Research

The Markland group develops and applies theoretical and computational methods to describe and elucidate the chemical dynamics of condensed phase quantum processes in disordered chemical environments, ranging from electronic energy transfer in molecular systems to proton transfer in enzyme active sites or proton exchange membranes and electron transfer at electrochemical surfaces, which are ubiquitous in systems of current interest. These processes are inherently quantum mechanical and understanding them often requires developing methods to accurately treat the quantum nature of both the electrons and nuclei and to simulate and analyze their advanced spectroscopy. Underpinning all our research are the objectives of developing methods that can accurately and efficiently simulate chemical systems and of using these tools to reveal fundamental insights into concepts that govern the reactivity and selectivity in disordered chemical systems. Our research intersects closely with experiments and synergistically develops new theoretical tools to directly target specific chemical systems and novel experiments. The Markland group is the main development base for the OpenMM software ecosystem (including software such as OpenMM, OpenMM-ML, and PDBFixer), with the main OpenMM package receiving 2.1 million downloads in 2025.

Theoretical and simulation methods that occur frequently in our research include:

The path integral formulation of quantum mechanics
Generalized quantum and classical master equations
Semiclassical methods and mapping
Electronic structure theory
Machine learning
Ab initio molecular dynamics

Please contact us for full details of upcoming projects and openings. The table of contents below can be used to navigate summaries of some of our recent and historical research interests and representative publications, but for the most up-to-date research, please see our publications and Google Scholar pages.

Structure Elucidation and Prediction from Spectroscopy using Machine Learning

Machine Learning Electronic Surfaces

Excited States and Reactive Systems

Biochemical Systems

Software for Molecular Simulation and Machine Learning

Electronic Structure and Dynamics of Electron and Hole Transfer

Theoretical and Simulation Methods for Treating Condensed Phase Quantum Processes

Ground State Processes

Excited State Processes

Spectroscopy and Reactivity at Interfaces

Exploiting Timescale Separation for Efficient Simulations

Quantum Dynamics

Classical Dynamics and Biochemical Processes

Hydrogen Bonding and Proton Transport

Developing Approaches to Simulate Novel Spectroscopies

Enzymes and Electric Fields in Condensed Phase Systems.

Isotope Fractionation

Glassy Systems

Structure Elucidation and Prediction from Spectroscopy using Machine Learning

Rapid determination of molecular structures can greatly accelerate workflows across many chemical disciplines. However, elucidating structure using only spectra remains an extremely challenging problem because of the combinatorial explosion of the number of possible molecules as the number of constituent atoms is increased. Our work in this area has shown how using machine learning based frameworks one can make complete structure elucidation from routinely collected 1D NMR spectra for molecules of up to 19 heavy (non-hydrogen) atoms, a size for which there are trillions of possible structures. Without relying on any prior chemical knowledge such as the molecular formula, we have shown that our approach predicts the exact molecule 69.6% of the time within the first 15 predictions, reducing the search space by up to 11 orders of magnitude.

Above: Overview of the full multitask structure elucidation workflow (top) and substructure-to-structure workflow (bottom) for structure elucidation from NMR spectra.

Representative publications

Pushing the Limits of One-dimensional NMR Spectroscopy for Automated Structure Elucidation Using Artificial Intelligence

F. Hu, J. M. Tubb, D. Argyropoulos, S. Golotvin, M. Elyashberg, G. M. Rotskoff, M. W. Kanan, and T. E. Markland

J. Chem. Inf. Model. 66, 12, 6992-7002 (2026)

Accurate and efficient structure elucidation from routine one-dimensional NMR spectra using multitask machine learning.
F. Hu, M. S. Chen, G. M. Rotskoff, M. W. Kanan, and T. E. Markland ACS Cent. Sci., 10, 11, 2162–2170 (2024)
A framework for automated structure elucidation from routine NMR spectra. Z. Huang, M. S. Chen, C. P. Woroch, T. E. Markland, and M. W. Kanan Chem. Sci., 12, 15329 (2021)

Machine Learning Electronic Surfaces

Machine-learned potential energy surfaces offer the ability to obtain the accuracy of ab initio molecular dynamics at a computational cost comparable to molecular mechanics. Our work focuses on developing datasets and highly data-efficient strategies to develop accurate machine-learned models of condensed-phase ground- and excited-state potential energy surfaces.

Excited States and Reactive Systems

Machine learning potentials are an appealing way to simulate excited state and reactive systems on long, previously inaccessible timescales by avoiding the need to perform electronic structure calculations at every time step. For example, we have shown how one can train a machine-learned model to capture processes in liquid water like autoionization, along with hydroxide and proton transport. We have also shown how one can harness transfer learning to go beyond a DFT description of the electronic structure and provide condensed phase surfaces at the AFQMC and CCSD(T) levels of accuracy for ground state systems. For excited states, we have shown how using EOM-CCSD gives a physically different picture of the coupling of electronic excitations to the hydrogen bonding of the GFP anion in water. This research is motivated by the fact that capturing many interesting and relevant heterogeneous chemical systems such as those with extended interfaces (e.g. electrochemical interfaces, nanopores, proteins, or biological channels) requires treating larger systems and longer timescales than is currently possible with ab initio molecular dynamics, where the forces on the atoms are computed using electronic structure theory.

