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.

Investigation of the Dynamic Behaviour of H2 and D2 in a Kinetic Quantum Sieving System

Porous organic cages (POCs) are nanoporous materials composed of discrete molecular units that have uniformly distributed functional pores. The intrinsic porosity of these structures can be tuned accurately at the nanoscale by altering the size of the porous molecules, particularly to an optimal size of 3.6 Å, to harness the kinetic quantum sieving effect. Previous research on POCs for isotope separation has predominantly centered on differences in the quantities of adsorbed isotopes. However, nuclear quantum effects also contribute significantly to the dynamics of the sorption process, offering additional opportunities for separating H2 and D2 at practical operational temperatures. In this study, our investigations into H2 and D2 sorption on POC samples revealed a higher uptake of D2 compared to that of H2 under identical conditions. We employed quasi-elastic neutron scattering to study the diffusion processes of D2 and H2 in the POCs across various temperature and pressure ranges. Additionally, neutron Compton scattering was utilized to measure the values of the nuclear zero-point energy of individual isotopic species in D2 and H2. The results indicate that the diffusion coefficient of D2 is approximately one-sixth that of H2 in the POC due to the nuclear quantum effect. Furthermore, the results reveal that at 77 K, D2 has longer residence times compared to H2 when moving from pore to pore. Consequently, using the kinetic difference of H2 and D2 in a porous POC system enables hydrogen isotope separation using a temperature or pressure swing system at around liquid nitrogen temperatures.

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 .

Attachment of Hydrogen Molecules to Atomic Ions (Na+ , Cl- ): Examination of an Adiabatic Separation of the H2 Rotational Motion

Interactions between molecular hydrogen and ions are of interest in cluster science, astrochemistry and hydrogen storage. In dynamical simulations, H2 molecules are usually modelled as point particles, an approximation that can fail for anisotropic interactions. Here, we apply an adiabatic separation of the H2 rotational motion to build effective pseudoatom-ion potentials and in turn study the properties of (H2 )n Na+ /Cl- clusters. These interaction potentials are based on high-level ab initio calculations and Improved Lennard-Jones parametrizations, while the subsequent dynamics has been performed by quantum Monte Carlo calculations. By comparisons with simulations explicitly describing the molecular rotations, it is concluded that the present adiabatic model is very adequate. Interestingly, we find differences in the cluster stabilities and coordination shells depending on the spin isomer considered (para- or ortho-H2 ), especially for the anionic clusters.

Ring-polymer Molecular Dynamics Simulation for the Adsorption of H2 on Ice Clusters (H2 O)n (n=8, 10, and 12)

In the interstellar medium, the H₂ adsorption and desorption on the solid water ice are crucial for chemical and physical processes. We have recently investigated the probabilities of H₂ sticking on the (H₂ O)₈ ice, which has quadrilateral surfaces. We have extended the previous work using classical MD and ring-polymer molecular dynamics (RPMD) simulations to the larger ice clusters, (H₂ O)₁₀ and (H₂ O)₁₂ , which have pentagonal and hexagonal surfaces, respectively. The H₂ sticking probabilities decreased as the temperature increased for both cluster cases, whereas the cluster-size-independent profiles were observed. It is thought that the size independence of the probabilities is qualitatively understood from the similar binding energies for all the three cluster systems. Furthermore, the RPMD sticking probabilities are smaller than the classical ones because of the reduction in the binding energies owing to nuclear quantum effects, such as vibrational quantization.

Nuclear quantum effects in fullerene-fullerene aggregation in water

We studied the effects of the quantum delocalization in space of the hydrogen atoms of water in the aggregation process of two fullerene molecules. We considered a case using a purely repulsive water-fullerene interaction, as such a situation has shown that water-mediated effects play a key role in the aggregation process. This study becomes feasible, at a reduced computational price, by combining the path integral (PI) molecular dynamics (MD) method with a recently developed open-system MD technique. Specifically, only the mandatory solvation shell of the two fullerene molecules was considered at full quantum resolution, while the rest of the system was represented as a mean-field macroscopic reservoir of particles and energy. Our results showed that the quantum nature of the hydrogen atoms leads to a sizable difference in the curve of the free energy of aggregation; that is, that nuclear quantum effects play a relevant role.

