H2O inside the fullerene C60: Inelastic neutron scattering spectrum from rigorous quantum calculations.

We present a methodology that, for the first time, allows rigorous quantum calculation of the inelastic neutron scattering (INS) spectra of a triatomic molecule in a nanoscale cavity, in this case, H2O inside the fullerene C60. Both moieties are taken to be rigid. Our treatment incorporates the quantum six-dimensional translation-rotation (TR) wave functions of the encapsulated H2O, which serve as the spatial parts of the initial and final states of the INS transitions. As a result, the simulated INS spectra reflect the coupled TR dynamics of the nanoconfined guest molecule. They also exhibit the features arising from symmetry breaking observed for solid H2O@C60 at low temperatures. Utilizing this methodology, we compute the INS spectra of H2O@C60 for two incident neutron wavelengths and compare them with the corresponding experimental spectra. Good overall agreement is found, and the calculated spectra provide valuable additional insights.

The Endofullerene HF@C60: Inelastic Neutron Scattering Spectra from Quantum Simulations and Experiment, Validity of the Selection Rule, and Symmetry Breaking.

Accurate quantum simulations of the low-temperature inelastic neutron scattering (INS) spectra of HF@C60 are reported for two incident neutron wavelengths. They are distinguished by the rigorous inclusion of symmetry-breaking effects in the treatment and having the spectra computed with HF as the guest, rather than H2 or HD, as in the past work. The results demonstrate that the precedent-setting INS selection rule, originally derived for H2 and HD in near-spherical nanocavities, applies also to HF@C60, despite the large mass asymmetry of HF and the strongly mixed character of its translation-rotation eigenstates. This lends crucial support to the theoretical prediction made earlier that the INS selection rule is valid for any diatomic molecule in near-spherical nanoconfinement. The selection rule remains valid in the presence of symmetry breaking but is modified slightly in an interesting way. Comparison is made with the recently published experimental INS spectrum of HF@C60. The agreement is very good, apart from one peak for which our calculations suggest a reassignment. This reassignment is consistent with the measured INS spectrum presented in this work, which covers an extended energy range.

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.

General Selection Rule in the Inelastic Neutron Scattering Spectroscopy of a Diatomic Molecule Confined Inside a Near-Spherical Nanocavity.

Knowledge of the relevant selection rules is crucial for the accurate interpretation of experimental spectra in general. There has been a consensus for a long time that the incoherent inelastic neutron scattering (INS) spectroscopy of the vibrations of discrete molecular compunds is free from any selection rules. We contradict this widely held view by presenting an analytical derivation of the general selection rule for the INS spectroscopy of a hydrogen molecule inside a near-spherical nanocavity. It defines all forbidden transitions, originating in a range of initial translation-rotation (TR) states, ground and excited, of the caged para- and ortho-H2, as well as HD, that are unobservable in the INS spectra. These predictions are amenable to experimental verification. In addition, we demonstrate that the general selection rule applies to the INS spectroscopy of any diatomic molecule in a nanocavity with near-spherical symmetry, which exhibits strong TR coupling. Its existence strongly suggests that similar selection rules apply to the INS spectra of other molecular and supramolecular systems, and need to be identified.

The HD molecule in small and medium cages of clathrate hydrates: quantum dynamics studied by neutron scattering measurements and computation.

We report inelastic neutron scattering (INS) measurements on molecular hydrogen deuteride (HD) trapped in binary cubic (sII) and hexagonal (sH) clathrate hydrates, performed at low temperature using two different neutron spectrometers in order 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 molecule. For the clathrates with sII structure, there is a very good agreement with the rigorous fully quantum simulations which account for the subtle effects of the anisotropy, angular and radial, of the host cage on the HD microscopic dynamics. The sH clathrate sample presents a much greater challenge, due to the uncertainties regarding the crystal structure, which is known only for similar crystals with different promoter, but nor for HD (or H2) plus methyl tert-butyl ether (MTBE-d12).

Confirming a predicted selection rule in inelastic neutron scattering spectroscopy: the quantum translator-rotator H2 entrapped inside C60.

We report an inelastic neutron scattering (INS) study of a H2 molecule encapsulated inside the fullerene C60 which confirms the recently predicted selection rule, the first to be established for the INS spectroscopy of aperiodic, discrete molecular compounds. Several transitions from the ground state of para-H2 to certain excited translation-rotation states, forbidden according to the selection rule, are systematically absent from the INS spectra, thus validating the selection rule with a high degree of confidence. Its confirmation sets a precedent, as it runs counter to the widely held view that the INS spectroscopy of molecular compounds is not subject to any selection rules.

Experimental inelastic neutron scattering spectrum of hydrogen hexagonal clathrate-hydrate compared with rigorous quantum simulations.

