Efficient Subsystem TDDFT Calculations for Optical Rotatory Dispersion of Molecules in Solution: Converging the Configurational Averaging for Norbornenone in Acetonitrile

We present a comprehensive study on optical rotatory dispersion (ORD) calculations for a chiral molecule in solution by means of subsystem TDDFT (sTDDFT) for snapshots extracted from classical molecular dynamics (MD) trajectories. As a prototypical example, we study the ORD of norbornenone in acetonitrile. Uncovering the microscopic origin of the solvent effect on the ORD necessitates an explicit quantum chemical solvation model and robust configurational sampling, rendering such calculations computationally extremely heavy. Here, we employ sTDDFT to study the convergence of the ORD signal with respect to both the size of the solvation shell considered <i>and</i> the number of snapshots considered in the configurational sampling, as well as the interdependence of these two factors. We demonstrate that several thousand snapshots have to be considered to accurately converge the solvation effect even for comparatively small solvated clusters. By systematically studying solvent cages of increasing size, we observe a clear correlation between the radial distribution function of acetonitrile around norbornenone and the ORD dependence on the solvent-shell size. Larger solvation shells, unfortunately, usually also require more extensive configurational sampling. To facilitate such an averaging procedure on a quantum chemical basis, we introduce further algorithmic improvements to achieve an additional speed up in our sTDDFT calculations. We observe that sTDDFT accurately captures the qualitative features of the solvation-shell size dependence. In addition, a systematic empirical correction is developed to achieve quantitative agreement with the parent TDDFT results. Overall, sTDDFT in combination with classical MD for snapshot generation offers an economical approach toward obtaining converged ORD results in solution.