Tuning the Photophysical Properties of Pyrene-Based Systems: A

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Tuning the Photophysical Properties of Pyrene-Based Systems: A Theoretical Study Massimo Ottonelli,* Matteo Piccardo, Daniele Duce, Sergio Thea, and Giovanna Dellepiane INSTM and Dipartimento di Chimica e Chimica Industriale, Universita di Genova, Via Dodecaneso 31, I-16146 Genova, Italy

bS Supporting Information ABSTRACT: Recently new molecular systems based on the pyrene moiety were developed for photovoltaic applications. Here we present the results of a quantum chemical study focused on the effects induced by some different substituents on the electronic properties of pyrene, to obtain general hints for the molecular design of new pyrene-based systems. In particular, a series of electron-donating (hydroxy, amino, acetylamino) and electron-withdrawing (cyano, carbamoyl, formyl, ethynyl, ethenyl) groups were considered. Furthermore, in addition to the single pyrene molecule, two pyrene units linked by ethenylene, ethynylene, 2,5-thienylene, and ethynylene-pphenylene containing chains of different lengths were taken into account. For all of the model structures presented, the ground state geometries have been optimized using the density functional approach, while the vertical transition energies were calculated using the time-dependent density functional theory. We will show that the tuning of the lowest electronic excitation energy (i.e., the HOMOLUMO energy gap) as well as the localization of the spatial distributions of the frontier molecular orbitals (i.e., the nature of the electronhole pair, generated by photon absorption) can be obtained through the analysis of the pyrene frontier molecular orbitals. This approach allows to evaluate the most suitable position of the substituents on the pyrene moiety giving rise to enhanced electronic effects also in function of their electronic nature. In this way, pyrene-structures with tailored electronic properties could be modeled. Our screening shows that promising candidates for photovoltaic applications could be molecular structures formed by two pyrene units joined/linked by a short conjugated bridge containing double or triple bonds (henceforth pyrene-linked dimers). As far as the single pyrene units are considered, the most significant reduction of the transition energy of the lowest optical electronic excitation is obtained with disubstituted pyrenes with pushpull character.

1. INTRODUCTION In recent years, π-conjugated systems have been object of an increasing interest due to their electronic properties that have led to the development of a new electronics branch known as organic electronics.14 In fact, these molecules have proved to be a suitable class of materials for advanced electronic and photonic applications such as in organic light-emitting devices (OLEDs),58 optical storage devices,911 sensors,1214 hole transporting,1518 and last but not least, solar cells.1923 Each application requires that the organic systems used as active materials, to have specific electronic properties. In hole-transporting processes the molecules must have a small reorganization energy and high transfer integral to maximize the electron transfer rate. In OLED applications, instead, the π-conjugated systems must have efficient emission in the visible region. This requirement implies that the electronhole pair generations, after the charge injection, must be favored since the first step of the emission process takes place through the formations of a charge transfer or an exciton state. Consequently, to enhance the recombination of the injected free charges, molecular systems with strong-bonded electronhole pairs are needed. On the other hand, the organic dyes to be used as active materials for solar cell applications must have significant absorption cross sections in the visible region, r 2011 American Chemical Society

and this implies that the electronhole pair generated by the photon absorption must be weakly bonded, to increase the generation of free charges and consequently the photocurrent. To optimize the device performance, it is therefore necessary to develop new molecules or “engineer” old ones with electronic properties tailored in function of their applications. The pyrene molecule has a strong absorption cross section, excellent emission properties, and a long excited state lifetime. In fact its first excited state has, in nonpolar media, a lifetime of about 650 ns24 which ensures the possibility of electronhole pair dissociation. These properties make the pyrene a potential candidate for OLED (emission) or solar cell (absorption cross section) applications. However, it is well-known that this molecule can easily form excimers or π-aggregates that significantly reduce its quantum yield efficiency and consequently OLED performance. Furthermore, its use for photovoltaic applications was limited because the electronic absorption spectrum of pyrene lies in the UV region; consequently only a small fraction of the solar radiation could be converted into photocurrent. Received: September 2, 2011 Revised: November 21, 2011 Published: November 21, 2011 611

dx.doi.org/10.1021/jp2084764 | J. Phys. Chem. A 2012, 116, 611–630

The Journal of Physical Chemistry A

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Scheme 1. Simplified Representation of the Hybrid System

Nevertheless, as recently shown in the literature, these shortcomings of the pyrene moiety could be overcome through the development of new pyrene derivatives, where active materials based on this molecule were synthesized for OLED (as blueemitting dye)2531 and for solar cell3235 applications. The design of these new structures needs accurate knowledge of the effects induced by the substituents on the electronic properties of the pyrene moiety. Quantum chemical studies3645 can give a powerful test bench for an a priori correlation between the structural and electronic properties, thus helping to address the synthesis of new molecules for photovoltaic applications. In this field, the investigation of new hybrid systems based on organic dyes and noble metal (Ag, Au) or semiconductor (TiO2) nanoparticles, seen in Scheme 1, can be of particular interest. The possible synergic interactions between the organic and the inorganic subsystems could create peculiar electronic properties of the supramolecular structure.46 By using pyrene as a chromophore and by tuning its photophysical properties, molecules with an appreciable absorption cross section in the visible spectral region combined with efficient photoinduced charge separations able to enhance the charge transfer between the nanoparticle and the dye can be designed. In this work, we present a systematic quantum chemical study carried out for obtaining a general correlation between the electronic and the structural properties of pyrene derivatives that will allow to select the best potential dyes for the hybrid systems. In particular, two classes of pyrene molecules have been taken into account; the first one being composed by a single pyrene molecule, bearing one or two electron-donating (-withdrawing) groups, the second one being formed by two pyrene units linked through conjugated bridges (pyrene dimers). More specifically, we have used the hydroxyl (OH), amino (NH2), and acetylamino (NHCOCH3) groups as representative electron-donating systems, the cyano (CN), carbamoyl (CONH2), ethynyl (CtCH), ethenyl (CHdCH2), and formyl (CHO) functions as representative electron-withdrawing groups, and oligomers of thiophene, ethene, ethyne, and 1,4-phenyleneethyne as representative conjugated bridges. The geometries of all of the model systems were fully optimized by using the density functional theory (DFT) with the three-parameter hybrid exchange-correlation functional, B3LYP, proposed by Becke47,48 that is known to yield good results in structure predictions.49 The excitation energies and corresponding oscillator strengths were calculated by using the time-dependent DFT (TD-DFT) approach that gives reasonable predictions of the excitation energies with low computational cost and satisfactory accuracy.50 The aforesaid calculations were performed by using the 6-31G* basis set as implemented in the Gaussian 0351 and 9852 software on the Compaq DS20E Alpha Station available in our laboratory. We will show that the analysis of the pyrene molecular orbitals combined with that of the electronic nature of the substituents could allow the selection of

Figure 1. Molecular structure of 10-(1-pyrenylmethylamino)-10oxodecanoic acid.

Figure 2. Experimental (in CHCl3 solvent, continuous line) and theoretical (dotdashed line) normalized absorption spectra of Pyd1. The theoretical spectrum was obtained from the B3LYP/6-31G*//TDB3LYP/6-31G* calculations (only the electronic part was taken into account).

the most suitable substituent positions on the pyrene molecule to obtain a red-shift of its UVVis absorption spectrum. This implies a reduction of the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), since generally the lowest optical transition is dominated by the monoexcitation which involves these orbitals. As a useful outcome of this study, the design of photogenerated electronhole pairs with charge transfer character is also possible.

