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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

10 dThe tunneling doublets in the HT ht , HT ht , HT ht , and HT ht manifolds have splittings much less than 0.01 cm SP -1 sp for both values of HT ht . 2 bThe tunneling doublets in the HT ht , HT ht , HT ht , and HT ht manifolds have splittings much less than 0.01 cm SP -1 sp for all bases. [Extracted from the article]

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. [ABSTRACT FROM AUTHOR]

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. 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 lowestenergy 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. [ABSTRACT FROM AUTHOR]

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. 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 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. [ABSTRACT FROM AUTHOR]

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. Bačić, 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. [ABSTRACT FROM AUTHOR]

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) H2 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 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. Bačić, 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 . [ABSTRACT FROM AUTHOR]

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, Ħ 0, 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 Ħ0, 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The quantal translation-rotation (TR) states of the (p-H2)2@51264 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@51264 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. [ABSTRACT FROM AUTHOR]

The translation-rotation (TR) dynamics and spectroscopy of light molecules, e.g. H 2 , HD, HF, and H 2 O, inside nanoscale cavities such as those of fullerenes and in clathrate hydrates, is dominated by strong nuclear quantum effects (NQEs) to a degree that is without parallel among realistic molecular species. The NQEs include the large TR zero-point energy, quantisation of the translational centre-of-mass motions of the guest molecule, the coupling of various angular momenta in the system, and nuclear spin isomerism. They leave rich and intriguing fingerprints in the inelastic neutron scattering (INS) spectra arising from the transitions between the TR levels of the systems studied. Here we describe the major methodological advances made in the past decade, in both bound-state and scattering calculations that, when combined, have led to the novel and powerful approach for rigorous quantum simulations of the INS spectra a diatomic molecule, homo- and heteronuclear, inside a nanocavity of an arbitrary geometry. As illustrated by several demanding applications, these simulations have been indispensable, and very successful, for the assignment and interpretation of the measured INS spectra. Very surprisingly, this effort has also resulted in the completely unexpected, precedent-setting discovery of the INS selection rule for diatomic molecules in near-spherical nanocavities, overturning the widely accepted view that the INS has no selection rules. [ABSTRACT FROM AUTHOR]

We describe variational calculations of J=0 intermolecular states in Br2–4HeN 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. [ABSTRACT FROM AUTHOR]

Intermolecular kinetic-energy operators are derived (in the rigid monomer approximation) for solute–solvent[sub n] clusters of the type B–A[sub n], where B is a molecule and A is either an atom or a molecule. The operators are obtained for a body-fixed frame embedded in the B moiety and parallel to the principal axes of that species. They are expressed in terms of intermolecular coordinates that represent the projection along the body-fixed axes of position vectors pointing from the center of mass of B to the centers of mass of the A species. The results are particularly useful for calculations on clusters in which A–B interactions dominate over A–A interactions in the intermolecular potential energy surface and/or there is minimal interaction between subsets of the A moieties. This utility is demonstrated in variational calculations of intermolecular states in the (1|1) isomer of anthracene–He[sub 2]. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Examines the interaction between a polarized optical field and the polarizability of a symmetric top in the strong interaction limit. Use of the interaction as a tool in interpreting real measured band contours; Analysis of pendular eigenfunctions and eigenergies; Comparison of theoretical expectations regarding pendular band contours with direct numerical simulations.

Discusses the results of nonlinear Raman spectroscopy on the intermolecular transitions of the perprotonated and perdeuterated isotopomers of benzene-Ar. Bands observed for each species; Performance of band-contour measurements; Comparison of the results to simulated contours.

