Minzhong Xu

Coupled translation-rotation eigenstates of H2 in C60 and C70 on the spectroscopically optimized interaction potential: Effects of cage anisotropy on the energy level structure and assignments

We have developed a quantitatively accurate pairwise additive five-dimensional (5D) potential energy surface (PES) for H(2) in C(60) through fitting to the recently published infrared (IR) spectroscopic measurements of this system for H(2) in the vibrationally excited nu=1 state. The PES is based on the three-site H(2)-C pair potential introduced in this work, which in addition to the usual Lennard-Jones (LJ) interaction sites on each H atom of H(2) has the third LJ interaction site located at the midpoint of the H-H bond. For the optimal values of the three adjustable parameters of the potential model, the fully coupled quantum 5D calculations on this additive PES reproduce the six translation-rotation (T-R) energy levels observed so far in the IR spectra of H(2)@C(60) to within 0.6%. This is due in large part to the greatly improved description of the angular anisotropy of the H(2)-fullerene interaction afforded by the three-site H(2)-C pair potential. The same H(2)-C pair potential spectroscopically optimized for H(2)@C(60) was also used to construct the pairwise additive 5D PES of H(2) (nu=1) in C(70). This PES, because of the lower symmetry of C(70) (D(5h)) relative to that of C(60) (I(h)), exhibits pronounced anisotropy with respect to the direction of the translational motion of H(2) away from the cage center, unlike that of H(2) in C(60). As a result, the T-R energy level structure of H(2) in C(70) from the quantum 5D calculations on the optimized PES, the quantum numbers required for its assignment, and the degeneracy patterns which arise from the T-R coupling for translationally excited H(2) are all qualitatively different from those determined previously for H(2)@C(60) [M. Xu et al., J. Chem. Phys. 128, 011101 (2008).

Quantum dynamics of H2, D2, and HD in the small dodecahedral cage of clathrate hydrate: Evaluating H2-water nanocage interaction potentials by comparison of theory with inelastic neutron scattering experiments

We have performed rigorous quantum five-dimensional (5D) calculations and analysis of the translation-rotation (T-R) energy levels of one H(2), D(2), and HD molecule inside the small dodecahedral (H(2)O)(20) cage of the structure II clathrate hydrate, which was treated as rigid. The H(2)- cage intermolecular potential energy surface (PES) used previously in the molecular dynamics simulations of the hydrogen hydrates [Alavi et al., J. Chem. Phys. 123, 024507 (2005)] was employed. This PES, denoted here as SPC/E, combines an effective, empirical water-water pair potential [Berendsen et al., J. Phys. Chem. 91, 6269 (1987)] and electrostatic interactions between the partial charges placed on H(2)O and H(2). The 5D T-R eigenstates of HD were calculated also on another 5D H(2)-cage PES denoted PA-D, used by us earlier to investigate the quantum T-R dynamics of H(2) and D(2) in the small cage [Xu et al., J. Phys. Chem. B 110, 24806 (2006)]. In the PA-D PES, the hydrogen-water pair potential is described by the ab initio 5D PES of the isolated H(2)-H(2)O dimer. The quality of the SPC/E and the PA-D H(2)-cage PESs was tested by direct comparison of the T-R excitation energies calculated on them to the results of two recent inelastic neutron scattering (INS) studies of H(2) and HD inside the small clathrate cage. The translational fundamental and overtone excitations, as well as the triplet splittings of the j=0-->j=1 rotational transitions, of H(2) and HD in the small cage calculated on the SPC/E PES agree very well with the INS results and represent a significant improvement over the results computed on the PA-D PES. Our calculations on the SPC/E PES also make predictions about several spectroscopic observables for the encapsulated H(2), D(2), and HD, which have not been measured yet.

Quantum dynamics of coupled translational and rotational motions of H2 inside C60

We report rigorous quantum calculations of the translation-rotation (T-R) eigenstates of the H2 molecule in C60. The resulting level structure can be explained in terms of a few dominant features. These include the coupling between the orbital and the rotational angular momenta of H2 to give the total angular momentum lambda, and the splitting of the sevenfold degeneracy of T-R levels with lambda=3 by the nonsphericity of C60, according to the rules of the icosahedral I h group.

