and rapidly varying contributions. If the slowly varying contribution changes only slightly over the length scale of the ring polymer, it can be evaluated on a contracted ring polymer with fewer than the full n beads (or equivalently on a lower order Fourier decomposition of the imaginary time path). Here we develop and test this idea for systems with polarizable force fields. The development consists of iterating the induction on the contracted ring polymer and applying an appropriate transformation to obtain the forces on the original n beads. In combination with a splitting of the Coulomb potential into its short- and long-range parts, this results in a method with little more than classical computational effort in the limit of large system size. The method is illustrated with simulations of liquid water at 300 K and hexagonal ice at 100 K using a recently developed flexible and polarizable Thole-type potential energy model.

    View details for DOI 10.1063/1.3216520

    View details for Web of Science ID 000269625400003

    View details for PubMedID 19739844

  • Competing quantum effects in the dynamics of a flexible water model JOURNAL OF CHEMICAL PHYSICS Habershon, S., Markland, T. E., Manolopoulos, D. E. 2009; 131 (2)

    Abstract

    Numerous studies have identified large quantum mechanical effects in the dynamics of liquid water. In this paper, we suggest that these effects may have been overestimated due to the use of rigid water models and flexible models in which the intramolecular interactions were described using simple harmonic functions. To demonstrate this, we introduce a new simple point charge model for liquid water, q-TIP4P/F, in which the O-H stretches are described by Morse-type functions. We have parametrized this model to give the correct liquid structure, diffusion coefficient, and infrared absorption frequencies in quantum (path integral-based) simulations. The model also reproduces the experimental temperature variation of the liquid density and affords reasonable agreement with the experimental melting temperature of hexagonal ice at atmospheric pressure. By comparing classical and quantum simulations of the liquid, we find that quantum mechanical fluctuations increase the rates of translational diffusion and orientational relaxation in our model by a factor of around 1.15. This effect is much smaller than that observed in all previous simulations of empirical water models, which have found a quantum effect of at least 1.4 regardless of the quantum simulation method or the water model employed. The small quantum effect in our model is a result of two competing phenomena. Intermolecular zero point energy and tunneling effects destabilize the hydrogen-bonding network, leading to a less viscous liquid with a larger diffusion coefficient. However, this is offset by intramolecular zero point motion, which changes the average water monomer geometry resulting in a larger dipole moment, stronger intermolecular interactions, and a slower diffusion. We end by suggesting, on the basis of simulations of other potential energy models, that the small quantum effect we find in the diffusion coefficient is associated with the ability of our model to produce a single broad O-H stretching band in the infrared absorption spectrum.

    View details for DOI 10.1063/1.3167790

    View details for Web of Science ID 000267983100037

    View details for PubMedID 19603998

  • A refined ring polymer contraction scheme for systems with electrostatic interactions CHEMICAL PHYSICS LETTERS Markland, T. E., Manolopoulos, D. E. 2008; 464 (4-6): 256-261
  • An efficient ring polymer contraction scheme for imaginary time path integral simulations JOURNAL OF CHEMICAL PHYSICS Markland, T. E., Manolopoulos, D. E. 2008; 129 (2)

    Abstract

    A quantum simulation of an imaginary time path integral typically requires around n times more computational effort than the corresponding classical simulation, where n is the number of ring polymer beads (or imaginary time slices) used in the calculation. However, this estimate neglects the fact that the potential energies of many systems can be decomposed into a sum of rapidly varying short-range and slowly varying long-range contributions. For such systems, the computational effort of the path integral simulation can be reduced considerably by evaluating the long-range forces on a contracted ring polymer with fewer beads than are needed to evaluate the short-range forces. This idea is developed and then illustrated with an application to a flexible model of liquid water in which the intramolecular forces are evaluated with 32 beads, the oxygen-oxygen Lennard-Jones forces with seven, and the intermolecular electrostatic forces with just five. The resulting static and dynamic properties are within a few percent of those of a full 32-bead calculation, and yet they are obtained with a computational effort less than six times (rather than 32 times) that of a classical simulation. We hope that this development will encourage future studies of quantum mechanical fluctuations in liquid water and aqueous solutions and in many other systems with similar interaction potentials.

    View details for DOI 10.1063/1.2953308

    View details for Web of Science ID 000257629100006

    View details for PubMedID 18624514

  • Quantum diffusion of hydrogen and muonium atoms in liquid water and hexagonal ice JOURNAL OF CHEMICAL PHYSICS Markland, T. E., Habershon, S., Manolopoulos, D. E. 2008; 128 (19)

    Abstract

    We have used the ring polymer molecular dynamics method to study the diffusion of muonium, hydrogen, and deuterium atoms in liquid water and hexagonal ice over a wide temperature range (8-361 K). Quantum effects are found to dramatically reduce the diffusion of muonium in water relative to that predicted by classical simulation. This leads to a simple explanation for the lack of any significant isotope effect in the observed diffusion coefficients of these species in the room temperature liquid. Our results indicate that the mechanism of the diffusion in liquid water is similar to the intercavity hopping mechanism observed in ice, supplemented by the diffusion of the cavities in the liquid. Within the same model, we have also been able to simulate the observed crossover in the c-axis diffusion coefficients of hydrogen and deuterium in hexagonal ice. Finally, we have been able to obtain good agreement with experimental data on the diffusion of muonium in hexagonal ice at 8 K, where the process is entirely quantum mechanical.

    View details for DOI 10.1063/1.2925792

    View details for Web of Science ID 000256205200034

    View details for PubMedID 18500879