Vibrational frequency shift of HF in helium clusters: Quantum simulation and experiment

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.

Laser spectroscopy of helium solvated molecules: probing the inertial response

Helium is the only solvent within which molecules can "freely" rotate, albeit with an increased moment of inertia relative to the gas phase. Evidence for this can be obtained by performing infrared laser spectroscopy on molecules embedded large helium clusters (nanodroplets), which often reveals rotationally resolved lines that are more closely spaced than in vacuo. The additional rotational inertia results from coupling of the helium to the molecule (rotor), and decreases in going from heavy (e.g., SF₆) to light (e.g., CH₄) rotors due to a partial breakdown in the adiabatic (following) approximation; faster (lighter) rotors cannot couple as well to helium since their effective interaction with helium is less anisotropic. In addition to this "mass" dependence to the coupling, there is also a time dependence to it, which shows up in the IR spectra as an asymmetry in the rovibrational lineshapes; this results from a delay in the response of helium to the change in rotational speed of the solvated molecule (when ΔJ = ±1). In this perspective we discuss the coupling between various probe molecules and helium that have been investigated by infrared laser spectroscopy in the frequency domain.

Fragmentation dynamics of Ar4He1000 upon electron impact ionization: Competition between ion ejection and trapping

The fragmentation upon electron impact ionization of Ar₄He₁₀₀₀ is investigated by means of mixed quantum-classical dynamics simulations. The Ar₄ ⁺ dopant dynamics is described by a surface hopping method coupled with a diatomics-in-molecules model to properly take into account the multiple Ar₄ ⁺ electronic surfaces and possible transitions between them. Helium atoms are treated individually using zero-point averaged dynamics, a method based on the building of an effective He-He potential. Fast electronic relaxation is observed from less than 2 ps to ∼30 ps, depending on initial conditions. The main fragments observed are Ar₂ ⁺He_q and Ar₃ ⁺He_q (q ≤ 1000), with a strong contribution of the bare Ar₂ ⁺ ion, and neither Ar⁺ nor Ar⁺He_q fragments are found. The smaller fragments (q ≤ 50) are found to mostly come from ion ejection, whereas larger fragments (q > 500) originate from long-term ion trapping. Although the structure of the trapped Ar₂ ⁺ ions is the same as in the gas phase, trapped Ar₃ ⁺ and Ar₄ ⁺ are rather slightly bound Ar₂ ⁺⋯Ar and Ar₂ ⁺⋯Ar⋯Ar structures (i.e., an Ar₂ ⁺ core with one or two argon atoms roaming within the droplet). These loose structures can undergo geminate recombination and release Ar₃ ⁺He_q or Ar₄ ⁺He_q (q ≤ 50) in the gas phase and/or induce strong helium droplet evaporation. Finally, the translational energy of the fragment center of mass was found to be suitable to provide a clear signature of the broad variety of processes at play in our simulations.

Microsolvation of porphine molecules in superfluid helium nanodroplets as revealed by optical line shape at the electronic origin

We investigate the line shape at the electronic origin of single porphine molecules doped into superfluid helium droplets as a function of the droplet size. Helium droplets comprised of less than 10⁵ atoms are generated from an expansion of gaseous helium, while droplets with more than 10⁵ atoms originate from liquid helium. In contrast to our recent study on phthalocyanine, porphine is found to exhibit a solvent shift to the blue with respect to the gas-phase resonance frequency as well as a multiplet splitting. A comparison of the helium-induced features of phthalocyanine and porphine with those obtained in similar studies on tetracene and pentacene reveals that these occur chiefly as two kinds of excitations distinguished by their linewidths and their dependence on the droplet size. Moreover, at quasi-bulk conditions achieved with droplets in excess of 10⁶ helium atoms, none of these four dopant species yields an optical spectrum that can be assigned to a plausible rotational band structure.

