The 50 most-cited articles in The Journal of Chemical Physics, 2021

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is…

The recently proposed r2SCAN meta-generalized-gradient approximation (mGGA) of Furness and co-workers is used to construct an efficient composite electronic-structure method termed r2SCAN-3c. To this end, the unaltered r2SCAN functional is combined with a tailor-made triple-ζ Gaussian atomic orbital basis set as well as with refitted D4 and geometrical counter-poise corrections for London-dispersion and basis set superposition error. The performance of the new method is evaluated for the GMTKN55 database covering large parts of chemical space with about 1500 data points, as well as additional benchmarks for non-covalent interactions, organometallic reactions, and lattice energies of organic molecules and ices, as well as for the adsorption on polar salt and non-polar coinage-metal surfaces. These comprehensive tests reveal a spectacular performance and robustness of r2SCAN-3c: It by far surpasses its predecessor B97-3c at only twice the cost and provides one of the best results of all semi-local density-functional theory (DFT)/QZ methods ever tested for the GMTKN55 database at…

In the present work, we describe a more accurate and efficient variant of the chain-of-spheres algorithm (COSX) for exchange matrix computations. Higher accuracy for the numerical integration is obtained with new grids that were developed using global optimization techniques. With our new default grids, the average absolute energy errors are much lower than 0.1 kcal/mol, which is desirable to achieve "chemical accuracy." Although the size of the new grids is increased by roughly a factor of 2.5, the excellent efficiency of the original COSX implementation is still further improved in most cases. The evaluation of the analytic electrostatic potential integrals was significantly accelerated by a new implementation of rolled-out versions of the Dupuis-Rys-King and Head-Gordon-Pople algorithms. Compared to our earlier implementation, a twofold speedup is obtained for the frequently used triple-ζ basis sets, while up to a 16-fold speedup is observed for quadruple-ζ basis sets. These large gains are a consequence of both the more efficient integral evaluation and the intermediate exchange…

and Fe(II) in FeO is compared with theoretical predictions based on ab initio wavefunctions that accurately treat the final, core-hole, multiplets. The principal objectives of this comparison are to understand the multiplet structure and to evaluate the use of both the 2p and 3p spectra in determining oxidation states. In order to properly interpret the features of these spectra and to use the XPS to provide atomistic insights as well as atomic composition, it is necessary to understand the origin of the multiplet energies and intensities. The theoretical treatment takes into account the ligand field and spin-orbit splittings, the covalent mixing of ligand and Fe 3d orbitals, and the angular momentum coupling of the open shell electrons. These effects lead to the distribution of XPS intensity into a large number of final, ionic, states that are only partly resolved with energies spread over a wide range of binding energies. For this reason, it is necessary to record the Fe 2p and 3p XPS spectra over a wide energy range, which includes all the multiplets in the theoretical treatment…

Machine learning (ML) methods are being used in almost every conceivable area of electronic structure theory and molecular simulation. In particular, ML has become firmly established in the construction of high-dimensional interatomic potentials. Not a day goes by without another proof of principle being published on how ML methods can represent and predict quantum mechanical properties-be they observable, such as molecular polarizabilities, or not, such as atomic charges. As ML is becoming pervasive in electronic structure theory and molecular simulation, we provide an overview of how atomistic computational modeling is being transformed by the incorporation of ML approaches. From the perspective of the practitioner in the field, we assess how common workflows to predict structure, dynamics, and spectroscopy are affected by ML. Finally, we discuss how a tighter and lasting integration of ML methods with computational chemistry and materials science can be achieved and what it will mean for research practice, software development, and postgraduate training.

We combine a regularized variant of the strongly constrained and appropriately normed semilocal density functional [J. Sun, A. Ruzsinszky, and J. P. Perdew, Phys. Rev. Lett. 115, 036402 (2015)] with the latest generation semi-classical London dispersion correction. The resulting density functional approximation r2SCAN-D4 has the speed of generalized gradient approximations while approaching the accuracy of hybrid functionals for general chemical applications. We demonstrate its numerical robustness in real-life settings and benchmark molecular geometries, general main group and organo-metallic thermochemistry, and non-covalent interactions in supramolecular complexes and molecular crystals. Main group and transition metal bond lengths have errors of just 0.8%, which is competitive with hybrid functionals for main group molecules and outperforms them for transition metal complexes. The weighted mean absolute deviation (WTMAD2) on the large GMTKN55 database of chemical properties is exceptionally small at 7.5 kcal/mol. This also holds for metal organic reactions with an MAD of 3.3…

