Hydrogen Molecule in the Small Dodecahedral Cage of a Clathrate Hydrate: Quantum Five-Dimensional Calculations of the Coupled Translation−Rotation Eigenstates

Smolyak Algorithm Adapted to a System-Bath Separation: Application to an Encapsulated Molecule with Large-Amplitude Motions

A Smolyak algorithm adapted to system-bath separation is proposed for rigorous quantum simulations. This technique combines a sparse grid method with the system-bath concept in a specific configuration without limitations on the form of the Hamiltonian, thus achieving a highly efficient convergence of the excitation transitions for the "system" part. Our approach provides a general way to overcome the perennial convergence problem for the standard Smolyak algorithm and enables the simulation of floppy molecules with more than a hundred degrees of freedom. The efficiency of the present method is illustrated on the simulation of H₂ caged in an sII clathrate hydrate including two kinds of cage modes. The transition energies are converged by increasing the number of normal modes of water molecules. Our results confirm the triplet splittings of both translational and rotational (j = 1) transitions of the H₂ molecule. Furthermore, they show a slight increase of the translational transitions with respect to the ones in a rigid cage.

Graph-|Q⟩⟨C|, a Graph-Based Quantum/Classical Algorithm for Efficient Electronic Structure on Hybrid Quantum/Classical Hardware Systems: Improved Quantum Circuit Depth Performance

We present a procedure to reduce the depth of quantum circuits and improve the accuracy of results in computing post-Hartree-Fock electronic structure energies in large molecular systems. The method is based on molecular fragmentation where a molecular system is divided into overlapping fragments through a graph-theoretic procedure. This allows us to create a set of projection operators that decompose the unitary evolution of the full system into separate sets of processes, some of which can be treated on quantum hardware and others on classical hardware. Thus, we develop a procedure for an electronic structure that can be asynchronously spawned onto a potentially large ensemble of classical and quantum hardware systems. We demonstrate this method by computing Unitary Coupled Cluster Singles and Doubles (UCCSD) energies for a set of [H₂]_n clusters, with n ranging from 4 to 128. We implement our methodology using quantum circuits, and when these quantum circuits are processed on a quantum simulator, we obtain energies in agreement with the UCCSD energies in the milli-hartree energy range. We also show that our circuit decomposition approach yields up to 9 orders of magnitude reduction in the number of CNOT gates and quantum circuit depth for the large-sized clusters when compared to a standard quantum circuit implementation available on IBM's Quantum Information Science kit, known as Qiskit.

Path integral simulations of confined parahydrogen molecules within clathrate hydrates: Merging low temperature dynamics with the zero-temperature limit

Clathrate hydrates, or cages comprised solely of water molecules, have long been investigated as a clean storage facility for hydrogen molecules. A breakthrough occurred when hydrogen molecules were experimentally placed within a structure-II clathrate hydrate, which sparked much interest to determine their feasibility for energy storage [Mao et al., Science 297, 2247-2249 (2002)]. We use Path Integral Molecular Dynamics (PIMD) and Langevin equation Path Integral Ground State (LePIGS) for finite temperature and zero-temperature studies, respectively, to determine parahydrogen occupancy properties in the small dodecahedral (5¹²) and large hexakaidecahedral (5¹²6⁴) sized cages that comprise the structure-II unit cell. We look at energetic and structural properties of small clusters of hydrogen, treated as point-like particles, confined within each of the different sized clathrates, and treated as rigid, to determine energetic and structural properties in the zero-temperature limit. Our predicted hydrogen occupancy within these two cage sizes is consistent with previous literature values. We then calculate the energies as a function of temperature and merge the low temperature results calculated using finite temperature PIMD with the zero-temperature results using LePIGS, demonstrating that the two methods are compatible.

Does cage quantum delocalisation influence the translation–rotational bound states of molecular hydrogen in clathrate hydrate?

In this study, we examine the effect of a flexible description of the clathrate hydrate framework on the translation–rotation (TR) eigenstates of guest molecules such as molecular hydrogen.

Intra-cage dynamics of molecular hydrogen confined in cages of two different dimensions of clathrate hydrates

In porous materials the molecular confinement is often realized by means of weak Van der Waals interactions between the molecule and the pore surface. The understanding of the mechanism of such interactions is important for a number of applications. In order to establish the role of the confinement size we have studied the microscopic dynamics of molecular hydrogen stored in the nanocages of clathrate hydrates of two different dimensions. We have found that by varying the size of the pore the diffusive mobility of confined hydrogen can be modified in both directions, i.e. reduced or enhanced compared to that in the bulk solid at the same temperatures. In the small cages with a mean crystallographic radius of 3.95 Å the confinement reduces diffusive mobility by orders of magnitude. In contrast, in large cages with a mean radius of 4.75 Å hydrogen molecules displays diffusive jump motion between different equilibrium sites inside the cages, visible at temperatures where bulk H2 is solid. The localization of H2 molecules observed in small cages can promote improved functional properties valuable for hydrogen storage applications.