Above: A workflow for generating 2D electronic spectra using a neural network model of the electronic energy gap between the ground and first excited state of a biological chromophore in solution.

Above: A workflow for generating a machine learned potential of liquid water at CCSD, CCSD(T) and AFQMC accuracy by transfer learning from DFT.

Above: The free energy associated with aqueous proton transfer between hydronium and water (left) and hydroxide and water comparing AIMD (grey background) with a neural network potential (blue line).

Representative publications

Two-dimensional electronic spectroscopy in the condensed phase using equivariant transformer accelerated molecular dynamics simulations J. Kelly, F. Hu, A. Damiani, M. S. Chen, A. Snider, M. Son, A. Lee, P. Gupta, A. Montoya-Castillo, T. J. Zuehlsdorff, G. S. Schlau-Cohen, C. M. Isborn, and T. E. Markland J. Phys. Chem. Lett., 16, 5561-5569 (2025)
Developing machine-learned potentials to simultaneously capture the dynamics of excess protons and hydroxide ions in classical and path integral simulations. A. O. Atsango, T. Morawietz, O. Marsalek, and T. E. Markland J. Chem. Phys., 159, 074101 (2023)
Elucidating the role of hydrogen bonding in the optical spectroscopy of the solvated green fluorescent protein chromophore: using machine learning to establish the importance of high-level electronic structure. M. S. Chen, Y. Mao, A. Snider, P. Gupta, A. Montoya-Castillo, T. J. Zuehsldorff, C. M. Isborn, and T. E. Markland J. Phys. Chem. Lett., 14, 29, 6610 (2023)
Data-Efficient Machine Learning Potentials from Transfer Learning of Periodic Correlated Electronic Structure Methods: Liquid Water at AFQMC, CCSD, and CCSD(T) Accuracy. M. S. Chen, J. Lee, H.-Z. Ye, T. C. Berkelbach, D. R. Reichman and T. E. Markland J. Chem. Theory Comput. 19, 14, 4510 (2023)
Characterizing and contrasting structural proton transport mechanisms in azole hydrogen bond networks using ab initio molecular dynamics. A. O. Atsango, M. E. Tuckerman and T. E. Markland J. Phys. Chem. Lett., 12, 8749 (2021)

Biochemical Systems

Machine-learned Interatomic Potentials (MLIPs) provide a route to improve the accuracy of biochemical simulations compared to classical force fields. To further this goal, our work in this area has introduced new datasets (SPICE) for training potentials relevant to simulating drug-like small molecules interacting with proteins and have produced MLIP models (Nutmeg) from them. We are also interested in methods to bridge MLIPs and molecular mechanics force fields (ML/MM). Just as QM/MM simulations use quantum mechanics for only a small piece of a system while simulating the rest with classical mechanics, ML/MM simulations can simulate part with machine learning and the rest with a classical molecular mechanics force field. This can lead to considerable improvements in accuracy at a computational cost that is ~1000 lower than performing a QM/MM simulation.

Above: Simulation snapshot of the GFP anion in water simulated using an equivariant transformer-based machine-learned potential.

Above: Comparison of the probability distribution of a dihedral of GFP in water comparing the result obtained from the machine learned potential and that obtained from ab initio molecular dynamics.

Representative publications

Accuracy and Efficiency Benchmarks of Pretrained Machine Learning Potentials for Molecular Simulations P. Eastman, E. Pretti, and T. E. Markland J. Chem. Theory Comput., 22, 12, 6108-6117 (2026)
Nutmeg and SPICE: Models and Data for Biomolecular Machine Learning. P. Eastman, B. P. Pritchard, J. D. Chodera, and T. E. Markland, J. Chem. Theory Comput., 20, 19, 8583–8593 (2024)
Enhancing Protein-Ligand Binding Affinity Predictions using Neural Network Potentials. F. Sabanes Zariquiey, R. Galvelis, E. Gallicchio, J. D. Chodera, T. E. Markland, G. De Fabritiis J. Chem. Inf. Model. (2024)
OpenMM 8: Molecular Dynamics Simulation with Machine Learning Potentials. P. Eastman, R. Galvelis, R. P. Peláez, C. R. A. Abreu, S. E. Farr, E. Gallicchio, A. Gorenko, M. M. Henry, F. Hu, J. Huang, A. Krämer, J. Michel, J. A. Mitchell, V. S. Pande, J. PGLM Rodrigues, J. Rodriguez-Guerra, A. C. Simmonett, S. Singh, J. Swails, P. Turner, Y. Wang, I. Zhang, J. D. Chodera, G. De Fabritiis, and T. E. Markland J. Phys. Chem. B, 128, 1, 109-116 (2024)
SPICE: A Dataset of Drug-like Molecules and Peptides for Training Machine Learning Potentials. P. Eastman, P. Kumar Behara, D. L. Dotson, R. Galvelis, J. E. Herr, J. T. Horton, Y. Mao, J. D. Chodera, B. B. Pritchard, Y. Wang, G. De Fabritiis and T. E. Markland Scientific Data, 10, 11 (2023)
NNP/MM: Fast molecular dynamics simulations with machine learning potentials and molecular mechanics. R. Galvelis, A. Varela-Rial, S. Doerr, R. Fino, P. Eastman, T. E. Markland, J. D. Chodera, and G. De Fabritiis J. Chem. Inf. Model., 63, 18, 5701–5708 (2023)