Learning the Quantum Centroid Force Correction in Molecular Systems: A Localized Approach

Molecular mechanics (MM) is a powerful tool to study the properties of molecular systems in the fields of biology and materials science. With the development of ab initio force field and the application of ab initio potential energy surface, the nuclear quantum effect (NQE) is becoming increasingly important for the robustness of the simulation. However, the state-of-the-art path-integral molecular dynamics simulation, which incorporates NQE in MM, is still too expensive to conduct for most biological and material systems. In this work, we analyze the locality of NQE, using both analytical and numerical approaches, and conclude that NQE is an extremely localized phenomenon in nonreactive molecular systems. Therefore, we can use localized machine learning (ML) models to predict quantum force corrections both accurately and efficiently. Using liquid water as example, we show that the ML facilitated centroid MD can reproduce the NQEs in both the thermodynamical and the dynamical properties, with a minimal increase in computational time compared to classical molecular dynamics. This simple approach thus largely decreases the computational cost of quantum simulations, making it really accessible to the studies of large-scale molecular systems.

Theoretical perspectives on non-Born-Oppenheimer effects in chemistry

The Born-Oppenheimer approximation, which assumes that the electrons respond instantaneously to the motion of the nuclei, breaks down for a wide range of chemical and biological processes. The rate constants of such nonadiabatic processes can be calculated using analytical theories, and the real-time nonequilibrium dynamics can be described using numerical atomistic simulations. The selection of an approach depends on the desired balance between accuracy and efficiency. The computational expense of generating potential energy surfaces on-the-fly often favours the use of approximate, robust and efficient methods such as trajectory surface hopping for large, complex systems. The development of formally exact non-Born-Oppenheimer methods and the exploration of well-defined approximations to such methods are critical for providing benchmarks and preparing for the next generation of faster computers. Thus, the parallel development of rigorous but computationally expensive methods and more approximate but computationally efficient methods is optimal. This Perspective briefly summarizes the available theoretical and computational non-Born-Oppenheimer methods and presents examples illustrating how analytical theories and nonadiabatic dynamics simulations can elucidate the fundamental principles of chemical and biological processes. These examples also highlight how theoretical calculations are able to guide the interpretation of experimental data and provide experimentally testable predictions for nonadiabatic processes. This article is part of the theme issue 'Chemistry without the Born-Oppenheimer approximation'.

Static and Dynamic Correlations in Water: Comparison of Classical Ab Initio Molecular Dynamics at Elevated Temperature with Path Integral Simulations at Ambient Temperature

It is a common practice in ab initio molecular dynamics (AIMD) simulations of water to use an elevated temperature to overcome the overstructuring and slow diffusion predicted by most current density functional theory (DFT) models. The simulation results obtained in this distinct thermodynamic state are then compared with experimental data at ambient temperature based on the rationale that a higher temperature effectively recovers nuclear quantum effects (NQEs) that are missing in the classical AIMD simulations. In this work, we systematically examine the foundation of this assumption for several DFT models as well as for the many-body MB-pol model. We find for the cases studied that a higher temperature does not correctly mimic NQEs at room temperature, which is especially manifest in significantly different three-molecule correlations as well as hydrogen bond dynamics. In many of these cases, the effects of NQEs are the opposite of the effects of carrying out the simulations at an elevated temperature.

Nuclear Quantum Effects on the Charge-Density Wave Transition in NbX2 (X = S, Se)

Understanding the origin of charge-density wave (CDW) instability is important for manipulating novel collective electronic states. Many layered transition metal dichalcogenides (TMDs) share similarity in the structural and electronic instability, giving rise to diverse CDW phases and superconductivity. It is still puzzling that even isostructural and isoelectronic TMDs show distinct CDW features. For instance, bulk NbSe₂ exhibits CDW order at low temperature, while bulk NbS₂ displays no CDW instability. The CDW transitions in single-layer NbS₂ and NbSe₂ are also different. In the classic limit, we investigate the electron correlation effects on the dimensionality dependence of the CDW ordering. By performing ab initio path integral molecular dynamics simulations and comparative analyses, we further revealed significant nuclear quantum effects in these systems. Specifically, the quantum motion of sulfur anions significantly reduces the CDW transition temperature in both bulk and single-layer NbS₂, resulting in distinct CDW features in the NbS₂ and NbSe₂ systems.

Using Machine Learning to Greatly Accelerate Path Integral Ab Initio Molecular Dynamics

Ab initio molecular dynamics (AIMD) has become one of the most popular and robust approaches for modeling complicated chemical, liquid, and material systems. However, the formidable computational cost often limits its widespread application in simulations of the largest-scale systems. The situation becomes even more severe in cases where the hydrogen nuclei may be better described as quantized particles using a path integral representation. Here, we present a computational approach that combines machine learning with recent advances in path integral contraction schemes, and we achieve a 2 orders of magnitude acceleration over direct path integral AIMD simulation while at the same time maintaining its accuracy.

