Structural and Optical Properties of Subporphyrinoids: A TD-DFT

Article pubs.acs.org/JPCA

Structural and Optical Properties of Subporphyrinoids: A TD-DFT Study Cloé Azarias,† Mylène Pawelek,† and Denis Jacquemin*,†,‡ †

CEISAM, UMR CNRS 6230, BP 92208, Universite de Nantes, 2, Rue de la Houssiniere, 44322 Nantes, Cedex 3, France Institut Universitaire de France, 1, rue Descartes, F-75231 Paris Cedex 05, France

‡

S Supporting Information *

ABSTRACT: Using ab initio approaches accounting for environmental effects, we investigate the ground- and excited-state properties of four subporphyrinoids: subporphyrin, subporphyrazine, tribenzosubporphyrin, and subphthalocyanine. We first show that the selected level of theory, that is DFT(PBE0), is able to reproduce the structure and NMR spectra of all compounds. The aromaticity of these four macrocyclic entities are next quantified and it is showed that these bowl-shape induced molecules present very strong aromatic characters. Next we analyze the spectral signatures of all four compounds using an approach going beyond the vertical approximation. The 0−0 energies are reproduced with a mean absolute deviation smaller than 0.1 eV, and the very good agreement obtained between experimental and theoretical band shapes allows us to unravel the vibronic contributions responsible to the specific band shapes of these subporphyrinoids. Finally, we investigate a large series of substituted subporphyrins, demonstrate the quality of the trends that are obtained with theory and design new compounds presenting red-shifted optical bands.

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dyes.19−22 Indeed, due to the steric stress induced by the proximity of the three units, chemically stable macrocycles can only be reached when a central boron atom is used. Moreover, they all present a bowl-shape structure, meaning that, in contrast to porphyrins, the π-delocalization path is not strictly planar. In turn, this leads to several specific properties, such as a C3 or C1 point group symmetry, the latter being associated with a bowl chirality,23 as well as a concave π surface of particular interest in molecular recognition and in supramolecular chemistry, e.g., for fullerene encapsulation.24 Moreover, the axial group completing the coordination of the central boron atom can be replaced by several species, e.g., fluorophores,25 sensors26,27 drugs or hormones,28 fullerenes,29 ferrocenes,30 and cyclodextrins31 offering a wide panel of applications ranging from electronics to biology. It is worth underlying that subporphyrinoids present similar optical properties, but blueshifted bands, as their tetrapyrrolic counterparts. Indeed, the reduction of the π-conjugated pathway to 14 π electrons induces a hypsochromic displacement of the bands while their general profiles are conserved. For instance, SubP presents weakly allowed Q-bands at ca. 400−500 nm and strongly allowed Soret bands at ca. 350 nm.32 In analogy with porphyrins, the spectroscopic features of subporphyrinoids have been already applied in several fields, i.e., photodynamic therapy,33 organic photovoltaic cells,34,35 optical information recording media,36,37 and organic light-emitting diodes.34,38

INTRODUCTION Macrocylic derivatives constitute one of the most important classes of organic molecules. Indeed, their stability, their tunable properties and their abilities to complex a large panel of metallic cations have made macrocycles central elements in many research lines of biological, chemical and material sciences.1−5 The hallmark members of the family are without dispute porphyrins and phthalocyanines (Scheme 1a). These systems present four pyrrolic rings linked through methine groups (porphyrins) or imine units (phthalocyanines) and are strongly aromatic due to the formal ring delocalization of 18 π electrons. As a consequence, these macrocycles present an advantageous chemical stability and peculiar optical properties. More specifically, porphyrins typically present weak Q-bands at ca. 500−600 nm and intense Soret bands at ca. 400 nm. Using the well-known Gouterman four level model, one can qualitatively rationalize these spectroscopic features.6,7 To increase the range of possible applications of macrocycles, expanded porphyrinoid systems with more than four components have been proposed, e.g., rubyrins and superphthalocyanines (Scheme 1b) to cite two significant examples only.8−10 Likewise, smaller macrocycles, composed of three pyrrolic units have also been designed (Scheme 2), e.g., subporphyrin (SubP)11−13 and subporphyrazine (also called subazaporphyrin or subtriazaporphyrin, SubPz),14 as well as their phenyl-fused analogues, i.e., (tri)benzosubporphyrin (BzSubP)15,16 and subphthalocyanines (also called tribenzotriazaporphyrin SubPc).17 In the present theoretical investigation, we focus on these four subporphyrinoids. Experimentally, these systems show several features making them a distinguishable class of © 2017 American Chemical Society

Received: April 18, 2017 Revised: May 16, 2017 Published: May 17, 2017 4306

DOI: 10.1021/acs.jpca.7b03644 J. Phys. Chem. A 2017, 121, 4306−4317

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The Journal of Physical Chemistry A

Scheme 1. (a) Structures of Porphyrin (Left) and Phthalocyanine (Right) and (b) Representation of Rubyrin (Left) and a Superphthalocyanine (Right)

