Path integral methods for rotating molecules in superfluids

We present a path integral Monte Carlo (PIMC) methodology for quantum simulation of molecular rotations in superfluid environments such as helium and para-hydrogen that combines the sampling of rotational degrees of freedom for a molecular impurity with multilevel Metropolis sampling of Bose permutation exchanges for the solvating species. We show how the present methodology can be applied to the evaluation of imaginary time rotational correlation functions of the molecular impurity, from which the effective rotational constants can be extracted. The combined rotation/permutation sampling approach allows for the first time explicit assessment of the effect of Bose permutations on molecular rotation dynamics, and the converse, i.e., the effect of molecular rotations on permutation exchanges and local superfluidity. We present detailed studies showing that the effect of Bose permutations in the solvating environment is more significant for the dynamics of heavy than light molecules in helium, and that Bose permutation exchanges are slightly enhanced locally by molecular rotation. Finally, the examples studied here reveal a size dependence of rotational excitations for molecules possessing a strongly anisotropic interaction with helium in 4HeN clusters between N approximately 20 and N approximately 10(3).     

Rotational excitations of N2O in small helium clusters and the role of Bose permutation symmetry

We present a detailed study of the energetics, structures, and Bose properties of small clusters of (4)He containing a single nitrous oxide (N(2)O) molecule, from N=1 (4)He up to sizes corresponding to completion of the first solvation shell around N(2)O (N=16 (4)He). Ground state properties are calculated using the importance-sampled rigid-body diffusion Monte Carlo method, rotational excited state calculations are made with the projection operator imaginary time spectral evolution method, and Bose permutation exchange and associated superfluid properties are calculated with the finite temperature path integral method. For N< or =5 the helium atoms are seen to form an equatorial ring around the molecular axis, at N=6 helium density starts to occupy the second (local) minimum of the N(2)O-He interaction at the oxygen side of the molecule, and N=9 is the critical size at which there is onset of helium solvation all along the molecular axis. For N> or =8 six (4)He atoms are distributed in a symmetric, quasirigid ring around N(2)O. Path integral calculations show essentially complete superfluid response to rotation about the molecular axis for N> or =5, and a rise of the perpendicular superfluid response from zero to appreciable values for N> or =8. Rotational excited states are computed for three values of the total angular momentum, J=1-3, and the energy levels fitted to obtain effective spectroscopic constants that show excellent agreement with the experimentally observed N dependence of the effective rotational constant B(eff). The non-monotonic behavior of the rotational constant is seen to be due to the onset of long (4)He permutation exchanges and associated perpendicular superfluid response of the clusters for N> or =8. We provide a detailed analysis of the role of the helium solvation structure and superfluid properties in determining the effective rotational constants.     

Path integral Monte Carlo approach for weakly bound van der Waals complexes with rotations: algorithm and benchmark calculations

A path integral Monte Carlo technique suitable for the treatment of doped helium clusters with inclusion of the rotational degrees of freedom of the dopant is introduced. The extrapolation of the results to the limit of infinite Trotter number is discussed in detail. Benchmark calculations for small weakly bound (4)He(N)--OCS clusters are presented. The Monte Carlo results are compared with those of basis set calculations for the He--OCS dimer. A technique to analyze the orientational imaginary time correlation function is suggested. It allows one to obtain information regarding the effective rotational constant for a doped helium cluster based on a model for the rotational Hamiltonian. The renormalization of the effective rotational constant for (4)He(N)--OCS clusters derived from the orientational imaginary time correlation function is in good agreement with experimental results.     

Quantum Monte Carlo study of helium clusters doped with nitrous oxide: quantum solvation and rotational dynamics

Dynamical and structural properties of small (4)He(N)-N(2)O complexes have been analyzed using ground-state and finite-temperature Monte Carlo simulations. The effective rotational constants resulting from the ground-state calculations are in excellent agreement with the results of a recent spectroscopic study [Y. Xu et al., Phys. Rev. Lett. 91, 163401 (2003)]. After an initial decrease for cluster sizes up to N=8, the rotational constant increases, signaling a transition from a molecular complex to a quantum-solvated system. Such a turnaround is not present in the rotational constants extracted from the finite-temperature Monte Carlo calculations, performed for Boltzmann statistics, thus highlighting the importance of exchange effects to explain the decoupling between a solvated dopant and the helium motion.     