Simulating and predicting multiscale problems that couple multiple physics and dynamics across many orders of spatiotemporal scales is a great challenge that has not been investigated systematically by deep neural networks (DNNs). Herein, we develop a framework based on operator regression, the so-called deep operator network (DeepONet), with the long-term objective to simplify multiscale modeling by avoiding the fragile and time-consuming "hand-shaking" interface algorithms for stitching together heterogeneous descriptions of multiscale phenomena. To this end, as a first step, we investigate if a DeepONet can learn the dynamics of different scale regimes, one at the deterministic macroscale and the other at the stochastic microscale regime with inherent thermal fluctuations. Specifically, we test the effectiveness and accuracy of the DeepONet in predicting multirate bubble growth dynamics, which is described by a Rayleigh-Plesset (R-P) equation at the macroscale and modeled as a stochastic nucleation and cavitation process at the microscale by dissipative particle dynamics (DPD).…

“Δ-machine learning” refers to a machine learning approach to bring a property such as a potential energy surface (PES) based on low-level (LL) density functional theory (DFT) energies and gradients close to a coupled cluster (CC) level of accuracy. Here, we present such an approach that uses the permutationally invariant polynomial (PIP) method to fit high-dimensional PESs. The approach is represented by a simple equation, in obvious notation VLL→CC = VLL + ΔVCC–LL, and demonstrated for CH4, H3O+, and trans and cis-N-methyl acetamide (NMA), CH3CONHCH3. For these molecules, the LL PES, VLL, is a PIP fit to DFT/B3LYP/6-31+G(d) energies and gradients and ΔVCC–LL is a precise PIP fit obtained using a low-order PIP basis set and based on a relatively small number of CCSD(T) energies. For CH4, these are new calculations adopting an aug-cc-pVDZ basis, for H3O+, previous CCSD(T)-F12/aug-cc-pVQZ energies are used, while for NMA, new CCSD(T)-F12/aug-cc-pVDZ calculations are performed. With as few as 200 CCSD(T) energies, the new PESs are in excellent agreement with benchmark CCSD(T) results…

Intermolecular bonds are weak compared to covalent bonds, but they are strong enough to influence the properties of large molecular systems. In this work, we investigate how strong light-matter coupling inside an optical cavity can modify intermolecular forces and illustrate the varying necessity of correlation in their description. The electromagnetic field inside the cavity can modulate the ground state properties of weakly bound complexes. Tuning the field polarization and cavity frequency, the interactions can be stabilized or destabilized, and electron densities, dipole moments, and polarizabilities can be altered. We demonstrate that electron-photon correlation is fundamental to describe intermolecular interactions in strong light-matter coupling. This work proposes optical cavities as a novel tool to manipulate and control ground state properties, solvent effects, and intermolecular interactions for molecules and materials.

One of the most exciting and debated aspects of polariton chemistry is the possibility that chemical reactions can be catalyzed by vibrational strong coupling (VSC) with confined optical modes in the absence of external illumination. Here, we report an attempt to reproduce the enhanced rate of cyanate ion hydrolysis reported by Hiura et al. [chemRxiv:7234721 (2019)] when the collective OH stretching vibrations of water (which is both the solvent and a reactant) are strongly coupled to a Fabry-Pérot cavity mode. Using a piezo-tunable microcavity, we reproduce the reported vacuum Rabi splitting but fail to observe any change in the reaction rate as the cavity thickness is tuned in and out of the strong coupling regime during a given experiment. These findings suggest that there are subtleties involved in successfully realizing VSC-catalyzed reaction kinetics and therefore motivate a broader effort within the community to validate the claims of polariton chemistry in the dark.

We explore the role of long-range interactions in atomistic machine-learning models by analyzing the effects on fitting accuracy, isolated cluster properties, and bulk thermodynamic properties. Such models have become increasingly popular in molecular simulations given their ability to learn highly complex and multi-dimensional interactions within a local environment; however, many of them fundamentally lack a description of explicit long-range interactions. In order to provide a well-defined benchmark system with precisely known pairwise interactions, we chose as the reference model a flexible version of the Extended Simple Point Charge (SPC/E) water model. Our analysis shows that while local representations are sufficient for predictions of the condensed liquid phase, the short-range nature of machine-learning models falls short in representing cluster and vapor phase properties. These findings provide an improved understanding of the role of long-range interactions in machine learning models and the regimes where they are necessary.

Solid-state electrolyte materials with superior lithium ionic conductivities are vital to the next-generation Li-ion batteries. Molecular dynamics could provide atomic scale information to understand the diffusion process of Li-ion in these superionic conductor materials. Here, we implement the deep potential generator to set up an efficient protocol to automatically generate interatomic potentials for Li10GeP2S12-type solid-state electrolyte materials (Li10GeP2S12, Li10SiP2S12, and Li10SnP2S12). The reliability and accuracy of the fast interatomic potentials are validated. With the potentials, we extend the simulation of the diffusion process to a wide temperature range (300 K–1000 K) and systems with large size (∼1000 atoms). Important technical aspects such as the statistical error and size effect are carefully investigated, and benchmark tests including the effect of density functional, thermal expansion, and configurational disorder are performed. The computed data that consider these factors agree well with the experimental results, and we find that the three structures show…

