Parahydrogen Clusters Research Articles

Neural network interaction potentials for para-hydrogen with flexible molecules.

The study of molecular impurities in para-hydrogen (pH2) clusters is key to push forward our understanding of intra- and intermolecular interactions, including their impact on the superfluid response of this bosonic quantum solvent. This includes tagging with only one or very few pH2, the microsolvation regime for intermediate particle numbers, and matrix isolation with many solvent molecules. However, the fundamental coupling between the bosonic pH2 environment and the (ro-)vibrational motion of molecular impurities remains poorly understood. Quantum simulations can, in principle, provide the necessary atomistic insight, but they require very accurate descriptions of the involved interactions. Here, we present a data-driven approach for the generation of impurity⋯pH2 interaction potentials based on machine learning techniques, which retain the full flexibility of the dopant species. We employ the well-established adiabatic hindered rotor (AHR) averaging technique to include the impact of the nuclear spin statistics on the symmetry-allowed rotational quantum numbers of pH2. Embedding this averaging procedure within the high-dimensional neural network potential (NNP) framework enables the generation of highly accurate AHR-averaged NNPs at coupled cluster accuracy, namely, explicitly correlated coupled cluster single, double, and scaled perturbative triples, CCSD(T*)-F12a/aVTZcp, in an automated manner. We apply this methodology to the water and protonated water molecules as representative cases for quasi-rigid and highly flexible molecules, respectively, and obtain AHR-averaged NNPs that reliably describe the corresponding H2O⋯pH2 and H3O+⋯pH2 interactions. Using path integral simulations, we show for the hydronium cation, H3O+, that umbrella-like tunneling inversion has a strong impact on the first and second pH2 microsolvation shells. The automated and data-driven nature of our protocol opens the door to the study of bosonic pH2 quantum solvation for a wide range of embedded impurities.

On the accuracy and efficiency of different methods to calculate Raman vibrational shifts of parahydrogen clusters.

The Raman vibrational frequency shifts of pure parahydrogen and orthodeuterium clusters of sizes N = 4-9 are calculated using the Langevin equation path integral ground state method. The shifts are calculated using three different methods; the results obtained from each are compared to experiment and variance properties are assessed. The first method requires the direct calculation of energies from two simulations: one when the cluster is in the v = 0 vibrational state and one when the cluster has v = 1 total quantum of vibration. The shift is directly calculated from the difference in those two energies. The second method requires only a v = 0 simulation to be performed. The ground state energy is calculated as usual and the excited state energy is calculated by using the distribution of the v = 0 simulation and the ratio of the density matrices between the v = 1 state and the v = 0 state. The shift is calculated from the difference in those two energies. These first two are both exact methods. The final method is based on perturbation theory where the shift is calculated by averaging the pairwise difference potential over the pair distribution function. However, this is an approximate approach. It is found that for large enough system sizes, despite the approximations, the perturbation theory method has the strongest balance between accuracy and precision when weighing against computational cost.

Ground state chemical potential of parahydrogen clusters of size N = 21-40.

We report the ground state chemical potential of parahydrogen clusters between N = 21-40 calculated using the Langevin equation Path Integral Ground State method. There has been much debate in the past whether the chemical potential size evolution in this region is jagged (indicating magic number cluster sizes) or if it is smooth (indicating some quantum melting below 1K). We compare to previous diffusion Monte Carlo and Path Integral Ground State (PIGS) results, including very recent Variational Path Integral Molecular Dynamics (VPIMD) calculations [S. Miura, J. Chem. Phys. 148, 102333 (2018)]. We find that the ground state chemical potential is not a smooth curve and that magic number clusters are present, consistent with VPIMD and PIGS Monte Carlo results.

Muonium hydride: The lowest density crystal

A muonium hydride molecule is a bound state of muonium and hydrogen atoms. It has half the mass of a parahydrogen molecule and very similar electronic properties in its ground state. The phase diagram of an assembly of such particles is investigated by first principle quantum simulations. In the bulk limit, the low-temperature equilibrium phase is a crystal of extraordinarily low density, lower than that of any other known atomic or molecular crystal. Despite the low density and particle mass, the melting temperature is surprisingly high (close to 9 K). No (metastable) supersolid phase is observed. We investigated the physical properties of nanoscale clusters (up to 200 particles) of muonium hydride and found the superfluid response to be greatly enhanced compared to that of parahydrogen clusters. The possible experimental realization of these systems is discussed.

