Thomas Markland
Associate Professor of Chemistry
Web page: http://web.stanford.edu/dept/chemistry/faculty/markland
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 lengthscales, 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 nonadiabatic 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 zeropoint energy and tunneling in the dynamics of reactive condensed phase systems. The group has also developed methods to treat nonequilibrium excited state dynamics by exploiting the combination of quantumclassical 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 largescale condensed phase systems.
Please visit the Markland Group website to learn more.
Administrative Appointments

Member, Stanford PULSE Institute, SLAC National Accelerator Laboratory (2014  Present)
Honors & Awards

Kavli Emerging Leader in Chemistry Lecture, Kavli Foundation (2019)

Camille Dreyfus TeacherScholar Award, Camille and Henry Dreyfus Foundation (2017)

Terman Fellow, Stanford University (2017)

NSF CAREER award, National Science Foundation (2016)

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 lengthscales 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 zeropoint 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 liquidglass transition as well as introducing methods to perform path integral calculations at near classical computational cost, expanding our ability to treat largescale condensed phase systems.
202021 Courses
 Department Colloquium
CHEM 300 (Aut, Win)  Foundations of Physical Chemistry
CHEM 171 (Spr)  Physical Chemistry Seminar
CHEM 379 (Aut, Win, Spr) 
Independent Studies (5)
 Advanced Undergraduate Research
CHEM 190 (Aut, Win, Spr, Sum)  Directed Instruction/Reading
CHEM 90 (Win, Spr, Sum)  Research
PHYSICS 490 (Aut)  Research and Special Advanced Work
CHEM 200 (Aut, Win, Spr, Sum)  Research in Chemistry
CHEM 301 (Aut, Win, Spr, Sum)
 Advanced Undergraduate Research

Prior Year Courses
201920 Courses
 Computational Chemistry
CHEM 261 (Aut)  Physical Chemistry III
CHEM 175 (Win)  Physical Chemistry Seminar
CHEM 379 (Aut, Win, Spr)
201819 Courses
 Computational Chemistry
CHEM 261 (Aut)  Physical Chemistry III
CHEM 175 (Win)  Physical Chemistry Seminar
CHEM 279 (Aut, Win, Spr)
201718 Courses
 Computational Chemistry
CHEM 261 (Aut)  Physical Chemistry III
CHEM 175 (Win)  Physical Chemistry Seminar
CHEM 279 (Aut, Win, Spr)
 Computational Chemistry
Stanford Advisees

Doctoral Dissertation Reader (AC)
Chey Jones, Shujia Liang, Sean Roget, David Sanchez, Hannah WaymentSteele, Hayley Weir, Steven Yamada 
Postdoctoral Faculty Sponsor
Yuezhi Mao 
Doctoral Dissertation Advisor (AC)
Austin Atsango, Michael Chen
All Publications

Exploiting Machine Learning to Efficiently Predict Multidimensional Optical Spectra in Complex Environments.
The journal of physical chemistry letters
2020: 7559–68
Abstract
The excitedstate dynamics of chromophores in complex environments determine a range of vital biological and energy capture processes. Timeresolved, multidimensional optical spectroscopies provide a key tool to investigate these processes. Although theory has the potential to decode these spectra in terms of the electronic and atomistic dynamics, the need for large numbers of excitedstate electronic structure calculations severely limits firstprinciples predictions of multidimensional optical spectra for chromophores in the condensed phase. Here, we leverage the locality of chromophore excitations to develop machine learning models to predict the excitedstate energy gap of chromophores in complex environments for efficiently constructing linear and multidimensional optical spectra. By analyzing the performance of these models, which span a hierarchy of physical approximations, across a range of chromophoreenvironment interaction strengths, we provide strategies for the construction of machine learning models that greatly accelerate the calculation of multidimensional optical spectra from first principles.
View details for DOI 10.1021/acs.jpclett.0c02168
View details for PubMedID 32808797

On the advantages of exploiting memory in Markov state models for biomolecular dynamics.
The Journal of chemical physics
2020; 153 (1): 014105
Abstract
Biomolecular dynamics play an important role in numerous biological processes. Markov State Models (MSMs) provide a powerful approach to study these dynamic processes by predicting long time scale dynamics based on many short molecular dynamics (MD) simulations. In an MSM, protein dynamics are modeled as a kinetic process consisting of a series of Markovian transitions between different conformational states at discrete time intervals (called "lag time"). To achieve this, a master equation must be constructed with a sufficiently long lag time to allow interstate transitions to become truly Markovian. This imposes a major challenge for MSM studies of proteins since the lag time is bound by the length of relatively short MD simulations available to estimate the frequency of transitions. Here, we show how one can employ the generalized master equation formalism to obtain an exact description of protein conformational dynamics both at short and long time scales without the time resolution restrictions imposed by the MSM lag time. Using a simple kinetic model, alanine dipeptide, and WW domain, we demonstrate that it is possible to construct these quasiMarkov State Models (qMSMs) using MD simulations that are 510 times shorter than those required by MSMs. These qMSMs only contain a handful of metastable states and, thus, can greatly facilitate the interpretation of mechanisms associated with protein dynamics. A qMSM opens the door to the study of conformational changes of complex biomolecules where a Markovian model with a few states is often difficult to construct due to the limited length of available MD simulations.
View details for DOI 10.1063/5.0010787
View details for PubMedID 32640825

