Inclusion Of Nuclear Quantum Effects Research Articles

Nuclear quantum effects on the vibrational dynamics of the water-air interface.

We have applied path-integral molecular dynamics simulations to investigate the impact of nuclear quantum effects on the vibrational dynamics of water molecules at the water-air interface. The instantaneous fluctuations in the frequencies of the O-H stretch modes are calculated using the wavelet method of time series analysis, while the time scales of vibrational spectral diffusion are determined from frequency-time correlation functions and joint probability distributions. We find that the inclusion of nuclear quantum effects leads not only to a redshift in the vibrational frequency distribution by about 120 cm-1 for both the bulk and interfacial water molecules but also to an acceleration of the vibrational dynamics at the water-air interface by as much as 35%. In addition, a blueshift of about 45 cm-1 is seen in the vibrational frequency distribution of interfacial water molecules compared to that of the bulk. Furthermore, the dynamics of water molecules beyond the topmost molecular layer was found to be rather similar to that of bulk water.

Nuclear Quantum Effects in Hydroxide Hydrate Along the H-Bond Bifurcation Pathway.

Path integral (PI) simulations are used to explore nuclear quantum effects (NQEs) in hydroxide hydrate and its perdeuterated isotopomer along the H-bond bifurcation pathway. Toward this, a new potential energy surface using the symmetric gradient domain machine learning method with ab initio data at the CCSD(T)/aug-cc-pVTZ level is built. From PI umbrella sampling (US) simulations, free energy profiles along the bifurcation coordinate are explored as a function of temperature. At ambient temperature, the bifurcation barrier is increased upon inclusion of NQEs. At low temperatures in the deep tunneling regime, the barrier is strongly decreased and flattened. These trends are examined, and the role of the O-O distance is also investigated through two-dimensional US simulations.

Effect of Quantum Delocalization on Temperature Dependent Double Proton Transfer in Molecular Crystals of Terephthalic Acid.

Double proton transfers (DPTs) are important for several physical processes, both in molecules and in the condensed phase. While these have been widely studied in biological systems, their study in crystalline environments is rare. In this work, using path integral molecular dynamics simulations, we have studied temperature dependent DPT in molecular crystals of terephthalic acid (TPA). In accordance with experimental reports, we find evidence for a double proton transfer induced order-to-disorder transition that is sensitive to the inclusion of nuclear quantum effects. Our simulations show that in addition to the presence of L and R tautomers of terepthalic acid, there are a small but non-negligible concentration of positive and negatively charged pairs of TPA molecules. At the onset of the transition at low temperatures, DPT likely occurs through a tunneling mechanism while at room temperature, likely involving the dominance of activated hopping. Through an analysis of the electronic structure of the system using Wannier functions, we show that the H atom shuttling between the donor and acceptor O atoms involves a proton.

Environmental and Nuclear Quantum Effects on Double Proton Transfer in the Guanine-Cytosine Base Pair.

In the present letter, we investigate the double proton transfer (DPT) tautomerization process in guanine-cytosine (GC) DNA base pairs. In particular, we study the influence of the biological environment on the mechanism, the kinetics and thermodynamics of such DPT. To this end, we present a molecular dynamics (MD) study in the tight-binding density functional theory framework, and compare the reactivity of the isolated GC dimer with that of the same dimer embedded in a small DNA structure. The impact of nuclear quantum effects (NQEs) is also evaluated using Path Integral based MD. Results show that in the isolated dimer, the DPT occurs via a concerted mechanism, while in the model biological environment, it turns into a stepwise process going through an intermediate structure. One of the water molecules in the vicinity of the proton transfer sites plays an important role as it changes H-bond pattern during the DPT reaction. The inclusion of NQEs has the effect of speeding up the tautomeric-to-canonical reaction, reflecting the destabilization of both the tautomeric and intermediate forms.

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.

Routine Molecular Dynamics Simulations Including Nuclear Quantum Effects: From Force Fields to Machine Learning Potentials.

