Design Principles of Electronic Couplings for Intramolecular Singlet

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Design Principles of Electronic Couplings for Intramolecular Singlet Fission in Covalently-Linked Systems Soichi Ito, Takanori Nagami, and Masayoshi Nakano J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b07153 • Publication Date (Web): 22 Jul 2016 Downloaded from http://pubs.acs.org on July 28, 2016

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The Journal of Physical Chemistry

Design Principles of Electronic Couplings for Intramolecular Singlet Fission in Covalently-Linked Systems Soichi Ito, Takanori Nagami, and Masayoshi Nakano* Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan [email protected] Tel: +81-6-6850-6265

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ABSTRACT We theoretically investigate the singlet fission in three types of covalently-linked systems, that is, ortho-, meta- and para-linked pentacene dimers, where these are shown to have significantly different singlet fission rates.

Each molecule is composed of two

chromophores (pentacenes), which are active sites for singlet fission, and covalent bridges linking them.

We clarify the origin of the difference in the electronic couplings in these

systems, which are found to well support a recent experimental observation.

It is also found

that the next-nearest-neighbor interaction is indispensable for intramolecular singlet fission in these systems.

On the basis of these results, we present design principles for efficient

intramolecular singlet fission in covalently-linked systems and demonstrate the performance by using several novel conjugated linkers.


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1. INTRODUCTION Singlet fission (SF) is a spin-allowed photochemical process where a singlet exciton splits into two triplet excitons in sub-picosecond time scale.1,2

This phenomenon has fascinated

researchers in a variety of fields due to its high possibilities of overcoming the Shockley-Queisser limit in photovoltaic cells3 as well as of ultrafast photo-switching.4 It is known that the exothermic condition, 2E(T1) – E(S1) < 0, where E(S1) and E(T1) are the excitation energies of the lowest singlet excited and triplet states, respectively, is important for efficient SF. 1,2,5

In addition to this energy level matching condition,1,2,5–9 electronic coupling

between neighboring chromophores is also known to be important.1,2

Although the crystal

engineering on relative configurations of chromophores is a possible way to modify the electronic coupling, 10,11 it is difficult to perform the rational design of crystal structure due to the complicated intermolecular or environmental interactions.

To overcome this difficulty,

the tuning of the electronic coupling in covalently-linked dimers has been investigated,12–21 where two chromophores are covalently linked via a bridge.

Zirzlmeier et al. have

discovered very high SF efficiency up to 156% in covalently-linked systems composed of two pentacenes linked via ortho-, meta- and para-diethynylbenzenes (referred to as o-Pc, m-Pc and p-Pc, respectively, see Scheme 1(a)-(c)), respectively.14 found significant difference in their SF time constants.

Interestingly, they have also

Nevertheless, the physical origin of

the difference, especially of the effect of bridges, has not been clarified sufficiently. Pentacene, which was used as a SF chromophore in that study, is one of the best-investigated molecules in for SF and is known to be exothermic for SF, 2E(T1) – E(S1) = –0.11 eV.22,23 This indicates that the electronic coupling is a key factor for understanding the different SF dynamics in these systems.

Indeed, although there have been a few studies focusing on the

effect of bridges on the electronic coupling based on ab initio calculations,12,13,17,19,21 the physical origin of the bridge effect and the relationship between the electronic coupling and



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the bridge structure still remain unclear.

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In this study, first, we theoretically investigate

covalently-linked systems with different linkers shown in Scheme 1(a)-(c) and clarify how these differ in the electronic couplings.

Then, on the basis of the analysis results, we present

design principles that realize moderate electronic couplings suitable for SF in covalently-linked systems and propose new bridges to demonstrate the performance of our design principles.

2. COMPUTATIONAL DETAILS From Fermi's golden rule combined with the symmetric form of the second-order quasi-degenerate perturbation theory,2, 24 the SF rate is predicted to be proportional to the square of the SF electronic coupling VSF,

,

(1)

where ES1S0, ETT and ECT represent the energies of singlet exciton, double-triplet exciton and charge-transfer exciton, respectively; Fij represent the Fock matrix elements; Hm and Ln represent the highest occupied molecular orbital (HOMO) and the lowest unoccupied orbital (LUMO), respectively, of the chromophore m and n.

The energies in the denominators in eq

1 are taken from experimental values ES1S0 = ES1 = 1.83 eV and ETT = 2ET1 = 0.86 x 2 = 1.72 eV.

