Size-dependent dynamics of a quantum solvent: Laser spectroscopy of HCN–(HD)n grown in helium nanodroplets

Electronic spectroscopy of Mg-phthalocyanine embedded in cold hydrogen clusters produced by a pulsed nozzle

Cold clusters of molecular hydrogen were created using a pulsed nozzle. The thermodynamical states of the clusters were characterized by measuring the cluster beam velocity and the laser-induced fluorescence (LIF) spectra of embedded molecules. Two distinct velocity components were identified in the beam that originates from different clustering mechanisms. The fast velocity component corresponds to the expansion of H₂ from the gas phase, while the slow velocity component corresponds to the expansion from the liquid phase. The velocity distribution of these two components showed no significant difference between the expansions of para and normal hydrogen. In this study, LIF spectroscopy of single Mg-phthalocyanine molecules embedded in the H₂ clusters consisting of 10⁵ H₂ molecules was used to investigate the properties of the fast component. The observed peak frequencies of the LIF signals, compared to those observed in helium droplets, were used to infer the possible presence of the liquid phase in the fast component of the H₂ clusters below 5 K. The shift, linewidth, and splitting in the spectra, which strongly depend on the ortho/para ratio, are attributed to the local configurations of hydrogen in the vicinity of the probe molecules.

Microscopic molecular superfluid response: theory and simulations

Since its discovery in 1938, superfluidity has been the subject of much investigation because it provides a unique example of a macroscopic manifestation of quantum mechanics. About 60 years later, scientists successfully observed this phenomenon in the microscopic world though the spectroscopic Andronikashvili experiment in helium nano-droplets. This reduction of scale suggests that not only helium but also para-H2 (pH2) can be a candidate for superfluidity. This expectation is based on the fact that the smaller number of neighbours and surface effects of a finite-size cluster may hinder solidification and promote a liquid-like phase. The first prediction of superfluidity in pH2 clusters was reported in 1991 based on quantum Monte Carlo simulations. The possible superfluidity of pH2 was later indirectly observed in a spectroscopic Andronikashvili experiment in 2000. Since then, a growing number of studies have appeared, and theoretical simulations have been playing a special role because they help guide and interpret experiments. In this review, we go over the theoretical studies of pH2 superfluid clusters since the experiment of 2000. We provide a historical perspective and introduce the basic theoretical formalism along with key experimental advances. We then present illustrative results of the theoretical studies and comment on the possible future developments in the field. We include sufficient theoretical details such that the review can serve as a guide for newcomers to the field.

Simulating Asymmetric Top Impurities in Superfluid Clusters: A para-Water Dopant in para-Hydrogen

We present the first simulation study of bosonic clusters doped with an asymmetric top molecule. The path-integral Monte Carlo method with the latest methodological advance in treating rigid-body rotation [Noya, E. G.; Vega, C.; McBride, C. J. Chem. Phys.2011, 134, 054117] is employed to study a para-water impurity in para-hydrogen clusters with up to 20 para-hydrogen molecules. The growth pattern of the doped clusters is similar in nature to that of pure clusters. The para-water molecule appears to rotate freely in the cluster. The presence of para-water substantially quenches the superfluid response of para-hydrogen with respect to the space-fixed frame.

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.

Molecular superfluid: nonclassical rotations in doped para-hydrogen clusters

Clusters of para-hydrogen (pH₂) have been predicted to exhibit superfluid behavior, but direct observation of this phenomenon has been elusive. Combining experiments and theoretical simulations, we have determined the size evolution of the superfluid response of pH₂ clusters doped with carbon dioxide (CO₂). Reduction of the effective inertia is observed when the dopant is surrounded by the pH₂ solvent. This marks the onset of molecular superfluidity in pH₂. The fractional occupation of solvation rings around CO₂ correlates with enhanced superfluid response for certain cluster sizes.