We report the implementation of a multi-CPU and multi-GPU massively parallel platform dedicated to the explicit inclusion of nuclear quantum effects (NQEs) in the Tinker-HP molecular dynamics (MD) package. The platform, denoted Quantum-HP, exploits two simulation strategies: the Ring-Polymer Molecular Dynamics (RPMD) that provides exact structural properties at the cost of a MD simulation in an extended space of multiple replicas and the adaptive Quantum Thermal Bath (adQTB) that imposes the quantum distribution of energy on a classical system via a generalized Langevin thermostat and provides computationally affordable and accurate (though approximate) NQEs. We discuss some implementation details, efficient numerical schemes, and parallelization strategies and quickly review the GPU acceleration of our code. Our implementation allows an efficient inclusion of NQEs in MD simulations for very large systems, as demonstrated by scaling tests on water boxes with more than 200,000 atoms (simulated using the AMOEBA polarizable force field). We test the compatibility of the approach with Tinker-HP's recently introduced Deep-HP machine learning potentials module by computing water properties using the DeePMD potential with adQTB thermostatting. Finally, we show that the platform is also compatible with the alchemical free energy estimation capabilities of Tinker-HP and fast enough to perform simulations. Therefore, we study how NQEs affect the hydration free energy of small molecules solvated with the recently developed Q-AMOEBA water force field. Overall, the Quantum-HP platform allows users to perform routine quantum MD simulations of large condensed-phase systems and will help to shed new light on the quantum nature of important interactions in biological matter.

Combined QM/MM, Machine Learning Path Integral Approach to Compute Free Energy Profiles and Kinetic Isotope Effects in RNA Cleavage Reactions.

We present a fast, accurate, and robust approach for determination of free energy profiles and kinetic isotope effects for RNA 2'-O-transphosphorylation reactions with inclusion of nuclear quantum effects. We apply a deep potential range correction (DPRc) for combined quantum mechanical/molecular mechanical (QM/MM) simulations of reactions in the condensed phase. The method uses the second-order density-functional tight-binding method (DFTB2) as a fast, approximate base QM model. The DPRc model modifies the DFTB2 QM interactions and applies short-range corrections to the QM/MM interactions to reproduce ab initio DFT (PBE0/6-31G*) QM/MM energies and forces. The DPRc thus enables both QM and QM/MM interactions to be tuned to high accuracy, and the QM/MM corrections are designed to smoothly vanish at a specified cutoff boundary (6 Å in the present work). The computational speed-up afforded by the QM/MM+DPRc model enables free energy profiles to be calculated that include rigorous long-range QM/MM interactions under periodic boundary conditions and nuclear quantum effects through a path integral approach using a new interface between the AMBER and i-PI software. The approach is demonstrated through the calculation of free energy profiles of a native RNA cleavage model reaction and reactions involving thio-substitutions, which are important experimental probes of the mechanism. The DFTB2+DPRc QM/MM free energy surfaces agree very closely with the PBE0/6-31G* QM/MM results, and it is vastly superior to the DFTB2 QM/MM surfaces with and without weighted thermodynamic perturbation corrections. 18O and 34S primary kinetic isotope effects are compared, and the influence of nuclear quantum effects on the free energy profiles is examined.

Initial state-selected scattering for the reactions H + CH4/CHD3 and F + CHD3 employing ring polymer molecular dynamics.

The inclusion of nuclear quantum effects (NQEs) in molecular dynamics simulations is one of the major obstacles for an accurate modeling of molecular scattering processes involving more than a couple of atoms. An efficient method to incorporate these effects is ring polymer molecular dynamics (RPMD). Here, we extend the scope of our recently developed method based on non-equilibrium RPMD (NE-RPMD) from triatomic chemical reactions to reactions involving more atoms. We test the robustness and accuracy of the method by computing the integral cross sections for the H/F + CH4/CHD3 reactions where the methane molecule is either initially in its vibrational ground or excited state (C-H stretch). Furthermore, we analyze the extent to which NQEs are described by NE-RPMD. The method shows significant improvement over the quasiclassical trajectory approach while remaining computationally efficient.

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, B97XD 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–1700 cm and 2300 cm–3400 cm in the gas phase and 600 cm–1800 cm and 2200 cm–3400 cm in the solid state for compound 1. The absorption regions for compound 2 were found as follows: 700 cm–1700 cm and 2300 cm–3300 cm for the gas phase and one broad absorption region in the solid state between 700 cm and 3100 cm. 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.