We have performed high-resolution inelastic neutron scattering (INS) measurements on binary hydrogen clathrate hydrates exhibiting the hexagonal structure (sH). Two samples, differing only in the ortho/para fraction of hydrogen, were prepared using heavy water and methyl tert-butyl ether as the promoter in its perdeuterated form. The INS spectrum of the translation-rotation (TR) excitations of the guest H2 molecule was obtained by subtracting the very weak signal due to the D2O lattice modes. By means of a subtraction procedure, it has been possible to obtain separately the spectra of caged p-H2 and o-H2. sH clathrates are comprised of three distinct types of cages, two of which, differing in shape and size, are each occupied by one H2 molecule only. Both contribute to the measured INS spectrum which is, therefore, rather complex and challenging to assign unambiguously. To assist with the interpretation, the INS spectra are calculated accurately utilizing the quantum methodology which incorporates the coupled five-dimensional TR energy levels and wave functions of the H2 molecule confined in each type of nanocage. The computed INS spectra are highly realistic and reflect the complexity of the coupled TR dynamics of the guest H2 in the anisotropic confining environment. The simulated INS spectra of p-H2 and o-H2 in the small and medium cages are compared with the experimental data, and are indispensable for their interpretation.

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.

Infrared spectroscopy of small-molecule endofullerenes.

Hydrogen is one of the few molecules that has been incarcerated in the molecular cage of C60 to form the endohedral supramolecular complex H2@C60. In this confinement, hydrogen acquires new properties. Its translation motion, within the C60 cavity, becomes quantized, is correlated with its rotation and breaks inversion symmetry that induces infrared (IR) activity of H2. We apply IR spectroscopy to study the dynamics of hydrogen isotopologues H2, D2 and HD incarcerated in C60. The translation and rotation modes appear as side bands to the hydrogen vibration mode in the mid-IR part of the absorption spectrum. Because of the large mass difference of hydrogen and C60 and the high symmetry of C60 the problem is almost identical to a vibrating rotor moving in a three-dimensional spherical potential. We derive potential, rotation, vibration and dipole moment parameters from the analysis of the IR absorption spectra. Our results were used to derive the parameters of a pairwise additive five-dimensional potential energy surface for H2@C60. The same parameters were used to predict H2 energies inside C70. We compare the predicted energies and the low-temperature IR absorption spectra of H2@C70.

H2 in solid C60: coupled translation-rotation eigenstates in the octahedral interstitial site from quantum five-dimensional calculations.

We report rigorous quantum five-dimensional (5D) calculations of the coupled translation-rotation (TR) energy levels and wave functions of an H2 molecule, in the ground (ν = 0) and vibrationally excited (ν = 1) states, confined inside the octahedral interstitial site of solid C60 with S6 symmetry. Translational and rotational excitations of H2 in this nanocavity have been measured by the inelastic neutron scattering (INS) and infrared (IR) spectroscopy, enabling direct comparison between theory and experiment. A pairwise additive 5D intermolecular potential energy surface (PES) was employed in the calculations. The quantum calculations cover the range of energies and types of translational and rotational excitations of the guest molecule which go substantially beyond those considered in the earlier theoretical investigations of this system, revealing new information about the TR energy level structure. The computed j = 1 and j = 2 rotational levels and their splittings, as well as the translational fundamental, are in semi-quantitative agreement with the available INS and IR data, indicating the need for a more accurate intermolecular PES. Our calculations reveal a strong dependence of the TR energy levels, in particular their splittings, on the setting angle which defines the orientation of the C60 molecules relative to their local threefold axes.

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.

Quantum dynamics of a hydrogen molecule inside an anisotropic open-cage fullerene: coupled translation-rotation eigenstates and comparison with inelastic neutron scattering spectroscopy.

We report rigorous quantum five-dimensional (5D) calculations of the translation-rotation (T-R) energy levels and wave functions of H(2) inside aza-thia-open-cage fullerene (ATOCF). Translational and rotational excitations of this endohedral complex have been measured in a recent inelastic neutron scattering (INS) study, enabling direct comparison between theory and experiment. ATOCF has no symmetry, and therefore the intermolecular potential energy surface (PES) governing the T-R dynamics of H(2) is strongly anisotropic. A pairwise additive PES is employed in the calculations. Inspection of the wave functions shows three regular quasi-1D translational modes aligned with the Cartesian x, y, and z axes, respectively. These and other translational excitations can be assigned with the Cartesian quantum numbers v(x), v(y), and v(z). The radial anisotropy of the cage environment causes the splitting of the translational fundamental into three excitations whose frequencies differ substantially; the z mode directed toward the ATOCF orifice has the lowest frequency and is the most anharmonic. All three translational modes exhibit negative anharmonicity. The j = 1 rotational level of H(2) is also split into a triplet, due to the angular anisotropy of the cage. The complete lifting of the degeneracies of the translational fundamental and the j = 1 triplet of the encapsulated H(2) molecule that emerges from the calculations is also observed in the INS spectra of H(2)@ATOCF. The calculated magnitudes of both splittings, as well as the energies of the individual sublevels, rotational and translational, are in good agreement with the INS data.