2. RESULTS AND DISCUSSION 2.1. Reference Structure and Unsubstituted Pyrene. According to the sketch shown in Scheme 1, the reference structure of our dye library is the 10-(1-pyrenylmethylamino)-10-oxodecanoic acid (Pyd1), as in Figure 1, where an alkyl tail of about 812 carbon atoms bearing a terminal carboxyl group as an anchor site for binding to the nanoparticle is added to the chromophore (i.e., the pyrene moiety). The choice of introducing this tail is due to the need of providing a conformational freedom degree sufficient to allow an efficient interaction between the dye and the nanoparticle during the charge-transfer process. The importance of the “reorganization” of the organic systems on the nanoparticle was also outlined in a recent paper 612

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Table 1. TD-B3LYP/6-31G* Excitation Energy, Oscillator Strength, and Monoexcitation Contribution to the Excited State (With Weights g5%) for the First Two Allowed Electronic Transitions of Pyd1 and Py Pyd1 λ (osc. strength) 341 nm (0.339)

Py λ (osc. strength)

single-excitation (weight) HOMO f LUMO (37%)

333 nm (0.256)

HOMO-1 f LUMO+1 (6%) 271 nm (0.223)

single-excitation (weight) HOMO f LUMO (37%) HOMO-1 f LUMO+1 (6%)

HOMO f LUMO+1 (14%) HOMO-1 f LUMO (15%)

266 nm (0.268)

HOMO f LUMO+1 (18%) HOMO-1 f LUMO (19%)

HOMO-3 f LUMO (7%)

where the interactions between the pyrene chromophores and the gold nanoparticle53 have been studied. The optimized B3LYP/6-31G* geometry of Pyd1 used for the TD-B3LYP/6-31G* calculations is shown in Figure S1 of the Supporting Information, while in Figure 2 the experimental and calculated UVVis absorption spectra are depicted. In the theoretical modelization, vibronic effects are not taken into account. The comparison between the experimental results and the TD-B3LYP simulations gives a further indication of the good performance of the TD-DFT approach in predicting the absorption spectra. In fact, the experimental peaks lying at 277 and 342 nm are predicted at 271 and 341 nm, respectively (i.e., only 6 and 1 nm blue-shifted with respect to the experimental values). Apparently, only a less satisfactory reproduction of the peak intensity is observed. In fact, the intensity ratio, r, between the first and the second optical electronic transitions is 0.99 and 1.67 from experiment and from theory, respectively. On the other hand, if we take into account that the oscillator strength of the lowest absorption peak is distributed on the entire vibronic bands, the experimental corrected value of r becomes 1.80, in good agreement with the quantum chemical result. Finally, due to the presence of a methylene spacer between the amide and the pyrene moieties, the experimental UVVis absorption spectrum of Pyd1 is virtually the same as that of pyrene (Py). In fact, the absorption spectrum of Py is characterized by three electronic bands at 239 nm (the most intense), 272 nm, and 335 nm, respectively.54 In the comparison, the first band cannot be taken into account since the spectrum of Pyd1 was not recorded below 270 nm. The intensity ratio r, of the other two peaks, is equal to 1.7. The experimental spectra of Pyd1 and Py are very close also in shape; that is, they both have the vibronic structure typical of the polycyclic aromatic molecules. The TD-B3LYP/6-31G* spectrum of Py shows three bands at 226, 266, and 333 nm, thus indicating that not only there is a good agreement with the experimental data as is in the Pyd1 case, but also that a similar behavior of Pyd1 and Py is found. In fact, for Pyd1 (Py) blueshifts of 6 (6) and 1 (2) nm of the calculated signals with respect to the experimental ones are obtained. Similarly, the shift between the experimental and the theoretical spectra of Pyd1 is very close to that of Py. Indeed, a red-shift of 5 and 7 nm for the former and a red-shift of 5 and 8 nm for the latter have been respectively found. For these reasons, in the next section we will focus our study of the substituent effects on the HOMOLUMO energy gap only on the pyrene moiety. Here we only analyze the reason for the slight red-shift observed in the Pyd1 spectrum relative to that of Py, the overall results being discussed in the next section. To do this, in Table 1 we report the contributions (with weights g5%) of the monoexcited configurations for the two lowest electronic excitations of

Figure 3. Molecular spatial distributions of some representative molecular orbitals of Pyd1 and Py with their corresponding energy (in eV).

these systems and in Figure 3 the spatial distributions of the molecular orbitals involved. From the data in Table 1, we can gather that the description of these electronic transitions implies a large number of configurations and that, however, those involving the following molecular orbitals (MO): HOMO-1, HOMO, LUMO, and LUMO+1 are the most representative and consequently we could restrict our discussion to this subspace. For example, in the lowest electronic transitions at 341 nm (Pyd1) and 333 nm (Py) the HOMOLUMO monoexcitation is the “dominant” one. In Table 1 we can see that for both absorption bands the corresponding electronic transitions have the same nature since the monoexcitation contributions are practically the same. However, from the analysis of the Pyd1 and Py molecular orbitals (Figure 3) we can note that in Pyd1, despite the methylene spacer, a small contribution from the methylcarbamoyl moiety occurs that acts as an electron drain from the π-systems of the pyrene ring. As a result, the Pyd1 MO's, and in particularly the LUMO, result in being stabilized relative 613



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concerned, the largest variation of the electronic properties should be expected when the substituent is in position 1. In particular, the order (14, 3, 1) should be the most important since the HOMOLUMO monoexcitations contribute appreciably to the nature of the lowest excite state (Table 1). For the doubly substituted pyrenes, taking into account that our objective is not only the decrease of the lowest transition energy of Py but also the increase of the associated absorption cross section, the analysis of the pyrene MOs (see details reported in note 1 of the Supporting Information) shows that if the two substituents have the same electronic nature the couple (1,13) is the best choice. On the contrary, when they have an opposite electronic nature the couple (1,8) followed by (1,13), (1,10), and (1,11) couples are the most suitable site ring candidates for substitution. A similar trend could be found for the geometry variation in function of the interaction of the substituents with the Py moiety. In this case, however, these effects should be more correctly correlated to the total electron density variation. Finally, to reduce the number of doubly substituted pyrene systems, when X = Y we have chosen as a model system the CONH2 group that should have the largest local electric dipole transition moment and averaged interaction effect with Py. For the pushpull molecule we have chosen instead X = CHO and Y= OH as substituents. Among the electron-withdrawing groups, CHO has an appreciable interaction with the conjugated π-system of pyrene (see Appendix 1) as well as an appreciable local electric dipole transition. Among electrondonating substituent the OH group exhibits averaged interaction properties. 2.2.1. Substituent Effects on the Pyrene Frontier Orbitals. The predictions on the better choice of the substitution sites, based only on the Py MO analysis, discussed in the previous section, can be checked by comparing the variations of the molecular energy levels with those of the unsubstituted Py, obtained from the B3LYP/6-31G* optimizations of the Py(X)i and Py(X)i(Y)j systems. The results are depicted in Figures 5a,b and 6 for the single electron-donating and withdrawing groups and for the pushpull systems, respectively. As expected, on the basis of previous discussions, we can see that the Py(X)i MOs appear to be destabilized, in particular the occupied ones (see Figure 5a). Instead, the HOMO-1 and HOMO energies increase following the trend predicted by the atomic MO coefficient values (see Table 2). For example, the HOMO of Py(NH2)1 and the HOMO-1 of Py(NH2)14 are, respectively, 0.67 and 0.84 eV higher in energy with respect to the corresponding Py orbitals. There is only a slight inversion for the virtual MO's of the NHCOCH3 group which may reflect the “double” nature of this substituent deriving from the presence of the COCH3 moiety with an electron-withdrawing character (see Appendix 1) and for the LUMO of Py(OH)14. Also the electronic effects induced by the OH group, in between those of the NH2 and NHCOCH3 groups, are in agreement with our hypothesis. Similar conclusions hold for the results shown in Figure 5b as well. The MO energies are stabilized relative to the corresponding orbitals of the unsubstituted Py following the order foreseen by the analysis of the pyrene molecular orbitals. For example the LUMO of Py(CONH2)1 and the LUMO+1 of Py(CONH2)14 are, respectively, 0.39 and 0.66 eV lower in energy with respect to the LUMO and LUMO+1 of Py, and the strongest effects are found for the CHO group. Little deviations to our general rule are only found for the occupied MOs of the CHdCH2 and CtCH groups. In both cases, for site 14 the HOMO-1

Figure 4. Sketch of the pyrene (D2h) atom labeling. The independent (and those correlated by symmetry) bond lengths are shown.