Scheme 2. Structures of the Subporporphyrin (SubP), Subporphyrazine (SubPz), Benzosubporphyrin (BzSubP), and Subphthalocyanine (SubPc) Investigated Herein18

Unsurprisingly, these subporphyrinoid structures have been studied theoretically, notably using density functional theory (DFT) and its time-dependent extension (TD-DFT). More specifically, the vast majority of the previous theoretical studies focused on the SubPz and SubPc systems and reported the structural properties, the molecular orbital levels as well as the vertical absorption spectra. These investigations also included studies of the impact of chemical modifications, i.e., (i) substituting the central boron atom,39,40 the heteoatoms of the macrocycle41,42 or the axial group;43,44 (ii) adding electroactive groups or fused-benzene rings on the pyrrolic units,39,45−48 and (iii) hydrogenating the external rings.49 Much less theoretical studies have been devoted to SubP and BzSubP systems.50,51 Other similar systems have been investigated as well.52 To the best of our knowledge, there is, for the compounds of Scheme 2, no specific studies going beyond the ground-state (GS) properties or vertical TD-DFT calculations. Here, we provide the first exploration of the excited-state (ES) potential energy surfaces of these compounds which allows the following: (i) determining the emission properties, (ii) computing the 0−0 energies that can be directly compared to the experimental absorption and fluorescence crossing point (AFCP), and (iii) calculating the vibronic couplings and consequently unraveling the origins of the shapes of the absorption and emission bands in terms of vibrational contributions. Moreover, as SubP presents methylene bridges, it offers additional sites for functionalization at the meso position in contrast to its azaanalogues. We have therefore investigated and rationalized the impact of meso-substitution on the SubP core. Among the available ab initio approaches allowing to model ES properties of medium and large size dyes, we have selected TD-DFT due to (i) its favorable 6 (N4) formal scaling with system size, (ii) its coupling with refined solvation models such as the polarizable continuum model (PCM)53 that enables accounting for environmental effects at a moderate computational cost, and (iii) the implementation of analytical geometrical derivatives, giving access to the three above-cited ES properties (fluorescence, 0−0 energies and vibronic couplings).54−56

Nevertheless, as the TD-DFT estimates can sometimes depend significantly on the chosen exchange-correlation functional, we have also used a wave function scheme, i.e., the second-order algebraic diagrammatic construction [ADC(2)] method in some test calculations. While ADC(2) presents a less favorable formal scaling with system size [6 (N5)] than TD-DFT, it still provides a good compromise between accuracy and computational cost. This paper is organized as follows: in the following section, we detail the applied computational procedures. Next, we present the results concerning the structure and aromaticity before focusing on the electronic spectra (vertical and vibrationally resolved absorption and emission spectra). Finally, we investigated the meso-substitution effect on the properties of SubP before concluding.

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COMPUTATIONAL METHODS AND BENCHMARKS All DFT and TD-DFT calculations have been performed using the Gaussian09 program.57 We have tightened the selfconsistent field (10−10 a.u.) and geometry optimization (10−5 a.u.) convergence thresholds and used the (99,590) pruned integration grid (the so-called ultraf ine grid). DFT and TDDFT Hessians were computed to confirm the nature (minima) of all GS and ES structures. These calculations also allowed the determination of zero-point vibrational energies (ZPVE). We note that both optimization and frequency calculations were performed under different conditions: (i) in the gas phase, in order to compare the geometry with the experimental X-ray structure as well as for computing the nucleus-independent chemical shifts (NICS, see below); (ii) with the use of an implicit solvation model (see below), for computing the NMR (chloroform) and optical spectra (dichloromethane for SubP and BzSubP, chloroform for SubPz and benzene for SubPc) that were experimentally obtained in solution. Environmental effects have been accounted for by using the PCM approach,53 as implemented in Gaussian09.57 All calculations have been performed with the linear-response (LR) PCM model.58,59 We have also addtionally determined 4307


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Figure 1. Top (top) and side (bottom) views of the optimized structure of the subporphyrinoids studied herein. For the sake of clarity, the hydrogen atoms have been omitted for the side views.

