Assessment of the Effects of Anisotropic Interactions among Hydrogen

Article

An Assessment of the Effects of Anisotropic Interactions Among Hydrogen Molecules and Their Isotopologues: A Diffusion Monte Carlo Investigation of Gas Phase and Adsorbed Clusters Massimo Mella, and Emanuele Curotto J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b03768 • Publication Date (Web): 15 Jun 2017 Downloaded from http://pubs.acs.org on June 18, 2017

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The Journal of Physical Chemistry

An Assessment of the Effects of Anisotropic Interactions Among Hydrogen Molecules and Their Isotopologues: a Diffusion Monte Carlo Investigation of Gas Phase and Adsorbed Clusters.

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Massimo Mella∗,‡ and E. Curotto∗,¶ Dipartimento di Scienza ed Alta Tecnologia, Universit` a degli Studi dell’Insubria, via Valleggio 9, 22100 Como (I), and Department of Chemistry and Physics, Arcadia University, Glenside, Pennsylvania, 19038-3295 E-mail: [email protected]; [email protected] Phone: +39 0312386625. Fax: +39 0312386630

† EC carried out the hydrogen cluster optimisations and contributed to the writing of the manuscript. MM carried out the diffusion Monte Carlo simulations, implemented the model potentials and algorithms for computing expectation values analysing the results, and contributed to the writing of the manuscript. ∗ To whom correspondence should be addressed ‡ Universit`a dell’Insubria ¶ Arcadia University

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Abstract Despite the fact that the para–hydrogen molecule (p–H2 ) and its isotopomers (o– D2 and p–T2 ) are commonly modelled as spherical objects due to the large separation between rotational states, there may be situations (e.g. adsorption in pores and on surfaces) in which such an approximation neglects important degrees of freedom (i.e. the rotational ones) and introduces uncontrolled biases in the predicted properties. To better understand when approximating such molecules as spheres introduces shortcomings in their representation, we employed diffusion Monte Carlo to simulate small/medium–sized molecular aggregates, either isolated in space or experiencing external model potentials, to compute energetic quantities and distribution functions. These were chosen to mimic situations possibly occurring in real systems, in which orientational isotropy is broken. The comparison between isolated clusters with molecules described as rigid rotors with a 4D potential or as spheres interacting via Adiabatic Hindered Rotor models shows that neither energetic nor structural quantities are affected by reducing the systems dimensionality. The orientational degrees of freedom of the rotors remains largely uncoupled from translational ones whatever the molecular mass. The same happens for rotors interacting with a frozen hydrogen molecule in the vicinity of a repulsive surface. Deviating from such behavior are molecular aggregates interacting with potentials mimicking the presence of ionic adsorption sites inside porous materials. Such difference is ascribable to the markedly anisotropic and longer ranged nature of those interactions, both features being relevant in defining the adsorption energy of the molecular species.

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Introduction

As one of the two archetypical quantum systems, aggregates of hydrogen molecules have been the subject of an intense theoretical investigation since the implementation of the first method capable of correctly describing quantum effects. 1 Apart from the thrust provided by the desire to better comprehend fundamental properties such the chance of inducing 2


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Bose–Einstein condensation 2 or the impact as a matrix for highly accurate spectroscopic measurements, 3 a part of the effort has been directed toward less speculative and more applied fields. Among these, we mention low–pressure hydrogen storage for automotive applications and the efficient separation of hydrogen isotopes. Leaving aside a handful of notable cases, 4–14 theoretical studies tend to neglect the rotational degrees of freedom of the involved diatomic species X2 (X=H, D, and T), treating them as spherical object interacting via radial potential and forsaking e.g. the quadrupolar nature of their change density. 2,15–26 While such an approach is convenient (and often justifiable) in terms of computational costs and algorithmic complexity, the underlaying assumption of a complete decoupling between orientational and translational degrees of freedom may not always be correct. Of course, whether or not such approximation is adequate is dictated by the ratio between the molecular rotational constants (defining the quantum energy gaps) and the difference in potential energy between minima and the transition states connecting them along paths that involve changes in orientations. 27,28 Thus, while considering H2 as a spherical object may be acceptable (but never shown to be correct) in describing its free pure clusters despite the variation of local properties upon increasing the distance between a molecule and cluster centers of mass (CoM), it is definitively not so when X2 is adsorbed into a narrow carbon nanotube (CNT) 9,10 or onto ammonia aggregates. 13,14 Currently, the only indirect evidences supporting the possibility of neglecting rotations in X2 clusters comes from the work by Roy et al., 26 where the shift in X2 vibrational frequency computed using adiabatically hindered rotor (AHR) interaction potentials 29 reproduced experimental results with good accuracy. In turn, such positive results also indicates that pair distribution functions is essentially correct. Among the properties of X2 aggregates that may change if one kept in full account the orientational anisotropy of interaction potentials, there are the total system energy, its components and derivatives (e.g. the chemical potential), the pair distribution functions and, consequently, the point density in localized systems. While the former are relevant in the

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context of separating isotopes via quantum sieving or chromatography, the latter plays a role in defining whether or not a hydrogen–adsorbing material is suitable for automotive–related applications. In spite of these possible applications, it seems to us that an insufficient effort has, so far, been paid to investigate how the properties of X2 aggregates or condensed phases are impacted by interaction potential anisotropy once rotational degrees of freedom are included in the description. In this respect, we should stress that, albeit approaches such as AHR can provide indications on the possibility of reducing degrees of freedom for two–body systems, 29,30 the potentially many–body nature of the orientational coupling requires, in principle, a many–body treatment for systems of size sufficiently large to guarantee decoupling between molecules placed at opposite far sides. In other words, it seems worth computing the energetic and structural properties of (X2 )n aggregates in, at least, a few cases, checking whether or not decoupling molecular rotations from translations may represent a sensible approximation. To do so, we employ recently developed diffusion Monte Carlo (DMC) algorithms for linear systems, simulating X2 aggregates in free space, and adsorbed onto surfaces or inside model cavities (vide infra Section 3 for a description). For these model systems, we used DMC to compute total, evaporation and kinetic energies, as well as probability distributions providing key information on the spatial density, relative distance distribution and the probability of observing a specific orientation between two molecules or a molecule and the position of an interaction source. The outline of this work is the following. In Section 2, we provide a few details on the numerical methodologies (DMC and optimisation methods) employed in this study. Section 3 describes the model systems and potentials we decided to investigate, providing rationale for their choice. The numerical results obtained are presented and discussed in Section 4; finally, the last section provides a more general discussion together with our conclusions.

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Methods

Before discussing the details of our methodologies, it seems useful to explicitly indicate the general analytical form of the Hamiltonian operator describing the systems (atomic units). This can be written as

H=

X j=1,n

(−

X X ∇2j,CoM Λ2j + )+ Vext (rj , Ωj ) + ujk (rj , Ωj , rk , Ωk ) 2mj 2Ij j=1,n j

Assessment of the Effects of Anisotropic Interactions among Hydrogen

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