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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 Bačić, 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., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

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., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)

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., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)

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.

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.

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, H 2 O inside the fullerene C 60 . Both moieties are taken to be rigid. Our treatment incorporates the quantum six-dimensional translation-rotation (TR) wave functions of the encapsulated H 2 O, 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 H 2 O@C 60 at low temperatures. Utilizing this methodology, we compute the INS spectra of H 2 O@C 60 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.

We present quantum five-dimensional bound-state calculations of the fully coupled intermolecular rovibrational states of H 2 O-CO 2 and D 2 O-CO 2 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 H 2 O-CO 2 [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 CO 2 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 H 2 O-CO 2 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.

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-H 2 O (DH), HCl-D 2 O (HD), and DCl-D 2 O (DD). The present study extends our recent theoretical investigation of the nine-dimensional (9D) vibrational level structure of the HCl-H 2 O (HH) dimer [Liu, Y.; Li, J.; Felker, P. M.; Bačić, 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 H 2 O and D 2 O, 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.

The interaction between HCl and H 2 O 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-H 2 O complex is quantitatively characterized in two ways. First, we report a new full-dimensional potential energy surface (PES) for the HCl + H 2 O 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 H 2 O, 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-H 2 O 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 H 2 O/D 2 O-CO and HDO-CO complexes [P. M. Felker and Z. Bačić, 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-H 2 O complex, the intramolecular vibrational fundamentals of both H 2 O 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-H 2 O dimer are in excellent agreement with the available spectroscopic data. The 9D computed dimer binding energy D 0 of 1334.63 cm -1 agrees extremely well with the experimental D 0 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 H 2 O, 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.

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 H 2 O-CO and D 2 O-CO complexes [Felker, P. M.; Bačić, 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.

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 H 2 O-CO and D 2 O-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. Bačić, 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 H 2 O-CO and D 2 O-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.

We present a rigorous and comprehensive theoretical treatment of the vibrational dynamics of benzene-H 2 O 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 (ν 2 ) overtone of H 2 O 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. Bačić, 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 H 2 O 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 H 2 O and HDO complexes, respectively, allowing for direct diagonalization. These calculations characterize in detail the H 2 O/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.

We present a method for efficient calculation of intramolecular vibrational excitations of H 2 O inside C 60 , together with the low-energy intermolecular translation-rotation states within each intramolecular vibrational manifold. Apart from assuming rigid C 60 , this nine-dimensional (9D) quantum treatment is fully coupled. Following the recently introduced approach [P. M. Felker and Z. Bačić, J. Chem. Phys. 151, 024305 (2019)], the full 9D vibrational Hamiltonian of H 2 O@C 60 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 H 2 O 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 H 2 O are blueshifted relative to those of the gas-phase H 2 O, the two stretch modes much more so than the bend. Excitation of the bend mode affects the energies of the low-lying H 2 O 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 H 2 O@C 60 and ab initio calculation of a high-quality 9D potential energy surface for this endohedral complex, neither of which is presently available.

We report the results of calculations pertaining to the HH intramolecular stretching fundamentals of (p-H 2 ) 2 encapsulated in the large cage of structure II clathrate hydrate. The eight-dimensional (8D) quantum treatment assumes rotationless (j = 0) H 2 moieties and a rigid clathrate structure but is otherwise fully coupled. The (H 2 ) 2 -clathrate interaction is constructed in a pairwise-additive fashion, by combining the ab initio H 2 -H 2 O pair potential for flexible H 2 and rigid H 2 O [D. Lauvergnat et al., J. Chem. Phys. 150, 154303 (2019)] and the six-dimensional (6D) H 2 -H 2 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 H 2 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 H 2 -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 H 2 O 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-H 2 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.

Accurate quantum simulations of the low-temperature inelastic neutron scattering (INS) spectra of HF@C 60 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 H 2 or HD, as in the past work. The results demonstrate that the precedent-setting INS selection rule, originally derived for H 2 and HD in near-spherical nanocavities, applies also to HF@C 60 , 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@C 60 . 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.

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.

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.

Symmetry breaking has been recently observed in the endofullerenes M@C 60 (M = H 2 , HF, H 2 O), manifesting in the splittings of the three-fold degenerate ground states of the endohedral ortho-H 2 , ortho-H 2 O 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 C 60 is considered, comprised of the central C 60 molecule surrounded by twelve nearest-neighbor (NN) C 60 molecules. The fullerenes have either P (major) or H (minor) orientational orderings, and are assumed to be rigid with I h symmetry. Only the central C 60 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 C 60 molecules and that on M inside the central C 60 give rise to the symmetry breaking responsible for the measured level splittings. Using this model, the M@C 60 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@C 60 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.