Quasiparticle Approach to Molecules Interacting with Quantum Solvents

Understanding the behavior of molecules interacting with superfluid helium represents a formidable challenge and, in general, requires approaches relying on large-scale numerical simulations. Here, we demonstrate that experimental data collected over the last 20 years provide evidence that molecules immersed in superfluid helium form recently predicted angulon quasiparticles [Phys. Rev. Lett. 114, 203001 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.203001]. Most important, casting the many-body problem in terms of angulons amounts to a drastic simplification and yields effective molecular moments of inertia as straightforward analytic solutions of a simple microscopic Hamiltonian. The outcome of the angulon theory is in good agreement with experiment for a broad range of molecular impurities, from heavy to medium-mass to light species. These results pave the way to understanding molecular rotation in liquid and crystalline phases in terms of the angulon quasiparticle.

A survey on pure sampling in quantum Monte Carlo methods

The most commonly employed diffusion Monte Carlo algorithm and some of its variants afford a way to sample configuration space from a so-called “mixed distribution”, the product of an input trial solution to the Schrödinger equation for the ground state and its unknown exact solution. This mixed distribution is sufficient to compute the ground state energy and other properties represented by operators that commute with the Hamiltonian. These energy-related properties are exact, save for a small bias introduced by the input trial function’s incorrect exchange nodes, the so-called “fixed-node error”. However, properties represented by operators that commute with the position operator are also of interest. When calculated by sampling from the mixed distribution, these properties are much more strongly biased by the input trial function. Our objective is to review methods that allow sampling from the desired “pure” distribution, one that is unbiased except for the exchange node error. Thereby, one accurately calculates physical properties such as the dipole and other electrical moments, electrical response properties of molecules, and particle distribution functions for clusters. We survey the results of calculations that employ pure-sampling methods through what has been published in year 2012. Our review also touches on truly exact sampling methods.

Spin-polarized Rb2 interacting with bosonic He atoms: potential energy surface and quantum structures of small clusters

A new full-dimension potential energy surface of the three-body He-Rb₂(³Σ(u)(+)) complex and a quantum study of small (⁴He)(N)-Rb₂(³Σ(u)(+)) clusters, 1 ≤ N ≤ 4, are presented. We have accurately fitted the ab initio points of the interaction to an analytical form and addressed the dopant's vibration, which is found to be negligible. A Variational approach and a Diffusion Monte Carlo technique have been applied to yield energy and geometric properties of the selected species. Our quantum structure calculations show a transition in the arrangements of the helium atoms from N = 2, where they tend to be separated across the diatomic bond, to N = 4, in which a closer packing of the rare gas particles is reached, guided by the dominance of the He-He potential over the weaker interaction of the latter adatoms with the doping dimer. The deepest well of the He-Rb₂ interaction is placed at the T-shape configuration, a feature which causes the dopant to be located as parallel to the helium "minidroplet". Our results are shown to agree with previous findings on this and on similar systems.

Water as a solute: competitive shell formation in (He,Ne) mixed microdroplets

Quantum Monte Carlo (QMC) stochastic calculations are carried out for a series of mixed rare gas clusters containing He and Ne which further include one H(2)O molecule as a single dopant. The ab initio potentials employed in the calculations, and the structural details provided by the QMC results, clearly reveal that the differences in the interaction forces which exist between the two solvent adatoms and the molecular solute are causing strongly competing environments that generate preferential shell structuring when surrounding the water molecule. The different behaviour of the two solvents, and the energetics of mixing, are analyzed in detail for small aggregates and for larger mixtures, revealing structural effects which originate from the different networking between solvent adatoms.

