First-principles spectroscopy of aqueous interfaces using machine-learned electronic and quantum nuclear effects.

Vibrational spectroscopy is a powerful approach to visualising interfacial phenomena. However, extracting structural and dynamical information from vibrational spectra is a challenge that requires first-principles simulations, including non-Condon and quantum nuclear effects. We address this challenge by developing a machine-learning enhanced first-principles framework to speed up predictive modelling of infrared, Raman, and sum-frequency generation spectra. Our approach uses machine learning potentials that encode quantum nuclear effects to generate quantum trajectories using simple molecular dynamics efficiently. In addition, we reformulate bulk and interfacial selection rules to express them unambiguously in terms of the derivatives of polarisation and polarisabilities of the whole system and predict these derivatives efficiently using fully-differentiable machine learning models of dielectric response tensors. We demonstrate our framework's performance by predicting the IR, Raman, and sum-frequency generation spectra of liquid water, ice and the water-air interface by achieving near quantitative agreement with experiments at nearly the same computational efficiency as pure classical methods. Finally, to aid the experimental discovery of new phases of nanoconfined water, we predict the temperature-dependent vibrational spectra of monolayer water across the solid-hexatic-liquid phases transition.

Many-Body Methods for Surface Chemistry Come of Age: Achieving Consensus with Experiments.

The adsorption energy of a molecule onto the surface of a material underpins a wide array of applications, spanning heterogeneous catalysis, gas storage, and many more. It is the key quantity where experimental measurements and theoretical calculations meet, with agreement being necessary for reliable predictions of chemical reaction rates and mechanisms. The prototypical molecule-surface system is CO adsorbed on MgO, but despite intense scrutiny from theory and experiment, there is still no consensus on its adsorption energy. In particular, the large cost of accurate many-body methods makes reaching converged theoretical estimates difficult, generating a wide range of values. In this work, we address this challenge, leveraging the latest advances in diffusion Monte Carlo (DMC) and coupled cluster with single, double, and perturbative triple excitations [CCSD(T)] to obtain accurate predictions for CO on MgO. These reliable theoretical estimates allow us to evaluate the inconsistencies in published temperature-programed desorption experiments, revealing that they arise from variations in employed pre-exponential factors. Utilizing this insight, we derive new experimental estimates of the (electronic) adsorption energy with a (more) precise pre-exponential factor. As a culmination of all of this effort, we are able to reach a consensus between multiple theoretical calculations and multiple experiments for the first time. In addition, we show that our recently developed cluster-based CCSD(T) approach provides a low-cost route toward achieving accurate adsorption energies. This sets the stage for affordable and reliable theoretical predictions of chemical reactions on surfaces to guide the realization of new catalysts and gas storage materials.

Quantum dynamics using path integral coarse-graining.

The vibrational spectra of condensed and gas-phase systems are influenced by thequantum-mechanical behavior of light nuclei. Full-dimensional simulations of approximate quantum dynamics are possible thanks to the imaginary time path-integral (PI) formulation of quantum statistical mechanics, albeit at a high computational cost which increases sharply with decreasing temperature. By leveraging advances in machine-learned coarse-graining, we develop a PI method with the reduced computational cost of a classical simulation. We also propose a simple temperature elevation scheme to significantly attenuate the artifacts of standard PI approaches as well as eliminate the unfavorable temperature scaling of the computational cost. We illustrate the approach, by calculating vibrational spectra using standard models of water molecules and bulk water, demonstrating significant computational savings and dramatically improved accuracy compared to more expensive reference approaches. Our simple, efficient, and accurate method has prospects for routine calculations of vibrational spectra for a wide range of molecular systems - with an explicit treatment of the quantum nature of nuclei.

The first-principles phase diagram of monolayer nanoconfined water.

