Elucidating Heavy Atom Tunneling Kinetics in the Cope Rearrangement of Semibullvalene.

In this work, we characterize the temperature dependence of kinetic properties in heavy atom tunneling reactions by means of molecular dynamics simulations, including nuclear quantum effects (NQEs) via Path Integral theory. To this end, we consider the prototypical Cope rearrangement of semibullvalene. The reaction was studied in the 25-300K temperature range observing that the inclusion of NQEs modifies the temperature behavior of both free energy barriers and dynamical recrossing factors with respect to classical dynamics. Notably, while in classical simulations the activation free energy shows a very weak temperature dependence, it becomes strongly dependent on temperature when NQEs are included. This temperature behavior shows a transition from a regime where the quantum effects are limited and can mainly be traced back to zero point energy, to a low temperature regime where tunneling plays a dominant role. In this regime, the free energy curve tunnels below the potential energy barrier along the reaction coordinate,  allowing much faster reaction rates. Finally, the temperature dependence of the rate constants obtained from molecular dynamics simulations was compared with available experimental data and with semi-classical transition state theory calculations, showing comparable behaviors and similar transition temperatures from  thermal to (deep) tunneling regime.

When Quantum Fluctuations Meet Structural Instabilities: The Isotope- and Pressure-Induced Phase Transition in the Quantum Paraelectric NaOH.

Anhydrous sodium hydroxide, a common and structurally simple compound, shows spectacular isotope effects: NaOD undergoes a first-order transition, which is absent in NaOH. By combining ab initio electronic structure calculations with Feynman path integrals, we show that NaOH is an unusual example of a quantum paraelectric: zero-point quantum fluctuations stretch the weak hydrogen bonds (HBs) into a region where they are unstable and break. By strengthening the HBs via isotope substitution or applied pressure, the system can be driven to a broken-symmetry antiferroelectric phase. In passing, we provide a simple quantitative criterion for HB breaking in layered crystals and show that nuclear quantum effects are crucial in paraelectric to ferroelectric transitions in hydrogen-bonded hydroxides.

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.

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.

Quantum versus classical unimolecular fragmentation rate constants and activation energies at finite temperature from direct dynamics simulations.

In the present work, we investigate how nuclear quantum effects modify the temperature dependent rate constants and, consequently, the activation energies in unimolecular reactions. In the reactions under study, nuclear quantum effects mainly stem from the presence of a large zero point energy. Thus, we investigate the behavior of methods compatible with direct dynamics simulations, the quantum thermal bath (QTB) and ring polymer molecular dynamics (RPMD). To this end, we first compare them with quantum reaction theory for a model Morse potential before extending this comparison to molecular models. Our results show that, in particular in the temperature range comparable with or lower than the zero point energy of the system, the RPMD method is able to correctly capture nuclear quantum effects on rate constants and activation energies. On the other hand, although the QTB provides a good description of equilibrium properties including zero-point energy effects, it largely overestimates the rate constants. The origin of the different behaviours is in the different distance distributions provided by the two methods and in particular how they differently describe the tails of such distributions. The comparison with transition state theory shows that RPMD can be used to study fragmentation of complex systems for which it may be difficult to determine the multiple reaction pathways and associated transition states.

Improving Condensed-Phase Water Dynamics with Explicit Nuclear Quantum Effects: The Polarizable Q-AMOEBA Force Field.