The Loss of Size Sensitivity in para-Hydrogen Clusters Due to the Strong Quantum Delocalization.

para-Hydrogen (pH2)N clusters have been the focus of numerous computational studies. Originally motivated by the possibility of observing superfluidity, these studies also revealed rich and complex structural properties of (pH2)N. However, their structural analysis was typically limited to attempts to identify "magic number clusters" by computing their ground state energies EN and the chemical potential μN = EN-EN-1 as a function of N. This was followed by structural analysis based on an ill-defined radial density profile. Surprisingly, however, there were remarkable discrepancies between the results reported in the literature for cluster sizes beyond approximately N = 25, and this ambiguity remained unsettled until now. In the present paper, we apply the diffusion Monte Carlo method to resolve inconsistencies in cluster sizes within the range (N = 24-28). Here, we try to avoid speculations based on the highly demanding energy calculations whose numerical accuracy harbors ambiguity. Instead, we focus on the direct and unambiguous structural analysis of the ground state wavefunctions, which supports the conclusion that the clusters are structurally the same in the size range considered. That is, there are no magic number clusters at least in the range N = 24-28, contrary to what some of the previous publications have suggested. This lack of size sensitivity of para-hydrogen clusters is a direct consequence of the strong quantum delocalization in these systems.

Superfluid Response of Parahydrogen Clusters in Superfluid $$^4$$He

First principle computer simulations yield evidence of a finite superfluid response at low temperature of a parahydrogen cluster of 15 molecules in bulk superfluid He-4. The superfluid fraction is worth ~44% at T=0.25 K, growing to about 66% at T=0.15 K, i.e., it is substantially reduced compared to that of the same cluster in vacuo, due to higher molecular localization. The implications of these findings on the interpretation of experiments with linear molecules embedded in parahydrogen clusters immersed in superfluid helium are discussed.

Suppression of Parahydrogen Superfluidity in a Doped Nanoscale Bose Fluid Mixture.

Helium (^{4}He) nanodroplets provide a unique environment to observe the microscopic origins of superfluidity. The search for another superfluid substance has been an ongoing quest in the field of quantum fluids. Nearly two decades ago, experiments on doped parahydrogen (p-H_{2}) clusters embedded in ^{4}He droplets displayed anomalous spectroscopic signatures that were interpreted as a sign of the superfluidity of p-H_{2} [S. Grebenev etal., Science 289, 1532 (2000)SCIEAS0036-807510.1126/science.289.5484.1532]. Here, we observe, using first-principles quantum MonteCarlo simulations, a phase separation between a symmetric and localized p-H_{2} core and ^{4}He shells. The p-H_{2} core has minimal superfluid response. These findings are consistent with the recorded spectra but not with their original interpretation, and lead us to conclude that doped p-H_{2} clusters form a nonsuperfluid core in ^{4}He droplets.

Computer Simulation Study of Nanoscale Size Parahydrogen Clusters

We present results of computer simulations of a parahydrogen cluster of a thousand molecules, corresponding to approximately 4 nm in diameter, at temperatures between 1 K and 10 K. Examination of structural properties suggests that the local environment experienced by molecules is very similar to that in solid bulk parahydrogen, especially near the center of the cluster, where crystallization originates. Albeit strongly suppressed compared to helium, quantum-mechanical exchanges are not entirely negligible at the lowest temperature, resulting in a small but significant molecular mobility enhancement with respect to the bulk crystalline phase. Although the overall superfluid response at the lowest temperature is only a few percents, there is evidence of a surprising "supersolid" core, as well as of a superfluid outer shell. Much like in fluid parahydrogen at the melting temperature, quantum-mechanical signatures can be detected in the momentum distribution.

Physisorption of H2 on Fullerenes and the Solvation of C60 by Hydrogen Clusters at Finite Temperature: A Theoretical Assessment.

The interaction between hydrogen and carbonaceous nanostructures is of fundamental interest in various areas of physical chemistry. In this contribution we have revisited the physisorption of hydrogen molecules and H2 clusters on fullerenes, following a first-principles approach in which the interaction is quantitatively evaluated for the C20 system using high-level electronic structure methods. Relative to coupled cluster data at the level of single, double, and perturbative triple excitations taken as a benchmark, the results for rotationally averaged physisorbed H2 show a good performance of MP2 variants and symmetry-adapted perturbation theory, but significant deviations and basis set convergence issues are found for dispersion-corrected density functional theory. These electronic structure data are fitted to produce effective coarse-grained potentials for use in larger systems such as C60-H2. Using path-integral molecular dynamics, the potentials are also applied to parahydrogen clusters solvated around fullerenes, across the regime where the first solvation shell becomes complete and as a function of increasing temperature. For C60 our findings indicate a sensible dependence of the critical solvation size on the underlying potential. As the temperature is increased, a competition is found between the surface and radial expansions of the solvation shell, with one molecule popping away at intermediate temperatures but getting reinserted at even higher temperatures.

