Communication: A new ab initio potential energy surface for HCl–H2O, diffusion Monte Carlo calculations of D0 and a delocalized zero-point wavefunction

MBX: A many-body energy and force calculator for data-driven many-body simulations

Many-Body eXpansion (MBX) is a C++ library that implements many-body potential energy functions (PEFs) within the "many-body energy" (MB-nrg) formalism. MB-nrg PEFs integrate an underlying polarizable model with explicit machine-learned representations of many-body interactions to achieve chemical accuracy from the gas to the condensed phases. MBX can be employed either as a stand-alone package or as an energy/force engine that can be integrated with generic software for molecular dynamics and Monte Carlo simulations. MBX is parallelized internally using Open Multi-Processing and can utilize Message Passing Interface when available in interfaced molecular simulation software. MBX enables classical and quantum molecular simulations with MB-nrg PEFs, as well as hybrid simulations that combine conventional force fields and MB-nrg PEFs, for diverse systems ranging from small gas-phase clusters to aqueous solutions and molecular fluids to biomolecular systems and metal-organic frameworks.

Data-Driven Many-Body Potential Energy Functions for Generic Molecules: Linear Alkanes as a Proof-of-Concept Application

We present a generalization of the many-body energy (MB-nrg) theoretical/computational framework that enables the development of data-driven potential energy functions (PEFs) for generic covalently bonded molecules, with arbitrary quantum mechanical accuracy. The "nearsightedness of electronic matter" is exploited to define monomers as "natural building blocks" on the basis of their distinct chemical identity. The energy of generic molecules is then expressed as a sum of individual many-body energies of incrementally larger subsystems. The MB-nrg PEFs represent the low-order n-body energies, with n = 1-4, using permutationally invariant polynomials derived from electronic structure data carried out at an arbitrary quantum mechanical level of theory, while all higher-order n-body terms (n > 4) are represented by a classical many-body polarization term. As a proof-of-concept application of the general MB-nrg framework, we present MB-nrg PEFs for linear alkanes. The MB-nrg PEFs are shown to accurately reproduce reference energies, harmonic frequencies, and potential energy scans of alkanes, independently of their length. Since, by construction, the MB-nrg framework introduced here can be applied to generic covalently bonded molecules, we envision future computer simulations of complex molecular systems using data-driven MB-nrg PEFs, with arbitrary quantum mechanical accuracy.

Noncovalently bound molecular complexes beyond diatom–diatom systems: full-dimensional, fully coupled quantum calculations of rovibrational states

The methodological advances made in recent years have significantly extended the range and dimensionality of noncovalently bound molecular complexes for which full-dimensional quantum calculations of their rovibrational states are feasible.

Femtochemistry of bimolecular reactions from weakly bound complexes: computational study of the H + H'OD → H'OH + D or HOD + H' exchange reactions

A full-dimensional wavepacket propagation describing the bimolecular exchange reactions H + H'OD → H'OH + D or HOD + H' initiated by photolysis of HCl in the hydrogen-bound complex (HCl)⋯(HOD) is reported. The dynamics of this reaction is carried out with the MCTDH method on an ab initio potential energy surface (PES) of H₃O and the initial state is derived from the ground state wavefunction of the complex obtained by relaxation on its own electronic ground state ab initio PES. The description of the system makes use of polyspherical coordinates parametrizing a set of Radau and Jacobi vectors. The calculated energy- and time-resolved reaction probabilities show, owing to the large collision energies at play stemming from the (almost full) photolysis of HCl, that the repulsion between oxygen in the H'OD molecule and the incoming hydrogen atom is the main feature of the collision and leads to non-reactive scattering. No abstraction reaction products are observed. However, both exchange processes are still observable, with a preference in O-H' bond dissociation over that of O-D. The selectivity is reversed upon vibrational pre-excitation of the O-D stretching mode in the H'OD molecule. It is shown that, after the collision, the hydrogen atom of HCl does most likely not encounter the almost stationary chlorine atom again but we also consider the limit case where the H atom is forced to collide multiple times against H'OD as a result of being pushed back by the Cl atom.

