HCl trimer: HCl-stretch excited intramolecular and intermolecular vibrational states from 12D fully coupled quantum calculations employing contracted intra- and inter-molecular bases.

We present fully coupled, full-dimensional quantum calculations of the inter- and intra-molecular vibrational states of HCl trimer, a paradigmatic hydrogen-bonded molecular trimer. They are performed utilizing the recently developed methodology for the rigorous 12D quantum treatment of the vibrations of the noncovalently bound trimers of flexible diatomic molecules [Felker and Bacic, J. Chem. Phys. 158, 234109 (2023)], which was previously applied to the HF trimer by us. In this work, the many-body 12D potential energy surface (PES) of (HCl)3 [Mancini and Bowman, J. Phys. Chem. A 118, 7367 (2014)] is employed. The calculations extend to the intramolecular HCl-stretch excited vibrational states of the trimer with one- and two-quanta, together with the low-energy intermolecular vibrational states in the two excited v = 1 intramolecular vibrational manifolds. They reveal significant coupling between the intra- and inter-molecular vibrational modes. The 12D calculations also show that the frequencies of the v = 1 HCl stretching states of the HCl trimer are significantly redshifted relative to those of the isolated HCl monomer. Detailed comparison is made between the results of the 12D calculations on the two-body PES, obtained by removing the three-body term from the original 2 + 3-body PES, and those computed on the 2 + 3-body PES. It demonstrates that the three-body interactions have a strong effect on the trimer binding energy as well as on its intra- and inter-molecular vibrational energy levels. Comparison with the available spectroscopic data shows that good agreement with the experiment is achieved only if the three-body interactions are included. Some low-energy vibrational states localized in a secondary minimum of the PES are characterized as well.

H2O-HCN complex: A new potential energy surface and intermolecular rovibrational states from rigorous quantum calculations.

In this work the H2O-HCN complex is quantitatively characterized in two ways. First, we report a new rigid-monomer 5D intermolecular potential energy surface (PES) for this complex, calculated using the symmetry-adapted perturbation theory based on density functional theory method. The PES is based on 2833 ab initio points computed employing the aug-cc-pVQZ basis set, utilizing the autoPES code, which provides a site-site analytical fit with the long-range region given by perturbation theory. Next, we present the results of the quantum 5D calculations of the fully coupled intermolecular rovibrational states of the H2O-HCN complex for the total angular momentum J values of 0, 1, and 2, performed on the new PES. These calculations rely on the quantum bound-state methodology developed by us recently and applied to a variety of noncovalently bound binary molecular complexes. The vibrationally averaged ground-state geometry of H2O-HCN determined from the quantum 5D calculations agrees very well with that from the microwave spectroscopic measurements. In addition, the computed ground-state rotational transition frequencies, as well as the B and C rotational constants calculated for the ground state of the complex, are in excellent agreement with the experimental values. The assignment of the calculated intermolecular vibrational states of the H2O-HCN complex is surprisingly challenging. It turns out that only the excitations of the intermolecular stretch mode can be assigned with confidence. The coupling among the angular degrees of freedom (DOFs) of the complex is unusually strong, and as a result most of the excited intermolecular states are unassigned. On the other hand, the coupling of the radial, intermolecular stretch mode and the angular DOFs is weak, allowing straightforward assignment of the excitation of the former.

HF trimer: 12D fully coupled quantum calculations of HF-stretch excited intramolecular and intermolecular vibrational states using contracted bases of intramolecular and intermolecular eigenstates.