Quantum kinetic energy and isotope fractionation in aqueous ionic solutions.
Physical chemistry chemical physics : PCCP
2020
Abstract
At room temperature, the quantum contribution to the kinetic energy of a water molecule exceeds the classical contribution by an order of magnitude. The quantum kinetic energy (QKE) of a water molecule is modulated by its local chemical environment and leads to uneven partitioning of isotopes between different phases in thermal equilibrium, which would not occur if the nuclei behaved classically. In this work, we use ab initio path integral simulations to show that QKEs of the water molecules and the equilibrium isotope fractionation ratios of the oxygen and hydrogen isotopes are sensitive probes of the hydrogen bonding structures in aqueous ionic solutions. In particular, we demonstrate how the QKE of water molecules in path integral simulations can be decomposed into translational, rotational and vibrational degrees of freedom, and use them to determine the impact of solvation on different molecular motions. By analyzing the QKEs and isotope fractionation ratios, we show how the addition of the Na+, Cl and HPO42 ions perturbs the competition between quantum effects in liquid water and impacts their local solvation structures.
View details for DOI 10.1039/c9cp06483d
View details for PubMedID 31942581

Elucidating the Proton Transport Pathways in Liquid Imidazole with FirstPrinciples Molecular Dynamics.
The journal of physical chemistry letters
2020: 6156–63
Abstract
Imidazole is a promising anhydrous proton conductor with a high conductivity comparable to that of water at a similar temperature relative to its melting point. Previous theoretical studies of the mechanism of proton transport in imidazole have relied either on empirical models or on ab initio trajectories that have been too short to draw significant conclusions. Here, we present the results of multiple timestep ab initio molecular dynamics simulations of an excess proton in liquid imidazole reaching 1 ns in total simulation time. We find that the proton transport is dominated by structural diffusion, with the diffusion constant of the proton defect being ∼8 times higher than that of selfdiffusion of the imidazole molecules. By using correlation function analysis, we decompose the mechanism for proton transport into a series of firstorder processes and show that the proton transport mechanism occurs over three distinct time and length scales. Although the mechanism at intermediate times is dominated by hopping along pseudoonedimensional chains, at longer times the overall rate of diffusion is limited by the reformation of these chains. These results provide a more complete picture of the traditional idealized Grotthuss structural diffusion mechanism.
View details for DOI 10.1021/acs.jpclett.0c01744
View details for PubMedID 32633523

Excited state diabatization on the cheap using DFT: Photoinduced electron and hole transfer.
The Journal of chemical physics
2020; 153 (24): 244111
Abstract
Excited state electron and hole transfer underpin fundamental steps in processes such as exciton dissociation at photovoltaic heterojunctions, photoinduced charge transfer at electrodes, and electron transfer in photosynthetic reaction centers. Diabatic states corresponding to charge or excitation localized species, such as locally excited and charge transfer states, provide a physically intuitive framework to simulate and understand these processes. However, obtaining accurate diabatic states and their couplings from adiabatic electronic states generally leads to inaccurate results when combined with lowtier electronic structure methods, such as timedependent density functional theory, and exorbitant computational cost when combined with highlevel wavefunctionbased methods. Here, we introduce a density functional theory (DFT)based diabatization scheme that directly constructs the diabatic states using absolutely localized molecular orbitals (ALMOs), which we denote as ΔALMO(MSDFT2). We demonstrate that our method, which combines ALMO calculations with the ΔSCF technique to construct electronically excited diabatic states and obtains their couplings with chargetransfer states using our MSDFT2 scheme, gives accurate results for excited state electron and hole transfer in both charged and uncharged systems that underlie DNA repair, charge separation in donoracceptor dyads, chromophoretosolvent electron transfer, and singlet fission. This framework for the accurate and efficient construction of excited state diabats and evaluation of their couplings directly from DFT thus offers a route to simulate and elucidate photoinduced electron and hole transfer in large disordered systems, such as those encountered in the condensed phase.
View details for DOI 10.1063/5.0035593
View details for PubMedID 33380087

Resolving Heterogeneous Dynamics of Excess Protons in Aqueous Solution with Rate Theory.
The journal of physical chemistry. B
2020
Abstract
Rate theories have found great utility across the chemical sciences by providing a physically transparent way to analyze dynamical processes. Here we demonstrate the benefits of using transition state theory and Marcus theory to study the rate of proton transfer in HCl solutions. By using long ab initio molecular dynamics simulations, we show that good agreement is obtained between these two different formulations of rate theory and how they can be used to study the pathways and lifetime of proton transfer in aqueous solution. Since both rate theory formulations utilize identical sets of molecular data, this provides a selfconsistent theoretical picture of the rates of aqueous phase proton transfer. Specifically, we isolate and quantify the rates of proton transfer, ionpair dissociation, and solvent exchange in concentrated HCl solutions. Our analysis predicts a concentration dependence to both proton transfer and ionpairing. Moreover, our estimate of the lifetime for the Zundel species is 0.8 and 1.3 ps for 2 M and 8 M HCl, respectively. We demonstrate that concentration effects can indeed be quantified through the combination of stateoftheart simulation and theory and provides a picture of the important correlations between the cation (hydronium) and the counterion in acid solutions.
View details for DOI 10.1021/acs.jpcb.0c02649
View details for PubMedID 32482074