We study how inertia affects the behavior of self-propelled particles moving through a viscous solvent by employing the underdamped version of the active Ornstein-Uhlenbeck model. We consider both potential-free and harmonically confined underdamped active particles and investigate how the single-particle trajectories change as the drag coefficient is varied. In both cases, we obtain the matrix of correlations between the position, velocity, and self-propulsion and the explicit form of the steady-state probability distribution function. Our results reveal the existence of marked equal-time correlations between velocity and active force in the non-equilibrium steady state. Inertia also affects the time-dependent properties of the active particles and leads to non-monotonic decay of the two-time correlation functions of particle positions and velocities. We also study how the virial pressure of particles confined to harmonic traps changes as one goes from the overdamped to the underdamped regime. Finally, the study of the correlations in the underdamped regime is extended to the case…

The ability to make sense of the massive amounts of high-dimensional data generated from molecular dynamics simulations is heavily dependent on the knowledge of a low-dimensional manifold (parameterized by a reaction coordinate or RC) that typically distinguishes between relevant metastable states, and which captures the relevant slow dynamics of interest. Methods based on machine learning and artificial intelligence have been proposed over the years to deal with learning such low-dimensional manifolds, but they are often criticized for a disconnect from more traditional and physically interpretable approaches. To deal with such concerns, in this work we propose a deep learning based state predictive information bottleneck approach to learn the RC from high-dimensional molecular simulation trajectories. We demonstrate analytically and numerically how the RC learnt in this approach is connected to the committor in chemical physics and can be used to accurately identify transition states. A crucial hyperparameter in this approach is the time delay or how far into the future the…

Coupling molecules to the confined light modes of an optical cavity is showing great promise for manipulating chemical reactions. However, to fully exploit this principle and use cavities as a new tool for controlling chemistry, a complete understanding of the effects of strong light-matter coupling on molecular dynamics and reactivity is required. While quantum chemistry can provide atomistic insight into the reactivity of uncoupled molecules, the possibilities to also explore strongly coupled systems are still rather limited due to the challenges associated with an accurate description of the cavity in such calculations. Despite recent progress in introducing strong coupling effects into quantum chemistry calculations, applications are mostly restricted to single or simplified molecules in ideal lossless cavities that support a single light mode only. However, even if commonly used planar mirror micro-cavities are characterized by a fundamental mode with a frequency determined by the distance between the mirrors, the cavity energy also depends on the wave vector of the incident…

Machine-learning models have emerged as a very effective strategy to sidestep time-consuming electronic-structure calculations, enabling accurate simulations of greater size, time scale, and complexity. Given the interpolative nature of these models, the reliability of predictions depends on the position in phase space, and it is crucial to obtain an estimate of the error that derives from the finite number of reference structures included during model training. When using a machine-learning potential to sample a finite-temperature ensemble, the uncertainty on individual configurations translates into an error on thermodynamic averages and leads to a loss of accuracy when the simulation enters a previously unexplored region. Here, we discuss how uncertainty quantification can be used, together with a baseline energy model, or a more robust but less accurate interatomic potential, to obtain more resilient simulations and to support active-learning strategies. Furthermore, we introduce an on-the-fly reweighing scheme that makes it possible to estimate the uncertainty in thermodynamic…

We report the results of an attempt to reproduce a reported cavity catalysis of the ester hydrolysis of para-nitrophenyl acetate due to vibrational strong coupling. While we achieved the same light-matter coupling strength and detuning, we did not observe the reported ten-fold increase in the reaction rate constant. Furthermore, no obvious detuning dependence was observed. The inconsistency with the reported literature suggests that cavity catalysis is sensitive to experimental details beyond the onset of vibrational strong coupling. This indicates that other important factors are involved and have been overlooked so far. We find that more investigation into the limits, key factors, and mechanisms to reliably actualize cavity modified reactions is needed.

Particle Mesh Ewald (PME) has become a standard method for treating long-range electrostatics in molecular simulations. Although the method has inferior asymptotic computational complexity to its linear scaling competitors, it remains enormously popular due to its high efficiency, which stems from the use of fast Fourier transforms (FFTs). This use of FFTs provides great challenges for scaling the method up to massively parallel systems, in large part because of the need to transfer large amounts of data. In this work, we demonstrate that this data transfer volume can be greatly reduced as a natural consequence of the structure of the PME equations. We also suggest an alternative algorithm that supplants the FFT with a linear algebra approach, which further decreases communication costs at the expense of increased asymptotic computational complexity. This linear algebra based approach is demonstrated to have great potential for latency hiding by interleaving communication and computation steps of the short- and long-range electrostatic terms.

When selecting a solvent for a given solute, the strongly held idiom "like dissolves like", meaning that polar solvents are used for polar solutes, is often used. This idea has resulted from the concept that most molecular solvents are homogeneous. In a deep eutectic solvent (DES), however, both components can be ionic or non-ionic, polar or non-polar. By tuning the components, DESs can solubilize a wide variety of solutes, often mixing hydrophobic and hydrophilic components, and the mixture can be designed to control phase behavior. The liquids often contain significant short-length order, and preferential solvation of one component often occurs. The addition of small polar molecules such as water or alcohols results in non-homogeneous liquids, which have significantly decreased viscosity and increased ionic conductivity. Accordingly, the areas covered in this special issue focus on structure and dynamics, solvation, the mobility of charged species, and the ability to obtain controllable phase behavior by adding polar diluents or using hydrophobic DESs.

