Importance Of Nuclear Quantum Effects Research Articles

Modelling infrared spectra of the O-H stretches in liquid H2O based on a deep learning potential, the importance of nuclear quantum effects

ABSTRACT In this study, we have trained a deep learning (DL) potential for water using training datasets obtained from the DPLibrary (https://dplibrary.deepmd.net/). Subsequently, we conducted classical molecular dynamics simulation (DeePMD) and path-integral MD simulation (PI-DeePMD) of liquid water based on this deep potential (DP). Using the velocity-velocity auto-correlation function (VVAF) formula, we constructed infrared (IR) spectra for the O-H stretching mode based on the DeePMD simulation trajectories. Our results showed that the DeePMD/VVAF approach accurately captured the experimental result for O-H stretching vibration, with the O-H vibrational peak located at 3400 cm−1. Additionally, the PI-DeePMD approach successfully predicted the red-shift and broadening of the O-H stretching band of water, emphasising the importance of nuclear quantum effects (NQEs). In particular, the PI-DeePMD simulation correctly reproduced the shoulder located at 3250 cm−1, which was underestimated by classical DeePMD simulation. The success of the PI-DeePMD/VVAF approach can be attributed to the following reasons: (1) the DeePMD simulation improves the accuracy of calculating atomic velocities due to the DFT-level accuracy of the DP model; (2) the PI-DeePMD simulation takes into account the contribution from nuclear quantum effects; (3) the non-Condon effect is considered in the VVAF formalism.

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

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

The Importance of Nuclear Quantum Effects on the Thermodynamic and Structural Properties of Low-Density Amorphous Ice: A Comparison with Hexagonal Ice.

We study the nuclear quantum effects (NQE) on the thermodynamic properties of low-density amorphous ice (LDA) and hexagonal ice (Ih) at P = 0.1 MPa and T ≥ 25 K. Our results are based on path-integral molecular dynamics (PIMD) and classical MD simulations of H2O and D2O using the q-TIP4P/F water model. We show that the inclusion of NQE is necessary to reproduce the experimental properties of LDA and ice Ih. While MD simulations (no NQE) predict that the density ρ(T) of LDA and ice Ih increases monotonically upon cooling, PIMD simulations indicate the presence of a density maximum in LDA and ice Ih. MD and PIMD simulations also predict a qualitatively different T-dependence for the thermal expansion coefficient αP(T) and bulk modulus B(T) of both LDA and ice Ih. Remarkably, the ρ(T), αP(T), and B(T) of LDA are practically identical to those of ice Ih. The origin of the observed NQE is due to the delocalization of the H atoms, which is identical in LDA and ice Ih. H atoms delocalize considerably (over a distance ≈ 20-25% of the OH covalent-bond length) and anisotropically (preferentially perpendicular to the OH covalent bond), leading to less linear hydrogen bonds HB (larger HOO angles and longer OO separations) than observed in classical MD simulations.

Anharmonic lattice dynamics from vibrational dynamical mean-field theory

We present a vibrational dynamical mean-field theory (VDMFT) of the dynamics of atoms in solids with anharmonic interactions. Like other flavors of DMFT, VDMFT maps the dynamics of a periodic anharmonic lattice of atoms onto those of a self-consistently defined impurity problem with local anharmonicity and coupling to a bath of harmonic oscillators. VDMFT is exact in the harmonic and molecular limits, nonperturbative systematically improvable through its cluster extensions, usable with classical or quantum impurity solvers (depending on the importance of nuclear quantum effects) and can be combined with existing low-level diagrammatic theories of anharmonicity. When tested on models of anharmonic optical and acoustic phonons; we find that classical VDMFT gives good agreement with classical molecular dynamics, including the temperature dependence of phonon frequencies and lifetimes. Using a quantum impurity solver, signatures of nuclear quantum effects are observed at low temperatures. We test the description of nonlocal anharmonicity via cellular VDMFT and the combination with self-consistent phonon (SCPH) theory, yielding the powerful SCPH $+$ VDMFT approach.