Table 2. Atomic Coefficients for Some Representative Molecular Orbitals of the B3LYP/6-31G* Optimized Pyrene. Only the Symmetry Independent Substitution Sites Are Shown MOs/pyrene sitea

C3 b

0.10pz, 0.07p0 z

HOMO-1

0.17pz, 0.14p0 z 0

0.22pz, 0.18p z 0

0.18pz, 0.19p0 z 0

0.23pz, 0.25p z

LUMO

0

0.10pz, 0.14p z

LUMO+1

C14 b

0.08pz, 0.06p0 z 0.25pz, 0.19p0 z

0

HOMO

a

C1 b

0.08pz, 0.10p0 z

0.27pz, 0.33p0 z

b

See Figure 4. The prime on the atomic orbitals refers to the double-ζ nature of the valence functions.

to those of Py. In fact, the LUMO energy decrease is greater with respect to that of the HOMO, and consequently the HOMO LUMO energy gap for Pyd1 is smaller (by 0.074 eV) relative to that of Py; the same trend should occur for the transition energy obtained from the TD-B3LYP calculations. 2.2. Substituted Pyrene. The pyrene systems studied here will be indicated with the notation: Py(X)i(Y)j, where i (j) represent the site positions on the Py ring, according to the atom labeling displayed in Figure 4, and X (Y) are the substituents. It should be reminded that the latter can be one of the following groups: OH, NHCOCH3, NH2, CN, CtCH, CHO, CONH2, and CHdCH2, chosen as representative models of electron-donating or electron-withdrawing groups, characterized by their different “ability” to interact through their lone pairs or π-bonds with the π-conjugated systems of pyrene. The tuning of the optical electronic excitation, and in particular of the lowest one, implies the variations at first/second order of the HOMOLUMO/ (HOMO-1)(LUMO+1) energy gap (Table 1) and, consequently, the modification of the correlated MO energy levels. For the desk-design of these new structures the general rule discussed in Appendix 1 has been followed, asserting that electron-donating substituents destabilize the MO energies, in particular those of the HOMO, while the electron-withdrawing groups stabilize the MO energies, in particular those of the LUMO. Obviously, these effects will be more important when stronger interactions among the substituents and the Py MOs occur. This implies that the Py atoms where the different molecular groups are located should be those where the frontier orbitals have large atomic coefficients. In Figure 3, with the aid of the data shown in Table 2, we can see that for the HOMO and LUMO these interactions should increase with the following site order: 14, 3, 1, while for the HOMO-1 and LUMO+1 the 3, 1, 14 order is obtained. These results suggest that, as far as monosubstituted pyrenes are 614



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Figure 5. Energy level diagrams for some representative molecular orbitals of the unsubstituted pyrene and monosubstituted pyrenes bearing (a) electron-donating and (b) electron-withdrawing groups.

becomes destabilized in energy as is the HOMO of the Py(CHCH2)1. Finally, in Figure 6 the results obtained for Py(CONH2)1,13 and Py(CHO)i(OH)j, are reported, where i = 1 and j = 8, 10, 11, and 13 as previously discussed. For the latter systems, 12 structures can be still derived. Therefore, since the

higher atomic coefficients on the MOs are in the LUMO or LUMO+1 and the electron-withdrawing moiety stabilizes these orbitals, we fixed the position of the CHO moiety on site 1. For Py(CONH2)1,13 the substituents effects are synergically enhanced, while for Py(CHO)1(OH)j the destabilization/stabilization 615



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Figure 6. Energy level diagram for some representative molecular orbitals of the unsubstituted and disubstituted pyrenes.

Table 3. Optimized B3LYP/6-31G*, Experimental, Mean Bond (dM) Distances, and the Bond Length Alternation Parameter (BLA), in Å, for the Ground State of Pyrene

a

bond typea

a

b

c

d

e

f

dM

BLA (102)

B3LYP/6-31G*

1.3940

1.4043

1.4377

1.4284

1.3617

1.4267

1.4109

2.351

experimental b

1.3865

1.4020

1.4363

1.4220

1.3530

1.427

1.4060

2.580

experimental c

1.395

1.406

1.438

1.425

1.367

1.430

1.4114

2.187

See Figure 4. b X-ray data from refs 56 and 57. c Neutron diffraction data from ref 58.

effects of the two substituents are somewhat linearly added, and in this case, the contributions rising from the electron-withdrawing group are dominant over those of the electron-donating ones. According to the analysis of the Py MO atomic coefficients, the electronic effects are strong when the two substituents are on positions (1,8) or (1,13), that is, on those positions where both sites have the greatest atomic coefficients and appreciable for sites (1,10) or (1,11) where in position 10 or 11 smaller atomic coefficients are present. 2.2.2. Substituent Effects on the Pyrene Geometry. In this section, the results obtained from the molecular geometry optimization are shown, and a possible correlation with the lowest optical excitation is proposed. We introduce two geometry parameters to describe the global variations of the CC bond distances: (a) the mean length (dM) as descriptive index of the relaxation or contraction of the Py ring and (b) the bond length alternation (BLA) that for linear conjugated molecules was successfully correlated with their linear and nonlinear optical properties.55 Despite its straightforward definition in linear systems, no general definition like this has been proposed for the polycyclic aromatic hydrocarbons (PHAs) like pyrene. In this paper, we have adopted the BLA definition generally used for PAHs, which is correlated to the aromaticity index, that is, the

standard deviations of the CC ring bonds: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 BLA ¼ ðdi dM Þ2 N i

∑

Here N is the total number of CC bonds and di the i-th bond length. Therefore, when all of the CC distances are the same as in benzene, the BLA is equal to zero, while if the CC bonds are not equivalent because their bond order is changed as a consequence of the π-electron localizations, the BLA increases. In Table 3, the B3LYP/6-31G* optimized bond lengths of the unsubstituted Py, compared with X-ray56,57 and neutron diffraction58 data, are collected. A very good agreement between theoretical and experimental CC distances as well as for dM and BLA is found that underlines the good performance of the B3LYP functionals in the geometry predictions. The results obtained for the other Py derivatives are shown in Figure S2 of the Supporting Information. In Figures 7 and 8, the dependences of dM and BLA versus the Py ring sites for the different substituent groups are reported. In the plots the site order 14, 3, 1 has been considered, in agreement with the previous discussion on the MOs energy. For the Py(X)i systems (Figure 7), the dM values are higher than that of Py, 616



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Figure 7. Dependence of the mean bond length (dM) of the pyrene ring for different mono- and disubstituted pyrene systems.

Figure 8. Dependence of the bond length alternation (BLA, see text for definition) of the pyrene ring for different mono- and disubstituted pyrene systems.

except for Py(OH)14, and two different trends for dM are apparently found (in function of the electronic effect of X). For the electron-donating groups (OH, NH2, and NHCOCH3) a linear dependence between dM and the ring positions is observed, while for the electron-withdrawing ones (CN, CH, CHO, CONH2, and CHdCH2) a maximum for i = 3 is obtained. The different behavior exhibited by the two substituent classes can be easily understood by reminding that the plot ordering along the x-axis follows the site order obtained from the analysis of the frontier orbitals of Py and that the global geometry effects should be more correctly correlated to the total electronic

density. This point, as well as the apparently different behaviors of the two trends, is further discussed in note 2 of the Supporting Information. The strength of the interaction between the lone pair of the heavy atoms and the conjugated π-system could be derived by analyzing the variations of dM with respect to that obtained for Py. For the electron-donating groups, independently of their position, we have found the order OH < NHCOCH3 < NH2, which reflects the different availability of the electron lone pair of the different moieties. As for the electron-withdrawing groups, on the contrary, a dependence on the substituent locations in the 617



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Figure 9. Oscillator strength vs transition energy of the lowest optical transition for different Py(X)i(Y)j systems.

Py moiety is observed: when they are on site 14, the following interaction order CONH2 < CHO < CN < CHdCH2 < CtCH is obtained, while for sites 1 and 3 the order CN < CtCH ≈ CHO ≈ CONH2 < CHdCH2 is observed. In the case of the disubstituted pyrenes, Py(X)i(Y)j, we can see (Figure 7) that, for the symmetric structure Py(CONH2)1(CONH2)13, there is a significant synergic effect of the two carbamoyl groups, and consequently an appreciable increase of dM, as expected. On the other hand, for the Py(CHO)1(OH)j pushpull systems dM is close to those of Py(CHO)1 and practically independent of the OH group position. The results obtained for BLA are reported in Figure 8. Different from the dM results, no general behavior relative to the electronic nature of the substituent groups is observed here. By using the BLA of Py as a reference, smaller values are obtained for Py(X)i with X = OH, CtCH, and CN and greater ones for X = CHO, independently of their positions on the Py moiety. Instead, in the case of X = NH2, NHCOCH3, CHCH2, and CONH2 substituents, the calculated BLA values are either greater or smaller with respect to the reference value as a function of their positions. Finally, we wish to underline that for the Py(X)i(Y)j systems the BLA variations in the symmetric case Py(CONH2)1(CONH2)13, with respect to Py(CONH2)1, are less important than those found for dM but seem to be more sensible to the variation of the structure of our pushpull systems. 2.2.3. Substituent Effects on the Electronic Excitation of Pyrene. For the substituted Py's, the excitation energies of the lowest allowed electronic transition versus the corresponding oscillator strengths are reported in Figure 9, and the most representative monoexcitations (obtained from TD-B3LYP/631G* calculations) that describe these electronic transitions are given in Table S1 of the Supporting Information. For almost all the Py(X)i derivatives, the lowest electronic transition of the unsubstituted Py (333 nm) is red-shifted, and the shift increases with the site order 14 < 3 < 1, as previously discussed. In fact, this behavior is accounted for by the large contribution given to this transition by the HOMOLUMO excitations (Table S1 of the SI). Only for the CN and CHO

