Dept. of Chemistry
Ohio State University
100 W. 18th Ave.
Columbus, OH 43210

412 CBEC


John Herbert research group

Electronic structure theory, molecular quantum mechanics, and software design

Schroedinger's Ket, a painting by J.M.H.
Schrödinger's Ket
(a J.M.H. original in acrylic paint)

The primary goal of our research is to extend ab initio electronic structure theory ("quantum chemistry") into the condensed-phase environments where most chemistry actually happens. This requires the development of novel, low-cost electronic structure models and new algorithms; these topics are the primary focus of the work in our group. In some cases, we are interested in developing more efficient QM algorithms but in other cases we aim to model the enviroment at a classical level of theory, albeit with improved accuracy as regards the QM/MM interaction. More efficient QM/MM algorithms are a perennial topic of interest, and occasionally we have even managed to contribute something useful to the classical MD simulation literature. Ultimately, we aim to apply these new QM and QM/MM methods and fast algorithms to chemically interesting problems that were not previously amenable to quantum chemistry calculations.

New methods and algorithms developed in our group are incorporated into state-of-the-art quantum chemistry software packages (primarily Q-Chem) ensuring that our efforts will have a real impact on practical quantum chemistry.

Recent and current projects along these lines are described below. Click on a project title to obtain a more detailed description.

Excited states in macromolecules and condensed phases

Molecular orbitals in DNA
The HOMO and LUMO of
a base pair in DNA.

The excited electronic states of many small chromophores are well-characterized in the gas phase, but much less is known regarding how these states are perturbed by a solvent, or by some other condensed-phase environment such as the interior of a protein. The location of conical intersections, as well as energy barriers along an excited-state reaction pathway, may be profoundly different in the condensed phase than they are in the gas phase, and these details ultimately dictate whether the energy deposited into a chromophore by a visible or UV photon manifests as fluorescence, radiationless decay to the ground state (internal conversion), or else initiates some excited-state (photochemical) reaction. To understand condensed-phase electronic spectroscopy at a theoretical level, and to simulate condensed-phase photochemistry and photophysics, it is crucial that we develop methods that afford realistic models of the environment of a chromophore, including possible electronic coupling to other chromophores. Our group is working to develop and refine ab initio simulation methods that can be applied to excited-state reactions in the condensed phase.

Structure and dynamics of aqueous ions and radicals

aqueous electron wavefunctions
The s → p excitation of the aqueous
electron, which is responsible for its
optical absorption spectrum.

Just as we are working to extend excited-state quantum chemistry into condensed-phase environments, we also aim to achieve an understanding of open-shell species (in both ground and electronic states) in liquid solution. Modern ultrafast spectroscopy provides a variety of new experimental tools to study radicals and ions in liquid solution, and we seek to develop comparable theoretical tools to understand observable spectroscopic signatures. Often for open-shell species, there are gaps in our knowledge of structural and dynamical aspects of solvation such as diffusion mechanisms, coordination numbers, or the extent to which solvent molecular orbitals contribute to the electronic structure of the radical in question. In liquid water, a detailed understanding of the spectroscopy of H atom, OH radical, and the "hydrated electron"—the three most important radicals generated when water is exposed to ionizing radiation—is necessary in order to provide a detailed picture of aqueous radiation chemistry. Further complicating the issue is the fact that radical reactivity can be very different at interfaces than in bulk solution. A complete, molecular-level understanding of these phenomena will require not only accurate quantum mechanics (since molecular mechanics force fields are often unavailable or unreliable for open-shell species) but also good statistical mechanics, i.e. proper averaging over bulk solvation environments, rather than the sort of "microsolvation" approaches that are commonly used in quantum-chemical calculations.

Non-covalent interactions in many-body systems

JPC cover artwork
Illustrative applications of XSAPT
(Cover art from a JPC Feature Article)

Accurate and efficient calculation of intermolecular interactions is a challenging problem for electronic structure theory. Although the van der Waals interaction is one of the most fundamental concepts in chemistry, from a quantum-mechanical point of view it arises purely from electron correlation, and thus demands a high-level theoretical treatments if it is to be described properly. However, such calculations are seldom amenable to large collections of monomers, and certainly not to liquids, and thus cannot be used to describe the important cooperative (non-additive or many-body) effects present in clusters and in the condensed phase. We are working to develop ab initio methods for many-body systems that exploit monomer-based SCF calculations whose cost scales linearly with the number of monomers. These calculations are then coupled to two- and three-body treatments of the intermolecular interactions, to obtain accurate many-body interaction energies (comparable to the best supersystem ab initio calculations) at dramatically reduced cost.

