He Inclusion in Ice-like and Clathrate-like Frameworks: A Benchmark Quantum Chemistry Study of Guest-Host Interactions

Analysing the stability of He-filled hydrates: how many He atoms fit in the sII crystal?

Clathrate hydrates have the ability to encapsulate atoms and molecules within their cavities, and thus they could be potentially large storage capacity materials. The present work studies the multiple cage occupancy effects in the recently discovered He@sII crystal. On the basis of previous theoretical and experimental findings, the stability of He(1/1)@sII, He(1/4)@sII and He(2/4)@sII crystals was analysed in terms of structural, mechanical and energetic properties. For this purpose, first-principles DFT/DFT-D computations were performed by using both semi-local and non-local functionals, not only to elucidate which configuration is the most energetically favoured, but also to scrutinize the relevance of the long-range dispersion interactions in these kinds of compounds. We have encountered that dispersion interactions play a fundamental role in describing the underlying interactions, and different tendencies were observed depending on the choice of the functional. We found that PW86PBE-XDM shows the best performance, while the non-local functionals tested here were not able to correctly account for them. The present results reveal that the most stable configuration is the one presenting singly occupied D cages and tetrahedrally occupied H cages (He(1/4)@sII) in line with the experimental observation.

Computational investigations of stable multiple-cage-occupancy He clathrate-like hydrostructures

One of the several possibilities offered by the interesting clathrate hydrates is the opportunity to encapsulate several atoms or molecules, in such a way that more efficient storage materials could be explored or new molecules that otherwise do not exist could be created. These types of applications are receiving growing attention from technologists and chemists, given the future positive implications that they entail. In this context, we investigated the multiple cage occupancy of helium clathrate hydrates, to establish stable novel hydrate structures or ones similar to those predicted previously by experimental and theoretical studies. To this purpose, we analyzed the feasibility of including an increased number of He atoms inside the small (D) and large (H) cages of the sII structure through first-principles properly assessed density functional approaches. On the one hand, we have computed energetic and structural properties, in which we examined the guest-host and guest-guest interactions in both individual and two-adjacent clathrate-like sII cages by means of binding and evaporation energies. On the other hand, we have carried out a thermodynamical analysis on the stability of such He-containing hydrostructures in terms of changes in enthalpy, ΔH, Gibbs free energy, ΔG, and entropy, ΔS, during their formation process at various temperature and pressure values. In this way, we have been able to make a comparison with experiments, reaffirming the ability of computational DFT approaches to describe such weak guest-host interactions. In principle, the most stable structure involves the encapsulation of one and four He atoms inside the D and H sII cages, respectively; however, more He atoms could be entrapped under lower temperature and/or higher pressure thermodynamic conditions. We foresee such accurate computational quantum chemistry approaches contributing to the current emerging machine-learning model development.

Modeling of Structure H Carbon Dioxide Clathrate Hydrates: Guest-Lattice Energies, Crystal Structure, and Pressure Dependencies

We performed first-principles computations to investigate the complex interplay of molecular interaction energies in determining the lattice structure and stability of CO₂@sH clathrate hydrates. Density functional theory computations using periodic boundary conditions were employed to characterize energetics and the key structural properties of the sH clathrate crystal under pressure, such as equilibrium lattice volume and bulk modulus. The performance of exchange-correlation functionals together with recently developed dispersion-corrected schemes was evaluated in describing interactions in both short-range and long-range regions of the potential. Structural relaxations of the fully CO₂-filled and empty sH unit cells yield crystal structure and lattice energies, while their compressibility parameters were derived by including the pressure dependencies. The present quantum chemistry computations suggest anisotropy in the compressibility of the sH clathrate hydrates, with the crystal being less compressible along the a-axis direction than along the c-axis one, in distinction from nearly isotropic sI and sII structures. The detailed results presented here give insight into the complex nature of the underlying guest-host interactions, checking earlier assumptions, providing critical tests, and improving estimates. Such entries may eventually lead to better predictions of thermodynamic properties and formation conditions, with a direct impact on emerging hydrate-based technologies.

