An “adiabatic-hindered-rotor” treatment allows para-H2 to be treated as if it were spherical

Neural network interaction potentials for para-hydrogen with flexible molecules

The study of molecular impurities in para-hydrogen ( pH2) clusters is key to push forward our understanding of intra- and intermolecular interactions, including their impact on the superfluid response of this bosonic quantum solvent. This includes tagging with only one or very few pH2, the microsolvation regime for intermediate particle numbers, and matrix isolation with many solvent molecules. However, the fundamental coupling between the bosonic pH2 environment and the (ro-)vibrational motion of molecular impurities remains poorly understood. Quantum simulations can, in principle, provide the necessary atomistic insight, but they require very accurate descriptions of the involved interactions. Here, we present a data-driven approach for the generation of impurity⋯ pH2 interaction potentials based on machine learning techniques, which retain the full flexibility of the dopant species. We employ the well-established adiabatic hindered rotor (AHR) averaging technique to include the impact of the nuclear spin statistics on the symmetry-allowed rotational quantum numbers of pH2. Embedding this averaging procedure within the high-dimensional neural network potential (NNP) framework enables the generation of highly accurate AHR-averaged NNPs at coupled cluster accuracy, namely, explicitly correlated coupled cluster single, double, and scaled perturbative triples, CCSD(T*)-F12a/aVTZcp, in an automated manner. We apply this methodology to the water and protonated water molecules as representative cases for quasi-rigid and highly flexible molecules, respectively, and obtain AHR-averaged NNPs that reliably describe the corresponding H2O⋯ pH2 and H3O+⋯ pH2 interactions. Using path integral simulations, we show for the hydronium cation, H3O+, that umbrella-like tunneling inversion has a strong impact on the first and second pH2 microsolvation shells. The automated and data-driven nature of our protocol opens the door to the study of bosonic pH2 quantum solvation for a wide range of embedded impurities.

On the accuracy and efficiency of different methods to calculate Raman vibrational shifts of parahydrogen clusters

The Raman vibrational frequency shifts of pure parahydrogen and orthodeuterium clusters of sizes N = 4–9 are calculated using the Langevin equation path integral ground state method. The shifts are calculated using three different methods; the results obtained from each are compared to experiment and variance properties are assessed. The first method requires the direct calculation of energies from two simulations: one when the cluster is in the v = 0 vibrational state and one when the cluster has v = 1 total quantum of vibration. The shift is directly calculated from the difference in those two energies. The second method requires only a v = 0 simulation to be performed. The ground state energy is calculated as usual and the excited state energy is calculated by using the distribution of the v = 0 simulation and the ratio of the density matrices between the v = 1 state and the v = 0 state. The shift is calculated from the difference in those two energies. These first two are both exact methods. The final method is based on perturbation theory where the shift is calculated by averaging the pairwise difference potential over the pair distribution function. However, this is an approximate approach. It is found that for large enough system sizes, despite the approximations, the perturbation theory method has the strongest balance between accuracy and precision when weighing against computational cost.

Vibrational Raman Shifts of Spin Isomer Combinations of Hydrogen Dimers and Isotopologues

Binding energies for para-para, ortho-para, and ortho-ortho hydrogen dimers (H₂)₂ are calculated using the six-dimensional (6D) interaction potential developed by Hinde [ J. Chem. Phys. 2008, 128, 154308]. The eigenstates of the dimers are computed by diagonalization using, as a basis, products of the rovibrational states of the monomers, a radial grid for the distance between the monomers, and spherical harmonics for the end-over-end rotation of the dimer. We describe the overall nuclear spin symmetry and use these properties to determine the relative population of various states, making use of a Boltzmann factor for each spin isomer to assess the effect of temperature. A predicted Raman spectrum in the Q(0) and Q(1) region of the hydrogen dimer is produced. To assess the accuracy of our model, we verify our produced shifts with experimental results obtained previously by Montero et al. [ Eur. Phys. J. D 2009, 52, 31-34] and find good agreement. These results are extended to other cases involving the deuterium (D₂)₂ and tritium dimer (T₂)₂ isotopologues, to predict Raman shifts.

