Extension of the Time-Dependent Density Functional Complex Polarizability Algorithm to Circular Dichroism: Implementation and Applications to Ag₈ and Au₃₈(SC₂H₄C₆H₅)₂₄

We detail the calculation of rotatory strengths as an extension of the complex polarizability algorithm of time dependent density functional theory (TDDFT) proposed in a recent publication (O. Baseggio, G. Fronzoni, M. Stener, J. Chem. Phys. 2015, 143, 024106). To demonstrate the generality and applicability of the proposed algorithm, we calculate the photoabsorption and circular dichroism (CD) spectra of Ag₈ (as a validation case), Au₃₈(SCH₃)₂₄, and Au₃₈(SCH₂CH₂Ph)₂₄ monolayer-protected gold clusters (as a system of great current interest for their optical properties). For Au₃₈(SCH₂CH₂Ph)₂₄, the computed CD spectrum agrees well with the experimental data from the literature. Furthermore, a comparison of the calculated CD spectra of the two thiolate-protected nanoclusters reveals that the most distinctive features of the spectra are rather insensitive to the nature of the thiolate tail groups, which, however, play a significant role in shaping optical and dichroic response of the systems, especially in the higher energy portion of the spectrum.