Software for Molecular Simulation and Machine Learning

The Markland Group (via lead software developer Dr. Peter Eastman and Dr. Evan Pretti) is the primary developer of the OpenMM software ecosystem. OpenMM is a widely used toolkit for molecular simulation and modeling (>7.4 million downloads). It provides a unique combination of excellent performance on GPUs and extreme flexibility. Through a mix of Python scripting, custom forces, custom integrators, PyTorch integration, and plugins, it allows users to define entirely new algorithms, force fields, and simulation protocols that in other packages would require far more effort and/or code changes to the core library. It is used both as a standalone simulation package and as an internal simulation engine within other important projects. OpenMM's features are constantly evolving - one particular recent focus has been on supporting a wide range of foundational and user-defined Machine Learned Interatomic Potentials (MLIPs) and their integration into systems containing Molecular Mechanics (MM) potentials via OpenMM-ML.

Representative publications

OpenMM 8: Molecular Dynamics Simulation with Machine Learning Potentials. P. Eastman, R. Galvelis, R. P. Peláez, C. R. A. Abreu, S. E. Farr, E. Gallicchio, A. Gorenko, M. M. Henry, F. Hu, J. Huang, A. Krämer, J. Michel, J. A. Mitchell, V. S. Pande, J. PGLM Rodrigues, J. Rodriguez-Guerra, A. C. Simmonett, S. Singh, J. Swails, P. Turner, Y. Wang, I. Zhang, J. D. Chodera, G. De Fabritiis, and T. E. Markland J. Phys. Chem. B, 128, 1, 109-116 (2024)
TorchMD-Net 2.0: Fast Neural Network Potentials for Molecular Simulations. R. P. Pelaez, G. Simeon, R. Galvelis, A. Mirarchi, P. Eastman, P. Thölke, T. E. Markland, and G. De Fabritiis J. Chem. Theory Comput., 20, 10, 4076-4087 (2024)
NNP/MM: Fast molecular dynamics simulations with machine learning potentials and molecular mechanics. R. Galvelis, A. Varela-Rial, S. Doerr, R. Fino, P. Eastman, T. E. Markland, J. D. Chodera, and G. De Fabritiis J. Chem. Inf. Model., 63, 18, 5701–5708 (2023)
AENET-LAMMPS and AENET-TINKER: Interfaces for accurate and efficient molecular dynamics simulations with machine learning potentials M. S. Chen, T. Morawietz, H. Mori, T. E. Markland and N. Artrith J. Chem. Phys., 155, 074801 (2021)
i-PI 2.0: A universal force engine for advanced molecular simulations. V. Kapil, M. Rossi, O. Marsalek, R. Petraglia, Y. Litman, T. Spura, B. Cheng, A. Cuzzocrea, R. H. Meissner, D. M. Wilkins, P. Juda, S. P. Bienvenue, J. Kessler, I. Poltavsky, S. Vandenbrande, J. Wieme, C. Corminboeuf, T. D. Kuhne, D. E. Manolopoulos, T. E. Markland, J. O. Richardson, A. Tkatchenko, G. A. Tribello, V. Van Speybroeck and M. Ceriotti Comp. Phys. Comm., 236, 214-223 (2019)

Electronic Structure and Dynamics of Electron and Hole Transfer

Electron transfer and hole transfer are fundamental steps in many chemical and biochemical processes, ranging from charge and energy transport in photovoltaic materials to electrocatalysis and enzyme-catalyzed reactions. Accurately capturing these processes requires treating the quantum dynamics and electronic structure of large systems including donor and acceptor molecules or electrodes and their solvation environments. We have developed methods for generating chemically intuitive diabatic states as well as generalized mapping approaches for treating the coupled nuclear and electronic quantum dynamics.

Representative publications

Electron transfer at electrode interfaces via a straightforward quasiclassical fermionic mapping approach. K. A. Jung. J. Kelly, and T. E. Markland J. Chem. Phys., 159, 014109 (2023)
Excited state diabatization on the cheap using DFT: Photoinduced electron and hole transfer. Y. Mao, A. Montoya-Castillo and T. E. Markland J. Chem. Phys., 153, 244111 (2020)
A derivation of the conditions under which bosonic operators exactly capture fermionic structure and dynamics. A. Montoya-Castillo and T. E. Markland J. Chem. Phys., 158, 094112 (2023)
Accurate and efficient DFT-based diabatization for hole and electron transfer using absolutely localized molecular orbitals. Y. Mao, A. Montoya-Castillo and T. E. Markland J. Chem. Phys., 151, 164114 (2019)
On the exact continuous mapping of fermions. A. Montoya-Castillo and T. E. Markland Sci. Rep., 8, 12929 (2018)