Sensitivity of Intra- and Intermolecular Interactions of Benzo[h]quinoline from Car-Parrinello Molecular Dynamics and Electronic Structure Inspection.

The O-H...N and O-H...O hydrogen bonds were investigated in 10-hydroxybenzo[h]quinoline (HBQ) and benzo[h]quinoline-2-methylresorcinol complex in vacuo, solvent and crystalline phases. The chosen systems contain analogous donor and acceptor moieties but differently coupled (intra- versus intermolecularly). Car–Parrinello molecular dynamics (CPMD) was employed to shed light onto principle components of interactions responsible for the self-assembly. It was applied to study the dynamics of the hydrogen bonds and vibrational features as well as to provide initial geometries for incorporation of quantum effects and electronic structure studies. The vibrational features were revealed using Fourier transformation of the autocorrelation function of atomic velocity and by inclusion of nuclear quantum effects on the O-H stretching solving vibrational Schrödinger equation a posteriori. The potential of mean force (Pmf) was computed for the whole trajectory to derive the probability density distribution and for the O-H stretching mode from the proton vibrational eigenfunctions and eigenvalues incorporating statistical sampling and nuclear quantum effects. The electronic structure changes of the benzo[h]quinoline-2-methylresorcinol dimer and trimers were studied based on Constrained Density Functional Theory (CDFT) whereas the Electron Localization Function (ELF) method was applied for all systems. It was found that the bridged proton is localized on the donor side in both investigated systems in vacuo. The crystalline phase simulations indicated bridged proton-sharing and transfer events in HBQ. These effects are even more pronounced when nuclear quantization is taken into account, and the quantized Pmf allows the proton to sample the acceptor area more efficiently. The CDFT indicated the charge depletion at the bridged proton for the analyzed dimer and trimers in solvent. The ELF analysis showed the presence of the isolated proton (a signature of the strongest hydrogen bonds) only in some parts of the HBQ crystal simulation. The collected data underline the importance of the intramolecular coupling between the donor and acceptor moieties.

Progress and challenges in ab initio simulations of quantum nuclei in weakly bonded systems

Atomistic simulations based on the first-principles of quantum mechanics are reaching unprecedented length scales. This progress is due to the growth in computational power allied with the development of new methodologies that allow the treatment of electrons and nuclei as quantum particles. In the realm of materials science, where the quest for desirable emergent properties relies increasingly on soft weakly bonded materials, such methods have become indispensable. In this Perspective, an overview of simulation methods that are applicable for large system sizes and that can capture the quantum nature of electrons and nuclei in the adiabatic approximation is given. In addition, the remaining challenges are discussed, especially regarding the inclusion of nuclear quantum effects (NQEs) beyond a harmonic or perturbative treatment, the impact of NQEs on electronic properties of weakly bonded systems, and how different first-principles potential energy surfaces can change the impact of NQEs on the atomic structure and dynamics of weakly bonded systems.

Perfluoro effect on the electronic excited states of para-benzoquinone revealed by experiment and theory

We report a comprehensive study on the electronic excited states of tetrafluoro-1,4-benzoquinone, through high-resolution vacuum ultraviolet photoabsorption spectroscopy and time-dependent density functional theory calculations performed within the nuclear ensemble approach. Absolute cross section values were experimentally determined in the 3.8-10.8 eV energy range. The present experimental results represent the highest resolution data yet reported for this molecule and reveal previously unresolved spectral structures. The interpretation of the results was made in close comparison with the available data for para-benzoquinone [Jones et al., J. Chem. Phys., 2017, 146, 184303]. While the dominant absorption features for both molecules arise from analogous π* ← π transitions, some remarkable differences have been identified. The perfluoro effect manifests in different ways: shifts in band positions and cross sections, appearance of features associated with excitations to σCF* orbitals, and spectrum broadening by quenching of either vibrational or Rydberg progressions. The level of agreement between experiment and theory is very satisfactory, yet that required the inclusion of nuclear quantum effects in the calculations. We have also discussed the role of temperature on the absorption spectrum, as well as the involvement of core-excited resonances in promoting dissociative electron attachment reactions in the 3-5 eV range.

