Intramolecular Singlet Fission in Quinoidal Bi-and Tetrathiophenes: A

Sep 13, 2016 - In good agreement with their experimental findings, through complete active space second-order perturbation theory (CASPT2) computation...
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Intramolecular Singlet Fission in Quinoidal Bi- and Tetrathiophenes: A Comparative Study of Low-Lying Excited Electronic States and Potential Energy Surfaces Mohammad R. Momeni* Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2, Canada S Supporting Information *

ABSTRACT: Quinoidal bithiophene has recently been introduced (Varnavski, O. et al. J. Phys. Chem. Lett. 2015, 6, 1375−1384) as a very promising isolated organic compound for intramolecular singlet fission (iSF) with an outstanding SF quantum yield of ≈180%. In contrast, another recent study (Ren, L. et al. J. Am. Chem. Soc. 2015, 137, 11294−11302) revealed that quinoidal tetrathiophenes have no activity in the iSF process and are strong fluorophores instead, with measured fluorescent quantum yields up to 53.1%. Using DFT and TD-DFT methods, the authors of the second contribution attributed the marked differences between these compounds to faster reverse T2 → S1 intersystem crossing processes in the tetrathiophenes. To address this unprecedented discrepancy, quinoidal bithiophene and tetrathiophene compounds and their derivatives are carefully examined using the CASPT2 technique. Theoretical evidence is provided through detailed investigation of CASPT2 potential energy surfaces of different singlet and triplet states involved in the iSF process. Through comparison of the CASPT2 results with the CASSCF and RAS-2SF data, it is found that the dynamic electron correlation present in the CASPT2 method plays a crucial role for correct description of the multiexciton nature of the triplet pair 1[TT] state in quinoidal bi- and tetrathiophenes. Effects of substitution and structural modification on iSF activity of these compounds are also examined using the CASPT2 method where the obtained results are in accordance with previous experimental predictions. These results contribute to a better understanding of the iSF mechanism in quinoidal systems which could be relevant for designing new iSF active compounds.

1. INTRODUCTION Functionalized oligothiophenes are a very important class of organic chromophores shown to be promising building blocks for molecular electronic devices.1−4 α-Oligothiophenes, fully conjugated repeating thiophene units, provide homogeneous πelectron systems with excellent charge transport properties which are very suitable for such purposes (Scheme 1).

red-shift in absorption (fluorescence); from 247.5 nm (nonfluorescent) in the monomer to 556.5 nm (641.6 nm) in the 96-mer (Scheme 1).16 The length-dependent red-shift is more pronounced in quinoidal analogues of α-oligothiophene, with dicyanomethylene substituents on their terminal CC bonds, from 412 nm in the monomer up to 1371 nm in the hexamer (Scheme 1).17 The enormous red-shifts observed in the quinoidal α-oligothiophenes compared to their parent αoligothiophenes were accredited to their significant diradicaloid characteristics, e.g. 29% for the hexamer, determined from electron spin resonance intensities.17 Very recently, isolated tetracyano quinoidal bithiophene (n = 2, Scheme 1) was introduced as a very promising intramolecular singlet fission (iSF) candidate with an extraordinary SF quantum yield of ≈180%.18 Through the spin allowed SF process, absorbing light leads to generating a photosensitizer in its multiexcitonic state which then dissociates into two excited triplet species each capable of injecting one electron into the photovoltaic device.19−21 Varnavski et al. showed that direct photoexcitation of the tetracyano quinoidal bithiophene leads to the generation of the

Scheme 1

Perfluoroalkyl and perfluoroarene substituted forms of αoligothiophenes are shown to be applicable for fabricating highperformance n-channel organic semiconductors in photovoltaic devices.4,5 Owing to their excellent redox stabilities,6,7 αoligothiophenes have also found applications in organic light emitting devices,8 in field effect transistors,9−12 and also as photosensitizers in dye sensitized solar cells.13−15 Increasing the conjugation length in these compounds leads to a progressive © 2016 American Chemical Society