We introduce a new parametrization of the AMOEBA polarizable force field for water denoted Q-AMOEBA, for use in simulations that explicitly account for nuclear quantum effects (NQEs). This study is made possible thanks to the recently introduced adaptive Quantum Thermal Bath (adQTB) simulation technique which computational cost is comparable to classical molecular dynamics. The flexible Q-AMOEBA model conserves the initial AMOEBA functional form, with an intermolecular potential including an atomic multipole description of electrostatic interactions (up to quadrupole), a polarization contribution based on the Thole interaction model and a buffered 14-7 potential to model van der Waals interactions. It has been obtained by using a ForceBalance fitting strategy including high-level quantum chemistry reference energies and selected condensed-phase properties targets. The final Q-AMOEBA model is shown to accurately reproduce both gas-phase and condensed-phase properties, notably improving the original AMOEBA water model. This development allows the fine study of NQEs on water liquid phase properties such as the average H-O-H angle compared to its gas-phase equilibrium value, isotope effects, and so on. Q-AMOEBA also provides improved infrared spectroscopy prediction capabilities compared to AMOEBA03. Overall, we show that the impact of NQEs depends on the underlying model functional form and on the associated strength of hydrogen bonds. Since adQTB simulations can be performed at near classical computational cost using the Tinker-HP package, Q-AMOEBA can be extended to organic molecules, proteins, and nucleic acids opening the possibility for the large-scale study of the importance of NQEs in biophysics.

Anharmonic spectral features via trajectory-based quantum dynamics: A perturbative analysis of the interplay between dynamics and sampling.

The performance of different approximate algorithms for computing anharmonic features in vibrational spectra is analyzed and compared on model and more realistic systems that present relevant nuclear quantum effects. The methods considered combine approximate sampling of the quantum thermal distribution with classical time propagation and include Matsubara dynamics, path integral dynamics approaches, linearized initial value representation, and the recently introduced adaptive quantum thermal bath. A perturbative analysis of these different methods enables us to account for the observed numerical performance on prototypes for overtones and combination bands and to draw qualitatively correct trends for the numerical results obtained for Fermi resonances. Our results prove that the unequal performances of these approaches often derive from the method employed to sample initial conditions and not, as usually assumed, from the lack of coherence in the time propagation. Furthermore, as confirmed by the analysis reported in Benson and Althorpe, J. Chem. Phys. 130, 194510 (2021), we demonstrate, both via the perturbative approach and numerically, that path integral dynamics methods fail to reproduce the intensities of these anharmonic features and follow purely classical trends with respect to their temperature behavior. Finally, the remarkably accurate performance of the adaptive quantum thermal bath approach is documented and motivated.

Nuclear Quantum Effects in Liquid Water at Near Classical Computational Cost Using the Adaptive Quantum Thermal Bath.

We demonstrate the accuracy and efficiency of a recently introduced approach to account for nuclear quantum effects (NQEs) in molecular simulations: the adaptive quantum thermal bath (adQTB). In this method, zero-point energy is introduced through a generalized Langevin thermostat designed to precisely enforce the quantum fluctuation-dissipation theorem. We propose a refined adQTB algorithm with improved accuracy and report adQTB simulations of liquid water. Through extensive comparison with reference path integral calculations, we demonstrate that it provides excellent accuracy for a broad range of structural and thermodynamic observables as well as infrared vibrational spectra. The adQTB has a computational cost comparable to that of classical molecular dynamics, enabling simulations of up to millions of degrees of freedom.

Thermal and Nuclear Quantum Effects at the Antiferroelectric to Paraelectric Phase Transition in KOH and KOD Crystals.

Crystalline KOH undergoes an antiferroelectric (AFE) proton ordering phase transition at low temperatures, which results in a monoclinic bilayer structure held together by a network of weak hydrogen bonds (HBs). The Curie temperature shifts up when the compound is deuterated, an effect that classical MD is not able to catch. For deeper insights into the transition mechanism, we carry out ab initio MD simulations of KOH and KOD crystals by including quantum effects on the nuclei through Feynman path integrals. The geometric isotope effect and the evolution of the lattice parameters with temperature agree with the experimental data, while the purely classical description is not appropriate. Our results show that deuteration strengthens the HBs in the low-T AFE ordered phase. The transition is characterized by the flipping of OH/OD groups along a bending mode. Above the transition, the system is driven into a dynamical disordered paraelectric phase.

Semiconductor Quantum Plasmonics.