Enhanced Sampling Path Integral Methods Using Neural Network Potential Energy Surfaces with Application to Diffusion in Hydrogen Hydrates

AbstractThe high cost of ab initio molecular dynamics (AIMD) simulations to model complex physical and chemical systems limits its ability to address many key questions. However, new machine learning‐based representations of complex potential energy surfaces have been introduced in recent years to circumvent computationally demanding AIMD simulations while retaining the same level of accuracy. As these machine learning methods gain in popularity over the next decade, it is important to address the appropriate way to develop and integrate them with well‐established simulation methods. This paper details the parameterization and training, using accurate electronic structure calculations, of artificial neural network potentials (NNPs) to model the intermolecular interactions in a hydrogen clathrate hydrate, wherein hydrogen molecules are confined inside the cavities of the 3D crystalline framework of hydrogen‐bonded water molecules. This new NNP is used in conjunction with new path‐integral based enhanced sampling methods, for inclusion of nuclear quantum effects and promotion of free energy barrier crossing, in order to determine properties that are important for understanding the diffusion of hydrogen gas in the clathrate system. These simulations demonstrate the influence of cage occupancy on the free energy barriers that determine the diffusivity of hydrogen gas through the network of large cages.

Multidimensional Hydrogen Tunneling in Supported Molecular Switches: The Role of Surface Interactions.

The nuclear tunneling crossover temperature (T_{c}) of hydrogen transfer reactions in supported molecular-switch architectures can lie close to room temperature. This calls for the inclusion of nuclear quantum effects (NQEs) in the calculation of reaction rates even at high temperatures. However, computations of NQEs relying on standard parametrized dimensionality-reduced models quickly become inadequate in these environments. In this Letter, we study the paradigmatic molecular switch based on porphycene molecules adsorbed on metallic surfaces with full-dimensional calculations that combine density-functional theory for the electrons with the semiclassical ring-polymer instanton approximation for the nuclei. We show that the double intramolecular hydrogen transfer (DHT) rate can be enhanced by orders of magnitude due to surface fluctuations in the deep-tunneling regime. We also explain the origin of an Arrhenius temperature dependence of the rate below T_{c} and why this dependence differs at different surfaces. We propose a simple model to rationalize the temperature dependence of DHT rates spanning diverse fcc [110] surfaces.

Two-temperature warm dense hydrogen as a test of quantum protons driven by orbital-free density functional theory electronic forces

We consider a steady-state (but transient) situation in which a warm dense aggregate is a two-temperature system with equilibrium electrons at temperature Te, ions at Ti, and Te ≠ Ti. Such states are achievable by pump–probe experiments. For warm dense hydrogen in such a two-temperature situation, we investigate nuclear quantum effects (NQEs) on structure and thermodynamic properties, thereby delineating the limitations of ordinary ab initio molecular dynamics. We use path integral molecular dynamics (PIMD) simulations driven by orbital-free density functional theory (OFDFT) calculations with state-of-the-art noninteracting free-energy and exchange-correlation functionals for the explicit temperature dependence. We calibrate the OFDFT calculations against conventional (explicit orbitals) Kohn–Sham DFT. We find that when the ratio of the ionic thermal de Broglie wavelength to the mean interionic distance is larger than about 0.30, the ionic radial distribution function is meaningfully affected by the inclusion of NQEs. Moreover, NQEs induce a substantial increase in both the ionic and electronic pressures. This confirms the importance of NQEs for highly accurate equation-of-state data on highly driven hydrogen. For Te > 20 kK, increasing Te in the warm dense hydrogen has slight effects on the ionic radial distribution function and equation of state in the range of densities considered. In addition, we confirm that compared with thermostatted ring-polymer molecular dynamics, the primitive PIMD algorithm overestimates electronic pressures, a consequence of the overly localized ionic description from the primitive scheme.

Nuclear Quantum Effects Largely Influence Molecular Dissociation and Proton Transfer in Liquid Water under an Electric Field.