We present the computational methodology, which for the first time allows rigorous twelve-dimensional (12D) quantum calculations of the coupled intramolecular and intermolecular vibrational states of hydrogen-bonded trimers of flexible diatomic molecules. Its starting point is the approach that we introduced recently for fully coupled 9D quantum calculations of the intermolecular vibrational states of noncovalently bound trimers comprised of diatomics treated as rigid. In this paper, it is extended to include the intramolecular stretching coordinates of the three diatomic monomers. The cornerstone of our 12D methodology is the partitioning of the full vibrational Hamiltonian of the trimer into two reduced-dimension Hamiltonians, one in 9D for the intermolecular degrees of freedom (DOFs) and another in 3D for the intramolecular vibrations of the trimer, and a remainder term. These two Hamiltonians are diagonalized separately, and a fraction of their respective 9D and 3D eigenstates is included in the 12D product contracted basis for both the intra- and intermolecular DOFs, in which the matrix of the full 12D vibrational Hamiltonian of the trimer is diagonalized. This methodology is implemented in the 12D quantum calculations of the coupled intra- and intermolecular vibrational states of the hydrogen-bonded HF trimer on an ab initio calculated potential energy surface (PES). The calculations encompass the one- and two-quanta intramolecular HF-stretch excited vibrational states of the trimer and low-energy intermolecular vibrational states in the intramolecular vibrational manifolds of interest. They reveal several interesting manifestations of significant coupling between the intra- and intermolecular vibrational modes of (HF)3. The 12D calculations also show that the frequencies of the v = 1, 2 HF stretching states of the HF trimer are strongly redshifted in comparison to those of the isolated HF monomer. Moreover, the magnitudes of these trimer redshifts are much larger than that of the redshift for the stretching fundamental of the donor-HF moiety in (HF)2, most likely due to the cooperative hydrogen bonding in (HF)3. The agreement between the 12D results and the limited spectroscopic data for the HF trimer, while satisfactory, leaves room for improvement and points to the need for a more accurate PES.

Intermolecular vibrational states of HF trimer from rigorous nine-dimensional quantum calculations: Strong coupling between intermolecular bending and stretching vibrations and the importance of the three-body interactions.

We present the computational methodology that allows rigorous and efficient nine-dimensional (9D) quantum calculations of the intermolecular vibrational states of noncovalently bound trimers of diatomic molecules, with the monomers treated as rigid. The full 9D vibrational Hamiltonian of the trimer is partitioned into a 3D "frame" (or stretching) Hamiltonian and a 6D "bend" Hamiltonian. These two Hamiltonians are diagonalized separately, and a certain number of their lowest-energy eigenstates is included in the final 9D product contracted basis in which the full 9D intermolecular vibrational Hamiltonian is diagonalized. This methodology is applied to the 9D calculations of the intermolecular vibrational levels of (HF)3, a prototypical hydrogen-bonded trimer, on the rigid-monomer version of an ab initio calculated potential energy surface (PES). They are the first to include fully the stretch-bend coupling present in the trimer. The frequencies of all bending fundamentals considered from the present 9D calculations are about 10% lower than those from the earlier quantum 6D calculations that considered only the bending modes of the HF trimer. This means that the stretch-bend coupling is strong, and it is imperative to include it in any accurate treatment of the (HF)3 vibrations aiming to assess the accuracy of the PES employed. Moreover, the 9D results are in better agreement with the limited available spectroscopic data that those from the 6D calculations. In addition, the 9D results show sensitivity to the value of the HF bond length, equilibrium or vibrationally averaged, used in the calculations. The implication is that full-dimensional 12D quantum calculations will be required to obtain definitive vibrational excitation energies for a given PES. Our study also demonstrates that the nonadditive three-body interactions are very significant in (HF)3 and have to be included in order to obtain accurate intermolecular vibrational energy levels of the trimer.

Noncovalently bound molecular complexes beyond diatom-diatom systems: full-dimensional, fully coupled quantum calculations of rovibrational states.