Impact of the Condensed-Phase Environment on the Translation-Rotation Eigenstates and Spectra of a Hydrogen Molecule in Clathrate Hydrates

We systematically investigate the manifestations of the condensed-phase environment of the structure II clathrate hydrate in the translation-rotation (TR) dynamics and the inelastic neutron scattering (INS) spectra of an H2 molecule confined in the small dodecahedral cage of the hydrate. The aim is to elucidate the extent to which these properties are affected by the clathrate water molecules beyond the confining cage and the proton disorder of the water framework. For this purpose, quantum calculations of the TR eigenstates and INS spectra are performed for H2 inside spherical clathrate domains of gradually increasing radius and the number of water molecules ranging from 20 for the isolated small cage to more than 1800. For each domain size, several hundred distinct hydrogen-bonding topologies are constructed in order to simulate the effects of the proton disorder. Our study reveals that the clathrate-induced splittings of the j = 1 rotational level and the translational fundamental of the guest H2 are influenced by the condensed-phase environment to a dramatically different degree, the former very strongly and the latter only weakly.

Experimental, theoretical and computational investigation of the inelastic neutron scattering spectrum of a homonuclear diatomic molecule in a nearly spherical trap: H2@C60

In this paper we report a methodology for calculating the inelastic neutron scattering spectrum of homonuclear diatomic molecules confined within nano-cavities of spherical symmetry.

Competing quantum effects in the free energy profiles and diffusion rates of hydrogen and deuterium molecules through clathrate hydrates

Depending on the temperature, competing quantum effects are found to accelerate or decelerate the diffusion rate of hydrogen compared to deuterium in clathrates.

Dynamics of H2 adsorbed in porous materials as revealed by computational analysis of inelastic neutron scattering spectra

This perspective article reviews the different types of quantum and classical mechanical methods that have been implemented to interpret the INS spectra for H₂ adsorbed in porous materials.

Roto-translational states of the interstitial molecular hydrogen in silicon: A theoretical study

A theoretical study of the interstitial molecular hydrogen in the silicon single-crystal is reported. H2 and Si have been approximated as a rigid object and a static matrix, respectively. A five-dimensional numerical-analytical representation of an ab initio potential energy surface of the system has been constructed. This representation has been used to calculate rotational, translational, and roto-translational energy levels of the interstitial hydrogen, where three levels of theory, 2D, 3D, and 5D were considered. The potential energy surface, the band structure of energy levels, and the roto-translational states obtained are presented together with the symmetry analysis of the roto-translational wavefunctions.

Fully quantal calculation of H2 translation-rotation states in (H2)4@5(12)6(4) clathrate sII inclusion compounds

The quantal translation-rotation (TR) states of the (p-H2)4@5(12)6(4) and (o-D2)4@5(12)6(4) hydrate clathrate sII inclusion compounds have been computed by nuclear-orbital/configuration-interaction methods. The model of these compounds in a rigid, high-symmetry 5(12)6(4) cage is treated in detail. The low-energy TR level structures of both isotopomers within this model are found to consist of states that can be readily described in terms of a small number of single-H2 and double-H2 excitation modes. The use of the high-symmetry results to facilitate the calculation and interpretation of (p-H2)4 and (o-D2)4 TR states in low-symmetry physically realizable 5(12)6(4) cages is also reported.

Quantum simulations of the hydrogen molecule on ammonia clusters

Mixed ammonia-hydrogen molecule clusters [H2-(NH3)n] have been studied with the aim of exploring the quantitative importance of the H2 quantum motion in defining their structure and energetics. Minimum energy structures have been obtained employing genetic algorithm-based optimization methods in conjunction with accurate pair potentials for NH3-NH3 and H2-NH3. These include both a full 5D potential and a spherically averaged reduced surface mimicking the presence of a para-H2. All the putative global minima for n ≥ 7 are characterized by H2 being adsorbed onto a rhomboidal ammonia tetramer motif formed by two double donor and two double acceptor ammonia molecules. In a few cases, the choice of specific rhombus seems to be directed by the vicinity of an ammonia ad-molecule. Diffusion Monte Carlo simulations on a subset of the species obtained highlighted important quantum effects in defining the H2 surface distribution, often resulting in populating rhomboidal sites different from the global minimum one, and showing a compelling correlation between local geometrical features and the relative stability of surface H2. Clathrate-like species have also been studied and suggested to be metastable over a broad range of conditions if formed.

