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.

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.

Full empirical potential curves for the X(1)Σ(+) and A(1)Π states of CH(+) from a direct-potential-fit analysis.

All available "conventional" absorption/emission spectroscopic data have been combined with photodissociation data and translational spectroscopy data in a global analysis that yields analytic potential energy and Born-Oppenheimer breakdown functions for the X(1)Σ(+) and A(1)Π states of CH(+) and its isotopologues that reproduce all of the data (on average) within their assigned uncertainties. For the ground X(1)Σ(+) state, this fully quantum mechanical "Direct-Potential-Fit" analysis yielded an improved empirical well depth of 𝔇e = 34 362.8(3) cm(-1) and equilibrium bond length of re = 1.128 462 5 (58) Å. For the A(1)Π state, the resulting well depth and equilibrium bond length are 𝔇e = 10 303.7(3) cm(-1) and re = 1.235 896 (14) Å, while the electronic isotope shift from the hydride to the deuteride is ΔTe = - 5.99(±0.08) cm(-1).

Raman Vibrational Shifts of Small Clusters of Hydrogen Isotopologues.

Raman vibrational shifts of small parahydrogen (pH2), orthodeuterium (oD2), and paratritium (pT2) clusters with respect to the free molecules are calculated by combining a first order perturbation theory approach with Langevin equation Path Integral Ground State (LePIGS) simulations [ J. Phys. Chem. A 2013 , 117 , 7461 ]. Our theoretical predictions are compared to existing cryogenic free jet expansion results for pure (pH2)N clusters [ Phys. Rev. Lett. 2004 , 92 , 223401 ] and to new measurements for (oD2)N clusters reported here. This method has been successfully used before to predict the Raman vibrational shifts of (pH2)N clusters [ J. Chem. Phys. 2014 , 141 , 014310 ]. The 6-D interaction potential of Hinde [ J. Chem. Phys. 2008 , 128 , 154308 ] is reduced to 1-D using the Adiabatic Hindered Rotor approximation to yield effective pair potentials for both molecules being in the ground vibrational state, and for one of them carrying one quantum of vibrational excitation. These reduced 1-D potentials are fitted to a Morse Long Range analytic form for later convenience. Good agreement between experiment and theory is found for the smaller clusters, but significant deviations remain for the larger ones.

Dissociation energies and potential energy functions for the ground X (1)Σ(+) and "avoided-crossing" A (1)Σ(+) states of NaH.

A direct-potential-fit analysis of all accessible data for the A (1)Σ(+) - X (1)Σ(+) system of NaH and NaD is used to determine analytic potential energy functions incorporating the correct theoretically predicted long-range behaviour. These potentials represent all of the data (on average) within the experimental uncertainties and yield an improved estimate for the ground-state NaH well depth of 𝔇e = 15797.4 (±4.3) cm(-1), which is ∼20 cm(-1) smaller than the best previous estimate. The present analysis also yields the first empirical determination of centrifugal (non-adiabatic) and potential-energy (adiabatic) Born-Oppenheimer breakdown correction functions for this system, with the latter showing that the A-state electronic isotope shift is -1.1(±0.6) cm(-1) going from NaH to NaD.

First-principles prediction of the Raman shifts in parahydrogen clusters.

We report a first-principles prediction of the Raman shifts of parahydrogen (pH2) clusters of sizes N = 4-19 and 33, based on path integral ground-state simulations with an ab initio potential energy surface. The Raman shifts are calculated, using perturbation theory, as the average of the difference-potential energy surface between the potential energy surfaces for vibrationally excited and ground-state parahydrogen monomers. The radial distribution of the clusters is used as a weight function in this average. Very good overall agreement with experiment [G. Tejeda, J. M. Fernández, S. Montero, D. Blume, and J. P. Toennies, Phys. Rev. Lett. 92, 223401 (2004)] is achieved for p(H2)(2-8,13,33). A number of different pair potentials are employed for the calculation of the radial distribution functions. We find that the Raman shifts are sensitive to slight variations in the radial distribution functions.

Analytic Morse/long-range potential energy surfaces and predicted infrared spectra for CO-H2 dimer and frequency shifts of CO in (para-H2)N N = 1-20 clusters.