The results of nonlinear Raman experiments on two intermolecular bands of expansion-cooled naphthalene trimer at 0.03 cm-1 resolution are reported. The polarization and intensity dependences of the observed band contours strongly indicate that the observations pertain to transitions between pendular states that result from the interaction of a strong optical field and the permanent polarizability anisotropy of the trimer. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Mass-selective, ionization-detected stimulated Raman spectroscopies have been applied to a study of low-frequency structure in the ground states of benzene dimer isotopomers. The results reveal two Raman bands below 10 cm-1, as well as structure in the range of 47 to 53 cm-1. Tentative assignments for the bands are proposed. [ABSTRACT FROM AUTHOR]

In this and the accompanying paper we present a theoretical treatment and experimental study, respectively, of the phenomenon termed purely rotational coherence. This phenomenon has been demonstrated to be useful as a time domain means by which to obtain high resolution spectroscopic information on excited state rotational levels of large molecules [Felker et al., J. Phys. Chem. 90, 724 (1986); Baskin et al., J. Chem. Phys. 84, 4708 (1986)]. Here, the manifestations in temporally resolved, polarization-analyzed fluorescence of coherently prepared rotational levels in samples of isolated symmetric and asymmetric top molecules are considered. These manifestations, for reasonably large molecules at rotational temperatures characteristic of jet-cooled samples, take the form of polarization-dependent transients and recurrences with temporal widths of the order of tens of picoseconds or less. The transients, which arise from the thermal averaging of many single molecule coherences, are examined with respect to their dependences on molecular parameters (rotational constants, transition dipole directions) and experimental parameters (polarization directions and temperature). A physical picture of rotational coherence as a reflection of the time-dependent orientation of molecules in the sample is developed. And, the influence of rotational coherence in experiments designed to probe intramolecular energy flow is discussed. In the accompanying paper, we present experimental results for jet-cooled t-stilbene and anthracene. For t-stilbene we determine rotational constants for vibrational levels in the S1 electronic state (from the recurrences) and we monitor the trends in rotational coherence vs vibrational coherence as the total energy in the molecule increases. [ABSTRACT FROM AUTHOR]

In this paper we describe the results of picosecond fluorescence polarization (sub-Doppler) experiments designed to determine the role of purely rotational coherence in two jet-cooled molecules: trans-stilbene and anthracene. Observations of the manifestations of purely rotational coherence in t-stilbene are reported. The relationship of purely rotational coherence to molecular parameters (excited state rotational constants and transition dipole directions) is confirmed by comparison of our measurements with the results of the theory described in paper I [P. M. Felker and A. H. Zewail, J. Chem. Phys. 86, 2460 (1987)]. The sum of rotational constants B’ and C’ of the t-stilbene S1 electronic state is determined with a precision of better than 1 part in 700 (B’+C’=0.5132±0.0007 GHz). The influence of molecular beam expansion conditions and fluorescence detection conditions on our measurements is also investigated and compared with the theroretical findings of paper I. Also measurements of time-resolved and polarization-analyzed fluorescence as a function of excess vibrational energy in the S1 electronic states of both t-stilbene and anthracene are reported. We are able to distinguish the contribution of purely rotational coherence from the contributions of purely vibrational (or rovibrational) coherence to the evolution of fluorescence from the vibrationally excited molecule. The results are first analyzed on the basis of a model in which strict separability of vibrational and rotational motion is assumed. This provides a test of the extent of coupling of these motions and its influence on intramolecular vibrational energy redistribution (IVR). [ABSTRACT FROM AUTHOR]

Experimental results on jet-cooled anthracene pertaining to the role of rotations in IVR processes are presented. For theoretical comparison, we consider the effects of molecular rotational level structure on the beat-modulated decays that arise as manifestations of IVR. It is shown theoretically for anharmonic coupling that small differences in rotational constants between coupled vibrational states give rise to decays, the beat envelopes of which decay faster than the unmodulated portions of the decays. These envelope decay rates are shown to be rotational temperature dependent. The experimental results reveal behavior entirely consistent with the theoretical expectations. The results also show that although rotational effects are present in experimental decays, they are not so marked as to wash out the manifestations of vibrational coherence. [ABSTRACT FROM AUTHOR]

