# Chiroptical Symmetry Analysis of Trianglimines: A Case Study

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

**1**,

**2**, and

**3**(Figure 1) were optimized at cam-B3LYP [23,24] level using 6-311G(d,p) basis set. Subsequently, vibrational frequencies were calculated at the same level of theory to confirm that the obtained structures were true minima. The structural measures necessary for the CSA were extracted from the corresponding structures (Figure 2 and Figure 3). In addition, TD-DFT calculations were performed to compare the ECD spectra with those predicted by CSA. Particularly, the cam-B3LYP functional was chosen since the simulated spectra showed good agreement with the reported experimental ECD spectra [21]. On the other hand, UV/Vis and ECD spectra were simulated for analogue structures featuring only two and one chromophores (depicted in Figure 2 and Figure 3, respectively) by removing the rest of the structure and adding hydrogen atoms for each analogue without further optimization.

_{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. Concerning thee trianglimine derivatives under study, three identical chromophores are present in each structure (represented in different colors in Figure 1). According to the CSA, the chiroptical response of a system mainly originates from the contribution of each chromophore interacting cooperatively with the others due to their relative orientation. This implies that the symmetry of the system determines which chromophores interact simultaneously resulting in the ECD spectra. When a system with C

_{2}or D

_{2}symmetry presents two non-conjugated chromophores, the Davydov model allows for obtaining a picture of the approximate ECD spectra: The chromophores are represented by the corresponding Electric Dipole Transition Moment (EDTM), ${\overrightarrow{\mu}}_{i}^{t}$, and the interaction between them, V

_{12}, is given by Equation (1):

_{12}is in au units. The application of the perturbation theory to the originally degenerate first electronically-excited level yields an energy splitting, ΔE, between these two states and, consequently, the gap between the two main electronic excitations given by Equation (2):

_{3}symmetry, the ground electronic state belongs to the totally-symmetric representation (A1) and there are three equivalent monoexcitations. 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.

_{3}symmetry, we need to know the structural parameters of the molecule as well as the EDTM of the monomer in order to use CSA on each particular case. By this way, after calculation of V

_{12}and the rotatory strengths for each allowed transition, we will be able to predict the main features of the ECD spectra originated from the exciton coupling between the interacting independent chromophores. Therefore, we will predict one A2 and two degenerated E transitions per electronic transition of the independent chromophores. Since the chromophoric units in 1, 2, and 3 present respectively one, two, and three significant electronic transitions, by the CSA, we could simulate one, two, and three A2 along with one, two, and three pairs of E transitions, respectively.

## 3. Results

**1**,

**2**, and

**3**presenting three chromophores were hereby studied by CSA. Szymkowiak et al. demonstrated that TD-DFT calculations resemble the experimental ECD spectra of those compounds well [21]. Therefore, as mentioned above, DFT simulations were performed and compared with those obtained by CSA. As the EDTMs are origin independent, we can define an EDTM vector for each chromophoric transition (Figure 3). The molecular EDTM was obtained as a combination of individual vectors for each particular electronic transition to visualize the CSA and compared to those obtained from TD-DFT.

#### 3.1. Structure 1

**1**are presented in Table 1, whereas Figure 2 shows structure

**1**and a truncated system with only two chromophores. Regarding structure

**1**, the analysis was also performed for the analogue with only two chromophores as an example of application of the CSA. In the case of two-chromophore systems, two excited states result from the parallel and antiparallel combinations.

**1**with only two chromophores calculated by CSA are 1.80 and 3.15 au (see Figure S1 in the Supplementary Materials). These values agree very well with the ones predicted by cam-B3LYP, 1.71 and 3.09, respectively. For the total system

**1**presenting three chromophores and D

_{3}symmetry, considering the CSA, three electronic transitions are allowed where two of them are degenerated and the EDTMs for transitions are given by the expression:

#### 3.2. Structure 2

#### 3.3. Structure 3

## 4. Discussion

_{3}-axis has no comparable partner in the truncated system with only two chromophores. Notably, the EDTM and RS predicted with CSA are sufficient to reproduce the TD-DFT calculations well.