HD in C₆₀: theoretical prediction of the inelastic neutron scattering spectrum and its temperature dependence

We report rigorous quantum calculations of the inelastic neutron scattering (INS) spectra of HD@C₆₀, over a range of temperatures from 0 to 240 K and for two incident neutron wavelengths used in recent experimental investigations. The computations were performed using our newly developed methodology, which incorporates the coupled five-dimensional translation-rotation (T-R) eigenstates of the guest molecule as the initial and final states of the INS transitions, and yields highly detailed spectra. Depending on the incident neutron wavelength, the number of computed INS transitions varies from almost 500 to over 2000. The low-temperature INS spectra display the fingerprints of the coupling between the translational and rotational motions of the entrapped HD molecule, which is responsible for the characteristic splitting patterns of the T-R energy levels. INS transitions from the ground T-R state of HD to certain sublevels of excited T-R multiplets have zero intensity and are absent from the spectra. This surprising finding is explained by the new INS selection rule introduced here. The calculated spectra exhibit strong temperature dependence. As the temperature increases, numerous new peaks appear, arising from the transitions originating in excited T-R states which become populated. Our calculations show that the higher temperature features typically comprise two or more transitions close in energy and with similar intensities, interspersed with numerous other transitions whose intensities are negligible. This implies that accurately calculated energies and intensities of INS transitions which our methodology provides will be indispensable for reliable interpretation and assignment of the experimental spectra of HD@C₆₀ and related systems at higher temperatures.

Diffusive hydrogen inter-cage migration in hydrogen and hydrogen-tetrahydrofuran clathrate hydrates

Classical equilibrium molecular dynamics simulations have been performed to investigate the diffusive properties of inter-cage hydrogen migration in both pure hydrogen and mixed hydrogen-tetrahydrofuran sII hydrates at 0.05 kbar from 200 K and up to 250-260 K. For mixed H2-THF systems in which there is single H2 occupation of the small cage (labelled "1S1L"), we found that no H2 migration occurs. However, for more densely filled H2-THF and pure-H2 systems, in which there is more than single H2 occupation in the small cage, there is an onset of inter-cage H2 migration events from the small cages to neighbouring cavities at around 200 K. The mean square displacements of the hydrogen molecules were fitted to a mathematical model consisting of an anomalous term and a Fickian component, and nonlinear regression fitting was conducted to estimate long-time (inter-cage) diffusivities. An approximate Arrhenius temperature relationship for the diffusion coefficient was examined and an estimation of the hydrogen hopping energy barrier was calculated for each system.

Experimental and theoretical analysis of the rotational Raman spectrum of hydrogen molecules in clathrate hydrates

The Raman spectra of H(2) and HD molecules in simple hydrogen and binary hydrogen-tetrahydrofuran clathrate hydrates have been measured at temperatures as low as 20 K. The rotational bands of trapped molecules in simple and binary hydrates have been analyzed, and the contributions originating from hydrogen molecules in the large cages have been separated from those in the small cages. A theoretical model, consisting in rigid cages enclosing interacting hydrogen molecules, has been exploited to calculate, on the basis of quantum mechanics, the Raman intensity of the rotational transitions for up to two interacting molecules in one cage. A comparison with experiment leads to a clear interpretation of sidebands appearing in the Raman rotational lines. The quantitative agreement between theory and experiment obtained in some cases clarifies the importance of the choice of the interaction potential, and of the proton disorder in the clathrate crystal.

The effect of host relaxation and dynamics on guest molecule dynamics in H2/tetrahydrofuranhydrate

We use ab initio molecular dynamics simulations to obtain classically the effects of H2O cage motions on the potential-energy surface (PES) of encapsulated H2 in the H2/tetrahydrofuran-hydrate system. The significant differences between the PES for the H2 in rigid and flexible cages that we find will influence calculation of the quantum dynamics of the H2. Part of these differences arises from the relaxation of the H2O cage around the classical H2, with a second part arising from the coupling of both translational and rotational motions of H2 with the H20 cage. We find that isotopic substitution of 2H for 1H of the H2O cage affects the coupling, which has implications for experiments that require the use of 2H2O, including inelastic neutron scattering that uses 2H2O cages in order to focus on the H2 guest dynamics. Overall, this work emphasizes the importance of taking into account cage dynamics in any approach used to understand the dynamics of H2 guests in porous framework materials.