DCl-H2O, HCl-D2O, and DCl-D2O Dimers: Inter- and Intramolecular Vibrational States and Frequency Shifts from Fully Coupled Quantum Calculations on a Full-Dimensional Neural Network Potential Energy Surface

We report full-dimensional and fully coupled quantum calculations of the inter- and intramolecular vibrational states of three isotopologues of the hydrogen chloride-water dimer: DCl-H₂O (DH), HCl-D₂O (HD), and DCl-D₂O (DD). The present study extends our recent theoretical investigation of the nine-dimensional (9D) vibrational level structure of the HCl-H₂O (HH) dimer [Liu, Y.; Li, J.; Felker, P. M.; Bačić, Z. Phys. Chem. Chem. Phys. 2021, 23, 7101-7114]. It employs the same accurate 9D permutation invariant polynomial-neural network potential energy surface and the highly efficient bound-state methodology. The objective of this work is to elucidate the isotopologue variations of a range of bound-state properties of the hydrogen chloride-water dimer and compare them to those of the HH dimer. In order to achieve this, for the isotopologues considered, the rigorous 9D quantum calculations performed encompass all intramolecular vibrational fundamentals, and their frequency shifts relative to the isolated monomer values, together with the low-lying intermolecular vibrational states in each of the intramolecular vibrational manifolds of interest. Moreover, for the ground state of each isotopologue, several informative vibrationally averaged intermolecular geometric properties of the dimer are computed, as well as the three rotational constants. The energies of the intermolecular inversion and rock modes, which mainly involve the motions of the water moiety, differ greatly for H₂O and D₂O, but are much less sensitive to whether the hydrogen chloride isotopologue is HCl or DCl. On the other hand, the excitation of the HCl/DCl stretch changes significantly the energies of the water inversion and rock modes. The DCl stretch frequency shift computed in 9D for the DD dimer, -114.91 cm^-1, agrees extremely well with the corresponding experimental value of -115.20 cm^-1 measured by Saykally and co-workers.

HCl–H2O dimer: an accurate full-dimensional potential energy surface and fully coupled quantum calculations of intra- and intermolecular vibrational states and frequency shifts

The present work reports a new full-dimensional potential energy surface (PES) of the HCl–H₂O dimer, and the first fully coupled 9D quantum calculations of the intra- and intermolecular vibrational states of the complex, utilizing this PES.

Anharmonic quantum nuclear densities from full dimensional vibrational eigenfunctions with application to protonated glycine

The interpretation of molecular vibrational spectroscopic signals in terms of atomic motion is essential to understand molecular mechanisms and for chemical characterization. The signals are usually assigned after harmonic normal mode analysis, even if molecular vibrations are known to be anharmonic. Here we obtain the quantum anharmonic vibrational eigenfunctions of the 11-atom protonated glycine molecule and we calculate the density distribution of its nuclei and its geometry parameters, for both the ground and the O-H stretch excited states, using our semiclassical method based on ab initio molecular dynamics trajectories. Our quantum mechanical results describe a molecule elongated and more flexible with respect to what previously thought. More importantly, our method is able to assign each spectral peak in vibrational spectroscopy by showing quantitatively how normal modes involving different functional groups cooperate to originate that spectroscopic signal. The method will possibly allow for a better rationalization of experimental spectroscopy.

Probing the Partial Activation of Water by Open-Shell Interactions, Cl(H2O)1-4

The partial chemical activation of water by reactive radicals was examined computationally for small clusters of chlorine and water, Cl^•(H₂O)_n=1-4. Using an automated isomer-search procedure, dozens of unique, stable structures were computed. Among the resulting structural classes were intact, hydrated-chlorine isomers, as well as hydrogen-abstracted (HCl)(OH)(H₂O)_n-1 configurations. The latter showed increased stability as the degree of hydration increased, until n = 4, where a new class of structures was discovered with a chloride ion bound to an oxidized water network. The electronic structure of these three structural classes was investigated, and spectral signatures of this hydration-based evolution were connected to these electronic properties. An ancillary outcome of this detailed computational analysis, including coupled-cluster benchmarks, was the calibration of cost-effective quantum chemistry methods for future studies of these radical-water complexes.