The methodological advances made in recent years have significantly extended the range and dimensionality of noncovalently bound, hydrogen-bonded and van der Waals, molecular complexes for which full-dimensional and fully coupled quantum calculations of their rovibrational states are feasible. They exploit the unexpected implication that the weak coupling between the inter- and intramolecular rovibrational degrees of freedom (DOFs) of the complexes has for the ease of computing the high-energy eigenstates of the latter. This is done very effectively by using contracted eigenstate bases to cover both intra- and intermolecular DOFs. As a result, it is now possible to calculate rigorously all intramolecular rovibrational fundamentals, together with the low-lying intermolecular rovibrational states, of complexes involving two small molecules beyond diatomics, binary polyatomic molecule-large (rigid) molecule complexes, and endohedral complexes of light polyatomic molecules confined inside (rigid) fullerene cages. In this Perspective these advances are reviewed in considerable depth. The progress made thanks to them is illustrated by a number of representative applications. Whenever possible, direct comparison is made with the available infrared, far-infrared, and microwave spectroscopic data.

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.

Intermolecular rovibrational states of the H2O-CO2 and D2O-CO2 van der Waals complexes.

We present quantum five-dimensional bound-state calculations of the fully coupled intermolecular rovibrational states of H2O-CO2 and D2O-CO2 van der Waals (vdW) complexes in the rigid-monomer approximation for the total angular momentum J values of 0, 1, and 2. A rigid-monomer version of the recent ab initio full-dimensional (12D) potential energy surface of H2O-CO2 [Q. Wang and J. M. Bowman, J. Chem. Phys. 147, 161714 (2017)] is employed. This treatment provides for the first time a rigorous and comprehensive description of the intermolecular rovibrational level structure of the two isotopologues that includes the internal-rotation tunneling splittings and their considerable sensitivity to rotational and intermolecular vibrational excitations, as well as the rotational constants of the two vdW complexes. Two approaches are used in the calculations, which differ in the definition of the dimer-fixed (DF) frame and the coordinates associated with them. We demonstrate that with the approach introduced in this work, where the DF frame is fixed to the CO2 moiety, highly accurate results are obtained using significantly smaller basis sets in comparison to those for the alternative approach. In addition, the resulting wavefunctions tend to lend themselves better to physical interpretation and assignment. The H2O-CO2 ground-state internal-rotation tunneling splittings, the rotational transition frequencies, and the rotational constants of both vdW complexes are in excellent agreement with the experimental results. The calculated intermolecular vibrational fundamentals agree well with the scant terahertz spectroscopy data for these complexes in cryogenic neon matrices.

DCl-H2O, HCl-D2O, and DCl-D2O Dimers: Inter- and Intramolecular Vibrational States and Frequency Shifts from Fully Coupled Quantum Calculations on a Full-Dimensional Neural Network Potential Energy Surface.

We report full-dimensional and fully coupled quantum calculations of the inter- and intramolecular vibrational states of three isotopologues of the hydrogen chloride-water dimer: DCl-H2O (DH), HCl-D2O (HD), and DCl-D2O (DD). The present study extends our recent theoretical investigation of the nine-dimensional (9D) vibrational level structure of the HCl-H2O (HH) dimer [Liu, Y.; Li, J.; Felker, P. M.; Bacic, Z. Phys. Chem. Chem. Phys. 2021, 23, 7101-7114]. It employs the same accurate 9D permutation invariant polynomial-neural network potential energy surface and the highly efficient bound-state methodology. The objective of this work is to elucidate the isotopologue variations of a range of bound-state properties of the hydrogen chloride-water dimer and compare them to those of the HH dimer. In order to achieve this, for the isotopologues considered, the rigorous 9D quantum calculations performed encompass all intramolecular vibrational fundamentals, and their frequency shifts relative to the isolated monomer values, together with the low-lying intermolecular vibrational states in each of the intramolecular vibrational manifolds of interest. Moreover, for the ground state of each isotopologue, several informative vibrationally averaged intermolecular geometric properties of the dimer are computed, as well as the three rotational constants. The energies of the intermolecular inversion and rock modes, which mainly involve the motions of the water moiety, differ greatly for H2O and D2O, but are much less sensitive to whether the hydrogen chloride isotopologue is HCl or DCl. On the other hand, the excitation of the HCl/DCl stretch changes significantly the energies of the water inversion and rock modes. The DCl stretch frequency shift computed in 9D for the DD dimer, -114.91 cm-1, agrees extremely well with the corresponding experimental value of -115.20 cm-1 measured by Saykally and co-workers.

