*J Chem Phys ; 152(1): 014108, 2020 Jan 07.*

##### RESUMO

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

*J Chem Phys ; 151(12): 124311, 2019 Sep 28.*

##### RESUMO

We report the results of calculations pertaining to the HH intramolecular stretching fundamentals of (p-H2)2 encapsulated in the large cage of structure II clathrate hydrate. The eight-dimensional (8D) quantum treatment assumes rotationless (j = 0) H2 moieties and a rigid clathrate structure but is otherwise fully coupled. The (H2)2-clathrate interaction is constructed in a pairwise-additive fashion, by combining the ab initio H2-H2O pair potential for flexible H2 and rigid H2O [D. Lauvergnat et al., J. Chem. Phys. 150, 154303 (2019)] and the six-dimensional (6D) H2-H2 potential energy surface [R. J. Hinde, J. Chem. Phys. 128, 154308 (2008)]. The calculations are performed by first solving for the eigenstates of a reduced-dimension 6D "intermolecular" Hamiltonian extracted from the full 8D Hamiltonian by taking the H2 moieties to be rigid. An 8D contracted product basis for the solution of the full problem is then constructed from a small number of the lowest-energy 6D intermolecular eigenstates and two discrete variable representations covering the H2-monomer internuclear distances. Converged results are obtained already by including just the two lowest intermolecular eigenstates in the final 8D basis of dimension 128. The two HH vibrational stretching fundamentals are computed for three hydrate domains having an increasing number of H2O molecules. For the largest domain, the two fundamentals are found to be site-split by â¼0.5 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.

*J Phys Chem Lett ; 10(18): 5365-5371, 2019 Sep 19.*

##### RESUMO

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

*J Chem Phys ; 151(2): 024305, 2019 Jul 14.*

##### RESUMO

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.

*Faraday Discuss ; 212(0): 547-567, 2018 12 13.*

##### RESUMO

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.

*Phys Chem Chem Phys ; 19(46): 31274-31283, 2017 Nov 29.*

##### RESUMO

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

*J Chem Phys ; 146(8): 084303, 2017 Feb 28.*

##### RESUMO

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

*J Chem Phys ; 145(8): 084310, 2016 Aug 28.*

##### RESUMO

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, HË0, 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 HË0, 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.

*J Chem Phys ; 144(20): 201101, 2016 May 28.*

##### RESUMO

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.

*J Chem Phys ; 143(14): 144306, 2015 Oct 14.*

##### RESUMO

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 â¼2.5 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.

##### Assuntos

Fluorbenzenos/química , Estrutura Molecular , Rotação , Análise Espectral Raman , Fatores de Tempo*J Chem Phys ; 141(18): 184305, 2014 Nov 14.*

##### RESUMO

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.

*J Chem Phys ; 138(17): 174306, 2013 May 07.*

##### RESUMO

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.

*J Phys Chem A ; 117(18): 3835-43, 2013 May 09.*

##### RESUMO

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-Î¶ 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.

*J Chem Phys ; 138(4): 044309, 2013 Jan 28.*

##### RESUMO

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.

*J Chem Phys ; 137(7): 074305, 2012 Aug 21.*

##### RESUMO

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.

##### Assuntos

Acetileno/análogos & derivados , Argônio/química , Teoria Quântica , Acetileno/química , Espectroscopia de Luz Próxima ao Infravermelho*J Phys Chem A ; 113(17): 5212-6, 2009 Apr 30.*

##### RESUMO

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.

##### Assuntos

Argônio/química , Benzeno/química , Termodinâmica , Simulação por Computador , Modelos Químicos , Propriedades de Superfície*J Phys Chem A ; 111(49): 12466-70, 2007 Dec 13.*

##### RESUMO

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.

*J Phys Chem A ; 111(32): 7876-81, 2007 Aug 16.*

##### RESUMO

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.

*J Phys Chem A ; 110(49): 13259-63, 2006 Dec 14.*

##### RESUMO

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.

*J Chem Phys ; 125(18): 184313, 2006 Nov 14.*

##### RESUMO

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.