Rotational spectra of the van der Waals complexes of molecular hydrogen and OCS

The a- and b-type rotational transitions of the weakly bound complexes formed by molecular hydrogen and OCS, para-H2-OCS, ortho-H2-OCS, HD-OCS, para-D2-OCS, and ortho-D2-OCS, have been measured by Fourier transform microwave spectroscopy. All five species have ground rotational states with total rotational angular momentum J=0, regardless of whether the hydrogen rotational angular momentum is j=0 as in para-H2, ortho-D2, and HD or j=1 as in ortho-H2 and para-D2. This indicates quenching of the hydrogen angular momentum for the ortho-H2 and para-D2 species by the anisotropy of the intermolecular potential. The ground states of these complexes are slightly asymmetric prolate tops, with the hydrogen center of mass located on the side of the OCS, giving a planar T-shaped molecular geometry. The hydrogen spatial distribution is spherical in the three j=0 species, while it is bilobal and oriented nearly parallel to the OCS in the ground state of the two j=1 species. The j=1 species show strong Coriolis coupling with unobserved low-lying excited states. The abundance of para-H2-OCS relative to ortho-H2-OCS increases exponentially with decreasing normal H2 component in H2He gas mixtures, making the observation of para-H2-OCS in the presence of the more strongly bound ortho-H2-OCS dependent on using lower concentrations of H2. The determined rotational constants are A=22 401.889(4) MHz, B=5993.774(2) MHz, and C=4602.038(2) MHz for para-H2-OCS; A=22 942.218(6) MHz, B=5675.156(7) MHz, and C=4542.960(7) MHz for ortho-H2-OCS; A=15 970.010(3) MHz, B=5847.595(1) MHz, and C=4177.699(1) MHz for HD-OCS; A=12 829.2875(9) MHz, B=5671.3573(7) MHz, and C=3846.7041(6) MHz for ortho-D2-OCS; and A=13 046.800(3) MHz, B=5454.612(2) MHz, and C=3834.590(2) MHz for para-D2-OCS.

Infrared spectra of N2O–(ortho-D2)N and N2O–(HD)N clusters trapped in bulk solid parahydrogen

High-resolution infrared spectra of the clusters N2O-(ortho-D2)N and N2O-(HD)N, N=1-4, isolated in bulk solid parahydrogen at liquid helium temperatures are studied in the 2225 cm-1 region of the nu3 antisymmetric stretch of N2O. The clusters form during vapor deposition of separate gas streams of a precooled hydrogen mixture (ortho-D2para-H2 or HDpara-H2) and N2O onto a BaF2 optical substrate held at approximately 2.5 K in a sample-in-vacuum liquid helium cryostat. The cluster spectra reveal the N2O nu3 vibrational frequency shifts to higher energy as a function of N, and the shifts are larger for ortho-D2 compared to HD. These vibrational shifts result from the reduced translational zero-point energy for N2O solvated by the heavier hydrogen isotopomers. These spectra allow the N=0 peak at 2221.634 cm-1, corresponding to the nu3 vibrational frequency of N2O isolated in pure solid parahydrogen, to be assigned. The intensity of the N=0 absorption feature displays a strong temperature dependence, suggesting that significant structural changes occur in the parahydrogen solvation environment of N2O in the 1.8-4.9 K temperature range studied.

HF in clusters of molecular hydrogen: II. Quantum solvation by H2 isotopomers, cluster rigidity, and comparison with CO-doped parahydrogen clusters

We present a comprehensive theoretical study of the quantum solvation of the HF molecule by small clusters of the H2 isotopomers, p-H2, HD, and o-D2, with up to 13 hydrogen solvent molecules. This complements our earlier work on the HF-doped parahydrogen clusters [H. Jiang and Z. Bacic, J. Chem. Phys. 122, 244306 (2005)]. The ground-state properties of the clusters are calculated exactly using the diffusion Monte Carlo method. Detailed information is obtained regarding the size and isotopomer dependences of the energetics, vibrationally averaged structures, and their rigidity. The rigidity of these clusters is investigated further by analyzing the distributions of their principal moments of inertia from the diffusion Monte Carlo simulations. The clusters are found to be rather rigid, especially when compared with the pure parahydrogen clusters of the same size. Extensive comparison is made with the quantum Monte Carlo results for the CO-doped parahydrogen clusters and significant differences are observed in the size evolution of certain properties, notably the chemical potential.

Vibrational shifts of OCS in mixed clusters of parahydrogen and helium

We present a detailed theoretical study of the solvation structure and solvent induced vibrational shifts for an OCS molecule embedded in pure parahydrogen clusters and in mixed parahydrogen/helium clusters. The use of two recent OCS-(parahydrogen) and OCS-helium ab initio potential energy surfaces having explicit dependence on the asymmetric stretch of the OCS molecule allows calculation of the frequency shift of the OCS nu(3) vibration as a function of the cluster size and composition. We present results for clusters containing up to a full first solvation shell of parahydrogen (N=17 molecules), and up to M=128-N helium atoms. Due to the greater interaction strength of parahydrogen than helium with OCS, in the mixed clusters the parahydrogen molecules always displace He atoms in the first solvation shell around OCS and form multiple axial rings as in the pure parahydrogen clusters. In the pure clusters, the chemical potential of parahydrogen shows several magic numbers (N=8,11,14) that reflect an enhanced stability of axial rings containing one less molecule than required for complete filling at N=17. Only the N=14 magic number survives in the mixed clusters, as a result of different filling orders of the rings and greater delocalization of both components. The OCS vibration shows a redshift in both pure and mixed clusters, with N-dependent values that are in good agreement with the available experimental data. The dependence of the frequency shift on the cluster size and its composition is analyzed in terms of the parahydrogen and helium density distributions around the OCS molecule as a function of N and M. The frequency shift is found to be strongly dependent on the detailed distribution of the parahydrogen molecules in the pure parahydrogen clusters, and to be larger but show a smoother dependence on N in the presence of additional helium, consistent with the more delocalized nature of the mixed clusters.