Rotational fluctuation of molecules in quantum clusters. I. Path integral hybrid Monte Carlo algorithm

In this paper, we present a path integral hybrid Monte Carlo (PIHMC) method for rotating molecules in quantum fluids. This is an extension of our PIHMC for correlated Bose fluids [S. Miura and J. Tanaka, J. Chem. Phys. 120, 2160 (2004)] to handle the molecular rotation quantum mechanically. A novel technique referred to be an effective potential of quantum rotation is introduced to incorporate the rotational degree of freedom in the path integral molecular dynamics or hybrid Monte Carlo algorithm. For a permutation move to satisfy Bose statistics, we devise a multilevel Metropolis method combined with a configurational-bias technique for efficiently sampling the permutation and the associated atomic coordinates. Then, we have applied the PIHMC to a helium-4 cluster doped with a carbonyl sulfide molecule. The effects of the quantum rotation on the solvation structure and energetics were examined. Translational and rotational fluctuations of the dopant in the superfluid cluster were also analyzed.     

Rotational dynamics of CO solvated in small He clusters: a quantum Monte Carlo study

The rotational dynamics of CO single molecules solvated in small He clusters (CO @ HeN) has been studied using reptation quantum Monte Carlo simulations for cluster sizes up to N = 30. Our results are in good agreement with the rotovibrational features of the infrared spectrum recently determined for this system and provide a deep insight into the relation between the structure of the cluster and its dynamics. Simulations for large N also provide a prediction of the effective moment of inertia of CO in the He nanodroplet regime, which has not been measured so far.     

Rotational spectrum of cyanoacetylene solvated with helium atoms

The high resolution microwave spectra of He(N)-HCCCN clusters were studied in the size ranges of 1-18 and 25-31. In the absence of an accompanying infrared study, rotational excitation energies were computed by the reptation quantum Monte Carlo method and used to facilitate the search and assignment of R(0) transitions from N > 6, as well as R(1) transitions with N > 1. The assignments in the range of 25-31 are accurate to +/-2 cluster size units, with an essentially certain relative ordering. The rotational transition frequencies decrease with N = 1-6 and then show oscillatory behavior for larger cluster sizes, which is now recognized to be a manifestation of the onset and microscopic evolution of superfluidity. For cluster sizes beyond completion of the first solvation shell the rotational frequencies increase significantly above the large-droplet limit. This behavior, common to other linear molecules whose interaction with He features a strong nearly equatorial minimum, is analyzed using path integral Monte Carlo simulations. The He density in the incipient second solvation shell is shown to open a new channel for long permutation cycles, thus increasing the decoupling of the quantum solvent from the rotation of the dopant molecule.     

Rotational structure of small 4He clusters seeded with HF, HCl, and HBr molecules

Diffusion Monte Carlo calculations are performed for ground and excited rotational states of HX(4He)N, complexes with N相似文献   

Rovibrational spectra for the HCCCN*HCN and HCN*HCCCN binary complexes in 4He droplets

Rovibrational spectra are measured for the HCCCN*HCN and HCN*HCCCN binary complexes in helium droplets at low temperature. Though no Q-branch is observed in the infrared spectrum of the linear HCN*HCCCN dimer, which is consistent with previous experimental results obtained for other linear molecules, a prominent Q-branch is found in the corresponding infrared spectrum of the HCCCN*HCN complex. This Q-branch, which is reminiscent of the spectrum of a parallel band of a prolate symmetric top, implies that some component of the total angular momentum is parallel to the molecular axis. The appearance of this particular spectroscopic feature is analyzed here in terms of a nonsuperfluid helium density induced by the molecular interactions. Finite temperature path integral Monte Carlo simulations are performed using potential energy surfaces calculated with second-order M?ller-Plesset perturbation theory, to investigate the structural and superfluid properties of both HCCCN*HCN(4He)N and HCN*HCCCN(4He)N clusters with N < or = 200. Explicit calculation of local and global nonsuperfluid densities demonstrates that this difference in the rovibrational spectra of the HCCCN*HCN and HCN*HCCCN binary complexes in helium can be accounted for by local differences in the superfluid response to rotations about the molecular axis, i.e., different parallel nonsuperfluid densities. The parallel and perpendicular nonsuperfluid densities are found to be correlated with the locations and strengths of extrema in the dimer interaction potentials with helium, differences between which derive from the variable extent of polarization of the CN bond in cyanoacetylene and the hydrogen-bonded CH unit in the two isomers. Calculation of the corresponding helium moments of inertia and effective rotational constants of the binary complexes yields overall good agreement with the experimental values.     