groups a different trend is found, and the predicted red-shift increases with the order 14 < 1 < 3. This change in the red-shift order occurs for these groups since the HOMOLUMO energy gaps related to sites 1 and 3 are here very close, unlike all of the other cases where a difference of about 0.1 eV or greater is observed. This effect is very small for CN (Δλ = 0.7 nm) and small for CHO (Δλ = 13.7 nm) and might be explained by carrying out a close analysis of the nature of these electronic excitations (see the discussion in the note 3 of the Supporting Information). Also the results obtained for the Py(X)i(Y)j are in nice agreement with those from the previous analysis of the Py MOs. For the symmetric Py(CONH2)1(CONH2)13 we found, as expected, an appreciable increase of the excitation wavelength if compared with the largest obtained for the Py(CONH2)i systems. For the Py(CHO)1(OH)j the greatest red shift (67 nm) was obtained for j = 13. As a further check of our results, we have performed TD-B3LYP calculations for j = 3, 4, and 6, and as expected, the obtained red shifts are comparable with those for j = 11, 10, and 8, although with a smaller oscillator strength. There is a small exception for site position 3 where due to spatial interaction of the two substituents the oscillator strength is slightly higher than that obtained from the substitution on site 11. On the other hand, the enhancement obtained for the oscillator strength are globally less satisfactory than the results of the electronic transitions. For the monosubstituted Pys, despite the presence of polar moieties, the oscillator strengths are practically unchanged or even lower, in comparison to that of the unsubstituted Py. The only exceptions are the results obtained for the NHCOCH3 group and, surprisingly, for the CHdCH2 and CtCH moieties. Instead, somewhat better values are obtained from the disubstituted pyrenes. The oscillator strength of the symmetric Py(CONH2)1(CONH2)13 system is comparable to those of Py(CtCH)1 or Py(NHCOCH3)13. On the contrary, for the pushpull systems, although the energy gap increase follows the expected trend in function of the CHO/ OH distance, the oscillator strength enhancements are smaller 618



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Figure 10. (a) Transition energy of the lowest optical transition vs (a) dM and (b) BLA for different Py(X)i(Y)j systems.

than expected, probably due to the low “efficiency” of the donor moiety. Finally, in Figure 10 the correlations between the lowest optical transition energies (λexc) of the different Py(X)i(Y)j systems and the geometry parameters, dM and BLA, are shown. An almost linear dependence between dM and λexc is found, indicating that, when the mean CC bond lengths of the Py ring increase, generally, the same holds for λexc (Figure 10a). A similar trend, not shown here, was found by replacing dM with the HOMOLUMO energy gaps. The largest deviations from linearity are found for the CtCH and the CHdCH2 groups. For the BLA data instead, no significant correlation with λexc was found (Figure 10b). This fact suggests that so far, at least for the pyrene systems, the most suitable geometrical index to be used for geometry/excitation-energy correlation could be the dM parameter. However, a better definition of the BLA or a more representative parameter for describing the global variation of the geometry of this systems is still an open task. In conclusion, the

detailed analysis of the pyrene molecular orbitals has allowed the choice of the ring sites where the interaction between the Py and the substituent groups is maximized, with a promising prediction of the variation of the electronic energy associated to the lowest optical transition. Interesting results were also obtained for the oscillator strengths, although the enhancement effects were lower than those expected on the basis of the separations of the positive and negative charge centers during the photon absorption. This result is probably due to the compact structure of the pyrene ring which does not allow a large charge flux to takes place during the excitation, and consequently the oscillator strength associated to the electronic transitions of the pyrene derivatives does not increase appreciably. 2.3. Pyrene Dimers. To improve the red-shift and the oscillator strength of the lowest optical absorption of pyrene, in this section we will take into consideration molecular species where two Py units are linked through a conjugated chain (Py dimers) as model systems. In fact, on the basis of the previous 619



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compared with the value of 1.4109 Å of the unsubstituted Py and 1.4115 Å of Py(CHCH2)14. These small bond length variations correspond to an increase of the ring relaxations, and an equivalent trend holds for the BLA as well. Since the variation of the dM parameters is small in absolute value, to enlighten the bond relaxation/contraction of the Py moieties, bond lengths for the PyDXn(14,14) dimers (with n = 5 for X = E, D, T and n = 4 for X = AP) are shown in Table 4, where the results for the unsubstituted Py and for the corresponding monosubstituted Pys are also reported for comparison. These data show that the relaxation effects are more appreciable near the substitution site and that the bond relaxation/contraction slightly increases from the Py up to the Py dimers, as previously found for the monosubstituted pyrenes as a function of the substituent position. The small variations of dM, according to the results described in the previous section, seem to suggest that the possible red-shift of the lowest optical transitions of unsubstituted Py could be very close to those obtained for the substituted Pys. However, a deeper analysis of the PyDXn(i,j) systems (see note 4 of the Supporting Information) indicates that they fall within the case c discussed in Appendix 1. So, a further and significant decrease of the HOMOLUMO energy gap and consequently of the lowest optical absorption is expected. In fact, the possibility to achieve this effect is, as previously discussed, the reason for using pyrene dimers linked by a conjugated chain as model systems. The energy levels of the first four (two occupied and two virtual) frontier MOs for the PyDXn(14,14) dimers as a function of n, the bridge repeat units number, are shown in Figure 12a. It can be noted that for X = E, T, AP the situation described above holds, the virtual orbitals being stabilized in energy with respect to those of Py and the opposite trend occurring for the occupied orbitals. Only for the HOMO of PyDAn(14,14) the behavior usually found for the electron-withdrawing groups is observed. It is worth underlining that the magnitude of the HOMO destabilization for the Py-dimer increases with the number of the bridge repeat units as a result of the decrease of the unsubstituted bridge HOMO energy obtained by tuning the t parameter which decreases as the bridge length increases. This effect is more marked for PyDEn(14,14), the systems comprising double bonds, since the frontier MOs of the bridge are closer to those of unsubstituted Py. Of course, the description of the real systems PyDXn(14,14) could be more complicated with respect to our simple H€uckel model; nevertheless, the MOs correlations shown in Figure S4 of the Supporting Information indicate that this model still holds if the HOMO-1 and LUMO+1 of Py are assumed as reference orbitals. The variations of the transition energy of the lowest optical transitions of the Py-dimers and their associated oscillator strength, obtained from the TD-B3LYP\6-31G* calculations, are shown in Figure 13a, while the nature of the electronic transitions are described in Table S3 of the Supporting Information. As it can be expected from the HOMOLUMO energy gap analysis, a significant increase of the red-shift of these excitations is obtained with respect to the unsubstituted Py systems. We remark that for the bridge lengths considered here, this red-shift originates from the interaction between the Py and bridge moieties, and not simply by variations of the lowest optical transitions of the unsubstituted conjugated chain, which also is significantly red-shifted (see note 5 of the Supporting Information). For example, the oligomers En have the first allowed optical transitions (obtained from the TD-B3LYP calculations)

Figure 11. Sketch of the pyrene bridged dimers. The indexes i and j refer to the substitution positions on the pyrene rings.