Accurate and efficient DFTbased diabatization for hole and electron transfer using absolutely localized molecular orbitals.
The Journal of chemical physics
2019; 151 (16): 164114
Abstract
Diabatic states and the couplings between them are important for quantifying, elucidating, and predicting the rates and mechanisms of many chemical and biochemical processes. Here, we propose and investigate approaches to accurately compute diabatic couplings from density functional theory (DFT) using absolutely localized molecular orbitals (ALMOs). ALMOs provide an appealing approach to generate variationally optimized diabatic states and obtain their associated forces, which allows for the relaxation of the donor and acceptor orbitals in a way that is internally consistent in how the method treats both the donor and acceptor states. Here, we show that one can obtain more accurate electronic couplings between ALMObased diabats by employing the symmetrized transition density matrix to evaluate the exchangecorrelation contribution. We demonstrate that this approach yields accurate results in comparison to other commonly used DFTbased diabatization methods across a wide array of electron and hole transfer processes occurring in systems ranging from conjugated organic molecules, such as thiophene and pentacene, to DNA base pairs. We also show that this approach yields accurate diabatic couplings even when combined with lower tiers of the DFT hierarchy, opening the door to combining it with quantum dynamics approaches to provide an ab initio treatment of nonadiabatic processes in the condensed phase.
View details for DOI 10.1063/1.5125275
View details for PubMedID 31675855

Tracking Aqueous Proton Transfer by TwoDimensional Infrared Spectroscopy and ab Initio Molecular Dynamics Simulations
ACS CENTRAL SCIENCE
2019; 5 (7): 1269–77
View details for DOI 10.1021/acscentsci.9b00447
View details for Web of Science ID 000476928300020

iPI 2.0: A universal force engine for advanced molecular simulations
COMPUTER PHYSICS COMMUNICATIONS
2019; 236: 214–23
View details for DOI 10.1016/j.cpc.2018.09.020
View details for Web of Science ID 000458227100020

Efficient construction of generalized master equation memory kernels for multistate systems from nonadiabatic quantumclassical dynamics.
The Journal of chemical physics
2019; 150 (24): 244109
Abstract
Methods derived from the generalized quantum master equation (GQME) framework have provided the basis for elucidating energy and charge transfer in systems ranging from molecular solids to photosynthetic complexes. Recently, the nonperturbative combination of the GQME with quantumclassical methods has resulted in approaches whose accuracy and efficiency exceed those of the original quantumclassical schemes while offering significant accuracy improvements over perturbative expansions of the GQME. Here, we show that, while the nonMarkovian memory kernel required to propagate the GQME scales quartically with the number of subsystem states, the number of trajectories required scales at most quadratically when using quantumclassical methods to construct the kernel. We then present an algorithm that allows further acceleration of the quantumclassical GQME by providing a way to selectively sample the kernel matrix elements that are most important to the process of interest. We demonstrate the utility of these advances by applying the combination of Ehrenfest mean field theory with the GQME (MFGQME) to models of the FennaMatthewsOlson (FMO) complex and the light harvesting complex II (LHCII), with 7 and 14 states, respectively. This allows us to show that the MFGQME is able to accurately capture all the relevant dynamical time scales in LHCII: the initial nonequilibrium population transfer on the femtosecond time scale, the steady statetype trapping on the picosecond time scale, and the long time population relaxation. Remarkably, all of these physical effects spanning tens of picoseconds can be encoded in a memory kernel that decays only after ∼65 fs.
View details for DOI 10.1063/1.5095715
View details for PubMedID 31255061

Tracking Aqueous Proton Transfer by TwoDimensional Infrared Spectroscopy and ab Initio Molecular Dynamics Simulations.
ACS central science
2019; 5 (7): 1269–77
Abstract
Proton transfer in water is ubiquitous and a critical elementary event that, via proton hopping between water molecules, enables protons to diffuse much faster than other ions. The problem of the anomalous nature of proton transport in water was first identified by Grotthuss over 200 years ago. In spite of a vast amount of modern research effort, there are still many unanswered questions about proton transport in water. An experimental determination of the proton hopping time has remained elusive due to its ultrafast nature and the lack of direct experimental observables. Here, we use twodimensional infrared spectroscopy to extract the chemical exchange rates between hydronium and water in acid solutions using a vibrational probe, methyl thiocyanate. Ab initio molecular dynamics (AIMD) simulations demonstrate that the chemical exchange is dominated by proton hopping. The observed experimental and simulated acid concentration dependence then allow us to extrapolate the measured single step proton hopping time to the dilute limit, which, within error, gives the same value as inferred from measurements of the proton mobility and NMR line width analysis. In addition to obtaining the proton hopping time in the dilute limit from direct measurements and AIMD simulations, the results indicate that proton hopping in dilute acid solutions is induced by the concerted multiwater molecule hydrogen bond rearrangement that occurs in pure water. This proposition on the dynamics that drive proton hopping is confirmed by a combination of experimental results from the literature.
View details for DOI 10.1021/acscentsci.9b00447
View details for PubMedID 31403075
View details for PubMedCentralID PMC6661862

Hiding in the Crowd: Spectral Signatures of Overcoordinated HydrogenBond Environments.
The journal of physical chemistry letters
2019: 6067–73
Abstract
Molecules with an excess number of hydrogenbonding partners play a crucial role in fundamental chemical processes, ranging from anomalous diffusion in supercooled water to transport of aqueous proton defects and ordering of water around hydrophobic solutes. Here we show that overcoordinated hydrogenbond environments can be identified in both the ambient and supercooled regimes of liquid water by combining experimental Raman multivariate curve resolution measurements and machine learning accelerated quantum simulations. In particular, we find that OH groups appearing in spectral regions usually associated with nonhydrogenbonded species actually correspond to hydrogen bonds formed in overcoordinated environments. We further show that only these species exhibit a turnover in population as a function of temperature, which is robust and persists under both constant pressure and density conditions. This work thus provides a new tool to identify, interpret, and elucidate the spectral signatures of crowded hydrogenbond networks.
View details for DOI 10.1021/acs.jpclett.9b01781
View details for PubMedID 31549833