Path integral Monte Carlo study of CO2 solvation in 4He clusters

We present a finite temperature quantum mechanical study of the dynamical and structural properties of small (4)He(N)-CO(2) clusters (N< or =17) using a path integral Monte Carlo (PIMC) method. The simulations were based on a He-CO(2) interaction potential with explicit dependence on the asymmetric stretch of the CO(2) molecule obtained at the CCSD(T) level. The shift of the CO(2) antisymmetric stretching (nu(3)) band origin and effective rotational constant were calculated as a function of the cluster size. In excellent agreement with experimental observations, the CO(2) vibrational band origin shifts and rotational constant show a turnaround near N=5, corresponding to a donut structure with the He atoms in equatorial positions of the linear dopant molecule.     

Spectroscopic studies of OCS-doped 4He clusters with 9-72 helium atoms: observation of broad oscillations in the rotational moment of inertia

High-resolution spectra of HeN-OCS clusters with N up to 39 in the microwave region and up to 72 in the infrared region were observed with apparatus-limited line widths of about 15 kHz and 0.001 cm(-1), respectively. The cold (approximately 0.2 K) clusters were produced in pulsed supersonic jet expansions of very dilute OCS + He mixtures and probed using a microwave Fourier transform spectrometer or a tunable infrared diode laser spectrometer. Consistent analyses of the microwave and infrared data yield band origins for the carbonyl stretching vibration, together with rotational parameters for the ground and excited vibrational states. The rotational constant, B, passes through a minimum at N = 9 and then rises as the He atoms uncouple from the OCS rotational motion as a result of superfluid effects. There are broad unexpected oscillations in B, with maxima at N = 24 and 47 and minima at N = 36 and 62. The change in B upon vibrational excitation, which is negative for the OCS molecule, converges to positive values for N > 15. These results help to bridge the gap between individual molecules and bulk matter with atom-by-atom resolution over a significant range of cluster sizes.     

Computational spectroscopy of helium-solvated molecules: effective inertia, from small He clusters toward the nanodroplet regime

Accurate computer simulations of the rotational dynamics of linear molecules solvated in He clusters indicate that the large-size (nanodroplet) regime is attained quickly for light rotors (HCN) and slowly for heavy ones (OCS, N2O, and CO2), thus challenging previously reported results. Those results spurred the view that the different behavior of light rotors with respect to heavy ones-including a smaller reduction of inertia upon solvation of the former-would result from the lack of adiabatic following of the He density upon molecular rotation. We have performed computer experiments in which the rotational dynamics of OCS and HCN molecules was simulated using a fictitious inertia appropriate to the other molecule. These experiments indicate that the approach to the nanodroplet regime, as well as the reduction of the molecular inertia upon solvation, is determined by the anistropy of the potential, more than by the molecular weight. Our findings are in agreement with recent infrared and/or microwave experimental data which, however, are not yet totally conclusive by themselves.     

Computational spectroscopy of carbon monoxide isotopomers in helium clusters

The rotational excitation spectrum, including the vibrational shift of the rotational band, of several CO isotopomers solvated in He clusters has been calculated. Reptation quantum Monte Carlo simulations are used in conjunction with an accurate He-CO potential energy surface, which quantitatively describes the rovibrational spectrum of the binary complex. Our simulations, when compared with number-selective infrared spectra taken for different isotopomers, help discriminate among the alternative assignments proposed for cluster sizes around 15 He atoms. The origin of the vibrational band has a red shift that is nearly linear with the cluster size within the first solvation shell and is almost constant up to the largest cluster studied, well beyond completion of the second solvation shell. A blue upturn at even larger sizes would be needed to attain the nanodroplet limit, as recently estimated from the isotopic dependence of the measured R(0) transitions.     