We report on variational solutions to the twelve-dimensional (12D) Schrödinger equation appertaining to the translation-rotation (TR) eigenstates of H 2 O@C 60 dimer, associated with the quantized "rattling" motions of the two encapsulated H 2 O molecules. Both H 2 O and C 60 moieties are treated as rigid and the cage-cage geometry is taken to be fixed. We consider the TR eigenstates of H 2 O@C 60 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. Bačić, J. Chem. Phys. 144, 201101 (2016)]. We use these expressions to compute TR Hamiltonian matrices of H 2 O@C 60 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 H 2 O@C 60 monomers. The dimer results are also found to be markedly insensitive to any change in the orientations of the C 60 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 H 2 O in the powder samples of H 2 O@C 60 [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 H 2 O@C 60 assemblies, that will be required for more extensive modeling of crystalline H 2 O@C 60 .

We report an investigation of the translation-rotation (TR) level structure of H2 entrapped in C60, in the rigid-monomer approximation, by means of a low-order perturbation theory (PT). We focus in particular on the degree to which PT can accurately account for that level structure, by comparison with the variational quantum five-dimensional calculations. To apply PT to the system, the interaction potential of H2@C60 is decomposed into a sum over bipolar spherical tensors. A zeroth-order Hamiltonian, Hˆ0, is then constructed as the sum of the TR kinetic-energy operator and the one term in the tensor decomposition of the potential that depends solely on the radial displacement of the H2 center of mass (c.m.) from the cage center. The remaining terms in the potential are treated as perturbations. The eigenstates of Hˆ0, constructed to also account for the coupling of the angular momentum of the H2 c.m. about the cage center with the rotational angular momentum of the H2 about the c.m., are taken as the PT zeroth-order states. This zeroth-order level structure is shown to be an excellent approximation to the true one except for two types of TR-level splittings present in the latter. We then show that first-order PT accounts very well for these splittings, with respect to both their patterns and magnitudes. This allows one to connect specific features of the level structure with specific features of the potential-energy surface, and provides important new physical insight into the characteristics of the TR level structure.

We report rigorous quantum calculations of the translation-rotation (TR) eigenstates of para- and ortho-H2O@C60. They provide a comprehensive description of the dynamical behavior of H2O inside the fullerene having icosahedral (Ih) symmetry. The TR eigenstates are assigned in terms of the irreducible representations of the proper symmetry group of H2O@C60, as well as the appropriate translational and rotational quantum numbers. The coupling between the orbital and the rotational angular momenta of the caged H2O gives rise to the total angular momentum λ, which additionally labels each TR level. The calculated TR levels allow tentative assignments of a number of transitions in the recent experimental INS spectra of H2O@C60 that have not been assigned previously.

Femtosecond Raman rotational coherence spectroscopy (RCS) detected by degenerate four-wave mixing is a background-free method that allows to determine accurate gas-phase rotational constants of non-polar molecules. Raman RCS has so far mostly been applied to the regular coherence patterns of symmetric-top molecules, while its application to nonpolar asymmetric tops has been hampered by the large number of RCS transient types, the resulting variability of the RCS patterns, and the 10(3)-10(4) times larger computational effort to simulate and fit rotational Raman RCS transients. We present the rotational Raman RCS spectra of the nonpolar asymmetric top 1,4-difluorobenzene (para-difluorobenzene, p-DFB) measured in a pulsed Ar supersonic jet and in a gas cell over delay times up to ∼2.5 ns. p-DFB exhibits rotational Raman transitions with ΔJ = 0, 1, 2 and ΔK = 0, 2, leading to the observation of J -, K -, A -, and C-type transients, as well as a novel transient (S-type) that has not been characterized so far. The jet and gas cell RCS measurements were fully analyzed and yield the ground-state (v = 0) rotational constants A0 = 5637.68(20) MHz, B0 = 1428.23(37) MHz, and C0 = 1138.90(48) MHz (1σ uncertainties). Combining the A0, B0, and C0 constants with coupled-cluster with single-, double- and perturbatively corrected triple-excitation calculations using large basis sets allows to determine the semi-experimental equilibrium bond lengths re(C1-C2) = 1.3849(4) Å, re(C2-C3) = 1.3917(4) Å, re(C-F) = 1.3422(3) Å, and re(C2-H2) = 1.0791(5) Å.