Optical spectra in the condensed phase: Capturing anharmonic and vibronic features using dynamic and static approaches.
The Journal of chemical physics
2019; 151 (7): 074111
Abstract
Simulating optical spectra in the condensed phase remains a challenge for theory due to the need to capture spectral signatures arising from anharmonicity and dynamical effects, such as vibronic progressions and asymmetry. As such, numerous simulation methods have been developed that invoke different approximations and vary in their ability to capture different physical regimes. Here, we use several models of chromophores in the condensed phase and ab initio molecular dynamics simulations to rigorously assess the applicability of methods to simulate optical absorption spectra. Specifically, we focus on the ensemble scheme, which can address anharmonic potential energy surfaces but relies on the applicability of extreme nuclearelectronic time scale separation; the FranckCondon method, which includes dynamical effects but generally only at the harmonic level; and the recently introduced ensemble zerotemperature FranckCondon approach, which straddles these limits. We also devote particular attention to the performance of methods derived from a cumulant expansion of the energy gap fluctuations and test the ability to approximate the requisite time correlation functions using classical dynamics with quantum correction factors. These results provide insights as to when these methods are applicable and able to capture the features of condensed phase spectra qualitatively and, in some cases, quantitatively across a range of regimes.
View details for DOI 10.1063/1.5114818
View details for PubMedID 31438704

Beyond Badger's Rule: The Origins and Generality of the StructureSpectra Relationship of Aqueous Hydrogen Bonds.
The journal of physical chemistry letters
2019: 918–24
Abstract
The structure of hydrogen bonded networks is intimately intertwined with their dynamics. Despite the incredibly wide range of hydrogen bond strengths encountered in water clusters, ionwater clusters, and liquid water, we demonstrate that the previously reported correlation between the change in the equilibrium bond length of the hydrogen bonded OH covalent bond and the corresponding shift in its harmonic frequency in water clusters is much more broadly applicable. Surprisingly, this correlation describes the ratios for both the equilibrium OH bond length/harmonic frequency and the vibrationally averaged bond length/anharmonic frequency in water, hydronium water, and halide water clusters. Consideration of harmonic and anaharmonic data leads to a correlation of 19 ± 1 cm1/0.001 Å. The fundamental nature of this correlation is further confirmed through the analysis of ab initio Molecular Dynamics (AIMD) trajectories for liquid water. We demonstrate that this simple correlation for both harmonic and anharmonic systems can be modeled by the response of an OH bond to an external field. Treating the OH bond as a Morse oscillator, we develop analytic expressions, which relate the ratio of the shift in the vibrational frequency of the hydrogenbonded OH bond to the shift in OH bond length, to parameters in the Morse potential and the ratio of the first and second derivatives of the fielddependent projection of the dipole moment of water onto the hydrogenbonded OH bond. Based on our analysis, we develop a protocol for reconstructing the AIMD spectra of liquid water from the sampled distribution of the OH bond lengths. Our findings elucidate the origins of the relationship between the molecular structure of the fleeting hydrogenbonded network and the ensuing dynamics, which can be probed by vibrational spectroscopy.
View details for PubMedID 30735052

The Quest for Accurate Liquid Water Properties from First Principles
JOURNAL OF PHYSICAL CHEMISTRY LETTERS
2018; 9 (17): 5009–16
Abstract
Developing accurate ab initio molecular dynamics (AIMD) models that capture both electronic reorganization and nuclear quantum effects associated with hydrogen bonding is key to quantitative understanding of bulk water and its anomalies as well as its role as a universal solvent. For condensed phase simulations, AIMD has typically relied on the generalized gradient approximation (GGA) of density functional theory (DFT) as the underlying model chemistry for the potential energy surface, with nuclear quantum effects (NQEs) sometimes modeled by performing classical molecular dynamics simulations at elevated temperatures. Here we show that the properties of liquid water obtained from the metaGGA B97MrV functional, when evaluated using accelerated path integral molecular dynamics simulations, display accuracy comparable to a computationally expensive dispersioncorrected hybrid functional, revPBE0D3. We show that the metaGGA DFT functional reproduces bulk water properties including radial distribution functions, selfdiffusion coefficients, and infrared spectra with comparable accuracy of a much more expensive hybrid functional. This work demonstrates that the underlying quality of a good DFT functional requires evaluation with quantum nuclei and that hightemperature simulations are a poor proxy for properly treating NQEs.
View details for PubMedID 30118601

On the exact continuous mapping of fermions.
Scientific reports
2018; 8 (1): 12929
Abstract
We derive a rigorous, quantum mechanical map of fermionic creation and annihilation operators to continuous Cartesian variables that exactly reproduces the matrix structure of the manyfermion problem. We show how our scheme can be used to map a general manyfermion Hamiltonian and then consider two specific models that encode the fundamental physics of many fermionic systems, the Anderson impurity and Hubbard models. We use these models to demonstrate how efficient mappings of these Hamiltonians can be constructed using a judicious choice of index ordering of the fermions. This development provides an alternative exact route to calculate the static and dynamical properties of fermionic systems and sets the stage to exploit the quantumclassical and semiclassical hierarchies to systematically derive methods offering a range of accuracies, thus enabling the study of problems where the fermionic degrees of freedom are coupled to complex anharmonic nuclear motion and spins which lie beyond the reach of most currently available methods.
View details for PubMedID 30154503

