Converged Colored Noise Path Integral Molecular Dynamics Study of the Zundel Cation Down to Ultralow Temperatures at Coupled Cluster Accuracy

Origin of dielectric polarization suppression in confined water from first principles

It has long been known that the dielectric constant of confined water should be different from that in bulk. Recent experiments have shown that it is vanishingly small, however the origin of the phenomenon remains unclear. Here we used ab initio molecular dynamics simulations (AIMD) and AIMD-trained machine-learning potentials to understand water's structure and electronic properties underpinning this effect. For the graphene and hexagonal boron-nitride substrates considered, we find that it originates in the spontaneous anti-parallel alignment of the water dipoles in the first two water layers near the solid interface. The interfacial layers exhibit net ferroelectric ordering, resulting in an overall anti-ferroelectric arrangement of confined water. Together with constrained hydrogen-bonding orientations, this leads to much reduced out-of-plane polarization. Furthermore, we directly contrast AIMD and simple classical force-field simulations, revealing important differences. This work offers insight into a property of water that is critical in modulating surface forces, the electric-double-layer formation and molecular solvation, and shows a way to compute it.

Deciphering the Impact of Helium Tagging on Flexible Molecules: Probing Microsolvation Effects of Protonated Acetylene by Quantum Configurational Entropy

Helium, the lightest and most weakly interacting noble gas, is well-known for its unsurpassed chemical inertness. In many applications of helium in experimental techniques, such as tagging, messenger, or nanodroplet isolation action spectroscopy of molecules or complexes, it is assumed that the interaction of helium with the respective species, and thus the resulting interaction-induced perturbation, is small enough not to affect their structure and dynamics. Here, we probe the impact of one up to many attached helium atoms on protonated acetylene─an important nonclassical carbocation subject to three-center two-electron bonding in its ground state structure─using highly accurate interaction potentials in conjunction with entropy-based higher-order nonlinear correlation analysis. In particular, using neural network potentials at CCSD(T) accuracy, we disclose the specific structural perturbations due to the tagging of C₂H₃⁺ with up to 20 He atoms at a temperature of 1 K. Analysis reveals that microsolvation by helium influences the structure of C₂H₃⁺ noticeably, while our investigation of the quantum configurational information entropy additionally shows that correlations between individual orientational degrees of freedom are affected as a function of cluster size. In particular, it is found that the most probable bridge-like structure of the ro-vibrational quantum ground state of C₂H₃⁺, which is nonplanar and trans-bent in contrast to the perfectly planar equilibrium structure, becomes increasingly more localized upon adding helium atoms. The remarkably nonlinear behavior of the angular correlations as a function of cluster size is traced back to the buildup of the quantum microsolvation shell that enhances anisotropy up to N_He = 6 while more and more isotropic solvation takes over beyond six. Our approach is general and thus sets the stage to investigate the salient effects on the structure of flexible molecules due to tagging beyond the specific case.

Coupled Cluster Molecular Dynamics of Condensed Phase Systems Enabled by Machine Learning Potentials: Liquid Water Benchmark

Coupled cluster theory is a general and systematic electronic structure method, but in particular the highly accurate "gold standard" coupled cluster singles, doubles and perturbative triples, CCSD(T), can only be applied to small systems. To overcome this limitation, we introduce a framework to transfer CCSD(T) accuracy of finite molecular clusters to extended condensed phase systems using a high-dimensional neural network potential. This approach, which is automated, allows one to perform high-quality coupled cluster molecular dynamics, CCMD, as we demonstrate for liquid water including nuclear quantum effects. The machine learning strategy is very efficient, generic, can be systematically improved, and is applicable to a variety of complex systems.

Simulation of Nuclear Quantum Effects in Condensed Matter Systems via Quantum Baths

This paper reviews methods that aim at simulating nuclear quantum effects (NQEs) using generalized thermal baths. Generalized (or quantum) baths simulate statistical quantum features, and in particular zero-point energy effects, through non-Markovian stochastic dynamics. They make use of generalized Langevin Equations (GLEs), in which the quantum Bose–Einstein energy distribution is enforced by tuning the random and friction forces, while the system degrees of freedom remain classical. Although these baths have been formally justified only for harmonic oscillators, they perform well for several systems, while keeping the cost of the simulations comparable to the classical ones. We review the formal properties and main characteristics of classical and quantum GLEs, in relation with the fluctuation–dissipation theorems. Then, we describe the quantum thermostat and quantum thermal bath, the two generalized baths currently most used, providing several examples of applications for condensed matter systems, including the calculation of vibrational spectra. The most important drawback of these methods, zero-point energy leakage, is discussed in detail with the help of model systems, and a recently proposed scheme to monitor and mitigate or eliminate it—the adaptive quantum thermal bath—is summarised. This approach considerably extends the domain of application of generalized baths, leading, for instance, to the successful simulation of liquid water, where a subtle interplay of NQEs is at play. The paper concludes by overviewing further development opportunities and open challenges of generalized baths.

Helium Nanodroplet Infrared Action Spectroscopy of the Proton-Bound Dimer of Hydrogen Sulfate and Formate: Examining Nuclear Quantum Effects

The proton-bound dimer of hydrogen sulfate and formate is an archetypal structure for ionic hydrogen-bonding complexes that contribute to biogenic aerosol nucleation. Of central importance for the structure and properties of this complex is the location of the bridging proton connecting the two conjugate base moieties. The potential energy surface for bridging proton translocation features two local minima, with the proton localized at either the formate or hydrogen sulfate moiety. However, electronic structure methods reveal a shallow potential energy surface governing proton translocation, with a barrier on the order of the zero-point energy. This shallow potential complicates structural assignment and necessitates a consideration of nuclear quantum effects. In this work, we probe the structure of this complex and its isotopologues, utilizing infrared (IR) action spectroscopy of ions captured in helium nanodroplets. The IR spectra indicate a structure in which a proton is shared between the hydrogen sulfate and formate moieties, HSO₄^-···H⁺···^-OOCH. However, because of the nuclear quantum effects and vibrational anharmonicities associated with the shallow potential for proton translocation, the extent of proton displacement from the formate moiety remains unclear, requiring further experiments or more advanced theoretical treatments for additional insight.