the total and transition energies using the corrected LR (cLR)60 scheme and, as detailed in the Supporting Information, these calculations indicated that the LR model is the most suited for computing the excitation energies of subporphyrinoids. This is consistent with the work of Fukuda and Ehara on porphyrins.61 While we applied the equilibrium PCM limit during geometry optimizations, vibrational calculations and NMR spectra (slow phenomena), the absorption and fluorescence wavelengths as well as the AFCP energies are corrected for nonequilibrium effects (fast phenomena). The interested reader can find extra details about our approach to evaluate the AFCP energies elsewhere.62 The geometry optimizations, vibrational calculations and transition energy calculations have been performed with the PBE063 exchange-correlation functional in association with two atomic basis sets, following the general computational framework that has been proposed in ref 62. In more detail, we determined the geometrical and vibrational parameters with 631G(d) whereas the orbital energy levels, total and transition energies are corrected with a more extended atomic basis set, namely 6-311+G(2d,p). We have assessed the effect of the functional on the transition energies using PBE0 and M06-2X (that present an amount of exact exchange of 25% and 54%, respectively) which are both known for being efficient for ES.62,64−66 Comparisons given in the Supporting Information show that PBE0 yields a smaller average deviation with respect to experiments than M06-2X, a trend that was expected for valence π → π* excited-states.64 We have also used the ADC(2) approach (gas phase) to provide theoretical estimates of transition energies that are independent of the selected functional. We have first determined the ADC(2) total and transition energies with the aug-cc-pVDZ atomic basis on the (TD-)DFT geometries. Next, we have optimized the GS and ES at the ADC(2)/TZVPP level and determined “full” ADC(2) adiabatic energies through single-point ADC(2)/aug-cc-pVDZ on these geometries. These ADC(2) calculations were performed using the Turbomole code.67 These ADC(2) calculations relied on the so-called ADC(2)-s formalism68 and used the resolution of identity (RI) technique.69,70 Vibrationally resolved spectra have been obtained using the FCclasses program.71 The Franck−Condon (FC) approximation has been employed as we considered dipole-allowed ES ( f > 0.1).72,73 The reported spectra have been simulated by using convoluting Gaussian functions having a half width at halfmaximum (HWHM) that has been selected to allow accurate comparisons with experimental results (values specified in the captions). A maximum number of 25 overtones for each mode and 20 combination bands on each pair of modes were included in the calculation. The number of integrals to be

computed for each class was set to allow full convergence of the FC factor (≥0.9). The aromaticity was quantified through calculations of the NICS74 for the different rings of the macrocycle (see Figure 2, parts a and b). We performed this analysis at the B3LYP/6311+G(d,p) level of theory (in gas phase) following the reference protocol of ref 74. The NICS(0)/NICS(1) of the porphyrin, benzoporphyrine, porphyrazine, and phthalocyanine have been computed following at the same level of theory for comparison purposes. The NMR signals of the nuclei, as well as of the tetramethylsilane (TMS) reference for carbon and hydrogen atoms and BF3·OEt2 reference for the boron atom, were computed at the PCM-B3LYP/cc-pVTZ level of theory in chloroform.

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RESULTS AND DISCUSSION In this section, we first present and compare the structural parameters and the aromaticity of the four subporphyrinoids. Table 1. Mean Absolute Deviation (MAD) between Theoretical (th.) and Experimental (exp.) Bond Lengths and Bowl-Depth from Planes α (BDα) or β (BDβ) Given in Åa BDα SubP BzSubP SubPz SubPc

BDβ

MAD

exp.

th.

exp.

th.

 0.008 0.006 0.008

 1.41 1.76 1.51

1.47 1.33 1.77 1.54

 2.33  2.47

 2.13  2.58

a

The planes are defined in Figure 2a, whereas selected structural parameters are given in Table S-2 in the Supporting Information. The experimental data are taken from X-ray structures given in refs 15, 75, and 76 for BzSubP, SubPz and SubPc, respectively.

Next, we investigate the absorption and emission properties of these compounds, in an effort to reproduce and understand the origin of the shape of the experimental spectra. Finally, we focus on the SubP molecule, for which we investigated a series of substituents that were used experimentally before designing new compounds. Structure and Aromaticity. All optimized structures present a Cs point group symmetry with a bowl-shape geometry (see Figure 1). For the records, we failed to optimize the structures in C3 point group, as the optimization led back to the Cs symmetry. One can quantify the curvature of the macrocycle, namely the “bowl-depth” (BD), by computing the distance between the central boron atom and the plane defined by the 4308


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Figure 2. NICS centers (A, B, C) in the subporphyrinoids (a) and in reference compounds (b). The planes (α and β) are also defined in part a. The delocalization path of the 14 π electron is showed in bold. X corresponds to a methoxy group (SubP), a hydroxy group (BzSubP and SubPz), or a chlorine atom (SubPc).

Table 2. NICS Values (ppm) Computed at the Centers of the Rings of SubP, BzSubP, SubPz, and SubPc and the Porphyrin Referencea centers

O

A1

A2

B1

B2

C1

C2

SubP BzSubP SubPz SubPc porphyrin benzoporphyrin porphyrazine phthalocyanine benzene pyrrole 2H-isoindole pyridine pyrimidine 1,2-azaborinine 1,4-azaborinine

−20.6 −19.1 −20.7 −18.7 −14.7b −11.9b −13.4b −10.9b       

−8.6 −6.9 −8.0 −5.8 −12.2 −8.0 −9.0 −4.9  −13.6 −16.2    

−8.6 −7.1 −8.3 −5.8 −2.7 0.6 0.7 3.3       

 −8.5  −8.5  −8.3  −6.7 −8.0  −6.7    

 −8.4  −8.5  −6.9  −8.2       

−15.0 −13.7 −14.0 −12.9        −6.8 −5.5 −11.3 −12.5

−14.6 −13.9 −14.1 −12.8           

a We also report the NICS values taken from ref 74 for other reference compounds, computed at the same level of theory. The numbering of the centers is given in Figures 2a and b (we took into account the Cs symmetry so that A2 = A3, B2 = B3 and C2 = C3). All the data given corresponds to NICS(0), except for the center of the macrocycles, O, that have been placed at 1 Å from the boron atom towards the interior of the bowl. bNote that the value refers to the NICS(1): alike the subporphyrinoids, the center O have been placed at 1 Å from the center of the macrocycle. The NICS(0) at the center of the porphyrin, benzoporphyrin, porphyrazine, and phthalocyanine are −13.5, −12.9, −15.0, and −12.1 ppm, respectively.

