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 (beta). 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 beta response of these systems. Their relative orientation mostly determines the global beta tensor and affects the static beta response. The results underline the importance of finding low-energy conformers for modeling beta of flexible molecules. Additionally, we compare calculated and extrapolated experimental static beta. 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.