Theoretical Modeling of BODIPY-Helicene Circularly Polarized Luminescence

Abstract

Density functional theory (DFT) and its extension, time-dependent DFT (TD-DFT), have become fundamental tools for modeling chiral excited states and supporting experimental chiroptical spectroscopies. In this connection, the interest in understanding the asymmetric emission through the circularly polarized luminescence (CPL) technique peaked in the current decade. In the present work, we are computationally faced with an emerging class of luminophores which combines the luminogenic source of the BODIPY unit with the intrinsic chirality of the helicene pendant to obtain a chiral radiative deactivation. In particular, a meso-substituted BODIPY-[6]helicene was deeply examined through a DFT multistep approach to attain an appreciable level of theory for the CPL simulation. Among the multitude of alternatives, TPSSTPSS exchange-correlation functional with 6-311G(d,p) basis set revealed to be the best computational protocol to emulate the CPL spectral profile with regard to peak intensity, band position, and chiral sign for both M and P form.

1. Introduction

Beyond the fascinating pattern ubiquitous in many transversal human activities (art, symbolism, literature, building, etc.), helix design was also recently imparted to the molecular scale [1,2,3,4,5,6,7,8,9,10,11]. Excluding chiral torsions of flexible molecules [12,13,14,15,16], to obtain the unique twisted stereo helical structure, a well-defined polycyclic aromatic compound with nonplanar screw-shaped backbone, formed by ortho-fused aromatic rings must be reached [17,18,19,20,21,22]. In this sense, helicene motifs occupy a leading position as a result of the steric hindrance of their terminal rings which confers a C₂-symmetric axis perpendicular to the helical axis, causing intrinsic chiral features to the whole molecule [23,24,25,26,27,28,29,30]. This asymmetrical identity induces helicenes to spiral in opposite directions producing levorotatory (M) and dextrorotatory (P) configurations (Figure 1). Focusing on the twisting conformations between fused rings in carbohelicenes, it instantly emerges that the four-membered ([4]helicene) scaffold is the smallest condensed polyarene which guarantees a proper dihedral angle to have an initial helical unit [31,32,33,34,35]. At the same time, the six-membered system can wind to perfectly cover a complete 360° rotation of a screw [36,37,38,39,40] (Figure 1). Intentionally omitting higher carbohelicene and heterohelicene, whose synthetic procedures are often annoying [30,41,42,43,44,45], and smaller helicene (four- and five-membered) whose enantiomers are not stable [46,47,48,49,50], in the last decade [6]helicene proved to be a valid chiral inducer to explore the chiroptical activity of chromophoric platforms [51,52,53]. Specifically, most of these studies hinge on the circular dichroism (CD) which properly captures the extremely strong bisignate Cotton effect that peaks in the ¹B_a and ¹B_b transition regions of the [6]helicene [54,55,56,57]. On the other hand, very few examples of circularly polarized luminescence (CPL) are disseminated in the literature as a consequence of a typically very low fluorescence quantum yield of the pristine [6]helicene [58,59,60,61]. Among the different synthetic strategies for the design of more effective [6]helicene luminophores, the installation of the helical arm into a BODIPY core was very profitable [62]. In this sense, boron-dipyrromethene dyes condense a plethora of optical features (narrow emission bandwidths covering the entire visible spectral range, high peak intensities, small Stokes shifts, and high fluorescence quantum yields [63,64,65,66,67,68]) to gain decent CPL spectra combined with helicene units. In this less unexplored landscape, theoretical modeling regarding CPL spectra of covalently linked BODIPY-helicene assembly are still missing in the literature, notwithstanding in the last decade in which the in silico analyses for the chiral emission predictions of organic species are increasing [69,70,71,72,73]. With this contribution, a rigorous yet accessible computational plan to ably decode CPL spectral profile of a specific BODIPY-helicene will be presented. By exploiting the density functional theory (DFT), various DFT parameters will be scanned to reach a final computational level that furnishes a precise excited state transition description during the chiral emission.