**2**and

**3**are one higher and the other lower than 90°. Since this fact renders a flip in the sign of the RS, the main features of the predicted ECD spectra present a positive and a negative exciton couplet at the same time in the same spectra at different energies (Figure 7).

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Trianglimine derivatives 1, 2, and 3 under study. The three equivalent chromophores in each structure are depicted in blue, red and black.

**Figure 2.**Structural measures of

**1**. (

**a**) ${\overrightarrow{R}}_{12}$ vector is extracted from analogue structure of

**1**with two chromophores (

**b**) while θ is the angle between Electric Dipole Transition Moment (EDTM) of chromophores and C

_{3}axis, ω stems from the angle between the projection of EDTM for chromophores on the x–y plane with the x-axis. Light blue bars represent the EDTM associated with each independent chromophore.

**Figure 3.**Representation of EDTMs for analogue structures with only one chromophore in 1 (

**a**); 2.1 (

**b**); 2.2 (

**c**); 3.1 (

**d**); 3.2 (

**e**); and 3.3 (

**f**) simulated by TD-DFT calculations.

**Figure 4.**Representation of EDTMs for each chromophore (light blue, located in the chromophores) in structure

**1**and total EDTMs (dark blue, located in the center of the system) for (

**a**) A2 and (

**b**) E transitions originated from the exciton coupling of main excitation of independent chromophores (gold, located in the center of the system).

**Figure 5.**Representation of EDTMs for chromophores (light blue, located in the chromophores) in

**2**and total EDTM (dark blue, located in the center of the system) for A2 transitions from 2.1 (

**a**) and 2.2 (

**c**) and E transitions from 2.1 (

**b**) and 2.2 (

**d**) originated form the exciton coupling of two main excitations of independent chromophores (gold, located in the center of the system).

**Figure 6.**Representation of EDTMs for chromophores (light blue, located in the chromophores) in 3 and total EDTM (dark blue, located in the center of the system) for A2 transitions from (

**a**) 3.1 and 3.3 (

**c**) and transitions E from 3.1 (

**b**) and 3.3 (

**d**) originated from the exciton coupling of two of the three main excitations of the independent chromophores (gold, located in the center of the system).

**Figure 7.**Comparison of TD-DFT (red) and CSA (blue) results for trianglimine systems (

**a**)

**1**; (

**b**)

**2;**and (

**c**)

**3**. Rotatory strength values are represented in relative intensities’ energy as well as relative intensity of rotatory strength values resemble qualitatively those reported by Szymkowiak et al. [21].

**Table 1.**Structural measures for CSA analysis of

**1**. As illustrated in Figure 2, R

_{12}is the distance between origins of the ETDMs of two chromophores, θ is the angle between EDTM and C

_{3}-axis (z-axis) and ω is the angle between the projection of EDTM for chromophores on the xy plane with the x-axis (for D

_{3}symmetry, the required angle is 90°). V

_{12}value is obtained as indicated [3].

Structure | R_{12} | ω | θ | V_{12} |
---|---|---|---|---|

1 ^{1} | 12.3 bohr | 13.8° | 29.1° | 0.11 eV |

1 | 12.3 bohr | 90° | 77.7° | 0.11 eV |

^{1}Analogue structure of 1 with two chromophores.

**Table 2.**Parameters obtained from CSA analysis of

**1**. Rotatory strength values are given in ascending order of energy.

Structure | Splitting CSA/TD-DFT | Module of EDTM CSA/TD-DFT | Rotatory Strength CSA/TD-DFT |
---|---|---|---|

1^{1} | -/4.8026 eV | -/2.54 | -/- |

1^{2} | 0.22/0.20 | ^{3} 1.8:3.1/1.7:3.1 | ^{3} −334:334/−272:448 |

1 | 0.33/0.31 | 0.6:2.0/0.2:3.4 | ^{4} −1190/595/−363:332 |

^{1}Analogue structure of

**1**with only one chromophore, the energy displayed here corresponds with the most significant low energy electronic transition;

^{2}Analogue structure of 1 with two chromophores;

^{3}A:A.