Theoretical and Simulation Methods for Treating Condensed Phase Quantum Processes

Quantum structure and dynamics play an important role in many fundamental processes such as proton and electron transfer, vibrational relaxation, and electronic energy transfer. However, due to the large computational cost associated with solving the many-body quantum problem for systems of more than a few degrees of freedom approximations are necessary. Given the wide range of problems of interest in this area one must pick the correct quantum dynamics approach for a given application or often create new ones to obtain the correct balance between speed and accuracy. In particular, we develop approaches based on the path integral formalism of quantum mechanics, semiclassical mapping and methods that exploit timescale separation via generalized quantum master equations.

Ground State Processes

Path integral simulations provide an elegant method by which quantum fluctuations, such as zero-point energy and tunneling, can be included in complex systems. The imaginary time path integral formalism exploits the exact isomorphism between a set of quantum mechanical particles and that of a classical set of "ring polymers". As such, path integral simulations can be used to calculate exactly static equilibrium properties of quantum systems and also provide the basis for many successful approaches to treat quantum dynamics in the condensed phase. To improve the efficiency of these methods, we introduced the ring polymer contraction approach, which reduces the cost of performing path integral simulations by up to two orders of magnitude. This allows one to perform a simulation that includes the effects of zero-point energy and tunneling for a computational cost barely more than a classical simulation of the same system. We have also developed efficient path integral Langevin equation schemes to thermostat path integral simulations, as well as methods to compute isotope effects in chemical systems efficiently.

Above: A depiction of the isomorphism between a quantum mechanical particle and a classical ring polymer which arises in the imaginary time path integral formalism.

Representative publications

Nuclear quantum effects enter the mainstream. T. E. Markland and M. Ceriotti, Nature Rev. Chem., 2, 0109 (2018)
Ab initio molecular dynamics with nuclear quantum effects at classical cost: ring polymer contraction for density functional theory. O. Marsalek and T. E. Markland, J. Chem. Phys. 144, 054112 (2016)
Efficient methods and practical guidelines for simulating isotope effects. M. Ceriotti and T. E. Markland, J. Chem. Phys. 138, 014112 (2013)
Efficient stochastic thermostatting of path integral molecular dynamics. M. Ceriotti, M. Parrinello, T. E. Markland and D. E. Manolopoulos, J. Chem. Phys. 133, 124104 (2010)
A fast path integral method for polarizable force fields. G. S. Fanourgakis, T. E. Markland and D. E. Manolopoulos, J. Chem. Phys. 131, 094102 (2009)
A refined ring polymer contraction scheme for systems with electrostatic interactions. T. E. Markland and D. E. Manolopoulos, Chem. Phys. Lett. 464, 256-261 (2008)
An efficient ring polymer contraction scheme for imaginary time path integral simulations. T. E. Markland and D. E. Manolopoulos, J. Chem. Phys. 129, 024105 (2008)

Excited State Processes

Our work on excited state non-adiabatic quantum dynamics has focused on developing approaches that are compatible with atomistic simulations of these processes in condensed phase environments including electronic energy transfer, electron transfer, and the simulation of spectroscopic observables such as 2D electronic spectra.

Representative publications

Two-dimensional Electronic Spectra from Trajectory-based dynamics: Pure-state Ehrenfest and Spin-mapping Approaches. A. Z. Lieberherr, J. Kelly, J. E. Runeson, T. E. Markland, and D. E. Manolopoulos J. Chem. Phys., 163, 214111 (2025)
Electron transfer at electrode interfaces via a straightforward quasiclassical fermionic mapping approach. K. A. Jung. J. Kelly, and T. E. Markland J. Chem. Phys., 159, 014109 (2023)
An accurate and efficient Ehrenfest dynamics approach for calculating linear and nonlinear electronic spectra. A. O. Atsango, A. Montoya-Castillo and T. E. Markland J. Chem. Phys., 158, 074107 (2023)
A derivation of the conditions under which bosonic operators exactly capture fermionic structure and dynamics. A. Montoya-Castillo and T. E. Markland J. Chem. Phys., 158, 094112 (2023)
Efficient construction of generalized master equation memory kernels for multi-state systems from nonadiabatic quantum-classical dynamics. W. C. Pfalzgraff, A. Montoya-Castillo, A. Kelly and T. E. Markland J. Chem. Phys., 150, 244109 (2019)
On the exact continuous mapping of fermions. A. Montoya-Castillo and T. E. Markland Sci. Rep., 8, 12929 (2018)
Generalized Quantum Master Equations In and Out of Equilibrium: When Can One Win? A. Kelly, A. Montoya-Castillo, L. Wang and T. E. Markland J. Chem. Phys. 144, 184105 (2016)
Nonadiabatic dynamics in atomistic environments: harnessing quantum-classical theory with generalized quantum master equations. W. C. Pfalzgraff, A. Kelly and T. E. Markland J. Phys. Chem. Lett., 6, 4743-4748 (2015)
Accurate nonadiabatic quantum dynamics on the cheap: making the most of mean field theory with master equations. A. Kelly, N. J. Brackbill and T. E. Markland J. Chem. Phys. 142, 094110 (2015)
Efficient and accurate surface hopping for long time nonadiabatic quantum dynamics. A. Kelly and T. E. Markland J. Chem. Phys. 139, 014104 (2013)
Reduced density matrix hybrid approach: Application to electronic energy transfer. T. C. Berkelbach, T. E. Markland and D. R. Reichman J. Chem. Phys., 136, 084104 (2012)
Reduced density matrix hybrid approach: An efficient and accurate method for adiabatic and non-adiabatic quantum dynamics. T. C. Berkelbach, D. R. Reichman and T. E. Markland J. Chem. Phys. 136, 034113 (2012)