In this series of papers, theoretical and experimental results concerning the dynamical manifestations of intramolecular vibrational-energy redistribution (IVR) in temporally resolved fluorescence are presented. In this paper (I) we present a general treatment of IVR and coherence effects in multilevel vibrational systems. Specifically, the concern is with the derivation of the characteristics of the beat-modulated fluorescence decays which arise from vibrational coupling among N levels within a molecule. Relations connecting quantum beat frequencies, phases, and modulation depths to coupling parameters are presented. Likely sources of deviation of experimental results from theoretical predictions are considered. And, finally, the direct link between IVR and time-resolved fluorescence experiments is discussed with emphasis placed on the physical interpretation of vibrational quantum beats and the nature of IVR as a function of vibrational energy in a molecule. [ABSTRACT FROM AUTHOR]

The results of picosecond-resolved measurements of intramolecular vibrational-energy redistribution (IVR) in jet-cooled anthracene at different excess energies are presented. From these results, the nature of IVR as a function of vibrational energy, the relevant time scales for the process, and the details of pertinent vibrational couplings are determined. [ABSTRACT FROM AUTHOR]

We present methodology for variational calculation of the 6 n -dimensional translation-rotation (TR) eigenstates of assemblies of n H 2 O@C 60 moieties coupled by dipole-dipole interactions. We show that the TR Hamiltonian matrix for any n can be constructed from dipole-dipole matrix elements computed for n = 2 . We present results for linear H 2 O@C 60 assemblies. Two classes of eigenstates are revealed. One class comprises excitations of the 1 11 rotational level of H 2 O. The lowest-energy 1 11 -derived eigenstate for each assembly exhibits significant dipole ordering and shifts down in energy with the assembly size. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The quantal translation-rotation (TR) states of the (p-H2)4@51264 and (o-D2)4@51264 hydrate clathrate sII inclusion compounds have been computed by nuclear-orbital/configuration-interaction methods. The model of these compounds in a rigid, high-symmetry 51264 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 51264 cages is also reported. [ABSTRACT FROM AUTHOR]

The quantal translation-rotation states of two endohedral H2 moieties in C70 are computed by means of a nuclear-orbital/configuration-interaction method. H2 'nuclear orbitals' are calculated as the translation-rotation eigenfunctions of one H2 molecule interacting with C70 and the mean field of the second H2 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 (H2)2@C70 low-energy translation-rotation level structure that can be understood in terms of a small number of H2 excitation types. [ABSTRACT FROM AUTHOR]

We apply a method for the construction of rotational-intermolecular vibrational states to the van der Waals molecule benzene-N[sub 2]. The method, as described in Felker et al. [J. Chem. Phys. 114, 1233 (2001)] is based on the transformation of approximate rovibrational eigenfunctions from functions of coordinates referred to an Eckart body-fixed axis system to functions of coordinates referred to a more convenient body-fixed frame. This transformation allows the computation of approximate rovibrational eigenenergies, as well as other molecular properties, from one or a small set of J=0 eigenfunctions. By comparing rovibrational energies and matrix elements computed by this Eckart method with those computed variationally with a large basis, we show that the former yields excellent results for benzene-N[sub 2]. The results are particularly significant because of the presence of essentially free internal rotation in the species, a large-amplitude motion that complicates the definition of an Eckart frame. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In application to benzene-Ar we test a procedure that makes use of conveniently calculated J=0 intermolecular eigenstates to compute molecular constants and transition intensities without requiring explicit diagonalization of the full rotational/intermolecular vibrational Hamiltonian of the species. The approach relies on the ability to calculate the orientation of an Eckart body-fixed frame for each point on a grid over which a J=0 state is represented. That ability allows one to compute vibrational matrix elements of operators referred to the Eckart axes while working with J=0 eigenstates obtained in an entirely different body-fixed frame. Generally excellent agreement is found between the Eckart results and those obtained by others via diagonalization of the full rotational/intermolecular vibrational Hamiltonian. Finally, a general prescription for the construction of an efficient rovibrational basis from J=0 solutions in a convenient body-fixed frame is presented. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