results obtained with the vinyl and ethynyl groups, it could be inferred that better data should be obtained by using longer conjugated chains. The variation of the MO energy levels of the bridge with the number of repeat units could give rise to frontier orbitals with a more efficient interaction with the π-system of Py. Moreover, due to the larger size of the molecule, the charge flux during the photon absorption should be hopefully increased even further. The scheme of the pyrene bridged dimers, denoted as PyDXn(i,j), is shown in Figure 11, where X represents the bridge typology, n the number of repeat units, and i, j the sites of the two Py terminals that are linked to the conjugated chain. The X = T (2,5-thienylene) and AP (ethynylene-p-phenylene) cases were chosen because of the relative higher stability of the bridge and to differently modulate the MO energy. For X = E (ethenylene), A (ethynylene), and T, n was allowed to vary between 3 and 5, for X = AP between 2 and 4, due the larger size of this system and to keep a similar separation between the pyrene units. The dependence of the electronic properties of the PyDXn(i,j) systems from n was initially calculated by fixing i = j = 14, despite these are the pyrene site positions where the weakest interaction between the two Py rings and the bridge occurs. This choice was done for the following two reasons: (a) to minimize the possible steric interaction between the pyrene units and the bridge, to somewhat compensate the intrinsic weak interactions between the πsystems of the two pyrenes through a favorable reciprocal spatial orientation; (b) to obtain a lower bound of the electronic effects, due to the weak interactions between the two aromatic moieties. In this way we expected that the contributions of the two Py groups to the overall system could be more easily evidenced and it could be possible to determine the optimal bridge size where the electronic properties of the dimers originate from the interactions between the Py moieties instead of being dominated by the conjugated chain itself. In the following sections the effect arising from the variations of the i and j site positions will be considered. In particular, calculations will be carried out for the two couples (1,14) and (1,1) which are the positions where the strongest interaction occurs (1 is the position where interactions are the highest ever). 2.3.1. PyDXn(14,14) Systems. The optimized B3LYP/6-31G* geometries of the PyDXn(14,14), are shown in Figure S3 of the Supporting Information. For these systems we can see that the structures of the two Py moieties, for a given value of n, are the same and are only slightly modified as the number of repeat units increases. For instance, in the PyDEn(14,14) case with n = 3, dM is equal to 1.4118 Å and becomes 1.4119 Å for n = 5, to be 620



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Table 4. Optimized B3LYP/6-31G* Bond Distances, in Å, of the Pyrene Moiety for the Ground State of the Bridge (14,14) Systems. For Comparison, Data of the Unsubstituted and Monosubstituted (CHdCH2, CtCH) Pys Are Reported bond typea

a

a0

b

b0

c

c0

d

d0

e

f

1.3617

1.4267

1.3610 1.3609

1.4247 1.4241

1.4285

1.3612

1.4253

1.4287

1.3609

1.4248

1.4289

1.4287

1.3611

1.4249

1.4275

1.4284

1.3613

1.4239

b

1.3940

Py(CHCH2)14 PyDE5(14,14) c

1.4049 1.4082

1.3948 1.3948

1.3989 1.3977

1.4033 1.4031

1.4396 1.4399

1.4387 1.4388

1.4290 1.4294

1.4286 1.4287

Py(CCH)14

1.4050

1.3941

1.4001

1.4038

1.4387

1.4380

1.4284

PyDA5(14,14) c

1.4084

1.3941

1.3987

1.4036

1.4388

1.4381

1.4292

PyDAP4(14,14) c

1.4072

1.3941

1.3991

1.4037

1.4390

1.4381

PyDT5(14,14) c

1.4072

1.3945

1.3988

1.4035

1.4395

1.4384

pyrene

1.4043

1.4377

1.4284

a

See Figure 4. b The structure has D4h symmetry. c The pyrene moiety has a close C2h symmetry within a tolerance of 0.002 Å and negligible variations of the bonds lengths with the number of bridge repeat unit.

at 254.6, 299.6, and 341.8 nm for n = 3, 4, and 5, respectively, while the corresponding electronic transitions of PyDEn(14,14) occur at 422.0, 456.0, and 498.7 nm (for Py it is predicted to occur at 333.0 nm). When the contribution of the unsaturated bridge becomes more important as for the PyDAPn(14,14) systems, the first optical transitions are predicted to happen at 421.0, 445.1, and 461.6 nm for n = 2, 3, and 4, respectively, to be compared with the corresponding ones of APn that occur at 343.0, 392.2, and 425.3 nm. In other words, in the cases examined the dominance of the bridge electronic excitations is in nuce when n = 5, or 4 for PyDAPn(14,14), and we expect it will become more important for longer conjugated chains. A perusal of Figure 13a reveals that, for the lowest optical transition, a significant increase of the transition oscillator strength takes place. In fact, for these systems the oscillator strength is higher than those of the unsubstituted bridge as well as those of the unsubstituted, mono-, or disubstituted Pys. This enhancement is due, as predicted, to the charge transfer between the bridge and the Py moieties induced by the photon absorption. To shed light on this point, the nature of these electronic transitions is analyzed in Figure 14, as a function of some representative monoexcitations, for the PyDXn(14,14) systems with the higher n values. In the case of X = E (top-left panel of Figure 14) the charge transfer between the two moieties (Py units and the bridge) is clearly evidenced by the MO sketch. In fact, the monoexcitations HOMO-3 f LUMO+1, HOMO-2 f LUMO, and HOMO f LUMO+1 involve molecular orbitals localized on different parts of PyDE5(14,14). Such charge transfer character is present also for the HOMO f LUMO monoexcitation (which has the higher weight in the description of the corresponding excited state, Table S3 of the Supporting Information), despite that it is not evident in the MO picture. To overcome this point, a fragment analysis of the molecular orbitals has been carried out by simply defining the fraction of the MO belonging to a particular moiety of the molecule as: FMO moiety = ∑i∈moiety(cMO )2/∑j∈molecule(cMO )2, where cMO is the i-th coeffii j i cient of the atomic orbitals of the MO. In this way we found that, for PyDE5(14,14), the bridge (the pyrene units) accounts for the description of the HOMO and LUMO for 75% (25%) and 73% (27%), respectively, thus implying that in the HOMO f LUMO monoexcitation a charge transfer from the bridge to the pyrene units occurs. The MO fragment analysis can be used also to quantify the bridge contributions to the HOMO and LUMO as a function of the number of bridge repeat units and, consequently, the bridge dominance in the electronic excitation previously discussed. In this case we found that: FHOMO bridge = 61%, 69%, and 75%, FLUMO bridge = 56%, 66%, and 73% for n = 3, 4, and 5, respectively.

This result confirms that, for the PyDXn(14,14) systems, if n is smaller than 5, the electronic excitation originates from an interaction between the two moieties. With the increase of the number of bridge repeat units, the contribution of monoexcitations like HOMO-3 f LUMO+1 or HOMO-2 f LUMO or HOMO f LUMO+1 which have a charge transfer electronic nature, becomes more important, and consequently for the PyDEn(14,14) systems the oscillator strength is enhanced by increasing n (see Figure 13a). Globally, for the lowest optical transitions of PyDE5(14,14) a charge transfer from the bridge to the pyrene units is predicted. Similar results are obtained for the other systems shown in Figure 14. In fact, the most representative monoexcitation in PyDA5(14,14) is the HOMO f LUMO for which FHOMO bridge = LUMO LUMO 68% (FHOMO pyrene = 32%) and Fbridge = 70% (Fpyrene = 30%) so, again, a charge transfer from the bridge to pyrene units is predicted. In this case (see Figure 13a) the oscillator strength decreases with the increase of n. This trend follows the increase of the HOMO-3 f LUMO+1 contribution to the electronic excitation (see Table S3 of the Supporting Information), and from Figure 14 we can see that this monoexcitation involves MOs that are described in terms of the σ bonds of Py and of the π* electrons (i.e., those lying on the molecular plane) of the bridge which are known to originate optical forbidden electronic transitions. This explains the observed trend of the oscillator strength for this system. In the case of PyDTn(14,14), the contribution of the bridge moiety becomes prevalent starting LUMO HOMO‑1 from n = 5, where FHOMO = bridge = Fbridge = 90% and Fbridge LUMO+1 HOMO LUMO Fbridge = 72% (while for n = 3 Fbridge = 80, Fbridge = 79%, and FHOMO‑1 = FLUMO+1 = 0%), and the HOMO f LUMO and bridge bridge HOMO-1 f LUMO+1 monoexcitations do not show a charge transfer character. Nevertheless, a wide number of monoexcitations arising from lower (higher) occupied (virtual) orbitals, like the HOMO-5 f LUMO+2 one, have a charge transfer character which contributes to the electronic excitation and again an enhancement of the oscillator strength is obtained (despite the fact that these results are smaller with respect to those obtained for X = E and AP). Globally, for PyDT5(14,14) the charge flux is originated from the Py moieties to the bridge. Finally, in the bottom-right panel of Figure 14 the PyDAP4(14,14) case is shown, which somewhat recalls the PyDT5(14,14) system. Also in this case a large number of monoexcitations is predicted, with charge transfer nature but low weight in the description of the lowest optical excitation and the bridge contribution to the MOs of the HOMO f LUMO monoexcitation are FHOMO = 84% and bridge FLUMO bridge = 86%, respectively. This implies that for the latter one a small electron flux comes out from the Py units and that the charge transfer from the pyrene moieties to the bridge is slightly enhanced. 621