Received: July 25, 2016 Published: September 13, 2016 5067

DOI: 10.1021/acs.jctc.6b00737 J. Chem. Theory Comput. 2016, 12, 5067−5075

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Journal of Chemical Theory and Computation fully allowed excited singlet state (11Bu bright state) which in turn undergoes an ultrafast (≈1 ps) formation of the dipole forbidden multiexcitonic state, i.e. the 21Ag triplet pair state (1[TT]).18 Experimental data have revealed that this multiexcitonic state has an absorption at ≈570 nm with a lifetime of ≈57 μs. The magnetic field dependency and solvent and viscosity independency of the 1[TT] state in this molecule were indicated as evidence for its triplet-like properties.18 On the other hand, indirect excitation of this molecule by tetracene led to the formation of another excited electronic state with absorption at ≈600 nm and a lifetime of ≈111 μs. This state was interpreted as the first triplet excited electronic state (13Bu state) of the quinoidal bithiophene. In good agreement with their experimental findings, through complete active space second-order perturbation theory (CASPT2) computations with the cc-pVDZ basis set on the model system of the quinoidal bithiophene (i.e., with no substituents at the β and β′ positions, QBT−(CN)4 in Scheme 2), Varnavski et al. showed that this molecule strongly absorbs the light in the Franck−Condon (FC) region at 2.06 eV (2.25 eV experimentally).18

have tried to remedy this issue through addition of dynamic electron correlation using perturbation theory leading to the emergence of SF-CAS(h,p)32 and SF-CAS(S)33 methods. By fusing two extra thiophene rings to QBT−(CN)4, Ren et al. succeeded in synthesizing and characterizing several quinoidal tetrathiophenes (QBTT−(CN) 2 −(CO 2 Me) 2 , Scheme 2).34 Interestingly, an unprecedented strong fluorescent activity was observed for these systems despite their resemblance to the parent bithiophene, with measured fluorescence quantum yields up to ≈53%.18,34 Through DFT and TD-DFT computations with the B3LYP hybrid functional and 6-31G(d,p) basis set in the gas phase, the authors argued that a fast T2 → S1 reverse intersystem crossing process is responsible for the observed marked difference between quinoidal bi- and tetrathiophenes.34 TD-DFT assignment of symmetries of the S1 and the T2 states of these compounds is however unclear. Based on our CASPT2 analyses, see the Results and Discussion section for more details, the S1 bright state (with 11Bu symmetry) transition to the T2 state (with 13Ag symmetry) for both QBT-(CN) 4 and QBTT-(CN) 2 (CO2Me)2 is symmetry forbidden and hence should by definition be zero. Incorrect assignment of the intersystem crossing channel (i.e., 21Ag → 13Ag), which comes from the lack of attention to the 1[TT] dark state for quinoidal bi- and tetrathiophenes, makes their comparison for these systems incorrect. Also, considering the fact that these states were used for computing reorganization energies and energy barriers for S1 → T2 transition questions the ultimate conclusion about the high fluorescence quantum yield of quinoidal tetrathiophenes compared to bithiophenes. Therefore, a description of the iSF in these compounds which involves a close look at the 1[TT] state seems necessary. The 1[TT] state is already well-known to play a key role in the xSF process in carotenoids and pentacene.35,36 Moreover, the multiexcitonic nature of the 1 [TT] dark state necessitates the use of strongly correlated multireference methods compared to the conventional and computationally more efficient single-reference based methods such as linear response TD-DFT and coupled cluster methods. Herein, we present our results of CASPT2 computations on the excited state properties of quinoidal bi- and tetrathiophenes and their derivatives. To understand the role of electron correlation in these systems we compare and contrast our CASPT2 results with previously reported RAS-2SF data with the same basis set as well as to the complete active space selfconsistent field (CASSCF) data. Moreover, through detailed CASPT2 PES scans of rotations around the central and the terminal CC bonds and also full Breit-Pauli spin−orbit coupling (BP-SOC) computations the stark differences between these compounds will be thoroughly explained.

