Experiment and Theory Elucidate the Multichannel Predissociation Dynamics of the HCl Trimer: Breaking Up Is Hard To Do

HCl trimer: HCl-stretch excited intramolecular and intermolecular vibrational states from 12D fully coupled quantum calculations employing contracted intra- and inter-molecular bases

We present fully coupled, full-dimensional quantum calculations of the inter- and intra-molecular vibrational states of HCl trimer, a paradigmatic hydrogen-bonded molecular trimer. They are performed utilizing the recently developed methodology for the rigorous 12D quantum treatment of the vibrations of the noncovalently bound trimers of flexible diatomic molecules [Felker and Bačić, J. Chem. Phys. 158, 234109 (2023)], which was previously applied to the HF trimer by us. In this work, the many-body 12D potential energy surface (PES) of (HCl)3 [Mancini and Bowman, J. Phys. Chem. A 118, 7367 (2014)] is employed. The calculations extend to the intramolecular HCl-stretch excited vibrational states of the trimer with one- and two-quanta, together with the low-energy intermolecular vibrational states in the two excited v = 1 intramolecular vibrational manifolds. They reveal significant coupling between the intra- and inter-molecular vibrational modes. The 12D calculations also show that the frequencies of the v = 1 HCl stretching states of the HCl trimer are significantly redshifted relative to those of the isolated HCl monomer. Detailed comparison is made between the results of the 12D calculations on the two-body PES, obtained by removing the three-body term from the original 2 + 3-body PES, and those computed on the 2 + 3-body PES. It demonstrates that the three-body interactions have a strong effect on the trimer binding energy as well as on its intra- and inter-molecular vibrational energy levels. Comparison with the available spectroscopic data shows that good agreement with the experiment is achieved only if the three-body interactions are included. Some low-energy vibrational states localized in a secondary minimum of the PES are characterized as well.

Systematic analysis of electronic barrier heights and widths for concerted proton transfer in cyclic hydrogen bonded clusters: (HF)n, (HCl)n and (H2O)n where n = 3, 4, 5

The MP2 and CCSD(T) methods are paired with correlation consistent basis sets as large as aug-cc-pVQZ to optimize the structures of the cyclic minima for (HF)n, (HCl)n and (H2O)n where n = 3-5, as well as the corresponding transition states (TSs) for concerted proton transfer (CPT). MP2 and CCSD(T) harmonic vibrational frequencies confirm the nature of each minimum and TS. Both conventional and explicitly correlated CCSD(T) computations are employed to assess the electronic dissociation energies and barrier heights for CPT near the complete basis (CBS) limit for all 9 clusters. Results for (HF)n are consistent with prior studies identifying Cnh and Dnh point group symmetry for the minima and TSs, respectively. Our computations also confirm that CPT proceeds through Cs TS structures for the C1 minima of (H2O)3 and (H2O)5, whereas the process goes through a TS with D2d symmetry for the S4 global minimum of (H2O)4. This work corroborates earlier findings that the minima for (HCl)3, (HCl)4 and (HCl)5 have C3h, S4 and C1 point group symmetry, respectively, and that the Cnh structures are not minima for n = 4 and 5. Moreover, our computations show the TSs for CPT in (HCl)3, (HCl)4 and (HCl)5 have D3h, D2d, and C2 point group symmetry, respectively. At the CCSD(T) CBS limit, (HF)4 and (HF)5 have the smallest electronic barrier heights for CPT (≈15 kcal mol-1 for both), followed by the HF trimer (≈21 kcal mol-1). The barriers are appreciably higher for the other clusters (around 27 kcal mol-1 for (H2O)4 and (HCl)3; roughly 30 kcal mol-1 for (H2O)3, (H2O)5 and (HCl)4; up to 38 kcal mol-1 for (HCl)5). At the CBS limit, MP2 significantly underestimates the CCSD(T) barrier heights (e.g., by ca. 2, 4 and 7 kcal mol-1 for the pentamers of HF, H2O and HCl, respectively), whereas CCSD overestimates these barriers by roughly the same magnitude. Scaling the barrier heights and dissociation energies by the number of fragments in the cluster reveals strong linear relationships between the two quantities and with the magnitudes of the imaginary vibrational frequency for the TSs.