Table 3. Vertical Absorption Energies (Evert−a in eV and the Corresponding Wavelength in nm) and Oscillator Strength (f) of the First Singlet Excited States Involved in the Q and Soret Bands of SubP, BzSubP, SubPz, and SubPca SubP BzSubP SubPz SubPc

band

ES

Evert−a

λvert−a

f

Q soret Q soret Q soret Q soret

S1, S2 S4, S5 S1, S2 S3, S4 S1, S2 S7, S8 S1, S2 S10, S11

2.99 3.84 2.65 3.72 2.89 4.08 2.43 4.16

415 323 468 333 429 304 510 298

0.088 0.966 0.608 1.729 0.484 0.675 0.943 0.701

that experimental data are not available for SubP, as X-ray structures have not been determined for this exact structure. A comparison with two closely related subporphyrin derivatives, for which the crystallographic structures have been resolved, is given in the Supporting Information. It turns out that theory reproduces very accurately the experimental bond lengths, with a MAD smaller than 0.01 Å for all structures. This is a particularly remarkable result given the fact that our calculations are performed in gas phase whereas the experimental structures are determined in the solid state. For the BDs, one could expect stronger solid-state effects, but our gas-phase values are nevertheless fitting experimental values within 0.1 Å, and one does not notice systematic underestimation or overestimation of the measured BDs by theory. For this parameter, the following trends are observed: (i) the curvature is more pronounced when imine groups are used to bridge the pyrrolic/isoindole units instead of methine moieties, and (ii) the BDα is larger in SubP and SubPz than in their phenyl-fused counterparts. Another notable feature of these non planar structures is the delocalization of 14 π electrons on the conjugated path, giving an aromatic character to the molecules consistently with Hückel’s 4n + 2 rule. To estimate the aromaticity in organic systems, it is common to measure or calculate the NMR

a

Complete data can be found in Table S-4 in the Supporting Information.

six external carbon atom (plane α for SubP and SubPz and plane β for BzSubP and SubPc, see Figure 2a). In Table 1, we report the mean absolute deviation (MAD) between the theoretical and experimental (X-ray) bond lengths for the different macrocycles as well as the curvature of the compounds. Selected bond lengths and valence angles can be found in Table S-2 in the Supporting Information. We note 4309


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Figure 3. Density difference plots (isovalue = 0.0008 au) corresponding to the absorption of light of the first excited-states reported in Table 3 involved in the Q (top) and Soret (bottom) bands of subporphyrinoid systems. Red (blue) regions indicate a gain (loss) of electronic density upon photon absorption.

Table 4. Comparison between the Experimental (exp.) and Theoretical (th.) AFCP (EAFCP) Obtained with the PBE0, the Hybrid ADC(2)-PBE0, and the ADC(2) Methods Given in eV (E) and nm (λ) exp. SubP BzSubP SubPz SubPc a

PBE0

ADC(2)a

ADC(2)-PBE0

EAFCP exp.

λAFCP exp.

ref

EAFCP th.

ΔEth/exp

λAFCP th.

EAFCP th.

ΔEth/exp

λAFCP th.

EAFCP th.

ΔEth/exp

λAFCP th.

2.68 2.40 2.46 2.18

463 517 504 569

32 15 79 80

2.79 2.42 2.61 2.26

0.11 0.01 0.15 0.08

444 512 475 549

2.78 2.52 2.72 2.43

0.10 0.12 0.26 0.25

446 492 456 510

2.74 2.49 2.63 2.40

0.06 0.09 0.17 0.22

453 497 471 517

ADC(2) gas-phase adiabatic energies corrected for solvent and ZPVE effects through TD-DFT calculations.

Figure 4. Comparison between computed (stick and full lines) vibrationally resolved absorption (red) and emission (blue) spectra of BzSubP and the corresponding measured spectra (broken lines) in dichloromethane. A HWHM of 0.030 eV was used to convolute the theoretical stick spectrum. The experimental spectra are adapted from ref 15 with permission. Copyright 2006 Wiley Online Library.