Snowballs, quantum solvation and coordination: lead ions inside small helium droplets

Ab initio calculations are used to construct an analytical many-body potential for Pb(2+)He(n) and Pb(+)He(n) clusters which accounts for non pairwise additive interactions. The potential surface reproduces the global minima for cluster sizes ranging from n = 1 to n = 16 obtained from explicit ab initio calculations and found in a previous search for ultrahigh coordination numbers. Ground state energies and structures obtained by accurate diffusion quantum Monte Carlo calculations are used to investigate if quantum effects qualitatively affect the formation of coordination shells. For Pb(2+) doped clusters a first solvation shell is closed at n = 12 and gradually softened by additional helium atoms which start to form a distinct second shell only at n = 16. Spin-orbit coupling profoundly influences the structure of Pb(+)He(n) clusters and causes a gradual structural evolution without pronounced solvation shells.

Spectral shifts and helium configurations in 4He(N)-tetracene clusters

Spectral shifts of electronic transitions of tetracene in helium droplets are investigated in a theoretical study of (4)He(N)-tetracene clusters with 1 < or = N < or = 150. Utilizing a pairwise interaction for the S(0) state of tetracene with helium that is extended by semiempirical terms to construct a potential for the S(1) state of tetracene with helium, the spectral shift is calculated from path integral Monte Carlo calculations of the helium equilibrium properties with tetracene in the S(0) and S(1) states at T = 0 and at T = 0.625 K. The calculated spectral shifts are in quantitative agreement with available experimental measurements for small values of N (< or = 8) at T approximately 0.4 K and show qualitative agreement for larger N (10-20). The extrapolated value of the spectral shift in large droplets (N approximately 10(4)) is approximately 90% of the experimentally measured value. We find no evidence of multiple configurations of helium for any cluster size for either the S(0) or S(1) state of tetracene. These results suggest that the observed spectral splitting of electronic transitions of tetracene in large helium droplets is not due to the coexistence of static metastable helium densities, unlike the situation previously analyzed for the phthalocyanine molecule.

Fragmentation of ionized doped helium nanodroplets: theoretical evidence for a dopant ejection mechanism

We report a theoretical study of the effect induced by a helium nanodroplet environment on the fragmentation dynamics of a dopant. The dopant is an ionized neon cluster Ne(n) (+) (n=4-6) surrounded by a helium nanodroplet composed of 100 atoms. A newly designed mixed quantum/classical approach is used to take into account both the large helium cluster zero-point energy due to the light mass of the helium atoms and all the nonadiabatic couplings between the Ne(n) (+) potential-energy surfaces. The results reveal that the intermediate ionic dopant can be ejected from the droplet, possibly with some helium atoms still attached, thereby reducing the cooling power of the droplet. Energy relaxation by helium atom evaporation and dissociation, the other mechanism which has been used in most interpretations of doped helium cluster dynamics, also exhibits new features. The kinetic energy distribution of the neutral monomer fragments can be fitted to the sum of two Boltzmann distributions, one with a low kinetic energy and the other with a higher kinetic energy. This indicates that cooling by helium atom evaporation is more efficient than was believed so far, as suggested by recent experiments. The results also reveal the predominance of Ne(2) (+) and He(q)Ne(2) (+) fragments and the absence of bare Ne(+) fragments, in agreement with available experimental data (obtained for larger helium nanodroplets). Moreover, the abundance in fragments with a trimeric neon core is found to increase with the increase in dopant size. Most of the fragmentation is achieved within 10 ps and the only subsequent dynamical process is the relaxation of hot intermediate He(q)Ne(2) (+) species to Ne(2) (+) by helium atom evaporation. The dependence of the ionic fragment distribution on the parent ion electronic state reached by ionization is also investigated. It reveals that He(q)Ne(+) fragments are produced only from the highest electronic state, whereas He(q)Ne(2) (+) fragments originate from all the electronic states. Surprisingly, the highest electronic states also lead to fragments that still contain the original ionic dopant species. A mechanism is conjectured to explain this fragmentation inhibition.