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Figure 12. Energy level diagram for some representative molecular orbitals of the PyDXn(14,14) systems vs (a) the number of bridge repeat units and (b) the pyrene substitution sites. For comparison the corresponding Py MOs are shown.

between the π-systems of pyrene units and bridge, a significant red-shift of the lowest optical excitation with respect to those of the unsubstituted as well as those of the mono- or disubstituted Py's can be expected. Moreover, due to the “partial localization” of the MOs during the photon absorption, an appreciable

So, we have again an increase of the oscillator strength takes place which is in between that for X = E and X = T. In conclusion, the above results show that for the PyDXn(14,14) systems, despite the fact that the site substitution on the pyrene ring does not allow a strong ground state interaction 622



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PyDXn(14,14) systems, the interactions with the conjugated chain slightly increase the bond length variations of the Py moiety with respect to those of the monosubstituted systems. A perusal of Table S4 clearly shows that the most appreciable effects take place near the substitution site, in particular when site 1 is involved. Moreover, it is important to underline that, for the electronic ground state, the two pyrene units can be considered as noninteracting groups since the bond length variations are only related to the substitution site, and no extended conjugation pathway involving the three moieties occurs. For example, the geometry of the Py substituted at position 1 is virtually the same of that obtained for the PyDXn(14,1) and PyDXn(1,1) systems. The increased interaction between the π-systems of the Py and bridge moieties can be inferred from the MOs correlations shown in Figure S5, of the Supporting Information. In fact now the MOs in particular the HOMO and LUMO of the PyDXn(14,1) and PyDXn(1,1) systems are originated by interactions which involve the HOMO and the LUMO of the different molecular moieties and their degeneracy is removed with respect to the corresponding cases depicted in Figure S4. The stronger interaction between the two π-systems is also presented in Figure 12b, where the electronic effects induced by the substituents on the energy variations of the MOs energy levels are shown to be enhanced with respect to the results obtained for the PyDXn(14,14) systems (see Figure 12a), since the electronwithdrawing bridge stabilizes the LUMO and destabilizes the HOMO of Py (case c of our H€uckel model, see the remarks in note 4 of Supporting Information). For instance, in the PyDE4(i,j) dimers the (de)stabilization of the (HOMO) LUMO with respect to that Py, of (0.424) 0.607, (0.526) 0.686, and (0.611) 0.762 eV for the (14,14), (14,1), and (1,1) cases, respectively. Note that the energy variation trend of the HOMO is inverted when the bridge is the oligoethynylene chains (X = A). Remembering that also for these molecules the lowest optical transition is mainly described by the HOMOfLUMO monoexcitations (see Table S3 where their electronic nature is described as a function of the monoexcitation contribution) we expect that the predicted absorption peaks are further red-shifted with respect to all cases previously examined. The results of the TD-B3LYP transition energy calculations reported in Figure 13b nicely confirm this trend. Indeed, a further red-shift with respect to all previously examined cases is found, and as a general trend, moving from the (14,14) to the (1,1) systems (i.e., with an enhancement of the interaction between the two conjugated moieties), the decrease of the lowest optical transitions, energy increases. It is worth noting (see Figure 13b) that at the decrease of the lowest optical transition energy does not correspond generally an increase of the oscillator strength, which instead appears to be somewhat lower than those of the corresponding PyDXn(14,14) systems. Only for the X = A case both the red-shift of the transition energy and the oscillator strength are resultingly increased. To better illustrate these behaviors, the nature of the lowest optical electronic excitations as a function of some representative monoexcitations is depicted for the PyDXn(1,1) and PyDXn(14,1) systems in Figures 15 and S6, respectively. For example, the PyDA5(1,1) case is shown in the top-right panel of Figure 15, and it can be seen that, with respect to the PyDA5(14,14) case, (Figure 14), different monoexcitations contribute to this transition due to the stronger interactions between the bridge and Py moieties. This implies that, in this case, the forbidden excitation involving the π* of the bridge (HOMO-2 f LUMO+1) has a

Figure 13. Plots of the oscillator strengths vs the transition energies for the lowest optical transitions of PyDXn(i,j) systems. In the top panel (case a) the (14,14) linked dimers and in the bottom panel (case b) the (1,14) and (1,1) linked dimers are shown.

electron transfer occurs between the two Py's and bridge moieties, which increases the oscillator strength and, consequently, the absorption cross section of this class of molecules as well. 2.3.2. PyDXn(i,j) Systems. Two new classes of structures have been taken into account: the PyDXn(14,1) and PyDXn(1,1) dimers (with 1 as the site position where the HOMO and LUMO of the unsubstituted pyrene have the largest atomic coefficients). Here for X = A and T, n = 5 and for X = E and AP n = 4 were used. This choice has been dictated by previous results that have shown (for these bridge lengths) that the interaction effects between the conjugated chain and the pyrene moieties are of the same order of magnitude as for the X = A case and therefore (for a fixed value of n) to allow a better comparison between the two bridge typologies. The optimized B3LYP/6-31G* geometries of these systems are shown in Figure S3 of the Supporting Information. Here, we can note briefly that, as previously hypothesized, if the position 1 of the Py ring is involved in bond formation, when X = E or T the steric hindrance between nearby hydrogen atoms occurs that does not allow a planar molecular geometry to be achieved. In fact, the dihedral angles between Py and bridge planes are: 33.3° (at site 1) for PyDE4(14,1); 26.9° (at site 14) and 53.6° (at site 1) for PyDT5(14,1); 33.8° and 22.8° for PyDE4(1,1) and 47.1° and 53.8° for PyDT5(1,1). The bond lengths of the Py ring, compared with the corresponding ones of the homologous monosubstituted pyrenes, are shown in Table S4 of the Supporting Information. Similarly to what it was obtained for the 623



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Figure 14. Sketch of the contributions (in function of the line width) of some representative monoexcitation to the lowest optical electronic transitions of the PyDXn(14,14) systems with n = 5 for X = E, A, T and n = 4 for X = AP.

lower weight with respect to the corresponding one of PyDA5(14,14) (HOMO-3 f LUMO+1) or of PyDA5(14,1) (HOMO3 f LUMO+1). In fact, from Table S3 the weight of 15, 10, and 7% for the forbidden transitions is found for PyDA5(14,14), PyDA5(14,1), and PyDA5(1,1), respectively, and the magnitude of the oscillator strength increases in the same order. Moreover, the MO fragment analysis shows that the HOMO f LUMO monoexcitation which mainly contributes to the optical transitions has an enhanced charge transfer character. In fact, the LUMO following values: FHOMO bridge = 45% and Fbridge = 55% for PyDA5LUMO = 42% and F = 58% for PyDA5(14,1) can (1,1) and FHOMO bridge bridge be calculated, which implies that the electron moves from the pyrene units to the bridge. The results obtained for the PyDE4(1,1) molecule are shown in the top-left panel of Figure 15, for which the MO fragment LUMO analysis gives FHOMO bridge = 49% and Fbridge = 50%. This entails that when the interaction between the bridge and the pyrene units increases (we remind for PyDE4(14,14) FHOMO bridge = 69% and FLUMO bridge = 66%) a reduced charge transfer character of the HOMO f LUMO monoexcitations is expected since the MOs become more delocalized on the entire molecule. Never= 28%) and theless, for the HOMO f LUMO+2 (FLUMO+2 bridge = 31%) monoexcitations HOMO-2 f LUMO (FHOMO‑2 bridge

(which have a lower weight in the contribution to the excited state description) the charge transfer nature is preserved. Overall, the lowest optical transition of PyDE4(1,1) still features an electron flux from the bridge to the pyrene units, and the magnitude of its charge transfer is still greater with respect to those of the mono- or disubstituted Pys but somewhat smaller than that PyDE4(14,14); the same trend holds for the corresponding oscillator strength. Similar results are obtained for PyDE4(14,1) which results to be an intermediate case between those of = 27%, FHOMO PyDE4(14,14) and PyDE4(1,1) since FHOMO‑2 bridge bridge = LUMO+2 = 54%, and F = 24%. 53%, FLUMO bridge bridge The sketch of the lowest optical transitions for PyDT5(1,1) (left panel) and PyDAP4(1,1) (right panel) are shown in the bottom of Figure 15. The contributions to the HOMO and LUMO of the bridge moiety, as a function of the substitution position on the Py ring, reported in Table 5, clearly indicate that an enhancement of the interactions between the bridge and the pyrene units takes place and that for the AP4 bridge they are higher with respect to the T5 moiety case. The HOMO f LUMO monoexcitation of PyDT5(14,1), similarly to that of PyDAP4(14,14), does not have a charge transfer character which, instead, although a small amount is present in PyDT5(1,1). In both cases, as discussed for PyDT5(14,14), the global charge 624



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Figure 15. Sketch of the contributions (in function of the line width) of some representative monoexcitation to the lowest optical electronic transitions of the PyDXn(1,1) systems with n = 5 for X = A, T and n = 4 for X = E, AP.

