Nuclear quantum effects enter the mainstream

Machine-learning to predict anharmonic frequencies: a study of models and transferability

With more and more accurate electronic structure methods at hand, the inclusion of anharmonic effects in the post-processing of such data towards thermochemical properties is the next step. In this context, the description of anharmonicity has been an important topic of physical chemistry and chemical physics for a long time. In this study, anharmonic frequencies of various hydrogen-halides and halogenated hydrocarbon molecular clusters are calculated using harmonic as well as explicitly anharmonic methods, i.e., normal mode analysis and vibrational self-consistent field. Simple harmonic model based descriptors were used to predict anharmonic frequencies via multilinear regression and gradient boosting regression. Gradient boosting regression is capable of predicting reliable anharmonic data and even the simple multilinear regression model yields reasonable predictions that can account for mode-to-mode couplings. Moreover, the transferability to unseen chemical systems is assessed and it is confirmed that the machine-learned models can be applied to larger, unseen molecules.

After 50 Years of Vibrational Circular Dichroism Spectroscopy: Challenges and Opportunities of Increasingly Accurate and Complex Experiments and Computations

VCD research continues to thrive, driven by ongoing experimental and theoretical advances. Modern studies deal with increasingly complex samples featuring weak intermolecular interactions and shallow potential energy surfaces. Likewise, the combination of VCD measurements with, for instance, cryo-spectroscopic techniques has significantly increased their sensitivity. The extent to which such modern measurements enhance the informative value of VCD depends significantly on the quality of the theoretical models, which must adequately account for anharmonicity, solvation and molecular dynamics. We herein discuss how experimental advancements engage in a stimulating interplay with recent theoretical developments, pursuing either the static or the dynamic computational route. Both paths have their own strengths and limitations, each addressing fundamentally different problems. We give an outlook on future challenges of VCD research, including the possibility to combine static and dynamic approaches to obtain a full picture of the sample.

Perspective on Theoretical and Experimental Advances in Atmospheric Photochemistry

Research that explores the chemistry of Earth's atmosphere is central to the current understanding of global challenges such as climate change, stratospheric ozone depletion, and poor air quality in urban areas. This research is a synergistic combination of three established domains: earth observation, for example, using satellites, and in situ field measurements; computer modeling of the atmosphere and its chemistry; and laboratory measurements of the properties and reactivity of gas-phase molecules and aerosol particles. The complexity of the interconnected chemical and photochemical reactions which determine the composition of the atmosphere challenges the capacity of laboratory studies to provide the spectroscopic, photochemical, and kinetic data required for computer models. Here, we consider whether predictions from computational chemistry using modern electronic structure theory and nonadiabatic dynamics simulations are becoming sufficiently accurate to supplement quantitative laboratory data for wavelength-dependent absorption cross-sections, photochemical quantum yields, and reaction rate coefficients. Drawing on presentations and discussions from the CECAM workshop on Theoretical and Experimental Advances in Atmospheric Photochemistry held in March 2024, we describe key concepts in the theory of photochemistry, survey the state-of-the-art in computational photochemistry methods, and compare their capabilities with modern experimental laboratory techniques. From such considerations, we offer a perspective on the scope of computational (photo)chemistry methods based on rigorous electronic structure theory to become a fourth core domain of research in atmospheric chemistry.

Water-air interface revisited by means of path-integral ab initio molecular dynamics

Although nuclear quantum effects (NQEs) have been considered on bulk liquid water, the impact of these latter on the air-water interface has not yet been reported. Herein, by performing and comparing ab initio molecular dynamics (AIMD) and path integral AIMD (PI-AIMD) simulations, we reveal the impact of NQEs on structural, dynamical and electronic properties as well as IR spectra of the air-water interface at room temperature. NQEs, being able to describe a more accurate proton delocalization in H-bonded system than AIMD, reveal a different structural arrangement and dynamical behaviour of both bulk and interfacial water molecules in comparison to AIMD results. A more de-structured and de-bound water arrangement and coordination are identified when the quantum nature of nuclei are considered for both bulk and interfacial water molecules. Structural properties, such as inter-/intra-molecular bond lengths, coordination numbers and H-bonding angles of bulk and interfacial water molecules here calculated, are affected by NQEs mitigating the overstructured description given by AIMD. Further evidences of an AIMD overstructured description of bulk water are in the computed IR spectra, where an increased absorption peak intensity and an increased strength of the hydrogen-bond network are alleviated by NQEs. In addition, NQEs show a valuable impact on the electronic structure of the air-water interface, reducing the total valence bandwidth and the electronic energy band-gap when passing from bulk to interfacial water. This work proves how NQEs significantly affect properties and features of the air-water interface, that are essential to accurately describe H-bonded interfacial systems.

Impact of Nuclear Quantum Effects on the Structural Properties of Protonated Water Clusters

Nuclear quantum effects (NQEs) play a crucial role in hydrogen-bonded systems due to quantum tunneling and proton fluctuation. Our understanding of how NQEs affect microstructures mainly focuses on bulk phases of liquids and solids but remains deficient for water clusters, including their hydrogen nuclei, hydrogen-bonded configurations, and temperature dependence. Here, we conducted ab initio molecular dynamics (MD) and path integral MD simulations to investigate the influence of NQEs on the structural properties of protonated water clusters H+(H2O)n (n = 3, 6, 9, 12). The results reveal that the NQEs become less evident as the cluster size increases due to the competition between NQEs and electrostatic interactions. Simulations of several H+(H2O)6 isomers at different temperatures indicate that the effect of elevated temperature on proton transfer is related to the initial structure. Interestingly, the process of proton transfer also involves the interconversion between Zundel-type and Eigen-type isomers. These findings significantly deepen our understanding of ion-water and water-water interactions, opening new avenues for the study of hydrated ion clusters and related systems.

Extending non-adiabatic rate theory to strong electronic couplings in the Marcus inverted regime

Electron transfer reactions play an essential role in many chemical and biological processes. Fermi's golden rule (GR), which assumes that the coupling between electronic states is small, has formed the foundation of electron transfer rate theory; however, in short range electron/energy transfer reactions, this coupling can become very large, and, therefore, Fermi's GR fails to make even qualitatively accurate rate predictions. In this paper, I present a simple modified GR theory to describe electron transfer in the Marcus inverted regime at arbitrarily large electronic coupling strengths. This theory is based on an optimal global rotation of the diabatic states, which makes it compatible with existing methods for calculating GR rates that can account for nuclear quantum effects with anharmonic potentials. Furthermore, the optimal GR (OGR) theory can also be combined with analytic theories for non-adiabatic rates, such as Marcus theory and Marcus-Levich-Jortner theory, offering clear physical insights into strong electronic coupling effects in non-adiabatic processes. OGR theory is also tested on a large set of spin-boson models and an anharmonic model against exact quantum dynamics calculations, where it performs well, correctly predicting rate turnover at large coupling strengths. Finally, an example application to a boron-dipyrromethane-anthracene photosensitizer reveals that strong coupling effects inhibit excited state charge recombination in this system, reducing the rate of this process by a factor of 4. Overall, OGR theory offers a new approach to calculating electron transfer rates at strong couplings, offering new physical insights into a range of non-adiabatic processes.

