Chains of amino acids can model endogenous biotags for applications in second harmonic imaging microscopy. Such structures are inherently ﬂexible which may strongly aﬀect their structure-property relationship. Here, we explore quantum-mechanically the conformational space of a set of relatively large tryptophan-rich model peptides studied experimentally by Duboisset et al. [JPC B 2014 118]. This has become feasible because of the recently proposed meta-dynamics method based on eﬃcient tight-binding (TB) quantum chemical calculations. The TB version of the simpliﬁed time-dependent density functional theory (sTD-DFT-xTB) method is used to evaluate the ﬁrst hyperpolarizability. 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 ﬁrst hyperpolarizability of these systems is dominated by the indole chromophore in the tryptophan residues. Their relative orientation mostly determines the global β tensor and aﬀects the static ﬁrst hyperpolarizability response drastically. The results underline the importance of ﬁnding low-energy conformers for modeling the ﬁrst hyperpolarizabilities of ﬂexible molecules. Additionally, we compare calculated and extrapolated experimental static ﬁrst hyperpolarizabilities.
We conclude that 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.