Phys. Rev. A 106, 062826 (2022)

Shape fluctuations and radiation from thermally excited electronic states of boron clusters

T. Höltzl^1,2,*, P. Ferrari³, E. Janssens³, and K. Hansen^4,5,†

1 Furukawa Electric Institute of Technology, 1158 Budapest, Hungary

2 ELKH-BME Computation Driven Chemistry Research Group and Department of Inorganic and Analytical Chemistry, Budapest University of Technology and Economics, 1111 Budapest, Hungary

3 Quantum Solid-State Physics, Department of Physics and Astronomy, KU Leuven, 3001 Leuven, Belgium

4 Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou, Gansu 730000, China

5 Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, 92 Weijin Road, Tianjin 300072, China

*  tibor.holtzl@furukawaelectric.com
†  KlavsHansen@tju.edu.cn

Abstract

The effect of thermal shape fluctuations on the recurrent fluorescence of boron-cluster cations, $B_N{}^{+}$ $(N=9–14)$, has been investigated numerically, with a special emphasis on $B_{13}{}^{+}$. For this cluster, the electronic structures of the ground state and the four lowest electronically excited states were calculated using time-dependent density-functional theory and sampled on molecular dynamics trajectories of the cluster calculated at an experimentally relevant excitation energy. The sampled optical transition matrix elements for $B_{13}{}^{+}$ allowed us to construct its emission spectrum from the thermally populated electronically excited states. The spectrum was found to be broad, reaching down to at least 0.85 eV. This contrasts strongly with the static picture, where the lowest electronic transition happens at 2.3 eV. The low-lying electronic excitations produce a strong increase in the rates of recurrent fluorescence, calculated to peak at $4.6\times {10}^4{s}^{-1}$, with a time average of $8\times {10}^3{s}^{-1}$. The average value is one order of magnitude higher than the static result, approaching the measured radiation rate. Similar results were found for the other cluster sizes. The results indicate that the effect makes a significant contribution to the radiative cooling, even given the exploratory nature of the study. Furthermore, the radiationless crossing between the ground-state and first-electronic-excited-state surfaces of $B_{13}{}^{+}$ was calculated, found to be very fast compared to experimental timescales, justifying the thermal population assumption.