D. Vale Cofer-Shabica

We trace the history of phase space electronic structure theory (PSEST), highlighting how this powerful approach emerged from fundamental questions in semiclassical surface hopping dynamics and evolved into an alternative to standard Born–Oppenheimer-based electronic structure theory (with moving instead of frozen nuclei). Our goal herein is not to recapitulate the mathematical details of phase space electronic structure calculations, and few equations are presented so as to maximize readability. Instead, our goal is to provide intuition for those new to the field—both (i) regarding the physics present when solving the Schrödinger equation in a non-inertial frame and (ii) regarding why PSEST is a necessary step forward toward understanding chemical problems involving spin (with limited practical alternatives). We further highlight some of the many open questions in this fast developing area, which will hopefully inspire new practitioners in this field. This intuitive perspective lacks many equations and is meant to complement (rather than replace) the more technical review given in Bian et al. [Chem. Phys. Rev. 7, 011303 (2026)].

Proton transfer is coupled to electron transfer or electronic excitation energy transfer in proton-coupled electron transfer (PCET) and proton-coupled energy transfer (PCEnT) reactions, respectively. Although photoinduced PCET and PCEnT have been studied extensively in anthracene–phenol–pyridine molecular triads, the nuclear reaction coordinates for these two pathways are still unknown. Herein, we identify the nuclear reaction coordinates for PCET and PCEnT in the triads by sampling the seam space between the relevant intersecting diabatic states. The reaction coordinate has contributions mainly from anthracene and phenol for PCET but involves the entire triad, including pyridine, for PCEnT. Both reaction coordinates involve motions related to contraction of the phenol C–O bond as well as motions within the anthracene rings that differ for PCET and PCEnT due to different charge distributions. The proton acceptor motion contributes more to the PCEnT than the PCET reaction coordinate. Both PCET and PCEnT reactions are concerted in that there is no stable intermediate, but they are both most likely asynchronous. Our analysis also suggests that PCET proceeds through a conical intersection in its minimum energy pathway, whereas PCEnT moves through an avoided crossing. The quantum mechanical treatment of the transferring proton within a vibronically nonadiabatic framework suggests that the kinetic isotope effect may be greater for PCEnT than for PCET, although more extensive calculations are required for confirmation. Understanding the fundamental similarities and differences between PCET and PCEnT mechanisms will help guide the design of proton-coupled systems that favor either charge transfer or energy transfer.

We investigate the applicability of the Condon approximation (i.e., the notion that the diabatic coupling is invariant to geometry) in the context of both electron transfer (ET) and triplet energy transfer (TET) and compare the two cases. Although it is well appreciated that diabatic couplings usually arise from the interactions of electronic wave function tails, we show that ET tails are very different from TET tails. Using a simple model problem, our analysis explains in detail why the rates of TET decays with twice the rate of ET, while also leading to the hypothesis that the smaller diabatic couplings found for TET (versus ET) should imply more sensitivity to non-Condon fluctuations. As an example, for the classic sets of molecules investigated by Closs, we show that the Condon approximation is indeed less applicable for TET than for ET.

Marcus theory is the workhorse of theoretical chemistry for predicting the rates of charge and energy transfer. Marcus theory overwhelmingly agrees with experiment─both in terms of electron transfer and triplet energy transfer─for the famous set of naphthalene-bridge-biphenyl and naphthalene-bridge-benzophenone systems studied by Piotrowiak, Miller, and Closs. That being said, the agreement is not perfect, and in this manuscript, we revisit one key point of disagreement: the molecule C-13-ae ([3,equatorial]-naphthalene-cyclohexane-[1,axial]-benzophenone). To better understand the theory-experiment disagreement, we introduce and employ a novel scheme to sample the seam between two diabatic electronic states (E-SHAKE) through which we reveal the breakdown of the Condon approximation and the presence of a conical intersection for the C-13-ae molecule; we also predict an isotopic effect on the rate of triplet-triplet energy transfer.

We revisit the photodynamics of tetracyanoethylene-hexamethylbenzene (TCNE-HMB), the molecular complex studied by Hochstrasser et al. [J. Chem. Phys. 100, 4797-4810, 1994] that has long challenged the applicability of Marcus's theory of electron transfer for predicting photochemical reactions. Using a novel black-box electronic structure algorithm (time-dependent density functional theory with one double, TDDFT-1D) to efficiently run molecular dynamics that can treat charge recombination, we run ab initio surface hopping molecular dynamics and confirm that, for a polar solvent, charge recombination rates can be incredibly fast (indeed faster than the solvent relaxation time); for nonpolar solvents, the rate is much slower. We demonstrate that, although Marcus theory cannot be directly applied, these nonequilibrium (and sometimes incredibly fast) photoexcited dynamics can be effectively explained within a two-state model without any evidence of a transition through a conical intersection. Most importantly, for this paradigmatic model system, we are able to identify two nuclear coordinates of interest (rather than the single coordinate predicted by Marcus or a full set of internal quantum modes studied by Bixon and Jortner): the solvent relaxation in the first shell (that strongly modulates the energies of the charge transfer state and differentiates time scales for relaxation) and a nuclear displacement in the TCNE-HMB complex arising from a handful of vibrations that induces non-Born-Oppenheimer motion and eventually facilitates an abrupt electronic transition to the ground state. Altogether, these findings suggest a tractable generalization of Marcus theory for future simulations of photochemistry with non-innocent solvent environments in the spirit of a Hamiltonian suggested by Stuchebrukhov (J. Chem. Phys. 107, 3821, 1997).