Nuclear Quantum Effects on the Electronic Structure of Water and Ice

The electronic properties and optical response of ice and water are intricately shaped by their molecular structure, including the quantum mechanical nature of the hydrogen atoms. Despite numerous previous studies, a comprehensive understanding of the nuclear quantum effects (NQEs) on the electronic structure of water and ice at finite temperatures remains elusive. Here, we utilize molecular simulations that harness efficient machine-learning potentials and many-body perturbation theory to assess how NQEs impact the electronic bands of water and hexagonal ice. By comparing path-integral and classical simulations, we find that NQEs lead to a larger renormalization of the fundamental gap of ice, compared to that of water, ultimately yielding similar bandgaps in the two systems, consistent with experimental estimates. Our calculations suggest that the increased quantum mechanical delocalization of protons in ice, relative to water, is a key factor leading to the enhancement of NQEs on the electronic structure of ice.

Mesoscale Molecular Simulations of Fabry-Pérot Vibrational Strong Coupling

Developing theoretical frameworks for vibrational strong coupling (VSC) beyond the single-mode approximation is crucial for a comprehensive understanding of experiments with planar Fabry-Pérot cavities. Herein, a generalized cavity molecular dynamics (CavMD) scheme is developed to simulate VSC of a large ensemble of realistic molecules coupled to an arbitrary 1D or 2D photonic environment. This approach is built upon the Power-Zienau-Woolley Hamiltonian in the normal mode basis and uses a grid representation of the molecular ensembles to reduce the computational cost. When simulating the polariton dispersion relation for a homogeneous distribution of molecules in planar Fabry-Pérot cavities, our data highlight the importance of preserving the in-plane translational symmetry of the molecular distribution. In this homogeneous limit, CavMD yields the consistent polariton dispersion relation as an analytic theory, i.e., incorporating many cavity modes with varying in-plane wave vectors (k∥) produces the same spectrum as the system with a single cavity mode. Furthermore, CavMD reveals that the validity of the single-mode approximation is challenged when nonequilibrium polariton dynamics are considered, as polariton-polariton scattering occurs between modes with the nearest neighbor k∥. The procedure for numerically approaching the macroscopic limit is also demonstrated with CavMD by increasing the system size. Looking forward, our generalized CavMD approach may facilitate understanding vibrational polariton transport and condensation.

Molecular Insights into Chemical Reactions at Aqueous Aerosol Interfaces

Atmospheric aerosols facilitate reactions between ambient gases and dissolved species. Here, we review our efforts to interrogate the uptake of these gases and the mechanisms of their reactions both theoretically and experimentally. We highlight the fascinating behavior of N2O5 in solutions ranging from pure water to complex mixtures, chosen because its aerosol-mediated reactions significantly impact global ozone, hydroxyl, and methane concentrations. As a hydrophobic, weakly soluble, and highly reactive species, N2O5 is a sensitive probe of the chemical and physical properties of aerosol interfaces. We employ contemporary theory to disentangle the fate of N2O5 as it approaches pure and salty water, starting with adsorption and ending with hydrolysis to HNO3, chlorination to ClNO2, or evaporation. Flow reactor and gas-liquid scattering experiments probe even greater complexity as added ions, organic molecules, and surfactants alter the interfacial composition and reaction rates. Together, we reveal a new perspective on multiphase chemistry in the atmosphere.

Path Integral Simulations of Condensed-Phase Vibrational Spectroscopy

Recent theoretical and algorithmic developments have improved the accuracy with which path integral dynamics methods can include nuclear quantum effects in simulations of condensed-phase vibrational spectra. Such methods are now understood to be approximations to the delocalized classical Matsubara dynamics of smooth Feynman paths, which dominate the dynamics of systems such as liquid water at room temperature. Focusing mainly on simulations of liquid water and hexagonal ice, we explain how the recently developed quasicentroid molecular dynamics (QCMD), fast-QCMD, and temperature-elevated path integral coarse-graining simulations (Te PIGS) methods generate classical dynamics on potentials of mean force obtained by averaging over quantum thermal fluctuations. These new methods give very close agreement with one another, and the Te PIGS method has recently yielded excellent agreement with experimentally measured vibrational spectra for liquid water, ice, and the liquid-air interface. We also discuss the limitations of such methods.

Nuclear Quantum Effects on Nonadiabatic Dynamics of a Green Fluorescent Protein Chromophore Analogue: Ring-Polymer Surface-Hopping Simulation

Herein, we have used the "on-the-fly" ring-polymer surface-hopping simulation method with the centroid approximation (RPSH-CA), in combination with the multireference OM2/MRCI electronic structure calculations to study the photoinduced dynamics of a green fluorescent protein (GFP) chromophore analogue in the gas phase, i.e., o-HBI, at 50, 100, and 300 K with 1, 5, 10, and 15 beads (3600 1 ps trajectories). The electronic structure calculations identified five new minimum-energy conical intersection (MECI) structures, which, together with the previous one, play crucial roles in the excited-state decay dynamics of o-HBI. It is also found that the excited-state intramolecular proton transfer (ESIPT) occurs in an ultrafast manner and is completed within 20 fs in all the simulation conditions because there is no barrier associated with this ESIPT process in the S1 state. However, the other excited-state dynamical results are strongly related to the number of beads. At 50 and 100 K, the nuclear quantum effects (NQEs) are very important; therefore, the excited-state dynamical results change significantly with the bead number. For example, the S1 decay time deduced from time-dependent state populations becomes longer as the bead number increases. Nevertheless, an essentially convergent trend is observed when the bead number is close to 10. In contrast, at 300 K, the NQEs become weaker and the above dynamical results converge very quickly even with 1 bead. Most importantly, the NQEs seriously affect the excited-state decay mechanism of o-HBI. At 50 and 100 K, most trajectories decay to the S0 state via perpendicular keto MECIs, whereas, at 300 K, only twisted keto MECIs are responsible for the excited-state decay. The present work not only comprehensively explores the temperature-dependent photoinduced dynamics of o-HBI, but also demonstrates the importance and necessity of NQEs in nonadiabatic dynamics simulations, especially at relatively low temperatures.

Dynamic effects on the nonlinear optical properties of donor acceptor stenhouse adducts: insights from combined MD + QM simulations

The second-order nonlinear optical (NLO) responses of a donor-acceptor stenhouse adduct (DASA) are investigated by using a computational approach combining molecular dynamics simulations and density functional theory (DFT) calculations. Specific force fields for the open and closed photoswitching forms are first parameterized and validated according to the Joyce protocol, in order to finely reproduce the geometrical features and potential energy surfaces of both isomers in chloroform solution. Then, DFT calculations are performed on structural snapshots extracted at regular time steps of the MD trajectories to address the influence of the thermalized conformational dynamics on the NLO responses related to hyper-Rayleigh scattering (HRS) experiments. We show that accounting for the structural dynamics largely enhances the HRS hyperpolarizability (βHRS) compared to DFT calculations considering solely equilibrium geometries, and greatly improves the agreement with experimental measurements. Furthermore, we show that the NLO responses of the NLO-active open form are correlated with the bond order alternation along the triene bridge connecting the donor and acceptor moieties, which is rationalized using simple essential state models.