Quantum dynamics of small H2 and D2 clusters in the large cage of structure II clathrate hydrate: Energetics, occupancy, and vibrationally averaged cluster structures

We report diffusion Monte Carlo (DMC) calculations of the quantum translation-rotation (T-R) dynamics of one to five para-H(2) (p-H(2)) and ortho-D(2) (o-D(2)) molecules inside the large hexakaidecahedral (5(12)6(4)) cage of the structure II clathrate hydrate, which was taken to be rigid. These calculations provide a quantitative description of the size evolution of the ground-state properties, energetics, and the vibrationally averaged geometries, of small (p-H(2))(n) and (o-D(2))(n) clusters, n=1-5, in nanoconfinement. The zero-point energy (ZPE) of the T-R motions rises steeply with the cluster size, reaching 74% of the potential well depth for the caged (p-H(2))(4). At low temperatures, the rapid increase of the cluster ZPE as a function of n is the main factor that limits the occupancy of the large cage to at most four H(2) or D(2) molecules, in agreement with experiments. Our DMC results concerning the vibrationally averaged spatial distribution of four D(2) molecules, their mean distance from the cage center, the D(2)-D(2) separation, and the specific orientation and localization of the tetrahedral (D(2))(4) cluster relative to the framework of the large cage, agree very well with the low-temperature neutron diffraction experiments involving the large cage with the quadruple D(2) occupancy.

Hydrogen Molecules inside Fullerene C70: Quantum Dynamics, Energetics, Maximum Occupancy, And Comparison with C60

Recent synthesis of the endohedral complexes of C(70) and its open-cage derivative with one and two H(2) molecules has opened the path for experimental and theoretical investigations of the unique dynamic, spectroscopic, and other properties of systems with multiple hydrogen molecules confined inside a nanoscale cavity. Here we report a rigorous theoretical study of the dynamics of the coupled translational and rotational motions of H(2) molecules in C(70) and C(60), which are highly quantum mechanical. Diffusion Monte Carlo (DMC) calculations were performed for up to three para-H(2) (p-H(2)) molecules encapsulated in C(70) and for one and two p-H(2) molecules inside C(60). These calculations provide a quantitative description of the ground-state properties, energetics, and the translation-rotation (T-R) zero-point energies (ZPEs) of the nanoconfined p-H(2) molecules and of the spatial distribution of two p-H(2) molecules in the cavity of C(70). The energy of the global minimum on the intermolecular potential energy surface (PES) is negative for one and two H(2) molecules in C(70) but has a high positive value when the third H(2) is added, implying that at most two H(2) molecules can be stabilized inside C(70). By the same criterion, in the case of C(60), only the endohedral complex with one H(2) molecule is energetically stable. Our results are consistent with the fact that recently both (H(2))(n)@C(70) (n = 1, 2) and H(2)@C(60) were prepared, but not (H(2))(3)@C(70) or (H(2))(2)@C(60). The ZPE of the coupled T-R motions, from the DMC calculations, grows rapidly with the number of caged p-H(2) molecules and is a significant fraction of the well depth of the intermolecular PES, 11% in the case of p-H(2)@C(70) and 52% for (p-H(2))(2)@C(70). Consequently, the T-R ZPE represents a major component of the energetics of the encapsulated H(2) molecules. The inclusion of the ZPE nearly doubles the energy by which (p-H(2))(3)@C(70) is destabilized and increases by 66% the energetic destabilization of (p-H(2))(2)@C(60). For these reasons, the T-R ZPE has to be calculated accurately and taken into account for reliable theoretical predictions regarding the stability of the endohedral fullerene complexes with hydrogen molecules and their maximum H(2) content.

Coupled Translation-Rotation Eigenstates of H2, HD, and D2 in the Large Cage of Structure II Clathrate Hydrate: Comparison with the Small Cage and Rotational Raman Spectroscopy †