Deuterium Isotope Effects on Acid-Base Equilibrium of Organic Compounds

Deuterium isotope effects on acid-base equilibrium have been investigated using a combined path integral and free-energy perturbation simulation method. To understand the origin of the linear free-energy relationship of ΔpKa=pKaD2O-pKaH2O versus pKaH2O, we examined two theoretical models for computing the deuterium isotope effects. In Model 1, only the intrinsic isotope exchange effect of the acid itself in water was included by replacing the titratable protons with deuterons. Here, the dominant contribution is due to the difference in zero-point energy between the two isotopologues. In Model 2, the medium isotope effects are considered, in which the free energy change as a result of replacing H₂O by D₂O in solute-solvent hydrogen-bonding complexes is determined. Although the average ΔpKa change from Model 1 was found to be in reasonable agreement with the experimental average result, the pKaH2O dependence of the solvent isotope effects is absent. A linear free-energy relationship is obtained by including the medium effect in Model 2, and the main factor is due to solvent isotope effects in the anion-water complexes. The present study highlights the significant roles of both the intrinsic isotope exchange effect and the medium solvent isotope effect.

Naphthazarin Derivatives in the Light of Intra- and Intermolecular Forces

Our long-term investigations have been devoted the characterization of intramolecular hydrogen bonds in cyclic compounds. Our previous work covers naphthazarin, the parent compound of two systems discussed in the current work: 2,3-dimethylnaphthazarin (1) and 2,3-dimethoxy-6-methylnaphthazarin (2). Intramolecular hydrogen bonds and substituent effects in these compounds were analyzed on the basis of Density Functional Theory (DFT), Møller-Plesset second-order perturbation theory (MP2), Coupled Clusters with Singles and Doubles (CCSD) and Car-Parrinello Molecular Dynamics (CPMD). The simulations were carried out in the gas and crystalline phases. The nuclear quantum effects were incorporated a posteriori using the snapshots taken from ab initio trajectories. Further, they were used to solve a vibrational Schrödinger equation. The proton reaction path was studied using B3LYP, ωB97XD and PBE functionals with a 6-311++G(2d,2p) basis set. Two energy minima (deep and shallow) were found, indicating that the proton transfer phenomena could occur in the electronic ground state. Next, the electronic structure and topology were examined in the molecular and proton transferred (PT) forms. The Atoms In Molecules (AIM) theory was employed for this purpose. It was found that the hydrogen bond is stronger in the proton transferred (PT) forms. In order to estimate the dimers' stabilization and forces responsible for it, the Symmetry-Adapted Perturbation Theory (SAPT) was applied. The energy decomposition revealed that dispersion is the primary factor stabilizing the dimeric forms and crystal structure of both compounds. The CPMD results showed that the proton transfer phenomena occurred in both studied compounds, as well as in both phases. In the case of compound 2, the proton transfer events are more frequent in the solid state, indicating an influence of the environmental effects on the bridged proton dynamics. Finally, the vibrational signatures were computed for both compounds using the CPMD trajectories. The Fourier transformation of the autocorrelation function of atomic velocity was applied to obtain the power spectra. The IR spectra show very broad absorption regions between 700 cm-1-1700 cm-1 and 2300 cm-1-3400 cm-1 in the gas phase and 600 cm-1-1800 cm-1 and 2200 cm-1-3400 cm-1 in the solid state for compound 1. The absorption regions for compound 2 were found as follows: 700 cm-1-1700 cm-1 and 2300 cm-1-3300 cm-1 for the gas phase and one broad absorption region in the solid state between 700 cm-1 and 3100 cm-1. The obtained spectroscopic features confirmed a strong mobility of the bridged protons. The inclusion of nuclear quantum effects showed a stronger delocalization of the bridged protons.

Significance Of Nuclear Quantum Effects In Hydrogen Bonded Molecular Chains

In hydrogen-bonded systems, nuclear quantum effects such as zero-point motion and tunneling can significantly affect their material properties through underlying physical and chemical processes. Presently, direct observation of the influence of nuclear quantum effects on the strength of hydrogen bonds with resulting structural and electronic implications remains elusive, leaving opportunities for deeper understanding to harness their fascinating properties. We studied hydrogen-bonded one-dimensional quinonediimine molecular networks which may adopt two isomeric electronic configurations via proton transfer. Herein, we demonstrate that concerted proton transfer promotes a delocalization of π-electrons along the molecular chain, which enhances the cohesive energy between molecular units, increasing the mechanical stability of the chain and giving rise to distinctive electronic in-gap states localized at the ends. These findings demonstrate the identification of a class of isomeric hydrogen-bonded molecular systems where nuclear quantum effects play a dominant role in establishing their chemical and physical properties. This identification is a step toward the control of mechanical and electronic properties of low-dimensional molecular materials via concerted proton tunneling.