HCl-H2O dimer: an accurate full-dimensional potential energy surface and fully coupled quantum calculations of intra- and intermolecular vibrational states and frequency shifts.

The interaction between HCl and H2O is of considerable theoretical and experimental interest due to its important role in atmospheric chemistry and understanding the onset of the dissociation of HCl in water. In this work, the HCl-H2O complex is quantitatively characterized in two ways. First, we report a new full-dimensional potential energy surface (PES) for the HCl + H2O system. The nine-dimensional (9D) PES is based on circa 43 000 ab initio points calculated at the level of CCSD(T)-F12a/AVTZ with the basis set superposition error correction using the permutation invariant polynomial-neural network method, which can accurately and efficiently reproduce the geometries, energies, frequencies of the complex of HCl with H2O, as well as the relevant minimum energy path. Next, we present the results of the first fully coupled 9D quantum calculations of the intra- and intermolecular vibrational states of the HCl-H2O dimer, performed on the new PES. They employ the highly efficient bound-state methodology previously used to compute accurately the rovibrational level structure of the H2O/D2O-CO and HDO-CO complexes [P. M. Felker and Z. Bacic, J. Chem. Phys., 2020, 153, 074107; J. Phys. Chem. A, 2021, 125, 980]. The 9D calculations characterize the vibrationally averaged nonplanar ground-state geometry of the HCl-H2O complex, the intramolecular vibrational fundamentals of both H2O and HCl moieties, and their frequency shifts, as well as the low-energy intermolecular vibrational states in each of the intramolecular vibrational manifolds and the effects of the coupling between the two sets of modes. The calculated properties of the HCl-H2O dimer are in excellent agreement with the available spectroscopic data. The 9D computed dimer binding energy D0 of 1334.63 cm-1 agrees extremely well with the experimental D0 equal to 1334 ± 10 cm-1 [B. E. Casterline and A. K. Mollner and L. C. Ch'ng and H. Reisler, J. Chem. Phys., 2010, 114, 9774]. Moreover, the ground-state expectation value of the out-of-plane bend angle of H2O, 33.80°, and the computed HCl stretch frequency shift, -157.9 cm-1, both from the 9D calculations, are in very good accord with the corresponding experimental values.

HDO-CO Complex: D-Bonded and H-Bonded Isomers and Intra- and Intermolecular Rovibrational States from Full-Dimensional and Fully Coupled Quantum Calculations.

We report full-dimensional and fully coupled quantum bound-state calculations of the J = 0, 1 intra- and intermolecular rovibrational states of the isotopically asymmetric HDO-CO complex. They are performed on the ab initio nine-dimensional (9D) potential energy surface (PES) [Liu, Y.; Li, J. Phys. Chem. Chem. Phys. 2019, 21, 24101]. The present study complements our earlier theoretical investigation of the 9D rovibrational level structure of the H2O-CO and D2O-CO complexes [Felker, P. M.; Bacic, Z. J. Chem. Phys. 2020, 153, 074107]. What distinguishes HDO-CO is that, unlike the two isotopically symmetric isotopologues, it does not display hydrogen-interchange tunneling but has two distinct isomers, the lower-energy D-bonded HOD-CO and the higher-energy H-bonded DOH-CO. The highly efficient methodology employed in the present calculations derives from our earlier study referenced above, taking into account the lower symmetry of HDO-CO. The full 9D rovibrational Hamiltonian is partitioned into three reduced-dimension Hamiltonians: the 5D rigid-monomer intermolecular vibrational Hamiltonian and two intramolecular vibrational Hamiltonians, one for the HDO monomer (3D) and another for the CO monomer (1D), and a 9D remainder term. The reduced-dimension Hamiltonians are diagonalized separately, and small portions of their low-energy eigenstates are incorporated in the compact final 9D product contracted basis covering all internal, intra- and intermolecular degrees of freedom of the complex. The 9D rovibrational Hamiltonian is diagonalized in this fully contracted basis. The calculations show that the eigenstates belonging to the D-bonded and H-bonded isomers, designated as D and H, respectively, are easy to identify, owing to the near-complete localization of their wave functions in either of the two minima on the PES. The computed intramolecular vibrational frequencies of the two monomers are either blue- or red-shifted, depending on the mode. The excitations of the intramolecular vibrational modes affect the energies of the low-lying D and H intermolecular vibrational states in the respective intramolecular manifolds. Comparison is made with the experimental data available in the literature.