Understanding X-ray absorption in liquid water using triple excitations in multilevel coupled cluster theory

X-ray absorption (XA) spectroscopy is an essential experimental tool to investigate the local structure of liquid water. Interpretation of the experiment poses a significant challenge and requires a quantitative theoretical description. High-quality theoretical XA spectra require reliable molecular dynamics simulations and accurate electronic structure calculations. Here, we present the first successful application of coupled cluster theory to model the XA spectrum of liquid water. We overcome the computational limitations on system size by employing a multilevel coupled cluster framework for large molecular systems. Excellent agreement with the experimental spectrum is achieved by including triple excitations in the wave function and using molecular structures from state-of-the-art path-integral molecular dynamics. We demonstrate that an accurate description of the electronic structure within the first solvation shell is sufficient to successfully model the XA spectrum of liquid water within the multilevel framework. Furthermore, we present a rigorous charge transfer analysis of the XA spectrum, which is reliable due to the accuracy and robustness of the electronic structure methodology. This analysis aligns with previous studies regarding the character of the prominent features of the XA spectrum of liquid water.

Optimization of Quantum Nuclei Positions with the Adaptive Nuclear-Electronic Orbital Approach

The use of multicomponent methods has become increasingly popular over the last years. Under this framework, nuclei (commonly protons) are treated quantum mechanically on the same footing as the electronic structure problem. Under the use of atomic-centered orbitals, this can lead to some complications as the ideal location of the nuclear basis centers must be optimized. In this contribution, we propose a straightforward approach to determine the position of such centers within the self-consistent cycle of a multicomponent calculation, making use of individual proton charge centroids. We test the method on model systems including the water dimer, a protonated water tetramer, and a porphine system. Comparing to numerical gradient calculations, the adaptive nuclear-electronic orbital (NEO) procedure is able to converge the basis centers to within a few cents of an Ångström and with less than 0.1 kcal/mol differences in absolute energies. This is achieved in one single calculation and with a small added computational effort of up to 80% compared to a regular NEO- self-consistent field run. An example application for the human transketolase proton wire is also provided.

A Many-Body Perspective of Nuclear Quantum Effects in Aqueous Clusters

Nuclear quantum effects play an important role in the structure and thermodynamics of aqueous systems. By performing a many-body expansion with nuclear-electronic orbital (NEO) theory, we show that proton quantization can give rise to significant energetic contributions for many-body interactions spanning several molecules in single-point energy calculations of water clusters. Although zero-point motion produces a large increase in energy at the one-body level, nuclear quantum effects serve to stabilize higher-order molecular interactions. These results are significant because they demonstrate that nuclear quantum effects play a nontrivial role in many-body interactions of aqueous systems. Our approach also provides a pathway for incorporating nuclear quantum effects into water potential energy surfaces. The NEO approach is advantageous for many-body expansion analyses because it includes nuclear quantum effects directly in the energies.

DL_POLY Quantum 2.0: A modular general-purpose software for advanced path integral simulations

DL_POLY Quantum 2.0, a vastly expanded software based on DL_POLY Classic 1.10, is a highly parallelized computational suite written in FORTRAN77 with a modular structure for incorporating nuclear quantum effects into large-scale/long-time molecular dynamics simulations. This is achieved by presenting users with a wide selection of state-of-the-art dynamics methods that utilize the isomorphism between a classical ring polymer and Feynman's path integral formalism of quantum mechanics. The flexible and user-friendly input/output handling system allows the control of methodology, integration schemes, and thermostatting. DL_POLY Quantum is equipped with a module specifically assigned for calculating correlation functions and printing out the values for sought-after quantities, such as dipole moments and center-of-mass velocities, with packaged tools for calculating infrared absorption spectra and diffusion coefficients.

Nuclear Quantum Effects Accelerate Charge Recombination but Boost the Stability of Inorganic Perovskites in Mild Humidity

Experiments have demonstrated that mild humidity can enhance the stability of the CsPbBr3 perovskite, though the underlying mechanism remains unclear. Utilizing ab initio molecular dynamics, ring polymer molecular dynamics, and non-adiabatic molecular dynamics, our study reveals that nuclear quantum effects (NQEs) play a crucial role in stabilizing the lattice rigidity of the perovskite while simultaneously shortening the charge carrier lifetime. NQEs reduce the extent of geometric disorder and the number of atomic fluctuations, diminish the extent of hole localization, and thereby improve the electron-hole overlap and non-adiabatic coupling. Concurrently, these effects significantly suppress phonon modes and slow decoherence. As a result, these factors collectively accelerate charge recombination by a factor of 1.42 compared to that in scenarios excluding NQEs. The resulting sub-10 ns recombination time scales align remarkably well with experimental findings. This research offers novel insight into how moisture resistance impacts the stability and charge carrier lifetime in all-inorganic perovskites.

The energy landscape of the ribosome

The ribosome is a prototypical assembly that can be used to establish general principles and techniques for the study of biological molecular machines. Motivated by the fact that the dynamics of every biomolecule is governed by an underlying energy landscape, there has been great interest to understand and quantify ribosome energetics. In the present review, we will focus on theoretical and computational strategies for probing the interactions that shape the energy landscape of the ribosome, with an emphasis on more recent studies of the elongation cycle. These efforts include the application of quantum mechanical methods for describing chemical kinetics, as well as classical descriptions to characterize slower (microsecond to millisecond) large-scale (10-100 Å) rearrangements, where motion is described in terms of diffusion across an energy landscape. Together, these studies provide broad insights into the factors that control a diverse range of dynamical processes in this assembly.

Characterization of iron(III) in aqueous and alkaline environments with ab initio and ReaxFF potentials

The iron(III) complexes [Fe(H2O)n(OH)m]3-m (n + m = 5, 6, m ≤ 3) and corresponding proton transfer reactions are studied with total energy calculations, the nudged elastic band (NEB) method, and molecular dynamics (MD) simulations using ab initio and a modification of reactive force field potentials, the ReaxFF-AQ potentials, based on the implementation according to Böhm et al. [J. Phys. Chem. C 120, 10849-10856 (2016)]. Applying ab initio potentials, the energies for the reactions [Fe(H2O)n(OH)m]3-m + H2O → [Fe(H2O)n-1(OH)m+1]2-m + H3O+ in a gaseous environment are in good agreement with comparable theoretical results. In an aqueous (aq) or alkaline environment, with the aid of NEB computations, respective minimum energy paths with energy barriers of up to 14.6 kcal/mol and a collective transfer of protons are modeled. Within MD simulations at room temperature, a permanent transfer of protons around the iron(III) ion is observed. The information gained concerning the geometrical and energetic properties of water and the [Fe(H2O)n(OH)m]3-m complexes from the ab initio computations has been used as reference data to optimize parameters for the O-H-Fe interaction within the ReaxFF-AQ approach. For the optimized ReaxFF-AQ parameter set, the statistical properties of the basic water model, such as the radial distribution functions and the proton hopping functions, are evaluated. For the [Fe(H2O)n(OH)m]3-m complexes, it was found that while geometrical and energetic properties are in good agreement with the ab initio data for gaseous environment, the statistical properties as obtained from the MD simulations are only partly in accordance with the ab initio results for the iron(III) complexes in aqueous or alkaline environments.

Electronic friction near metal surface: Incorporating nuclear quantum effect with ring polymer molecular dynamics

The molecular dynamics with electronic friction (MDEF) approach can accurately describe nonadiabatic effects at metal surfaces in the weakly nonadiabatic limit. That being said, the MDEF approach treats nuclear motion classically such that the nuclear quantum effects are completely missing in the approach. To address this limitation, we combine Electronic Friction with Ring Polymer Molecular Dynamics (EF-RPMD). In particular, we apply the averaged electronic friction from the metal surface to the centroid mode of the ring polymer. We benchmark our approach against quantum dynamics to show that EF-RPMD can accurately capture zero-point energy as well as transition dynamics. In addition, we show that EF-RPMD can correctly predict the electronic transfer rate near metal surfaces in the tunneling limit as well as the barrier crossing limit. We expect that our approach will be very useful to study nonadiabatic dynamics near metal surfaces when nuclear quantum effects become essential.