Scheme 2

Also, the adiabatic excitation energy of the 1[TT] state was found to be 1.65 eV which is greater than twice that of the computed 0.60 eV value for the first excited triplet state. These data show that QBT−(CN)4 fulfills the energetic requirements for generation of two triplet excitons from the 1[TT] state in the iSF process. However, their restricted active space double spin-flip (RAS-2SF) potential energy surfaces (PESs) for rotations around the central and the terminal CC bonds of this molecule showed no crossing points between the 11Bu bright and 1[TT] states. These contradictory results question the applicability of the RAS-SF methods for studying the iSF process in QBT−(CN)4 and possibly similar systems. In the RAS-SF methods, one starts with a high spin restricted open shell Hartree−Fock determinant and then generates correlated states of interest with lower multiplicities by single or multiple spin flipping excitations within the active space.22−27 Computational cost of these methods is less than the traditional complete active space self-consistent-field (CASSCF) method and therefore is more applicable to larger correlated systems though the cost exponentially increases with the number of spin flips. Although these methods have been successfully employed in studying external SF (xSF) properties of tetracene and pentacene,28−31 however they suffer from not having enough dynamic electron correlation which can be a significant drawback in strongly correlated systems. This shortcoming could be indeed responsible for missing crossing points between the correlated 11Bu bright and 1[TT] states of QBT−(CN)4. Alternatively, Head-Gordon and co-workers

2. COMPUTATIONAL METHODS All geometry optimizations were performed using the stateaveraged complete active space self-consistent field (SACASSCF)37−39 method and the polarized split-valence 631G(d)40,41 basis set in the gas phase (see Table S4, Supporting Information (SI) for Cartesian coordinates of all optimized structures). The SA-CASSCF wave functions were constructed by using equal weights of ground and excited electronic states. For all singlet ground and excited state geometry optimizations and energy calculations, a state-averaged CASSCF comprised of the four lowest singlet states was employed, e.g. in the case of C2h symmetry structures: 11Ag, 21Ag (1[TT]), 11Bu, and 21Bu states. Also, the first three triplet states, e.g. 13Bu, 13Ag, and 23Bu 5068

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Table 1. Computed TD-DFT/PBE0, CASSCF, and CASPT2 Vertical Excitation Energies (in eV) Using SA-CASSCF/6-31G(d) 11Ag Ground State Optimized Structures in the Gas Phasea 1

species QBT−H4

QBT−(CN)4

QBT−(CN)2−(CO2Me)2

QBTT−H4

QBTT−(CN)4

QBTT−(CN)2−(CO2Me)2

[TT] (dark)

TD/PBE0 CASSCF[8π,6o] CASSCF(adia)[8π,6o] CASPT2[8π,6o] TD/PBE0 CASSCF[8π,7o] CASSCF(adia)[8π,7o] CASPT2[8π,7o] TD/PBE0 CASSCF[8π,7o] CASSCF(adia)[8π,7o] CASPT2[8π,7o] TD/PBE0 CASSCF[8π,6o] CASSCF(adia)[8π,6o] CASPT2[8π,6o] TD/PBE0 CASSCF[8π,7o] CASSCF(adia)[8π,7o] CASPT2[8π,7o] TD/PBE0 CASSCF[6π,6o] CASSCF(adia)[6π,6o] CASPT2[6π,6o]

4.302 3.160 3.152 4.003 2.972 3.035 4.117 3.142 3.273 4.769 3.003 3.703 4.420 3.336 3.530 4.389 3.437 3.640

11Bu (bright)b 3.026 4.847 4.471 3.524 2.571 4.632 3.950 3.002 2.574 4.625 3.992 3.188 3.007 4.890 3.741 3.627 2.622 4.656 3.928 3.218 2.603 4.527 4.130 3.240

(0.792)

21Bu 4.384 (0.000) 6.800

c

(1.222)

4.444 3.814 (0.000)d 5.110

(1.235)

4.062 3.731 (0.238) 5.185

(0.729)

4.309 4.086 (0.000)c 6.757

(1.100)

4.604 3.345 (0.052) 5.309

(1.111)

4.250 3.313 (0.037) 5.304 4.423

13Bu (T1)

13Ag (T2)

23Bu (T3)

0.832 2.169 1.256 1.472 0.646 1.854 0.844 1.364 0.763 1.911 0.995 1.507 1.271 2.477 1.081 1.868 1.135 2.152 1.448 1.774 1.173 2.100 1.469 1.781

2.575 3.472 2.936 2.935 2.290 3.286 2.747 2.873 2.409 3.370 2.955 2.990 2.697 3.679 2.547 3.177 2.377 3.428 2.921 3.039 2.494 3.507 2.957 3.185