The quantal translation-rotation (TR) states of the (p-H2)2@5(12)6(4) clathrate hydrate inclusion compound have been computed. The ten-dimensional problem (in the rigid-cage and rigid-H2 approximation) is solved by first approximating the H2 moieties as spherically symmetric and solving for their 6D translational eigenstates. These are then combined with H2 free rotational states in a product basis that is used to diagonalize the full TR hamiltonian. The computed low-energy eigenstates have translational components that are essentially identical to the 6D translational eigenstates and rotational components that are 99.9% composed of rotationally unexcited H2 moieties. In other words, TR coupling is minimal for the low-energy states of the species. The low-energy level structure is found to be substantially more congested than that of the more tightly packed (p-H2)4@5(12)6(4) clathrate species. The level structure is also shown to be understandable in terms of a model of (H2)2 as a semirigid diatomic species consisting of two spherically symmetric H2 pseudo-atoms.

Using the CCSD(T) model, we evaluated the intermolecular potential energy surfaces of the He-, Ne-, and Ar-phosgene complexes. We considered a representative number of intermolecular geometries for which we calculated the corresponding interaction energies with the augmented (He complex) and double augmented (Ne and Ar complexes) correlation-consistent polarized valence triple-ζ basis sets extended with a set of 3s3p2d1f1g midbond functions. These basis sets were selected after systematic basis set studies carried out at geometries close to those of the surface minima. The He-, Ne-, and Ar-phosgene surfaces were found to have absolute minima of -72.1, -140.4, and -326.6 cm(-1) at distances between the rare-gas atom and the phosgene center of mass of 3.184, 3.254, and 3.516 Å, respectively. The potentials were further used in the evaluation of rovibrational states and the rotational constants of the complexes, providing valuable results for future experimental investigations. Comparing our results to those previously available for other phosgene complexes, we suggest that the results for Cl2-phosgene should be revised.

The quantal translation-rotation (TR) states of the (p-H2)4@5(12)6(4) and (o-D2)4@5(12)6(4) hydrate clathrate sII inclusion compounds have been computed by nuclear-orbital/configuration-interaction methods. The model of these compounds in a rigid, high-symmetry 5(12)6(4) cage is treated in detail. The low-energy TR level structures of both isotopomers within this model are found to consist of states that can be readily described in terms of a small number of single-H2 and double-H2 excitation modes. The use of the high-symmetry results to facilitate the calculation and interpretation of (p-H2)4 and (o-D2)4 TR states in low-symmetry physically realizable 5(12)6(4) cages is also reported.

The quantal translation-rotation states of two endohedral H(2) moieties in C(70) are computed by means of a nuclear-orbital/configuration-interaction method. H(2) "nuclear orbitals" are calculated as the translation-rotation eigenfunctions of one H(2) molecule interacting with C(70) and the mean field of the second H(2) molecule. Configurations are constructed as symmetrized bilinear products of these orbitals. These configurations are employed as the basis in which the matrix of the translation-rotation Hamiltonian of the cluster is computed and diagonalized. We show that this scheme allows for an efficient means to calculate the Hamiltonian matrix elements. We show that the configuration basis states represent excellent first approximations to the eigenstates of the species. Finally, we present results pertaining to the (H(2))(2)@C(70) low-energy translation-rotation level structure that can be understood in terms of a small number of H(2) excitation types.

We evaluate the phenylacetylene-argon intermolecular potential energy surface by fitting a representative number of ab initio interaction energies to an analytic function. These energies are calculated at a grid of intermolecular geometries, using the CCSD(T) method and the aug-cc-pVDZ basis set extended with a series of 3s3p2d1f1g midbond functions. The potential is characterized by two equivalent global minima where the Ar atom is located above and below the phenylacetylene plane at a distance of 3.5781 Å from the molecular center of mass and at an angle of 9.08° with respect to the axis perpendicular to the phenylacetylene plane and containing the center of mass. The calculated interaction energy is -418.9 cm(-1). To check further the potential, we obtain the rovibrational spectrum of the complex and the results are compared to the available experimental data.