A nuclear configuration interaction approach to study nuclear spin effects: an application to ortho- and para-3 He2 @C60

We introduce a non-orthogonal configuration interaction approach to investigate nuclear quantum effects on energies and densities of confined fermionic nuclei. The Hamiltonian employed draws parallels between confined systems and many-electron atoms, where effective non-Coulombic potentials represent the interactions of the trapped particles. One advantage of this method is its generality, as it offers the potential to study the nuclear quantum effects of various confined species affected by effective isotropic or anisotropic potentials. As a first application, we analyze the quantum states of two 3 He atoms encapsulated in C60 . At the Hartree-Fock level, we observe the breaking of spin and spatial symmetries. To ensure wavefunctions with the correct symmetries, we mix the broken-symmetry Hartree-Fock states within the non-orthogonal configuration interaction expansion. Our proposed approach predicts singly and triply degenerate ground states for the singlet (para-3 He2 @C60 ) and triplet (ortho-3 He2 @C60 ) nuclear spin configurations, respectively. The ortho-3 He2 @C60 ground state is 5.69 cm-1 higher in energy than the para-3 He2 @C60 ground state. The nuclear densities obtained for these states exhibit the icosahedral symmetry of the C60 embedding potential. Importantly, our calculated energies for the lowest 85 states are in close agreement with perturbation theory results based on a harmonic oscillator plus rigid rotor model of 3 He2 @C60 .

Neural Network Corrections to Intermolecular Interaction Terms of a Molecular Force Field Capture Nuclear Quantum Effects in Calculations of Liquid Thermodynamic Properties

We incorporate nuclear quantum effects (NQE) in condensed matter simulations by introducing short-range neural network (NN) corrections to the ab initio fitted molecular force field ARROW. Force field NN corrections are fitted to average interaction energies and forces of molecular dimers, which are simulated using the Path Integral Molecular Dynamics (PIMD) technique with restrained centroid positions. The NN-corrected force field allows reproduction of the NQE for computed liquid water and methane properties such as density, radial distribution function (RDF), heat of evaporation (HVAP), and solvation free energy. Accounting for NQE through molecular force field corrections circumvents the need for explicit computationally expensive PIMD simulations in accurate calculations of the properties of chemical and biological systems. The accuracy and locality of pairwise NN NQE corrections indicate that this approach could be applicable to complex heterogeneous systems, such as proteins.

First-Principles Anharmonic Infrared and Raman Vibrational Spectra of Materials: Fermi Resonance in Dry Ice

We introduce a computational tool for the quantum-mechanical simulation of anharmonic infrared and Raman vibrational spectra of materials. The approach, implemented in the CRYSTAL software, stems from Taylor's expansion of the potential energy surface (PES) on the basis of normal modes up to cubic and quartic terms. The PES can be sampled with four different numerical schemes at the level of density functional theory (DFT), with local, generalized-gradient, and hybrid density functional approximations. Anharmonic states are obtained by solving Shrödinger's nuclear equation with either the vibrational self-consistent field (VSCF) or vibrational configuration interaction (VCI) methods. Nuclear quantum effects (NQEs) are thus fully accounted for. Infrared intensities are computed numerically through a Berry phase approach or analytically through a coupled-perturbed (CP) approach. Raman intensities are computed analytically via the CP approach. A variety of anharmonic features of vibrational spectra of materials can be simulated, including band shifts, combination bands, overtones, resonances (first-order Fermi, second-order Darling-Dennison), and hot bands. We showcase the effectiveness of the approach on the description of a first-order Fermi resonance (FR) in CO2 dry ice: a challenging test-case given that the FR occurs in the Raman spectrum, requires NQEs, and involves two- and three-mode couplings. Fundamental mechanistic differences with respect to the well-known FR in molecular CO2 are addressed. This application represents the first quantum-mechanical, periodic description of FR in dry ice.

Revealing the Unique Role of Water in the Formation of Benzothiazoles: an Experimental and Computational Study

We present here a joint experimental and computational study on the formation of benzothiazoles. Our investigation reveals a green protocol for accessing benzothiazoles from acyl chlorides using either water alongside a reducing agent as the reaction medium or in combination with stoichiometric amounts of a weak acid, instead of the harsh conditions and catalysts previously reported. Specifically, we show that a protic solvent, particularly water, enables the formation of 2-substituted benzothiazoles from N-acyl 1,2-aminothiophenols already at room temperature, without the need for strong acids or metal catalysts. DFT Molecular Dynamics simulations coupled with advanced enhanced sampling techniques provide a clear understanding of the catalytic role of water. We demonstrate how bulk water - due to its extended network of hydrogen bonds and an efficient Grotthuss mechanism - provides a reaction path that strongly reduces the reaction barriers compared to aprotic environments, namely more than 80 kJ/mol for the first reaction step and 250 kJ/mol for the second. Finally, we discuss the influence of different aliphatic and aromatic substituents with varying electronic properties on chemical reactivity. Besides providing in-depth mechanistic insights, we believe that our findings pave the way for a greener route toward an important class of bioactive molecules.

Squeezed Protons and Infrared Plasmonic Resonance Energy Transfer

Unusual nuclear quantum effects may emerge near noble metal nanostructures such as squeezed vibrational states in molecular junctions and plasmonic resonance energy transfer in the infrared domain. Herein, nuclear quantum effects near heavy metals are studied by nuclear-electronic orbital density functional theory (NEO-DFT) with an effective core potential. For a quantum proton sandwiched between a pair of gold tips modeled by two Au6 clusters, NEO-DFT calculations suggest that the quantum proton density can be squeezed as the tip distance decreases. For an HF molecule placed near a one-dimensional Au nanowire composed of up to 34 Au atoms, real-time NEO time-dependent density functional theory (RT-NEO-TDDFT) shows that the infrared plasmonic motion within the Au nanowire may resonantly transfer electronic energy to the HF proton vibrational stretch mode. Overall, these calculations illustrate the advantages of the NEO approach for probing nuclear quantum effects, such as squeezed proton vibrational states and infrared plasmonic resonance energy transfer.