Blueshift and intramolecular tunneling of NH3 umbrella mode in 4He n clusters

We present diffusion Monte Carlo calculations of the ground and first excited vibrational states of NH(3) (4)He(n) for n< or =40. We use the potential energy surface developed by one of us [M. P. Hodges and R. J. Wheatley, J. Chem. Phys. 114, 8836 (2001)], which includes the umbrella mode coordinate of NH(3). Using quantum Monte Carlo calculations of excited states, we show that this potential is able to reproduce qualitatively the experimentally observed effects of the helium environment, namely, a blueshift of the umbrella mode frequency and a reduction of the tunneling splittings in ground and first excited vibrational states of the molecule. These basic features are found to result regardless of whether dynamical approximations or exact calculations are employed.

Photodissociation of alkyl iodides in helium nanodroplets. II. Solvation dynamics

The solvation dynamics of nonthermal species in liquid helium has been investigated by photolyzing alkyl iodide molecules, CH3I, C2H5I, and CF3I, embedded in helium nanodroplets. Iodine and CH3 fragments are found to leave the droplets solvated by a finite number of helium atoms, this in contrast to C2H5 and CF3 fragments. The speed distributions of the IHeN and CH3HeN complexes show a prominent correlation with the degree of solvation N. It is argued that this correlation is caused by a dynamical adjustment of the solvation structure size to the relative speed of the traveling fragments as they pass through the helium bath. The absence of C2H5HeN and CF3HeN complexes is attributed to the large internal energy of these alkyl fragments which leads to a rapid destruction of any possibly formed complexes.

Structure and stability of Ne+He(n): experiment and diffusion quantum Monte Carlo theory with "on the fly" electronic structure

New data are reported for the mass-spectrometry fragmentation patterns of helium clusters, either pure or containing a Ne or an Ar atom. The patterns for He(n)+ and Ar+He(n) show clear evidence of structure, while those of Ne+He(n) do not. To better understand the surprising result for the Ne+He(n) fragments, diffusion quantum Monte Carlo (DMC) calculations of the energies and structural properties of these ions were performed using a diatomics-in-molecule (DIM) parametrization of the potential energy. Using DIM for electronic energy evaluation allows us to sample 10(9) configurations even for a cluster as large as Ne+He14. The results of the DMC calculation are very surprising. For n > 7, the DMC random walkers rarely venture within 100 cm(-1) of the minimum potential energy. Analysis of the resulting particle density distributions shows that the zero-point energy does more than spread the wave function around the potential-energy minima, resulting in very diffuse wave functions. For some of the clusters the quantum effects nearly exclude the region of the potential minimum from the overall wave function. An important result of this effect is that the incremental bonding energy of the nth helium atom varies quite smoothly with n, for n > 5. This eliminates the expected shell structure and explains the lack of magic-number-type features in the data.

The ground state tunneling splitting and the zero point energy of malonaldehyde: A quantum Monte Carlo determination

Quantum dynamics calculations of the ground state tunneling splitting and of the zero point energy of malonaldehyde on the full dimensional potential energy surface proposed by Yagi et al. [J. Chem. Phys. 1154, 10647 (2001)] are reported. The exact diffusion Monte Carlo and the projection operator imaginary time spectral evolution methods are used to compute accurate benchmark results for this 21-dimensional ab initio potential energy surface. A tunneling splitting of 25.7+/-0.3 cm-1 is obtained, and the vibrational ground state energy is found to be 15 122+/-4 cm-1. Isotopic substitution of the tunneling hydrogen modifies the tunneling splitting down to 3.21+/-0.09 cm-1 and the vibrational ground state energy to 14 385+/-2 cm-1. The computed tunneling splittings are slightly higher than the experimental values as expected from the potential energy surface which slightly underestimates the barrier height, and they are slightly lower than the results from the instanton theory obtained using the same potential energy surface.