Table 5. Fragment Molecular Orbital Analysis of the PyDT5(i,j) and PyDAP4(i,j) HOMO and LUMO PyDT5(i,j)

Accordingly, the same trend is predicted for the oscillator strength (see Figure 13b). The last point that is worth to be emphasized is that, due to the different stabilization/destabilization effects of the HOMO and LUMO (see Table S3 and Figure 12b), for these molecules the lowest optical transition is slightly blue-shifted with respect to that of PyDT5(14,14), where the two moieties are coplanar. Finally, for PyDAP4(14,1) and PyDAP4(1,1) we found a further appreciable red-shift of the lowest optical excitation and, also for this system, a small decrease of the oscillator strength, despite the fact that the HOMO f LUMO transition has an increased charge transfer character (the electron moves from the pyrene units to the bridge). This fact is due to the increasing weight of such monoexcitations as the HOMO-1 f = 68%, FLUMO+1 = 56%) for PyDAP4(14,1) LUMO+1 (FHOMO‑1 bridge bridge = 59%, FLUMO+2 = and the HOMO-2 f LUMO+2 (FHOMO‑2 bridge bridge 43%) for PyDAP4(1,1), where the electron flux is in opposite directions with respect to the HOMO f LUMO monoexcitation. This effect is somewhat greater for the former case, and consequently the oscillator strength of PyDAP4(14,1) is slightly smaller than that of PyDAP4(1,1) (see Figure 13b).

PyDAP4(i,j)

bridge moiety contribution %

(14,14)

(14,1)

(1,1)

(14,14)

(14,1)

(1,1)

FHOMO bridge FLUMO bridge

90

87

84

84

56

55

90

87

81

86

74

78

transfer character of the lowest optical transition is given by the contribution of a large number of monoexcitations which have a low weight in the description of the excited state like, e.g., the HOMO f LUMO+2. Moreover, since in this case the MOs are “more delocalized” (due the increasing of the π-systems of the moiety), the overall magnitude of the charge transfer is decreased with respect of that obtained for PyDT5(14,14). The MO fragment analysis of the lowest excitation of PyDT5(14,1) and PyDT5(1,1) (see Figures S6 and 15) shows that the charge transfer effects are slightly lower for the latter, since FHOMO bridge = = 4% and FHOMO = 84%, FLUMO+2 = 26% 87%, FLUMO+2 bridge bridge bridge for PyDT5(14,1) and PyDT5(1,1), are obtained, respectively. 625



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In conclusion, the results obtained for the PyDXn(14,1) and PyDAXn(1,1) systems shown that the substitution site on atom 1 of the Py ring enhances the interaction between the π-systems of the X bridge and the pyrene units thus increasing (with the exception for X = T) the red-shift of the lowest optical excitation of the unsubstituted pyrene. Moreover, the choice of the substitution site on the pyrene ring allows to control the photoinduced charge transfer between the bridge and the pyrene units, thus allowing us to tune the oscillator strength associated to the optical excitation.

Figure A1. Sketch of a substituted ethylene molecule (X is a general substituent), where the resonance integrals between the different atoms used in the model are shown.

taken as reference values, and for the X center we assume αx = γα0 and βx = δβ0. With these hypotheses, the matrix representation of the H€uckel Hamiltonian of our model system becomes: 1 0 x 1 0 C B C B 1 x δ C B ðA1Þ α ðγ 1Þ A @ 0 0 δ x þ β0

3. CONCLUSIONS A systematic study has been carried out to obtain information on the electronic and optical properties of pyrene-based systems. Our theoretical analysis, based on the pyrene frontier orbitals and a simple H€uckel model, has allowed selecting the most suitable sites for substitution in the pyrene moiety and the effects of different electron-donating or electron-withdrawing groups on the electronic properties of pyrene. In this way, the design of new molecular architectures was achieved within which the pyrene chromophore undergoes a remarkable red-shift of the lowest optical excitation as well as a significant increase of the associated oscillator strength. In particular, in the framework of the TDDFT approach, we have shown that small substituents in the pyrene moiety do not allow a significant separation of the exciton hole/electron centers, which implies a small enhancement of the oscillator strength. This limit can be overcome by joining the two pyrene units by means of conjugated chains. The interaction between the two pyrene units and the intervening conjugated bridge allows the formation, at variance with the unsubstituted, mono-, or disubstituted pyrene, of weakly bonded electronhole pairs bearing the charge centers localized on the two different moieties (pyrene and bridge), which results in a strong increase of the absorption cross section of the pyrene systems. The nature of the electronic excitation was investigated, and the electronic properties of the pyrene dimers here considered were shown to originate from the interactions between pyrene and bridge moieties when the number of repeat units in the latter is up to four or five. In the case of longer bridges, we expect that the first allowed optical transitions of the overall systems will be dominated by the conjugated chain. The molecular design of these new pyrene-based systems has shown that the most satisfactory result in terms of both the enhancement of the oscillator strength and of the decrease of the transition energy of the first optical transition are achieved when the linker is a conjugated chain of double and/or triple bonds, thus providing potential candidates for photovoltaic applications. Their possible use as active material in hybrid systems as well as their interaction with the inorganic materials will be the next subject of our study.

and, straightforwardly, the associated secular equation is: x3 tx2 ðδ2 þ 1Þx þ t ¼ 0

ðA2Þ

where the substitution t = α0(γ 1)/β0 has been made. The solution of this linear third degree equation is trivial and leads to the following roots: 9 8 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > > < 2 t 1 þ δ θ þ 2ði 1Þπ = 1 þ 2 1 þ 3 2 cos xi ¼ > 3> 3 t ; : i ¼ 1, 2, 3 ðA3Þ where:

8 8 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi9 > > > = < pffiffiffi ðδ4 þ 20δ2 8Þt 2 þ 4ðδ2 þ 1Þ3 þ 4t 4 > > > > > arctan 3 3 > 2 2 > > > t½9ðδ 2Þ þ 2t > ; : > > > > > 2 2 > < if t½9ðδ 2Þ þ 2t > 0 8 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi9 θ¼ > > > = < pffiffiffi ðδ4 þ 20δ2 8Þt 2 þ 4ðδ2 þ 1Þ3 þ 4t 4 > > > > > þ π arctan 3 3 > 2 2 > > > t½9ðδ 2Þ þ 2t > ; : > > > > > > : if t½9ðδ2 2Þ þ 2t 2 < 0

ðA4Þ To discuss the general results obtained in eq A3, typical values of t, for different X atoms, and of δ for the interactions between X and C(sp2) are collected in Table S2 of the Supporting Information, and three special limit cases can be highlighted: (a) The interaction between X and C atoms is weak: (δ/t)f0 and γ 6¼ 1. These conditions imply that the atomic orbital of X slightly interacts with the π-system of the ethylene moiety, due either to the higher/lower value of the coulomb integral of this site with respect to that of the C(sp2) atom or to the negligible value of the resonance integrals, as a consequence of symmetry constraints between the X and C AO's or of a low overlapping. Such situation holds for example when X = F for which t = 2.71 and δ = 0.52 (Table S2 of the Supporting Information). By assuming δ = 0, eq A1 becomes x3 tx2 x + t = 0,

’ APPENDIX 1 A well-known general rule that has been used in the main text describes the effects of an electron-donating or withdrawing substituents on the molecular energy levels of conjugated systems. In fact, it is known that the former destabilize the MO energies, especially those of the HOMO, while the latter stabilize the MO energies, and in particular those of the LUMO. Here, by using for sake of simplicity the substituted ethylene shown in Figure A1 as model systems and the H€uckel approach we justify the use of this rule. The Coulomb α0 and the resonance β0 integrals (both negative) of the sp2 hybridized carbon atom are 626



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Figure A2. Diagram of the solutions obtained from eq A2 for (a) δ f 0 (smooth lines) or for δ = 0 (bold lines); (b) γ f 1 (smooth lines) or γ = 1 (bold lines); (c) t ≈ ( δ (smooth lines) or for |t| = δ and θ = π/2 (bold lines).

