Chiroptical Symmetry Analysis: Exciton Chirality-Based Formulae to Understand the Chiroptical Responses of Cn and Dn Symmetric Systems

Abstract

The high sensitivity of chiroptical responses to conformational changes and supramolecular interactions has prompted an increasing interest in the development of chiroptical applications. However, prediction of and understanding the chiroptical responses of the necessary large systems may not be affordable for calculations at high levels of theory. In order to facilitate the development of chiroptical applications, methodologies capable of evaluating the chiroptical responses of large systems are necessary. The exciton chirality method has been extensively used for the interaction between two independent chromophores through the Davydov model. For systems presenting C2 or D2 symmetry, one can get the same results by applying the selection rules. In the present article, the analysis of the selection rules for systems with symmetries Cn and Dn with n = 3 and 4 is used to uncover the origin of their chiroptical responses. We foresee that the use of the Chiroptical Symmetry Analysis (CSA) for systems presenting the symmetries explored herein, as well as for systems presenting higher symmetries will serve as a useful tool for the development of chiroptical applications.

Chiroptical Symmetry Analysis of Trianglimines: A Case Study

“…All trianglimines under study have D 3 symmetry; therefore, the expressions obtained previously [20] for this symmetry were employed to predict the ECD spectra in a qualitative manner. The first step in the application of the CSA involves the identification of the chromophores that are responsible for optical properties in a molecule.…”

“…With this basis set, we are able to obtain the D 3 Symmetry-Adapted Linear Combinations for the first electronically-excited states. As we have shown earlier [20], the reducible representation of this basis can decompose into A1 and E when all the molecular orbitals (MOs) describing the excited state are σ or A2 and E when the excited state of the chromophore contains one π MO. In any case, the transition from the ground state will be only orbitally allowed for states A1 and E or A2 and E with 3V 12 energy difference between A1 or A2 and E. For systems presenting D3 symmetry, the ground electronic state belongs to the totallysymmetric representation (A1) and there are three equivalent monoexcitations.…”

“…The rotatory strengths are obtained from Equations (3) and (4). It is noteworthy that this approximation is only valid when the electronic transition of the independent chromophore presents negligible magnetic transition dipole moment (MTDM, for a more thorough explanation see reference [20]). Other studies have developed ab initio based exciton chirality methods [25]:…”

“…Nevertheless, the presence of more chromophores may be desired for designing powerful chiroptical systems [19]. In this respect, we previously revised the chiroptical symmetry analysis (CSA) for systems with three and four chromophores [20]. The main scope of this approach is to serve as a useful tool for developing particular systems rather than predicting experimental spectra of systems.…”

Chiroptical Sensing: A Conceptual Introduction

“…For systems presenting more than two independent chromophores, the chiroptical responses may be determined by the summation of the chiroptical responses originated for pairwise coupling between all chromophores. However, if the system presents higher symmetry, a chiroptical symmetry analysis can be emploied as alternative (Figure 17) [77]. For instance, for systems presenting D 3 and D 4 symmetry bearing three and four isolated crhomophores respectively, only one A 2 transition and two degenerated E transitions emerge.…”