3.640 5.453 4.287 3.086 4.264 3.995 3.036 4.310 4.064 3.290 5.605 3.999 2.776 4.178 3.807 2.804 4.270 3.946

a

Active spaces for multireference calculations are provided in brackets. SA-CASSCF adiabatic excitation energies are also provided (CASSCF(adia), except for S3 and T3 states). bTD-DFT/PBE0 computed oscillator strengths for the singlet excited states are given in parentheses. The 11Bu bright states correspond to HOMO → LUMO (π → π*) transitions. c11Bg symmetry. d31Ag symmetry.

2π ⟨Sn |Ĥ SO|Tm⟩2 × FCWD (1) ℏ where ⟨Sn|Ĥ SO|Tm⟩ are the SOC integrals between the pure spin states of Sn and Tm, and FCWD is the Franck−Condon weighted density of states which is close to unity for a set of similar species. Determining the ISC rate is extremely challenging for large molecules as it requires accurate assignment of different deactivation channels.50 Instead, semiquantitative approaches are usually preferred for such investigations.51 Full BP-SOC matrix elements between the 21Ag and 13Ag states were computed for all compounds. To correctly describe the SOC between the target states, different weights for the 11Ag (weight = 0) and the 21Ag (weight = 1) states were used. The SA-CASSCF optimized geometry of the 21Ag dark state was utilized for all SOC calculations. BP-SOC results were compared and contrasted to the spin−orbit coupling mean-field (MNF-SOC) quadratic response data for all compounds. The MNF-SOC method utilizes an effective one-electron operator in which the two electron terms are evaluated as a sum over all α and β spin orientations;52,53 for a comparison between different approaches for computing SOCs see ref 50 and references therein. All the DFT and TD-DFT computations were performed using the Gaussian 09 package.54 All CASSCF and CASPT2 computations as well as Breit-Pauli and mean-field SOC calculations were accomplished using the 2012 version of MOLPRO.55

states in the case of C2h symmetry systems, were included in the state-averaged CASSCF computations of the triplet states. The SA-CASSCF optimized geometries for different states of QBT−(CN)4 were compared and contrasted to the extended multistate CASPT2 optimized geometries reported by Chien et al.42 as well as to our own PBE043 hybrid density functional geometries with the same basis sets (see Section S1 and Table S1, SI for the results); for a comparison between TD-DFT and CASSCF/CASPT2 energetic data see Table 1. Due to the size of the systems investigated in this work, only some of the highest π and π* orbitals were included in the active spaces of our multireference computations; for details on different active spaces employed for different compounds see Figure S3, SI. Dynamic electron correlation effects were included through performing CASPT244 calculations using SA-CASSCF natural orbitals. The CASPT2 computations utilized the internally contracted RS2C program44 with an IPEA shift, which is a correction to the zeroth order Hamiltonian, of 0.3.45 The effect of enlarging the basis set from 6−31G(d) to 6-311+ +G(d,p)46,47 on the computed CASSCF and CASPT2 excitation energies of the unsubstituted forms of QBT− (CN)4 and its tetrathiophene analogue, i.e. QBT−H4 and QBTT−H4, is investigated, and the corresponding results are provided in Section S2 of the SI. Overall, increasing the size of the basis to 6-311++G(d,p) does not have a major impact on accuracy and the 6-31G(d) basis set seems to be a suitable and cost-efficient basis set. Hence, we utilized this basis set for all computations throughout this work unless otherwise stated. According to the Fermi Golden rule,48,49 the rate of nonradiative transition from any singlet excited state (Sn) to any triplet excited state (Tm) is expressed as

kISC =

3. RESULTS AND DISCUSSION 3.1. Excitation Energies of Quinoidal Bi- and Tetrathiophenes. To explore different determining factors 5069

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Table 2. Computed TD-DFT/PBE0, CASSCF, and CASPT2 Vertical Excitation Energies (in eV) Using SA-CASSCF/6-31G(d) 11Ag (11A in the Case of the C2 Symmetry Structure) Ground State Optimized Structures in the Gas Phasea

QBT−Ph (C2) state

TD/PBE0

1

[TT] 11B (S1) 21B (S2) 13B (T1) 13A (T2) 23B (T3)