Spectroscopy and Reactivity at Interfaces

Ion and proton structure and kinetics at liquid-liquid and solid-liquid electrochemical interfaces can be used to control their reactivity and selectivity. Our work in this area seeks to understand this by working with experimental groups to integrate molecularly precise, tunable measurements with advances in theoretical approaches for simulating these interfaces.

Representative publications

Ion-exchange-mediated pre-association gates interfacial PCET. N. B. Lewis, J. Kelly, J. G. Gardner, N. K. Razdan, S. Ardo, T. E. Markland, and Y. Surendranath, Chem, 12, 3, 102813 (2025)
Proton-transfer Kinetics at Liquid-liquid Interfaces. N. D’Antona, J. Kelly, N. Barnard, S. Ardo, Y. Wang, Y. Surendranath, T. E. Markland, P. A. Kempler, and S. Boettcher, J. Am. Chem. Soc., 147, 25, 21408-21418 (2025)
Electron transfer at electrode interfaces via a straightforward quasiclassical fermionic mapping approach. K. A. Jung. J. Kelly, and T. E. Markland J. Chem. Phys., 159, 014109 (2023)
Electrostatic control of regioselectivity in Au(I)-catalyzed hydroarylation. V. M. Lau, W. C. Pfalzgraff, T. E. Markland and M. W. Kanan J. Am. Chem. Soc., 139 (11), 4035-4041 (2017)
Unraveling the dynamics and structure of functionalized self-assembled monolayers on gold using 2D IR spectroscopy and MD simulations. C. Yan, R. Yuan, W. C. Pfalzgraff, J. Nishida, L. Wang, T. E. Markland, M. D. Fayer Proc. Natl. Acad. Sci., 113 (18), 4929-4934 (2016)

Exploiting Timescale Separation for Efficient Simulations

Quantum and classical dynamics processes in complex systems often occur across timescales spanning many orders of magnitude. This poses a challenge for atomistic-scale simulation methods since capturing all the relevant processes can require billions or trillions of time steps. The Generalized Master Equation (GME) and Generalized Quantum Master Equation (GQME) frameworks provide a formalism from which elegant approaches to alleviate these timescale issues can be obtained. We have provided methods and frameworks for exploiting GQMEs and GMEs for efficiently simulating quantum and classical processes, offering many orders of magnitude computational speed-ups while also providing physical insights into the timescales of the underlying physical processes.

Quantum Dynamics

We have shown how Generalized Quantum Master Equations (GQMEs) can be used to improve both the accuracy and efficiency of semiclassical methods and demonstrated these advantages in both model systems and fully atomistic simulations.

Above: Excitation dynamics in a model of the FMO complex. The solid line arrows correspond to an unshifted bath initial condition and subsequent excitation dynamics, whereas the dotted line arrow corresponds to an initial bath condition shifted to the minimum of site 1 in the complex, which leads to trapping of the excitation.

Representative publications

Efficient construction of generalized master equation memory kernels for multi-state systems from nonadiabatic quantum-classical dynamics. W. C. Pfalzgraff, A. Montoya-Castillo, A. Kelly and T. E. Markland J. Chem. Phys., 150, 244109 (2019)
Generalized Quantum Master Equations In and Out of Equilibrium: When Can One Win? A. Kelly, A. Montoya-Castillo, L. Wang and T. E. Markland J. Chem. Phys. 144, 184105 (2016)
Nonadiabatic dynamics in atomistic environments: harnessing quantum-classical theory with generalized quantum master equations. W. C. Pfalzgraff, A. Kelly and T. E. Markland J. Phys. Chem. Lett., 6, 4743-4748 (2015)
Accurate nonadiabatic quantum dynamics on the cheap: making the most of mean field theory with master equations. A. Kelly, N. J. Brackbill and T. E. Markland J. Chem. Phys. 142, 094110 (2015)
Efficient and accurate surface hopping for long time nonadiabatic quantum dynamics. A. Kelly and T. E. Markland J. Chem. Phys. 139, 014104 (2013)

Classical Dynamics and Biochemical Processes

Biomolecular processes occur over a wide range of timescales. We have shown how methods based on the Generalized Master Equation formalism, inspired by ideas originally developed for GQMEs, can go beyond previous Markovian (memoryless) theories, allowing for a dramatic reduction in the amount of simulation data required to construct physically interpretable models of biomolecular processes. We have also shown how one can exploit the inherent differences in the timescale of the interactions between particles to develop efficient multiple-timescale integration schemes for molecular dynamics simulations.