^{4}A2:E.

Structure | R_{12} | ω | Θ | V_{12}/eV |
---|---|---|---|---|

2.1 | 12.4 bohr | 90° | 99.7° | 0.05 eV |

2.2 | 12.4 bohr | 90° | 74.4° | 0.05 eV |

**Table 4.**Parameters employed for CSA analysis of structure

**2**. Rotatory strength values are given in ascending order of energy.

Structure | Splitting CSA/TD-DFT | Module of EDTM CSA/TD-DFT | Rotatory Strength CSA/TD-DFT |
---|---|---|---|

2.1 ^{1} | -/3.8879 eV | -/1.75 | -/- |

2.1 | 0.15/0.15 | ^{3} 0.6:1.7/0.6:2.26 | ^{3} 368:−184/649:−349 |

2.2 ^{2} | -/4.8181 eV | -/1.91 | -/- |

2.2 | 0.15/0.15 | ^{3} 0.8:1.6/0.58:2.57 | ^{3} −847:423/−665:325 |

^{1}Analogue structure 2.1 with only one chromophore, the energy displayed here corresponds with the most significant low energy electronic transition;

^{2}Analogue structure 2.2 with only one chromophore, the energy displayed here corresponds with the most significant second low energy electronic transition;

^{3}A2:E. 2.1 refers to the exciton coupling originated from the lowest electronic transition of the monomer and 2.2 to the second lowest.

Structure | R_{12} | ω | Θ | V_{12}/eV |
---|---|---|---|---|

3.1 | 12.4 bohr | 90° | 77° | 0.02 eV |

3.2 | 12.4 bohr | 90° | c.a. 90° | 0.04 eV |

3.3 | 12.4 bohr | 90° | 94° | 0.03 eV |

**Table 6.**Parameters employed for CSA analysis of structure

**3**. Rotatory strength values are given in ascending order of energy.

Structure | Splitting CSA/TD-DFT | Module of EDTM CSA/TD-DFT | Rotatory Strength CSA/TD-DFT |
---|---|---|---|

3.1 ^{1} | -/3.4007 eV | -/1.41 | -/- |

3.1 | 0.06/0.06 | ^{3} 1.3:1.0/1.09:1.50 | ^{3} −276:138/−801:304 |

3.3 ^{2} | -/5.7592 eV | -/2.05 | -/- |

3.3 | 0.09/0.14 | ^{3} 0.6:1.7/0.6:2.69 | ^{3} 313:−157/813:−535 |

^{1}Analogue structure 3.1 with only one chromophore, the energy displayed here corresponds with the most significant low energy electronic transition;

^{2}Analogue structure 3.3 with only one chromophore, the energy displayed here corresponds with the most significant third low energy electronic transition;

^{3}A2:E. 3.1 refers to the exciton coupling originated from the lowest electronic transition of the monomer and 3.2 to the second lowest.

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**MDPI and ACS Style**

Ozcelik, A.; Pereira-Cameselle, R.; Mosquera, R.A.; Peña-Gallego, Á.; Alonso-Gómez, J.L. Chiroptical Symmetry Analysis of Trianglimines: A Case Study. *Symmetry* **2019**, *11*, 1245.
https://doi.org/10.3390/sym11101245

**AMA Style**

Ozcelik A, Pereira-Cameselle R, Mosquera RA, Peña-Gallego Á, Alonso-Gómez JL. Chiroptical Symmetry Analysis of Trianglimines: A Case Study. *Symmetry*. 2019; 11(10):1245.
https://doi.org/10.3390/sym11101245

**Chicago/Turabian Style**

Ozcelik, Ani, Raquel Pereira-Cameselle, Ricardo A. Mosquera, Ángeles Peña-Gallego, and J. Lorenzo Alonso-Gómez. 2019. "Chiroptical Symmetry Analysis of Trianglimines: A Case Study" *Symmetry* 11, no. 10: 1245.
https://doi.org/10.3390/sym11101245