Figure 5. Comparison between computed (stick and full lines) vibrationally resolved absorption (red) and emission (blue) spectra of SubPc and the corresponding measured spectra (broken lines) in dichloromethane. A HWHM of 0.035 eV was used to convolute the theoretical stick spectrum. The experimental spectra are adapted from ref 80. Copyright 1998 American Chemical Society.

chemical shifts of different nuclei. To provide insights into aromaticity of these peculiar systems, one can also compute the NICS at the center of all cycles (see Figure 2b for the conventions used here). As NICS can only be obtained with theoretical approaches, we first compare the experimental and theoretical chemical shifts of the nuclei so to ascertain the quality of our magnetic shieldings. This NMR analysis can be found in Table S-3 in the Supporting Information and one can conclude that DFT provides accurate chemical shifts and reproduces the experimental trends with a good accuracy. In

Table 2, we report the NICS values obtained for the subporphyrinoids as well as for a series of reference compounds, modeled at the same level of theory. First, we observe that all NICS data of subporphyrinoids are negative, indicating that the rings forming the macrocycle as well as the macrocycle itself present aromatic characters. Interestingly, these subporphyrinoid compounds present a high aromatic character with a NICS(1) value at the O center that attains ca. −20 ppm, a value that is larger than in reference porphyrinoids. This latter observation is in line with previous investiga4310


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The Journal of Physical Chemistry A Table 5. Transition Energies and Wavelengths for the Compounds Represented in Scheme 3a experiment b

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

theory

experiment

solvent

ΔE

λ

ref

ΔE

λ

DCM DCM DCM DCM DCM CHCl3 CHCl3 DCM DCM DCM DCM DCM CHCl3 DCM DCM DCM DCM DCM DCM CHCl3 DCM

2.68 2.63 2.46 2.62 2.56 2.70 2.58 2.53 2.51 2.48 2.50 2.55 2.58 2.53 2.43 2.54 2.35 2.52 2.70 2.50 2.51

463 471 504 473 484 459 481 490 494 500 496 486 481 490 510 488 528 492 459 496 494

32 83 85 87 82 89 89 82 86 86 90 82 89 82 91 91 86 82 91 89 82

2.99 2.91 2.29 2.94 2.74 2.77 2.77 2.70 2.67 2.57 2.65 2.72 2.75 2.69 2.51 2.71 2.36 2.53 2.72 2.63 2.67

415 426 541 422 452 448 448 459 464 482 468 456 451 461 494 458 525 490 456 471 464

22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

theory

solvent

ΔE

λ

ref

ΔE

λ

DCM DCM DCM DCM DCM DCM DCM DCM DCM DCM DCM DCM DCM DCM DCM DCM DCM DCM DCM DCM

2.73 2.64 2.38 2.32 2.38 2.23 2.35 2.23

454 470 521 534 521 556 528 556

82 84 86 83 88 86 83 86

2.85 2.84 2.48 2.40 2.43 2.17 2.44 2.02 2.26 2.08 1.97 2.16 2.18 2.10 1.99 2.29 1.84 2.01 1.79 1.88

435 437 500 517 510 571 508 614 549 596 629 574 569 590 623 541 674 617 693 659

The experimental values (when available) correspond to the λmax, whereas the theoretical values are the LR-PCM TD-PBE0 vertical estimates. All values are given in eV (energies) and nm (wavelengths). b1 = SubP a

SubP by a carbocation, one obtains NICS values of −21.4, −11.9, and −16.0 ppm for positions O, A, and C, very similar to the values reported in Table 2, so that the presence of a formal positive charge is indeed explaining the large aromatic NICS response. The values obtained for the external phenyl rings in the largest systems are similar to those of benzene. In short, this analysis highlights the impact of the central boron atom that plays a role similar to the one of a carbocation in the magnetic properties of subporphyrinoids. Optical Properties. In this section, the nature of the electronic transitions of SubP, BzSubP, SubPz, and SubPc are first described before turning toward the impact of vibrational contributions on the topology of the absorption and emission bands. In Table 3, we report the energies and oscillator strengths of the electronic transition associated with the Q and Soret bands of the four subporphyrinoids. The symmetry of all the excitedstates as well as the molecular orbital (MO) contributions of each transition, and additional details, can be found in Table S4 in the Supporting Information. One can see that each transition is arising from two nearly degenerated A′ and A″ excited-states due to the quasi-C3 symmetry of these systems. The density difference plots corresponding to both Q and Soret absorption bands are displayed in Figure 3. We note that these plots correspond to the mean density of the two excited-states involved in the Q or Soret bands and the ground-state density, to account for the near-degeneracy. As expected, the plots show a highly symmetric density variation and we observe that these excitations can be characterized as π → π* transitions, without density variation on the central boron atom nor on the side alkyl chains, though in SubPz a small blue region is observed on the methyl groups at α positions. For the Q-bands, one observes that the excitation is mainly centered on the core of the subporphyrinoids, as much smaller density variations are observed on the side phenyl rings. In the central macrocycle,