Quantum solvation dynamics of HCN in a helium-4 droplet

Ultracold nanodroplets of helium-4, containing several thousands of He atoms, offer considerable promise as microscopic cryogenic chambers. Potential applications include the creation of tailor-made chemical or biomolecular complexes and studies of superfluidity in nanoscale systems. Recent experiments have succeeded in interrogating droplets of quantum solvent which consist of as few as 1-20 helium-4 atoms and which contain a single solute molecule. This allows the transition from a floppy, but essentially molecular, complex to a dissolved molecule to be followed and, surprisingly, the transition is found to occur quite rapidly, in some cases for as few as N = 7-20 solvent atoms. For example, in experiments on helium-4 droplets seeded with CO molecules [Tang and McKellar, J. Chem. Phys. 119, 754 (2003)], two series of transitions are observed which correlate with the a-type (Delta K = 0) and b-type (Delta K = +/-1) lines of the binary complex, CO-He (K is the quantum number associated with the projection of the total angular momentum onto the vector connecting the atom and the molecular center of mass). The a-type series, which evolves from the end-over-end rotational motion of the CO-He binary complex, saturates to the nanodroplet limit for as few as 10-15 helium-4 atoms, i.e., the effective moment of inertia of the molecule converges to its asymptotic (solvated) value quite rapidly. In contrast, the b-type series, which evolves from the free-molecule rotational mode, disappears altogether for N approximately 7 atoms. Similar behavior is observed in recent computational studies of HCN(4He)N droplets [Paolini et al., J. Chem. Phys. 123, 114306 (2005)]. In this article the quantum solvation of HCN in small helium-4 droplets is studied using a new fixed-node diffusion Monte Carlo (DMC) procedure. In this approach a Born-Oppenheimer-type separation of radial and angular motions is introduced as a means of computing nodal surfaces of the many-body wave functions which are required in the fixed-node DMC method. Excited rotational energies are calculated for HCN(4He)N droplets with N = 1-20: the adiabatic node approach also allows concrete physical mechanisms to be proposed for the predicted disappearance of the b-type series as well as the rapid convergence of the a-type series to the nanodroplet limit with increasing N. The behavior of the a-type series is traced directly to the mechanics of angular momentum coupling-and decoupling-between identical bosons and the molecular rotor. For very small values of N there exists significant angular momentum coupling between the molecule and the helium atoms: at N approximately 10 solvation appears to be complete as evidenced by significant decoupling of the molecule and solvent angular momenta. The vanishing of the b-type series is predicted to be a result of increasing He-He repulsion as the number of solvent atoms increases.

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).

Predicting atomic dopant solvation in helium clusters: The MgHen case

We present a quantum Monte Carlo study of the solvation and spectroscopic properties of the Mg-doped helium clusters MgHe(n) with n=2-50. Three high-level [MP4, CCSD(T), and CCSDT] MgHe interaction potentials have been used to study the sensitivity of the dopant location on the shape of the pair interaction. Despite the similar MgHe well depth, the pair distribution functions obtained in the diffusion Monte Carlo simulations markedly differ for the three pair potentials, therefore indicating different solubility properties for Mg in He(n). Moreover, we found interesting size effects for the behavior of the Mg impurity. As a sensitive probe of the solvation properties, the Mg excitation spectra have been simulated for various cluster sizes and compared with the available experimental results. The interaction between the excited 1P Mg atom and the He moiety has been approximated using the diatomics-in-molecules method and the two excited 1pi and 1sigma MgHe potentials. The shape of the simulated MgHe50 spectra shows a substantial dependency on the location of the Mg impurity, and hence on the MgHe pair interaction employed. To unravel the dependency of the solvation behavior on the shape of the computed potentials, exact density-functional theory has been adapted to the case of doped He(n) and various energy distributions have been computed. The results indicate the shape of the repulsive part of the MgHe potential as an important cause of the different behaviors.