Unraveling electronic absorption spectra using nuclear quantum effects: Photoactive yellow protein and green fluorescent protein chromophores in water
JOURNAL OF CHEMICAL PHYSICS
2018; 149 (2): 024107
Abstract
Many physical phenomena must be accounted for to accurately model solutionphase optical spectral line shapes, from the sampling of chromophoresolvent configurations to the electronicvibrational transitions leading to vibronic fine structure. Here we thoroughly explore the role of nuclear quantum effects, direct and indirect solvent effects, and vibronic effects in the computation of the optical spectrum of the aqueously solvated anionic chromophores of green fluorescent protein and photoactive yellow protein. By analyzing the chromophore and solvent configurations, the distributions of vertical excitation energies, the absorption spectra computed within the ensemble approach, and the absorption spectra computed within the ensemble plus zerotemperature FranckCondon approach, we show how solvent, nuclear quantum effects, and vibronic transitions alter the optical absorption spectra. We find that including nuclear quantum effects in the sampling of chromophoresolvent configurations using ab initio path integral molecular dynamics simulations leads to improved spectral shapes through three mechanisms. The three mechanisms that lead to line shape broadening and a better description of the highenergy tail are softening of heavy atom bonds in the chromophore that couple to the optically bright state, widening the distribution of vertical excitation energies from more diverse solvation environments, and redistributing spectral weight from the 00 vibronic transition to higher energy vibronic transitions when computing the FranckCondon spectrum in a frozen solvent pocket. The absorption spectra computed using the combined ensemble plus zerotemperature FranckCondon approach yield significant improvements in spectral shape and width compared to the spectra computed with the ensemble approach. Using the combined approach with configurations sampled from path integral molecular dynamics trajectories presents a significant step forward in accurately modeling the absorption spectra of aqueously solvated chromophores.
View details for PubMedID 30007372

Decoding the spectroscopic features and time scales of aqueous proton defects.
The Journal of chemical physics
2018; 148 (22): 222833
Abstract
Acid solutions exhibit a variety of complex structural and dynamical features arising from the presence of multiple interacting reactive proton defects and counterions. However, disentangling the transient structural motifs of proton defects in the water hydrogen bond network and the mechanisms for their interconversion remains a formidable challenge. Here, we use simulations treating the quantum nature of both the electrons and nuclei to show how the experimentally observed spectroscopic features and relaxation time scales can be elucidated using a physically transparent coordinate that encodes the overall asymmetry of the solvation environment of the proton defect. We demonstrate that this coordinate can be used both to discriminate the extremities of the features observed in the linear vibrational spectrum and to explain the molecular motions that give rise to the interconversion time scales observed in recent nonlinear experiments. This analysis provides a unified condensedphase picture of the proton structure and dynamics that, at its extrema, encompasses proton sharing and spectroscopic features resembling the limiting Eigen [H3O(H2O)3]+ and Zundel [H(H2O)2]+ gasphase structures, while also describing the rich variety of interconverting environments in the liquid phase.
View details for PubMedID 29907063

Nuclear quantum effects enter the mainstream
NATURE REVIEWS CHEMISTRY
2018; 2 (3)
View details for DOI 10.1038/s415700170109
View details for Web of Science ID 000427597900008

The Interplay of Structure and Dynamics in the Raman Spectrum of Liquid Water over the Full Frequency and Temperature Range
JOURNAL OF PHYSICAL CHEMISTRY LETTERS
2018; 9 (4): 851–57
Abstract
While many vibrational Raman spectroscopy studies of liquid water have investigated the temperature dependence of the highfrequency OH stretching region, few have analyzed the changes in the Raman spectrum as a function of temperature over the entire spectral range. Here, we obtain the Raman spectra of water from its melting to boiling point, both experimentally and from simulations using an ab initiotrained machine learning potential. We use these to assign the Raman bands and show that the entire spectrum can be well described as a combination of two temperatureindependent spectra. We then assess which spectral regions exhibit strong dependence on the local tetrahedral order in the liquid. Further, this work demonstrates that changes in this structural parameter can be used to elucidate the temperature dependence of the Raman spectrum of liquid water and provides a guide to the Raman features that signal water ordering in more complex aqueous systems.
View details for PubMedID 29394069

Proton Network Flexibility Enables Robustness and Large Electric Fields in the Ketosteroid Isomerase Active Site
JOURNAL OF PHYSICAL CHEMISTRY B
2017; 121 (42): 9807–15
Abstract
Hydrogenbond networks play vital roles in biological functions ranging from protein folding to enzyme catalysis. Here we combine electronic structure calculations and ab initio path integral molecular dynamics simulations, which incorporate both nuclear and electronic quantum effects, to show why the network of short hydrogen bonds in the active site of ketosteroid isomerase is remarkably robust to mutations along the network and how this gives rise to large local electric fields. We demonstrate that these properties arise from the network's ability to respond to a perturbation by shifting proton positions and redistributing electronic charge density. This flexibility leads to small changes in properties such as the partial ionization of residues and pKa isotope effects upon mutation of the residues, consistent with recent experiments. This proton flexibility is further enhanced when an extended hydrogenbond network forms in the presence of an intermediate analogue, which allows us to explain the chemical origins of the large electric fields in the enzyme's active site observed in recent experiments.
View details for PubMedID 28915043