The charge-transfer state energy ECT is treated as a parameter, ECT = ES1 + 0.6 eV = 2.43

eV.

The choice of ECT does not siginificantly change the evaluated VSF value, see the

Supporting Information.

The Fock matrix elements Fij in eq 1 are evaluated by using a

Green's function approach.25

In this approach, the Fock matrix elements are described as

matrix elements of the effective Fock operator: ,

(2)

where Fˆ and Fˆ eff are the original and effective Fock operators; I is the identity operator; P


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and Q are projection operators that project the one-electron orbital space onto the HOMO and LUMO of the chromophores, and onto the other MOs, respectively; Gˆ Qˆ †Qˆ is the Green's function depending on the Fermi energy E.

The details of the derivation and evaluation of

eq 2 are given in ref 25 and in the Supporting Information.

The Green’s function approach

allows us to partition each matrix element Fij into two types of contributions, "direct-overlap" and "bridge-mediated" couplings, which are the first and the second terms in eq 2, respectively.

The former is the direct interaction between π-orbitals of the chromophores,

while the latter is the indirect interaction between the chromophores’ MOs through the bridge MOs.

The advantage of the method will be seen in the analysis of the results. We here use a density functional theory (DFT) with the M06 xc-functional26 and

cc-pVDZ basis set27 to optimize the geometries with no point group symmetries and to evaluate the matrix elements.

In the radical molecule (Rad-Pc in Scheme 1(f)),

spin-unrestricted DFT calculation is performed and the Fock matrices of alpha and beta spins are averaged in the evaluation of eq 2.

High-level ab initio quantum chemistry methods are

found to give similar values of electronic couplings to those obtained by a method based on DFT.28–30

We consider one-electron coupling terms in this study, while we ignore

two-electron coupling ones, since the latter is known to be typically much smaller than the former,1,2,28–30 though there are some exceptions.19,21

The validity of this assumption will be

examined by comparing the calculation result and experimental observation.

All the

quantum chemistry calculations are performed by using the Gaussian 09 program package.31 The Green's function is evaluated combined with the Gaussian 09 program and a homemade program.

3. RESULTS AND DISCUSSION 3.1 Direct-Overlap and Bridge-Mediated Electronic Couplings 5 ACS Paragon Plus Environment


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First, we discuss the result about experimentally investigated systems o-, m- and p-Pc.

The

electronic couplings, that is, Fock matrix elements and VSF, are summarized in Table 1.

It is

found from Table 1 that the direct-overlap couplings are the largest in o-Pc, while they are two or three orders of magnitude smaller in m-Pc and p-Pc.

This feature is understood from

the geometry of o-Pc, which suggests significant direct π-orbital overlap between the chromophores (see Figure 1a).

On the other hand, it is also found that the bridge-mediated

couplings are two or three orders of magnitude larger in p-Pc and o-Pc than those in m-Pc. Therefore, the magnitude of total electronic coupling Fij, the sum of the direct-overlap and bridge-mediated couplings, is found to decrease in the order: o-Pc > p-Pc > m-Pc. ordering is also found in the SF coupling amplitude |VSF|.

The same

This tendency of |VSF| is found to

be in qualitative agreement with the SF rate observed by a transient spectroscopy.14

This

agreement with the experiment indicates that VSF in these systems are qualitatively but well explained by assuming that they are dominated by the one-electron coupling terms (direct-overlap and bridge-mediated couplings) rather than by two-electron coupling terms.

3.2 Analysis of Interference Effect in Bridge-Mediated Coupling In order to clarify the origin of the difference in the electronic couplings in o-, m- and p-Pc, we analyze the results by using physically appropriate approximations (see the Supporting Information).

The formula derived for the bridge-mediated term is expressed as,

,

(3)

where β is the resonance integral; c is a MO coefficient; subscripts i and j denote the H1, L1, H2, or L2; HB and LB indicate the HOMO and LUMO of the bridge with orbital energies EHB and ELB, respectively; subscripts 1, 2 and B represent the chromophore 1, 2 and the bridge, respectively; Greek subscripts with and without prime indicate a pair of carbon atoms, where a fragment pair (1 and B) or (2 and B) is linked with the chemical bond µ'–µ or ν'–ν; E 6 ACS Paragon Plus Environment

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denotes the Fermi energy level.

In eq 3, the denominators are positive because the Fermi

energy E is shown to lie in between EHB and ELB (see Figure S15).

The prefactor of eq 3

implies that the HOMO and LUMO of the chromophores are required to have moderate amplitudes at the linked carbon atoms for moderate bridge-mediated coupling, though its relative phase is not important.