We report fully coupled quantum five-dimensional calculations of the translation-rotation (T-R) energy levels of one H(2), HD, and D(2) molecule confined inside the large hexakaidecahedral (5(12)6(4)) cage of the structure II clathrate hydrate. Highly converged T-R eigenstates have been obtained for excitation energies beyond the j = 2 rotational levels of the guest molecules, in order to allow comparison with the recent Raman spectroscopic measurements. The translationally excited T-R states are assigned with the quantum numbers n and l of the 3D isotropic harmonic oscillator. However, the translational excitations are not harmonic, since the level energies depend not only on n but also on l. For l > 1, the T-R levels having the same n,l values are split into groups of almost degenerate levels. The splitting patterns follow the predictions of group theory for the environment of T(d) symmetry, which is created by the configuration of the oxygen atoms of the large cage. The 2j + 1 degeneracy of the j = 1 and 2 rotational levels of the encapsulated hydrogen molecule is lifted entirely by the angular anisotropy of the H(2)-cage interaction potential. The patterns and magnitudes of the j = 1, 2 rotational level splittings, and the energies of the sublevels, in the large cage are virtually identical with those calculated for the small cage. This is in agreement with, and sheds light on, the observation that the S(0)(0) (j = 0-->2) bands in the rotational Raman spectra measured for simple H(2) hydrate and the binary hydrate of H(2) with tetrahydrofuran are remarkably similar with respect to their frequencies, widths, shapes, and internal structure, when the H(2) occupancy of the large cage of simple H(2) hydrate is low.

Neutron Scattering Measurements and Computation of the Quantum Dynamics of Hydrogen Molecules Trapped in the Small and Large Cages of Clathrate Hydrates

We report inelastic neutron scattering (INS) measurements on molecular hydrogen trapped in simple (D2O) and binary (D2O plus perdeuterated tetrahydrofuran) clathrate hydrates, performed at a low temperature using two different neutron spectrometers to probe both energy and momentum transfer. The INS spectra of binary clathrate samples exhibit a rich structure containing sharp bands arising from both the rotational transitions and the rattling modes of the guest H2 molecule. They agree well with the rigorous fully quantum simulations, which account for the subtle effects of the anisotropy, angular and radial, of the host cage on the H2 microscopic dynamics and the resulting spectra. The simple clathrate samples present a much greater challenge, due to the multiple H2 occupancy of the large cages, which makes the quantum calculations an extremely difficult task. In addition, we discuss in detail various physical aspects of the experimental and simulated INS spectra, such as their temperature dependence, the effects of the cage geometry, and the different features associated with the ortho-hydrogen and para-hydrogen species.

Inelastic neutron scattering spectrum of H2@C60 and its temperature dependence decoded using rigorous quantum calculations and a new selection rule

In the supramolecular complex H2@C60, the lightest of molecules, H2, is encapsulated inside the most highly symmetric molecule C60. The elegance and apparent simplicity of H2@C60 conceal highly intricate quantum dynamics of the coupled translational and rotational motions of the guest molecule in a nearly spherical nanoscale cavity, which embodies some of the most fundamental concepts of quantum mechanics. Here we present the first rigorous and highly accurate quantum calculations of the inelastic neutron scattering (INS) spectra of this prototypical endohedral fullerene complex and their temperature dependence. The calculations enable complete assignment of the recently reported experimental INS spectra of H2@C60 measured at several temperatures. We also derive a new and unexpected selection rule for the INS spectroscopy of H2 in a near-spherical confinement, which explains why the INS transitions between certain translation-rotation eigenstates of H2 in C60 have zero intensity and do not appear in the spectra.

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.

ArnHF van der Waals clusters revisited : II. Energetics and HF vibrational frequency shifts from diffusion Monte Carlo calculations on additive and nonadditive potential-energy surfaces for n=1-12.

The ground-state energies and HF vibrational frequency shifts of Ar(n)HF clusters have been calculated on the nonadditive potential-energy surfaces (PESs) for n=2-7 and on the pairwise-additive PESs for the clusters with n=1-12, using the diffusion Monte Carlo (DMC) method. For n>3, the calculations have been performed for the lowest-energy isomer and several higher-lying isomers which are the closest in energy. They provide information about the isomer dependence of the HF redshift, and enable direct comparison with the experimental data recently obtained in helium nanodroplets. The agreement between theory and experiment is excellent, in particular, for the nonadditive DMC redshifts. The relative, incremental redshifts are reproduced accurately even at the lower level of theory, i.e., the DMC and quantum five-dimensional (rigid Ar(n)) calculations on the pairwise-additive PESs. The nonadditive interactions make a significant contribution to the frequency shift, on the order of 10%-12%, and have to be included in the PESs in order for the theory to yield accurate magnitude of the HF redshift. The energy gaps between the DMC ground states of the cluster isomers are very different from the energy separation of their respective minima on the PES, due to the considerable variations in the intermolecular zero-point energy of different Ar(n)HF isomers.