There has been recent interest in the deployment of ab initio density matrix renormalization group (DMRG) computations on high performance computing platforms. Here, we introduce a reformulation of the conventional distributed memory ab initio DMRG algorithm that connects it to the conceptually simpler and advantageous sum of the sub-Hamiltonian approach. Starting from this framework, we further explore a hierarchy of parallelism strategies that includes (i) parallelism over the sum of sub-Hamiltonians, (ii) parallelism over sites, (iii) parallelism over normal and complementary operators, (iv) parallelism over symmetry sectors, and (v) parallelism within dense matrix multiplications. We describe how to reduce processor load imbalance and the communication cost of the algorithm to achieve higher efficiencies. We illustrate the performance of our new open-source implementation on a recent benchmark ground-state calculation of benzene in an orbital space of 108 orbitals and 30 electrons, with a bond dimension of up to 6000, and a model of the FeMo cofactor with 76 orbitals and 113…

Three-dimensional (3D) organization of the human genome plays an essential role in all DNA-templated processes, including gene transcription, gene regulation, and DNA replication. Computational modeling can be an effective way of building high-resolution genome structures and improving our understanding of these molecular processes. However, it faces significant challenges as the human genome consists of over 6 × 109 base pairs, a system size that exceeds the capacity of traditional modeling approaches. In this perspective, we review the progress that has been made in modeling the human genome. Coarse-grained models parameterized to reproduce experimental data via the maximum entropy optimization algorithm serve as effective means to study genome organization at various length scales. They have provided insight into the principles of whole-genome organization and enabled de novo predictions of chromosome structures from epigenetic modifications. Applications of these models at a near-atomistic resolution further revealed physicochemical interactions that drive the phase separation…

Quantum electrodynamics coupled-cluster (QED-CC) theory is used to model vacuum-field-induced changes to ground-state properties of a series of sodium halide compounds (NaX, X = F, Cl, Br, and I) strongly coupled to an optical cavity. Ionization potentials (IPs) and electron affinities (EAs) are presented, and it is demonstrated that EAs are easily modulated by cavity interactions, while IPs for these compounds are far less sensitive to the presence of the cavity. EAs predicted by QED-CC can be reduced by as much as 0.22 eV (or ≈50%) when considering experimentally accessible coupling parameters.

We present OrbNet Denali, a machine learning model for an electronic structure that is designed as a drop-in replacement for ground-state density functional theory (DFT) energy calculations. The model is a message-passing graph neural network that uses symmetry-adapted atomic orbital features from a low-cost quantum calculation to predict the energy of a molecule. OrbNet Denali is trained on a vast dataset of 2.3 × 106 DFT calculations on molecules and geometries. This dataset covers the most common elements in biochemistry and organic chemistry (H, Li, B, C, N, O, F, Na, Mg, Si, P, S, Cl, K, Ca, Br, and I) and charged molecules. OrbNet Denali is demonstrated on several well-established benchmark datasets, and we find that it provides accuracy that is on par with modern DFT methods while offering a speedup of up to three orders of magnitude. For the GMTKN55 benchmark set, OrbNet Denali achieves WTMAD-1 and WTMAD-2 scores of 7.19 and 9.84, on par with modern DFT functionals. For several GMTKN55 subsets, which contain chemical problems that are not present in the training set, OrbNet…

Glassy solids exhibit a wide variety of generic thermomechanical properties, ranging from universal anomalous specific heat at cryogenic temperatures to nonlinear plastic yielding and failure under external driving forces, which qualitatively differ from their crystalline counterparts. For a long time, it has been believed that many of these properties are intimately related to nonphononic, low-energy quasilocalized excitations (QLEs) in glasses. Indeed, recent computer simulations have conclusively revealed that the self-organization of glasses during vitrification upon cooling from a melt leads to the emergence of such QLEs. In this Perspective, we review developments over the past three decades toward understanding the emergence of QLEs in structural glasses and the degree of universality in their statistical and structural properties. We discuss the challenges and difficulties that hindered progress in achieving these goals and review the frameworks put forward to overcome them. We conclude with an outlook on future research directions and open questions.