We revisit the naked transition metal cation (Ti⁺) and methanol reaction and go beyond the standard Landau-Zener (LZ) picture when modeling the intersystem crossing (ISC) rate between the lowest doublet and quartet states. We use both (i) unconstrained Born-Oppenheimer molecular dynamics (BOMD) calculations with an approximate two-state method to estimate population transfer between spin diabats and (ii) constrained dynamics to explore energetically accessible portions of the N_DOF - 1 crossing seam, where N_DOF is the total number of internal degrees of freedom. Whereas previous LZ calculations (that necessarily relied on the Condon approximation to be valid) fell short and predicted much slower crossing probabilities than shown in experiment, we show that ISC can occur rapidly because the spin-orbit coupling (SOC) between the doublet and quartet surfaces can vary by 2 orders of magnitude (depending on where in the seam the crossing occurs during dynamics) and the crossing region is revisited multiple times during a dynamics run of a few hundred femtoseconds. We further isolate the two important nuclear coordinates that tune the SOC and modulate the transition, highlighting exactly how and why organometallic ISC can occur rapidly for small systems with floppy internal nuclear vibrational modes.

We implement a rare-event sampling scheme for quantifying the rate of thermally activated nonadiabatic transitions in the condensed phase. Our Quantum mechanics/molecular mechanics (QM/MM) methodology uses the recently developed Interface for NonAdiabatic QM/MM in Solvent (INAQS) package to interface an elementary electronic structure package and a popular open-source molecular dynamics software (GROMACS) to simulate an electron transfer event between two stationary ions in a solution of acetonitrile solvent molecules. Nonadiabatic effects are implemented through a surface hopping scheme, and our simulations allow further quantitative insight into the participation ratio of a solvent and the effect of ion separation distance as far as facilitating electron transfer. We also demonstrate that the standard gas-phase approaches for treating frustrated hops and velocity reversal must be refined when working in the condensed phase with many degrees of freedom. The code and methodology developed here can be easily expanded upon and modified to incorporate other systems and should provide a great deal of new insight into a wide variety of condensed phase nonadiabatic phenomena.

Photoinduced processes play a crucial role in a multitude of important molecular phenomena. Accurately modeling these processes in an environment other than a vacuum requires a detailed description of the electronic states involved as well as how energy flows are coupled to the surroundings. Nonadiabatic effects must also be included in order to describe the exchange of energy between electronic and nuclear degrees of freedom correctly. In this work, we revisit the ring-opening reaction 1,3-cylohexadiene (CHD) in a solvent environment. Using our newly developed Interface for Non-Adiabatic Quantum mechanics/molecular mechanics in Solvent (INAQS) we trace the evolution of the reaction via hybrid quantum mechanics/molecular mechanics (QM/MM) surface hopping with a focus on the solvent's participation in the nonadiabatic relaxation process and the long-time approach to equilibrium. We explicitly include the MM solvent contribution to the nonadiabatic coupling vector─enabling an accurate approach to equilibrium at long times─and find that in highly multidimensional systems gradients can have little or nothing to do with the nonadiabatic couplings.

We report robust initial guesses for the amplitudes and z-vectors in a configuration interaction singles or Tamm–Dancoff approximation calculation that consistently reduce the total number of iterations required for an excited state calculation often by over 50%. The end result of these guesses is that the practicing chemist can expect to generate excited state optimized structures with a total wall time reduced by as much as 30% in the future without any approximations—simply by using information gathered at one geometry and applying it to another geometry.

We present a new software package called M-Chem that is designed from scratch in C++ and parallelised on shared-memory multi-core architectures to facilitate efficient molecular simulations. Currently, M-Chem is a fast molecular dynamics (MD) engine that supports the evaluation of energies and forces from two-body to many-body all-atom potentials, reactive force fields, coarse-grained models, combined quantum mechanics molecular mechanics (QM/MM) models, and external force drivers from machine learning, augmented by algorithms that are focused on gains in computational simulation times. M-Chem also includes a range of standard simulation capabilities including thermostats, barostats, multi-timestepping, and periodic cells, as well as newer methods such as fast extended Lagrangians and high quality electrostatic potential generation. At present M-Chem is a developer friendly environment in which we encourage new software contributors from diverse fields to build their algorithms, models, and methods in our modular framework. The long-term objective of M-Chem is to create an interdisciplinary platform for computational methods with applications ranging from biomolecular simulations, reactive chemistry, to materials research. GRAPHICAL ABSTRACT