Exploring HCl-HCl interactions: QZVPP calculations, improved Lennard-Jones potential, and second virial coefficient analysis for thermodynamics and industrial applications

In this paper, we present a comprehensive analysis of HCl-HCl interactions, including QZVPP calculations, energy fitting, conformation validation, and the determination of the second virial coefficient B using improved Lennard-Jones (ILJ) potential parameters. To acquire accurate interaction energies, initial QZVPP calculations are performed on approximately 1851 randomly generated HCl-HCl conformations. Then, these energies are used to fit an improved Lennard-Jones potential energy surface, allowing for a robust description of HCl-HCl interactions. The ILJ potential parameters are then used to validate particular HCl dimer conformations, ensuring their stability and consistency with experimental observations. The correlation between calculated and experimental conformations strengthens the validity of the ILJ potential parameters. In addition, the second viral coefficient B is calculated at various temperatures using the ILJ potential. The obtained B values are compared to experimental data, demonstrating close agreement, and validating the ILJ potential's ability to accurately capture the intermolecular interactions and gas-phase behavior of the HCl-HCl system. The results of this study demonstrate the effective implementation of QZVPP calculations, energy fitting, and ILJ potential parameters in validating HCl-HCl conformations and accurately determining the second virial coefficient B. The high degree of concordance between calculated B values and experimental data demonstrates the validity of the ILJ potential and its suitability for modeling HCl-HCl interactions. This research contributes to a greater comprehension of HCl-HCl interactions and their implications for numerous chemical and atmospheric processes. The validated conformations, energy fitting method, and calculated second virial coefficients provide valuable instruments for future research and pave the way for more accurate modeling and simulations of HCl-HCl systems.

A computational inspection of the dissociation energy of mid-sized organic dimers

The gas-phase value of the dissociation energy ( D0) is a key parameter employed in both experimental and theoretical descriptions of noncovalent complexes. The D0 data were obtained for a set of mid-sized organic dimers in their global minima which was located using geometry optimizations that applied ample basis sets together with either the conventional second-order Møller–Plesset (MP2) method or several dispersion-corrected density-functional theory (DFT-D) schemes. The harmonic vibrational zero-point (VZP) and deformation energies from the MP2 calculations were combined with electronic energies from the coupled cluster theory with singles, doubles, and iterative triples [CCSD(T)] extrapolated to the complete basis set (CBS) limit to estimate D0 with the aim of inspecting values that were most recently measured, and an analogous comparison was performed using the DFT-D data. In at least one case (namely, for the aniline⋯methane cluster), the D0 estimate that employed the CCSD(T)/CBS energies differed from experiment in the way that could not be explained by a possible deficiency in the VZP contribution. Curiously, one of the DFT-D schemes (namely, the B3LYP-D3/def2-QZVPPD) was able to reproduce all measured D0 values to within 1.0 kJ/mol from experimental error bars. These findings show the need for further measurements and computations of some of the complexes. In order to facilitate such studies, the physical nature of intermolecular interactions in the investigated dimers was analyzed by means of the DFT-based symmetry-adapted perturbation theory.