1.336 (0.382) 2.663 (0.059) −0.689 1.977 2.038

CASSCF 3.370 3.316 4.168 2.135 2.173 2.470

QBT−Py (C2h) CASSCFadia 1.972 2.552 1.300 1.741

CASPT2

state

TD/PBE0

CASSCF

CASSCFadia

CASPT2

2.300 (0.938) 3.301 (0.025) 0.640 2.100 2.682

2.768 2.669 3.304 1.576 1.998 2.627

2.427 2.319

2.101 2.144 2.726 1.472 1.673 1.949

1

2.230 2.139 2.799 1.433 1.465 1.992

[TT] 11Bu (S1) 31Ag (S2) 13Bu (T1) 13Ag (T2) 23Bu (T3)

0.930 1.663

a

An active space comprised of 8π electrons in 7 orbitals [8π,7o] is used for all multireference calculations. SA-CASSCF adiabatic excitation energies are also provided (CASSCF(adia), except for S3 and T3 states). TD-DFT/PBE0 computed oscillator strengths for the bright singlet excited states are given in parentheses.

According to our computed CASPT2/6-31G(d) excitation energies for QBT−(CN)4, the bright 11Bu state is 0.033 eV more stable that the 1[TT] dark one. This is in rather good agreement with the Chien et al.42 reported energy gap of 0.06 eV computed at the XMS-CASPT2/6-31G(d)//XMSCASPT2/6-31G(d) and Varnavski et al.18 value of 0.013 eV computed at the CASPT2/cc-pVDZ//CASPT2/cc-pVDZ level. Substituting the terminal −CN group of QBT−(CN)4 with −CO2Me produces QBT−(CN)2−(CO2Me)2 with computed vertical CASPT2 excitation energies of 3.188 and 3.273 eV for its bright and dark states, respectively. The CASPT2 method predicts a 0.238 eV blue-shift for the experimentally observed (in toluene solution) red-shift of 0.037 eV (10 nm) by going from QBT−(CN)4 to QBTT− (CN)2−(CO2Me)2, while the corresponding blue-shift for TDDFT/PBE0 is 0.032 eV (see Table 1). The TD-DFT/PBE0 computed vertical excitation energies of the bright states of the QBT−(CN)4 and QBTT−(CN)2−(CO2Me)2 compounds are, respectively, 2.571 and 2.603 eV overestimating the experimental values by 0.396 and 0.465 eV, respectively. From energetic viewpoints, a photosensitizer is capable of generating two triplet excitons in the external or internal SF process if the energy of the double-excitonic 1[TT] state (the 21Ag state for C2h symmetries) is equal or greater than twice the first triplet state energy, i.e., 1[TT] ≥ 2 × 13Bu. As can be seen from Table 1, all bithiophenes are able to fulfill this requirement. It is also clear that replacing −CN with −CO2Me in QBT−(CN)2− (CO2Me)2 and QBTT−(CN)2−(CO2Me)2 leads to the destabilization of all states, except the T3 state in QBT− (CN)2−(CO2Me)2, computed at the CASPT2 level. Interestingly, QBTT−(CN)2−(CO2Me)2 seems to be the only tetrathiophene that can fulfill the above-mentioned energetic requirement; however, we will see in the CASPT2 PES scans section why this molecule shows no activity in iSF. Very recently, it has been shown that even small modifications of photosensitizers backbone can have a decisive impact on their singlet fission characteristics.56−61 Similarly, to gain more insight into how structural modifications can alter photophysical properties of quinoidal bithiophenes in iSF, QBT−(CN)4 was fused with benzene and pyridine rings, resulting in structures QBT−Ph and QBT−Py, respectively, which in turn resemble the tetrathiophene compound (see