Equation of state and first principles prediction of the vibrational matrix shift of solid parahydrogen

We generate the equation of state (EOS) of solid parahydrogen (para-H₂) using a path-integral Monte Carlo (PIMC) simulation based on a highly accurate first-principles adiabatic hindered rotor potential energy curve for the para-H₂ dimer. The EOS curves for the fcc and hcp structures of solid para-H₂ near the equilibrium density show that the hcp structure is the more stable of the two, in agreement with experiment. To accurately reproduce the structural and energy properties of solid para-H₂, we eliminated by extrapolation the systematic errors associated with the choice of simulation parameters used in the PIMC calculation. We also investigate the temperature dependence of the EOS curves, and the invariance of the equilibrium density with temperature is satisfyingly reproduced. The pressure as a function of density and the compressibility as a function of pressure are both calculated using the obtained EOS and are compared with previous simulation results and experiments. We also report the first ever a priori prediction of a vibrational matrix shift from first-principles two-body potential functions, and its result for the equilibrium state agrees well with experiment.

Suppression of Parahydrogen Superfluidity in a Doped Nanoscale Bose Fluid Mixture

Helium (^{4}He) nanodroplets provide a unique environment to observe the microscopic origins of superfluidity. The search for another superfluid substance has been an ongoing quest in the field of quantum fluids. Nearly two decades ago, experiments on doped parahydrogen (p-H_{2}) clusters embedded in ^{4}He droplets displayed anomalous spectroscopic signatures that were interpreted as a sign of the superfluidity of p-H_{2} [S. Grebenev et al., Science 289, 1532 (2000)SCIEAS0036-807510.1126/science.289.5484.1532]. Here, we observe, using first-principles quantum Monte Carlo simulations, a phase separation between a symmetric and localized p-H_{2} core and ^{4}He shells. The p-H_{2} core has minimal superfluid response. These findings are consistent with the recorded spectra but not with their original interpretation, and lead us to conclude that doped p-H_{2} clusters form a nonsuperfluid core in ^{4}He droplets.

Full quantum calculation of the rovibrational states and intensities for a symmetric top-linear molecule dimer: Hamiltonian, basis set, and matrix elements

The rovibrational energy levels and intensities of the CH₃F-H₂ dimer have been obtained using our recent global intermolecular potential energy surface [X.-L. Zhang et al., J. Chem. Phys. 148, 124302 (2018)]. The Hamiltonian, basis set, and matrix elements are derived and given for a symmetric top-linear molecule complex. This approach to the generation of energy levels and wavefunctions can readily be utilized for studying the rovibrational spectra of other van der Waals complexes composed of a symmetric top molecule and a linear molecule, and may readily be extended to other complexes of nonlinear molecules and linear molecules. To confirm our method, the rovibrational levels of the H₂O-H₂ dimer have been computed and shown to be in good agreement with experiment and with previous theoretical results. The rovibrational Schrödinger equation has been solved using a Lanczos algorithm together with an uncoupled product basis set. As expected, dimers containing ortho-H₂ are more strongly bound than dimers containing para-H₂. Energies and wavefunctions of the discrete rovibrational levels of CH₃F-paraH₂ complexes obtained from the direct vibrationally averaged 5-dimensional potentials are in good agreement with the results of the reduced 3-dimensional adiabatic-hindered-rotor (AHR) approximation. Accurate calculations of the transition line strengths for the orthoCH₃F-paraH₂ complex are also carried out, and are consistent with results obtained using the AHR approximation. The microwave spectrum associated with the orthoCH₃F-orthoH₂ dimer has been predicted for the first time.