On the other hand, the two terms in the parenthesis imply

that the relative phase between the HB and LB is crucial for moderate bridge-mediated coupling: it becomes constructive when the relative sign of the products in the numerators is different, while destructive when that is the same.

In alternant hydrocarbons, this is the case

for the bridges in o-, m- and p-Pc, where all the carbon atoms can be grouped into starred and non-starred carbon atoms in the way that any neighboring carbon atoms belong to the different group exclusively, the relative phase of the HB and LB at the linked carbon atoms is predicted by Coulson-Rushbrooke pairing theorem.32

The theorem states that only the

starred-carbon atoms change their MO coefficients in sign between the HOMO and LUMO. This theorem results in large bridge-mediated coupling when two chromophores are linked at starred and non-starred carbons of a bridge, while small when linked at two starred (or two non-starred) carbons of a bridge.

o-Pc and p-Pc are classified into the former and thus are

predicted to have opposite sign at the linked carbon in the HB and LB, while m-Pc is classified into the latter and thus is predicted to have the same sign.

These predictions on

the relative phase of the MOs are in agreement with the results by ab initio calculation as shown in Figure 1a–c.

For further confirmation of the validity of the above prediction and

its effect on bridge-mediated coupling, we decompose the bridge-mediated coupling into the contributions of each bridge MO (see Figure 2).

In Figure 2, bridge-mediated couplings are

evaluated using eq S25 in the Supporting Information, which is the parent formula of eq 3 and is found to give essentially the same result with that from eq 2 (shown in Table 1 as a result). From Figure 2, constructive interferences, that is, the same sign of contributions from HB–i



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and LB+i (i = 0, 1, 2, ...), are found in o-Pc and p-Pc, while destructive interference in m-Pc, which are in agreement with the prediction above obtained from eq 3 and the pairing theorem.

3.3 Design Principles for Covalently-Linked Singlet Fission Systems On the basis of these results, we present new practical design principles for efficient intramolecular SF in addition to the previous two types of bridges, that is, bridges putting two chromophores in a small distance such as o-Pc, and using alternant hydrocarbon bridges linked at starred and non-starred carbons such as p- and o-Pc. Recall that although our explanations of the experimental SF rates and its relationship with electronic couplings are based on alternancy symmetry of the bridges, the simplified formula eq 3 itself is not restricted in use for other systems. additional design principles.

Setting eq 3 as the starting point, we present three

First, non-alternant hydrocarbons like azulene are expected to

have neither constructive nor destructive interference in eq 3 because only one of the two terms in the parentheses is present when the linking position is chosen properly (see below). Second, considering the denominators in eq 3, destruction of the MO energy symmetry about the 2p atomic orbital energy level, which corresponds to "α" in the Hückel theory, is expected to be another way to realize moderate electronic coupling even in meta-conjugated systems such as m-Pc.

For example, the MO energy symmetry is expected to be broken by

introducing heteroatoms such as nitrogen and boron, and donor/acceptor substituents into the bridge.

As a result, the residue term due to incomplete destructive interference is predicted

to give moderate contribution.

Third, a bridge with a radical is also speculated to give

moderate electronic couplings since such a bridge is expected to have a small gap between the energy of a singly occupied MO and the Fermi energy.

Note that these situations are not

exclusive with each other. As application examples of these principles, we have designed three types of


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bridges shown in scheme 1(d)-(f), which are referred to Az-Pc, Nm-Pc and Rad-Pc, respectively.

It is found that these bridges induce moderate and a wide range of VSF (1–138

meV) (see Table 1).

The validity of the mechanisms that induces moderate electronic

coupling in them can be confirmed by checking the shape and energy of MOs in the bridges. In the bridge of Az-Pc (see Figure 1d), the LB has significant amplitude at the linked carbon atoms, while the HB does not because these carbon atoms correspond to a node, resulting in significant and zero contributions in the bridge-mediated coupling from LB and HB, respectively, that is, moderate VSF.

In Nm-Pc, we find the breaking of orbital energy

symmetry (Figure S1 and S2) be the key for enhancement in two orders in magnitude of VSF, from 0.01 meV to 1 meV.

In Rad-Pc, as expected, small energy difference in the

denominator (Figure S15) is turned out to be crucial for moderate VSF in this system. details in other systems, Nm-Pc and Rad-Pc, see the Supporting Information.