Artificial neural network-based path integral simulations of hydrogen isotope diffusion in palladium

The contribution of nuclear quantum effects (NQEs) to the kinetics and dynamics of interstitial H isotopes in face-centered cubic Pd was intensively investigated using several path-integral techniques, along with a newly developed machine-learning interatomic potential based on artificial neural networks for Pd–H alloys. The diffusion coefficients (D) of protium, deuterium, and tritium in Pd were predicted over a wide temperature range (50–1500 K) based on quantum transition-state theory (QTST) combined with path-integral molecular-dynamics simulations. The importance of NQEs even at high temperatures was illustrated in terms of the characteristic temperature dependence of the activation free energies for H-isotope migration in Pd. This illuminates the overall picture of anomalous D crossovers among the three H isotopes in Pd. In addition, the D of protium in Pd was directly computed using two approximate quantum-dynamics methods based on Feynman’s path-integral theory, i.e. centroid molecular dynamics (CMD) and ring-polymer molecular dynamics (RPMD), in the temperature range 370–1500 K. The D values obtained from the CMD and RPMD simulations were very similar and agreed better with the reported experimental values than the QTST results in this temperature range. Our machine learning-based path-integral calculations elucidate the underlying quantum nature of the ‘reversed S’-type nonlinear behavior of D for the three H isotopes in Pd on the Arrhenius plots.

Importance of Nuclear Quantum Effects for Molecular Cocrystals with Short Hydrogen Bonds.

Many efforts have been recently devoted to the design and investigation of multicomponent pharmaceutical solids, such as salts and cocrystals. The experimental distinction between these solid forms is often challenging. Here, we show that the transformation of a salt into a cocrystal with a short hydrogen bond does not occur as a sharp phase transition but rather a smooth shift of the positional probability of the hydrogen atoms. A combination of solid-state NMR spectroscopy, X-ray diffraction, and diffuse reflectance measurements with density functional theory calculations that include nuclear quantum effects (NQEs) provides evidence of temperature-induced hydrogen atom shift in cocrystals with short hydrogen bonds. We demonstrate that for the predictions of the salt/cocrystal solid forms with short H-bonds, the computations have to include NQEs (particularly hydrogen nuclei delocalization) and temperature effects.

H/D Isotope Effects in Keto-Enol Tautomerism of β-Dicarbonyl Compounds —Importance of Nuclear Quantum Effects of Hydrogen Nuclei—

Abstract Deuterium isotope effects in the keto-enol tautomerism of β-dicarbonyl compounds (malonaldehyde, acetylacetone, dibenzoylmethane, and avobenzone) have been studied using a B3LYP+D functional level of multi-component density functional theory (MC_DFT), which can directly take nuclear quantum effects (NQEs) of the hydrogen nuclei into account. We clearly show that the keto-enol energy difference becomes smaller by deuterium substitution, which is in reasonable agreement with the corresponding experimental evidence. Our MC_DFT study also reveals the hydrogen/deuterium (H/D) isotope effect in geometries and shows that the deuterium substitution weakens the intramolecular hydrogen-bonded interaction in the enol form. Direct treatment of NQEs of hydrogen nuclei via the MC_DFT method is essential for analyzing the H/D isotope effect in keto-enol tautomerism of β-dicarbonyl compounds. Such isotope effects cannot be reproduced in the conventional DFT scheme with harmonic zero-point vibrational corrections.

Molecular vibrational frequencies from analytic Hessian of constrained nuclear-electronic orbital density functional theory.

Nuclear quantum effects are important in a variety of chemical and biological processes. The constrained nuclear-electronic orbital density functional theory (cNEO-DFT) has been developed to include nuclear quantum effects in energy surfaces. Herein, we develop the analytic Hessian for cNEO-DFT energy with respect to the change in nuclear (expectation) positions, which can be used to characterize stationary points on energy surfaces and compute molecular vibrational frequencies. This is achieved by constructing and solving the multicomponent cNEO coupled-perturbed Kohn-Sham (cNEO-CPKS) equations, which describe the response of electronic and nuclear orbitals to the displacement of nuclear (expectation) positions. With the analytic Hessian, the vibrational frequencies of a series of small molecules are calculated and compared to those from conventional DFT Hessian calculations as well as those from the vibrational second-order perturbation theory (VPT2). It is found that even with a harmonic treatment, cNEO-DFT significantly outperforms DFT and is comparable to DFT-VPT2 in the description of vibrational frequencies in regular polyatomic molecules. Furthermore, cNEO-DFT can reasonably describe the proton transfer modes in systems with a shared proton, whereas DFT-VPT2 often faces great challenges. Our results suggest the importance of nuclear quantum effects in molecular vibrations, and cNEO-DFT is an accurate and inexpensive method to describe molecular vibrations.