Investigating the influence of intramolecular bond lengths on the intermolecular interaction of H2-AgCl complex: Binding energy, intermolecular vibrations, and isotope effects

In this paper, we performed a theoretical study on the influence of intramolecular bond lengths on the intermolecular interactions between H₂ and AgCl molecules. Using four sets of bond lengths for the monomers of H₂ and AgCl, four-dimensional intermolecular potential energy surfaces (PESs) were constructed from ab initio data points at the level of single and double excitation coupled cluster method with noniterative perturbation treatment of triple excitations. A T-shaped global minimum was found on the PES. Interestingly, both the binding energies and Ag-H₂ distances present a linear relationship with the intramolecular bond lengths of H₂-AgCl. The accuracy of these PESs was validated by the available spectroscopic data via the bound state calculations, and the predicted rotational transition frequencies can reproduce the experimental observations with a root-mean-squared error of 0.0003 cm^-1 based on the PES constructed with r(H-H) and r(Ag-Cl) fixed at 0.795 and 2.261 Å, respectively. The intermolecular vibrational modes were assigned unambiguously with a simple pattern by analyzing the wave functions. Isotope effects were also investigated by the theoretical calculations, and the results are in excellent agreement with the available spectroscopic data. The transition frequencies for the isotopolog D₂-AgCl are predicted with the accuracy of 0.3 MHz.

Analytic Morse/long-range potential energy surfaces and "adiabatic-hindered-rotor" treatment for a symmetric top-linear molecule dimer: A case study of CH3F-H2

A first effective six-dimensional ab initio potential energy surface (PES) for CH₃F-H₂ which explicitly includes the intramolecular Q₃ stretching normal mode of the CH₃F monomer is presented. The electronic structure computations have been carried out at the explicitly correlated coupled cluster level of theory [CCSD(T)-F12a] with an augmented correlation-consistent triple zeta basis set. Five-dimensional analytical intermolecular PESs for ν₃(CH₃F) = 0 and 1 are then obtained by fitting the vibrationally averaged potentials to the Morse/Long-Range (MLR) potential function form. The MLR function form is applied to the nonlinear molecule-linear molecule case for the first time. These fits to 25 015 points have root-mean-square deviations of 0.74 cm^-1 and 0.082 cm^-1 for interaction energies less than 0.0 cm^-1. Using the adiabatic hindered-rotor approximation, three-dimensional PESs for CH₃F-paraH₂ are generated from the 5D PESs over all possible orientations of the hydrogen monomer. The infrared and microwave spectra for CH₃F-paraH₂ dimer are predicted for the first time. These analytic PESs can be used for modeling the dynamical behavior in CH₃F-(H₂)_N clusters, including the possible appearance of microscopic superfluidity.

Diffusion Monte Carlo simulations of gas phase and adsorbed D2-(H2)n clusters

We have computed ground state energies and analyzed radial distributions for several gas phase and adsorbed D₂(H₂)_n and HD(H₂)_n clusters. An external model potential designed to mimic ionic adsorption sites inside porous materials is used [M. Mella and E. Curotto, J. Phys. Chem. A 121, 5005 (2017)]. The isotopic substitution lowers the ground state energies by the expected amount based on the mass differences when these are compared with the energies of the pure clusters in the gas phase. A similar impact is found for adsorbed aggregates. The dissociation energy of D₂ from the adsorbed clusters is always much higher than that of H₂ from both pure and doped aggregates. Radial distributions of D₂ and H₂ are compared for both the gas phase and adsorbed species. For the gas phase clusters, two types of hydrogen-hydrogen interactions are considered: one based on the assumption that rotations and translations are adiabatically decoupled and the other based on nonisotropic four-dimensional potential. In the gas phase clusters of sufficiently large size, we find the heavier isotopomer more likely to be near the center of mass. However, there is a considerable overlap among the radial distributions of the two species. For the adsorbed clusters, we invariably find the heavy isotope located closer to the attractive interaction source than H₂, and at the periphery of the aggregate, H₂ molecules being substantially excluded from the interaction with the source. This finding rationalizes the dissociation energy results. For D₂-(H₂)_n clusters with n≥12, such preference leads to the desorption of D₂ from the aggregate, a phenomenon driven by the minimization of the total energy that can be obtained by reducing the confinement of (H₂)₁₂. The same happens for (H₂)₁₃, indicating that such an effect may be quite general and impact on the absorption of quantum species inside porous materials.