Water in nanoscale cavities is ubiquitous and of central importance to everyday phenomena in geology and biology. However, the properties of nanoscale water can be substantially different from those of bulk water, as shown, for example, by the anomalously low dielectric constant of water in nanochannels1, near frictionless water flow2 or the possible existence of a square ice phase3. Such properties suggest that nanoconfined water could be engineered for technological applications in nanofluidics4, electrolyte materials5 and water desalination6. Unfortunately, challenges in experimentally characterizing water at the nanoscale and the high cost of first-principles simulations have prevented the molecular-level understanding required to control the behaviour of water. Here we combine a range of computational approaches to enable a first-principles-level investigation of a single layer of water within a graphene-like channel. We find that monolayer water exhibits surprisingly rich and diverse phase behaviour that is highly sensitive to temperature and the van der Waals pressure acting within the nanochannel. In addition to multiple molecular phases with melting temperatures varying non-monotonically by more than 400 kelvins with pressure, we predict a hexatic phase, which is an intermediate between a solid and a liquid, and a superionic phase with a high electrical conductivity exceeding that of battery materials. Notably, this suggests that nanoconfinement could be a promising route towards superionic behaviour under easily accessible conditions.

General embedded cluster protocol for accurate modeling of oxygen vacancies in metal-oxides.

The O vacancy (Ov) formation energy, EOv, is an important property of a metal-oxide, governing its performance in applications such as fuel cells or heterogeneous catalysis. These defects are routinely studied with density functional theory (DFT). However, it is well-recognized that standard DFT formulations (e.g., the generalized gradient approximation) are insufficient for modeling the Ov, requiring higher levels of theory. The embedded cluster method offers a promising approach to compute EOv accurately, giving access to all electronic structure methods. Central to this approach is the construction of quantum(-mechanically treated) clusters placed within suitable embedding environments. Unfortunately, current approaches to constructing the quantum clusters either require large system sizes, preventing application of high-level methods, or require significant manual input, preventing investigations of multiple systems simultaneously. In this work, we present a systematic and general quantum cluster design protocol that can determine small converged quantum clusters for studying the Ov in metal-oxides with accurate methods, such as local coupled cluster with single, double, and perturbative triple excitations. We apply this protocol to study the Ov in the bulk and surface planes of rutile TiO2 and rock salt MgO, producing the first accurate and well-converged determinations of EOv with this method. These reference values are used to benchmark exchange-correlation functionals in DFT, and we find that all the studied functionals underestimate EOv, with the average error decreasing along the rungs of Jacob's ladder. This protocol is automatable for high-throughput calculations and can be generalized to study other point defects or adsorbates.

A complete description of thermodynamic stabilities of molecular crystals.

Predictions of relative stabilities of (competing) molecular crystals are of great technological relevance, most notably for the pharmaceutical industry. However, they present a long-standing challenge for modeling, as often minuscule free energy differences are sensitively affected by the description of electronic structure, the statistical mechanics of the nuclei and the cell, and thermal expansion. The importance of these effects has been individually established, but rigorous free energy calculations for general molecular compounds, which simultaneously account for all effects, have hitherto not been computationally viable. Here we present an efficient "end to end" framework that seamlessly combines state-of-the art electronic structure calculations, machine-learning potentials, and advanced free energy methods to calculate ab initio Gibbs free energies for general organic molecular materials. The facile generation of machine-learning potentials for a diverse set of polymorphic compounds-benzene, glycine, and succinic acid-and predictions of thermodynamic stabilities in qualitative and quantitative agreement with experiments highlight that predictive thermodynamic studies of industrially relevant molecular materials are no longer a daunting task.

Efficient Quantum Vibrational Spectroscopy of Water with High-Order Path Integrals: From Bulk to Interfaces.

Vibrational spectroscopy is key in probing the interplay between the structure and dynamics of aqueous systems. To map different regions of experimental spectra to the microscopic structure of a system, it is important to combine them with first-principles atomistic simulations that incorporate the quantum nature of nuclei. Here we show that the large cost of calculating the quantum vibrational spectra of aqueous systems can be dramatically reduced compared with standard path integral methods by using approximate quantum dynamics based on high-order path integrals. Together with state-of-the-art machine-learned electronic properties, our approach gives an excellent description not only of the infrared and Raman spectra of bulk water but also of the 2D correlation and the more challenging sum-frequency generation spectra of the water-air interface. This paves the way for understanding complex interfaces such as water encapsulated between or in contact with hydrophobic and hydrophilic materials through robust and inexpensive surface-sensitive and multidimensional spectra with first-principles accuracy.

Importance of Nuclear Quantum Effects for NMR Crystallography.