Delving into guest-free and He-filled sI and sII clathrate hydrates: a first-principles computational study

The dynamics of the formation of a specific clathrate hydrate as well as its thermodynamic transitions depend on the interactions between the trapped molecules and the host water lattice. The molecular-level understanding of the different underlying processes benefits not only the description of the properties of the system, but also allows the development of multiple technological applications such as gas storage, gas separation, energy transport, etc. In this work we investigate the stability of periodic crystalline structures, such as He@sI and He@sII clathrate hydrates by first-principles computations. We consider such host water networks interacting with a guest He atom using selected density functional theory approaches, in order to explore the effects on the encapsulation of a light atom in the sI/sII crystals, by deriving all energy components (guest-water, water-water, guest-guest). Structural properties and energies were first computed by structural relaxations of the He-filled and empty sI/sII unit cells, yielding lattice and compressibility parameters comparable to experimental and theoretical values available for those hydrates. According to the results obtained, the He enclathration in the sI/sII unit cells is a stabilizing process, and both He@sI and He@sII clathrates, considering single cage occupancy, are predicted to be stable whatever the XDM or D4 dispersion correction applied. Our results further reveal that despite the weak underlying interactions the He encapsulation has a rather notable effect on both lattice parameters and energetics, with the He@sII being the most energetically favorable in accord with recent experimental observations.

Assessment of DFT approaches in noble gas clathrate-like clusters: stability and thermodynamics

We have assessed the performance and accuracy of different wavefunction-based electronic structure methods, such as DFMP2 and domain-based local pair-natural orbital (DLPNO-CCSD(T)), as well as a variety of density functional theory (DFT) approaches on He@(H₂O)_N cage systems. We have selected representative clathrate-like structures corresponding to the building blocks present in each of the sI, sII and sH natural gas clathrate hydrates, and we have carefully studied the interaction between a He atom with each of their individual cages. We reported well-converged DFMP2 and DLPNO-CCSD(T) reference data, together with interaction and cohesive energies of four different density functionals (two GGA, revPBE and PW86PBE, and two hybrids, B3LYP and PBE0), including diverse dispersion correction schemes (D3(0), D3(BJ), D4 and XDM) for both He-filled and empty clathrate-like cages. After the analysis of the results, we came to the conclusion that the PW86PBE functional, with both XDM and D4 corrections, and the PBE0-D4 functional present reasonably adequate approaches to describe the guest-host noncovalent interactions that take place in such He clathrate hydrates. Taking into account that the He@sII is the only helium clathrate that scientists have been able to synthesize recently, we have performed a thermodynamic study on the individual 5¹² and 5¹²6⁴ cages present in the sII crystal. We determined the change in enthalpy, ΔH, and in Gibbs free energy, ΔG, at various temperatures and pressures, and we found out that in the range of experimental conditions the reactions associated with the encapsulation of the He atom inside the cages are exothermic and spontaneous. Finally, we highlighted the importance of an accurate description of the interaction in He@water mixtures, as a crucial component in construction of reliable data-driven models.

Encapsulation of a Water Molecule inside C60 Fullerene: The Impact of Confinement on Quantum Features

We introduce an efficient quantum fully coupled computational scheme within the multiconfiguration time-dependent Hartree (MCTDH) approach to handle the otherwise extremely costly computations of translational-rotational-vibrational states and energies of light-molecule endofullenes. Quantum calculations on energy levels are reported for a water molecule inside C60 fullerene by means of such a systematic approach that includes all nine degrees of freedom of H2O@C60 and does not consider restrictions above them. The potential energy operator is represented as a sum of natural potentials employing the n-mode expansion, along with the exact kinetic energy operator, by introducing a set of Radau internal coordinates for the H2O molecule. On the basis of the present rigorous computations, various aspects of the quantized intermolecular dynamics upon confinement of H2O@C60 are discussed, such as the rotational energy level splitting and the significant frequency shifts of the encapsulated water molecule vibrations. The impact of water encapsulation on quantum features is explored, and insights into the nature of the underlying forces are provided, highlighting the importance of a reliable first-principles description of the guest-host interactions.