Ab initio potential energy surface and microwave spectra for the H2-HCCCN complex

We present a four-dimensional ab initio potential energy surface of the H₂-HCCCN complex at the coupled-cluster singles and doubles with noniterative inclusion of connected triples [CCSD(T)]-F12 level with a large basis set including an additional set of bond functions. The artificial neural networks method was extended to fit the intermolecular potential energy surface. The complex has a planar linear global minimum with the well depth of 199.366 cm^-1 located at R = 5.09 Å, φ = 0°, θ₁ = 0°, and θ₂ = 180°. An additional planar local minimum is also found with a depth of 175.579 cm^-1 that is located at R = 3.37 Å, φ = 0°, θ₁ = 110°, and θ₂ = 104°. The radial discrete variable representation/angular finite basis representation and the Lanczos algorithm were employed to calculate the rovibrational energy levels for four species of H₂-HCCCN (pH₂-HCCCN, oH₂-HCCCN, pD₂-HCCCN, and oD₂-HCCCN). The rotational frequencies and spectroscopic parameters were also determined for four complexes, which agree well with the experimental values.

Adsorption of molecular hydrogen on coronene with a new potential energy surface

Adsorption of molecular hydrogen on coronene studied with a new potential energy surface. Path integral Monte Carlo and basin-hopping calculations have been performed to investigate energies and structures of the corresponding (H₂)_N-coronene clusters.

A new ab initio potential energy surface for the collisional excitation of N2H(+) by H2

We compute a new potential energy surface (PES) for the study of the inelastic collisions between N2H(+) and H2 molecules. A preliminary study of the reactivity of N2H(+) with H2 shows that neglecting reactive channels in collisional excitation studies is certainly valid at low temperatures. The four dimensional (4D) N2H(+)-H2 PES is obtained from electronic structure calculations using the coupled cluster with single, double, and perturbative triple excitation level of theory. The atoms are described by the augmented correlation consistent triple zeta basis set. Both molecules were treated as rigid rotors. The potential energy surface exhibits a well depth of ≃2530 cm(-1). Considering this very deep well, it appears that converged scattering calculations that take into account the rotational structure of both N2H(+) and H2 should be very difficult to carry out. To overcome this difficulty, the "adiabatic-hindered-rotor" treatment, which allows para-H2(j = 0) to be treated as if it were spherical, was used in order to reduce the scattering calculations to a 2D problem. The validity of this approach is checked and we find that cross sections and rate coefficients computed from the adiabatic reduced surface are in very good agreement with the full 4D calculations.

Microwave spectroscopy of the seeded binary and ternary clusters CO-(pH2)2, CO-pH2-He, CO-HD, and CO-(oD2)(N=1,2)

We report the Fourier transform microwave spectra of the a-type J = 1-0 transitions of the binary and ternary CO-(pH2)2, CO-pH2-He, CO-HD, and CO-(oD2)N=1,2 clusters. In addition to the normal isotopologue of CO for all clusters, we observed the transitions of the minor isotopologues, (13)C(16)O, (12)C(18)O, and (13)C(18)O, for CO-(pH2)2 and CO-pH2-He. All transitions lie within 335 MHz of the experimentally or theoretically predicted values. In comparison to previously reported infrared spectra [Moroni et al., J. Chem. Phys. 122, 094314 (2005)], we are able to tentatively determine the vibrational shift for CO-pH2-He, in addition to its b-type J = 1-0 transition frequency. The a-type frequency of CO-pH2-He is similar to that of CO-He2 [Surin et al., Phys. Rev. Lett. 101, 233401 (2008)], suggesting that the pH2 molecule has a strong localizing effect on the He density. Perturbation theory analysis of CO-oD2 reveals that it is approximately T-shaped, with an anisotropy of the intermolecular potential amounting to ∼9 cm(-1).