Inspired by recent experimental observations of anomalously large decay lengths in concentrated electrolytes, we revisit the Restricted Primitive Model (RPM) for an aqueous electrolyte. We investigate the asymptotic decay lengths of the one-body ionic density profiles for the RPM in contact with a planar electrode using classical Density Functional Theory (DFT) and compare these with the decay lengths of the corresponding two-body correlation functions in bulk systems, obtained in previous Integral Equation Theory (IET) studies. Extensive Molecular Dynamics (MD) simulations are employed to complement the DFT and IET predictions. Our DFT calculations incorporate electrostatic interactions between the ions using three different (existing) approaches: one is based on the simplest mean-field treatment of Coulomb interactions (MFC), while the other two employ the Mean Spherical Approximation (MSA). The MSAc invokes only the MSA bulk direct correlation function, whereas the MSAu also incorporates the MSA bulk internal energy. Although MSAu yields profiles that are in excellent agreement…

Liquid-liquid phase separation (LLPS) is widely utilized by the cell to organize and regulate various biochemical processes. Although the LLPS of proteins is known to occur in a sequence-dependent manner, it is unclear how sequence properties dictate the nature of the phase transition and thereby influence condensed phase morphology. In this work, we have utilized grand canonical Monte Carlo simulations for a simple coarse-grained model of disordered proteins to systematically investigate how sequence distribution, sticker fraction, and chain length impact the formation of finite-size aggregates, which can preempt macroscopic phase separation for some sequences. We demonstrate that a normalized sequence charge decoration (SCD) parameter establishes a "soft" predictive criterion for distinguishing when a model protein undergoes macroscopic phase separation vs finite aggregation. Additionally, we find that this order parameter is strongly correlated with the critical density for phase separation, highlighting an unambiguous connection between sequence distribution and condensed phase…

Post-self-consistent dispersion corrections are now the norm when applying density-functional theory to systems where non-covalent interactions play an important role. However, there is a wide range of base functionals and dispersion corrections available from which to choose. In this work, we opine on the most desirable requirements to ensure that both the base functional and dispersion correction, individually, are as accurate as possible for non-bonded repulsion and dispersion attraction. The base functional should be dispersionless, numerically stable, and involve minimal delocalization error. Simultaneously, the dispersion correction should include finite damping, higher-order pairwise dispersion terms, and electronic many-body effects. These criteria are essential for avoiding reliance on error cancellation and obtaining correct results from correct physics.

We have developed a software package, namely, PASP (Property Analysis and Simulation Package for materials), to analyze the structural, electronic, magnetic, and thermodynamic properties of complex condensed matter systems. Our package integrates several functionalities including symmetry analysis, global structure searching methods, effective Hamiltonian methods, and Monte Carlo simulation methods. In conjunction with first-principles calculations, PASP has been successfully applied to diverse physical systems. In this paper, we give a brief introduction to its main features and underlying theoretical formulism. Some typical applications are provided to demonstrate the usefulness, high efficiency, and reliability of PASP. We expect that further developments will make PASP a general-purpose tool for material simulation and property calculation of condensed matters.

A factorization of the matrix elements of the Dyall Hamiltonian in N-electron valence state perturbation theory allowing their evaluation with a computational effort comparable to the one needed for the construction of the third-order reduced density matrix at the most is presented. Thus, the computational bottleneck arising from explicit evaluation of the fourth-order density matrix is avoided. It is also shown that the residual terms arising in the case of an approximate complete active space configuration interaction solution and containing even the fifth-order density matrix for two excitation classes can be evaluated with little additional effort by choosing again a favorable factorization of the corresponding matrix elements. An analogous argument is also provided for avoiding the fourth-order density matrix in complete active space second-order perturbation theory. Practical calculations indicate that such an approach leads to a considerable gain in computational efficiency without any compromise in numerical accuracy or stability.

Two-photon absorption (TPA) and other nonlinear interactions of molecules with time-frequency-entangled photon pairs have been predicted to display a variety of fascinating effects. Therefore, their potential use in practical quantum-enhanced molecular spectroscopy requires close examination. This Tutorial presents a detailed theoretical study of one- and two-photon absorption by molecules, focusing on how to treat the quantum nature of light. We review some basic quantum optics theory and then we review the density-matrix (Liouville) derivation of molecular optical response, emphasizing how to incorporate quantum states of light into the treatment. For illustration, we treat in detail the TPA of photon pairs created by spontaneous parametric down conversion, with an emphasis on how quantum light TPA differs from that with classical light. In particular, we treat the question of how much enhancement of the TPA rate can be achieved using entangled states. This Tutorial includes a review of known theoretical methods and results as well as some extensions, especially the comparison of…

By adopting a perspective informed by contemporary liquid-state theory, we consider how to train an artificial neural network potential to describe inhomogeneous, disordered systems. We find that neural network potentials based on local representations of atomic environments are capable of describing some properties of liquid-vapor interfaces but typically fail for properties that depend on unbalanced long-ranged interactions that build up in the presence of broken translation symmetry. These same interactions cancel in the translationally invariant bulk, allowing local neural network potentials to describe bulk properties correctly. By incorporating explicit models of the slowly varying long-ranged interactions and training neural networks only on the short-ranged components, we can arrive at potentials that robustly recover interfacial properties. We find that local neural network models can sometimes approximate a local molecular field potential to correct for the truncated interactions, but this behavior is variable and hard to learn. Generally, we find that models with explicit…

