Dynamic Structural Effects on the Second-Harmonic Generation of Tryptophane-Rich Peptides and Gramicidin A

Peptide chains can model endogenous biotags for applications in second-harmonic imaging microscopy. Such structures are flexible which may strongly affect their structure-property relationship. Here, we explore quantum-mechanically the conformational space of a set of tryptophan-rich model peptides. This has become feasible because of the recently proposed meta-dynamics method based on efficient tight-binding (TB) calculations. The TB version of the simplified time-dependent density functional theory (sTD-DFT-xTB) method is used to evaluate the first hyperpolarizability (β). These new tools enable us to calculate nonlinear optical properties for systems with several thousand atoms and/or to screen large structure ensembles. First, we show that the indole chromophore in tryptophan residues dominates the β response of these systems. Their relative orientation mostly determines the global β tensor and affects the static β response. The results underline the importance of finding low-energy conformers for modeling β of flexible molecules. Additionally, we compare calculated and extrapolated experimental static β. The sTD-DFT-xTB method is capable of providing reliable second-harmonic generation values for tryptophan-rich systems at a fraction of the computational cost of the commonly used TD-DFT/TD-HF levels of theory.