tions,41,77 and can be partly attributed to the specific bowlshape of these compounds that contrasts with the planarity of most porphyrionoids. The impact of curvature on the aromaticity has been recently studied in details by Casabianca.78 In that work, it was stated that when the curvature increases, the increasing distortion from planarity, that should be detrimental for aromaticity, is expected to decrease the NICS on both convex and concave sides. However, the reverse is found because “since a nucleus placed near [the concave] face now feels ring current ef fects not only f rom the central aromatic ring, but also stronger ring currents f rom the outer aromatic rings”.78 In any case, one cannot observe a direct structure-aromaticity correlation, i.e., the BDx distances are not strongly correlated with the NICS values at the center of the compounds. Alike their tetrapyrrolic analogues, the absolute NICS values are slightly larger in the smaller SubP and SubPz compounds than in their π-extended counterparts. When replacing the methine bridge with an imine one, no impact on the NICS at the O center can be detected for the smallest systems whereas one finds a slight decrease from BzSubP to SubPc following the trends of ”standard” porphyrinoids systems. The NICS at the center of all the pyrrolic units A are quasi-equivalent in the subporphyrinoid series. The absolute value decreases in the SubP to SubPz, BzSubP and SubPc series but the A1 and A2 cycles still present an aromatic character contrasting to porphyrinoid compounds in which the A2 cycles become non aromatic or antiaromatic when going from the porphyrin to its aza and/or phenyl-fused analogues. The same trends are found for the six-membered cycles C, that possess a strong aromatic character, attributed to the presence of an electron deficient boron atom. Indeed, when going from pyridine to pyrimidine, i.e., when inserting an extra nitrogen atom in the six-membered ring, the NICS decreases whereas a significant increase is observed when going to azaborine, i.e., when inserting a boron atom into pyridine. In fact, if one replaces the boron atom in 4311


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Scheme 3. Structures of the Meso-Substituted Subporporphyrin (SubP) That Have Been Experimentally Characterized (in Black) or Newly Designed (in Blue)a

a

Note that X = OMe except in 6, 7, 13, and 20 for which X = OH.

Figure 6. Density difference plots for four selected compounds. See caption of Figure 3 for more details.

there is an alternation of atoms gaining and loosing electron density after absorption in the Q region. Indeed, in all systems, the nitrogen atoms of the pyrrolic units as well as the atoms at the meso position gain electronic density upon absorption of light (mostly in red in Figure 3) while the carbon atoms at α positions loose electronic density (mostly in blue in the same figure). The density difference plots of the Soret bands show more delocalized electronic reorganization, but with qualitative differences between the different compounds. In SubP the

excitation is mainly involving the pyrrolic rings with small changes on the methine bridges. In BzSubP, the bridging nitrogen atoms act as donor, whereas the double bonds of the five-membered rings gain density (acceptors). In contrast, for the two latter dyes, namely, SubPz and SubPc, one notices a charge-transfer (CT) from the periphery (mostly in blue) toward the central macrocycle (mostly in red). For the sake of completeness, let us now briefly discuss the evolution of the MO energy levels of these systems and their 4312


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emission. This success holds also for the molar absorptivity coefficient (ϵ) that is calculated to be 1.1 × 105 M−1·cm−1 with TD-DFT, in very good agreement with the experimental value of 9 × 104 M−1·cm−1, giving confidence in the vibronic analysis. Theory indicates that the shoulder appearing at ca. 500 nm in the absorption spectra is mainly arising from one vibrational mode of the ES (#47 at 736 cm−1), which is a symmetric breathing mode involving the three central six-member cycles (see the Supporting Information for movie and representation). In contrast, the second maximum at ca. 475 nm can be mainly ascribed to three vibrations (#100, #105 and #116) taking place at 1406, 1459, and 1573 cm−1, respectively, and they all imply significant changes in the single/double bond pattern of the macrocycle (see the Supporting Information). In the emission spectrum, the shoulder at ca. 535 nm mainly arises from two vibrational modes of the GS (#27 at 510 cm−1 and #46 at 750 cm−1), whereas the maxima at 565 nm combines three modes similarly to the absorption (#100, #104, and #115 at 1418, 1469, and 1572 cm−1, respectively). Unsurprisingly given the near-mirror shape nature of the absorption and fluorescence spectra, these GS modes are similar to the ES vibrations that are responsible for the specific band shape of the absorption (see the Supporting Information). For SubPc, Figure 5 indicates a less impressive match between theory and experiment, than for BzSubP, but the major trends are still well-reproduced by TD-DFT. We underline again that the computed ϵ (7.2 × 104 M−1.cm−1) matches very well the measurements (7.0 × 104 M−1.cm−1). The first shoulder in the absorption band occurring at ca. 550 nm is mainly due to two ES vibrations (#27 and #43 at 484 and 734 cm−1, respectively) whereas the second shoulder at ca. 510 nm is mainly arising from two higher-energy vibrations (#92 and #106 at 1415 and 1535 cm−1, respectively), that is, this second shoulder is not due to a double excitation of the vibrations involved in the first. These modes are displayed in the Supporting Information. Interestingly, mode #43 at 734 cm−1 is also a breathing mode of the central core as in BzSubP, but is asymmetric, which contrasts with this previous case. Modes #92 and #106 involve strong deformation of one external phenyl ring and two internal five-member rings, respectively. Concerning the emission, the shoulder at ca. 575 nm is related to four GS vibrations (#26, #39, #40, and #43 at 513, 657, 721, and 745 cm−1, respectively) whereas the shoulder at ca. 600 nm mainly arises from two vibronic transitions involving GS vibrations (#92 and #104 at 1398 and 1531 cm−1, respectively). Auxochromic Effects for SubP. In Table 5, we present a comparison between vertical theoretically estimated and experimentally measured transition energies for the 28 mesosubstituted SubP represented in Scheme 3. We considered exactly the same structures as in the experiments but for the alkyl chains that were replaced by methyl groups in order to save computational time. Indeed, these alkyl chains are not expected to play a significant role in the optical properties. We recall that such comparison should be viewed as qualitative, as vertical TD-DFT estimates do not correspond to λmax. Nevertheless, as we consider here a homologous series of dyes, one can reasonably expect that vibronic effects are rather similar for all compounds, so that the auxochromic effects can be nicely captured by the vertical estimates. Indeed, for the compounds of Table 5, we found a linear correlation coefficient between theory and experiment, R, of 0.92 and a relatively small mean absolute deviation (0.14 eV). As we will see below, some