Quantum structural fluctuation in para-hydrogen clusters revealed by the variational path integral method.

In this paper, the ground state of para-hydrogen clusters for size regime N ≤ 40 has been studied by our variational path integral molecular dynamics method. Long molecular dynamics calculations have been performed to accurately evaluate ground state properties. The chemical potential of the hydrogen molecule is found to have a zigzag size dependence, indicating the magic number stability for the clusters of the size N = 13, 26, 29, 34, and 39. One-body density of the hydrogen molecule is demonstrated to have a structured profile, not a melted one. The observed magic number stability is examined using the inherent structure analysis. We also have developed a novel method combining our variational path integral hybrid Monte Carlo method with the replica exchange technique. We introduce replicas of the original system bridging from the structured to the melted cluster, which is realized by scaling the potential energy of the system. Using the enhanced sampling method, the clusters are demonstrated to have the structured density profile in the ground state.

Coating of $$\hbox {C}_{60}$$ C 60 by para- $$\hbox {H}_2$$ H 2 and ortho- $$\hbox {D}_2$$ D 2 : revisiting the solvation shell—CMMSE

The solvation of Buckminsterfullerene \(\hbox {C}_{60}\) by para-hydrogen and ortho-deuterium clusters has been modeled using a dedicated potential and path-integral molecular dynamics simulations at low temperature (2 K). The solvation shell obtained from the distribution of radial distances is found to be complete near 50 molecules, in agreement with recent mass spectrometry measurements. Deuteration increases the shell size by one, indicating a denser shell owing to less prominent vibrational delocalization for this heavier isotope.

Variational path integral molecular dynamics and hybrid Monte Carlo algorithms using a fourth order propagator with applications to molecular systems.

In the present study, variational path integral molecular dynamics and associated hybrid Monte Carlo (HMC) methods have been developed on the basis of a fourth order approximation of a density operator. To reveal various parameter dependence of physical quantities, we analytically solve one dimensional harmonic oscillators by the variational path integral; as a byproduct, we obtain the analytical expression of the discretized density matrix using the fourth order approximation for the oscillators. Then, we apply our methods to realistic systems like a water molecule and a para-hydrogen cluster. In the HMC, we adopt two level description to avoid the time consuming Hessian evaluation. For the systems examined in this paper, the HMC method is found to be about three times more efficient than the molecular dynamics method if appropriate HMC parameters are adopted; the advantage of the HMC method is suggested to be more evident for systems described by many body interaction.

Ro-vibrational Spectra of (para-H2 )N -CH4 in He Droplets.

In this work, we report on the infrared spectroscopic study of clusters of CH4 molecules with up to N=80 para-hydrogen molecules assembled inside He droplets. Upon increase of the number of the added para-hydrogen molecules up to about N=12, both the rotational constant, B, and the origin frequency of the υ3 band of CH4 decrease gradually. In the range of 6 ≤N≤12, the spectra indicate some abrupt changes of B and υ3 with both values being approximately constant at N≥12. The origin of this effect is discussed. Comparison of the spectra of methane molecules in para-hydrogen clusters to that in solid para-hydrogen is also presented.

A Density Functional Approach to Para-hydrogen at Zero Temperature

We have developed a density functional (DF) built so as to reproduce either the metastable liquid or the solid equation of state of bulk para-hydrogen, as derived from quantum Monte Carlo zero temperature calculations. As an application, we have used it to study the structure and energetics of small para-hydrogen clusters made of up to \(N=40\) molecules. We compare our results for liquid clusters with diffusion Monte Carlo (DMC) calculations and find a fair agreement between them. In particular, the transition found within DMC between hollow-core structures for small N values and center-filled structures at higher N values is reproduced. The present DF approach yields results for (pH\(_2\))\(_N\) clusters indicating that for small N values a liquid-like character of the clusters prevails, while solid-like clusters are instead energetically favored for \(N \ge 15\).

Raman Vibrational Shifts of Small Clusters of Hydrogen Isotopologues.

Raman vibrational shifts of small parahydrogen (pH2), orthodeuterium (oD2), and paratritium (pT2) clusters with respect to the free molecules are calculated by combining a first order perturbation theory approach with Langevin equation Path Integral Ground State (LePIGS) simulations [ J. Phys. Chem. A 2013 , 117 , 7461 ]. Our theoretical predictions are compared to existing cryogenic free jet expansion results for pure (pH2)N clusters [ Phys. Rev. Lett. 2004 , 92 , 223401 ] and to new measurements for (oD2)N clusters reported here. This method has been successfully used before to predict the Raman vibrational shifts of (pH2)N clusters [ J. Chem. Phys. 2014 , 141 , 014310 ]. The 6-D interaction potential of Hinde [ J. Chem. Phys. 2008 , 128 , 154308 ] is reduced to 1-D using the Adiabatic Hindered Rotor approximation to yield effective pair potentials for both molecules being in the ground vibrational state, and for one of them carrying one quantum of vibrational excitation. These reduced 1-D potentials are fitted to a Morse Long Range analytic form for later convenience. Good agreement between experiment and theory is found for the smaller clusters, but significant deviations remain for the larger ones.