A Critical Assessment on Calculating Vibrational Spectra in Nanostructured Materials

Vibrational spectroscopy is an omnipresent spectroscopic technique to characterize functional nanostructured materials such as zeolites, metal-organic frameworks (MOFs), and metal-halide perovskites (MHPs). The resulting experimental spectra are usually complex, with both low-frequency framework modes and high-frequency functional group vibrations. Therefore, theoretically calculated spectra are often an essential element to elucidate the vibrational fingerprint. In principle, there are two possible approaches to calculate vibrational spectra: (i) a static approach that approximates the potential energy surface (PES) as a set of independent harmonic oscillators and (ii) a dynamic approach that explicitly samples the PES around equilibrium by integrating Newton's equations of motions. The dynamic approach considers anharmonic and temperature effects and provides a more genuine representation of materials at true operating conditions; however, such simulations come at a substantially increased computational cost. This is certainly true when forces and energy evaluations are performed at the quantum mechanical level. Molecular dynamics (MD) techniques have become more established within the field of computational chemistry. Yet, for the prediction of infrared (IR) and Raman spectra of nanostructured materials, their usage has been less explored and remain restricted to some isolated successes. Therefore, it is currently not a priori clear which methodology should be used to accurately predict vibrational spectra for a given system. A comprehensive comparative study between various theoretical methods and experimental spectra for a broad set of nanostructured materials is so far lacking. To fill this gap, we herein present a concise overview on which methodology is suited to accurately predict vibrational spectra for a broad range of nanostructured materials and formulate a series of theoretical guidelines to this purpose. To this end, four different case studies are considered, each treating a particular material aspect, namely breathing in flexible MOFs, characterization of defects in the rigid MOF UiO-66, anharmonic vibrations in the metal-halide perovskite CsPbBr3, and guest adsorption on the pores of the zeolite H-SSZ-13. For all four materials, in their guest- and defect-free state and at sufficiently low temperatures, both the static and dynamic approach yield qualitatively similar spectra in agreement with experimental results. When the temperature is increased, the harmonic approximation starts to fail for CsPbBr3 due to the presence of anharmonic phonon modes. Also, the spectroscopic fingerprints of defects and guest species are insufficiently well predicted by a simple harmonic model. Both phenomena flatten the potential energy surface (PES), which facilitates the transitions between metastable states, necessitating dynamic sampling. On the basis of the four case studies treated in this Review, we can propose the following theoretical guidelines to simulate accurate vibrational spectra of functional solid-state materials: (i) For nanostructured crystalline framework materials at low temperature, insights into the lattice dynamics can be obtained using a static approach relying on a few points on the PES and an independent set of harmonic oscillators. (ii) When the material is evaluated at higher temperatures or when additional complexity enters the system, e.g., strong anharmonicity, defects, or guest species, the harmonic regime breaks down and dynamic sampling is required for a correct prediction of the phonon spectrum. These guidelines and their illustrations for prototype material classes can help experimental and theoretical researchers to enhance the knowledge obtained from a lattice dynamics study.

On selection rules in two-dimensional terahertz-infrared-visible spectroscopy

Two-dimensional terahertz-infrared-visible (2D TIRV) spectroscopy directly measures the coupling between quantum high-frequency vibrations and classical low-frequency modes of molecular motion. In addition to coupling strength, the signal intensity in 2D TIRV spectroscopy can also depend on the selection rules of the excited transitions. Here, we explore the selection rules in 2D TIRV spectroscopy by studying the coupling between the high-frequency CH3 stretching and low-frequency vibrations of liquid dimethyl sulfoxide (DMSO). Different excitation pathways are addressed using variations in laser pulse timing and different polarizations of exciting pulses and detected signals. The DMSO signals generated via different excitation pathways can be readily distinguished in the spectrum. The intensities of different excitation pathways vary unequally with changes in polarization. We explain how this difference stems from the intensities of polarized and depolarized Raman and hyper-Raman spectra of high-frequency modes. These results apply to various systems and will help design and interpret new 2D TIRV spectroscopy experiments.

Nuclear quantum effects in the acetylene:ammonia plastic co-crystal

Organic molecular solids can exhibit rich phase diagrams. In addition to structurally unique phases, translational and rotational degrees of freedom can melt at different state points, giving rise to partially disordered solid phases. The structural and dynamic disorder in these materials can have a significant impact on the physical properties of the organic solid, necessitating a thorough understanding of disorder at the atomic scale. When these disordered phases form at low temperatures, especially in crystals with light nuclei, the prediction of material properties can be complicated by the importance of nuclear quantum effects. As an example, we investigate nuclear quantum effects on the structure and dynamics of the orientationally disordered, translationally ordered plastic phase of the acetylene:ammonia (1:1) co-crystal that is expected to exist on the surface of Saturn's moon Titan. Titan's low surface temperature (∼90 K) suggests that the quantum mechanical behavior of nuclei may be important in this and other molecular solids in these environments. By using neural network potentials combined with ring polymer molecular dynamics simulations, we show that nuclear quantum effects increase orientational disorder and rotational dynamics within the acetylene:ammonia (1:1) co-crystal by weakening hydrogen bonds. Our results suggest that nuclear quantum effects are important to accurately model molecular solids and their physical properties in low-temperature environments.

Beyond the Condon limit: Condensed phase optical spectra from atomistic simulations

While dark transitions made bright by molecular motions determine the optoelectronic properties of many materials, simulating such non-Condon effects in condensed phase spectroscopy remains a fundamental challenge. We derive a Gaussian theory to predict and analyze condensed phase optical spectra beyond the Condon limit. Our theory introduces novel quantities that encode how nuclear motions modulate the energy gap and transition dipole of electronic transitions in the form of spectral densities. By formulating the theory through a statistical framework of thermal averages and fluctuations, we circumvent the limitations of widely used microscopically harmonic theories, allowing us to tackle systems with generally anharmonic atomistic interactions and non-Condon fluctuations of arbitrary strength. We show how to calculate these spectral densities using first-principles simulations, capturing realistic molecular interactions and incorporating finite-temperature, disorder, and dynamical effects. Our theory accurately predicts the spectra of systems known to exhibit strong non-Condon effects (phenolate in various solvents) and reveals distinct mechanisms for electronic peak splitting: timescale separation of modes that tune non-Condon effects and spectral interference from correlated energy gap and transition dipole fluctuations. We further introduce analysis tools to identify how intramolecular vibrations, solute-solvent interactions, and environmental polarization effects impact dark transitions. Moreover, we prove an upper bound on the strength of cross correlated energy gap and transition dipole fluctuations, thereby elucidating a simple condition that a system must follow for our theory to accurately predict its spectrum.

First-Principles Approach for Coupled Quantum Dynamics of Electrons and Protons in Heterogeneous Systems

The coupled quantum dynamics of electrons and protons is ubiquitous in many dynamical processes involving light-matter interaction, such as solar energy conversion in chemical systems and photosynthesis. A first-principles description of such nuclear-electronic quantum dynamics requires not only the time-dependent treatment of nonequilibrium electron dynamics but also that of quantum protons. Quantum mechanical correlation between electrons and protons adds further complexity to such coupled dynamics. Here we extend real-time nuclear-electronic orbital time-dependent density functional theory (RT-NEO-TDDFT) to periodic systems and perform first-principles simulations of coupled quantum dynamics of electrons and protons in complex heterogeneous systems. The process studied is an electronically excited-state intramolecular proton transfer of o-hydroxybenzaldehyde in water and at a silicon (111) semiconductor-molecule interface. These simulations illustrate how environments such as hydrogen-bonding water molecules and an extended material surface impact the dynamical process on the atomistic level. Depending on how the molecule is chemisorbed on the surface, excited-state electron transfer from the molecule to the semiconductor surface can inhibit ultrafast proton transfer within the molecule. This Letter elucidates how heterogeneous environments influence the balance between the quantum mechanical proton transfer and excited electron dynamics. The periodic RT-NEO-TDDFT approach is applicable to a wide range of other photoinduced heterogeneous processes.

Nuclear Quantum Effects Made Accessible: Local Density Fitting in Multicomponent Methods

The simulation of nuclear quantum effects (NQEs) is crucial for an accurate description of systems and processes involving light nuclei, such as hydrogen atoms. Within the last years, the importance of those effects has been highlighted for a vast range of systems with tremendous implications in chemistry, biology, physics, and materials sciences. However, while electronic structure theory methods have become routine tools for quantum chemical investigations, there is still a lack of approaches to address NQEs that are computationally accessible and straightforward to use. To address this, we present the first combination of the nuclear-electronic orbital Hartree-Fock approach with both local and density fitting approximations (LDF-NEO-HF). This results in a low-order scaling approach that enables the inclusion of NQEs for large systems within a fraction of a day and for small to medium size systems in minutes. Moreover, we demonstrate the qualitative accuracy and robustness of our approach to retrieve NQEs for three real-use cases motivated by chemical, biological, and materials science applications.

