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. Traditionally, the water cage structure is assumed to be rigid, thus ignoring the quantum nature of hydrogen nuclei in the water framework. However, it has been shown that protons in a water molecule possess a marked delocalised character in many situations, ranging from water clusters to proton transfer in the bulk. In the case of water clathrates, all previous TR bound-state calculations of guest molecules consider that the caging water molecules are fixed at their equilibrium geometry. Only recently, a static investigation of the role of proton configurations was performed by Bačić and co-workers by sampling a very large number of different static structures of water clathrates. Here, we investigate the importance of the rotational degrees of freedom of the water cage on the TR levels of the guest molecule using an efficient adiabatic decoupling scheme. Our approach combines rigid body diffusion Monte Carlo calculations for the description of the rotational degree of freedom of water molecules surrounding the guest molecular hydrogen to an efficient Smolyak sparse-grid technique for the calculation of the TR levels. This approach allows us to take into account the highly anharmonic nature of the rotational water motions in a high-dimensional system. The clathrate-induced splittings of the j = 1 rotational levels are much more sensitive to the quantum hydrogen delocalisation than the translational transitions. This result is in good agreement with the previous static study of Bačić and co-workers

State-To-State Inelastic Rotational Cross Sections in Five-Atom Systems with the Multiconfiguration Time Dependent Hartree Method

We present a MultiConfiguration Time Dependent Hartree (MCTDH) method as an attractive alternative approach to the usual quantum close-coupling method that approaches some computational limits in the calculation of rotational excitation (and de-excitation) between polyatomic molecules (here collisions between triatomic and diatomic rigid molecules). We have performed a computational investigation of the rotational (de-)excitation of the benchmark rigid rotor H2O-H2 system on a recently developed Potential Energy Surface of the complex using the MCTDH method. We focus here on excitations and de-excitations from the 000, 111, and 110 states of H2O with H2 in its ground rotational state, looking at all the potential transitions in the energy range 1-200 cm-1. This work follows a recently completed study on the H2O-H2 cluster where we characterized its spectroscopy and more generally serves a broader goal to describe inelastic collision processes of high dimensional systems using the MCTDH method. We find that the cross sections obtained from the MCTDH calculations are in excellent agreement with time independent calculations from previous studies but does become challenging for the lower kinetic energy range of the de-excitation process: that is, below approximately 20 cm-1 of collision energy, calculations with a relative modest basis become unreliable. The MCTDH method therefore appears to be a useful complement to standard approaches to study inelastic collision for various collision partners, even at low energy, though performing better for rotational excitation than for de-excitation

Intermolecular rovibrational bound states of H2O–H2 dimer from a multiconfiguration time dependent Hartree approach

We compute the rovibrational eigenstates of the H2O–H2 Van der Waals complex using the accurate rigid-rotor potential energy surface of Valiron et al. (2008) with the MultiConfiguration Time Dependent Hartree (MCTDH) method. The J=0–2 rovibrational bound states calculations are done with the Block Improved Relaxation procedure of MCTDH and the subsequent assignment of the states is achieved by inspection of the wavefunctions’ properties. The results of this work are found to be in close agreement with previous time independent calculations reported for this complex and therefore supports the use of the MCTDH approach for the rovibrational spectroscopic study of such weakly bound complexes

H2, HD, and D2 in the small cage of structure II clathrate hydrate: vibrational frequency shifts from fully coupled quantum six-dimensional calculations of the vibration-translation-rotation eigenstates

We report the first fully coupled quantum six-dimensional (6D) bound-state calculations of the vibration-translation-rotation eigenstates of a flexible H2, HD, and D2 molecule confined inside the small cage of the structure II clathrate hydrate embedded in larger hydrate domains with up to 76 H2O molecules, treated as rigid. Our calculations use a pairwise-additive 6D intermolecular potential energy surface for H2 in the hydrate domain, based on an ab initio 6D H2–H2O pair potential for flexible H2 and rigid H2O. They extend to the first excited (v = 1) vibrational state of H2, along with two isotopologues, providing a direct computation of vibrational frequency shifts. We show that obtaining a converged v = 1 vibrational state of the caged molecule does not require converging the very large number of intermolecular translation-rotation states belonging to the v = 0 manifold up to the energy of the intramolecular stretch fundamental (≈4100 cm−1 for H2). Only a relatively modest-size basis for the intermolecular degrees of freedom is needed to accurately describe the vibrational averaging over the delocalized wave function of the quantum ground state of the system. For the caged H2, our computed fundamental translational excitations, rotational j = 0 → 1 transitions, and frequency shifts of the stretch fundamental are in excellent agreement with recent quantum 5D (rigid H2) results [A. Powers et al., J. Chem. Phys. 148, 144304 (2018)]. Our computed frequency shift of −43 cm−1 for H2 is only 14% away from the experimental value at 20 K

The effect of the condensed-phase environment on the vibrational frequency shift of a hydrogen molecule inside clathrate hydrates

