Theoretical study of Rb2 in He(N): potential energy surface and Monte Carlo simulations

An analytical potential energy surface for a rigid Rb? in the 3Σ(u)? state interacting with one helium atom based on accurate ab initio computations is proposed. This 2-dimensional potential is used, together with the pair approximation approach, to investigate Rb? attached to small helium clusters He(N) with N = 1-6, 12, and 20 by means of quantum Monte Carlo studies. The limit of large clusters is approximated by a flat helium surface. The relative orientation of the dialkali axis and the helium surface is found to be parallel. Dynamical investigations of the pendular and of the in-plane rotation of the rigid Rb? molecule on the surface are presented.     

Excited Li and Na in He(n): influence of the dimer potential energy curves

The X(2)Σ ground and the A(2)Π and B(2)Σ first two excited states of Li-He and Na-He are determined using high level complete active space self-consistent field-multireference configuration interaction ab initio method. The obtained potentials differ from the ones proposed by Pascale [Phys. Rev. A 28, 632 (1983)], more strongly for the ground than for the excited states. Quantum diffusion Monte Carlo studies of small Li(?)He(n) and Na(?)He(n) with n ≤ 5 are performed using a diatomics-in-molecule approach to model the non-pair additive interaction potential. The sensitivity of our results to the A(2)Π and B(2)Σ potentials used is assessed by an analysis of the structure and of the energetics of the clusters. For these small clusters, the physical conclusions are essentially independent of the diatomic curves employed.     

Mg impurity in helium droplets

Within the diffusion Monte Carlo approach, we have determined the structure of isotopically pure and mixed helium droplets doped with one magnesium atom. For pure (4)He clusters, our results confirm those of Mella et al. [J. Chem. Phys. 123, 054328 (2005)] that the impurity experiences a transition from a surface to a bulk location as the number of helium atoms in the droplet increases. Contrarily, for pure (3)He clusters Mg resides in the bulk of the droplet due to the smaller surface tension of this isotope. Results for mixed droplets are presented. We have also obtained the absorption spectrum of Mg around the 3s3p?(1)P(1) ← 3s(2)?(1)S(0) transition.     

One- and two-photon spectroscopy of highly excited states of alkali-metal atoms on helium nanodroplets

Alkali-metal atoms captured on the surface of superfluid helium droplets are excited to high energies (≈3?eV) by means of pulsed lasers, and their laser-induced-fluorescence spectra are recorded. We report on the one-photon excitation of the (n+1)p←ns transition of K, Rb, and Cs (n=4, 5, and 6, respectively) and on the two-photon one-color excitation of the 5d←5s transition of Rb. Gated-photon-counting measurements are consistent with the relaxation rates of the bare atoms, hence consistent with the reasonable expectation that atoms quickly desorb from the droplet and droplet-induced relaxation need not be invoked.     

Molecular impurities in helium clusters

We review recently developed theories of molecular interactions with helium clusters. Ground state energies and structures are obtained from Monte Carlo and density functional calculations for a variety of impurities and a range of cluster sizes. Of particular interest are chemical potentials, location of the impurity, and shape of the helium density surrounding it. Included in the work summarized here are results for light molecules (H₂ and D₂) which interact weakly with He and results for heavier molecules (Cl₂ and SF₆) which interact more strongly with He. Finally, theoretical and experimental results are compared for SF₆ in helium clusters.     

Size and isotope effects of helium clusters and droplets: identification of surface and bulk-volume excitations

We report a comprehensive investigation of the electronically excited states of helium clusters and droplets of sizes ranging from a few to several 10(7) atoms using time-resolved fluorescence excitation spectroscopy and quantum chemical ab initio calculations. We employ various approaches for our analysis considering the lifetime-dependence of the fluorescence intensity, spectral shifts, intensity scaling with cluster size, isotopic dependence, and density-dependence of the calculated electron wave function radii. A unique feature of helium clusters and droplets is their radially varying particle density. Our results show that short-lived fluorescence is sensitive to regions of increased density and probes excitations located in the bulk volume, whereas long-lived fluorescence is sensitive to regions of reduced density such as for small clusters or for the surface of large droplets. Spectra of (3)He droplets serve as a reference for low density, but are free from contributions of small clusters. This allows us to distinguish regions of reduced density as these can be due to both surface states or small clusters. Our analysis reveals a picture where spectral features are related to regions of different density due to isotopic composition, cluster size, and surface or bulk volume location of the excitations. The 2s and 2p related excitations appear as blue-shifted wings for small clusters or for excited atoms within the surface layer, whereas in the bulk-volume of large droplets, they appear as distinct bands with large intensities, dominating the entire spectrum. Excitations at energies higher than 23 eV are unambiguously assigned to regions of low and medium density location within the deeper parts of the surface layer but show no relation to the bulk volume. Our findings support the idea that in liquid helium high-lying states and, in particular, Rydberg states are quenched in favor of the 2s and 2p excitations.     