High resolution infrared spectra of a carbon dioxide molecule solvated with helium atoms

Infrared spectra of He(N)-CO(2) clusters with N up to about 20 have been studied in the region of the CO(2) nu(3) fundamental band ( approximately 2350 cm(-1)) using a tunable diode laser spectrometer and pulsed supersonic jet source with cooled (>-150 degrees C) pinhole or slit nozzles and high backing pressures (<40 atm). Compared to previous studies of He(N)-OCS and -N(2)O clusters, the higher symmetry of CO(2) results in simpler spectra but less information content. Discrete rotation-vibration transitions have been assigned for N=3-17, and their analysis yields the variation of the vibrational band origin and B rotational constant over this size range. The band origin variation is similar to He(N)-OCS, with an initial blueshift up to N=5, followed by a monotonic redshift, consistent with a model where the first five He atoms fill a ring around the equator of the molecule, forcing subsequent He atom density to locate closer to the ends. The B value initially drops as expected for a normal molecule, reaching a minimum for N=5. Its subsequent rise for N=6 to 11 can be interpreted as the transition from a normal (though floppy) molecule to a quantum solvation regime, where the CO(2) molecule starts to rotate separately from the He atoms. For N>13, the B value becomes approximately constant with a value about 17% larger than that measured in much larger helium nanodroplets.     

A path-integral Langevin equation treatment of low-temperature doped helium clusters

We present an implementation of path integral molecular dynamics for sampling low temperature properties of doped helium clusters using Langevin dynamics. The robustness of the path integral Langevin equation and white-noise Langevin equation [M. Ceriotti, M. Parrinello, T. E. Markland, and D. E. Manolopoulos, J. Chem. Phys. 133, 124104 (2010)] sampling methods are considered for those weakly bound systems with comparison to path integral Monte Carlo (PIMC) in terms of efficiency and accuracy. Using these techniques, convergence studies are performed to confirm the systematic error reduction introduced by increasing the number of discretization steps of the path integral. We comment on the structural and energetic evolution of He(N)-CO(2) clusters from N = 1 to 20. To quantify the importance of both rotations and exchange in our simulations, we present a chemical potential and calculated band origin shifts as a function of cluster size utilizing PIMC sampling that includes these effects. This work also serves to showcase the implementation of path integral simulation techniques within the molecular modelling toolkit [K. Hinsen, J. Comp. Chem. 21, 79 (2000)], an open-source molecular simulation package.     

Infrared spectra of CO2-doped 4He clusters, 4HeN-CO2, with N=1-60

High resolution spectra of (4)He(N)-CO(2) clusters are studied in the region of the CO(2) nu(3) fundamental band (approximately 2300 cm(-1)). The clusters are produced in a pulsed supersonic jet expansion from a cooled nozzle source and probed by direct absorption using a tunable diode laser operating in a rapid-scan mode. Four carbon dioxide isotopes ((16)O(12)C(16)O, (16)O(13)C(16)O, (18)O(13)C(18)O, and (16)O(13)C(18)O) are used to support the analysis, and because additional rotational transitions are allowed for the asymmetric one ((16)O(13)C(18)O). Resolved R(0) (J=1<--0) rotation-vibration transitions are observed for clusters up to N=60. A detailed rotational analysis is possible up to N approximately 20 and, with some assumptions, to N approximately 37 and beyond. The derived rotational constants (B values) vary smoothly with N and show evidence for broad oscillations similar to those already reported for He(N)-OCS and He(N)-N(2)O. Possible indications of a disruption are observed in the J=2 levels of larger clusters (N>22) which could be caused by interactions with a "dark" helium cluster modes.     

Theoretical analysis of the anomalous spectral splitting of tetracene in 4He droplets

