English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We investigate the translational eigenstates of the endofullerene systemHe@C$_{60}$ and the importance of angular dependence and cage breathing with afour-dimensional Potential Energy Surface (PES): three He translational degreesof freedom and C$_{60}$ cage radius.  We compare MP2, SCS-MP2, SOS-MP2 and RPA@PBE to calibrate and gain confidencein the choice of electronic structure method. Due to the high cost of thesecalculations, the PES is interpolated using Gaussian Process Regression (GPR),owing to its effectiveness with sparse training data. The PES is split into atwo-dimensional radial surface, to which corrections are applied to achieve anoverall four-dimensional surface.  With the PES, the nuclear Hamiltonian is diagonalised using an outer productbasis of three-dimensional harmonic oscillator (3D HO) functions to describethe He translation, with one-dimensional harmonic oscillator functions todescribe the C$_{60}$ cage breathing. The degeneracy of the 3D HO energies withprincipal quantum number $n$ is lifted due to the anharmonicity in the radialpotential. The $(2l+1)$-fold degeneracy of the angular momentum states is alsoweakly lifted, due to the angular dependence in the potential.  We calculate the fundamental frequency to range between 96cm$^{-1}$ and110cm$^{-1}$ depending on the electronic structure method used, with MP2providing the best match to the spectroscopic data and RPA@PBE a close second.The cage breathing shows no observable coupling to the translational modes ofthe He atom.  Wavefunctions are also compared by considering their overlap and Hellingerdistance to the one-dimensional empirical potential. While MP2 has betteragreement than RPA@PBE, due to its higher computational efficiency andcomparable performance, we recommend RPA as an alternative electronic structuremethod of choice to MP2 for these systems.

Translational eigenstates of He@C$_{60}$ from four-dimensional  \textit{ab initio} Potential Energy Surfaces interpolated using Gaussian  Process Regression