H2O-CO and D2O-CO complexes: Intra- and intermolecular rovibrational states from full-dimensional and fully coupled quantum calculations.

We present efficient yet rigorous, full-dimensional quantum bound-state calculations of the fully coupled J = 0 and one intra- and intermolecular rovibrational levels of H2O-CO and D2O-CO complexes. The new ab initio nine-dimensional (9D) potential energy surface (PES) [Y. Liu and J. Li, Phys. Chem. Chem. Phys. 21, 24101 (2019)] is employed. In the spirit of the recently introduced general procedure [P. M. Felker and Z. Bacic, J. Chem. Phys. 151, 024305 (2019)], the 9D rovibrational Hamiltonian is partitioned into a 5D (rigid-monomer) intermolecular Hamiltonian, two intramolecular vibrational Hamiltonians-one for the water monomer (3D) and another for the CO monomer (1D), and a 9D remainder term. The low-energy eigenstates of the three reduced-dimension Hamiltonians are used to build up the 9D product contracted basis, in which the matrix of the full rovibrational Hamiltonian is diagonalized. In line with the findings of our earlier study referenced above, the 5D intermolecular eigenstates included in the 9D bases extend up to at most 230 cm-1 above the lowest-energy state of the given parity, much less than the intramolecular fundamentals of the two complexes that span the range of energies from about 1200 cm-1 to 3800 cm-1. The resulting Hamiltonian matrices are small for the 9D quantum problem considered, ≈ 10 000 for J = 0 and 13 500 for J = 1 calculations, allowing for direct diagonalization. The 9D calculations permit exploring a number of features of the rovibrational level structure of H2O-CO and D2O-CO that are beyond the quantum 5D rigid-monomer treatments reported to date. These include the differences in the magnitudes of the hydrogen-exchange tunneling splittings computed in 9D and 5D, the sensitivity of the tunneling splittings to the intramolecular vibrational excitation, the frequency shifts of the intramolecular vibrational modes, which, depending on the mode, can be either blue- or redshifts, and the effects of the excitation of the intramolecular fundamentals on the low-lying intermolecular eigenstates. Also examined is the extent of the eigenstate delocalization over the two minima on the PES. Whenever possible, a comparison is made with the experimental data in the literature.

Benzene-H2O and benzene-HDO: Fully coupled nine-dimensional quantum calculations of flexible H2O/HDO intramolecular vibrational excitations and intermolecular states of the dimers, and their infrared and Raman spectra using compact bases.