Excited State Intramolecular Proton Transfer with Nuclear-Electronic Orbital Ehrenfest Dynamics.

The recent development of the Ehrenfest dynamics approach in the nuclear-electronic orbital (NEO) framework provides a promising way to simulate coupled nuclear-electronic dynamics. Our previous study showed that the NEO-Ehrenfest approach with a semiclassical traveling proton basis method yields accurate predictions of molecular vibrational frequencies. In this work, we provide a more thorough analysis of the semiclassical traveling proton basis method to elucidate its validity and convergence behavior. We also conduct NEO-Ehrenfest dynamics simulations to study an excited state intramolecular proton transfer process. These simulations reveal that nuclear quantum effects influence the predictions of proton transfer reaction rates and kinetic isotope effects due to the intrinsic delocalized nature of the quantum nuclear wave function. This work illustrates the importance of nuclear quantum effects in coupled nuclear-electronic dynamical processes and shows that the NEO-Ehrenfest approach can be a powerful tool for providing insights and predictions for these processes.

Importance of nuclear quantum effects on the hydration of chloride ion

Path-integral ab initio molecular dynamics (PI-AIMD) calculations have been employed to probe the nature of chloride ion solvation in aqueous solution. Nuclear quantum effects (NQEs) are shown to weaken hydrogen bonding between the chloride anion and the solvation shell of water molecules. As a consequence, the disruptive effect of the anion on the solvent water structure is significantly reduced compared to what is found in the absence of NQEs. The chloride hydration structure obtained from PI-AIMD agrees well with information extracted from neutron scattering data. Inparticular, the observed satellite peak in the hydrogen-chloride-hydrogen triple angular distribution serves as a clear signature of NQEs. The present results suggest that NQEs are likely to play acrucial role in determining the structure of saline solutions.

Capturing the nuclear quantum effects in molecular dynamics for lattice thermal conductivity calculations: Using ice as example.

Molecular dynamics (MD) is a powerful (and the most viable) tool to compute the thermal conductivities of solid disordered materials. However, conventional classical MD fails to describe the nuclear quantum effects (NQEs), so it may give inaccurate results for light materials at low temperatures. While the importance of NQE has been widely acknowledged, yet we do not have a fully reliable method to account for NQE in the MD thermal conductivity calculations. In this work, we will investigate and analyze the performances of a number of path-integral-based quantum MD methods, using ordered ice as a test case. To establish the validity of these methods, we will compare the MD results with the lattice dynamics results, in both classical and quantum limits. Through such a comparison, we will show that methods such as ring polymer MD stand as a good approach for a complex solid with short phonon lifetimes but could be problematic when describing long-living acoustic phonons. In addition, we will show that the rigid water model, which is the state-of-the-art model in the studies of ice/water systems, fails to capture most of the NQEs in ice thermal conductivity. Neglecting librational and translational NQEs leads to essential errors, which clearly demonstrates the importance of a true quantum simulation method that treats all modes at a consistent quantum level.

Modeling voltammetry curves for proton coupled electron transfer: The importance of nuclear quantum effects.

We investigate rates of proton-coupled electron transfer (PCET) in potential sweep experiments for a generalized Anderson-Holstein model with the inclusion of a quantized proton coordinate. To model this system, we utilize a quantum classical Liouville equation embedded inside of a classical master equation, which can be solved approximately with a recently developed algorithm combining diffusional effects and surface hopping between electronic states. We find that the addition of nuclear quantum effects through the proton coordinate can yield quantitatively (but not qualitatively) different IV curves under a potential sweep compared to electron transfer (ET). Additionally, we find that kinetic isotope effects give rise to a shift in the peak potential, but not the peak current, which would allow for quantification of whether an electrochemical ET event is proton-coupled or not. These findings suggest that it will be very difficult to completely understand coupled nuclear-electronic effects in electrochemical voltammetry experiments using only IV curves, and new experimental techniques will be needed to draw inferences about the nature of electrochemical PCET.

The importance of nuclear quantum effects in spectral line broadening of optical spectra and electrostatic properties in aromatic chromophores.