Mode-specific vibrational predissociation dynamics of (HCl)2 via the free and bound HCl stretch overtones

Velocity-map ion imaging has been used to study the vibrational predissociation dynamics of the HCl dimer following infrared (IR) excitation in the HCl stretch overtone region near 1.77 Å. HCl monomer predissociation products were detected state-selectively using 2 + 1 resonance-enhanced multiphoton ionization spectroscopy. The IR action spectrum shows the free HCl stretch (2ν₁), the bound HCl stretch (2ν₂), and a combination band involving the intermolecular van der Waals stretching mode (2ν₂ + ν₄). Fragment speed distributions extracted from ion images obtained for a range of HCl(v = 0, 1; J) levels following vibrational excitation on the 2ν₁ and 2ν₂ bands yield the correlated product pair distributions. All product pairs comprise HCl(v = 1) + HCl(v = 0) and show a strong propensity to minimize the recoil kinetic energy. Highly non-statistical and mode-dependent HCl product rotational distributions are observed, in contrast to that observed following stretch fundamental excitation. Predissociation lifetimes are also mode-dependent: excitation of the free HCl leads to τ_VP = 13 ± 1 ns, while the bound stretch has a shorter lifetime τ_VP ≤ 6 ns. The dimer dissociation energy determined from energy conservation (D₀ = 397 ± 7 cm^-1) is slightly smaller than the previously reported values. The results are discussed in the context of previous observations for (HF)₂ and (HCl)₂ after excitation of HX stretch fundamentals and models for vibrational predissociation.

Vibrational predissociation of the phenol-water dimer: a view from the water

The vibrational predissociation (VP) dynamics of the phenol-water (PhOH-H₂O) dimer were studied by detecting H₂O fragments and using velocity map imaging (VMI) to infer the internal energy distributions of PhOH cofragments, pair-correlated with selected rotational levels of the H₂O fragments. Following infrared (IR) laser excitation of the hydrogen-bonded OH stretch fundamental of PhOH (Pathway 1) or the asymmetric OH stretch localized on H₂O (Pathway 2), dissociation to H₂O + PhOH was observed. H₂O fragments were monitored state-selectively by using 2+1 Resonance-Enhanced Multiphoton Ionization (REMPI) combined with time-of-flight mass spectrometry (TOF-MS). VMI of H₂O in selected rotational levels was used to derive center-of-mass (c.m.) translational energy (E_T) distributions. The pair-correlated internal energy distributions of the PhOH cofragments derived via Pathway 1 were well described by a statistical prior distribution. On the other hand, the corresponding distributions obtained via Pathway 2 show a propensity to populate higher-energy rovibrational levels of PhOH than expected from a statistical distribution and agree better with an energy-gap model. The REMPI spectra of the H₂O fragments from both pathways could be fit by Boltzmann plots truncated at the maximum allowed energy, with a higher temperature for Pathway 2 than that for Pathway 1. We conclude that the VP dynamics depends on the OH stretch level initially excited.

Long time scale dynamics of vibrationally excited (HBr)n clusters

We investigated the photodissociation dynamics of vibrationally excited HBr molecules and clusters. The species were generated in a molecular beam and excited with an IR laser to a v = 1 vibrational state. A subsequent ultraviolet (UV)-pulse with 243 nm radiation photolysed the molecules to yield H-fragments, which were resonantly ionized by the same UV-pulse (2 + 1 REMPI) and detected in a velocity map imaging (VMI) experiment. We performed action spectroscopy to distinguish between two expansion regimes: (i) expansion leading to isolated HBr molecules and (ii) generation of large (HBr)_n clusters. Photodissociation of isolated HBr ( v = 1) molecules in particular J ro-vibrational states yielded faster H-fragments (by approximately 0.3 eV) with respect to the photodissociation of the ground state HBr ( v = 0). On the contrary, the IR excitation of molecules in (HBr) _n clusters enhanced the yield of the H-fragments UV-photodissociated from the ground-state HBr ( v = 0) molecules. Our findings show that these molecules are photodissociated within clusters, and they are not free molecules evaporated from clusters after the IR excitation. Nanosecond IR-UV pump-probe experiments show that the IR-excitation enhances the H-fragment UV-photodissociation yield up to ∼100 ns after the IR excitation. After these long IR-UV delays, excitation of HBr molecules in clusters does not originate from the IR-excitation but from the UV-photodissociation and subsequent caging of HBr molecules in v > 0 states. We show that even after ∼100 ns the IR-excited larger (HBr) _n clusters do not decay to individual molecules, and the excitation is still present in some form within these clusters enhancing their UV-photodissociation.