For

Before

closing this section, we note that heteroatom substitution is a well-known strategy in SF research area, where it is conducted to modify the energy levels of singlet and triplet excited states.9, 33, 34

They are, however, not based on the same motivation as that in this study.

The heteroatom substitution in the bridge proposed in this study is not to modify the excitation energies but to enhance the electronic coupling VSF.

3.4 Next-Nearest-Neighbor Interaction Finally, we discuss the importance of the next-nearest-neighbor (NNN) interaction and its contribution for realizing SF, though the discussion below does not affect the design principles discussed above qualitatively.

A role of the NNN interaction on intramolecular SF

was pointed out in ref 9, where the authors discussed the effect in, roughly speaking, what we call the direct-overlap coupling. bridge-mediated coupling.

Here, we discuss the NNN interaction effect in the

For realizing moderate amplitude of SF coupling VSF in eq 1, not



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only the amplitude of each electronic coupling Fij, but also the difference between FH1H2 and FL1L2 is required to be large.

Note that we here consider a symmetric system, where FH1L2

and FL1H2 are equal, and this is the case of the present systems (see also Sec S-VIII on the relative phase of the MOs, which is crucial for the sign of the coupling matrix elements Fij.). It is found that the difference between bridge-mediated contributions in FH1H2 and FL1L2 does not come from the nearest-neighbor interaction but actually from the NNN interaction.

This

is because, at least, in the Hückel-like approximation including only the nearest-neighbor interactions, the bridge-mediated contributions in FH1H2 and FL1L2 coincide with each other in systems with alternant hydrocarbon chromophores due to the pairing theorem, that is, the prefactor in eq 3, cµ'icν'jβ2, is the same for any pairs of i and j.

In Figure 3, the red and blue

lines indicate the nearest-neighbor and NNN carbon atoms, respectively. We see there is one nearest-neighbor contribution described as (a, a') pair, and are three contributions partly or purely including the NNN interaction described as (a, b'), (b, a') and (b, b') pairs.

Here, since

the chromophore, pentacene, is also an alternant hydrocarbon, the orbital coefficients at the starred carbon atoms indicated by * and *' in Figure 3 also have the opposite sign between the HOMO and LUMO in each chromophore, while those at the non-starred carbon atoms the same sign.

Thus, the two NNN contributions indicated by (a, b') and (b, a') pairs are

expected to give mutually opposite sign between FH1H2 and FL1L2, resulting in |FH1H2| > |FL1L2|, that is, non-zero VSF (see Table 1).

On the contrary, the pure NNN contribution indicated by

(b, b') pair is expected to give no contribution to the difference between FH1H2 and FL1L2 because they are the same in sign and amplitude by the pairing theorem.

It is therefore

found that as long as we consider alternant hydrocarbon chromophores, where SF active sites and the linked sites are the same for both chromophores, the difference between FH1H2 and FL1L2 is always expected to be non-zero, resulting in non-zero VSF.

This is in contrast to the

case of non-linked chromophores in crystal phase, where VSF is highly sensitive to the crystal


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packing and is sometimes almost zero by accidentally or by symmetry.1,2

This mechanism

of enhancing the difference between |FH1H2| and |FL1L2| is an advantage of covalently-linked systems rather than non-linked systems, which strongly promotes further investigation of those systems.

Note that although our analysis results, where constructive and destructive

interference effects are well-explained by the Hückel approximation and the paring theorem, actually have been known in a different field, molecular conductivity,35 in that field, the NNN interaction is usually unnoticed due to its insignificant effect in such an application.

This is

not the case in SF as shown here, where the bridge-mediated SF coupling would be zero without consideration of the NNN interaction.

We also note that, although the NNN

interaction is necessary for obtaining a finite value of VSF, this does not affect, at least qualitatively, the design principles described in the previous section.

4. CONCLUDING REMARKS In the present study, we have investigated the intramolecular SF in covalently-linked systems using the Green's function approach with ab initio MO calculations by partitioning the electronic couplings into the direct-overlap and bridge-mediated contributions.

On the basis

of the analysis of the results, we have found a structure–property relationship on the bridge-mediated electronic coupling: moderate electronic couplings originating from the additive contribution is obtained when chromophores are linked at starred and non-starred carbons with alternant hydrocarbon bridges, while negligible electronic coupling from the subtractive contribution is obtained when linked at two starred carbons.

The present results

have been found to qualitatively reproduce the relative SF rates observed in the experiment. From those results, we have presented new and practical design principles for alternative



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promising bridges toward efficient intramolecular SF, i.e., non-alternant hydrocarbons, heteroatom- and donor/acceptor-substituted bridges, and radical species.