We present a rigorous and comprehensive theoretical treatment of the vibrational dynamics of benzene-H2O and benzene-HDO dimers, where the quantum bound-state calculations of the coupled intra- and intermolecular vibrational states of the dimers are complemented by the quantum simulations of their infrared (IR) and Raman spectra utilizing the computed eigenstates. Apart from taking benzene to be rigid, the methodology for the nine-dimensional (9D) vibrational quantum calculations introduced in this study is fully coupled. The approach yields the intramolecular vibrational fundamentals and the bend (ν2) overtone of H2O and HDO in the complex, together with the low-lying intermolecular vibrational states in each of the intramolecular vibrational manifolds considered. Following the recently introduced general procedure [P. M. Felker and Z. Bacic, J. Chem. Phys. 151, 024305 (2019)], the full 9D vibrational Hamiltonian of the dimer is divided into a 6D intermolecular Hamiltonian, a 3D intramolecular Hamiltonian, and a 9D remainder term. A 9D contracted product basis is constructed from the low-energy eigenstates of the two reduced-dimension Hamiltonians, and the full vibrational dimer Hamiltonian is diagonalized in it. The symmetry present in the dimers is exploited to reduce the Hamiltonian matrix to a block diagonal form. Guided by the findings of our earlier study referenced above, the 6D intermolecular contracted bases for each symmetry block include only 40 eigenstates with energies up to about 225 cm-1, far below the stretch and bend fundamentals of H2O and HDO, which range between 1400 cm-1 and 3800 cm-1. As a result, the matrices representing the symmetry blocks of the 9D Hamiltonian are small for the high-dimensional quantum problem, 1360 and 1680 for the H2O and HDO complexes, respectively, allowing for direct diagonalization. These calculations characterize in detail the H2O/HDO intramolecular vibrations, their frequency shifts, and couplings to the large-amplitude-motion intermolecular vibrational sates. The computed IR spectra of the two complexes in the OH-stretch region, as well as the intermolecular Raman spectra, are compared to the experimental spectra in the literature.

Flexible water molecule in C60: Intramolecular vibrational frequencies and translation-rotation eigenstates from fully coupled nine-dimensional quantum calculations with small basis sets.

We present a method for efficient calculation of intramolecular vibrational excitations of H2O inside C60, together with the low-energy intermolecular translation-rotation states within each intramolecular vibrational manifold. Apart from assuming rigid C60, this nine-dimensional (9D) quantum treatment is fully coupled. Following the recently introduced approach [P. M. Felker and Z. Bacic, J. Chem. Phys. 151, 024305 (2019)], the full 9D vibrational Hamiltonian of H2O@C60 is partitioned into two reduced-dimension Hamiltonians, a 6D one for the intermolecular vibrations and another in 3D for the intramolecular degrees of freedom, and a 9D remainder term. The two reduced-dimension Hamiltonians are diagonalized, and their eigenvectors are used to build up a product contracted basis in which the full vibrational Hamiltonian is diagonalized. The efficiency of this methodology derives from the insight of our earlier study referenced above that converged high-energy intramolecular vibrational excitations of weakly bound molecular complexes can be obtained from fully coupled quantum calculations where the full-dimensional product contracted basis includes only a small number of intermolecular vibrational eigenstates spanning the range of energies much below those of the intramolecular vibrational states of interest. In this study, the eigenstates included in the 6D intermolecular contacted basis extend to only 410 cm-1 above the ground state, which is much less than the H2O stretch and bend fundamentals, at ≈3700 and ≈1600 cm-1, respectively. The 9D calculations predict that the fundamentals of all three intramolecular modes, as well as the bend overtone, of the caged H2O are blueshifted relative to those of the gas-phase H2O, the two stretch modes much more so than the bend. Excitation of the bend mode affects the energies of the low-lying H2O rotational states significantly more than exciting either of the stretching modes. The center-of-mass translational fundamental is virtually unaffected by the excitation of any of the intramolecular vibrational modes. Further progress hinges on the experimental measurement of the vibrational frequency shifts in H2O@C60 and ab initio calculation of a high-quality 9D potential energy surface for this endohedral complex, neither of which is presently available.

Intramolecular stretching vibrational states and frequency shifts of (H2)2 confined inside the large cage of clathrate hydrate from an eight-dimensional quantum treatment using small basis sets.