Efficient time-dependent vibrational coupled cluster computations with time-dependent basis sets at the two-mode coupling level: Full and hybrid TDMVCC[2]

The computation of the nuclear quantum dynamics of molecules is challenging, requiring both accuracy and efficiency to be applicable to systems of interest. Recently, theories have been developed for employing time-dependent basis functions (denoted modals) with vibrational coupled cluster theory (TDMVCC). The TDMVCC method was introduced along with a pilot implementation, which illustrated good accuracy in benchmark computations. In this paper, we report an efficient implementation of TDMVCC, covering the case where the wave function and Hamiltonian contain up to two-mode couplings. After a careful regrouping of terms, the wave function can be propagated with a cubic computational scaling with respect to the number of degrees of freedom. We discuss the use of a restricted set of active one-mode basis functions for each mode, as well as two interesting limits: (i) the use of a full active basis where the variational modal determination amounts essentially to the variational determination of a time-dependent reference state for the cluster expansion; and (ii) the use of a single function as an active basis for some degrees of freedom. The latter case defines a hybrid TDMVCC/TDH (time-dependent Hartree) approach that can obtain even lower computational scaling. The resulting computational scaling for hybrid and full TDMVCC[2] is illustrated for polyaromatic hydrocarbons with up to 264 modes. Finally, computations on the internal vibrational redistribution of benzoic acid (39 modes) are used to show the faster convergence of TDMVCC/TDH hybrid computations towards TDMVCC compared to simple neglect of some degrees of freedom.

Koopmans' theorem for acidic protons

The famous Brønsted acidity, which is relevant in many areas of experimental and synthetic chemistry, but also in biochemistry and other areas, is investigated from a new perspective. Nuclear electronic orbital methods, which explicitly account for the quantum character of selected protons, are applied. The resulting orbital energies of the proton wavefunction are interpreted and related to enthalpies of deprotonation and acid strength in analogy to the Koopmans' theorem for electrons. For a set of organic acids, we observe a correlation which indicates the validity of such a NEO-Koopmans' approach and opens up new opportunities for the computational investigation of more complex acidic systems.

Sustained Hydrogen Spillover on Pt/Cu(111) Single-Atom Alloy: Dynamic Insights into Gas-Induced Chemical Processes

Hydrogen spillover, involving the surface migration of dissociated hydrogen atoms from active metal sites to the relatively inert catalyst support, plays a crucial role in hydrogen-involved catalytic processes. However, a comprehensive understanding of how H atoms are driven to spill over from active sites onto the catalyst support is still lacking. Here, we examine the atomic-scale perspective of the H spillover process on a Pt/Cu(111) single atom alloy surface using machine-learning accelerated molecular dynamics calculations based on density functional theory. Our results show that when an impinging H2 dissociates at an active Pt site, the Pt atom undergoes deactivation due to the dissociated hydrogen atoms that attach to it. Interestingly, collisions between H2 and sticking H atoms facilitate H spillover onto the host Cu, leading to the reactivation of the Pt atom and the realization of a continuous H spillover process. This work underscores the importance of the interaction between gas molecules and adsorbates as a driving force in elucidating chemical processes under a gaseous atmosphere, which has so far been underappreciated in thermodynamic studies.

Knowledge-driven learning, optimization, and experimental design under uncertainty for materials discovery

Significant acceleration of the future discovery of novel functional materials requires a fundamental shift from the current materials discovery practice, which is heavily dependent on trial-and-error campaigns and high-throughput screening, to one that builds on knowledge-driven advanced informatics techniques enabled by the latest advances in signal processing and machine learning. In this review, we discuss the major research issues that need to be addressed to expedite this transformation along with the salient challenges involved. We especially focus on Bayesian signal processing and machine learning schemes that are uncertainty aware and physics informed for knowledge-driven learning, robust optimization, and efficient objective-driven experimental design.

Solvent-induced local environment effect in plasmonic catalysis

Solvents are known to affect the local surface plasmon resonance of metal nanoparticles; however, how solvents can be used to manipulate the interfacial charge and energy transfer in plasmonic catalysis remains to be explored. Here, using NH3 decomposition on a Ru-doped Cu surface as an example, we report density functional theory (DFT) and delta self-consistent field (SCF) calculations, through which we investigate the effect of different protic solvent molecules on interfacial charge transfer by calculating excitation energy of an electronic transition between the metal and the molecular reactant. We find that the H-bonds between water and NH3 can alter the direct interfacial charge transfer due to the shift of the molecular frontier orbitals with respect to the metal Fermi level. These effects are also observed when the H-bonds are formed between methanol (or phenol) and ammonia. We show that the solvent possessing stronger basicity induces a more pronounced effect on the excitation energy. This work thus provides valuable insights for tuning the excitation energy and controlling different routes to channel the photon energy into plasmonic catalysis.

Quadratic scaling bosonic path integral molecular dynamics

Bosonic exchange symmetry leads to fascinating quantum phenomena, from exciton condensation in quantum materials to the superfluidity of liquid 4He. Unfortunately, path integral molecular dynamics (PIMD) simulations of bosons are computationally prohibitive beyond ∼100 particles, due to a cubic scaling with the system size. We present an algorithm that reduces the complexity from cubic to quadratic, allowing the first simulations of thousands of bosons using PIMD. Our method is orders of magnitude faster, with a speedup that scales linearly with the number of particles and the number of imaginary time slices (beads). Simulations that would have otherwise taken decades can now be done in days. In practice, the new algorithm eliminates most of the added computational cost of including bosonic exchange effects, making them almost as accessible as PIMD simulations of distinguishable particles.

Mechanistic Insights into Water Autoionization through Metadynamics Simulation Enhanced by Machine Learning

Characterizing the free energy landscape of water ionization has been a great challenge due to the limitations from expensive ab initio calculations and strong rare-event features. Lacking equilibrium sampling of the ionization pathway will cause ambiguities in the mechanistic study. Here, we obtain convergent free energy surfaces through nanosecond timescale metadynamics simulations with classical nuclei enhanced by atomic neural network potentials, which yields good reproduction of the equilibrium constant (pK_{w}=14.14) and ionization rate constant (1.369×10^{-3}  s^{-1}). The character of transition state unveils the triple-proton transfer occurs through a concerted but asynchronous mechanism. Conditional ensemble average analyses establish the dual-presolvation mechanism, where a pair of hypercoordinated and undercoordinated waters bridged by one H_{2}O cooperatively constitutes the initiation environment for autoionization, and contributes extremely to the local electric field fluctuation to promote water dissociation.