A five-dimensional ab initio potential energy surface (PES) for CO-H2 that explicitly incorporates dependence on the stretch coordinate of the CO monomer has been calculated. Analytic four-dimensional PESs are obtained by least-squares fitting vibrationally averaged interaction energies for vCO = 0 and 1 to the Morse/long-range potential function form. These fits to 30,206 points have root-mean-square (RMS) deviations of 0.087 and 0.082 cm(-1), and require only 196 parameters. The resulting vibrationally averaged PESs provide good representations of the experimental infrared data: for infrared transitions of para H2-CO and ortho H2-CO, the RMS discrepancies are only 0.007 and 0.023 cm(-1), which are almost in the same accuracy as those values of 0.010 and 0.018 cm(-1) obtained from full six-dimensional ab initio PESs of V12 [P. Jankowski, A. R. W. McKellar, and K. Szalewicz, Science 336, 1147 (2012)]. The calculated infrared band origin shift associated with the fundamental of CO is -0.179 cm(-1) for para H2-CO, which is the same value as that extrapolated experimental value, and slightly better than the value of -0.176 cm(-1) obtained from V12 PESs. With these potentials, the path integral Monte Carlo algorithm and a first order perturbation theory estimate are used to simulate the CO vibrational band origin frequency shifts of CO in (para H2)N-CO clusters for N = 1-20. The predicted vibrational frequency shifts are in excellent agreement with available experimental observations. Comparisons are also made between these model potentials.

Accurate analytic potential and Born-Oppenheimer breakdown functions for MgH and MgD from a direct-potential-fit data analysis.

New high-resolution visible Fourier transform emission spectra of the A (2)Π â†’ X (2)Σ(+) and B' (2)Σ(+) → X (2)Σ(+) systems of (24)MgD and of the B' (2)Σ(+) → X (2)Σ(+) systems of (25,26)MgD and (25,26)MgH have been combined with earlier results for (24)MgH in a multi-isotopologue direct-potential-fit analysis to yield improved analytic potential energy and Born-Oppenheimer breakdown functions for the ground X (2)Σ(+) state of MgH. Vibrational levels of the ground state of (24)MgD were observed up to v" = 15, which is bound by only 30.6 ± 0.10 cm(-1). Including deuteride and minor magnesium isotopologue data allowed us also to determine the adiabatic Born-Oppenheimer breakdown effects in this molecule. The fitting procedure used the recently developed Morse/Long-Range (MLR) potential energy function, whose asymptotic behavior incorporates the correct inverse-power form. A spin-splitting radial correction function to take account of the (2)Σ spin-rotation interaction was also determined. Our refined value for the ground-state dissociation energy of the dominant isotopologue ((24)MgH) is D(e) = 11,104.25 ± 0.8 cm (-1), in which the uncertainty also accounts for the model dependence of the fitted D(e) values for a range of physically acceptable fits. We were also able to determine the marked difference in the well depths of (24)MgH and (24)MgD (with the deuteride potential curve being 7.58 ± 0.30 cm(-1) deeper than that of the hydride) as well as smaller well-depth differences for the minor (25,26)Mg isotopologues. This analytic potential function also predicts that the highest bound level of (24)MgD is v" = 16 and that it is bound by only 2.73 ± 0.10 cm(-1).

A new six-dimensional potential energy surface for H2-N2O and its adiabatic-hindered-rotor treatment.

A six-dimensional ab initio potential energy surface (PES) for H2-N2O which explicitly includes the symmetric and asymmetric vibrational coordinates Q1 and Q3 of N2O is calculated at the coupled-cluster singles and doubles with noniterative inclusion of connected triple level using an augmented correlation-consistent polarized-valence quadruple-zeta basis set together with midpoint bond functions. Four-dimensional intermolecular PESs are then obtained by fitting the vibrationally averaged interactions energies for υ3(N2O) = 0 and 1 to the Morse∕long-range analytical form. In the fits, fixing the long-range parameters at theoretical values smoothes over the numerical noise in the ab initio points in the long-range region of the potential. Using the adiabatic hindered-rotor approximation, two-dimensional PESs for hydrogen-N2O complexes with different isotopomers of hydrogen are generated by averaging the 4D PES over the rotation of the hydrogen molecule within the complex. The band-origin shifts for the hydrogen-N2O dimers calculated using both the 4D PESs and the angle-averaged 2D PESs are all in good agreement with each other and with the available experimental observations. The predicted infrared transition frequencies for para-H2-N2O and ortho-D2-N2O are also consistent with the observed spectra.

On the analytical representation of free energy profiles with a Morse/long-range model: application to the water dimer.