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 103–104 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. [ABSTRACT FROM AUTHOR]

A study of the intermolecular potential-energy surface (IPS) and the intermolecular states of the perprotonated and perdeuterated benzene–He complex is reported. From a fit to ab initio data computed within the coupled cluster singles and doubles including connected triples model for 280 interaction geometries, an analytic IPS including two- to four-body atom–atom terms is obtained. This IPS, and two other Lennard-Jones atom–atom surfaces from the literature, are each employed in dynamically exact (within the rigid-monomer approximation) calculations of J=0 intermolecular states of the isotopomers. Rotational constants and Raman-scattering coefficients for intermolecular vibrational transitions are also calculated for each of the three surfaces. The calculated results are compared with experimental results reported herein pertaining to intermolecular Raman spectra of benzene–He. The calculated rotational constants are compared with experimental values from the literature. The fitted IPS of this work leads to calculated observables that match the experimental results very well. The IPSs from the literature are not as successful, specifically in regard to the intermolecular Raman spectra. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The intermolecular potential-energy surface pertaining to the interaction between benzene and N[sub 2] is investigated theoretically and experimentally. Accurate intermolecular interaction energies are evaluated for the benzene-N[sub 2] van der Waals complex using the coupled cluster singles and doubles including connected triples [CCSD(T)] method and the aug-cc-pVDZ basis set extended with a set of 3s3p2d1f1g midbond functions. After fitting the energies to an analytic function, the intermolecular Schrödinger equation is solved to yield energies, rotational constants, and Raman-scattering coefficients for the lowest intermolecular levels of several benzene-N[sub 2] isotopomers. Experimentally, intermolecular Raman spectra of jet-cooled h[sub 6]- and d[sub 6]-benzene-N[sub 2] measured at 0.03 cm[sup -1] resolution by mass-selective, ionization-detected stimulated Raman spectroscopies are reported. Seven intermolecular bands are assigned for each isotopomer, including transitions involving intermolecular bending and stretching vibrations and internal rotation about the benzene C[sub 6] axis. These Raman data, together with measured rotational constants and binding energies obtained by other groups on benzene-N[sub 2], agree well with the theoretical results. Such agreement points to the promise of the quantum chemical methodology employed herein in future investigations of larger van der Waals complexes. [ABSTRACT FROM AUTHOR]

We present a perturbation theory analysis of four time-resolved fluorescence depletion schemes that are useful, or potentially useful, in rotational coherence spectroscopy. The analysis shows that ground-state rotational constants determine the rotational coherence effects in fully resonant, time-resolved stimulated Raman-induced fluorescence depletion (TRSRFD), excited-state rotational constants determine such effects in time-resolved stimulated emission spectroscopy (TRSES), and both ground- and excited-state constants do so in time-resolved fluorescence depletion (TRFD). An analysis of a variant of the TRSRFD scheme in which the stimulated Raman process is not resonance-enhanced shows that this method gives rise to qualitatively different rotational coherence effects than fully resonant TRSRFD. It is argued that the scheme may, nevertheless, be a viable means of ground-state rotational coherence spectroscopy. Expressions for the calculation of rotational coherence effects in TRFD, TRSRFD, and TRSES traces are also presented. Such expressions are used to show that the magnitudes of rotational coherence transients are similar in all three schemes. Finally, experimental results on molecular iodine are presented to show that, indeed, both ground- and excited-state rotational coherence effects are manifest in TRFD traces. [ABSTRACT FROM AUTHOR]