We report the results of calculations pertaining to the HH intramolecular stretching fundamentals of (p-H2)2 encapsulated in the large cage of structure II clathrate hydrate. The eight-dimensional (8D) quantum treatment assumes rotationless (j = 0) H2 moieties and a rigid clathrate structure but is otherwise fully coupled. The (H2)2-clathrate interaction is constructed in a pairwise-additive fashion, by combining the ab initio H2-H2O pair potential for flexible H2 and rigid H2O [D. Lauvergnat et al., J. Chem. Phys. 150, 154303 (2019)] and the six-dimensional (6D) H2-H2 potential energy surface [R. J. Hinde, J. Chem. Phys. 128, 154308 (2008)]. The calculations are performed by first solving for the eigenstates of a reduced-dimension 6D "intermolecular" Hamiltonian extracted from the full 8D Hamiltonian by taking the H2 moieties to be rigid. An 8D contracted product basis for the solution of the full problem is then constructed from a small number of the lowest-energy 6D intermolecular eigenstates and two discrete variable representations covering the H2-monomer internuclear distances. Converged results are obtained already by including just the two lowest intermolecular eigenstates in the final 8D basis of dimension 128. The two HH vibrational stretching fundamentals are computed for three hydrate domains having an increasing number of H2O molecules. For the largest domain, the two fundamentals are found to be site-split by ∼0.5 cm-1 and to be redshifted by about 24 cm-1 from the free-H2 monomer stretch frequency, in excellent agreement with the experimental value of 26 cm-1. A first-order perturbation theory treatment gives results that are nearly identical to those of the 8D quantum calculations.

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.

Weakly bound molecular dimers: Intramolecular vibrational fundamentals, overtones, and tunneling splittings from full-dimensional quantum calculations using compact contracted bases of intramolecular and low-energy rigid-monomer intermolecular eigenstates.

We present a method for the efficient calculation of intramolecular vibrational frequencies, and their tunneling splittings, in weakly bound molecular dimers, together with the intermolecular vibrational states within each intramolecular vibrational manifold. The approach involves the partitioning of the dimer's vibrational Hamiltonian into two reduced-dimension Hamiltonians, a rigid-monomer one for the intermolecular vibrations and the other for all intramolecular vibrational degrees of freedom, and a remainder. The eigenstates of the two reduced-dimension Hamiltonians are used to build up a product contracted basis for the diagonalization of the full vibrational Hamiltonian. The key idea is that because of weak coupling between inter- and intra-molecular vibrational modes, the full-dimensional eigenstates in the low-energy portions of the manifolds associated with the intramolecular vibrational excitations can be computed accurately in a compact basis that includes a relatively small number of rigid-monomer intermolecular eigenstates, spanning a range of energies much below those of the intramolecular vibrational states of interest. In the application to the six-dimensional (6D) problem of (HF)2, we show that this approach produces results in excellent agreement with those in the literature, with a fraction of the basis states required by other methods. In fact, accurate energies of the intramolecular vibrational fundamentals and overtones are obtained using 6D bases that include 4D rigid-monomer intermolecular vibrational eigenstates extending to only 500-1000 cm-1, far below the HF-stretch fundamental of about 4000 cm-1. The method thus holds particular promise with respect to calculations on complexes with greater numbers of vibrational degrees of freedom.

Effects of symmetry breaking on the translation-rotation eigenstates of H2, HF, and H2O inside the fullerene C60.

Splittings of the translation-rotation (TR) eigenstates of the solid light-molecule endofullerenes M@C60 (M = H2, H2O, HF) attributed to the symmetry breaking have been observed in the infrared (IR) and inelastic neutron scattering spectra of these species in the past couple of years. In a recent paper [Felker et al., Phys. Chem. Chem. Phys., 2017, 19, 31274], we established that the electrostatic, quadrupolar interaction between the guest molecule M and the twelve nearest-neighbor C60 cages of the solid is the main source of the symmetry breaking. The splittings of the three-fold degenerate ground states of the endohedral ortho-H2, ortho-H2O and the j = 1 level of HF calculated using this model were found to be in excellent agreement with the experimental results. Utilizing the same electrostatic model, this theoretical study investigates the effects of the symmetry breaking on the excited TR eigenstates of the three species, and how they manifest in their simulated low-temperature (5-6 K) near-IR (NIR) and far-IR (FIR) spectra. The TR eigenstates are calculated variationally for both the major P and minor H crystal orientations. For the H orientation, the calculated splittings of all of the TR levels of these species are less than 0.1 cm-1. For the dominant P orientation, the splittings vary strongly depending on the character of the excitations involved. In all of the species, the splittings of the higher rotationally excited levels are comparable in magnitude to those for the j = 1 levels. For the levels corresponding to purely translational excitations, the calculated splittings are about an order of magnitude smaller than those of the purely rotational eigenstates. Based on the computed TR eigenstates, the low-temperature NIR (for M = H2) and FIR (for M = HF and H2O) spectra are simulated for both the P and H orientations, and also combined as their weighted sum (0.15H + 0.85P). The weighted sum spectra computed for M = H2 and HF match quantitatively the corresponding measured spectra, while for M = H2O, the weighted sum FIR spectrum predicts features that can potentially be observed experimentally.