Dissociative ionization of neon clusters Nen, n=3 to 14: A realistic multisurface dynamical study

The molecular dynamics with quantum transitions (MDQT) method is applied to study the fragmentation dynamics of neon clusters following vertical ionization of neutral clusters with 3 to 14 atoms. The motion of the neon atoms is treated classically, while transitions between the adiabatic electronic states of the ionic clusters are treated quantum mechanically. The potential energy surfaces are described by the diatomics-in-molecules model in a minimal basis set consisting of the effective 2p orbitals on each neon atom for the missing electron. The fragmentation mechanism is found to be rather explosive, with a large number of events where several atoms simultaneously dissociate. This is in contrast with evaporative atom by atom fragmentation. The dynamics are highly nonadiabatic, especially at shorter times and for the larger clusters. Initial excitation of the neutral clusters does not affect the fragmentation pattern. The influence of spin-orbit coupling is also examined and found to be small, except for the smaller size systems for which the proportion of the Ne+ fragment is increased up to 43%. From the methodological point of view, most of the usual momentum adjustment methods at hopping events are shown to induce nonconservation of the total nuclear angular momentum because of the nonzero electronic to rotation coupling in these systems. A new method for separating out this coupling and enforcing the conservation of the total nuclear momentum is proposed. It is applied here to the MDQT method of Tully but it is very general and can be applied to other surface hopping methods.

Probing charge-transfer processes in helium nanodroplets by optically selected mass spectrometry (OSMS): charge steering by long-range interactions

Electron impact ionization of a helium atom in a helium nanodroplet is followed by rapid charge migration, which can ultimately result in the localization of the charge on an atomic or molecular solute. This process is studied here for the cases of hydrogen cyanide, acetylene, and cyanoacetylene in helium, using a new experimental method we call optically selected mass spectrometry (OSMS). The method combines infrared laser spectroscopy with mass spectrometry to separate the contributions to the overall droplet beam mass spectrum from the various species present under a given set of conditions. This is done by vibrationally exciting a specific species that exists in a subset of the droplets (for example, the droplets containing a single HCN molecule). The resulting helium evaporation leads to a concomitant reduction in the ionization cross sections for these droplets. This method is used to study the charge migration in helium and reveals that the probability of charge transfer to a solvated molecule does not approach unity for small droplets and depends on the identity of the solvated molecule. The experimental results are explained quantitatively by considering the effect of the electrostatic potential (between the charge and the embedded molecule) on the trajectory of the migrating charge.

Photodissociation of hydrogen iodide on the surface of large argon clusters: The orientation of the librational wave function and the scattering from the cluster cage

A set of photodissociation experiments and simulations of hydrogen iodide (HI) on Arn clusters, with an average size n = 139, has been carried out for different laser polarizations. The doped clusters are prepared by a pick-up process. The HI molecule is then photodissociated by a UV laser pulse and the outgoing H fragment is ionized by resonance enhanced multiphoton ionization in a (2 + 1) excitation scheme within the same laser pulse at the wavelength of 243 nm. The measured time-of-flight spectra are transformed into hydrogen kinetic energy distributions. They exhibit a strong fraction of caged H atoms at zero-kinetic energy and peaks at the unperturbed cage exit for both spin-orbit channels nearly independent of the polarization. At this dissociation wavelength, the bare HI molecule exhibits a strict state separation, with a parallel transition to the spin-orbit excited state and perpendicular transitions to the ground state. The experimental results have been reproduced using molecular simulation techniques. Classical molecular dynamics was used to estimate the HI dopant distribution after the pick-up procedure. Subsequently, quasi-classical molecular dynamics (Wigner trajectories approach) has been applied for the photodissociation dynamics. The following main results have been obtained: (i) The HI dopant lands on the surface of the argon cluster during the pick-up process, (ii) zero-point energy plays a dominant role for the hydrogen orientation in the ground state of HI-Arn surface clusters, qualitatively changing the result of the photodissociation experiment upon increasing the number of argon atoms, and, finally, (iii) the scattering of hydrogen atoms from the cage which originate from different dissociation states seriously affects the experimentally measured kinetic energy distributions.