Bosonic helium clusters doped by alkali metal cations: interaction forces and analysis of their most stable structures

Ab initio potentials are computed for alkali metal cationic partners interacting with ⁴He and an overall many-body potential is constructed for each of the ionic dopants in helium clusters. The structures are then obtained via a genetic algorithm approach and results compared with Basin-Hopping Monte Carlo simulations. The classical arrangements are analyzed and quantum effects discussed in comparison with what has been found with Diffusion Monte Carlo calculations. Further corrections to the classical picture by including three-body forces and radial delocalization of the helium adatoms are also considered and their effects analyzed. This work is dedicated to the late Nando Bernardi, an eclectic and gifted scientist and a dear friend whose early departure has left a sad void in our community.     

Excited electronic state calculations by the transcorrelated variational Monte Carlo method: application to a helium atom

We have implemented the excited electronic state calculations for a helium atom by the transcorrelated variational Monte Carlo (TC-VMC) method. In this method, Jastrow-Slater-type wave function is efficiently optimized not only for the Jastrow factor but also for the Slater determinant. Since the formalism for the TC-VMC method is based on the variance minimization, excited states as well as the ground state calculations are feasible. It is found that both the first and the second excitation energies given by TC-VMC are much closer to the experimental data than those given by the variational Monte Carlo method with using the Hartree-Fock orbitals. The successful results in the TC-VMC method are considered to be due to the nodal optimization of the wave functions.     

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.     

Rydberg states of small NaAr(n)* clusters

The 4s and 5s Rydberg excited states of NaAr(n)* clusters are investigated using a pseudopotential quantum-classical method. While NaAr(n) clusters in their ground state are known to be weakly bound van der Waals complexes with Na lying at the surface of the argon cluster, isomers in 4s or 5s electronically excited states of small NaAr(n)* clusters (n< or =10) are found to be stable versus dissociation. The relationship between electronic excitation and cluster geometry is analyzed as a function of cluster size. For both 4s and 5s states, the stable exciplex isomers essentially appear as sodium-centered structures with similar topologies, converging towards those of the related NaAr(n)+ positive ions when the excitation level is increased. This is consistent with a Rydberg-type picture for the electronically excited cluster, described by a central sodium ion solvated by an argon shell, and an outer diffuse electron orbiting around this NaAr(n)+ cluster core.     

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.     

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.     

Unraveling the absorption spectra of alkali metal atoms attached to helium nanodroplets

The absorption spectra of the first electronic exited state of alkali metal atoms on helium nanodroplets formed of both 4He and 3He isotopes were studied experimentally as well as theoretically. In the experimental part new data on the 2p<--2s transition of lithium on 3He nanodroplets are presented. The absorption spectrum changes drastically when compared to 4He droplets, in contrast to sodium where only marginal differences were observed in former studies. To explain these large differences and to answer some still open questions concerning the interaction of alkali metal atoms with helium nanodroplets, a model calculation was performed. New helium density profiles as well as a refined model allowed us to achieve good agreement with the experimental findings. For the first time the red-shifted intensities in the lithium and sodium spectra are explained in terms of enhanced binding configurations in the excited state displaced spatially from the ground state configurations.     

Predicting atomic dopant solvation in helium clusters: the MgHe(n) 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.     

Anionic microsolvation in helium droplets: OH- (He)N structures from classical and quantum calculations

Diffusion Monte Carlo calculations are carried out for clusters of OH- (1Sigma+) with N 4He atoms, N varying up to 15, while classical configurations from a genetic algorithm optimization are obtained up to N=20. The overall interaction potential is assembled from ab initio data for the partners using the sum-of-potentials scheme. In contrast with the cationic dopants' behavior, the results indicate a very marked spatial delocalization and quantum features of the solvent adatoms surrounding the anionic impurity, thus making classical calculations of solvent's spatial locations of only limited use. In spite of the generally known repulsive interaction of negative charges in He droplets, the calculations show that this polar molecular anion is solvated by a liquidlike solvent layer, reminiscent of what happens in pure helium droplets.     

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.     

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.     

87Rb electron spin resonance on helium nanodroplets: the influence of optical pumping

Hyperfine resolved electron spin resonance (ESR) measurements of single rubidium ((87)Rb) atoms isolated on superfluid helium nanodroplets are presented. In accordance with our previous work on (85)Rb, we find a relative increase of the hyperfine constant a(HFS) by about 400 ppm, depending on the size of the droplets. In order to optimize the ESR signal intensities, the processes of optical pumping of Rb atoms on helium droplets and of optical detection of the ESR transitions are investigated in detail. Both the laser intensity and polarization influences the ESR signal intensities. A simple model for optical pumping of Rb atoms on helium droplets is presented, which agrees well with the experimental results.     

Quantum Monte Carlo calculations for ground and excited states

A brief overview of the diffusion quantum Monte Carlo method is given. We illustrate the application to ground‐state calculations by a study of the relative stability of carbon clusters near the crossover to fullerene stability, thereby determining the smallest stable fullerene. The application to excited states is illustrated via a study of excitonic states in small hydrogenated silicon clusters. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001