Infrared spectra of seeded hydrogen clusters: (para-H2)N–N2O and (ortho-H2)N–N2O, N=2–13

High-resolution infrared spectra of clusters containing para-H2 and/or ortho-H2 and a single nitrous oxide molecule are studied in the 2225-cm(-1) region of the upsilon1 fundamental band of N2O. The clusters are formed in pulsed supersonic jet expansions from a cooled nozzle and probed using a tunable infrared diode laser spectrometer. The simple symmetric rotor-type spectra generally show no resolved K structure, with prominent Q-branch features for ortho-H2 but not para-H2 clusters. The observed vibrational shifts and rotational constants are reported. There is no obvious indication of superfluid effects for para-H2 clusters up to N=13. Sharp transitions due to even larger clusters are observed, but no definite assignments are possible. Mixed (para-H2)N-(ortho-H2)M-N2O cluster line positions can be well predicted by linear interpolation between the corresponding transitions of the pure clusters.

HF in clusters of molecular hydrogen. I. Size evolution of quantum solvation by parahydrogen molecules

We present a theoretical study of the quantum solvation of the HF molecule by a small number of parahydrogen molecules, having n = 1-13 solvent particles. The minimum-energy cluster structures determined for n = 1-12 have all of the H(2) molecules in the first solvent shell. The first solvent shell closes at n = 12 and its geometry is icosahedral, with the HF molecule at the center. The quantum-mechanical ground-state properties of the clusters are calculated exactly using the diffusion Monte Carlo method. The zero-point energy of (p-H(2))(n)HF clusters is unusually large, amounting to 86% of the potential well depth for n > 7. The radial probability distribution functions (PDFs) confirm that the first solvent shell is complete for n = 12, and that the 13th p-H(2) molecule begins to fill the second solvent shell. The p-H(2) molecules execute large-amplitude motions and are highly mobile, making the solvent cage exceptionally fluxional. The anisotropy of the solvent, very pronounced for small clusters, decreases rapidly with increasing n, so that for n approximately 8-9 the solvent environment is practically isotropic. The analysis of the pair angular PDF reveals that for a given n, the parahydrogen solvent density around the HF is modulated in a pattern which clearly reflects the lowest-energy cluster configuration. The rigidity of the solvent clusters displays an interesting size dependence, increasing from n = 6 to 9, becoming floppier for n = 10, and increasing again up to n = 12, as the solvent shell is filled. The rigidity of the solvent cage appears to reach its maximum for n = 12, the point at which the first solvent shell is closed.

Small para-hydrogen clusters doped with carbon monoxide: Quantum Monte Carlo simulations and observed infrared spectra

The structures and rotational dynamics of clusters of a single carbon monoxide molecule solvated in para-hydrogen, (paraH(2))(N)-CO, have been simulated for sizes up to N=17 using the reptation Monte Carlo technique. The calculations indicate the presence of two series of R(0) rotational transitions with J=1<--0 for cold clusters, similar to those predicted and observed in the case of He(N)-CO. Infrared spectra of these clusters have been observed in the region of the C-O stretch ( approximately 2143 cm(-1)) in a pulsed supersonic jet expansion using a tunable diode laser probe. With the help of the calculations, the observed R(0) rotational transitions have been assigned up to N=9 for the b-type series and N=14 for the a-type series. Theory and experiment agree rather well, except that theory tends to overestimate the b-type energies. The (paraH(2))(12)-CO cluster is calculated to be particularly stable and (relatively) rigid, corresponding to completion of the first solvation shell, and it is observed to have the strongest a-type transition.

Infrared spectra of seeded hydrogen clusters: (paraH2)N–OCS, (orthoH2)N–OCS, and (HD)N–OCS, N=2–7

Infrared spectra of hydrogen-carbonyl sulfide clusters containing paraH2, orthoH2, or HD have been studied in the 2060 cm(-1) region of the C-O stretching vibration. The clusters were formed in pulsed supersonic jet expansions and probed using a tunable infrared diode laser spectrometer. Simple symmetric rotor type spectra were observed and assigned for clusters containing up to N = 7 hydrogen molecules. There was no resolved K structure, and Q-branch features were present for orthoH2 and HD but absent for paraH2. These characteristics can be rationalized in terms of near symmetric rotor structures, very low effective rotational temperatures (0.15 to 0.6 K), and nuclear spin statistics. The observed vibrational shifts were compared with those from recent observations on the same clusters embedded in helium nanodroplets. The observed rotational constants for the paraH2 clusters are in good agreement with a recent quantum Monte Carlo simulation. Some mixed clusters were also observed, such as HD-HD-He-OCS and paraH2 - orthoH2 - OCS.