Estimating Free Energy Barriers for Heterogeneous Catalytic Reactions with Machine Learning Potentials and Umbrella Integration

Predicting the rate constants of elementary reaction steps is key for the computational modeling of catalytic processes. Within transition state theory (TST), this requires an accurate estimation of the corresponding free energy barriers. While sophisticated methods for estimating free energy differences exist, these typically require extensive (biased) molecular dynamics simulations that are computationally prohibitive with the first-principles electronic structure methods that are typically used in catalysis research. In this contribution, we show that machine-learning (ML) interatomic potentials can be trained in an automated iterative workflow to perform such free energy calculations at a much reduced computational cost as compared to a direct density functional theory (DFT) based evaluation. For the decomposition of CHO on Rh(111), we find that thermal effects are substantial and lead to a decrease in the free energy barrier, which can be vanishingly small, depending on the DFT functional used. This is in stark contrast to previously reported estimates based on a harmonic TST approximation, which predicted an increase in the barrier at elevated temperatures. Since CHO is the reactant of the putative rate limiting reaction step in syngas conversion on Rh(111) and essential for the selectivity toward oxygenates containing multiple carbon atoms (C2+ oxygenates), our results call into question the reported mechanism established by microkinetic models.

Quantum Nuclear Delocalization and its Rovibrational Fingerprints

Quantum mechanics dictates that nuclei must undergo some delocalization. In this work, emergence of quantum nuclear delocalization and its rovibrational fingerprints are discussed for the case of the van der Waals complexHHe 3 + ${{\rm{HHe}}_3^ + }$ . The equilibrium structure ofHHe 3 + ${{\rm{HHe}}_3^ + }$ is planar and T-shaped, one He atom solvating the quasi-linear He-H+ -He core. The dynamical structure ofHHe 3 + ${{\rm{HHe}}_3^ + }$ , in all of its bound states, is fundamentally different. As revealed by spatial distribution functions and nuclear densities, during the vibrations of the molecule the solvating He is not restricted to be in the plane defined by the instantaneously bentHHe 2 + ${{\rm{HHe}}_2^ + }$ chomophore, but freely orbits the central proton, forming a three-dimensional torus around theHHe 2 + ${{\rm{HHe}}_2^ + }$ chromophore. This quantum delocalization is observed for all vibrational states, the type of vibrational excitation being reflected in the topology of the nodal surfaces in the nuclear densities, showing, for example, that intramolecular bending involves excitation along the circumference of the torus.

Experimental Access to Mode-Specific Coupling between Quantum Molecular Vibrations and Classical Bath Modes

The interaction of quantum-mechanical systems with a fluctuating thermal environment (bath) is fundamental to molecular mechanics and energy transport/dissipation. Its complete picture requires mode-specific measurements of this interaction and an understanding of its nature. Here, we present a combined experimental and theoretical study providing detailed insights into the coupling between a high-frequency vibrational two-level system and thermally excited terahertz modes. Experimentally, two-dimensional terahertz-infrared-visible spectroscopy reports directly on the coupling between quantum oscillators represented by CH3 streching vibrations in liquid dimethyl sulfoxide and distinct low-frequency modes. Theoretically, we present a mixed quantum-classical formalism of the sample response to enable the simultaneous quantum description of high-frequency oscillators and a classical description of the bath. We derive the strength and nature of interaction and find different coupling between CH3 stretch and low-frequency modes. This general approach enables quantitative and mode-specific analysis of coupled quantum and classical dynamics in complex chemical systems.

Nuclear Quantum Dynamics of Three-Dimensional Condensed-Phase Systems by Constant Uncertainty Molecular Dynamics

Constant uncertainty molecular dynamics (CUMD), which was developed to include nuclear quantum effects (NQEs) in molecular dynamics (MD) simulations, is extended to three-dimensional condensed-phase systems. Its applicability was verified via CUMD simulations of bulk water and ice Ih with the q-TIP4P/F potential model. The simulated radial distribution functions, proton momentum distributions, and infrared spectra were compared with those of previous studies in which the simulations were carried out on the basis of the imaginary-time path-integral formalism. We found that CUMD can function as an alternative trajectory-based simulation method for including static and dynamic NQEs in MD simulations of three-dimensional condensed-phase systems.

Fully First-Principles Surface Spectroscopy with Machine Learning

Our current understanding of the structure and dynamics of aqueous interfaces at the molecular level has grown substantially due to the continuous development of surface-specific spectroscopies, such as vibrational sum-frequency generation (VSFG). As in other vibrational spectroscopies, we must turn to atomistic simulations to extract all of the information encoded in the VSFG spectra. The high computational cost associated with existing methods means that they have limitations in representing systems with complex electronic structure or in achieving statistical convergence. In this work, we combine high-dimensional neural network interatomic potentials and symmetry-adapted Gaussian process regression to overcome these constraints. We show that it is possible to model VSFG signals with fully ab initio accuracy using machine learning and illustrate the versatility of our approach on the water/air interface. Our strategy allows us to identify the main sources of theoretical inaccuracy and establish a clear pathway toward the modeling of surface-sensitive spectroscopy of complex interfaces.

Isolated and solvated chiroptical behavior in conformationally flexible butanamines

The nonresonant optical activity of two highly flexible aliphatic amines, (2R)-3-methyl-2-butanamine (R-MBA) and (2R)-(3,3)-dimethyl-2-butanamine (R-DMBA), has been probed under isolated and solvated conditions to examine the roles of conformational isomerism and to explore the influence of extrinsic perturbations. The optical rotatory dispersion (ORD) measured in six solvents presented uniformly negative rotatory powers over the 320-590 nm region, with the long-wavelength magnitude of chiroptical response growing nearly monotonically as the dielectric constant of the surroundings diminished. The intrinsic specific optical rotation,α λ T (in deg dm-1 [g/mL]-1 ), extracted for ambient vapor-phase samples of R-MBA [-11.031(98) and -2.29 (11)] and R-DMBA [-9.434 (72) and -1.350 (48)] at 355 and 633 nm were best reproduced by counterintuitive solvents of high polarity (yet low polarizability) like acetonitrile and methanol. Attempts to interpret observed spectral signatures quantitatively relied on the linear-response frameworks of density-functional theory (B3LYP, cam-B3LYP, and dispersion-corrected analogs) and coupled-cluster theory (CCSD), with variants of the polarizable continuum model (PCM) deployed to account for the effects of implicit solvation. Building on the identification of several low-lying equilibrium geometries (nine for R-MBA and three for R-DMBA), ensemble-averaged ORD profiles were calculated at T = 300 K by means of the independent-conformer ansatz, which enabled response properties predicted for the optimized structure of each isomer to be combined through Boltzmann-weighted population fractions derived from corresponding relative internal-energy or free-energy values, the latter of which stemmed from composite CBS-APNO and G4 analyses. Although reasonable accord between theory and experiment was realized for the isolated (vapor-phase) species, the solution-phase results were less satisfactory and tended to degrade progressively as the solvent polarity increased. These trends were attributed to solvent-mediated changes in structural parameters and energy metrics for the transition states that separate and putatively isolate the equilibrium conformations supported by the ground electronic potential-energy surface, with the resulting displacement of barrier locations and/or decrease of barrier heights compromising the underlying premise of the independent-conformer ansatz.