We investigate the frontier between classical and quantum plasmonics in highly doped semiconductor layers. The choice of a semiconductor platform instead of metals for our study permits an accurate description of the quantum nature of the electrons constituting the plasmonic response, which is a crucial requirement for quantum plasmonics. Our quantum model allows us to calculate the collective plasmonic resonances from the electronic states determined by an arbitrary one-dimensional potential. Our approach is corroborated with experimental spectra, realized on a single quantum well, in which higher order longitudinal plasmonic modes are present. We demonstrate that their energy depends on the plasma energy, as is also the case for metals, but also on the size confinement of the constituent electrons. This work opens the way toward the applicability of quantum engineering techniques for semiconductor plasmonics.

Quantum driven proton diffusion in brucite-like minerals under high pressure.

Transport of hydrogen in hydrous minerals under high pressure is a key step for the water cycle within the Earth interior. Brucite Mg(OH)2 is one of the simplest minerals containing hydroxyl groups and is believed to decompose under the geological condition of the deep Earth's mantle. In the present study, we investigate the proton diffusion in brucite under high pressure, which results from a complex interplay between two processes: the O-H reorientations motion around the c axis and O-H covalent bond dissociations. First-principle path-integral molecular dynamics simulations reveal that the increasing pressure tends to lock the former motion, while, in contrast, it activates the latter which is mainly triggered by nuclear quantum effects. These two competing effects therefore give rise to a pressure sweet spot for proton diffusion within the mineral. In brucite Mg(OH)2, proton diffusion reaches a maximum for pressures close to 70GPa, while the structurally similar portlandite Ca(OH)2 never shows proton diffusion within the pressure range and time scale that we explored. We analyze the different behavior of brucite and portlandite, which might constitute two prototypes for other minerals with same structure.

Sampling the thermal Wigner density via a generalized Langevin dynamics.

The Wigner thermal density is a function of considerable interest in the area of approximate (linearized or semiclassical) quantum dynamics where it is employed to generate initial conditions for the propagation of appropriate sets of classical trajectories. In this paper, we propose an original approach to compute the Wigner density based on a generalized Langevin equation. The stochastic dynamics is nontrivial in that it contains a coordinate-dependent friction coefficient and a generalized force that couples momenta and coordinates. These quantities are, in general, not known analytically and have to be estimated via auxiliary calculations. The performance of the new sampling scheme is tested on standard model systems with highly nonclassical features such as relevant zero point energy effects, correlation between momenta and coordinates, and negative parts of the Wigner density. In its current brute force implementation, the algorithm, whose convergence can be systematically checked, is accurate and has only limited overhead compared to schemes with similar characteristics. We briefly discuss potential ways to further improve its numerical efficiency.

The Fluctuation-Dissipation Theorem as a Diagnosis and Cure for Zero-Point Energy Leakage in Quantum Thermal Bath Simulations.

Quantum thermal bath (QTB) simulations reproduce statistical nuclear quantum effects via a Langevin equation with a colored random force. Although this approach has proven efficient for a variety of chemical and condensed-matter problems, the QTB, as many other semiclassical methods, suffers from zero-point energy leakage (ZPEL). The absence of a reliable criterion to quantify the ZPEL without resorting to demanding comparisons with path integral-based calculations has so far hindered the use of the QTB for the simulation of real systems. In this work, we establish a quantitative connection between ZPEL in the QTB framework and deviations from the quantum fluctuation-dissipation theorem (FDT) that can be monitored along the simulation. This provides a rigorous general criterion to detect and quantify the ZPEL without any a priori knowledge of the system under study. We then use this criterion to build an adaptive QTB method that strictly enforces the quantum FDT at all frequencies via an on-the-fly, spectrally resolved fine-tuning of the system-bath coupling coefficients. The validity of the adaptive approach is first demonstrated on a simple two-oscillator model. It is then applied to two more realistic problems: the description of the vibrational properties of a model aluminum crystal at low temperature and the simulation of the liquid-solid phase transition in a 13-atom neon cluster. In both systems, the standard QTB results are strongly altered by the ZPEL, which can be essentially eliminated using the adaptive approach.