Dielectric continuum solvation models

molecule-shaped cavity
Electrostatic potential map at
the solute/continuum interface

Apparent surface charge, reaction-field solvation models, better known as "polarizable continuum models" (PCMs), represent the most widely-used class of implicit solvent models in quantum chemistry. Given a definition for a solute cavity (e.g., a van der Waals surface) that defines the interface between the solute molecule and the structureless dielectric representation of the solvent, these models provide an approximate solution for Poisson's equation or the linearized Poisson-Boltzmann equation using relatively efficient two-dimensional surface integration, rather than the three-dimensional sampling that is required to solve these differential equations directly. PCMs greatly accelerate conformational or phase-space sampling, since explicit solvent degrees of freedom are absent. Furthermore, as compared to empirical solvation models that are intended only to predict solvation free energies, PCMs are physically-motivated models that are directly interwoven into the system's Hamiltonian, and can thus be used to explore the effects of solvation on a variety of chemical and physical properties. These include solution-phase geometries, vibrational frequencies, electronic excitation energies, and more.

Development of TD-DFT methods

Natural transition orbitals for the aqueous electron
Natural transition orbitals for
excited states of e(aq)

Time-dependent density functional theory (TD-DFT) is currently the only tractable ab initio method for calculating electronic excitation energies in systems with more than 20–30 atoms. For a wide variety of organic molecules, the (statistical) accuracy of these excitation energies is ≈ 0.3 eV (at the ground-state geometry), good enough to make the method useful in many chemistry applications. However, the high level of accuracy exhibited by TD-DFT in small-molecule calculations does not always carry over to larger systems. Moreover, the calculation of excited states in very large molecules (those containing hundreds of atoms described at the DFT level), while technically feasible, is neither trivial nor routine. QM/MM methods, with the chromophore as the QM region, are an obvious way to reduce the cost of such calculations, but sometimes very large QM regions are necessary, in order to include explicit QM solvent molecules, or to incorporate electronic coupling between multiple chromophores. Thus, we are working to extend both the computational feasibility (via improved algorithms) and the accuracy (by means of improved functionals) of large-molecule TD-DFT calculations. Much of this work is tightly integrated with other ongoing projects in our group, including the development of QM/MM methods and continuum solvation models.

Polarizable QM/MM models

Emissive state of DMABN
S0 ← S1 emission in the DMABN
molecule, which exhibits
intramolecular CT character

Electronic excitation is characterized by an instantaneous (and possibly drastic) change in the electron density of the molecular or functional group that absorbs the photon. In particular, intramolecular charge-transfer excited states such as those present in "donor-π-acceptor" or "push-pull" chromophores, can change the dipole moment of the chromophore by 10 debye or more. In a condensed-phase environment, a proper description of such an event should allow the electronic degrees of freedom of the environment to remain in equilibrium with those of the chromophore, i.e., the chromophore and its environment should polarize one another in a self-consistent fashion. In addition, the most accurate molecular mechanics (MM) force fields are often polarizable ones. In the context of QM/MM calculations, the increased cost associated with using a polarizable force field should be insignificant, provided that the QM/MM algorithm is designed in a reasonable way. We are developing computationally-efficient QM/MM models that utilize polarizable MM force fields ("QM/polMM" models), in an effort to describe excited states in solution. We aim for solvation models that are accurate across the entire range of system sizes, from small clusters to bulk solvation. These new methods enable us to explore the role of solvent polarization, which is especially important for the description of charge-separated excited states, and to make contact with both condensed-phase electronic spectroscopy, as well as gas-phase cluster experiments.

Improved algorithms for ab initio molecular dynamics

ELMD equations of motion
Equations of motion for extended-
Lagrangian ab initio molecular dynamics.

Efficient algorithms developed in our group are expanding the frontiers of ab initio molecular dynamics (AIMD) simulations, in which on-the-fly quantum chemistry (i.e., a quantum-mechanical treatment of the electrons) is used to calculate the forces required for a classical molecular dynamics simulation, thus obviating the need for parametrized force fields. This is especially important for unusual or reactive species (such as the hydrated electron and other aqueous radicals), for which it is extremely difficult to construct accurate force fields. Improvements to the efficiency of AIMD algorithms translate directly into longer simulation time scales and larger system sizes, for a fixed quantity of computer resources.

Software development

Q-Chem logo
Furry logo

Our group contributes to the development of Q-Chem, a state-of-the-art electronic structure program package. (See also IQMol, a structure builder and graphical front-end for Q-Chem.) Herbert group members have the opportunity to become co-authors of future versions of the software. We are also developing an efficient and general Fourier-grid code, Furry (ver. A), for performing low-dimensional exact QM with analytic potentials (either fixed-charge or polarizable). A stand-alone code, Fragme∩t, for performing fragment-based quantum chemistry calculations (interfacing with Q-Chem) is also under development.

Last modified December 19, 2014

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