Unravelling the influence of quantum proton delocalization on electronic charge transfer through the hydrogen bond
CHEMICAL PHYSICS LETTERS
2017; 678: 289–95
View details for DOI 10.1016/j.cplett.2017.04.034
View details for Web of Science ID 000402218100045

Quantum Dynamics and Spectroscopy of Ab Initio Liquid Water: The Interplay of Nuclear and Electronic Quantum Effects
JOURNAL OF PHYSICAL CHEMISTRY LETTERS
2017; 8 (7): 15451551
Abstract
Understanding the reactivity and spectroscopy of aqueous solutions at the atomistic level is crucial for the elucidation and design of chemical processes. However, the simulation of these systems requires addressing the formidable challenges of treating the quantum nature of both the electrons and nuclei. Exploiting our recently developed methods that provide acceleration by up to 2 orders of magnitude, we combine path integral simulations with onthefly evaluation of the electronic structure at the hybrid density functional theory level to capture the interplay between nuclear quantum effects and the electronic surface. Here we show that this combination provides accurate structure and dynamics, including the full infrared and Raman spectra of liquid water. This allows us to demonstrate and explain the failings of lowerlevel density functionals for dynamics and vibrational spectroscopy when the nuclei are treated quantum mechanically. These insights thus provide a foundation for the reliable investigation of spectroscopy and reactivity in aqueous environments.
View details for DOI 10.1021/acs.jpclett.7b00391
View details for Web of Science ID 000398884800035
View details for PubMedID 28296422

Electrostatic Control of Regioselectivity in Au(I)Catalyzed Hydroarylation
JOURNAL OF THE AMERICAN CHEMICAL SOCIETY
2017; 139 (11): 40354041
Abstract
Competing pathways in catalytic reactions often involve transition states with very different charge distributions, but this difference is rarely exploited to control selectivity. The proximity of a counterion to a charged catalyst in an ion paired complex gives rise to strong electrostatic interactions that could be used to energetically differentiate transition states. Here we investigate the effects of ion pairing on the regioselectivity of the hydroarylation of 3substituted phenyl propargyl ethers catalyzed by cationic Au(I) complexes, which forms a mixture of 5 and 7substituted 2Hchromenes. We show that changing the solvent dielectric to enforce ion pairing to a SbF6() counterion changes the regioselectivity by up to a factor of 12 depending on the substrate structure. Density functional theory (DFT) is used to calculate the energy difference between the putative productdetermining isomeric transition states (ΔΔE(‡)) in both the presence and absence of the counterion. The change in ΔΔE(‡) upon switching from the unpaired transition states in high solvent dielectric to ion paired transition states in low solvent dielectric (Δ(ΔΔE(‡))) was found to be in good agreement with the experimentally observed selectivity changes across several substrates. Our calculations indicate that the origin of Δ(ΔΔE(‡)) lies in the preferential electrostatic stabilization of the transition state with greater charge separation by the counterion in the ion paired case. By performing calculations at multiple different values of the solvent dielectric, we show that the role of the solvent in changing selectivity is not solely to enforce ion pairing, but rather that interactions between the ion paired complex and the solvent also contribute to Δ(ΔΔE(‡)). Our results provide a foundation for exploiting electrostatic control of selectivity in other ion paired systems.
View details for DOI 10.1021/jacs.6b11971
View details for Web of Science ID 000397477700021
View details for PubMedID 28225605

Nuclear Quantum Effects in Water and Aqueous Systems: Experiment, Theory, and Current Challenges
CHEMICAL REVIEWS
2016; 116 (13): 75297550
Abstract
Nuclear quantum effects influence the structure and dynamics of hydrogenbonded systems, such as water, which impacts their observed properties with widely varying magnitudes. This review highlights the recent significant developments in the experiment, theory, and simulation of nuclear quantum effects in water. Novel experimental techniques, such as deep inelastic neutron scattering, now provide a detailed view of the role of nuclear quantum effects in water's properties. These have been combined with theoretical developments such as the introduction of the principle of competing quantum effects that allows the subtle interplay of water's quantum effects and their manifestation in experimental observables to be explained. We discuss how this principle has recently been used to explain the apparent dichotomy in water's isotope effects, which can range from very large to almost nonexistent depending on the property and conditions. We then review the latest major developments in simulation algorithms and theory that have enabled the efficient inclusion of nuclear quantum effects in molecular simulations, permitting their combination with onthefly evaluation of the potential energy surface using electronic structure theory. Finally, we identify current challenges and future opportunities in this area of research.
View details for DOI 10.1021/acs.chemrev.5b00674
View details for Web of Science ID 000379794000004
View details for PubMedID 27049513

Generalized quantum master equations in and out of equilibrium: When can one win?
JOURNAL OF CHEMICAL PHYSICS
2016; 144 (18)
Abstract
Generalized quantum master equations (GQMEs) are an important tool in modeling chemical and physical processes. For a large number of problems, it has been shown that exact and approximate quantum dynamics methods can be made dramatically more efficient, and in the latter case more accurate, by proceeding via the GQME formalism. However, there are many situations where utilizing the GQME approach with an approximate method has been observed to return the same dynamics as using that method directly. Here, for systems both in and out of equilibrium, we provide a more detailed understanding of the conditions under which using an approximate method can yield benefits when combined with the GQME formalism. In particular, we demonstrate the necessary manipulations, which are satisfied by exact quantum dynamics, that are required to recast the memory kernel in a form that can be analytically shown to yield the same result as a direct application of the dynamics regardless of the approximation used. By considering the connections between these forms of the kernel, we derive the conditions that approximate methods must satisfy if they are to offer different results when used in conjunction with the GQME formalism. These analytical results thus provide new insights as to when proceeding via the GQME approach can be used to improve the accuracy of simulations.
View details for DOI 10.1063/1.4948612
View details for Web of Science ID 000377711900006
View details for PubMedID 27179469