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Figure A3. Comparison between the MO's of the substituted (for part a, see case b of Appendix 1; for part b, see case c) and unsubstituted ethylene molecule.

whose roots are x1 = 1, x2 = 1, and x3 = t. Depending on the t sign, the X atom is a site more (t > 0 f γ > 1) or less (t < 0 f γ < 1) electronegative with respect to C, and since α0 ≈ 10β0 we can assume that |t| > 1. These results are summarized in Figure A2a, where the MO's energies and the corresponding coefficients of the atomic orbitals for δf0 are depicted. Notice that, in function of the t sign, the x3 root correspond to the lowest or highest solution. (b) The X atom has γf1. In this case, the X site is the C atom or, alternatively, its coulomb integral is equal or close to α0 (as is the case of

the Si atom), see Table S2 of the Supporting Information. By assuming γ = 1 (i.e., t = 0), eq A1 becomes x3 (δ2 + 1)x = 0, and its roots are: x1 = (1 + δ2)1/2, x2 = 0 and x1 = (1 + δ2)1/2. Sketches of these results are depicted in Figure A2b, where the MO's energies and the coefficients of the atomic orbitals for δ < 1, δ = 1, and δ > 1 cases are shown. Notice that when δ = 1 and γ = 1, our model coincides with the allylic system, and the interaction effects (at a fixed δ value) are the greatest ones. This situation should hold also for the CHO group, where on the C atom site we should expect γ = 1 and δ > 1, due to 628



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the presence of the neighboring oxygen which increases the π-electron withdrawing effect. (c) The X atom has γ ≈ 1 ( (β0/α0)δ. Despite the fact that this condition (equivalent to t ≈ ( δ) seems to be a very special case, the perusal of Table S2 of the Supporting Information shows that this approximation holds to at least as order of magnitude. With this approximation, eq A1 becomes x3 tx2 (t2 + 1)x + t = 0, whose solutions are similar to those of eq A3. Since for different types of X sites (Table S2) as well as for different types of C atoms hybridization the condition t ≈ 1.3 holds, which implies θfπ/2, to simplify the general solutions we assume θ = π/2, and therefore from eq A3 we obtain that the following new roots: rffiffiffiffiffiffiffiffiffiffiffiffiffiffi! pffiffiffi t 3 t 1 3 4 þ 2 , x2 ¼ , x1 ¼ 3 t 3 ! rffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi t 3 x3 ¼ 1 þ 3 4 þ 2 3 t The corresponding energy level ordering of the MO's atomic orbital coefficients for the γ > 1 and γ < 1 cases is depicted in Figure A2c. It is interesting to note that, as a function of the t values the root x1 could be greater of 1 and that this implies, as discussed below, a different trend for the energy variations of the occupied and virtual orbitals. We anticipate that this situation could hold for the nitrogen atoms (as a function of both their hybridizations and the nature of neighboring atoms). The MO energy trends, obtained using the general solutions given by eqs A3 and A4, are shown in Figure A2ac by smooth lines, while for each approximation, the corresponding MO energy levels are depicted as bold lines. The results previously obtained, are compared with the energy levels of ethylene (x1 = 1, x2 = 1 in the framework of the H€uckel theory) shows how the presence of the X site modifies the MOs energies of this molecule. Case a is straightforward, since when the resonance integral is zero or close to zero, no interaction effects occur between the X site and the ethylene moiety, thus leaving the MOs virtually unchanged. Case b, when the X site has the same electronegativity of the C atom (γ = 1) or close to that, is depicted on the left/right side of Figure A3a, where X is an electron-donating/-withdrawing group. For the former case, the energy changes of the HOMO and LUMO are Δ1 = 1 and Δ2 = 1 (1 + δ2)1/2, respectively. Since, it can be generally assumed that δ < 31/2 (see Table S2) both the MOs are destabilized with respect to ethylene, and since Δ1 < Δ2 the HOMO results to be the one that exhibits the highest increase in energy. The opposite situation occurs for the electron-withdrawing case (right panel of Figure A3a) where the HOMO and LUMO energies of the substituted systems are smaller than those of the unsubstituted one. In this case the MO energy variation becomes Δ1 = (1 + δ2)1/2 1 and Δ2 = 1, respectively. We have again Δ2 > Δ1, but now they are positive numbers ,and consequently the MOs are stabilized, in particular the LUMO level which has the higher energy decrease. Finally, in Figure A3b the cases arising from point c are depicted, which depend on the X site being more (X = Y, γ > 1) or less (X = Z, γ < 1) electronegative than the C atom. Similarly to the previously found results, when Y or Z released

electrons to the ethylene moiety, the HOMO and LUMO are destabilized (especially the first one). Instead, if Y or Z withdraw electrons from the π-system, the frontier orbitals and in particular the LUMO of the substituted ethylene gain stabilization. In fact, referring to the Y case (left panel of Figure A3b), when the site is electron-donating the energy variations of the HOMO and LUMO are Δ1 = (t/3 1) and Δ2 = [t(1 31/2(4 + 3/t2)1/2)/3] + 1, respectively. Instead, when Y is an electron-withdrawing group the energy variations of the HOMO and LUMO are Δ4 = [t(1 + 31/2(4 + 3/t2)1/2)/3] 1 and Δ3 = (t/3 + 1), respectively. When t < 1.5 (as occurs for many atoms, see Table S2) the result is that Δ1 < Δ2 and Δ3 > Δ4, and consequently, the ordering of the energy stabilization or destabilization is proved. Similar results can be obtained for the X = Z case by taking into account that in this case the energy variations, Δi, change their signs. Finally, is interesting to highlight the Δi dependence on the t parameters. In fact, if t < 0.5 it is easily shown that for X = Y the LUMO or for X = Z the HOMO becomes, in absolute value, smaller in energy with respect to the corresponding orbitals of ethylene. This implies that when Y has an electron-donating nature, the LUMO should to be slightly stabilized instead of being destabilized, and the opposite holds for the HOMO when Z is an electron-withdrawing group. An inspection of Table S2 shows that this situation holds, for example, with different “types” of nitrogen atoms.

’ ASSOCIATED CONTENT

bS

Supporting Information. Note 1: The choice of the best ring site substitution for disubstituted pyrenes. Note 2: Nature of the different trends observed in Figures 7 and 8. Note 3: Analysis of the electronic nature of the lowest optical transitions of the Py(CN)i and Py(CHO)i systems. Note 4: Correspondence of the PyDXn(i,j) systems with the case c of Appendix 1. Note 5: Reference moiety of the PyDXn(14,14) systems in the red-shift evaluation with respect to the unsubstituted molecules. Figures S1S3: Geometries of the pyrene derivatives presented in the main text obtained from the B3LYP/6-31G* geometry optimization. Figures S4 and S5: Correlation energy diagram for the first eight frontier orbitals of some representative PyDXn(i,j) systems. Figure S6: Sketch of the contributions of some representative monoexcitation to the lowest optical electronic transitions of the PyDXn(14,1) systems with n = 5 for X = A, T and n = 4 for X = E, AP. Table S1: TD-B3LYP/6-31G* excitation energy, oscillator strength, ΔELUMOHOMO, ΔE(LUMO+1)‑(HOMO‑1), and contributions of the monoexcitations describing the lowest optical transitions of the pyrene and its mono or bisubstituted derivatives. Table S2: H€uckel δ and t parameters for different atoms. Table S3: TD-B3LYP/6-31G* excitation energy, oscillator strength, ΔELUMOHOMO, and contributions of the monoexcitations describing the lowest optical transitions of the pyrene dimers. Table S4: Optimized B3LYP/6-31G* bond distances of the pyrene moiety for the ground state of the (1,14) and (1,1) bridged systems. For comparison data of the unsubstituted and monosubstituted (CHdCH2, CtCH) Py's are reported. This material is available free of charge via the Internet at http://pubs. acs.org.

’ ACKNOWLEDGMENT We acknowledge financial support from the University of Genoa through the CUP: D31J110000300005 project and the 629



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Italian MIUR (Ministry of the Education, University and Research) through the PRIN 2007PBWN44 and 2009PRAM8L_007 projects.

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Tuning the Photophysical Properties of Pyrene-Based Systems: A

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