contribution in the excitations. The topology and energy of the frontier MO involved in the two first electronic transitions (Q bands) are given in Figure S-1 in the Supporting Information. One first observes that the LUMOs are all nearly degenerated and are stabilized by ca. 0.3 eV (0.6 eV) when extending the πconjugation path (when going from methine to imine bridges). There is also a stabilization of the HOMO when replacing the carbon atoms with nitrogen atoms in the bridges, but, in contrast, the HOMO are destabilized when adding extra phenyl rings to SubP or SubPz. The HOMO−LUMO gap is therefore decreasing when going from SubP to SubPz, BzSubP, and SubPc in line with the observed red-shifts of the Q bands. The topologies and energies of the HOMO−1 to HOMO−6 for the four subporphyrinoids can be found in Figure S-2 in the Supporting Information. These MOs are involved in the Soret band, as can be seen in Table S-4. In Figure S-2, one notices some inversions in the energy levels of the different macrocycles, e.g., the topology of the HOMO−1 in SubP and BzSubP corresponds to HOMO−4 and HOMO−6 in SubPz and SubPc, respectively. This in turn, explains the different MO contributions in the TD-DFT transitions listed in Table S-4. While the analysis provided above does allow to unravel the nature of the different excited-states, it does not permit physically well-grounded comparisons with experiments. Indeed, to reach such comparisons, one needs to determine 0−0 energies, that correspond to the AFCP in solution, and band shapes, and we consider these two properties below. First, for the AFCP, we compare in Table 4 the values obtained with TD-PBE0, with a mixed approach in which the transition energies have been determined with ADC(2) on DFT/TDDFT structures, and with the “full” ADC(2) method. More detailed comparisons of the results obtained with these approaches can be found in ref 81. One observes that while TD-PBE0 slightly overestimates the experimental energies, it provides a very good agreement with a MAE of 0.09 eV, a small error for this approach,62 confirming that PBE0 is adequate for our purposes. Using ADC(2) to correct the TD-DFT estimates does not improve the accuracy as the MAE actually increases to reach 0.18 eV. This error remains in line with expectations, i.e., the MAE obtained for a large set of organic compounds with the ADC(2)-DFT approach was 0.14 eV.81 Optimizing the structures at the ADC(2) level does improve slightly the estimates compared to the hybrid approach, though the average error (0.14 eV) still exceeds its TD-PBE0 counterpart. Besides, the ADC(2) calculations provide rationales for the success of TD-DFT for the present molecules. Indeed, we notice that, on the one hand, the MP2 D1 diagnostic returns a value smaller than the warning level for significant multireference character [D1(MP2) ≤ 0.04] for all four subporphyrinoid systems, and, on the other hand, the ADC(2) calculations confirm that single excitation contributions are strongly dominating the electronic transitions (percentage exceeding 90% in all cases). Vibrationally Resolved Spectra. We have determined for the first time the vibrationally resolved spectra of two subporphyrinoids presenting nontrivial band shapes, namely BzSubP and SubPc. A comparison between the experimental and theoretical absorption and emission spectra can be found in Figures 4 and 5 for BzSubP and SubPc, respectively. For the former compound, one clearly finds an excellent match between the experimental and theoretical band shapes, TDDFT reproducing the position and relative intensities of the shoulder and the second maximum for both absorption and 4313