Unraveling the dynamics and structure of functionalized selfassembled monolayers on gold using 2D IR spectroscopy and MD simulations
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
2016; 113 (18): 49294934
Abstract
Functionalized selfassembled monolayers (SAMs) are the focus of ongoing investigations because they can be chemically tuned to control their structure and dynamics for a wide variety of applications, including electrochemistry, catalysis, and as models of biological interfaces. Here we combine reflection 2D infrared vibrational echo spectroscopy (R2D IR) and molecular dynamics simulations to determine the relationship between the structures of functionalized alkanethiol SAMs on gold surfaces and their underlying molecular motions on timescales of tens to hundreds of picoseconds. We find that at higher head group density, the monolayers have more disorder in the alkyl chain packing and faster dynamics. The dynamics of alkanethiol SAMs on gold are much slower than the dynamics of alkylsiloxane SAMs on silica. Using the simulations, we assess how the different molecular motions of the alkyl chain monolayers give rise to the dynamics observed in the experiments.
View details for DOI 10.1073/pnas.1603080113
View details for Web of Science ID 000375395700026
View details for PubMedID 27044113
View details for PubMedCentralID PMC4983838

Ab initio molecular dynamics with nuclear quantum effects at classical cost: Ring polymer contraction for density functional theory
JOURNAL OF CHEMICAL PHYSICS
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

Simulating Nuclear and Electronic Quantum Effects in Enzymes.
Methods in enzymology
2016; 577: 389418
Abstract
An accurate treatment of the structures and dynamics that lead to enhanced chemical reactivity in enzymes requires explicit treatment of both electronic and nuclear quantum effects. The former can be captured in ab initio molecular dynamics (AIMD) simulations, while the latter can be included by performing ab initio path integral molecular dynamics (AIPIMD) simulations. Both AIMD and AIPIMD simulations have traditionally been computationally prohibitive for large enzymatic systems. Recent developments in streaming computer architectures and new algorithms to accelerate path integral simulations now make these simulations practical for biological systems, allowing elucidation of enzymatic reactions in unprecedented detail. In this chapter, we summarize these recent developments and discuss practical considerations for applying AIMD and AIPIMD simulations to enzymes.
View details for DOI 10.1016/bs.mie.2016.05.047
View details for PubMedID 27498646

Nonadiabatic Dynamics in Atomistic Environments: Harnessing QuantumClassical Theory with Generalized Quantum Master Equations
JOURNAL OF PHYSICAL CHEMISTRY LETTERS
2015; 6 (23): 47434748
View details for DOI 10.1021/acs.jpclett.5b02131
View details for Web of Science ID 000366008500012

Accurate nonadiabatic quantum dynamics on the cheap: Making the most of mean field theory with master equations.
journal of chemical physics
2015; 142 (9): 094110?
View details for DOI 10.1063/1.4913686
View details for PubMedID 25747064

Accurate nonadiabatic quantum dynamics on the cheap: making the most of mean field theory with master equations.
journal of chemical physics
2015; 142 (9): 094110?
Abstract
In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MFGQME) approach is a nonperturbative and nonMarkovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MFGQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speedups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantumclassical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.
View details for DOI 10.1063/1.4913686
View details for PubMedID 25747064

Nonadiabatic Dynamics in Atomistic Environments: Harnessing QuantumClassical Theory with Generalized Quantum Master Equations.
The journal of physical chemistry letters
2015; 6 (23): 4743–48
Abstract
The development of methods that can efficiently and accurately treat nonadiabatic dynamics in quantum systems coupled to arbitrary atomistic environments remains a significant challenge in problems ranging from exciton transport in photovoltaic materials to electron and proton transfer in catalysis. Here we show that our recently introduced MFGQME approach, which combines Ehrenfest mean field theory with the generalized quantum master equation framework, is able to yield quantitative accuracy over a wide range of chargetransfer regimes in fully atomistic environments. This is accompanied by computational speedups of up to 3 orders of magnitude over a direct application of Ehrenfest theory. This development offers the opportunity to efficiently investigate the atomistic details of nonadiabatic quantum relaxation processes in regimes where obtaining accurate results has previously been elusive.
View details for PubMedID 26563917

Quantum delocalization of protons in the hydrogenbond network of an enzyme active site.
Proceedings of the National Academy of Sciences of the United States of America
2014; 111 (52): 1845418459
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 hydrogenbonded tyrosine residues within the active site of the enzyme ketosteroid isomerase (KSI) facilitates quantum proton delocalization. This delocalization dramatically stabilizes the deprotonation of an activesite tyrosine residue, resulting in a very large isotope effect on its acidity. When an intermediate analog is docked, it is incorporated into the hydrogenbond 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 hydrogenbond 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 PubMedID 25503367
View details for PubMedCentralID PMC4284547