© 2018 Author(s). We report a theoretical study of the frequency shift (redshift) of the stretching fundamental transition of an H 2 molecule confined inside the small dodecahedral cage of the structure II clathrate hydrate and its dependence on the condensed-phase environment. In order to determine how much the hydrate water molecules beyond the confining small cage contribute to the vibrational frequency shift, quantum five-dimensional (5D) calculat ions of the coupled translation-rotation eigenstates are performed for H 2 in the v=0 and v=1 vibrational states inside spherical clathrate hydrate domains of increasing radius and a growing number of water molecules, ranging from 20 for the isolated small cage to over 1900. In these calculations, both H 2 and the water domains are treated as rigid. The 5D intermolecular potential energy surface (PES) of H 2 inside a hydrate domain is assumed to be pairwise additive. The H 2 -H 2 O pair interaction, represented by the 5D (rigid monomer) PES that depends on the vibrational state of H 2 , v=0 or v=1, is derived from the high-quality ab initio full-dimensional (9D) PES of the H 2 -H 2 O complex [P. Valiron et al., J. Chem. Phys. 129, 134306 (2008)]. The H 2 vibrational frequency shift calculated for the largest clathrate domain considered, which mimics the condensed-phase environment, is about 10% larger in magnitude than that obtained by taking into account only the small cage. The calculated splittings of the translational fundamental of H 2 change very little with the domain size, unlike the H 2 j = 1 rotational splittings that decrease significantly as the domain size increases. The changes in both the vibrational frequency shift and the j = 1 rotational splitting due to the condensed-phase effects arise predominantly from the H 2 O molecules in the first three complete hydration shells around H 2

OVERTONE VIBRATIONAL SPECTROSCOPY AND DYNAMICS IN H2_2-H2_2O COMPLEXES: A COMBINED THEORETICAL AND EXPERIMENTAL STUDY

Author Institution: JILA, University of Colorado and National Institute of; Standards and Technology, Boulder, Colorado; CNRS-Universite de Bourgogne, Dijon, France; CNRS, Institut de Planetologie et d'Astrophysique de Grenoble, France; Radboud University, 6525 AJ Nijmegen, The NetherlandsH$_2$ is the most abundant molecule in the universe and also H$_2$O occurs in relatively high concentrations in various interstellar environments. Processes that occur through the interaction of these molecules may, for example, play a role in the mechanism producing the observed H$_2$O maser activity. Spectroscopic studies of the H$_2$-H$_2$O complex in different stable and metastable states will be reported in the accompanying talk; theoretical studies will be presented here. The latter involve calculations of the bound rovibrational levels of the complex with both monomers in their vibrational ground state, as well as of the metastable levels with H$_2$O in its OH stretch overtone state, on the appropriate \textit{ab initio} five-dimensional intermolecular potential surfaces. Also the line strengths of all the allowed transitions between these levels that may occur in combination with the $v_{\rm OH} = 2 \leftarrow 0$ overtone transition were computed, for all four ortho/para H$_2$ and ortho/para H$_2$O variants of the complex. The spectrum simulated with these data agrees very well with the measured spectrum and was used to assign this spectrum. In addition, the information obtained from the theory was useful to understand the observed predissociation dynamics of the complex

Suitable sparse grid scheme for the calculation of the vibration-translation-rotation eigenstates of confined molecular system

International audienceThe quantum dynamics studies of molecular bound states are actually limited by the well known dimensionality problem. Indeed even for molecules of medium size, usual quadrature techniques have already reached their limit since a multidimensional direct-product grid can be very large. An alternative to avoid the direct-product grid is to use the Smolyak sparse-grid techniques, recently investigated by Avila and Carrington [1] for the calculation of vibrational bound states of semi-rigid molecules. Lauvergnat and Nauts [2] have proposed a new implementation of such sparse grid for the study of the torsional levels of methanol in full dimensionality in order to treat one large amplitude motion. The efficiency of this kind of grid is related to the substitution of a single large direct-product grid by a sum of small direct-product grids. We will present a recent adaptation of this kind of sparse grid scheme for the calculation of six-dimensional (6D) vibration-translation-rotation bound states of confined molecule such as H$_2$ (and its isotopologues) in water clathrate [3]. In particular, we are able to use a combination of 2D-grids associated to spherical harmonic basis functions and the usual 1D-gaussian quadrature grids to form the Smolyak sparse-grid [4]. We will discuss the efficiency of this approach for the calculation the intramolecular vibrational shift of H$_2$ as well as the effect of the condensed phase environment.[1] A. Avila and T. Carrington, J. Chem. Phys. 131 (2009), 174103.[2] D. Lauvergnat and A. Nauts, Spectrochim. Acta. Part A 119 (2014), 18.[3] D. Lauvergnat and P. Felker and Y. Scribano and D. Benoit and Z. Bacic, J. Chem. Phys.150 (2019), 154303.[4] A. Powers and Y. Scribano and D. Lauvergnat and E. Mebe and D. Benoit and Z. Bacic, J.Chem. Phys. 148 (2018), 144304

A quantum study of the water-hydrogen complex : from dimer to hydrogen clathrate hydrate

International audienceFloppy molecular systems are very challenging since a normal mode description is not possible for the description of large amplitude motion. In this talk, I will present a spectroscopic analysis of the accuracy of therecent ab initio potential of H2O-H2 for which several experimental data are now available. I willalso present the efficiency of a reduced dimensional model which can reproduce rovibrational boundstates with a good accuracy. In the last part, I will present the application of this two-body potentialfor the calculation of Translation-Rotation states of hydrogen in water clathrates