Dynamics & Spectroscopy with Neutrons-Recent Developments & Emerging Opportunities

This work provides an up-to-date overview of recent developments in neutron spectroscopic techniques and associated computational tools to interrogate the structural properties and dynamical behavior of complex and disordered materials, with a focus on those of a soft and polymeric nature. These have and continue to pave the way for new scientific opportunities simply thought unthinkable not so long ago, and have particularly benefited from advances in high-resolution, broadband techniques spanning energy transfers from the meV to the eV. Topical areas include the identification and robust assignment of low-energy modes underpinning functionality in soft solids and supramolecular frameworks, or the quantification in the laboratory of hitherto unexplored nuclear quantum effects dictating thermodynamic properties. In addition to novel classes of materials, we also discuss recent discoveries around water and its phase diagram, which continue to surprise us. All throughout, emphasis is placed on linking these ongoing and exciting experimental and computational developments to specific scientific questions in the context of the discovery of new materials for sustainable technologies.

Impact of nuclear quantum effects on the structural inhomogeneity of liquid water

The 2D Raman-terahertz (THz) response of liquid water is studied in dependence of temperature and isotope substitution ([Formula: see text]O, [Formula: see text]O, and [Formula: see text]O). In either case, a very short-lived (i.e., between 75 and 95 fs) echo is observed that reports on the inhomogeneity of the low-frequency intermolecular modes and hence, on the heterogeneity of the hydrogen bond networks of water. The echo lifetime slows down by about 20% when cooling the liquid from room temperature to the freezing point. Furthermore, the echo lifetime of [Formula: see text]O is [Formula: see text] slower than that of [Formula: see text]O, and both can be mapped on each other by introducing an effective temperature shift of [Formula: see text] K. In contrast, the temperature-dependent echo lifetimes of [Formula: see text]O and [Formula: see text]O are the same within error. [Formula: see text]O and [Formula: see text]O have identical masses, yet [Formula: see text]O is much closer to [Formula: see text]O in terms of nuclear quantum effects. It is, therefore, concluded that the echo is a measure of the structural inhomogeneity of liquid water induced by nuclear quantum effects.

Ab initio thermodynamics of liquid and solid water

Thermodynamic properties of liquid water as well as hexagonal (Ih) and cubic (Ic) ice are predicted based on density functional theory at the hybrid-functional level, rigorously taking into account quantum nuclear motion, anharmonic fluctuations, and proton disorder. This is made possible by combining advanced free-energy methods and state-of-the-art machine-learning techniques. The ab initio description leads to structural properties in excellent agreement with experiments and reliable estimates of the melting points of light and heavy water. We observe that nuclear-quantum effects contribute a crucial [Formula: see text] to the stability of ice Ih, making it more stable than ice Ic. Our computational approach is general and transferable, providing a comprehensive framework for quantitative predictions of ab initio thermodynamic properties using machine-learning potentials as an intermediate step.

Molecular Calculation of the Critical Parameters of Classical Helium

We compute the vapor-liquid critical coordinates of a model of helium in which nuclear quantum effects are absent. We employ highly accurate ab initio pair and three-body potentials and calculate the critical parameters rigorously in two ways. First, we calculate the virial coefficients up to the seventh and find the point where an isotherm satisfies the critical conditions. Second, we use Gibbs Ensemble Monte Carlo (GEMC) to calculate the vapor-liquid equilibrium, and extrapolate the phase envelope to the critical point. Both methods yield results that are consistent within their uncertainties. The critical temperature of "classical helium" is 13.0 K (compared to 5.2 K for real helium), the critical pressure is 0.93 MPa, and the critical density is 28.4 mol·L-1, with expanded uncertainties (corresponding to a 95% confidence interval) on the order of 0.1 K, 0.02 MPa, and 0.5 mol·L-1, respectively. The effect of three-body interactions on the location of the critical point is small (lowering the critical temperature by roughly 0.1 K), suggesting that we are justified in ignoring four-body and higher interactions in our calculations. This work is motivated by the use of corresponding-states models for mixtures containing helium (such as some natural gases) at higher temperatures where quantum effects are expected to be negligible; in these situations, the distortion of the critical properties by quantum effects causes problems for the corresponding-states treatment.