Above: Ability of our GME approach to accurately predict the dynamics of the FiP35 WW domain.

Above: Using the GLE-RESPA approach the Ramachandran plot of alanine dipeptide can be accurately obtained using time-steps of in excess of 12fs. Using standard multiple time-step techniques only 2fs is possible.

Representative publications

Building insightful, memory-enriched models to capture long-time biochemical processes from short-time simulations. A. J. Dominic III, T. Sayer, S. Cao, T. E. Markland, X. Huang, and A. Montoya-Castillo Proc. Natl. Acad. Sci., 120 (12) e2221048120 (2023)
On the Advantages of Exploiting Memory in Markov State Models for Biomolecular Dynamics. S. Cao, A. Montoya-Castillo, W. Wang, T. E. Markland and X. Huang J. Chem. Phys., 153, 014105 (2020)
Multiple Time Step Integrators in Ab Initio Molecular Dynamics. N. Luehr, T. E. Markland and T. J. Martinez J. Chem. Phys., 140, 084116 (2014)
Efficient multiple time scale molecular dynamics: Using colored noise thermostats to stabilize resonances. J. A. Morrone, T. E. Markland, M. Ceriotti and B. J. Berne J. Chem. Phys. 134, 014103 (2011)

Hydrogen Bonding and Proton Transport

Hydrogen bonded systems play vital roles in areas ranging from chemistry to biology to materials science and geology. Hydrogen bonding also provides a mechanism for water to autoionize and efficiently transport its ionization products through its hydrogen bond network. This fundamental characteristic of water underlies multiple processes ranging from acid–base chemistry to the operation of proton exchange membrane fuel cells and voltage-gated proton channels in biological cell membranes. We have characterized proton transport pathways in systems like imidazole, utilized ab initio molecular dynamics and machine learned potentials to observe proton transport in water, and demonstrated opposing quantum effects in hydrogen bonded systems. We have also demonstrated that hydrogen bonded systems, such as water, exhibit two different and opposite nuclear quantum effects (“competing quantum effects”). The former of these is due to the long appreciated disruption of the hydrogen bond network which leads to destruction of the liquid and faster dynamics. However, a second effect exists in which the quantum kinetic energy in the OH covalent bond allows it to stretch and form shorter and stronger hydrogen bonds, which partially cancels the disruptive effect.

Above: Schematic representation of the two competing quantum effects present in water. The degree of cancellation is sensitive to properties such as the OH bond anharmonicity, temperature and pressure.

Above: Proton transfer in liquid imidazole from ab initio molecular dynamics simulations.

Representative publications

Developing machine-learned potentials to simultaneously capture the dynamics of excess protons and hydroxide ions in classical and path integral simulations. A. O. Atsango, T. Morawietz, O. Marsalek, and T. E. Markland J. Chem. Phys., 159, 074101 (2023)
Elucidating the role of hydrogen bonding in the optical spectroscopy of the solvated green fluorescent protein chromophore: using machine learning to establish the importance of high-level electronic structure. M. S. Chen, Y. Mao, A. Snider, P. Gupta, A. Montoya-Castillo, T. J. Zuehsldorff, C. M. Isborn, and T. E. Markland J. Phys. Chem. Lett., 14, 29, 6610 (2023)
Characterizing and contrasting structural proton transport mechanisms in azole hydrogen bond networks using ab initio molecular dynamics. A. O. Atsango, M. E. Tuckerman and T. E. Markland J. Phys. Chem. Lett., 12, 8749 (2021)
Elucidating the proton transport pathways in liquid imidazole. Z. Long, A. O. Atsango, J. A. Napoli, T. E. Markland and M. E. Tuckerman J. Phys. Chem. Lett., 11, 6156-6163 (2020)
Resolving heterogeneous dynamics of excess protons in aqueous solution with rate theory. S. Roy, G. K. Schenter, J. A. Napoli, M. D. Baer, T. E. Markland and C. J. Mundy J. Phys. Chem. B, 124, 27, 5665-5675 (2020)
Hiding in the crowd: Spectral signatures of overcoordinated hydrogen bond environments. T. Morawietz, A. Urbina, P. K. Wise, X. Wu, W. Lu, D. Ben-Amotz and T. E. Markland J. Phys. Chem. Lett., 10, 6067-6073 (2019)
Tracking aqueous proton transfer by 2D-IR spectroscopy and ab initio molecular dynamics simulations. R. Yuan, J. A. Napoli, C. Yan, O. Marsalek, T. E. Markland and M. D. Fayer ACS Cent. Sci., 5, 1269-1277 (2019)
The quest for accurate liquid water properties from first principles. L. R. Pestana, O. Marsalek, T. E. Markland and T. Head-Gordon J. Phys. Chem. Lett., 9, 5009-5016 (2018)
Unraveling the influence of quantum proton delocalization on electronic charge transfer through the hydrogen bond. C. Schran, O. Marsalek and T. E. Markland Chem. Phys. Lett., Frontiers, 678, 289-295 (2017)
Isotope effects in water as investigated by neutron diffraction and path integral molecular dynamics. A. Zeidler, P. S. Salmon, H. E. Fischer, J. C. Neuefeind, J. M. Simonson and T. E. Markland J. Phys. Condens. Mat. 24, 284126 (2012)
Oxygen as a Site Specific Probe of the Structure of Water and Oxide Materials. A. Zeidler, P. S. Salmon, H. E. Fischer, J. C. Neuefeind, J. M. Simonson, H. Lemmel, H. Rauch, and T. E. Markland Phys. Rev. Lett., 107, 145501 (2011)
Competing quantum effects in the dynamics of a flexible water model. S. Habershon, T. E. Markland and D. E. Manolopoulos J. Chem. Phys. 131, 024501 (2009)
Proton network flexibility enables robustness and large electric fields in the ketosteroid isomerase active site. L. Wang, S. D. Fried and T. E. Markland J. Phys. Chem. B., 121 (42), 9807-9815 (2017)
Quantum delocalization of protons in the hydrogen bond network of an enzyme active site. L. Wang, S. D. Fried, S. G. Boxer and T. E. Markland Proc. Natl. Acad. Sci., 111 (52), 18454-18459 (2014)