2. Materials and Methods

The crystallographic structures of BODIPY-aza[7]helicene (1) and (2) were extracted from the Cambridge Structural Database (CCDC: 1976460, 1976458) and DFT-optimized in the gas phase by employing the following exchange-correlation functionals: B3LYP, CAM-B3LYP, ωB97XD, OLYP, M06-2X, MN15, X3LYP, PBEPBE, B97D3, and APFD combined with def2-TZVP basis set, utilizing a superfine grid and a tight criterion for energy and geometry optimization convergence. Thanks to the previous DFT analyses, our target compound (BODIPY-[6]helicene in both P and M forms) was energy-minimized at M06-2X/def2-TZVP level in the gas phase for the ground and first excited state. TD-DFT calculations were run using TPSSTPSS, HCTH, M06L, M11L, B3LYP, O3LYP, mPW1PW91, LC-ωHPBE, CAM-B3LYP, and ωB97XD for the functional evaluation (6-311G(d,p) basis set was kept fixed). For the basis set screening, TPSSTPSS was associated with LanL2DZ, aug-cc-pVTZ, def2-TZVP, Jorge-TZP, and 6-311G(d,p). Consequently, the same modus operandi was maintained for testing the Pople family: 6-31G, 6-311G, 6-311G(d,p), 6-311+G(d,p), 6-311++G(d,p), and 6-311++G(2df,2pd). In the end, Grimme’s dispersion corrections (D3) [74] were embedded into the TPSSTPSS/6-311G(d,p) level. In the calculated spectra, CPL intensities were determined as follows: [75]

$$\Delta \mathrm{I}={\displaystyle \frac{16{\mathrm{E}}_{\mathrm{emi}}^3{*\mathrm{R}}_{0\mathrm{m} }*\rho \left({\mathrm{E}}_{\mathrm{emi}}\right)}{3{\hslash }^4*{\mathrm{c}}^3}}$$

(1)

where ħ is the reduced Planck’s constant, c is the speed of light, ρ(E_emi) is the Gaussian band shape centered in the E_emi energy, and R_0m is the rotational strength associated with the transition 0 ← 1 (expressed as R length). Equation (1) is formulated in cgs units and the band shape was assumed as Gaussian with a bandwidth of 600 cm⁻¹. All the computational jobs were carried out with the Gaussian16 package [76].

3. Results and Discussion

To date, excluding distorted π-extended fused BODIPY [77,78] and helically wrapped N,N,O,O-boron chelated dipyrromethenes [79], very few examples of CPL active BODIPY-helicene were collected in the literature and only one contemplates a pure [6]helicene with a pristine BODIPY platform [62]. Figure 2 clearly shows how Maeda et al. excellently capitalized the incorporation of BF₂ into an aza[7]helicenes moiety to generate four chiral carbazole-based boron complexes (fused BODIPY-heterohelicene) [80]. Lastly, Silber et al. ingeniously synthetized the first BODIPY-[6]helicene through the condensation of pyrrole with 2-formyl-[6]helicene [62]. This unicum can be seen as a bimodular CPL system in which helical substituent in meso position acts as a chiral donor while the BODIPY dye serves as a light emitter.

With these premises, we decided to adopt BODIPY-[6]helicene as a computational probe to realize an in-depth evaluation of the different factors affecting the prediction of the CPL spectrum, including the exchange-correlation functionals, the type of basis set, the extension of the basis set, and the dispersion effects. In order to follow computationally the chiroptical radiative process, well-established theoretical methodologies suggest finding the ground (S0) and the excited (S1) state geometries [81,82,83,84]. For S0 energy minima, it is a common practice to rank the DFT functionals by virtue of benchmarks targeting the accurate prediction of X-ray preferential conformations [85,86,87], while for the S1 potential energy surface (PES), optical properties (emission energies, band shape, and spectral profile) are often checked [88,89,90]. Unfortunately, in this specific case (BODIPY-6[helicene]) crystallographic data are missing. Consequently, the X-ray atomic coordinates of two BODIPY-aza[7]helicenes (reported in Figure 2) were employed to assess the most appropriate functional for the DFT description of the BODIPY-helicene in its ground state (S₀). This selection is justified by the fact that BODIPY-aza[7]helicenes belong to the same class of compounds, exhibiting not only structural similarities but also analogous chiroptical properties, such as comparable emission ranges and dissymmetry factors. With the aim of having a balanced DFT list, we resolved to condense exchange-correlation functionals deputed for the BODIPY core optimizations [91,92,93] with those particularly suitable to reproduce the helicene fashion [40,57,94]. In fact, B3LYP, CAM-B3LYP, ωB97XD, OLYP, M06-2X, MN15, X3LYP, PBEPBE, B97D3, and APFD were approved in the gas phase in order to allow relevant comparisons with X-ray crystal coordinates.