Dual QM and MM Approach for Computing Equilibrium Isotope Fractionation Factor of Organic Species in Solution

A dual QM and MM approach for computing equilibrium isotope effects has been described. In the first partition, the potential energy surface is represented by a combined quantum mechanical and molecular mechanical (QM/MM) method, in which a solute molecule is treated quantum mechanically, and the remaining solvent molecules are approximated classically by molecular mechanics. In the second QM/MM partition, differential nuclear quantum effects responsible for the isotope effect are determined by a statistical mechanical double-averaging formalism, in which the nuclear centroid distribution is sampled classically by Newtonian molecular dynamics and the quantum mechanical spread of quantized particles about the centroid positions is treated using the path integral (PI) method. These partitions allow the potential energy surface to be properly represented such that the solute part is free of nuclear quantum effects for nuclear quantum mechanical simulations, and the double-averaging approach has the advantage of sampling efficiency for solvent configuration and for path integral convergence. Importantly, computational precision is achieved through free energy perturbation (FEP) theory to alchemically mutate one isotope into another. The PI-FEP approach is applied to model systems for the 18O enrichment found in cellulose of trees to determine the isotope enrichment factor of carbonyl compounds in water. The present method may be useful as a general tool for studying isotope fractionation in biological and geochemical systems.

Nuclear quantum effect with pure anharmonicity and the anomalous thermal expansion of silicon

Despite the widespread use of silicon in modern technology, its peculiar thermal expansion is not well understood. Adapting harmonic phonons to the specific volume at temperature, the quasiharmonic approximation, has become accepted for simulating the thermal expansion, but has given ambiguous interpretations for microscopic mechanisms. To test atomistic mechanisms, we performed inelastic neutron scattering experiments from 100 K to 1,500 K on a single crystal of silicon to measure the changes in phonon frequencies. Our state-of-the-art ab initio calculations, which fully account for phonon anharmonicity and nuclear quantum effects, reproduced the measured shifts of individual phonons with temperature, whereas quasiharmonic shifts were mostly of the wrong sign. Surprisingly, the accepted quasiharmonic model was found to predict the thermal expansion owing to a large cancellation of contributions from individual phonons.

Electrolytes induce long-range orientational order and free energy changes in the H-bond network of bulk water

Electrolytes interact with water in many ways: changing dipole orientation, inducing charge transfer, and distorting the hydrogen-bond network in the bulk and at interfaces. Numerous experiments and computations have detected short-range perturbations that extend up to three hydration shells around individual ions. We report a multiscale investigation of the bulk and surface of aqueous electrolyte solutions that extends from the atomic scale (using atomistic modeling) to nanoscopic length scales (using bulk and interfacial femtosecond second harmonic measurements) to the macroscopic scale (using surface tension experiments). Electrolytes induce orientational order at concentrations starting at 10 μM that causes nonspecific changes in the surface tension of dilute electrolyte solutions. Aside from ion-dipole interactions, collective hydrogen-bond interactions are crucial and explain the observed difference of a factor of 6 between light water and heavy water.

Nuclear Quantum Effects in the Layering and Diffusion of Hydrogen Isotopes in Carbon Nanotubes

Although recent experimental studies have demonstrated that H2 and D2 molecules wet the inner surface of supergrowth carbon nanotubes at low temperatures, characterization of the structural and dynamical properties in this regime is challenging. This Letter presents a theoretical study of self-diffusion in pure and binary H2, D2, and T2 contact monolayer films formed on the inner surface of a carbon nanotube. Our results show that monolayer formation and self-diffusion both in pure hydrogen isotopes and in H2/T2 and H2/D2 isotope mixtures is impacted by nuclear quantum effects, suggesting potential applications of carbon nanotubes for the separation of hydrogen isotopes.

Quantum delocalization of protons in the hydrogen-bond network of an enzyme active site

Enzymes use protein architectures to create highly specialized structural motifs that can greatly enhance the rates of complex chemical transformations. Here, we use experiments, combined with ab initio simulations that exactly include nuclear quantum effects, to show that a triad of strongly hydrogen-bonded tyrosine residues within the active site of the enzyme ketosteroid isomerase (KSI) facilitates quantum proton delocalization. This delocalization dramatically stabilizes the deprotonation of an active-site tyrosine residue, resulting in a very large isotope effect on its acidity. When an intermediate analog is docked, it is incorporated into the hydrogen-bond network, giving rise to extended quantum proton delocalization in the active site. These results shed light on the role of nuclear quantum effects in the hydrogen-bond network that stabilizes the reactive intermediate of KSI, and the behavior of protons in biological systems containing strong hydrogen bonds.