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The Journal of Physical Chemistry A systems present a significant CT character and hence PBE0 might be unsuited. For this reason, we provide in Table S-5 in the Supporting Information the same information as in Table 5 but determined with the M06-2X level of theory. This functional however yields a smaller R (0.91) and a larger average absolute deviation (0.26 eV) than PBE0. To rationalize the trends of Table 5, we provide in Figure 6 representations of the ES of selected compounds. For 10, one notices a rather moderate delocalization on the peripheral πconjugated segments, explaining the moderate (−0.20 eV experimentally) bathochromic shift compared to SubP. Let us also note that the ethynyl segments appear in blue, that is, they play the role of donor groups here, the pyrrolic units of the core playing the role of acceptors. If more conjugated segments are used, as the bithienyl groups, in 27, a stronger bathochromic effect is reached (−0.45 eV) as the excited-state becomes more delocalized. Logically, the same trend is found in 17 where the donor dialkylamino groups allow increasing the charge-transfer toward the core, leading to a stronger redshift (−0.33 eV) than in 10. In these two cases, it is noteworthy that PBE0 overestimates the bathochromic displacement significantly (Table 5) as expected, whereas M06-2X delivers more accurate auxochromic shifts (see Table S-5 in the Supporting Information). Using external electron-withdrawing groups as in 18, allows one to revert the charge-transfer direction (from the core to the periphery), but is less effective to induce redshifts, as the role played by the central pyrrolic centers becomes negligible. Eventually, we have designed 12 new compounds (30−41 in Table 5) in an effort to more strongly redshift the absorption bands. As can be seen, the results obtained confirm that using strong electron-withdrawing groups at the periphery does not constitute the most effective strategy to reach that goal. Indeed, according to our calculations 34 and 35 should present similar absorption maxima, though the strength of the (accepting) groups added in the latter dye is much higher than in the former (donating) compound. Actually, by combining increasingly long thienyl segments to additional donor groups (36, 38, and 40), one can significantly displace the absorption maximum to the red, as low as ca. 1.8 eV (690 nm), which would be an excellent performance for a rather compact chromophore. We note that M06-2X (Table S-5) yields the same conclusions, i.e., that 36, 38, and 40 present the most red-shifted absorption band, though, as expected M06-2X deliver larger transition energies. It is also noteworthy that the oscillator strengths of these transitions are large, i.e., 1.24, 2.08, and 2.86 for 36, 38, and 40, respectively (PBE0 values, the M06-2X oscillator strengths are similar), all larger than in the parent 1.

topologies obtained through vibronic calculations are also strongly ressembling their experimental counterparts. We have showed that all four macrocyclic entities are strongly aromatic due to their bowl topology and their formal carbocationic nature, which induces, on the internal (concave) side a high density of π electrons, so that the determined NICS(1) are on the order of −20 ppm for all structures. The analysis of the density reorganization upon photon absorption revealed that the Q-bands involve changes mainly localized in the center of the subporphyrinoids, the nitrogen atoms of the pyrrolic units and the atoms at the meso position gaining electronic density, the α carbon atoms losing density. The Soret band involves more delocalized excited-states. For BzSubP and SubPc, the analysis of the vibrational modes mainly responsible for the presence of shoulders/maxima in the recorded absorption and emission bands indicated that two families of modes play a key role: the first at 500−750 cm−1 accounting for the shoulder at ca. 15 nm from the 0−0 band, the second at 1400−1500 cm−1 being responsible for the presence of a secondary maximum (BzSubP) or the enlargement of the band (SubPc). Finally, we investigated a large series of subporphyrins substituted at their meso positions, first to demonstrate that vertical TD-DFT can reproduce the experimental auxochromic effects, second, to design several compounds with strongly red-shifted optical bands. Indeed, by adding donor-substituted thienyl side chains, one can increase the periphery to core charge-transfer character of the lowest transition and hence move the absorption band to the red. It is our hope that this will stimulate further experimental studies in the field.

CONCLUSIONS We have investigated the structural, magnetic, and optical properties of the four subporphyrinoids: subporphyrin, subporphyrazine, tribenzosubporphyrin and subphthalocyanine, using a theoretical approach based on PCM-TD-DFT. From the methodological point of view, we have showed that neither the use of ADC(2) energy correction nor the application of state-specific corrections for solvent effects improves the accuracy of the estimates obtained with the LR-PCM approach combined to the TD-PBE0 scheme. This level of theory is indeed able to reproduce the structure, NMR and optical spectra of all compounds. In particular, the 0−0 energies were determined and were shown to match experiment with a mean absolute deviation smaller than 0.1 eV, whereas the band

ORCID

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b03644. Benchmark of the vertical absorption energies, additional structural parameters and NMR analysis, nature of the electronic transitions, topology and energy of the molecular orbitals, key vibrational modes involved in the vibronic couplings, and equivalent of Table 5 obtained with M06-2X (PDF) Movies showing molecurlar motion (ZIP)

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AUTHOR INFORMATION

Corresponding Author

*(D.J.) E-mail: [email protected]. Telephone: +33 (0) 2 51 12 55 67.

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Denis Jacquemin: 0000-0002-4217-0708 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS C.A. acknowledges the support of the Agence Nationale de La Recherche (ANR-EMA grant) for her Ph.D. grant. D.J. is indebted to Dr. P. Giraudeau for his kind and rapid technical help. The authors thank the Région des Pays de la Loire for the LUMOMAT RFI project. This research used resources of the GENCI-CINES/IDRIS, of the CCIPL (Centre de Calcul Intensif des Pays de Loire), and of a local Troy cluster. 4314


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