A perturbation theory analysis of Fourier transform (interferometric) versions of coherent Raman scattering and ionization-detected (or fluorescence-detected) stimulated Raman scattering is presented. The analysis has the principal aim of examining the information content of these spectroscopies as a function of the temporal characteristics of the excitation fields. The general conclusion of the analysis is that the information content of the techniques does not depend on excitation pulsewidths and, in particular, that spectral resolution is not limited by such pulsewidths. This is an important result because it allows for the use of short-pulse laser systems in implementing the methods. It is also shown, however, that the temporal characteristics of the excitation fields do influence the practical implementations of the spectroscopies significantly in that signal-to-noise ratios, Doppler broadening, etc. can be dependent on these characteristics. [ABSTRACT FROM AUTHOR]

Usingthe CCSD(T) model, we evaluated the intermolecular potentialenergy surfaces of the He–, Ne–, and Ar–phosgenecomplexes. We considered a representative number of intermoleculargeometries for which we calculated the corresponding interaction energieswith the augmented (He complex) and double augmented (Ne and Ar complexes)correlation-consistent polarized valence triple-ζ basis setsextended with a set of 3s3p2d1f1g midbond functions. These basis setswere selected after systematic basis set studies carried out at geometriesclose to those of the surface minima. The He–, Ne–,and Ar–phosgene surfaces were found to have absolute minimaof −72.1, −140.4, and −326.6 cm–1at distances between the rare-gas atom and the phosgene center ofmass of 3.184, 3.254, and 3.516 Å, respectively. The potentialswere further used in the evaluation of rovibrational states and therotational constants of the complexes, providing valuable resultsfor future experimental investigations. Comparing our results to thosepreviously available for other phosgene complexes, we suggest thatthe results for Cl2–phosgene should be revised. [ABSTRACT FROM AUTHOR]

The structure of the 1-naphthol (NH[SUB3])[SUB2] cluster was investigated by rotational coherence spectroscopy (RCS), mass selective one- and two-color resonant two-photon ionization (R2PI) experiments and ab initio calculations. RCS measurements yielded rotational constants of 1-naphthol (NH[SUB3])[SUB2] as A = 1197, B = 500, and C = 413 MHz, as well as those for several isotopomers. The counterpoise-corrected second-order Mφller-Plesset perturbation theory (MP2) method predicts two isomers A and B. Both structures have hydrogen bonded naphthol-OH… NH[SUB3]… (NH[SUB3] chains, with the second NH[SUB3] (bent above the proximal aromatic ring and pointing towards the p-electron system and have nearly the same binding energy. The experimental rotational constants agree better with those calculated for structure B. The B3LYP and PW91 density functional methods also predict two isomers A, B with the rotational constants of B in acceptable agreement with experiment. Based on two-color R2PI experiments using low ionization frequency to suppress cluster fragmentation, the S[SUB1]←S[SUB0] electronic origin region of the 1-naphthol (NH[SUB3])] [SUB2 - 4] cluster series as reassigned, in agreement with the work of Dedonder-Lardeux et al. [Phys. Chem. Chem. Phys. 3, 4316 (2001)]. In one-color experiments, the 1-naphthol (NH[SUB3])[SUB3] cluster fragments with nearly 100% efficiency into the 1-naphthol (NH[SUB3])[SUB2SUP+] mass channel. [ABSTRACT FROM AUTHOR]

Presents an approach toward the dynamically exact calculation of intermolecular states in molecule-large molecule complexes. Employment of an intermolecular Hamiltonian; Use of filter diagonalization techniques to diagonalize the Hamiltonian; Interpretation of the results of the calculation in terms of five internal rotation states.