Superfluid response of two-dimensional parahydrogen clusters in confinement.

We study by computer simulations the effect of confinement on the superfluid properties of small two-dimensional (2D) parahydrogen clusters. For clusters of fewer than twenty molecules, the superfluid response in the low temperature limit is found to remain comparable in magnitude to that of free clusters, within a rather wide range of depth and size of the confining well. The resilience of the superfluid response is attributable to the "supersolid" character of these clusters. We investigate the possibility of establishing a bulk 2D superfluid "cluster crystal" phase of p-H2, in which a global superfluid response would arise from tunnelling of molecules across adjacent unit cells. The computed energetics suggests that for clusters of about ten molecules, such a phase may be thermodynamically stable against the formation of the equilibrium insulating crystal, for values of the cluster crystal lattice constant possibly allowing tunnelling across adjacent unit cells.

First-principles prediction of the Raman shifts in parahydrogen clusters.

We report a first-principles prediction of the Raman shifts of parahydrogen (pH2) clusters of sizes N = 4-19 and 33, based on path integral ground-state simulations with an ab initio potential energy surface. The Raman shifts are calculated, using perturbation theory, as the average of the difference-potential energy surface between the potential energy surfaces for vibrationally excited and ground-state parahydrogen monomers. The radial distribution of the clusters is used as a weight function in this average. Very good overall agreement with experiment [G. Tejeda, J. M. Fernández, S. Montero, D. Blume, and J. P. Toennies, Phys. Rev. Lett. 92, 223401 (2004)] is achieved for p(H2)(2-8,13,33). A number of different pair potentials are employed for the calculation of the radial distribution functions. We find that the Raman shifts are sensitive to slight variations in the radial distribution functions.

Publisher's Note: “Systematics of small parahydrogen clusters in two dimensions” [J. Chem. Phys. 140, 204310 (2014)

Publisher's Note: “Systematics of small parahydrogen clusters in two dimensions” [J. Chem. Phys. 140, 204310 (2014)

Inclusion of trial functions in the Langevin equation path integral ground state method: application to parahydrogen clusters and their isotopologues.

We developed and studied the implementation of trial wavefunctions in the newly proposed Langevin equation Path Integral Ground State (LePIGS) method [S. Constable, M. Schmidt, C. Ing, T. Zeng, and P.-N. Roy, J. Phys. Chem. A 117, 7461 (2013)]. The LePIGS method is based on the Path Integral Ground State (PIGS) formalism combined with Path Integral Molecular Dynamics sampling using a Langevin equation based sampling of the canonical distribution. This LePIGS method originally incorporated a trivial trial wavefunction, ψT, equal to unity. The present paper assesses the effectiveness of three different trial wavefunctions on three isotopes of hydrogen for cluster sizes N = 4, 8, and 13. The trial wavefunctions of interest are the unity trial wavefunction used in the original LePIGS work, a Jastrow trial wavefunction that includes correlations due to hard-core repulsions, and a normal mode trial wavefunction that includes information on the equilibrium geometry. Based on this analysis, we opt for the Jastrow wavefunction to calculate energetic and structural properties for parahydrogen, orthodeuterium, and paratritium clusters of size N = 4 - 19, 33. Energetic and structural properties are obtained and compared to earlier work based on Monte Carlo PIGS simulations to study the accuracy of the proposed approach. The new results for paratritium clusters will serve as benchmark for future studies. This paper provides a detailed, yet general method for optimizing the necessary parameters required for the study of the ground state of a large variety of systems.

Systematics of small parahydrogen clusters in two dimensions.

We studied by means of computer simulations the low temperature properties of two-dimensional parahydrogen clusters comprising between N = 7 and 30 molecules. Computed energetics is in quantitative agreement with that reported in the only previous study [M. C. Gordillo and D. M. Ceperley, Phys. Rev. B 65, 174527 (2002)], but a generally stronger superfluid response is obtained here for clusters with more than ten molecules. Moreover, all the clusters, including the smallest one, display a well-defined, clearly identifiable solidlike structure; with only one possible exception, those with fewer than N = 25 molecules are (almost) entirely superfluid at the lowest temperature considered here (i.e., T = 0.25 K), and can thus be regarded as nanoscale "supersolids." The implications of these results on a possible bulk two-dimensional superfluid phase of parahydrogen are discussed.