The resolving power of solid-state nuclear magnetic resonance (NMR) crystallography depends heavily on the accuracy of computational predictions of NMR chemical shieldings of candidate structures, which are usually taken to be local minima in the potential energy. To test the limits of this approximation, we systematically study the importance of finite-temperature and quantum nuclear fluctuations for 1H, 13C, and 15N shieldings in polymorphs of three paradigmatic molecular crystals: benzene, glycine, and succinic acid. The effect of quantum fluctuations is comparable to the typical errors of shielding predictions for static nuclei with respect to experiments, and their inclusion improves the agreement with measurements, translating to more reliable assignment of the NMR spectra to the correct candidate structure. The use of integrated machine-learning models, trained on first-principles energies and shieldings, renders rigorous sampling of nuclear fluctuations affordable, setting a new standard for the calculations underlying NMR structure determinations.

Simulating the ghost: quantum dynamics of the solvated electron.

The nature of the bulk hydrated electron has been a challenge for both experiment and theory due to its short lifetime and high reactivity, and the need for a high-level of electronic structure theory to achieve predictive accuracy. The lack of a classical atomistic structural formula makes it exceedingly difficult to model the solvated electron using conventional empirical force fields, which describe the system in terms of interactions between point particles associated with atomic nuclei. Here we overcome this problem using a machine-learning model, that is sufficiently flexible to describe the effect of the excess electron on the structure of the surrounding water, without including the electron in the model explicitly. The resulting potential is not only able to reproduce the stable cavity structure but also recovers the correct localization dynamics that follow the injection of an electron in neat water. The machine learning model achieves the accuracy of the state-of-the-art correlated wave function method it is trained on. It is sufficiently inexpensive to afford a full quantum statistical and dynamical description and allows us to achieve accurate determination of the structure, diffusion mechanisms, and vibrational spectroscopy of the solvated electron.

Uncertainty estimation for molecular dynamics and sampling.

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 averages extracted from long trajectories. We present examples covering different types of structural and thermodynamic properties and systems as diverse as water and liquid gallium.

Inexpensive modeling of quantum dynamics using path integral generalized Langevin equation thermostats.

The properties of molecules and materials containing light nuclei are affected by their quantum mechanical nature. Accurate modeling of these quantum nuclear effects requires computationally demanding path integral techniques. Considerable success has been achieved in reducing the cost of such simulations by using generalized Langevin dynamics to induce frequency-dependent fluctuations. Path integral generalized Langevin equation methods, however, have this far been limited to the study of static, thermodynamic properties due to the large perturbation to the system's dynamics induced by the aggressive thermostatting. Here, we introduce a post-processing scheme, based on analytical estimates of the dynamical perturbation induced by the generalized Langevin dynamics, which makes it possible to recover meaningful time correlation properties from a thermostatted trajectory. We show that this approach yields spectroscopic observables for model and realistic systems that have an accuracy comparable to much more demanding approximate quantum dynamics techniques based on full path integral simulations.

Accurate Description of Nuclear Quantum Effects with High-Order Perturbed Path Integrals (HOPPI).

Imaginary time path-integral (PI) simulations that account for nuclear quantum effects (NQE) beyond the harmonic approximation are increasingly employed together with modern electronic-structure calculations. Existing PI methods are applicable to molecules, liquids, and solids; however, the computational cost of such simulations increases dramatically with decreasing temperature. To address this challenge, here, we propose to combine high-order PI factorization with perturbation theory (PT). Already for conventional second-order PI simulations, the PT ansatz increases the accuracy 2-fold compared to fourth-order schemes with the same settings. In turn, applying PT to high-order path integrals (HOPI) further improves the efficiency of simulations for molecular and condensed matter systems especially at low temperatures. We present results for bulk liquid water, the aspirin molecule, and the CH5+ molecule. Perturbed HOPI simulations remain both efficient and accurate down to 20 K and provide a convenient method to estimate the convergence of quantum-mechanical observables.

Barely porous organic cages for hydrogen isotope separation.