Dissociation Energy of the H2O···HF Dimer

Even though (H₂O)₂ and (HF)₂ are arguably the most thoroughly characterized prototypes for hydrogen bonding, their heterogeneous analogue H₂O···HF has received relatively little attention. Here we report that the experimental dissociation energy ( D₀) of this important paradigm for heterogeneous hydrogen bonding is too large by 2 kcal mol^-1 or 30% relative to our computed value of 6.3 kcal mol^-1. For reference, computational procedures similar to those employed here to compute D₀ (large basis set CCSD(T) computations with anharmonic corrections from second-order vibrational perturbation theory) provide results within 0.1 kcal mol^-1 of the experimental values for (H₂O)₂ and (HF)₂. Near the CCSD(T) complete basis set limit, the electronic dissociation energy for H₂O···HF is ∼4 kcal mol^-1 larger than those for (H₂O)₂ and (HF)₂ (∼9 kcal mol^-1 for the heterogeneous dimer vs ∼5 kcal mol^-1 for the homogeneous dimers). Results reported here from symmetry-adapted perturbation theory computations suggest that this large difference is primarily due to the induction contribution to the interaction energy.

Acid Dissociation in HCl-Water Clusters is Temperature Dependent and Cannot be Detected Based on Dipole Moments

The dissociation of acids in aqueous environments at low temperatures in the presence of a limited amount of water is underlying a wealth of processes from atmospheric to interstellar science. For the paradigmatic case of HCl(H_{2}O)_{n} clusters, our extensive ab initio path integral simulations quantify in terms of free energy differences and barriers that n=4 water molecules are indeed required to dissociate HCl at low temperatures. Increasing the temperature, however, reverses the process and thus counteracts dissociation by fluctuation-driven recombination. The size of the electric dipole moment is shown to not correlate with the acid being in its dissociated or molecular state, thus rendering its measurement as a function of n unable to detect the dissociation transition.

Perturbation Approach for Computing Infrared Spectra of the Local Mode of Probe Molecules

Linear and two-dimensional infrared (IR) spectroscopy of site-specific probe molecules provides an opportunity to gain a molecular-level understanding of the local hydrogen-bonding network, conformational dynamics, and long-range electrostatic interactions in condensed-phase and biological systems. A challenge in computation is to determine the time-dependent vibrational frequencies that incorporate explicitly both nuclear quantum effects of vibrational motions and an electronic structural representation of the potential energy surface. In this paper, a nuclear quantum vibrational perturbation (QVP) method is described for efficiently determining the instantaneous vibrational frequency of a chromophore in molecular dynamics simulations. Computational efficiency is achieved through the use of (a) discrete variable representation of the vibrational wave functions, (b) a perturbation theory to evaluate the vibrational energy shifts due to solvent dynamic fluctuations, and (c) a combined QM/MM potential for the systems. It was found that first-order perturbation is sufficiently accurate, enabling time-dependent vibrational frequencies to be obtained on the fly in molecular dynamics. The QVP method is illustrated in the mode-specific linear and 2D-IR spectra of the H-Cl stretching frequency in the HCl-water clusters and the carbonyl stretching vibration of acetone in aqueous solution. To further reduce computational cost, a hybrid strategy was proposed, and it was found that the computed vibrational spectral peak position and line shape are in agreement with experimental results. In addition, it was found that anharmonicity is significant in the H-Cl stretching mode, and hydrogen-bonding interactions further enhance anharmonic effects. The present QVP method complements other computational approaches, including path integral-based molecular dynamics, and represents a major improvement over the electrostatics-based spectroscopic mapping procedures.

Vibrational predissociation and vibrationally induced isomerization of 3-aminophenol-ammonia

We investigate the vibrational predissociation dynamics of the hydrogen-bonded 3-aminophenol-ammonia cluster (3-AP-NH3) in the OH and NH stretching regions. Vibrational excitation provides enough energy to dissociate the cluster into its constituent 3-AP and NH3 monomers, and we detect the 3-AP fragments via (1 + 1) resonance-enhanced multiphoton ionization (REMPI). The distribution of vibrational states of the 3-AP fragment suggests the presence of two distinct dissociation pathways. The first dissociation channel produces a broad, unstructured feature in the REMPI-action spectrum after excitation of any of the OH or NH stretching vibrations, pointing to a nearly statistical dissociation pathway with extensive coupling among the vibrations in the cluster during the vibrational predissociation. The second dissociation channel produces distinct, resolved features on top of the broad feature but only following excitation of the OH or symmetric NH3 stretch in the cluster. This striking mode-specificity is consistent with strong coupling of these two modes to the dissociation coordinate (the O-H⋯N bond). The presence of clearly resolved transitions to the electronic origin and to the 10a(2) + 10b(2) state of the cis-3-AP isomer shows that vibrational excitation is driving the isomerization of the trans-3-AP-NH3 isomer to the cis-3-AP-NH3 isomer in the course of the dissociation.