Explaining the symmetry breaking observed in the endofullerenes H2@C60, HF@C60, and H2O@C60.

Symmetry breaking has been recently observed in the endofullerenes M@C60 (M = H2, HF, H2O), manifesting in the splittings of the three-fold degenerate ground states of the endohedral ortho-H2, ortho-H2O and the j = 1 level of HF. The nature of the interaction causing the symmetry breaking is established in this study. A fragment of the solid C60 is considered, comprised of the central C60 molecule surrounded by twelve nearest-neighbor (NN) C60 molecules. The fullerenes have either P (major) or H (minor) orientational orderings, and are assumed to be rigid with Ih symmetry. Only the central C60 is occupied by the guest molecule M, while the NN fullerenes are all empty. The key proposition of the study is that the electrostatic interactions between the charge densities on the NN C60 molecules and that on M inside the central C60 give rise to the symmetry breaking responsible for the measured level splittings. Using this model, the M@C60 level splittings of interest are calculated variationally and using perturbation theory, for both the P and H orientations. Those obtained for the dominant P orientation are in excellent agreement with the experimental results, with respect to the splitting magnitudes and patterns, for all three M@C60 systems considered, pointing strongly to the quadrupolar M-NN interactions as the main cause of the symmetry breaking. The level splittings calculated for the H orientation are about 30 times smaller than the ones in the P orientation.

Electric-dipole-coupled H2O@C60 dimer: Translation-rotation eigenstates from twelve-dimensional quantum calculations.

We report on variational solutions to the twelve-dimensional (12D) Schrödinger equation appertaining to the translation-rotation (TR) eigenstates of H2O@C60 dimer, associated with the quantized "rattling" motions of the two encapsulated H2O molecules. Both H2O and C60 moieties are treated as rigid and the cage-cage geometry is taken to be fixed. We consider the TR eigenstates of H2O@C60 monomers in the dimer to be coupled by the electric dipole-dipole interaction between water moieties and develop expressions for computing the matrix elements of that interaction in a dimer basis composed of products of monomer 6D TR eigenstates reported by us recently [P. M. Felker and Z. Bacic, J. Chem. Phys. 144, 201101 (2016)]. We use these expressions to compute TR Hamiltonian matrices of H2O@C60 dimer for two values of the water dipole moment and for various dimer geometries. 12D TR eigenstates of the dimer are then obtained by filter diagonalization. The results reveal two classes of eigenstates, distinguished by the leading order (first or second) at which dipole-dipole coupling contributes to them. The two types of eigenstates differ in the general magnitude of their dipole-induced energy shifts and in the dependence of those shifts on the value of the water dipole moment and on the distance between the H2O@C60 monomers. The dimer results are also found to be markedly insensitive to any change in the orientations of the C60 cages. Finally, the results lend some support for the interpretation that electric dipole-dipole coupling is at least partially responsible for the apparent reduced-symmetry environment experienced by H2O in the powder samples of H2O@C60 [K. S. K. Goh et al., Phys. Chem. Chem. Phys. 16, 21330 (2014)], but only if the water dipole is taken to have a magnitude close to that of free water. The methodology developed in the paper is transferable directly to the calculation of TR eigenstates of larger H2O@C60 assemblies, that will be required for more extensive modeling of crystalline H2O@C60.