Sharon Hammes-Schiffer

Hydrogen tunneling is central to many chemical and biological processes. Herein, we introduce the vibronic-SHAKE (V-SHAKE) approach to comprehensively sample energy-conserving molecular configurations enabling hydrogen tunneling. A constrained form of nuclear–electronic orbital multistate density functional theory (NEO-MSDFT) dynamics, where the tunneling hydrogen nucleus is quantized, is used to sample geometries in the diabatic seam space corresponding to the intersection of the reactant and product NEO-DFT diabatic vibronic surfaces. V-SHAKE is applied to hydrogen and deuterium tunneling in 4-cyanobutanolate and (Z)-4-hydroxybut-3-en-2-one. The vibronic coupling is found to vary significantly in the diabatic seam space, mainly due to changes in the donor–acceptor distance. The reaction coordinate and gradient of the vibronic coupling at the minimum energy crossing point are nearly orthogonal and are dominated by motions stabilizing the product relative to the reactant or decreasing the donor–acceptor distance, respectively. V-SHAKE provides fundamental insights and qualitative support for assumptions underlying rate theories.

We present Chronus Quantum (ChronusQ) 1.0, an open-source software platform for modern electronic structure theory with particular emphasis on the molecular Dirac–Coulomb–Breit Hamiltonian, relativistic many-body methods, multicomponent quantum chemistry, and time-dependent phenomena. Rather than serving as another general-purpose quantum chemistry package, ChronusQ is designed to develop and disseminate new theoretical methodologies through reusable, interoperable, and extensible software frameworks. At the heart of the software is a unified relativistic infrastructure spanning the molecular Dirac–Coulomb–Breit Hamiltonian, exact two-component methods, atomic-orbital integral engines, Cholesky decomposition, finite-magnetic-field gauge-including atomic orbitals, and distributed tensor computations. Building upon these shared components, ChronusQ provides relativistic self-consistent-field and density functional theory, multiconfigurational methods based on the small-tensor-product distributed active space framework, relativistic coupled-cluster theory, nuclear–electronic orbital methods, and real-time quantum dynamics. This article presents the scientific capabilities, software architecture, and development philosophy of ChronusQ, illustrating how interoperable software infrastructures can accelerate the development of modern electronic structure methods while providing a flexible and sustainable platform for future advances in molecular quantum science.

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.

Polaritons offer the possibility of modifying chemical properties through the strong coupling of molecules to photons confined in optical cavities. From a first-principles perspective, understanding how these strong light–matter interactions cause chemical changes requires quantum mechanical descriptions of electrons, nuclei, and photons. Herein, we develop the ab initio cavity quantum electrodynamic nuclear–electronic orbital complete active space configuration interaction (QED-NEO-CASCI) method, in which electrons, specified nuclei, and cavity photons are all treated quantum mechanically. Using this method, we are able to describe hydrogen tunneling under vibrational strong coupling and geometry changes in a hydrogen-bonded complex coupled to a cavity. Under vibronic strong coupling, we observe features in the polaritonic absorption spectrum that correspond to Raman active transitions outside a cavity. We also develop the real-time variant, denoted time-dependent configuration interaction (QED-NEO-TDCI). This method allows us to simulate nonadiabatic hydrogen tunneling dynamics and observe the real-time quantum mechanical transfer of energy between the molecule and cavity photons. These methods provide the ab initio foundation for studying correlated electronic–nuclear–photonic chemical physics.

Nuclear–electronic orbital (NEO) methods treat specified nuclei, typically protons, quantum mechanically on the same level as electrons within quantum chemical calculations. This approach allows the computationally efficient inclusion of nuclear quantum effects such as nuclear delocalization, anharmonic zero-point energy, and tunneling into energy calculations, geometry optimizations, and dynamics. NEO coupled cluster (NEO-CC) methods recover correlation to an extent that enables prediction of accurate ground-state properties for moderately sized systems. Herein, NEO-CCSD(T), which includes all relevant single and double electron and nucleus excitations, as well as perturbative triple excitations, is formulated with the nuclear Hartree product representation for an arbitrary number of quantum nuclei. Compared to the nuclear Slater determinant representation, iterative convergence of the t-amplitude equations, as well as the preceding NEO Hartree–Fock procedure, is significantly faster for multiple quantum protons. Moreover, perturbative corrections in methods such as NEO second-order Møller–Plesset perturbation theory and NEO-CCSD(T) are more accurate using the nuclear Hartree product representation, most likely due to more physically reasonable virtual orbitals. Electronic frozen natural orbital truncation is implemented to extend the accessible system size while maintaining accuracy. These combined methods are used to calculate interaction energies of systems with multiple hydrogen bonds, as well as energies of water clusters with up to 24 quantum protons. In addition, NEO-CCSD(T) with the nuclear Hartree product representation is used to predict hydrogen/deuterium geometric isotope effects, incorporating the necessary anharmonic zero-point energy, for FHF–, a water dimer, and HF clusters of up to five molecules. These examples show that NEO-CCSD(T) with the nuclear Hartree product representation is an efficient and accurate method for incorporating nuclear quantum effects into ground-state calculations.