Developing Approaches to Simulate Novel Spectroscopies

Linear and nonlinear spectroscopies and scattering techniques are a powerful tool for probing the structure and dynamics of chemical systems. Our work seeks to simulate and understand the information encoded in spectroscopies ranging from linear infrared, Raman, and electronic spectroscopies to their two-dimensional counterparts (2DES and 2DIR), as well as X-ray and neutron scattering and recent INXS experiments that harness optically induced anisotropy in time-resolved scattering.

Representative publications

Streamlining Analysis and Design of Two-Dimensional Electronic Spectroscopy using Machine Learning N. I. Hausman, J. Kelly, M. S. Chen, F. Hu, A. Lee, A. Montoya-Castillo, G. S. Schlau-Cohen, and T. E. Markland (2026)
Two-dimensional Electronic Spectra from Trajectory-based dynamics: Pure-state Ehrenfest and Spin-mapping Approaches. A. Z. Lieberherr, J. Kelly, J. E. Runeson, T. E. Markland, and D. E. Manolopoulos J. Chem. Phys., 163, 214111 (2025)
Two-dimensional electronic spectroscopy in the condensed phase using equivariant transformer accelerated molecular dynamics simulations J. Kelly, F. Hu, A. Damiani, M. S. Chen, A. Snider, M. Son, A. Lee, P. Gupta, A. Montoya-Castillo, T. J. Zuehlsdorff, G. S. Schlau-Cohen, C. M. Isborn, and T. E. Markland J. Phys. Chem. Lett., 16, 5561-5569 (2025)
2D spectroscopies from condensed phase dynamics: Accessing third-order response properties from equilibrium multi-time correlation functions. K. A. Jung and T. E. Markland J. Chem. Phys., 157, 094111 (2022)
An accurate and efficient Ehrenfest dynamics approach for calculating linear and nonlinear electronic spectra. A. O. Atsango, A. Montoya-Castillo and T. E. Markland J. Chem. Phys., 158, 074107 (2023)
Optically induced anisotropy in time-resolved scattering: Imaging molecular scale structure and dynamics in disordered media with experiment and theory. A. Montoya-Castillo, M. S. Chen, S. L. Raj, K. A. Jung, K. S. Kjaer, T. Morawietz, K. J. Gaffney, T. B. van Driel and T. E. Markland Phys. Rev. Lett., 129, 056001 (2022)
Optical spectra in the condensed phase: Capturing anharmonic and vibronic features using dynamic and static approaches. T. J. Zuehlsdorff, A. Montoya-Castillo, J. A. Napoli, T. E. Markland and C. M. Isborn J. Chem. Phys., 51, 074111 (2019)
Unraveling electronic absorption spectra using nuclear quantum effects: Photoactive yellow protein and green fluorescent protein chromophores in water. T. J. Zuehlsdorff, J. A. Napoli, J. M. Milanese, T. E. Markland and C. M. Isborn J. Chem. Phys., 149, 024107 (2018)
Decoding the spectroscopic features and timescales of aqueous proton defects. J. Napoli, O. Marsalek and T. E. Markland J. Chem. Phys., 148, 222833 (2018)

Enzymes and Electric Fields in Condensed Phase Systems.

We have recently used this concept to explain the anomalous acidity observed in the Ketosteroid isomerase enzyme active site where nuclear quantum delocalization leads to a 10,000 change in the acidity of a critical residue. These simulations, which include both electronic and nuclear quantum effects in the enzyme active site were made possible by combining our recent algorithmic advances as well as GPU accelerated electronic structure calculations.