We investigate the analytical representation of potentials of mean force (pmf) using the Morse/long-range (MLR) potential approach. The MLR method had previously been used to represent potential energy surfaces, and we assess its validity for representing free-energies. The advantage of the approach is that the potential of mean force data only needs to be calculated in the short to medium range region of the reaction coordinate while the long range can be handled analytically. This can result in significant savings in terms of computational effort since one does not need to cover the whole range of the reaction coordinate during simulations. The water dimer with rigid monomers whose interactions are described by the commonly used TIP4P model [W. Jorgensen and J. Madura, Mol. Phys. 56, 1381 (1985)] is used as a test case. We first calculate an "exact" pmf using direct Monte Carlo (MC) integration and term such a calculation as our gold standard (GS). Second, we compare this GS with several MLR fits to the GS to test the validity of the fitting procedure. We then obtain the water dimer pmf using metadynamics simulations in a limited range of the reaction coordinate and show how the MLR treatment allows the accurate generation of the full pmf. We finally calculate the transition state theory rate constant for the water dimer dissociation process using the GS, the GS MLR fits, and the metadynamics MLR fits. Our approach can yield a compact, smooth, and accurate analytical representation of pmf data with reduced computational cost.

A new four-dimensional ab initio potential energy surface for N2O-He and vibrational band origin shifts for the N2O-He(N) clusters with N = 1-40.

A new four-dimensional ab initio potential energy surface for N(2)O-He is constructed at the CCSD(T) level with an aug-cc-pVQZ basis set together with bond functions. The vibrational coordinates Q(1) and Q(3) of N(2)O are explicitly included, due to the strong coupling between the symmetric and asymmetric stretches of N(2)O. A global potential energy surface is obtained by fitting the original potential points to a four-dimensional Morse∕long range (MLR) analytical form. In the fitting, the ab initio noise in the long range region of the potential is smoothed over by theoretically fixed long range parameters. Two-dimensional intermolecular potentials for both the ground and the excited υ(3) states of N(2)O are then constructed by vibrationally averaging the four-dimensional potential. Based on the two-dimensional potentials, we use the path integral Monte Carlo algorithm to calculate the vibrational band origin shifts for the N(2)O-He(N) clusters using a first order perturbation theory estimate. The calculated shifts agree reasonably well with the experimental values and reproduce the evolution tendency from dimer to large clusters.

Rapid, accurate calculation of the s-wave scattering length.

Transformation of the conventional radial Schrödinger equation defined on the interval r ∈ [0, ∞) into an equivalent form defined on the finite domain y(r) ∈ [a, b] allows the s-wave scattering length a(s) to be exactly expressed in terms of a logarithmic derivative of the transformed wave function φ(y) at the outer boundary point y = b, which corresponds to r = ∞. In particular, for an arbitrary interaction potential that dies off as fast as 1/r(n) for n ≥ 4, the modified wave function φ(y) obtained by using the two-parameter mapping function r(y; ̄r,ß) = ̄r[1 + 1/ß tan(πy/2)] has no singularities, and a(s) = ̄r[1 + 2/πß 1/φ(1) dφ(1)/dy]. For a well bound potential with equilibrium distance r(e), the optimal mapping parameters are ̄r ≈ r(e) and ß ≈ n/2 - 1. An outward integration procedure based on Johnson's log-derivative algorithm [J. Comp. Phys. 13, 445 (1973)] combined with a Richardson extrapolation procedure is shown to readily yield high precision a(s)-values both for model Lennard-Jones (2n, n) potentials and for realistic published potentials for the Xe-e(-), Cs(2)(aΣ(u)(+)(3)), and (3, 4)He(2)(XΣ(g)(+)(1)) systems. Use of this same transformed Schrödinger equation was previously shown [V. V. Meshkov et al., Phys. Rev. A 78, 052510 (2008)] to ensure the efficient calculation of all bound levels supported by a potential, including those lying extremely close to dissociation.

"Adiabatic-hindered-rotor" treatment of the parahydrogen-water complex.

Inspired by a recent successful adiabatic-hindered-rotor treatment for parahydrogen pH(2) in CO(2)-H(2) complexes [H. Li, P.-N. Roy, and R. J. Le Roy, J. Chem. Phys. 133, 104305 (2010); H. Li, R. J. Le Roy, P.-N. Roy, and A. R. W. McKellar, Phys. Rev. Lett. 105, 133401 (2010)], we apply the same approximation to the more challenging H(2)O-H(2) system. This approximation reduces the dimension of the H(2)O-H(2) potential from 5D to 3D and greatly enhances the computational efficiency. The global minimum of the original 5D potential is missing from the adiabatic 3D potential for reasons based on solution of the hindered-rotor Schrödinger equation of the pH(2). Energies and wave functions of the discrete rovibrational levels of H(2)O-pH(2) complexes obtained from the adiabatic 3D potential are in good agreement with the results from calculations with the full 5D potential. This comparison validates our approximation, although it is a relatively cruder treatment for pH(2)-H(2)O than it is for pH(2)-CO(2). This adiabatic approximation makes large-scale simulations of H(2)O-pH(2) systems possible via a pairwise additive interaction model in which pH(2) is treated as a point-like particle. The poor performance of the diabatically spherical treatment of pH(2) rotation excludes the possibility of approximating pH(2) as a simple sphere in its interaction with H(2)O.