Theoretical and experimental results pertaining to the excitation of intermolecular vibrations in the Raman and vibronic spectra of aromatic-containing, weakly bound complexes and clusters are reported. The theoretical analysis of intermolecular Raman activity is based on the assumption that the polarizability tensor of a weakly bound species is given by the sum of the polarizability tensors of its constituent monomers. The analysis shows that the van der Waals bending fundamentals in aromatic–rare gas complexes may be expected to be strongly Raman active. More generally, it predicts strong Raman activity for intermolecular vibrations that involve the libration or internal rotation of monomer moieties having appreciable permanent polarizability anisotropies. The vibronic activity of intermolecular vibrations in aromatic-rare gas complexes is analyzed under the assumption that every vibronic band gains its strength from an aromatic-localized transition. It is found that intermolecular vibrational excitations can accompany aromatic-localized vibronic excitations by the usual Franck–Condon mechanism or by a mechanism dependent on the librational amplitude of the aromatic moiety during the course of the pertinent intermolecular vibration. The latter mechanism can impart appreciable intensity to bands that are forbidden by rigid-molecule symmetry selection rules. The applicability of such rules is therefore called into question. Finally, experimental spectra of intermolecular transitions, obtained by mass-selective, ionization-detected stimulated Raman spectroscopies, are reported for benzene–X (X=Ar, –Ar2, N2, HCl, CO2, and –fluorene), fluorobenzene–Ar and –Kr, aniline–Ar, and fluorene–Ar and –Ar2. The results support the conclusions of the theoretical analyses and provide further evidence for the value of Raman methods in characterizing intermolecular vibrational level structures. [ABSTRACT FROM AUTHOR]

Size-selective Raman spectra of carbazole–(Ar)n clusters (n=0–14) obtained between about 1305 and 1325 cm-1 by mass-selective ionization-loss stimulated Raman spectroscopy are reported. The spectra are interpreted with respect to vibrational energy flow and argon evaporation, and are compared with vibronic spectroscopic results on the species. [ABSTRACT FROM AUTHOR]

The characteristics and origin of a new type of rotational coherence effect—asymmetry transients—are considered. Asymmetry transients are of two types, which we call C-type and A-type, respectively. C-type features are spaced by time intervals equal to 1/(4C). A-type features are spaced by time intervals equal to 1/(4A). Both types of transients can provide information on rotational constants that is not available from other types of rotational coherence effects. We show that the C-type transients arise from coherences between rotational eigenstates of the form Jτ and (J+2)τ-2 (in the Jτ notation) and that the A-type ones arise from coherences between eigenstates Jτ and (J+2)τ+2. The fact that such coherences produce asymmetry transients is shown to be a consequence of the limiting behavior of asymmetric top energy levels at high values of J. Experimental results in which asymmetry transients are present are reported for jet-cooled perylene, tryptamine (D conformer), 1-naphthol–water, and fluorene–benzene. [ABSTRACT FROM AUTHOR]

Theoretical and experimental results relating to the picosecond laser implementation of Fourier transform stimulated emission spectroscopy (FT-SES) and Fourier transform hole-burning spectroscopy (FT-HBS) in molecular beams are presented. It is shown that the resolution in the schemes is only limited by the length of the interferogram taken, and not by factors such as the excitation pulsewidths, excitation bandwidths, or the delay between the pump and probe laser pulses. In addition, the factors which determine the homogeneous and Doppler broadening in FT-SES and FT-HBS spectra are examined. It is found that ground-state damping factors determine the homogeneous broadening in FT-SES and excited-state damping factors determine such broadening in FT-HBS. Doppler broadening in both of the methods is shown to be that associated with two-photon resonant vibrational transition frequencies rather than one-photon resonant vibronic transition frequencies. The characteristics of the Fourier transform methods are compared to those of their frequency-domain counterparts. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We report the results of nonlinear Raman spectroscopy measurements of intermolecular transitions in the hydrogen-bonded complexes 1-naphthol-H[sub 2]O and 1-naphthol-NH[sub 3]. Bands are assigned, primarily by pendular band-contour analysis and by reference to calculated results from Knochenmuss et al. [J. Phys. Chem. 102, 1935 (1998)], to transitions involving the three hydrogen-bond vibrations in which there is relative translational motion between the two molecules in the complex. Splittings due to tunneling between hydrogen-bond torsional states are also identified. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]