Calculation of Excitations of Superfluid Helium Nanodroplets Roman

Calculation of Excitations of Superfluid Helium Nanodroplets Roman Schmied and Kevin K. Lehmann Department of Chemistry Princeton University 60 th Ohio State University International Symposium on Molecular Spectroscopy Columbus, June 23, 2005

Electronic HENDI spectra (HElium Nano. Droplet Isolation) glyoxal: • Phonon wings in 4 He nanodroplets: demonstrate superfluidity? • Why is the ZPL split? • How to estimate the phonon spectrum? from Stienkemeier and Vilesov JCP 115 (22), 2001, 10119

First-Principles Approaches • Quantum Monte Carlo techniques • Only lowest excitations of each symmetry • Only small droplets C 6 H 6 – He 14 excitations from DMC: Excitations localized around C 6 H 6: from Huang and Whaley, PRB 67, 2003, 155419

DFT to the rescue! • • • !! Helium density, NOT electron density Bose symmetry included continuum theory Hydrodynamic description of flow Excitations as eigenmodes of oscillation

• 1 D simulations • Excitations with any angular momentum • No real-time dynamics, only phonons (normal mode analysis) • No phonon-phonon interactions: linear theory density / nm-3 Spherical Simulations DFT helium density around a 4 He atom

How good is DFT? (I) Orsay-Trento Density Functional (OTDF): Dalfovo et al. , PRB 52(2), 1995, 1193 Calibration: energy / cm-1 • bulk Energy(P) • bulk density(P) • static response function (P=0), in particular the bulk compressibility • bulk phonon spectrum (+pressure dependence) momentum / nm-1

How good is DFT? (II) DFT Ag–He 100: • Energy: – 358. 8 cm– 1 – DMC: – 357. 3(6) cm– 1 • Chemical potential: 3. 2 cm– 1 – DMC: 3. 1(1) cm– 1 from Mella, Colombo, Morosi, JCP 117 (21), 2002, 9695

procedure • Input: • Output: – Pair potentials – Number of helium atoms – Helium density – Phonons – Superfluid fraction 1. minimize energy 2. for each L: • diagonalize dynamics matrix

Finite droplet excitations N=5000: 10 x phonon energy / cm-1 Compare to liquid-drop model: es lk bu e ac f r su v wa ves a w angular momentum L

Excitations around a dopant energy / cm-1 • Some excitations are lowered “under” roton minimum • Freezing: some phonons become unstable (imaginary frequency) • DFT is (for now) unable to do freezing e=39 cm-1 (5. 5 He-He), s=0. 2556 nm momentum / nm-1

Split zero-phonon lines lowest L=5 excitation / cm-1 • ZPL can split in 2 or 3 lines • Peaks on phonon wing

Superfluidity • Thermally populated phonons induce normal fluid moment of inertia: Superfluid fraction:

local normal-fluid fraction “local superfluid fraction” • Superfluidity is a global quantity • We can define a local quantity • Influence of dopant is minor unless frozen solvation shell

local normal-fluid fraction

local normal-fluid fraction --> Q branches in spectra of (HCN)n, (HCCCN)n

Conclusions • We can compute: – Density – Phonons – Superfluid fraction • • • Large droplets Doped bulk Doped droplets ZPL splitting in electronic HENDI spectra Q branches

Acknowledgments • Kevin Lehmann • Charlotte Elizabeth Procter Fellowship

density / nm-3 Freezing in solvation shell 0. 1 x • Very low energy phonons “under” roton minimum • Localized in first solvation shell • Such modes are few and far apart • Explanation of ZPL splittings?

Pair-correlation function • Density around a helium atom in bulk • DFT: Does not include Bose exchange of that atom with the fluid DFT DMC, exp. from Ceperley, RMP 67 (2), 1995, 279