Qualitative

prediction of the NNN interaction has illuminated its importance for non-zero VSF in covalently-linked systems.

Further exploration of efficient intramolecular SF systems based

on the design principles as well as on the SF dynamics are necessary for comprehensive understanding of intramolecular SF.

ASSOCIATED CONTENT Supporting Information Details of the Green's function theory and electronic structure calculation. energy symmetry breaking.

Full effective Fock matrix elements.

in this work for evaluating VSF. exact and effective Fock matrices.

Effect of orbital

Energy parameters used

Discussion on partitioning arbitrariness.

Eigenvalues of

Molecular orbitals of bridges and chromophores.

This

material is available free of charge via the Internet at http://pubs.acs.org.

ACKNOWLEDGEMENTS This work is supported by JSPS KAKENHI Grant Number JPA2645050 in JSPS Research Fellowship for Young Scientists, Grant Number JP25248007 in Scientific Research (A), Grant Number JP24109002 in Scientific Research on Innovative Areas “Stimuli-Responsive Chemical Species”, Grant Number JP15H00999 in Scientific Research on Innovative Areas “π-System Figuration”, and Grant Number JP26107004 in Scientific Research on Innovative Areas “Photosynergetics”.

Theoretical calculations were partly performed using the

Research Center for Computational Science, Okazaki, Japan.


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Long-Lived Triplet Excited States of Bent-Shaped Pentacene Dimers by Intramolecular Singlet Fission. J. Phys. Chem. A 2016, 120, 1867–1875. (21) Fuemmeler, E. G.; Sanders, S. N.; Pun, A. B.; Kumarasamy, E.; Zeng, T.; Miyata, K.; Steigerwald, M. L.; Zhu, X.-Y.; Sfeir, M. Y.; Campos, L. M. et al. A Direct Mechanism of Ultrafast Intramolecular Singlet Fission in Pentacene Dimers. ACS Cent. Sci. 2016, 2, 316−324. (22) Sebastian, L.; Weiser, G.; Bässler, H. Charge Transfer Transitions in Solid Tetracene and Pentacene Studied by Electroabsorption. Chem. Phys. 1981, 61, 125–135. (23) Burgos, J.; Pope, M.; Swenberg, C. E.; Alfano, R. R. Heterofission in Pentacene-doped Tetracene Single Crystals. Phys. Status Solidi B 1977, 83, 249–256. (24) Shavitt, I.; Redmon, L. T. Quasidegenerate perturbation theories. A Canonical van Vleck Formalism and Its Relationship to Other Approaches. J. Chem. Phys. 1980, 73, 5711–5717. (25) de Andrade, P. C. P.; Freire, J. A. Electron Transfer in Proteins: Nonorthogonal Projections onto Donor–acceptor Subspace of the Hilbert Space. J. Chem. Phys. 2004, 120, 7811–7819. (26) Zhao, Y.; Truhlar, D. G. The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited states, and Transition Elements: Two New Functionals and Systematic Testing of Four M06-class Functionals and 12 Other Functionals. Theor. Chem. Acc. 2008, 120, 215–241. (27) Dunning Jr., T. H. Gaussian Basis Sets for Use in Correlated Molecular Calculations. I. The Atoms Boron through Neon and Hydrogen. J. Chem. Phys. 1989, 90, 1007–1023. (28) Chan, W.-L.; Berkelbach, T. C.; Provorse, M. R.; Monahan, N. R.; Tritsch, J. R.; Hybertsen, M. S.; Reichman, D.; Gao, J.; Zhu, Z.-Y. The Quantum Coherent Mechanism for Singlet Fission: Experiment and Theory. Acc. Chem. Res. 2013, 46, 1321–1329. (29) Zeng, T.; Hoffmann, R.; Ananth, N. The Low-Lying Electronic States of Pentacene and



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Their Roles in Singlet Fission. J. Am. Chem. Soc. 2014, 136, 5755−5764. (30) Parker, S. M.; Seideman, T.; Ratner, M. A.; Shiozaki, T. Model Hamiltonian Analysis of Singlet Fission from First Principles. J. Phys. Chem. C 2015, 118, 12700–12705. (31) Gaussian 09, Revision B.01, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A. et al. Gaussian, Inc., Wallingford CT, 2009. (32) Coulson, C. A.; O’Leary, B.; Mallion, R. B. Hückel Theory for Organic Chemists, Academic Press, London, 1978. (33) Zeng, T.; Ananth, N.; Hoffmann, R. Seeking Small Molecules for Singlet Fission: A Heteroatom Substitution Strategy. J. Am. Chem. Soc. 2014, 136, 12638−12647. (34) Chen, Y.; Shen, L.; Li, X. Effects of Heteroatoms of Tetracene and Pentacene Derivatives on Their Stability and Singlet Fission. J. Phys. Chem. A 2014, 118, 5700−5708. (35) Tada, T.; Yoshizawa, K. Phys. Chem. Chem. Phys. 2015, 17, 32099–32110.