Nuclear quantum effects play a critical role throughout chemistry, biology, and materials science. This Perspective presents the nuclear–electronic orbital (NEO) framework as a viable approach for incorporating nuclear quantum effects into calculations of relatively large, complex systems. The NEO approach treats specified nuclei, often protons or deuterons, quantum mechanically on the same level as the electrons using wave function theories or density functional theory. This approach incorporates nuclear quantum effects such as zero-point energy, nuclear delocalization, and nuclear tunneling into quantum chemistry calculations and molecular dynamics simulations. Nonadiabatic effects beyond the standard Born–Oppenheimer approximation between electrons and nuclei are also incorporated. NEO methods are computationally practical, straightforward to use, and accessible to nonexperts. This Perspective highlights the broad applicability of the NEO framework and emphasizes the fundamental insights provided by NEO calculations. The applications discussed include water clusters, double proton transfer dynamics, proton-coupled electron transfer, hydrogen tunneling dynamics, enzymatic reactions, pKa calculations, kinetic isotope effects, hydrogen and deuterium adsorption and water monolayers at metal electrode surfaces, geometric isotope effects, phase transitions in hydrogen-rich materials such as superconducting hydrides and ice, photoinduced proton transfer, plasmon-induced H2 dissociation, vibrational spectroscopy, and polaritonic chemistry. These examples showcase the ubiquitous importance of nuclear quantum effects as well as the accessibility of the NEO approach.

Intramolecular hydrogen-bonded networks have been designed and synthesized to control quinone redox thermodynamics in a family of anthraquinone (AQ) derivatives. The networks contain imidazole fused to AQ, which is hydrogen-bonded to the AQ carbonyl, and the extended motifs include phenol (P) and benzimidazole (BI). Cyclic voltammetry reveals a systematic anodic displacement of the AQ/AQ•– couple as the hydrogen-bonded network is extended, resulting in a cumulative +440 mV shift. Visible spectroelectrochemistry provides direct reduced-state markers: AQ exhibits AQ•– bands at ∼410 and ∼539 nm, whereas the intramolecular hydrogen-bonded constructs display only blue-shifted AQ•– signatures at ∼490 nm (BI–AQ), ∼505 nm (BIP–AQ), and ∼494 nm (BI2P–AQ), consistent with hydrogen-bond-dependent perturbation of the reduced quinone electronic structure. Infrared spectroelectrochemistry further resolves the underlying hydrogen-bonding interactions, revealing depletion of the neutral AQ ν(C═O) band (∼1667 cm–1) under reductive polarization with the emergence of hydrogen-bonded AQ•– band at ∼1480 cm–1 in the AQ derivatives. Oxidative polarization, yielding the phenoxyl radical, induces benzimidazolium formation and a blue-shifted AQ ν(C═O) band (∼1678 cm–1), highlighting the directional dependence of the perturbation and the role of the AQ carbonyl as a reporter of the interaction with the intramolecular hydrogen-bonded network. Treating the hydrogen-bonding protons quantum mechanically, nuclear−electronic orbital density functional theory calculations show strengthening of the hydrogen bonds cooperatively across the network upon one-electron reduction and oxidation, correctly predicting the observed stabilization of the AQ•– state. These fundamental insights will assist in the design of more precisely tuned catalysts.

Interfacial water structure is theoretically envisioned as the master regulator of electrocatalytic reaction kinetics, but the direct experimental validation of this role has remained a formidable challenge. Probing kinetic isotope effects (KIEs) is paramount to deciphering the elusive proton-coupled electron transfer (PCET) mechanisms in alkaline media, a long-standing enigma in electrocatalysis. Such precision, however, demands the uncompromising rigor of atomic-level-precise single-crystal electrodes and ultrapure D2O to ensure definitive results. Here, we uncover a hydrogen evolution reaction KIE that varies sharply with the surface structure: ∼6 for Pt(100), ∼1 for Pt(111), and intermediate values for Pt(110). Through a combination of nuclear–electronic orbital density functional theory (NEO-DFT) and in situ laser-induced temperature-jump (LITJ) experiments, we propose that this disparity originates from the difference between a rigid, hexagonal H-bonded network on Pt(111) and a more disordered, flexible interfacial layer on Pt(100) that would be more sensitive to isotopic substitution, as well as from differences in H/D adsorption sites, which would influence the effective proton transfer distances. Furthermore, measurements with stepped surfaces show that step density acts as a critical dial to tune these water environments. Finally, to bridge the knowledge gap between bulk single-crystals and practical nanoparticles, {100}-oriented Pt nanocubes and {111}-oriented Pt nanotetrahedrons reveal a facet-dependent KIE trend comparable to their single-crystal counterparts. These insights provide a transformative framework for the rational design of high-performance interfaces for green hydrogen production.

Nuclear quantum effects and non-Born–Oppenheimer effects play a vital role in many chemical and biological processes, motivating the incorporation of such effects into dynamical simulations. In real-time nuclear–electronic orbital time-dependent density functional theory (RT-NEO-TDDFT), the electronic and nuclear densities are propagated numerically in time according to the time-dependent Schrödinger equation. In this framework, specified protons are treated quantum mechanically on the same level as the electrons. The classical nuclei can be propagated on the instantaneous NEO vibronic surface using Ehrenfest dynamics. A traveling proton basis (TPB) can be used to describe the dynamics of moving protons in conjunction with Gaussian-type protonic and electronic basis sets for each quantum proton. Herein, we present a constrained TPB (c-TPB) approach that ensures each protonic basis function center coincides with the corresponding proton position expectation value during the dynamics. This approach produces accurate nuclear–electronic quantum dynamics and rigorously conserves energy. We demonstrate the accuracy and stability of this approach for computing molecular vibrational frequencies as well as simulating excited-state intramolecular proton transfer and double proton transfer in the o-hydroxybenzaldehyde and [2,2′-bipyridyl]-3,3′-diol molecules. These applications show that the c-TPB method provides accurate dynamics, conserves energy, and is computationally efficient.