Experimental and theoretical investigations of energy transfer and hydrogen-bond breaking in small water and HCl clusters

Water is one of the most pervasive molecules on earth and other planetary bodies; it is the molecule that is searched for as the presumptive precursor to extraterrestrial life. It is also the paradigm substance illustrating ubiquitous hydrogen bonding (H-bonding) in the gas phase, liquids, crystals, and amorphous solids. Moreover, H-bonding with other molecules and between different molecules is of the utmost importance in chemistry and biology. It is no wonder, then, that for nearly a century theoreticians and experimentalists have tried to understand all aspects of H-bonding and its influence on reactivity. It is somewhat surprising, therefore, that several fundamental aspects of H-bonding that are particularly important for benchmarking theoretical models have remained unexplored experimentally. For example, even the binding strength between two gas-phase water molecules has never been determined with sufficient accuracy for comparison with high-level electronic structure calculations. Likewise, the effect of cooperativity (nonadditivity) in small H-bonded networks is not known with sufficient accuracy. An even greater challenge for both theory and experiment is the description of the dissociation dynamics of H-bonded small clusters upon acquiring vibrational excitation. This is because of the long lifetimes of many clusters, which requires running classical trajectories for many nanoseconds to achieve dissociation. In this Account, we describe recent progress and ongoing research that demonstrates how the combined and complementary efforts of theory and experiment are enlisted to determine bond dissociation energies (D0) of small dimers and cyclic trimers of water and HCl with unprecedented accuracy, describe dissociation dynamics, and assess the effects of cooperativity. The experimental techniques rely on IR excitation of H-bonded X-H stretch vibrations, measuring velocity distributions of fragments in specific rovibrational states, and determining product state distributions at the pair-correlation level. The theoretical methods are based on high-level ab initio potential energy surfaces used in quantum and classical dynamical calculations. We achieve excellent agreement on D0 between theory and experiments for all of the clusters that we have compared, as well as for cooperativity in ring trimers of water and HCl. We also show that both the long-range and the repulsive parts of the potential must be involved in bond breaking. We explain why H-bonds are so resilient and hard to break, and we propose that a common motif in the breaking of cyclic trimers is the opening of the ring following transfer of one quantum of stretch excitation to form open-chain structures that are weakly bound. However, it still takes many vibrational periods to release one monomer fragment from the open-chain structures. Our success with water and HCl dimers and trimers led us to embark on a more ambitious project: studies of mixed water and HCl small clusters. These clusters eventually lead to ionization of HCl and serve as prototypes of acid dissociation in water. Measurements and calculations of such ionizations are yet to be achieved, and we are now characterizing these systems by adding monomers one at a time. We describe our completed work on the HCl-H2O dimer and mention our recent theoretical results on larger mixed clusters.

Effects of Zero-Point Delocalization on the Vibrational Frequencies of Mixed HCl and Water Clusters

We demonstrate the significant effect that large-amplitude zero-point vibrational motion can have on the high-frequency fundamental vibrations of molecular clusters, specifically small (HCl)n-(H2O)m clusters. Calculations were conducted on a many-body potential, constructed from a mix of new and previously reported semiempirical and high-level ab initio potentials. Diffusion Monte Carlo simulations were performed to determine ground-state wave functions. Visualization of these wave functions indicates that the clusters exhibit delocalized ground states spanning multiple stationary point geometries. The ground states are best characterized by planar ring configurations, despite the clusters taking nonplanar configurations at their global minima. Vibrational calculations were performed at the global minima and the Diffusion Monte Carlo predicted configurations and also using an approach that spans multiple stationary points along a rectilinear normal-mode reaction path. Significantly better agreement was observed between the calculated vibrational frequencies and experimental peak positions when the delocalized ground state was accounted for.