Rotationally adiabatic pair interactions of para- and ortho-hydrogen with the halogen molecules F2, Cl2, and Br2

The present work is concerned with the weak interactions between hydrogen and halogen molecules, i.e., the interactions of pairs H2-X2 with X = F, Cl, Br, which are dominated by dispersion and quadrupole-quadrupole forces. The global minimum of the four-dimensional (4D) coupled cluster with singles and doubles and perturbative triples (CCSD(T)) pair potentials is always a T shaped structure where H2 acts as the hat of the T, with well depths (De) of 1.3, 2.4, and 3.1 kJ/mol for F2, Cl2, and Br2, respectively. MP2/AVQZ results, in reasonable agreement with CCSD(T) results extrapolated to the basis set limit, are used for detailed scans of the potentials. Due to the large difference in the rotational constants of the monomers, in the adiabatic approximation, one can solve the rotational Schrödinger equation for H2 in the potential of the X2 molecule. This yields effective two-dimensional rotationally adiabatic potential energy surfaces where pH2 and oH2 are point-like particles. These potentials for the H2-X2 complexes have global and local minima for effective linear and T-shaped complexes, respectively, which are separated by 0.4-1.0 kJ/mol, where oH2 binds stronger than pH2 to X2, due to higher alignment to minima structures of the 4D-pair potential. Further, we provide fits of an analytical function to the rotationally adiabatic potentials.

Quantum simulations of the hydrogen molecule on ammonia clusters

Mixed ammonia-hydrogen molecule clusters [H2-(NH3)n] have been studied with the aim of exploring the quantitative importance of the H2 quantum motion in defining their structure and energetics. Minimum energy structures have been obtained employing genetic algorithm-based optimization methods in conjunction with accurate pair potentials for NH3-NH3 and H2-NH3. These include both a full 5D potential and a spherically averaged reduced surface mimicking the presence of a para-H2. All the putative global minima for n ≥ 7 are characterized by H2 being adsorbed onto a rhomboidal ammonia tetramer motif formed by two double donor and two double acceptor ammonia molecules. In a few cases, the choice of specific rhombus seems to be directed by the vicinity of an ammonia ad-molecule. Diffusion Monte Carlo simulations on a subset of the species obtained highlighted important quantum effects in defining the H2 surface distribution, often resulting in populating rhomboidal sites different from the global minimum one, and showing a compelling correlation between local geometrical features and the relative stability of surface H2. Clathrate-like species have also been studied and suggested to be metastable over a broad range of conditions if formed.

Theoretical and experimental study of weakly bound CO2-(pH2)2 trimers

The infrared spectrum of CO(2)-(pH(2))(2) trimers is predicted by performing exact basis-set calculations on a global potential energy surface defined as the sum of accurately known two-body pH(2)-CO(2) (J. Chem. Phys. 2010, 132, 214309) and pH(2)-pH(2) potentials (J. Chem. Phys. 2008, 129, 094304). These results are compared with new spectroscopic measurements for this species, for which 13 transitions are now assigned. A reduced-dimension treatment of the pH(2) rotation has been employed by applying the hindered-rotor averaging technique of Li, Roy, and Le Roy (J. Chem. Phys. 2010, 133, 104305). Three-body effects and the quality of the potential are discussed. A new technique for displaying the three-dimensional pH(2) density in the body-fixed frame is used, and shows that in the ground state the two pH(2) molecules are localized much more closely together than is the case for the two He atoms in the analogous CO(2)-(He)(2) species. A clear tunneling splitting is evident for the torsional motion of the two pH(2) molecules on a ring about the CO(2) molecular axis, in contrast to the case of CO(2)-(He)(2) where a more regular progression of vibrational levels reflects the much lower torsional barrier.