Calculated linear and nonlinear optical absorption spectra of phosphine-ligated gold clusters

Abstract

Although prediction of optical excitations of ligated gold clusters by time-dependent density functional theory (TDDFT) is relatively well-established, limitations still exist, for example in the choice of the exchange–correlation functional. In aiming to improve on the accuracy of the calculated linear absorption, we report a theoretical study on phosphine-ligated gold clusters, specifically Au₉(PR₃)₈³⁺ and Au₈(PR₃)₇²⁺ characterized by highly resolved UV/Vis spectra, using mass-selective electronic absorption photofragmentation spectroscopy (A. Cirri, H. M. Hernández and C. J. Johnson, J. Phys. Chem. A, 2020, 124, 1467–1479, and references therein). The optical absorption spectra of the Au₉(PR₃)₈³⁺ and Au₈(PR₃)₇²⁺ clusters were calculated using TDDFT and the many-body GW (G-Green's function, and W-screened Coulomb interaction)-BSE (Bethe Salpeter Equation) method, and compared to the experimental measurements. The evGW-BSE results demonstrated fair agreement with the experimental data, comparable to the TDDFT results, but with less dependence on the reference exchange–correlation functional. Experimentally observed ligand-effects in these materials were reproduced in our calculations as well. Finally, to assess the utility of the materials for nonlinear optical absorption, a theoretical evaluation of two-photon absorption cross-sections is included.