Multiscale Ab-initio Modelling of Quantum Nuclear Motion in Helium and Para-Hydrogen Clusters

Multiscale Ab-initio Modelling of Quantum Nuclear Motion in Helium and Para-Hydrogen Clusters

It is well-known that molecular spectroscopic measurements in helium droplets by the group of Prof. Peter Toennies demonstrated the existence of very different spectral profiles depending on the nature of the isotope considered, 3He or 4He [Grebenev, Toennies, and Vilesov, Science 279 (1998) 2083]. Thus, the infrared spectra of OCS inside 3He droplets showed broad spectral profiles, while insights into molecular super-fluidity were found in 4He droplets as the recovering of a spectrum with sharp rotational lines when atoms of this isotope are added to the 3He droplet. Since 4He atoms can be considered (composite) spin-less bosonic particles while 3He atoms are fermionic particles with a nuclear spin equals to ½, the key role of nuclear spin statistical effects was disclosed. Further spectroscopic probes of molecules in rather small doped helium clusters provided insights into the onset of molecular superfluidity with just a few He atoms. Thus, for example, Surin et al. [Surin, Phys. Rev. Lett. 101 (2008) 233401] showed a non-classical behaviour of the dopant rotational constant in (4He)N-CO clusters as a function of the cluster size and suggested that the dopant rotation is almost free for N > 5.

As opposed to the case of the 4He isotope, the spectroscopy of dopant species solvated by the 3He isotope has been much less explored, and, up to our knowledge, there are no experimental measurements on small doped 3He clusters. However, it is clear that the comparison of low-temperature spectroscopy of (well-characterized) molecules in small 3He and 4He clusters is ideally suited to provide a more comprehensive and deeper understanding of incipient superfluidity effects for the 4He isotope. The earliest fundamental insights following this direction were obtained at Hartree-Fock level. Truncated pair potentials were employed to alleviate the hard-core interaction problem of these strongly correlated systems [de Lara-Castells et al., Phys. Rev. A 71 (2005) 033203]. Later, the free-parameter Full-Configuration-Interaction-type Nuclear Orbital (FCI-NO) approach was developed. This FCI-NO treatment was able to provide solvent states for the two isotopes, to accurately deal with the hard-core  interaction problem [de Lara-Castells et al., J. Chem. Phys. 125 (2006) 221101], and to automatically include all the nuclear-statistic-induced (bosonic or fermionic) effects. It handles the many-body problem by expanding the Hamiltonian operator with quantum single-particle basis functions followed by a special diagonalization technique. The method resembles the traditional CI method of quantum electronic structure theory and was originally developed to treat fermionic (doped) 3He clusters (e.g., see [de Lara-Castells et al., J. Chem. Phys. 131 (2009) 194101])  and further extended to deal with bosonic systems (see, e.g., [Aguirre et al., Phys. Chem. Chem. Phys. 15 (2013) 10126]) composed by 4He atoms or para-H2 molecules. One advantage of the FCI-NO method is its capability of providing excited and disentangled solvent states with similar accuracy to the ground state. This capability has been used for the characterization of collective rotational solvent states (see figure below, from [de Lara-Castells and Mitrushchenkov, J. Phys. Chem. Lett. 2 (2011) 2145]. The FCI-NO approach has been also applied to calculate the vib-rotational Raman spectroscopy of homonuclear diatomic molecules immersed in very small 3He/4He clusters (see figure above, from [Aguirre et al., Chem. Phys. Lett. 555 (2013) 12]).

The embedding concept applied to helium density functional theory: Aimed to extend the application of microscopic approaches to droplets composed by hundreds of 4He atoms, we are adapting density functional embedding theory for electronic structure problems to 4He atoms (see, e.g., [Wesolowski and Warshel, J. Phys. Chem. 97 (1993) 8050]).The basic idea is to link the helium density functional treatment of 4He atoms [Dalfovo et al., Phys. Rev. B 52 (1995) 1193] to the FCI-NO method, with possible extensions to implementations of the Quantum Monte Carlo treatment.

As a first step forward, within the framework of our collaboration with Andreas W. Hauser (Graz University of Technology) and Alexander O. Mitrushchenkov (Université Paris-Est), we have applied the embedding concept to a superfluid helium droplet with immersed carbon nanotubes (see figure below, from [Hauser, Mitrushchenkov, and de Lara-Castells, J. Phys. Chem. C 121 (2017) 3807–3821]).


Figure from [Hauser, Mitrushchenkov, and de Lara-Castells, J. Phys. Chem. C 121 (2017) 3807–3821]: Radial distribution of one 4He2000 droplet for fully immersed carbon nanotubes (CNT) of several chiral (n,n) indices at z = 0. Right panel: He/CNT(9,9)  interaction potential along with radial density of the 4He ground-state wave function (shown in sea-green). The embedding potential account for the influence of second and following helium layers on the central laryer. Notice that, adding the embedding potential from the second and following helium layers (see inset picture), the global potential minimum is shifted to the center of the nanotube, as the 4He wave function is.

Our most recent progress has consisted in describing a long-range electron transfer or harpoon-type reaction from Cs and Cs2 to C60 in a superfluid helium droplet [de Lara-Castells, Hauser and Mitrushchenkov, J. Phys. Chem. Lett. 8 (2017) 4284]). The heliophobic Cs or Cs2 species were initially located at the droplet surface (see figure below), while the heliophilic C60 molecule is fully immersed in the droplet. First, probabilities for the electron transfer in the gas phase were calculated for reactants with velocities below the critical Landau velocity of 57 m/s to account for the superfluid helium environment. Next, reaction pathways were derived that also included the repulsive contribution from the extrusion of helium upon the approach of the two reactants. Our results were in perfect agreement with recent experimental measurements of electron ionization mass spectroscopy [Renzler, M.; et al., J. Chem. Phys. 2016, 145, 181101], showing a high possibility for the formation of a Cs2−C60 complex inside of the droplet through a direct harpoon-type electron transfer involving the rotation of the molecule but a negligibly low reactivity for atomic Cs.