We present a theoretical analysis of the electronic absorption spectra of tetracene in (4)He droplets based on many-body quantum simulations. Using the path integral ground state approach, we calculate one- and two-body reduced density matrices of the most strongly localized He atoms near the molecule surface and use these to investigate the helium ground-state quantum coherence and correlations when tetracene is in its electronic ground and excited states. We identify a trio of quasi-one-dimensional, strongly localized atoms adsorbed along the long axis of the molecule that show some quantum coherence among themselves but far less with the remaining solvating helium. We evaluate the single-particle natural orbitals of the localized He atoms by diagonalization of the one-body density matrix and use these to construct single- and many-particle solvating helium basis states with which the zero-phonon spectral features of the tetracene-(4)He(N) absorption spectrum are then calculated. The absorption spectrum resulting from the three-body density matrix for the strongly bound trio of helium atoms is in very good agreement with the experimental data, accounting quantitatively for the anomalous splitting of the zero-phonon line [Hartmann, M.; Lindinger, A.; Toennies, J. P.; Vilesov, A. F. Chem. Phys. 1998, 239, 139; Krasnokutski, S.; Rouillé, G.; Huisken, F. Chem. Phys. Lett. 2005, 406, 386]. Our results indicate that the combination of strong localization and the quasi-one-dimensional nature of trios of helium atoms adsorbed along the long axis of tetracene leads to a quantum coherent, yet highly correlated ground state for the helium density closest to the molecule. The spectroscopic analysis shows that this feature accounts quantitatively for the anomalous splittings and hitherto unexplained fine structure observed in the absorption spectra of tetracene and suggests that it may be responsible for the corresponding zero-phonon splittings in other quasi-one-dimensional planar aromatic molecules.     

Raman spectra of (He)N-Br2(X) clusters: the role of boson/fermion statistics in a quantum solvent

The aim of this paper is to elucidate the role played by the bosonic/fermionic character of N He atoms solvating a Br2(X) molecule. To this end, an adiabatic model in the molecular stretching coordinate is assumed and the ground energy levels of the complexes are searched by means of Hartree (or Hartree-Fock) Quantum Chemistry calculations for 4He (or 3He) solvent atoms. Simulations of vib-rotational Raman spectra point at the spin multiplicity as the main feature responsible for the drastic difference in the rotational structures of molecules embedded in boson or fermion helium drops as already observed by the experiments of Grebenev et al. [S. Grebenev, J. P. Toennies, and A. F. Vilesov, Science 279 (1998) 2083].     

Multiple solvation configurations around phthalocyanine in helium droplets

Recent measurements of the emission spectrum of phthalocyanine solvated in superfluid helium nanodroplets exhibit a constant 10.3 cm(-1) splitting of each emission line relative to the absorption spectrum. This splitting has been attributed to two distinct helium environments near the surface of the phthalocyanine molecule. Rigid-body path-integral Monte Carlo provides a means of investigating the origin of the splitting on a detailed microscopic level. Path-integral Monte Carlo simulations of 4He(N)-phthalocyanine at 0.625 K with N ranging from 24 to 150 show two distinct helium configurations. One configuration is commensurate with the molecular substrate and the other is a triangular lattice. We investigate the energetics of these two configurations and use a method for calculating electronic spectral shifts for aromatic molecule-rare-gas clusters due to dispersive interactions to estimate the spectral splitting that would arise from the two helium configurations seen for N=150. The results are in reasonable agreement with the experimentally measured splitting, supporting the existence of two distinct local helium environments near the surface of the molecule in the nanodroplets.     

Quantum features of a barely bound molecular dopant: Cs2(3Σu) in bosonic helium droplets of variable size

We present in this work the study of small (4)He(N)-Cs(2)((3)Σ(u)) aggregates (2 ≤ N ≤ 30) through combined variational, diffusion Monte Carlo (DMC), and path integral Monte Carlo (PIMC) calculations. The full surface is modeled as an addition of He-Cs(2) interactions and He-He potentials. Given the negligible strength and large range of the He-Cs(2) interaction as compared with the one for He-He, a propensity of the helium atoms to pack themselves together, leaving outside the molecular dopant is to be expected. DMC calculations determine the onset of helium gathering at N = 3. To analyze energetic and structural properties as a function of N, PIMC calculations with no bosonic exchange, i.e., Boltzmann statistics, at low temperatures are carried out. At T = 0.1 K, although acceptable one-particle He-Cs(2) distributions are obtained, two-particle He-He distributions are not well described, indicating that the proper symmetry should be taken into account. PIMC distributions at T = 1 K already compare well with DMC ones and show minor exchange effects, although binding energies are still far from having converged in terms of the number of quantum beads. As N increases, the He-He PIMC pair correlation function shows a clear tendency to coincide with the experimental boson-liquid helium one at that temperature. It supports the picture of a helium droplet which carries the molecular impurity on its surface, as found earlier for other triplet dimers.