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.

Methane molecule confined in the small and large cages of structure I clathrate hydrate: Quantum six-dimensional calculations of the coupled translation-rotation eigenstates.

We report fully coupled quantum six-dimensional (6D) calculations of the translation-rotation (T-R) energy levels of CH(4) molecule inside the small dodecahedral (5(12)) and large tetracaidecahedral (5(12)6(2)) cages of the structure I clathrate hydrate. The quantum dynamics of the three translational and three rotational degrees of freedom of CH(4) are treated rigorously, while the guest molecule and the host cavities are taken to be rigid. The matrix of the full 6D T-R Hamiltonian is diagonalized in the product basis of contracted translational and angular basis functions, generated by solving two reduced-dimension (3D) eigenvalue problems. A pairwise additive CH(4)-cage 6D potential energy surface (PES) is employed, constructed using the anisotropic CH(4)-H(2)O pair potential which was utilized previously in the molecular dynamics simulations of methane hydrate. Our calculations elucidate the key features of the T-R energy level structure of the nanoconfined CH(4). The rotational levels of methane exhibit an elaborate pattern of splittings caused by the angular anisotropy of the environment; the splitting patterns are identical for both types of cages. Translationally excited T-R states in the small cage are assigned in terms of the quantum numbers n and l of the 3D isotropic harmonic oscillator and those in the large cage using the Cartesian quantum numbers. Extensive comparison is made with the data from the inelastic neutron scattering studies of methane hydrate, allowing an assessment of the accuracy of the 6D PES employed.

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.

Coupled translation-rotation eigenstates of H(2) in C(60) and C(70) 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 the vibrations of helium bound to the nanosurface of a large planar organic molecule: phthalocyanine . He van der Waals complex.

We report rigorous quantum three-dimensional calculations of highly excited intermolecular vibrational states of the van der Waals (vdW) complex phthalocyanine.He (Pc.He). The Pc molecule was treated as rigid and the intermolecular potential energy surface (IPES) was represented as a sum of atom-atom Lennard-Jones pair potentials. The IPES has four equivalent global minima on the diagonals of the square-shaped Pc, inside its five-membered rings, and four slightly shallower local minima between them, creating a distinctive corrugation pattern of the molecular nanosurface. The vdW vibrational states analyzed in this work extend to about two-thirds of the well depth of the IPES. For the assignment of the in-plane (xy) vdW vibrational excitations it was necessary to resort to two sets of quantum numbers, the Cartesian quantum numbers [nu(x), nu(y)] and the quantum numbers (v, l) of the 2D isotropic oscillator, depending on the nodal structure and the symmetry of the wave functions. The delocalization of the He atom parallel to the molecular surface is large already in the ground vdW state. It increases rapidly with the number of quanta in the in-plane vdW vibrations, with the maximum root-mean-square amplitudes Deltax and Deltay of about 7 au at the excitation energies around 40 cm(-1). The wave functions of the highly excited states tend to be delocalized over the entire nanosurface and often have a square shape, reflecting that of the substrate.

H2, HD, and D2 inside C60: coupled translation-rotation eigenstates of the endohedral molecules from quantum five-dimensional calculations.

We have performed rigorous quantum five-dimensional (5D) calculations of the translation-rotation (T-R) energy levels and wave functions of H(2), HD, and D(2) inside C(60). This work is an extension of our earlier investigation of the quantum T-R dynamics of H(2)@C(60) [M. Xu et al., J. Chem. Phys. 128, 011101 (2008)] and uses the same computational methodology. Two 5D intermolecular potential energy surfaces (PESs) were employed, differing considerably in their well depths and the degree of confinement of the hydrogen molecule. Our calculations revealed pronounced sensitivity of the endohedral T-R dynamics to the differences in the interaction potentials, and to the large variations in the masses and the rotational constants of H(2), HD, and D(2). The T-R levels vary significantly in their energies and ordering on the two PESs, as well as from one isotopomer to another. Nevertheless, they all display the same distinctive patterns of degeneracies, which can be qualitatively understood and assigned in terms the model which combines the isotropic three-dimensional harmonic oscillator, the rigid rotor, and the coupling between the orbital and the rotational angular momenta of H(2)/HD/D(2). The quantum number j associated with the rotation of H(2), HD, and D(2) was found to be a good quantum number for H(2) and D(2) on both PESs, while most of the T-R levels of HD exhibit strong mixing of two or more rotational basis functions with different j values.

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.