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.

An "adiabatic-hindered-rotor" treatment allows para-H(2) to be treated as if it were spherical.

In para-H(2)-{molecule} interactions, the common assumption that para-H(2) may be treated as a spherical particle is often substantially in error. For example, quantum mechanical eigenvalues on a full four-dimensional (4D) potential energy surface for para H(2)-{linear molecule} species often differ substantially from those calculated from the corresponding two-dimensional (2D) surface obtained by performing a simple spherical average over the relative orientations of the H(2) moiety. However, use of an "adiabatic-hindered-rotor" approximation can yield an effective 2D surface whose spectroscopic properties are an order of magnitude closer to those yielded by a full 4D treatment.

Analytic Morse/long-range potential energy surfaces and predicted infrared spectra for CO2-H2.

Five-dimensional ab initio potential energy surfaces (PESs) for CO(2)-H(2) that explicitly incorporate dependence on the Q(3) asymmetric-stretch normal-mode coordinate of the CO(2) monomer and are parametrically dependent on its Q(1) symmetric-stretch coordinate have been calculated. Analytic four-dimensional PESs are obtained by least-squares fitting vibrationally averaged interaction energies for v(3)(CO(2)) = 0, and 1 to the Morse/long-range potential function form. These fits to 23,113 points have root-mean-square (rms) deviations of 0.143 and 0.136 cm(-1), and require only 167 parameters. The resulting vibrationally averaged PESs provide good representations of the experimental infrared data: for infrared transitions of para- and ortho-H(2)-CO(2), the rms discrepancies are only 0.004 and 0.005 cm(-1), respectively. The calculated infrared band origin shifts associated with the nu(3) fundamental of CO(2) are -0.179 and -0.092 cm(-1) for para-H(2)-CO(2) and ortho-H(2)-CO(2), in good agreement with the (extrapolated) experimental values of -0.198 and -0.096 cm(-1).

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.

Accurate analytic potentials for Li(2)(X (1)Sigma(g) (+)) and Li(2)(A (1)Sigma(u) (+)) from 2 to 90 A, and the radiative lifetime of Li(2p).

Extensions of the recently introduced "Morse/long-range" (MLR) potential function form allow a straightforward treatment of a molecular state for which the inverse-power long-range potential changes character with internuclear separation. Use of this function in a direct-potential-fit analysis of a combination of new fluorescence data for (7,7)Li(2), (6,6)Li(2), and (6,7)Li(2) with previously reported data for the A((1)Sigma(u) (+)) and X((1)Sigma(g) (+)) states yields accurate, fully analytic potentials for both states, together with the analytic "adiabatic" Born-Oppenheimer breakdown radial correction functions which are responsible for the difference between the interaction potentials and well depths for the different isotopologues. This analysis yields accurate well depths of D(e)=8516.709(+/-0.004) and 8516.774(+/-0.004) cm(-1) and scattering lengths of 18.11(+/-0.05) and 23.84(+/-0.05) A for the ground-states of (7,7)Li(2) and (6,6)Li(2), respectively, as well as improved atomic radiative lifetimes of tau(2p)=27.1018(+/-0.0014) ns for (7)Li(2p) and 27.1024(+/-0.0014) ns for (6)Li(2p).

Predicted bound states and microwave spectrum of N2-He van der Waals complexes.

Numerical calculations show that four modern potential energy surfaces for N(2)-He all support 18 bound intermolecular states for the homonuclear isotopologues (14,14)N(2)-(4)He and (15,15)N(2)-(4)He, and 12 (or 13, for one surface) truly bound states for (14,15)N(2)-He. This contradicts a recent statement [Patel et al., J. Chem. Phys. 119, 909 (2003)] that one of these surfaces supports no bound states, and it yields predictions for 27 allowed pure rotational transitions among the truly bound states of the homonuclear isotopologues of this complex.

Path-integral Monte Carlo simulation of nu3 vibrational shifts for CO2 in (He)n clusters critically tests the He-CO2 potential energy surface.

Path-integral Monte Carlo simulations of the nu(3) vibrational band origin frequency shifts of CO(2) in (He)(n) clusters for n=1-40 show that although only the asymmetric-stretch mode of CO(2) is being excited, the effect of the associated change in the average value of Q(1) cannot be ignored. When this fourth degree of freedom is taken into account, the resulting predicted vibrational frequency shifts are in excellent agreement with experiment across this whole range of cluster size. It is also shown that the quality of predictions obtained from simulations on a given potential energy surface can depend significantly on the choice of the analytic function used to represent it.