Favored by the limited fluxionality of the analyzed structures (1 and 2),

Table 1. Root-mean-square deviation values (Å) for the set of exchange-correlation functionals.

Functional	RMSD (Å)
	BODIPY-aza[7]helicene (1) (X = O)	BODIPY-aza[7]helicene (2) (X = S)
B3LYP	0.361	0.350
CAM-B3LYP	0.347	0.336
ωB97XD	0.395	0.248
OLYP	0.364	0.268
M06-2X	0.341	0.194
MN15	0.372	0.202
X3LYP	0.356	0.347
PBEPBE	0.354	0.345
B97D3	0.381	0.268
APFD	0.391	0.240

displayed minute fluctuations in the functionals’ performances in terms of RMSD. Within this modest interval, the hybrid functional from the Truhlar group [95], M06-2X, appeared as the best candidate to duplicate the crystal structures of 1 and 2 (the lowest RSMDs in both cases) in S0. This evidence perfectly fits with previous theoretical studies which anticipated the goodness of M06-2X for boron dipyrrin derivatives [81]. Once a convenient DFT level of theory (M06-2X/def2-TZVP) for the S0 BODIPY-helicene optimizations was found, our leader compound (BODIPY-[6]helicene) was energetically minimized (Figure 3). At this point, convinced by antecedent articles in the literature [96,97,98], we arranged to use M06-2X/def2-TZVP with the goal of mapping the first singlet excited state, necessary to access to the chiral emissive pathway. Superpositions of the ground state with the first excited state (Figure 3) distinctly indicate two key discrepancies between S0 and S1 geometries: (1) A typical distortion in the BODIPY core which transits from a planar disposition to a curved one [99]. (2) A significant changing (~10°) in the dihedral angle involving the meso position, 127.95° for S0 and 137.97° for S1. Both events can be attributed to the tendency of a π-conjugation enlargement upon the photoexcitation.

At this stage, we have all the ingredients to execute a TD-DFT screening for quantifying realistically the CPL phenomenon. Bearing in mind that BODIPY-[6]helicene reported a broad band in the visible region (~550–700 nm) with a maximum at 608 nm, we initially tried to individuate an adequate functional to simulate the correct CPL emission energy. For this scope, pure (TPSSTPSS, HCTH, M06L, M11L), hybrid (B3LYP, O3LYP, mPW1PW91), long-range corrected (LC-ωHPBE, CAM-B3LYP), and dispersion embedded (ωB97XD) functionals were tested. In this situation, the Pople basis set (6-311G(d,p)), normally practiced for the theoretical characterization of the second-period elements [100,101,102,103], was coupled with the aforementioned functionals. Although in each case the spectral pseudo-Gaussian band and the chiral sign (negative, M form) were efficiently delineated, Figure 4 immediately illustrates a multi-variegated picture in which the checked functionals cover a large portion of the visible region. First of all, ωB97XD, LC-ωHPBE, and CAM-B3LYP failed due to silent signals generated by very low rotational strengths (Table S1, Supporting Information) while the rest of the functionals presented a comparable but smaller chiroptical intensity than the experimental values. In detail, mPW1PW91, B3LYP, and O3LYP conferred an excessive blue shift in the peak position; on the contrary, HCTH located its CPL spectral maximum at lower frequencies. M11L, M06L, and TPSSTPSS crowded the salient section of the emission energies with 590 nm, 592 nm, and 611 nm, respectively. Taking into account the almost imperceptible difference between the latter and the CPL experimental peak (608 nm) we elected TPSSTPSS as the best exchange-correlation functional performer.