Above: An ab initio QM/MM path integral simulation snapshot from our work on the ketosteroid isomerase (KSI) enzyme. The simulation consists of 50,000 atoms with the active site treated with electronic and nuclear quantum effects. Nuclear quantum effects lead to delocalization of protons throughout the enzyme active site stabilizing the intermediate.

Above: Simulations of the electric fields experienced by a C-D bond in different solvents can be used to calibrate it as a Stark probe, enabling its use to understand both the magnitude and direction of fields in the liver alcohol dehydrogenase (LADH) enzyme active site.

Representative publications

Beyond the Vibrational Stark Effect: Unraveling the Large Redshifts of Alkyne C-H Bond in Solvation Environments. C. Zheng, Y. Mao, T. E. Markland, and S. G. Boxer, J. Am. Chem. Soc., 147, 7, 6227–6235 (2025)
A two-directional vibrational probe reveals different electric field orientations in solution and an enzyme active site. C. Zheng, Y. Mao, J. Kozuch, A. O. Atsango, Z. Ji, T. E. Markland and S. G. Boxer, Nature Chem., 14, 891–897 (2022)
Tuning solvent organization and electrostatic environment via structural modification of solutes: Amide vs. non-amide carbonyls. S. D. E. Fried, C. Zheng, Y. Mao, T. E. Markland and S. G. Boxer J. Phys. Chem. B, 126, 31, 5876-5886 (2022)
Proton network flexibility enables robustness and large electric fields in the ketosteroid isomerase active site. L. Wang, S. D. Fried and T. E. Markland, J. Phys. Chem. B., 121 (42), 9807-9815 (2017)
Quantum delocalization of protons in the hydrogen bond network of an enzyme active site. L. Wang, S. D. Fried, S. G. Boxer and T. E. Markland, Proc. Natl. Acad. Sci., 111 (52), 18454-18459 (2014)

Isotope Fractionation

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 has a number of fortuitous consequences, which are utilized in hydrology and geology. For instance, by comparing the ratio of H to D, one can estimate the origins of a water sample, the temperature at which it was formed, and the altitude at which precipitation occurred. Fractionation therefore provides both an excellent test of the ability of theory to accurately predict the magnitude of quantum effects in hydrogen bonded systems and also allows insights into fractionation processes in the world's climate. Our previous work in this area has demonstrated the importance of anharmonicty in correctly describing H/D fractionation between liquid water and its vapor. We have recently developed new approaches to efficiently compute isotope effects from path integral calculations and applied them to show that ab initio prediction of fractionation ratios for systems found in the earth's climate can be achieved.

Above: A depiction of the equilibrium which determines H/D fractionation between liquid water and its vapor. The free energy change associated with the process would be zero in the absence of quantum effects and so is entirely a consequence of quantum mechanics.

Representative publications

Quantum kinetic energy and isotope fractionation in aqueous ionic solutions. L. Wang, M. Ceriotti and T. E. Markland Phys. Chem. Chem. Phys., 22, 10490-10499 (2020)
Quantum fluctuations and isotope effects in ab initio descriptions of water. L. Wang, M. Ceriotti, T. E. Markland., J. Chem. Phys., 141, 104502 (2014)
Unraveling quantum mechanical effects in water using isotopic fractionation. T. E. Markland and B. J. Berne, Proc. Natl. Acad. Sci., 109, 7988-7991 (2012)

Glassy Systems

Glasses are dynamically arrested states of matter that do not exhibit the long-range periodic structure of crystals. While simple structural indicators suggest the structure of glass forming systems to be barely different from the liquid that produced them the dynamics can be as slow as observed in the crystalline state. Hence, investigating the growing static and dynamic length-scales which instill liquids with this rigidity provides an intruiging challenge.

Our interests in glasses have previously involved three primary areas:

Investigating how quantum mechanics affects the liquid-glass transition.
Understanding the interplay between the structure of glass forming liquids and their dynamics using techniques such as point-to-set correlations.
Developing methods for efficiently exploring the rough free energy landscapes characteristic of glassy systems.

Above: Snapshots from a quantum path integral (RPMD) simulation of a supercooled liquid. In the left image, the polymer is extended as it tunnels between cavities in the liquid, and in the right image it is localized in one well.

Representative publications

Quantum fluctuations can promote or inhibit glass formation. T. E. Markland, J. A. Morrone, B. J. Berne, K. Miyazaki, E. Rabani and D. R. Reichman, Nature Phys., 7, 134-137 (2011)
Theory and simulations of quantum glass forming liquids. T. E. Markland, J. A. Morrone, K. Miyazaki, B. J. Berne, D. R. Reichman and E. Rabani, J. Chem. Phys., 136, 074511 (2012)
Growing point-to-set length scale correlates with growing relaxation times in model supercooled liquids. G. M. Hocky, T. E. Markland and D. R. Reichman, Phys. Rev. Lett. 108 225506 (2012)
Interface limited growth of heterogeneously nucleated ice in supercooled water. R. A. Nistor, T. E. Markland, B. J. Berne, J. Phys. Chem. B, 118 (3), 752-760 (2014)

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