Exploring CO2 @sI Clathrate Hydrates as CO2 Storage Agents by Computational Density Functional Approaches

The formation of specific clathrate hydrates and their transformation at given thermodynamic conditions depends on the interactions between the guest molecule/s and the host water lattice. Understanding their structural stability is essential to control structure-property relations involved in different technological applications. Thus, the energetic aspects relative to CO₂ @sI clathrate hydrate are investigated through the computation of the underlying interactions, dominated by hydrogen bonds and van der Waals forces, from first-principles electronic structure approaches. The stability of the CO₂ @sI clathrate is evaluated by combining bottom-up and top-down approaches. Guest-free and CO₂ guest-filled aperiodic cages, up to the gradually CO₂ occupation of the entire sI periodic unit cells were considered. Saturation, cohesive and binding energies for the systems are determined by employing a variety of density functionals and their performance is assessed. The dispersion corrections on the non-covalent interactions are found to be important in the stabilization of the CO₂ @sI energies, with the encapsulation of the CO₂ into guest-free/empty cage/lattice being always an energetically favorable process for most of the functionals studied. The PW86PBE functional with XDM or D3(BJ) dispersion corrections predicts a lattice constant in accord to the experimental values available, and simultaneously provides a reliable description for the guest-host interactions in the periodic CO₂ @sI crystal, as well as the energetics of its progressive single cage occupancy process. It has been found that the preferential orientation of the single CO₂ in the large sI crystal cages has a stabilizing effect on the hydrate, concluding that the CO₂ @sI structure is favored either by considering the individual building block cages or the complete sI unit cell crystal. Such benchmark and methodology cross-check studies benefit new data-driven model research by providing high-quality training information, with new insights that indicate the underlying factors governing their structure-driven stability, and triggering further investigations for controlling the stabilization of these promising long-term CO₂ storage materials.

Computational density-functional approaches on finite-size and guest-lattice effects in CO2@sII clathrate hydrate

We performed first-principles computations to investigate guest-host/host-host effects on the encapsulation of the CO₂ molecule in sII clathrate hydrates from finite-size clusters up to periodic 3D crystal lattice systems. Structural and energetic properties were first computed for the individual and first-neighbors clathrate-like sII cages, where highly accurate ab initio quantum chemical methods are available nowadays, allowing in this way the assessment of the density functional (DFT) theoretical approaches employed. The performance of exchange-correlation functionals together with recently developed dispersion-corrected schemes was evaluated in describing interactions in both short-range and long-range regions of the potential. On this basis, structural relaxations of the CO₂-filled and empty sII unit cells yield lattice and compressibility parameters comparable to experimental and previous theoretical values available for sII hydrates. According to these data, the CO₂ enclathration in the sII clathrate cages is a stabilizing process, either by considering both guest-host and host-host interactions in the complete unit cell or only the guest-water energies for the individual clathrate-like sII cages. CO₂@sII clathrates are predicted to be stable whatever the dispersion correction applied and in the case of single cage occupancy are found to be more stable than the CO₂@sI structures. Our results reveal that DFT approaches could provide a good reasonable description of the underlying interactions, enabling the investigation of formation and transformation processes as a function of temperature and pressure.

Structural Stability of the CO2 @sI Hydrate: a Bottom-Up Quantum Chemistry Approach on the Guest-Cage and Inter-Cage Interactions

Through reliable first-principles computations, we have demonstrated the impact of CO₂ molecules enclathration on the stability of sI clathrate hydrates. Given the delicate balance between the interaction energy components (van der Waals, hydrogen bonds) present on such systems, we follow a systematic bottom-up approach starting from the individual 5¹² and 5¹² 6² sI cages, up to all existing combinations of two-adjacent sI crystal cages to evaluate how such clathrate-like models perform on the evaluation of the guest-host and first-neighbors inter-cage effects, respectively. Interaction and binding energies of the CO₂ occupation of the sI cages were computed using DF-MP2 and different DFT/DFT-D electronic structure methodologies. The performance of selected DFT functionals, together with various semi-classical dispersion corrections schemes, were validated by comparison with reference ab initio DF-MP2 data, as well as experimental data from x-ray and neutron diffraction studies available. Our investigation confirms that the inclusion of the CO₂ in the cage/s is an energetically favorable process, with the CO₂ molecule preferring to occupy the large 5¹² 6² sI cages compared to the 5¹² ones. Further, the present results conclude on the rigidity of the water cages arrangements, showing the importance of the inter-cage couplings in the cluster models under study. In particular, the guest-cage interaction is the key factor for the preferential orientation of the captured CO₂ molecules in the sI cages, while the inter-cage interactions seems to cause minor distortions with the CO₂ guest neighbors interactions do not extending beyond the large 5¹² 6² sI cages. Such findings on these clathrate-like model systems are in accord with experimental observations, drawing a direct relevance to the structural stability of CO₂ @sI clathrates.