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Table 1. Electronic Couplingsa [meV] Calculated at RM06/cc-pVDZ26,27 Level of Theory and Experimental SF Time Constant τSF [ps] Direct-overlap coupling Bridge-mediated coupling Molecule FH1H2 FH1L2 FL1L2 FH1H2 FH1L2 FL1L2 |VSF| τSFb 47 -117 347 120 97 82 169 0.5 o-Pc 6 -1 3 3 0 -1 0.01 63 m-Pc 1 -6 4 -129 -101 -81 10 2.7 p-Pc -2 6 -3 158 117 91 16 N/A Az-Pc -2 2 0 40 26 18 1 N/A Nm-Pc 15 -1 -9 444 329 244 138 N/A Rad-Pc a FL1H2 is almost the same as FH1L2 due to the approximate symmetry of the molecular structures (see Table S1–3 and S5–7), and thus is not shown here. b Ref 14.



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FIGURE CAPTIONS

Scheme 1. Molecular structures of pentacene dimers linked with diethynylphenyl bridges. The chromophores and bridge are indicated by red and blue lines, respectively.

The

substituent R in (a)-(c) is a hydrogen atom in this study, though triisobutylsilylethynyl substituent is employed in the experiment.14

The carbons in the bridge of (a)-(c) are grouped

into starred and non-starred carbons (see text). (d)-(f) are newly proposed molecules in this study (see text).

Figure 1. Molecular orbitals in the bridge moiety of (a) o-Pc, (b) m-Pc, (c) p-Pc and (d) Az-Pc.

Isovalue is ±0.03 au. Note the relative phase and amplitude in the HB and LB at

linked carbons. See the Supporting Information for more details.

Figure 2. Contributions through each bridge MO for the bridge-mediated coupling in (a) o-Pc, (b) m-Pc and (c) p-Pc.

Here, the "B" of H and L indicating the bridge MO is omitted.

"Sum" denotes the total sum of all the contributions.

Figure 3. The largest nearest-neighbor (chemical bond) contribution (a, a'), the second largest contribution partly including the next-nearest-neighbor interaction ((a, b') and (b, a')), and the third largest contribution from only the next-nearest-neighbor interaction (b, b') in p-Pc, as an example, are shown. non-starred groups.

In each molecule, all the carbon sites are grouped into starred and Unessential parts of the chemical structure are omitted.


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Scheme 1. Molecular structures of pentacene dimers linked with diethynylphenyl bridges. The chromophores and bridge are indicated by red and blue lines, respectively.

The

substituent R in (a)-(c) is a hydrogen atom in this study, though triisobutylsilylethynyl substituent is employed in the experiment.14

The carbons in the bridge of (a)-(c) are grouped

into starred and non-starred carbons (see text). (d)-(f) are newly proposed molecules in this study (see text).



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Figure 1. Molecular orbitals in the bridge moiety of (a) o-Pc, (b) m-Pc, (c) p-Pc and (d) Az-Pc.

Isovalue is ±0.03 au. Note the relative phase and amplitude in the HB and LB at

linked carbons. See the Supporting Information for more details.


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Figure 2. Contributions through each bridge MO for the bridge-mediated coupling in (a) o-Pc, (b) m-Pc and (c) p-Pc.

Here, the "B" of H and L indicating the bridge MO is omitted.

"Sum" denotes the total sum of all the contributions.



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Figure 3. The largest nearest-neighbor (chemical bond) contribution (a, a'), the second largest contribution partly including the next-nearest-neighbor interaction ((a, b') and (b, a')), and the third largest contribution from only the next-nearest-neighbor interaction (b, b') in p-Pc, as an example, are shown. non-starred groups.

In each molecule, all the carbon sites are grouped into starred and Unessential parts of the chemical structure are omitted.


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JPCA


Design Principles of Electronic Couplings for Intramolecular Singlet

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