The separation of hydrogen isotopes for applications such as nuclear fusion is a major challenge. Current technologies are energy intensive and inefficient. Nanoporous materials have the potential to separate hydrogen isotopes by kinetic quantum sieving, but high separation selectivity tends to correlate with low adsorption capacity, which can prohibit process scale-up. In this study, we use organic synthesis to modify the internal cavities of cage molecules to produce hybrid materials that are excellent quantum sieves. By combining small-pore and large-pore cages together in a single solid, we produce a material with optimal separation performance that combines an excellent deuterium/hydrogen selectivity (8.0) with a high deuterium uptake (4.7 millimoles per gram).

Assessment of Approximate Methods for Anharmonic Free Energies.

Quantitative evaluation of the thermodynamic properties of materials-most notably their stability, as measured by the free energy-must take into account the role of thermal and zero-point energy fluctuations. While these effects can easily be estimated within a harmonic approximation, corrections arising from the anharmonic nature of the interatomic potential are often crucial and require computationally costly path integral simulations to obtain results that are essentially exact for a given potential. Consequently, different approximate frameworks for computing affordable estimates of the anharmonic free energies have been developed over the years. Understanding which of the approximations involved are justified for a given system, and therefore choosing the most suitable method, is complicated by the lack of comparative benchmarks. To facilitate this choice we assess the accuracy and efficiency of some of the most commonly used approximate methods: the independent mode framework, the vibrational self-consistent field, and self-consistent phonons. We compare the anharmonic correction to the Helmholtz free energy against reference path integral calculations. These benchmarks are performed for a diverse set of systems, ranging from simple weakly anharmonic solids to flexible molecular crystals with freely rotating units. The results suggest that, for simple solids such as allotropes of carbon, these methods yield results that are in excellent agreement with the reference calculations, at a considerably lower computational cost. For more complex molecular systems such as polymorphs of ice and paracetamol the methods do not consistently provide a reliable approximation of the anharmonic correction. Despite substantial cancellation of errors when comparing the stability of different phases, we do not observe a systematic improvement over the harmonic approximation even for relative free energies. We conclude that, at least for the classes of materials considered here, efforts toward obtaining computationally feasible anharmonic free energies should therefore be directed toward reducing the expense of path integral methods.

Thermal Engineering of Metal-Organic Frameworks for Adsorption Applications: A Molecular Simulation Perspective.

Thermal engineering of metal-organic frameworks for adsorption-based applications is very topical in view of their industrial potential, in particular, since heat management and thermal stability have been identified as important obstacles. Hence, a fundamental understanding of the structural and chemical features underpinning their intrinsic thermal properties is highly sought-after. Herein, we investigate the nanoscale behavior of a diverse set of frameworks using molecular simulation techniques and critically compare properties such as thermal conductivity, heat capacity, and thermal expansion with other classes of materials. Furthermore, we propose a hypothetical thermodynamic cycle to estimate the temperature rise associated with adsorption for the most important greenhouse and energy-related gases (CO2 and CH4). This macroscopic response on the heat of adsorption connects the intrinsic thermal properties with the adsorption properties and allows us to evaluate their importance.

Modeling the Structural and Thermal Properties of Loaded Metal-Organic Frameworks. An Interplay of Quantum and Anharmonic Fluctuations.

Metal-organic frameworks show both fundamental interest and great promise for applications in adsorption-based technologies, such as the separation and storage of gases. The flexibility and complexity of the molecular scaffold pose a considerable challenge to atomistic modeling, especially when also considering the presence of guest molecules. We investigate the role played by quantum and anharmonic fluctuations in the archetypical case of MOF-5, comparing the material at various levels of methane loading. Accurate path integral simulations of such effects are made affordable by the introduction of an accelerated simulation scheme and the use of an optimized force field based on first-principles reference calculations. We find that the level of statistical treatment that is required for predictive modeling depends significantly on the property of interest. The thermal properties of the lattice are generally well described by a quantum harmonic treatment, with the adsorbate behaving in a classical but strongly anharmonic manner. The heat capacity of the loaded framework-which plays an important role in the characterization of the framework and in determining its stability to thermal fluctuations during adsorption/desorption cycles-requires, however, a full quantum and anharmonic treatment, either by path integral methods or by a simple but approximate scheme. We also present molecular-level insight into the nanoscopic interactions contributing to the material's properties and suggest design principles to optimize them.