The incorporation of nuclear quantum effects and non-Born-Oppenheimer behavior into quantum chemistry calculations and molecular dynamics simulations is a longstanding challenge. The nuclear-electronic orbital (NEO) approach treats specified nuclei, typically protons, quantum mechanically on the same level as the electrons with wave function and density functional theory methods. This approach inherently includes nuclear delocalization and zero-point energy in molecular energy calculations, geometry optimizations, reaction paths, and dynamics. It can also provide accurate descriptions of excited electronic, vibrational, and vibronic states as well as nuclear tunneling and nonadiabatic dynamics. Nonequilibrium nuclear-electronic dynamics simulations beyond the Born-Oppenheimer approximation can be used to investigate a wide range of excited state processes. This Perspective provides an overview of the foundational NEO methods and enumerates the prospects for using these methods as building blocks for future developments. The conceptual simplicity and computational efficiency of the…

Inspired by the formulation of quantum-electrodynamical time-dependent density functional theory (QED-TDDFT) by Rubio and co-workers [Flick et al., ACS Photonics 6, 2757-2778 (2019)], we propose an implementation that uses dimensionless amplitudes for describing the photonic contributions to QED-TDDFT electron-photon eigenstates. This leads to a Hermitian QED-TDDFT coupling matrix that is expected to facilitate the future development of analytic derivatives. Through a Gaussian atomic basis implementation of the QED-TDDFT method, we examined the effect of dipole self-energy, rotating-wave approximation, and the Tamm-Dancoff approximation on the QED-TDDFT eigenstates of model compounds (ethene, formaldehyde, and benzaldehyde) in an optical cavity. We highlight, in the strong coupling regime, the role of higher-energy and off-resonance excited states with large transition dipole moments in the direction of the photonic field, which are automatically accounted for in our QED-TDDFT calculations and might substantially affect the energies and compositions of polaritons associated with…

Accurate modeling of the solvent environment for biological molecules is crucial for computational biology and drug design. A popular approach to achieve long simulation time scales for large system sizes is to incorporate the effect of the solvent in a mean-field fashion with implicit solvent models. However, a challenge with existing implicit solvent models is that they often lack accuracy or certain physical properties compared to explicit solvent models as the many-body effects of the neglected solvent molecules are difficult to model as a mean field. Here, we leverage machine learning (ML) and multi-scale coarse graining (CG) in order to learn implicit solvent models that can approximate the energetic and thermodynamic properties of a given explicit solvent model with arbitrary accuracy, given enough training data. Following the previous ML-CG models CGnet and CGSchnet, we introduce ISSNet, a graph neural network, to model the implicit solvent potential of mean force. ISSNet can learn from explicit solvent simulation data and be readily applied to molecular dynamics…

Quantum chemistry simulations of some industrially relevant molecules are reported, employing variational quantum algorithms for near-term quantum devices. The energies and dipole moments are calculated along the dissociation curves for lithium hydride (LiH), hydrogen sulfide, lithium hydrogen sulfide, and lithium sulfide. In all cases, we focus on the breaking of a single bond to obtain information about the stability of the molecular species being investigated. We calculate energies and a variety of electrostatic properties of these molecules using classical simulators of quantum devices, with up to 21 qubits for lithium sulfide. Moreover, we calculate the ground-state energy and dipole moment along the dissociation pathway of LiH using IBM quantum devices. This is the first example, to the best of our knowledge, of dipole moment calculations being performed on quantum hardware.

We theoretically demonstrate that the chemical reaction rate constant can be significantly suppressed by coupling molecular vibrations with an optical cavity, exhibiting both the collective coupling effect and the cavity frequency modification of the rate constant. When a reaction coordinate is strongly coupled to the solvent molecules, the reaction rate constant is reduced due to the dynamical caging effect. We demonstrate that collectively coupling the solvent to the cavity can further enhance this dynamical caging effect, leading to additional suppression of the chemical kinetics. This effect is further amplified when cavity loss is considered.

Numerous linear and non-linear spectroscopic techniques have been developed to elucidate structural and functional information of complex systems ranging from natural systems, such as proteins and light-harvesting systems, to synthetic systems, such as solar cell materials and light-emitting diodes. The obtained experimental data can be challenging to interpret due to the complexity and potential overlapping spectral signatures. Therefore, computational spectroscopy plays a crucial role in the interpretation and understanding of spectral observables of complex systems. Computational modeling of various spectroscopic techniques has seen significant developments in the past decade, when it comes to the systems that can be addressed, the size and complexity of the sample types, the accuracy of the methods, and the spectroscopic techniques that can be addressed. In this Perspective, I will review the computational spectroscopy methods that have been developed and applied for infrared and visible spectroscopies in the condensed phase. I will discuss some of the questions that this has…

The development of new energetic materials (EMs) is accompanied by significant hazards, prompting interest in their computational design. Before reliable in silico design strategies can be realized, however, approaches to understand and predict EM response to mechanical impact must be developed. We present here a fully ab initio model based on phonon up-pumping that successfully ranks the relative impact sensitivity of a series of organic EMs. The methodology depends only on the crystallographic unit cell and Brillouin zone center vibrational frequencies. We, therefore, expect this approach to become an integral tool in the large-scale screening of potential EMs.

