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



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 page.  

Machine Learning Potential Energy 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 State 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

Biochemical Systems

Machine-learned potentials (MLPs) 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 MLP models (Nutmeg) from them. We are also interested in methods to bridge MLPs 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. [J. Phys. Chem. B, 128, 1, 109-116 (2024)]
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

Software for Molecular Simulation and Machine Learning

The Markland Group (via lead programmer Dr. Peter Eastman) is one of the primary developers of the OpenMM software. OpenMM is a widely used toolkit for molecular simulation and modeling (>1.4 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.

We also aim to contribute our theoretical and algorithmic developments to other codes where possible. Some of these are detailed in the representative publications below.

Representative publications

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

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

Excited State Processes

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Representative publications

Spectroscopy and Reactivity at Interfaces

As part of the NSF Center for Chemical Innovation Center for Interfacial Ionics we are working to expand the understanding of ion-transfer kinetics at liquid-liquid and solid-liquid electrochemical interfaces by integrating molecularly precise and tunable measurements with developments in theoretical approaches for simulations of these interfaces. 

Representative publications

Exploiting Timescale Separation for Efficient Simulations

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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: Schematic diagram of excitation dynamics in a model of the FMO complex. Q1 and Q2 correspond to collective bath coordinates. The solid line arrows correspond to an un-shifted 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

Classical Dynamics and Biochemical Processes

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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

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.

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Representative publications

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, as well as x-ray and neutron scattering and recent experiments that harness optically induced anisotropy in time-resolved scattering.

Representative publications

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: Simulation snapshot from our work on the KSI enzyme. The simulation consisted 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.

Representative publications

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

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:

Above: Snapshots from an 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 it is localized in one well.

Representative publications