Simplified Time-Dependent DFT for all-Atom Simulations of Second Harmonic Generation Responses: A Case Study...

Predicting the nonlinear optical (NLO) properties of large, disordered supramolecular aggregates is challenging because fully capturing dynamic fluctuations and intermolecular interactions requires a quantum-mechanical treatment of aggregation effects that remains out of reach for conventional computational methods. In the simplified time-dependent density functional theory (sTD-DFT) framework, we present a fully automated protocol for optimally tuning the Mataga-Nishimoto-Ohno-Klopman (MNOK) expressions of the two-electron integrals, enabling the prediction of NLO responses at a fraction of the cost of conventional TD-DFT. Using ground-state molecular orbitals from either DFT or extended tight-binding (xTB) calculations, the transferability of the optimized parameters is validated across isolated molecules, small model aggregates, and supramolecular clusters representative of azobenzene self-assembled monolayers (SAMs) extracted from molecular dynamics (MD) simulations. The results show that sTD-DFT reliably reproduces TD-DFT NLO responses and allows the treatment of large, disordered aggregates. Comparison of cluster- and fragment-based NLO responses shows that aggregation significantly reduces the second-harmonic generation (SHG) signal in azobenzene SAMs. Furthermore, comparing full sTD-DFT calculations with those relying on an electrostatic embedding of the environment reveals that both the trans/cis NLO contrast and the anisotropy of the SHG responses can differ substantially when all molecules are treated on an equal quantum-mechanical footing. These results demonstrate that combining MD simulations with optimally tuned sTD-DFT provides a practical strategy for evaluating NLO responses in complex supramolecular systems, fully capturing aggregation effects at an all-atom quantum mechanical (AQM) level.