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Optical excitations of small Na clusters using TDHF and BSE methods

Small Na clusters may provide insights into metallic behaviour. However the threshold for collective excitations in these systems lies well above 20 atoms.

The threshold number of atoms in small sodium clusters at which they begin to exhibit metallic character has been the topic of both experimental and theoretical studies.  A metallic system can be expected to display strong collective excitations such as plasmons.  Many-body approaches such as TDHF or BSE contain the local field effects necessary to describe such collective excitations. In this work excitations of Na clusters containing up to 20 atoms were computed using TDHF and BSE methods, with and without the Tamm-Dancoff Approximation (TDA). The BSE method can be regarded as the approximation in which the electron-hole attraction in TDHF is screened. Na clusters have low electron counts and screening is relatively weak up to 20 atoms.  This is reflected in the predictions of TDHF compared to BSE, which are very similar for most clusters in that size range.  Introduction of the TDA to either TDHF or BSE results in significant changes in predicted spectra.


(left) BSE and TDHF absorption spectra for Na20 compared to experiment. (right) Atomic structure of Na20 with Cs symmetry.

Photoabsorption Spectra of Small Na Clusters: TDHF and BSE versus CI and experiment
C. H. Patterson, Phys. Rev. Mater. 3, 043804 (2019)

The Thomas-Reiche-Kuhn (TRK) sum rule states that the sum of oscillator strengths for a molecule or cluster is equal to the number of electrons. In this work core electrons were excluded from optical excitations and hence the sum of oscillator strengths is expected to equal the number of valence electrons. We found that both TDHF and BSE methods gave predictions in excellent agreement with the TRK rule for clusters with three to 20 atoms. However, when the TDA was applied the disagreement with the TRK was large and increased with cluster size.

This work was published in Physical Review Materials where TDHF and BSE calculations were compared to configuration interaction calculations which used the same basis sets and atomic structures.