on photophysical properties of QBT−(CN)4 and QBTT− (CN)2−(CO2Me)2, we chose to design quinoidal systems with different substituents on the terminal CC bonds (see Scheme 2). Our nomenclature for the designed quinoidal biand tetrathiopheness is based on the type of substituents, i.e., −CN and/or −CO2Me on the terminal CC bonds. By comparing these molecules to each other and to their unsubstituted forms, i.e. QBT−H4 and QBTT−H4, one can distinctively investigate different factors such as effects of functionalization of the terminal bonds and also fusing more thiophene rings. Vertical and adiabatic CASSCF and CASPT2 as well as linear response TD-DFT excitation energies of quinoidal bi- and tetrathiophenes considered in this work are presented in Table 1. We note that single-reference methods such as TD-DFT are not by definition able to capture the multiexcitonic nature of the 1[TT] states and hence are not collected in Table 1. The computed TD-DFT/PBE0 oscillator strengths of the 11Bu bright states of all the bithiophene species are greater than their tetrathiophene analogues. Also, the computed vertical excitation energies of all the 11Bu bright states are underestimated with respect to their corresponding CASPT2 values (from 0.498 eV in QBT−H4 to 0.637 eV in QBTT−(CN)2−(CO2Me)2, Table 1). As stated before, a complete understanding of the iSF process in quinoidal bi- and tetrathiophenes demands a thorough analysis of the 1[TT] state which acts as a bridge for the forbidden 11Bu → 13Bu transition and hence is essential for generating two triplet excitons and ultimately injection of two electrons into the photovoltaic devices. Hence, to take into account the double-excitonic nature of this state and to capture the energy gap between this state and the nearby 11Bu bright state, one needs to employ a strongly correlated multireference method. Considering the size of these systems, the CASPT2 method seems to be an excellent choice for these studies since a multideterminant wave function (static electron correlation) and dynamic electron correlation from second order perturbation theory are simultaneously present in this technique. Despite differences between structures and substituents in QBT−(CN)4 and QBTT−(CN)2−(CO2Me)2, there is a rather large hypsochromic shift for all the computed excitation energies of the bright states with respect to their experimental values (2.175 and 2.138 eV, respectively) (see Table 1). 5070

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Figure 1. CASPT2/6-31G(d) PESs of rotations around the central CC bonds (i.e., trans to cis isomerization, left graphs) and one of the terminal CC bonds (right graphs) of QBT−(CN)4 (top) and QBTT−(CN)2−(CO2Me)2 (bottom). Positions of the crossing points between the S1 bright and the 1[TT] dark states are illustrated with arrows. Energies are computed relative to their corresponding 11Ag ground state optimized geometries. See Table 1 for absolute values of the trans isomers. For comparison between CASPT2 and CASSCF PESs see Figure S1, SI.

different singlet (11Ag S0, 1[TT] dark, and 11Bu S1 bright) and triplet (13Bu T1) states (Figure 1). The corresponding CASSCF/6-31G(d) PESs are provided in Figure S1, SI, for comparison. Positions of the crossing points between the 1 [TT] dark and 11Bu S1 bright states are depicted with black arrows. We note that these crossing points are single point energies and therefore might or might not refer to actual minima between these states. All states become destabilized upon rotation around either central or terminal CC bonds (see Figure 1). The central CC bond rotations, which correspond to trans to cis isomerizations in these compounds, create multiple crossing points on the QBT−(CN)4 PESs at the CASPT2/6-31G(d) level. This finding is in complete contrast to the results of Chien et al. (cf. Figure 6 in ref 42) and also Varnavski et al. (cf. Figure S7, SI, in ref 18) as they did not find any crossing point between the mentioned states at the RAS2SF level with 6-31G(d) and cc-pVDZ basis sets, respectively. This discrepancy between RAS-2SF and CASPT2 methods clearly illustrates the importance of the dynamic electron correlation for an accurate description of the correlated states in these systems. The crossing points between the dark and the bright states in QBT−(CN)4 are located very close to the energy of the trans isomer which justifies the experimentally observed ultrafast (≈1 ps) formation of the dark state from the bright one. All energies required to reach these crossing points are in the vibrational region of this compound, i.e. 1466 cm−1 (0.182 eV) for the central CC stretching mode strongly coupled to the 1[TT] dark state.62 The CASPT2 computed energy barriers for trans to cis isomerizations are 1.463, 0.994, and 0.877 eV for the 11Ag ground state, 1[TT] dark, and 11Bu bright states, respectively. This shows that at room temperature the complete trans to cis transformations are unlikely to occur. In contrast to QBT−(CN)4, QBTT−(CN)2−(CO2Me)2 shows no crossing point between the dark and the bright states upon central CC bond rotation. There exists one