Operando Modeling of Zeolite-Catalyzed Reactions Using First-Principles Molecular Dynamics Simulations

Within this Perspective, we critically reflect on the role of first-principles molecular dynamics (MD) simulations in unraveling the catalytic function within zeolites under operating conditions. First-principles MD simulations refer to methods where the dynamics of the nuclei is followed in time by integrating the Newtonian equations of motion on a potential energy surface that is determined by solving the quantum-mechanical many-body problem for the electrons. Catalytic solids used in industrial applications show an intriguing high degree of complexity, with phenomena taking place at a broad range of length and time scales. Additionally, the state and function of a catalyst critically depend on the operating conditions, such as temperature, moisture, presence of water, etc. Herein we show by means of a series of exemplary cases how first-principles MD simulations are instrumental to unravel the catalyst complexity at the molecular scale. Examples show how the nature of reactive species at higher catalytic temperatures may drastically change compared to species at lower temperatures and how the nature of active sites may dynamically change upon exposure to water. To simulate rare events, first-principles MD simulations need to be used in combination with enhanced sampling techniques to efficiently sample low-probability regions of phase space. Using these techniques, it is shown how competitive pathways at operating conditions can be discovered and how broad transition state regions can be explored. Interestingly, such simulations can also be used to study hindered diffusion under operating conditions. The cases shown clearly illustrate how first-principles MD simulations reveal insights into the catalytic function at operating conditions, which could not be discovered using static or local approaches where only a few points are considered on the potential energy surface (PES). Despite these advantages, some major hurdles still exist to fully integrate first-principles MD methods in a standard computational catalytic workflow or to use the output of MD simulations as input for multiple length/time scale methods that aim to bridge to the reactor scale. First of all, methods are needed that allow us to evaluate the interatomic forces with quantum-mechanical accuracy, albeit at a much lower computational cost compared to currently used density functional theory (DFT) methods. The use of DFT limits the currently attainable length/time scales to hundreds of picoseconds and a few nanometers, which are much smaller than realistic catalyst particle dimensions and time scales encountered in the catalysis process. One solution could be to construct machine learning potentials (MLPs), where a numerical potential is derived from underlying quantum-mechanical data, which could be used in subsequent MD simulations. As such, much longer length and time scales could be reached; however, quite some research is still necessary to construct MLPs for the complex systems encountered in industrially used catalysts. Second, most currently used enhanced sampling techniques in catalysis make use of collective variables (CVs), which are mostly determined based on chemical intuition. To explore complex reactive networks with MD simulations, methods are needed that allow the automatic discovery of CVs or methods that do not rely on a priori definition of CVs. Recently, various data-driven methods have been proposed, which could be explored for complex catalytic systems. Lastly, first-principles MD methods are currently mostly used to investigate local reactive events. We hope that with the rise of data-driven methods and more efficient methods to describe the PES, first-principles MD methods will in the future also be able to describe longer length/time scale processes in catalysis. This might lead to a consistent dynamic description of all steps-diffusion, adsorption, and reaction-as they take place at the catalyst particle level.

Nuclear-Electronic Orbital Quantum Dynamics of Plasmon-Driven H2 Photodissociation

Leveraging localized surface plasmon resonances of metal nanoparticles to trigger chemical reactions is a promising approach for heterogeneous catalysis. First-principles modeling of such processes is challenging due to the large number of electrons and electronic excited states as well as the significance of nuclear quantum effects when hydrogen is involved. Herein, the nonadiabatic nuclear-electronic quantum dynamics of plasmon-induced H2 photodissociation near an Al13- cluster is simulated with real-time nuclear-electronic orbital time-dependent density functional theory (RT-NEO-TDDFT). This approach propagates the nonequilibrium quantum dynamics of both electrons and protons. The plasmonic oscillations are shown to inject hot electrons into the antibonding orbital of H2, thereby inducing H2 dissociation. The quantum mechanical treatment of the hydrogen nuclei leads to faster H2 photodissociation and slightly larger isotope effects. Analysis of the nonequilibrium electronic density suggests that these findings stem from enhanced excited-state electronic coupling between the plasmonic mode and the H2 antibonding orbital due to proton delocalization or zero-point energy effects. Given the low computational overhead for including nuclear quantum effects with the RT-NEO-TDDFT approach, this work paves the way for simulating nonadiabatic nuclear-electronic quantum dynamics in other plasmonic systems.

Developing machine-learned potentials to simultaneously capture the dynamics of excess protons and hydroxide ions in classical and path integral simulations

The transport of excess protons and hydroxide ions in water underlies numerous important chemical and biological processes. Accurately simulating the associated transport mechanisms ideally requires utilizing ab initio molecular dynamics simulations to model the bond breaking and formation involved in proton transfer and path-integral simulations to model the nuclear quantum effects relevant to light hydrogen atoms. These requirements result in a prohibitive computational cost, especially at the time and length scales needed to converge proton transport properties. Here, we present machine-learned potentials (MLPs) that can model both excess protons and hydroxide ions at the generalized gradient approximation and hybrid density functional theory levels of accuracy and use them to perform multiple nanoseconds of both classical and path-integral proton defect simulations at a fraction of the cost of the corresponding ab initio simulations. We show that the MLPs are able to reproduce ab initio trends and converge properties such as the diffusion coefficients of both excess protons and hydroxide ions. We use our multi-nanosecond simulations, which allow us to monitor large numbers of proton transfer events, to analyze the role of hypercoordination in the transport mechanism of the hydroxide ion and provide further evidence for the asymmetry in diffusion between excess protons and hydroxide ions.

Ring Polymer Molecular Dynamics Approach to Quantum Dissociative Chemisorption Rates

A ring polymer molecular dynamics (RPMD) method is proposed for the calculation of the dissociative chemisorption rate coefficient on surfaces. The RPMD rate theory is capable of handling quantum effects such as the zero-point energy and tunneling in dissociative chemisorption, while it relies on classical trajectories for the simulation. Applications to H2 dissociative chemisorption are demonstrated. For the highly activated process on Ag(111), strong deviations from Arrhenius behavior are found at low temperatures and attributed to tunneling. On Pt(111), where the dissociation has a barrierless pathway, the RPMD rate coefficient is found to agree with the experimentally derived thermal sticking coefficient within a factor of 2 over a large temperature range. Significant quantum effects are also found.

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

Hydrogen bonding interactions with chromophores in chemical and biological environments play a key role in determining their electronic absorption and relaxation processes, which are manifested in their linear and multidimensional optical spectra. For chromophores in the condensed phase, the large number of atoms needed to simulate the environment has traditionally prohibited the use of high-level excited-state electronic structure methods. By leveraging transfer learning, we show how to construct machine-learned models to accurately predict the high-level excitation energies of a chromophore in solution from only 400 high-level calculations. We show that when the electronic excitations of the green fluorescent protein chromophore in water are treated using EOM-CCSD embedded in a DFT description of the solvent the optical spectrum is correctly captured and that this improvement arises from correctly treating the coupling of the electronic transition to electric fields, which leads to a larger response upon hydrogen bonding between the chromophore and water.

The development of nucleic acids force fields: From an unchallenged past to a competitive future

Molecular dynamics simulations have strongly matured as a method to study biomolecular processes. Their validity, however, is determined by the accuracy of the underlying force fields that describe the forces between all atoms. In this article, we review the development of nucleic acids force fields. We describe the early attempts in the 1990s and emphasize their strong influence on recent force fields. State-of-the-art force fields still use the same Lennard-Jones parameters derived 25 years ago in spite of the fact that these parameters were in general not fitted for nucleic acids. In addition, electrostatic parameters also are deprecated, which may explain some of the current force field deficiencies. We compare different force fields for various systems and discuss new tests of the recently developed Tumuc1 force field. The OL-force fields and Tumuc1 are arguably the best force fields to describe the DNA double helix. However, no force field is flawless. In particular, the description of sugar-puckering remains a problem for nucleic acids force fields. Future refinements are required, so we review methods for force field refinement and give an outlook to the future of force fields.