In this work, we examine the importance of nuclear quantum effects on capturing the line broadening and vibronic structure of optical spectra. We determine the absorption spectra of three aromatic molecules indole, pyridine, and benzene using time dependent density functional theory with several molecular dynamics sampling protocols: force-field based empirical potentials, ab initio simulations, and finally path-integrals for the inclusion of nuclear quantum effects. We show that the absorption spectrum for all these chromophores are similarly broadened in the presence of nuclear quantum effects regardless of the presence of hydrogen bond donor or acceptor groups. We also show that simulations incorporating nuclear quantum effects are able to reproduce the heterogeneous broadening of the absorption spectra even with empirical force fields. The spectral broadening associated with nuclear quantum effects can be accounted for by the broadened distribution of chromophore size as revealed by a particle in the box model. We also highlight the role that nuclear quantum effects have on the underlying electronic structure of aromatic molecules as probed by various electrostatic properties.

Maxima in the thermodynamic response and correlation functions of deeply supercooled water.

Femtosecond x-ray laser pulses were used to probe micrometer-sized water droplets that were cooled down to 227 kelvin in vacuum. Isothermal compressibility and correlation length were extracted from x-ray scattering at the low-momentum transfer region. The temperature dependence of these thermodynamic response and correlation functions shows maxima at 229 kelvin for water and 233 kelvin for heavy water. In addition, we observed that the liquids undergo the fastest growth of tetrahedral structures at similar temperatures. These observations point to the existence of a Widom line, defined as the locus of maximum correlation length emanating from a critical point at positive pressures in the deeply supercooled regime. The difference in the maximum value of the isothermal compressibility between the two isotopes shows the importance of nuclear quantum effects.

Effects of temperature and isotopic substitution on electron attachment dynamics of guanine–cytosine base pair: Ring-polymer and classical molecular dynamics simulations

The dynamical process of electron attachment to a guanine–cytosine pair in the normal (h-GC) and deuterated (d-GC) forms has been studied theoretically by semiclassical ring-polymer molecular dynamics (RPMD) simulations using the empirical valence bond model. The initially formed dipole-bound anion is converted rapidly to the valence-bound anion within about 0.1ps in both h-GC and d-GC. However, the subsequent proton transfer in h-GC occurs with a rate five times greater than the deuteron transfer in d-GC. The change of rates with isotopic substitution and temperature variation in the RPMD simulations are quantitatively and qualitatively different from those in the classical molecular dynamics (MD) simulations, demonstrating the importance of nuclear quantum effects on the dynamics of this system.

Communication: On the consistency of approximate quantum dynamics simulation methods for vibrational spectra in the condensed phase.

Including quantum mechanical effects on the dynamics of nuclei in the condensed phase is challenging, because the complexity of exact methods grows exponentially with the number of quantum degrees of freedom. Efforts to circumvent these limitations can be traced down to two approaches: methods that treat a small subset of the degrees of freedom with rigorous quantum mechanics, considering the rest of the system as a static or classical environment, and methods that treat the whole system quantum mechanically, but using approximate dynamics. Here, we perform a systematic comparison between these two philosophies for the description of quantum effects in vibrational spectroscopy, taking the Embedded Local Monomer model and a mixed quantum-classical model as representatives of the first family of methods, and centroid molecular dynamics and thermostatted ring polymer molecular dynamics as examples of the latter. We use as benchmarks D2O doped with HOD and pure H2O at three distinct thermodynamic state points (ice Ih at 150 K, and the liquid at 300 K and 600 K), modeled with the simple q-TIP4P/F potential energy and dipole moment surfaces. With few exceptions the different techniques yield IR absorption frequencies that are consistent with one another within a few tens of cm(-1). Comparison with classical molecular dynamics demonstrates the importance of nuclear quantum effects up to the highest temperature, and a detailed discussion of the discrepancies between the various methods let us draw some (circumstantial) conclusions about the impact of the very different approximations that underlie them. Such cross validation between radically different approaches could indicate a way forward to further improve the state of the art in simulations of condensed-phase quantum dynamics.