Persuaded by the accuracy of TPSSTPSS, we focused on the possible dependence of the basis set family on the CPL spectral figure. For this reason, an assorted group of the basis set was verified: LanL2DZ, aug-cc-pVTZ, def2-TZVP, Jorge-TZP, and the already calculated 6-311G(d,p). Among the different types of basis sets, it rapidly crops up that the triple-Z valence (aug-cc-pVTZ, def2-TZVP, Jorge-TZP, and 6-311G(d,p)) operate better than the double-Z (LanL2DZ) both in terms of band position and intensity (Figure 5A and Table S2, Supporting Information). Among the triple-Z, Pople 6-311G(d,p) turned out to be the leader, while aug-cc-pVTZ, def2-TZVP, and Jorge-TZP moderately red-shifted the spectral band (618–619 nm). Stimulated by these outcomes, we tried to determine the impact of the expansion of the Pople basis through the influence of polarization and diffusion functions on the CPL spectral line. Therefore, a gradually more extended Pople basis set was applied: 6-31G, 6-311G, 6-311+G(d,p), 6-311++G(d,p), and 6-311++G(2df,2pd). Although the emission energies are compressed in a 10 nm range, the main variations still regard the chiroptical magnitudes, in fact also in this case, the double-Z basis set (6-31G) recorded the lowest rotational strengths (Figure 5B and Table S3, Supporting Information), while the signal intensity progressively obtains better transiting from double- to triple-Z considering the polarization functions (6-311G < 6-311+G(d,p) < 6-311++G(d,p) < 6-311++G(2df,2pd)). Conversely, the role of the diffusion functions seems marginal, with a perfect match between 6-311+G(d,p) and 6-311++G(d,p) (light blue line belonging to 6-311++G(d,p) is totally retraced by the 6-311+G(d,p) red one, Figure 5B). The best compromise, both in terms of chiroptical amplitude and peak position, was further confirmed by the triple-Z associated with polarization functions (6-311G(d,p)). Finally, in light of the highly conjugated π-cloud which invests BODIPY-[6]helicene, nonlocal effects accounting for London dispersion forces were incorporated in the TD-DFT calculations. Although the introduction of the Grimme’s dispersion corrections can be useful in excited state treatments [104,105,106,107], in our case it originated a negligible shift in the wavelength emission and unchanged intensities (Figure 5C and Table S4, Supporting Information).

Now, the transferability of our privileged TPSSTPSS/6-311G(d,p) level must obey the enantio-differentiation, producing a mirror-spectrum for the P form in the helical segment. Figure 6 shows how the peak positions are equal (Δ~0.43nm) and the chiral sign is exactly inverted with a specular amplitude (Table S5, Supporting Information). Finally, frontier orbitals (HOMO and LUMO) participating in the deactivation process suggest that the CPL mechanism implies an intramolecular charge transfer from the helicene framework (which prevalently occupies HOMO) to the BODIPY moiety (which dominates LUMO) (Figures S2 and S3, Supporting Information), coherently with previous studies on similar structures [80].

4. Conclusions

Prompted by the recent rapid growth in enthusiasm for circularly polarized luminescence of organic species, we have computationally centered on a nascent class of chromophores which govern the helical chirality of the non-racemic helicene entity with the fluorescent activity of BODIPY frame to activate a chiral emission. The theoretical guide announced here, through a step-by-step inspection of the DFT parameters impacting on the chiroptical luminescence, aimed to construct a solid DFT level for cloning the CPL spectral identity of the BODIPY-[6]helicene. An initial exchange-correlation functional benchmark elected M06-2X as the best performer to refine the chemical structure in the ground state. A comparative matching between the ground and excited states spotlighted that the meso position, bearing the chiral inducer (helicene portion), assumed a more twisted arrangement in S1 owing to the photoexcitation. Our accumulative workflow demonstrated that TPSSTPSS/6-311G(d,p) TD-DFT level meticulously recreated the CPL spectrum adhering to the experimental peak position, band shape, and chiral sign for P and M forms. Our research intends to be a starting model to computationally rationalize the chiroptical emission of future chromophoric platforms based on meso-substituted BODIPY-helicene derivatives.