Quantum fluctuations and isotope effects in ab initio descriptions of water
JOURNAL OF CHEMICAL PHYSICS
2014; 141 (10)
Abstract
Isotope substitution is extensively used to investigate the microscopic behavior of hydrogen bonded systems such as liquid water. The changes in structure and stability of these systems upon isotope substitution arise entirely from the quantum mechanical nature of the nuclei. Here, we provide a fully ab initio determination of the isotope exchange free energy and fractionation ratio of hydrogen and deuterium in water treating exactly nuclear quantum effects and explicitly modeling the quantum nature of the electrons. This allows us to assess how quantum effects in water manifest as isotope effects, and unravel how the interplay between electronic exchange and correlation and nuclear quantum fluctuations determine the structure of the hydrogen bond in water.
View details for DOI 10.1063/1.4894287
View details for Web of Science ID 000342209400040

Quantum fluctuations and isotope effects in ab initio descriptions of water.
journal of chemical physics
2014; 141 (10): 104502?
Abstract
Isotope substitution is extensively used to investigate the microscopic behavior of hydrogen bonded systems such as liquid water. The changes in structure and stability of these systems upon isotope substitution arise entirely from the quantum mechanical nature of the nuclei. Here, we provide a fully ab initio determination of the isotope exchange free energy and fractionation ratio of hydrogen and deuterium in water treating exactly nuclear quantum effects and explicitly modeling the quantum nature of the electrons. This allows us to assess how quantum effects in water manifest as isotope effects, and unravel how the interplay between electronic exchange and correlation and nuclear quantum fluctuations determine the structure of the hydrogen bond in water.
View details for DOI 10.1063/1.4894287
View details for PubMedID 25217932

Multiple time step integrators in ab initio molecular dynamics.
journal of chemical physics
2014; 140 (8): 084116?
Abstract
Multiple timescale algorithms exploit the natural separation of timescales 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 timescale 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 timescale 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 BornOppenheimer 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

InterfaceLimited Growth of Heterogeneously Nucleated Ice in Supercooled Water
JOURNAL OF PHYSICAL CHEMISTRY B
2014; 118 (3): 752760
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 selfassembly 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
2013; 139 (1)
Abstract
The quantumclassical 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 fewestswitches surface hopping and mean field approaches fail to obtain either the correct rates or longtime 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
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 quasiharmonic 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

RingPolymer Molecular Dynamics: Quantum Effects in Chemical Dynamics from Classical Trajectories in an Extended Phase Space
ANNUAL REVIEW OF PHYSICAL CHEMISTRY, VOL 64
2013; 64: 387413
Abstract
This article reviews the ringpolymer molecular dynamics model for condensedphase quantum dynamics. This model, which involves classical evolution in an extended ringpolymer phase space, provides a practical approach to approximating the effects of quantum fluctuations on the dynamics of condensedphase systems. The review covers the theory, implementation, applications, and limitations of the approximation.
View details for DOI 10.1146/annurevphyschem040412110122
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 PHYSICSCONDENSED MATTER
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 intramolecular OD and OH bond distances of 0.985(5) and 0.990(5) Å, were found to be in best agreement with those obtained by using the flexible anharmonic TTM3F water model. Both techniques show a difference of ≃ 0.5% between the OD and OH intramolecular 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 intramolecular and intermolecular quantum contributions. Further consideration of the OO correlations is needed in order to improve agreement with experiment.
View details for DOI 10.1088/09538984/24/28/284126
View details for Web of Science ID 000305786400028
View details for PubMedID 22738936

Zeidler et al. Reply
PHYSICAL REVIEW LETTERS
2012; 108 (25)
View details for DOI 10.1103/PhysRevLett.108.259604
View details for Web of Science ID 000305569200010

Growing PointtoSet Length Scale Correlates with Growing Relaxation Times in Model Supercooled Liquids
PHYSICAL REVIEW LETTERS
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 "pointtoset" 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
2012; 109 (21): 79887991
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 widerange 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
View details for PubMedCentralID PMC3361433

Reduced density matrix hybrid approach: Application to electronic energy transfer
JOURNAL OF CHEMICAL PHYSICS
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 FennaMatthewsOlson 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
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 modecoupling 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 nonadiabatic quantum dynamics
JOURNAL OF CHEMICAL PHYSICS
2012; 136 (3)
Abstract
We present a new approach to calculate realtime 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 spinboson 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 systembath 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
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 OH and OD pair correlations are in excellent agreement with path integral molecular dynamics simulations, both techniques showing a difference of ≃0.5% between the OH and OD 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
2011; 7 (2): 134137
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
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
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, frequencyoptimized sampling. The sampling efficiencies of these thermostats are compared with that of the more conventional NoséHoover chain (NHC) thermostat for a number of physically relevant properties of the liquid water and hydrogeninpalladium 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 nearoptimum 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
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 longrange 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 Tholetype 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
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, qTIP4P/F, in which the OH stretches are described by Morsetype functions. We have parametrized this model to give the correct liquid structure, diffusion coefficient, and infrared absorption frequencies in quantum (path integralbased) 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 hydrogenbonding 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 OH 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
2008; 464 (46): 256261
View details for DOI 10.1016/j.cplett.2008.09.019
View details for Web of Science ID 000260259000026

An efficient ring polymer contraction scheme for imaginary time path integral simulations
JOURNAL OF CHEMICAL PHYSICS
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 shortrange and slowly varying longrange contributions. For such systems, the computational effort of the path integral simulation can be reduced considerably by evaluating the longrange forces on a contracted ring polymer with fewer beads than are needed to evaluate the shortrange 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 oxygenoxygen LennardJones 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 32bead 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
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 (8361 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 caxis 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