I-PI: A Python interface for ab initio path integral molecular dynamics simulations

Recent developments in path integral methodology have significantly reduced the computational expense of including quantum mechanical effects in the nuclear motion in ab initio molecular dynamics simulations. However, the implementation of these developments requires a considerable programming effort, which has hindered their adoption. Here we describe i-PI, an interface written in Python that has been designed to minimise the effort required to bring state-of-the-art path integral techniques to an electronic structure program. While it is best suited to first principles calculations and path integral molecular dynamics, i-PI can also be used to perform classical molecular dynamics simulations, and can just as easily be interfaced with an empirical forcefield code. To give just one example of the many potential applications of the interface, we use it in conjunction with the CP2K electronic structure package to showcase the importance of nuclear quantum effects in high-pressure water. Program summaryProgram title: i-PICatalogue identifier: AERN_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AERN_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 3No. of lines in distributed program, including test data, etc.: 138626No. of bytes in distributed program, including test data, etc.: 3128618Distribution format: tar.gzProgramming language: Python.Computer: Multiple architectures.Operating system: Linux, Mac OSX, Windows.RAM: Less than 256 MbClassification: 7.7.External routines: NumPyNature of problem:Bringing the latest developments in the modelling of nuclear quantum effects with path integral molecular dynamics to ab initio electronic structure programs with minimal implementational effort.Solution method:State-of-the-art path integral molecular dynamics techniques are implemented in a Python interface. Any electronic structure code can be patched to receive the atomic coordinates from the Python interface, and to return the forces and energy that are used to integrate the equations of motion.Restrictions:This code only deals with distinguishable particles. It does not include fermonic or bosonic exchanges between equivalent nuclei, which can become important at very low temperatures.Running time:Depends dramatically on the nature of the simulation being performed. A few minutes for short tests with empirical force fields, up to several weeks for production calculations with ab initio forces. The examples provided with the code run in less than an hour.

Towards a predictive first-principles description of solid molecular hydrogen with density functional theory

We examine the influence of the main approximations employed in density-functional theory descriptions of the solid phase of molecular hydrogen near dissociation. We consider the importance of nuclear quantum effects on equilibrium properties and find that they strongly influence intramolecular properties, such as bond fluctuations and stability. We demonstrate that the combination of both thermal and quantum effects make a drastic change to the predicted optical properties of the molecular solid, suggesting a limited value to dynamical, e.g., finite-temperature, predictions based on classical ions and static crystals. We also consider the influence of the chosen exchange--correlation density functional on the predicted properties of hydrogen, in particular, the pressure dependence of the band gap and the zero-point energy. Finally, we use our simulations to make an assessment of the accuracy of typically employed approximations to the calculation of the Gibbs free energy of the solid, namely the quasi-harmonic approximation for solids. We find that, while the approximation is capable of producing free energies with an accuracy of ~10 meV, this is not enough to make reliable predictions of the phase diagram of hydrogen from first-principles due to the small free energy differences seen between several potential structures for the solid; direct free energy calculations for quantum protons are required in order to make definite predictions.

Application of ring-polymer molecular dynamics to electronically nonadiabatic excess electron dynamics in water clusters: Importance of nuclear quantum effects

The ring-polymer molecular dynamics (RPMD) method was applied to the real-time excess electron dynamics in water clusters within a one-electron pseudo-potential model, where the excess electron motion is described with the grid-based wave function while nuclear motions of water are described with RPMD. We have simulated electronically non-adiabatic relaxation dynamics associated with s→p excitation of an excess electron in the (H2O)50− water anion cluster. We compared the RPMD results to the corresponding results obtained from classical MD simulations. It was found that nuclear quantum effects are playing a very important role in determining nonadiabatic relaxation time.

Quantum–Thermal Crossover of Hydrogen and Tritium Diffusion in α-Iron

The diffusion coefficients of hydrogen (H) and tritium (T) in α-Fe have been computed using two approximate quantum dynamical techniques, that is, centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD), in the temperature range of T = 100–1000 K using the embedded atom method (EAM) potential. It has been found that the RPMD and CMD methods give very similar results. From a further analysis based on quantum transition-state theory (centroid density QTST) combined with path integral molecular dynamics (PIMD), it has been clear that there is a crossover between thermal and quantum mechanisms at about T = 500 and 300 K for H and T diffusions, respectively. The importance of nuclear quantum effects at low temperatures has been illustrated in terms of the effective free-energy surface map.