Proton transfer in liquid water controls acid-base chemistry, crucial enzyme reactions, and the functioning of fuel cells. Externally applied static electric fields in water are capable of dissociating molecules and transferring protons across the H-bond network. However, the impact of nuclear quantum effects (NQEs) on these fundamental field-induced phenomena has not yet been reported. By comparing state-of-the-art ab initio molecular dynamics (AIMD) and path integral AIMD simulations of water under electric fields, I show that quantum delocalization of the proton lowers the molecular ionization threshold to approximately one-third. Moreover, also the water behavior as a protonic semiconductor is considerably modified by the inclusion of NQEs. In fact, when the quantum nature of the nuclei is taken into account, the proton conductivity is ∼50% larger. This work proves that NQEs sizably affect the protolysis phenomenon and proton transfer in room-temperature liquid water.

Fully consistent density functional theory determination of the insulator-metal transition boundary in warm dense hydrogen

Using conceptually and procedurally consistent density functional theory (DFT) calculations with an advanced meta-GGA exchange-correlation functional in ab initio molecular dynamics simulations, we determine the insulator-metal transition (IMT) of warm dense fluid hydrogen over the pressure range 50 to 300 GPa. Inclusion of nuclear quantum effects via path-integral molecular dynamics (PIMD) sharpens the metallic transition and lowers the transition temperature relative to results from Born-Oppenheimer (BO) MD. BOMD itself gives improved agreement with experimental results compared to previous DFT predictions. Examination of the ionic pair correlation function in the context of the abrupt conductivity increase at the transition confirms a metallic transition due to the dissociation of molecular hydrogen that coincides with an abrupt band gap closure. Direct comparison of the PIMD and BOMD results clearly demonstrates an isotope effect on the IMT. Distinct from stochastic simulations, these results do not depend upon any ad hoc combination of ground-state and finite-T methodologies.

On the importance of accounting for nuclear quantum effects in ab initio calibrated force fields in biological simulations

In many important processes in chemistry, physics, and biology the nuclear degrees of freedom cannot be described using the laws of classical mechanics. At the same time, the vast majority of molecular simulations that employ wide-coverage force fields treat atomic motion classically. In light of the increasing desire for and accelerated development of quantum mechanics (QM)-parameterized interaction models, we reexamine whether the classical treatment is sufficient for a simple but crucial chemical species: alkanes. We show that when using an interaction model or force field in excellent agreement with the "gold standard" QM data, even very basic simulated properties of liquid alkanes, such as densities and heats of vaporization, deviate significantly from experimental values. Inclusion of nuclear quantum effects via techniques that treat nuclear degrees of freedom using the laws of classical mechanics brings the simulated properties much closer to reality.

Activation Energy of Organic Cation Rotation in CH3NH3PbI3 and CD3NH3PbI3: Quasi-Elastic Neutron Scattering Measurements and First-Principles Analysis Including Nuclear Quantum Effects.

The motion of CH3NH3+ cations in the low-temperature phase of the promising photovoltaic material methylammonium lead triiodide (CH3NH3PbI3) is investigated experimentally as well as theoretically, with a particular focus on the activation energy. Inelastic and quasi-elastic neutron scattering measurements reveal an activation energy of ∼48 meV. Through a combination of experiments and first-principles calculations, we attribute this activation energy to the relative rotation of CH3 against an NH3 group that stays bound to the inorganic cage. The inclusion of nuclear quantum effects through path integral molecular dynamics gives an activation energy of ∼42 meV, in good agreement with the neutron scattering experiments. For deuterated samples (CD3NH3PbI3), both theory and experiment observe a higher activation energy for the rotation of CD3 against NH3, which results from the smaller nuclear quantum effects in CD3. The rotation of the NH3 group, which is bound to the inorganic cage via strong hydrogen bonding, is unlikely to occur at low temperatures due to its high energy barrier of ∼120 meV.

Inclusion of nuclear quantum effects for simulations of nonlinear spectroscopy.

The computation and interpretation of nonlinear vibrational spectroscopy is of vital importance for understanding a wide range of dynamical processes in molecular systems. Here, we introduce an approach to evaluate multi-time response functions in terms of multi-time double symmetrized Kubo transformed thermal correlation functions. Furthermore, we introduce a multi-time extension of ring polymer molecular dynamics to evaluate these Kubo transforms. Benchmark calculations show that the approximations are useful for short times even for nonlinear operators, providing a consistent improvement over classical simulations of multi-time correlation functions. The introduced methodology thus provides a practical way of including nuclear quantum effects in multi-time response functions of non-linear optical spectroscopy.