Table 2). These backbone modifications might also guide us to finding possible trends in these systems and help us to design new bithiophene based photosensitizers for iSF. While all the quinoidal bi- and tetrathiophenes investigated thus far have had planar geometries and C 2h symmetries, the QBT−Ph compound has a twisted geometry with a reduced C2 symmetry. The SA-CASSCF computed dihedral angles around the central CC bonds for the 11A (S0), 1[TT] dark, and 11B bright geometries are, respectively, 118.2°, 172.6°, and 158.7° and for its 13B (T1) and 13A (T2) states are 169.1° and 128.2°, respectively (see Table S4, SI for coordinates of the optimized geometries). In contrast, QBT−Py is planar and conserves its C2h symmetry for all of its singlet and triplet states (Table S4, SI). Having the same substituents on their terminal CC bonds as QBT−(CN)4, both QBT−Ph and QBT−Py systems shift the computed CASPT2 excitation energies of the dark and the bright states to the red region by ≈0.8 eV (Tables 1 and 2). In the case of the triplet excitation energies, CASPT2 predicts that the T1 and the T2 states are very close in energy and are almost degenerate in the case of the QBT−Ph system (Table 2). Considering the energetic requirement, one can see that none of these structurally modified versions of QBT−(CN)4 can serve as photosensitizers in the iSF process. Therefore, one can conclude that even a small modification of either the main framework or substituents on the terminal CC bonds can impose a great impact on both the structures and energetics of the quinoidal bi- and tetrathiophenes. This is in complete agreement with other studies on biradicaloid heterocycles,56,57 iSF in BN substituted azulene monomers58 and dimers,60 xSF in silicon substituted anthracene,59 and also xSF in pentacene derivatives.61 3.2. CASPT2 Potential Energy Surfaces. CASPT2/631G(d) potential energy surfaces (PESs) of rotations around the central and one of the terminal CC bonds of QBT− (CN)4 and QBTT−(CN)2−(CO2Me)2 are computed for 5071

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Figure 2. CASPT2/6-31G(d) PESs of rotations around the central (i.e., trans to cis isomerization, left graphs) and one of the terminal (right graphs) CC bonds of QBT−H4, QBTT−H4, QBT−(CN)2−(CO2Me)2, and QBTT−(CN)4 molecules. Energies are computed relative to their corresponding ground state optimized geometries. See Tables 1 and S2, SI, for absolute values of the trans isomers. For comparison between CASPT2 and CASSCF PESs see Figure S2, SI.

the case of the QBTT−(CN)2−(CO2Me)2 system as the two states reach at a crossing point at 90° (Figure 1). It has been very recently shown by Busby et al. that the presence of donor−acceptor interactions in organic compounds and polymers creates charge transfer states that can boost the iSF process by strengthening the coupling between the dark and the bright states.63 Through applying this strategy, they successfully designed and synthesized small molecules and polymers with SF quantum yields up to 170%. To probe this strategy in quinoidal systems, we chose to compare the effects of different substituents on the computed CASPT2 PESs of

crossing point after 45° rotation around the terminal CC bond; however, a non-negligible energy of 0.410 eV (9.46 kcal/ mol) is required to reach this crossing point which is not likely to be provided at room temperature. These theoretical findings are in complete agreement with the experimental results that the fluorescence quantum yields of tetrathiophenes are at least 25 times higher than their bithiophene analogues.34 Also, CASPT2 PESs of QBT−(CN)4 show that the 11Ag and the 1 [TT] states approach each other upon rotations around the terminal CC bonds which is in contrast to the previously reported RAS-2SF data.18,42 The situation is more dramatic in 5072

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Journal of Chemical Theory and Computation QBT−(CN) 4 and QBTT−(CN)2 −(CO2 Me)2 molecules (Figure 2); their corresponding CASSCF/6-31G(d) PESs are provided in Figure S2, SI, for comparison. In order to gain more insights, the results for the functionalized systems are compared and contrasted to their unsubstituted forms, i.e. QBT−H4 and QBTT−H4 compounds. The crossing point between the dark and the bright states in QBT−H4 occurs at 15° compared to