We develop new methods to efficiently propagate the hierarchical equations of motion (HEOM) by using the Tucker and hierarchical Tucker (HT) tensors to represent the reduced density operator and auxiliary density operators. We first show that by employing the split operator method, the specific structure of the HEOM allows a simple propagation scheme using the Tucker tensor. When the number of effective modes in the HEOM increases and the Tucker representation becomes intractable, the split operator method is extended to the binary tree structure of the HT representation. It is found that to update the binary tree nodes related to a specific effective mode, we only need to propagate a short matrix product state constructed from these nodes. Numerical results show that by further employing the mode combination technique commonly used in the multi-configuration time-dependent Hartree approaches, the binary tree representation can be applied to study excitation energy transfer dynamics in a fairly large system including over 104 effective modes. The new methods may thus provide a…

Recent experiments have observed that the chemical and photophysical properties of molecules can be modified inside an optical Fabry-Pérot microcavity under collective vibrational strong coupling (VSC) conditions, and such modification is currently not well understood by theory. In an effort to understand the origin of such cavity-induced phenomena, some recent studies have focused on the effect of the cavity environment on the nonlinear optical response of the molecular subsystem. Here, we use a recently proposed protocol for classical cavity molecular dynamics simulations to numerically investigate the linear and the nonlinear response of liquid carbon dioxide under such VSC conditions following an optical pulse excitation. We find that applying a strong pulse of excitation to the lower hybrid light-matter state, i.e., the lower polariton (LP), can lead to an overall molecular nonlinear absorption that is enhanced by up to two orders of magnitude relative to the excitation outside the cavity. This polariton-enhanced multiphoton absorption also causes an ultrashort LP lifetime (0.2…

Strong coupling between various kinds of material excitations and optical modes has recently shown potential to modify chemical reaction rates in both excited and ground states. The ground-state modification in chemical reaction rates has usually been reported by coupling a vibrational mode of an organic molecule to the vacuum field of an external optical cavity, such as a planar Fabry-Pérot microcavity made of two metallic mirrors. However, using an external cavity to form polaritonic states might (i) limit the scope of possible applications of such systems and (ii) might be unnecessary. Here, we highlight the possibility of using optical modes sustained by materials themselves to self-couple to their own electronic or vibrational resonances. By tracing the roots of the corresponding dispersion relations in the complex frequency plane, we show that electronic and vibrational polaritons are natural eigenstates of bulk and nanostructured resonant materials that require no external cavity. Several concrete examples such as a slab of the excitonic material and a spherical water droplet…

In this work, we provide a nuanced view of electron correlation in the context of transition metal complexes, reconciling computational characterization via spin and spatial symmetry breaking in single-reference methods with qualitative concepts from ligand-field and molecular orbital theories. These insights provide the tools to reliably diagnose the multi-reference character, and our analysis reveals that while strong (i.e., static) correlation can be found in linear molecules (e.g., diatomics) and weakly bound and antiferromagnetically coupled (monometal-noninnocent ligand or multi-metal) complexes, it is rarely found in the ground-states of mono-transition-metal complexes. This leads to a picture of static correlation that is no more complex for transition metals than it is, e.g., for organic biradicaloids. In contrast, the ability of organometallic species to form more complex interactions, involving both ligand-to-metal σ-donation and metal-to-ligand π-backdonation, places a larger burden on a theory's treatment of dynamic correlation. We hypothesize that chemical bonds in…

Efficient computer implementations of the GW approximation must approximate a numerically challenging frequency integral; the integral can be performed analytically, but doing so leads to an expensive implementation whose computational cost scales as O(N6), where N is the size of the system. Here, we introduce a new formulation of the full-frequency GW approximation by exactly recasting it as an eigenvalue problem in an expanded space. This new formulation (1) avoids the use of time or frequency grids, (2) naturally obviates the need for the common “diagonal” approximation, (3) enables common iterative eigensolvers that reduce the canonical scaling to O(N5), and (4) enables a density-fitted implementation that reduces the scaling to O(N4). We numerically verify these scaling behaviors and test a variety of approximations that are motivated by this new formulation. The new formulation is found to be competitive with conventional O(N4) methods based on analytic continuation or contour deformation. In this new formulation, the relation of the GW approximation to configuration…