Machine Learning Force Fields

In recent years, the use of machine learning (ML) in computational chemistry has enabled numerous advances previously out of reach due to the computational complexity of traditional electronic-structure methods. One of the most promising applications is the construction of ML-based force fields (FFs), with the aim to narrow the gap between the accuracy of ab initio methods and the efficiency of classical FFs. The key idea is to learn the statistical relation between chemical structure and potential energy without relying on a preconceived notion of fixed chemical bonds or knowledge about the relevant interactions. Such universal ML approximations are in principle only limited by the quality and quantity of the reference data used to train them. This review gives an overview of applications of ML-FFs and the chemical insights that can be obtained from them. The core concepts underlying ML-FFs are described in detail, and a step-by-step guide for constructing and testing them from scratch is given. The text concludes with a discussion of the challenges that remain to be overcome by the next generation of ML-FFs.

Persistent Homology Metrics Reveal Quantum Fluctuations and Reactive Atoms in Path Integral Dynamics

Nuclear quantum effects (NQEs) are known to impact a number of features associated with chemical reactivity and physicochemical properties, particularly for light atoms and at low temperatures. In the imaginary time path integral formalism, each atom is mapped onto a "ring polymer" whose spread is related to the quantum mechanical uncertainty in the particle's position, i.e., its thermal wavelength. A number of metrics have previously been used to investigate and characterize this spread and explain effects arising from quantum delocalization, zero-point energy, and tunneling. Many of these shape metrics consider just the instantaneous structure of the ring polymers. However, given the significant interest in methods such as centroid molecular dynamics and ring polymer molecular dynamics that link the molecular dynamics of these ring polymers to real time properties, there exists significant opportunity to exploit metrics that also allow for the study of the fluctuations of the atom delocalization in time. Here we consider the ring polymer delocalization from the perspective of computational topology, specifically persistent homology, which describes the 3-dimensional arrangement of point cloud data, (i.e. atomic positions). We employ the Betti sequence probability distribution to define the ensemble of shapes adopted by the ring polymer. The Wasserstein distances of Betti sequences adjacent in time are used to characterize fluctuations in shape, where the Fourier transform and associated principal components provides added information differentiating atoms with different NQEs based on their dynamic properties. We demonstrate this methodology on two representative systems, a glassy system consisting of two atom types with dramatically different de Broglie thermal wavelengths, and ab initio molecular dynamics simulation of an aqueous 4 M HCl solution where the H-atoms are differentiated based on their participation in proton transfer reactions.

Dynamical strengthening of covalent and non-covalent molecular interactions by nuclear quantum effects at finite temperature

Nuclear quantum effects (NQE) tend to generate delocalized molecular dynamics due to the inclusion of the zero point energy and its coupling with the anharmonicities in interatomic interactions. Here, we present evidence that NQE often enhance electronic interactions and, in turn, can result in dynamical molecular stabilization at finite temperature. The underlying physical mechanism promoted by NQE depends on the particular interaction under consideration. First, the effective reduction of interatomic distances between functional groups within a molecule can enhance the n → π* interaction by increasing the overlap between molecular orbitals or by strengthening electrostatic interactions between neighboring charge densities. Second, NQE can localize methyl rotors by temporarily changing molecular bond orders and leading to the emergence of localized transient rotor states. Third, for noncovalent van der Waals interactions the strengthening comes from the increase of the polarizability given the expanded average interatomic distances induced by NQE. The implications of these boosted interactions include counterintuitive hydroxyl-hydroxyl bonding, hindered methyl rotor dynamics, and molecular stiffening which generates smoother free-energy surfaces. Our findings yield new insights into the versatile role of nuclear quantum fluctuations in molecules and materials.

Reduced rovibrational coupling Cartesian dynamics for semiclassical calculations: Application to the spectrum of the Zundel cation

We study the vibrational spectrum of the protonated water dimer, by means of a divide-and-conquer semiclassical initial value representation of the quantum propagator, as a first step in the study of larger protonated water clusters. We use the potential energy surface from the work of Huang et al. [J. Chem. Phys. 122, 044308 (2005)]. To tackle such an anharmonic and floppy molecule, we employ fully Cartesian dynamics and carefully reduce the coupling to global rotations in the definition of normal modes. We apply the time-averaging filter and obtain clean power spectra relative to suitable reference states that highlight the spectral peaks corresponding to the fundamental excitations of the system. Our trajectory-based approach allows for the physical interpretation of the very challenging proton transfer modes. We find that it is important, for such a floppy molecule, to selectively avoid initially exciting lower energy modes, in order to obtain cleaner spectra. The estimated vibrational energies display a mean absolute error (MAE) of ∼29 cm^-1 with respect to available multiconfiguration time-dependent Hartree calculations and MAE ∼ 14 cm^-1 when compared to the optically active experimental excitations of the Ne-tagged Zundel cation. The reasonable scaling in the number of trajectories for Monte Carlo convergence is promising for applications to higher dimensional protonated cluster systems.

Quantum nature of the hydrogen bond from ambient conditions down to ultra-low temperatures

Quantum simulations reveal strong temperature effects for weak hydrogen bonds and differences in quantum delocalization between various hydrogen-bonded systems.