The benzene-Ar ground-state S(0) intermolecular potential energy surface is evaluated using the coupled cluster singles and doubles model including connected triple corrections and the augmented correlation consistent polarized valence triple-zeta basis set extended with a set of 3s3p2d1f1g midbond functions. The surface is characterized by absolute minima of -390.1 cm(-1) where the argon atom is located on the benzene C(6) axis at distances of +/-3.536 A, and has a general shape close to the available ground-state S(0) and the first singlet S(1) and triplet T(1) excited-state surfaces. Using the potential, the intermolecular level structure of the complex is evaluated. The new intermolecular potential energy surface gives very accurate results and improves those previously available.

We report stimulated Raman spectra at 0.2 and 0.03 cm(-1) resolution in the CH-stretching region of jet-cooled fluorene. The results were obtained by a version of ionization-gain stimulated Raman spectroscopy in which resonant two-photon ionization probing of the state-population changes arising from stimulated Raman transitions is assisted by the process of intramolecular vibrational redistribution (IVR) in the Raman-excited molecule. The fluorene spectra reveal extensive vibrational coupling interactions involving both the aliphatic and aromatic CH-stretching first excited states with nearby background states. Results pertaining to the symmetric aliphatic CH-stretching fundamental are consistent with a tier model of IVR and point to vibrational energy flow out of the CH stretch on a approximately 1 ps time scale with subsequent redistribution on a approximately 5 ps time scale.

We evaluate the first excited-state (S1) intermolecular potential energy surface for the fluorobenzene-Ar van der Waals complex using the coupled cluster method and the augmented correlation-consistent polarized valence double-zeta basis set extended with a set of 3s3p2d1f1g midbond functions. To calculate the S(1) interaction energies, we use ground-state interaction energies evaluated with the same basis set and the coupled cluster singles and doubles (CCSD) including connected triple excitations [CCSD(T)] model and interaction and excitation energies evaluated at the CCSD level. The surface minima are characterized by the Ar atom located above and below the fluorobenzene ring at a distance of 3.5060 A with respect to the fluorobenzene center of mass and at an angle of 5.89 degrees with respect to the axis perpendicular to the fluorobenzene plane. The corresponding interaction energy is -425.226 cm(-1). The surface is used in the evaluation of the intermolecular level structure of the complex, and the results are compared to the experimental data available and to those found in previous theoretical papers on ground-state potentials for similar complexes.

The first excited state (S1) intermolecular potential energy surface for the p-difluorobenzene-Ar van der Waals complex is evaluated using the coupled-cluster method and the augmented correlation consistent polarized valence double-zeta basis set extended with a set of 3s3p2d1f1g midbond functions. In order to calculate the S1 interaction energies we use the ground state surface evaluated with the same basis set and the coupled-cluster singles and doubles [CCSD] including connected triple excitations [CCSD(T)] model, and interaction and excitation energies evaluated at the CCSD level. The surface minima are characterized by the Ar atom located above and below the p-difluorobenzene center of mass at a distance of 3.4736 A. The corresponding interaction energy is -435.233 cm-1. The surface is used in the evaluation of the intermolecular level structure of the complex.

We describe variational calculations of J=0 intermolecular states in Br(2)-(4)He(N) clusters. The method employed is analogous to configuration-interaction calculations in electronic-structure work and relies on the ability to express the intermolecular Hamiltonian H(v) as a sum of one- and two-body terms. A basis set is built up from solutions to the Schrödinger equation in which only the one-body terms of H(v) are included. These configurations are products of N=1 eigenstates. The matrix of H(v) in a symmetry-adapted configuration basis is then computed, the two-body terms of H(v) serving to couple different configurations. This computation involves integrals of dimension five or less. Filter diagonalization is then used to obtain energies and eigenfunctions within a selected energy range. Results on clusters having N=2-5 are reported.

The ground state intermolecular potential energy surface for the p-difluorobenzene-Ar van der Waals complex is evaluated using the coupled cluster singles and doubles including connected triple excitations [CCSD(T)] model and the augmented correlation consistent polarized valence double-zeta basis set extended with a set of 3s3p2d1f1g midbond functions. The surface minima are characterized by the Ar atom located above and below the difluorobenzene center of mass at a distance of 3.5290 A. The corresponding binding energy is -398.856 cm(-1). The surface is used in the evaluation of the intermolecular level structure of the complex. The results clearly improve previously available data and show the importance of using a good correlation method and basis set when dealing with van der Waals complexes.