The energy difference (ΔEST) between the lowest singlet (S1) state and the triplet (T1) excited state of a set of azaphenalene compounds, which is theoretically and experimentally known to violate Hund’s rule, giving rise to the inversion of the order of those states, is calculated here with a family of double-hybrid density functionals. That excited-state inversion is known to be very challenging to reproduce for time-dependent density functional theory employing common functionals, e.g., hybrid or range-separated expressions, but not for wavefunction methods due to the inclusion of higher-than-single excitations. Therefore, we explore here if the last developed family of density functional expressions (i.e., double-hybrid models) is able to provide not only the right excited-state energy order but also accurate ΔEST values, thanks to the approximate inclusion of double excitations within these models. We herein employ standard double-hybrid (B2-PLYP, PBE-QIDH, and PBE0-2), range-separated (ωB2-PLYP and RSX-QIDH), spin-scaled (SCS/SOS-B2PLYP21, SCS-PBE-QIDH, and SOS-PBE-QIDH), and…

The interplay of kinetics and thermodynamics governs reactive processes, and their control is key in synthesis efforts. While sophisticated numerical methods for studying equilibrium states have well advanced, quantitative predictions of kinetic behavior remain challenging. We introduce a reactant-to-barrier (R2B) machine learning model that rapidly and accurately infers activation energies and transition state geometries throughout the chemical compound space. R2B exhibits improving accuracy as training set sizes grow and requires as input solely the molecular graph of the reactant and the information of the reaction type. We provide numerical evidence for the applicability of R2B for two competing text-book reactions relevant to organic synthesis, E2 and SN2, trained and tested on chemically diverse quantum data from the literature. After training on 1–1.8k examples, R2B predicts activation energies on average within less than 2.5 kcal/mol with respect to the coupled-cluster singles doubles reference within milliseconds. Principal component analysis of kernel matrices reveals the…

Geometry optimization is an important part of both computational materials and surface science because it is the path to finding ground state atomic structures and reaction pathways. These properties are used in the estimation of thermodynamic and kinetic properties of molecular and crystal structures. This process is slow at the quantum level of theory because it involves an iterative calculation of forces using quantum chemical codes such as density functional theory (DFT), which are computationally expensive and which limit the speed of the optimization algorithms. It would be highly advantageous to accelerate this process because then one could do either the same amount of work in less time or more work in the same time. In this work, we provide a neural network (NN) ensemble based active learning method to accelerate the local geometry optimization for multiple configurations simultaneously. We illustrate the acceleration on several case studies including bare metal surfaces, surfaces with adsorbates, and nudged elastic band for two reactions. In all cases, the accelerated…

Among the many existing molecular models of water, the MB-pol many-body potential has emerged as a remarkably accurate model, capable of reproducing thermodynamic, structural, and dynamic properties across water's solid, liquid, and vapor phases. In this work, we assessed the performance of MB-pol with respect to an important set of properties related to vapor-liquid coexistence and interfacial behavior. Through direct coexistence classical molecular dynamics simulations at temperatures of 400 K < T < 600 K, we calculated properties such as equilibrium coexistence densities, vapor-liquid interfacial tension, vapor pressure, and enthalpy of vaporization and compared the MB-pol results to experimental data. We also compared rigid vs fully flexible variants of the MB-pol model and evaluated system size effects for the properties studied. We found that the MB-pol model predictions are in good agreement with experimental data, even for temperatures approaching the vapor-liquid critical point; this agreement was largely insensitive to system sizes or the rigid vs flexible treatment of the…

We present a new implementation of a trust-region augmented Hessian approach (TRAH-SCF) for restricted and unrestricted Hartree–Fock and Kohn–Sham methods. With TRAH-SCF, convergence can always be achieved even with tight convergence thresholds, which requires just a modest number of iterations. Our convergence benchmark study and our illustrative applications focus on open-shell molecules, also antiferromagnetically coupled systems, for which it is notoriously complicated to converge the Roothaan–Hall self-consistent field (SCF) equations. We compare the number of TRAH iterations to reach convergence with those of Pulay’s original and Kollmar’s (K) variants of the direct inversion of the iterative subspace (DIIS) method and also analyze the obtained SCF solutions. Often, TRAH-SCF finds a symmetry-broken solution with a lower energy than DIIS and KDIIS. For unrestricted calculations, this is accompanied by a larger spin contamination, i.e., larger deviation from the desired spin-restricted ⟨S2⟩ expectation value. However, there are also rare cases in which DIIS finds a solution with…

Strong light-matter coupling to form exciton- and vibropolaritons is increasingly touted as a powerful tool to alter the fundamental properties of organic materials. It is proposed that these states and their facile tunability can be used to rewrite molecular potential energy landscapes and redirect photophysical pathways, with applications from catalysis to electronic devices. Crucial to their photophysical properties is the exchange of energy between coherent, bright polaritons and incoherent dark states. One of the most potent tools to explore this interplay is transient absorption/reflectance spectroscopy. Previous studies have revealed unexpectedly long lifetimes of the coherent polariton states, for which there is no theoretical explanation. Applying these transient methods to a series of strong-coupled organic microcavities, we recover similar long-lived spectral effects. Based on transfer-matrix modeling of the transient experiment, we find that virtually the entire photoresponse results from photoexcitation effects other than the generation of polariton states. Our results…