Molecular dynamics in finding nonadiabatic coupling for β-NaYF₄: Ce³⁺ nanocrystals

Abstract

Optical and electronic properties of cerium ions doped into solid host matrices are explored by density functional theory (DFT). A spin-polarised (unrestricted) DFT + U approach is applied to β-NaYF₄: Ce³⁺ nanocrystals, in which the Hubbard U − J value is determined through experimental fitting to be 8.5 eV for yttrium, and 2.9 eV for cerium. Molecular dynamics simulations indicate that the energies of the localised f-like orbitals of the Ce³⁺ dopant exhibit strong thermal fluctuations compared to that of the p- and d-shaped orbitals due to charge-density localisation. Our observation of mixing between the d and f orbitals of Ce³⁺ ion is consistent with experimental results. Combining time-dependent density matrix methodology, ab initio molecular dynamics, and on-the-fly nonadiabatic couplings simulates nonradiative transitions between electronic states at ambient temperature. Transition rates between individual orbitals decrease with their energy difference, which is similar to the format of the energy gap law. These transitions contribute to integrated rates of nonradiative thermalisation of different electronic excitations to the lowest excited state through multiple pathways. The integrated rates of thermalisation decrease with energy difference of the initial photoexcitation and the final excitation.

Keywords:

• spin-polarised DFT
• Hubbard U
• Redfield tensor
• density matrix
• nonradiative decay
• cascade thermalization

Acknowledgements

The USD high performance computing facilities maintained by D. Jennewein are gratefully acknowledged. Authors thank J. Mottishaw for proofreading.

Additional information

Funding

This research was supported by South Dakota Governor's Office of Economic Development, NSF awards EPS-0903804, CHE-1413614 and by DOE, BES – Chemical Sciences, NERSC Contract No. DE-AC02-05CH11231, allocation Awards 85213, 86185, 86898 ‘Computational Modeling of Photo-catalysis and Photoinduced Charge Transfer Dynamics on Surfaces’.