Predissociation dynamics of the HCl-(H2O)3 tetramer: An experimental and theoretical investigation

The cyclic HCl-(H₂O)₃ tetramer is the largest observed neutral HCl-(H₂O)_n cluster. The vibrational predissociation of HCl-(H₂O)₃ is investigated by theory, quasiclassical trajectory (QCT) calculations, and experiment, following the infrared excitation of the hydrogen-bonded OH-stretch fundamental. The energetically possible dissociation pathways are HCl + (H₂O)₃ (Pathway 1) and H₂O + HCl-(H₂O)₂ (Pathway 2). The HCl and H₂O monomer fragments are observed by 2 + 1 resonance enhanced multiphoton ionization combined with time-of-flight mass spectrometry, and their rotational energy distributions are inferred and compared to the theoretical results. Velocity map images of the monomer fragments in selected rotational levels are used for each pathway to obtain pair-correlated speed distributions. The fragment speed distributions obtained by experiment and QCT calculations are broad and structureless, encompassing the entire range of allowed speeds for each pathway. Bond dissociation energies, D₀, are estimated experimentally from the endpoints of the speed distributions: 2100 ± 300 cm^-1 and 2400 ± 100 cm^-1 for Pathway 1 and Pathway 2, respectively. These values are lower but in the same order as the corresponding calculated D₀: 2426 ± 23 cm^-1 and 2826 ± 19 cm^-1. The differences are attributed to contributions from vibrational hot bands of the clusters that appear in the high-speed tails of the experimental pair-correlated distributions. Satisfactory agreement between theory and experiment is achieved when comparing the monomer fragments' rotational energies, the shapes of the speed distributions, and the average fragment speeds and center-of-mass translational energies. Insights into the dissociation mechanism and lifetime are gained from QCT calculations performed on a previously reported many-body potential energy surface. It is concluded that the dissociation lifetime is on the order of 10 ps and that the final trimer products are in their lowest energy cyclic forms.

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.

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 of the HCl-(H2O)3 Tetramer

The vibrational predissociation of the HCl-(H₂O)₃ tetramer, the largest HCl-(H₂O)_n cluster for which HCl is not predicted to be ionized, is reported. This work focuses on the predissociation pathway giving rise to H₂O + HCl-(H₂O)₂ following IR laser excitation of the H-bonded OH stretch fundamental. H₂O fragments are monitored state selectively by 2 + 1 resonance-enhanced multiphoton ionization (REMPI) combined with time-of-flight mass spectrometry (TOF-MS). Velocity map images of H₂O in selected rotational levels are used to determine translational energy distributions from which the internal energy distributions in the pair-correlated cofragments are derived. From the maximum translational energy release, the bond dissociation energy, D₀ = 2400 ± 100 cm^-1, is determined for the investigated channel. The energy distributions in the fragments are broad, encompassing the entire range of allowed states. The importance of cooperative (nonpairwise) interactions is discussed.

How Many Water Molecules Does it Take to Dissociate HCl?

The potential energy surfaces of the HCl(H2O)n (n is the number of water molecules) clusters are systematically explored using density functional theory and high-level ab initio computations. On the basis of electronic energies, the number of water molecules needed for HCl dissociation is four as reported by some experimental groups. However, this number is five owing to the inclusion of entropic factors. Wiberg bond indices are calculated and analyzed, and the results provide a quadratic correlation and classification of clusters according to the nondissociated, partially dissociated, and fully dissociated character of the H-Cl bond. Our computations show that if temperature is not controlled during the experiment, the values obtained for the dipole moment (or for any measurable property) are susceptible to change, providing a different picture of the number of water molecules needed for HCl dissociation in a nanoscopic droplet.

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.