Density Analysis of Intra- and Intermolecular Vibronic Couplings

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Letter

Density Analysis of Intra- and Inter-Molecular Vibronic Couplings Toward Bath Engineering for Singlet Fission Soichi Ito, Takanori Nagami, and Masayoshi Nakano J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.5b02249 • Publication Date (Web): 01 Dec 2015 Downloaded from http://pubs.acs.org on December 2, 2015

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The Journal of Physical Chemistry Letters

Density Analysis of Intra- and Inter-Molecular Vibronic Couplings Toward Bath Engineering for Singlet Fission 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]

1 ACS Paragon Plus Environment


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ABSTRACT The vibronic coupling plays a crucial role in singlet fission whereby a singlet exciton splits into two triplet excitons.

In order to reveal the physico-chemical origin of the

vibronic coupling associated with singlet fission as well as to clarify its relationship with chemical structure, we evaluate relevant vibronic couplings from the viewpoint of their spatial contributions described by the vibronic coupling density.

From the analysis using a model

tetracene dimer, a typical singlet fission system, the frequency dependence of vibronic couplings in each electronic state is found to be significantly different from each other depending on the nature of electronic structure (intra-/inter-molecular excitation) and the related vibrational motion.

These findings contribute not only to the fundamental

understanding of singlet fission mechanism from the viewpoint of vibronic couplings, but also to opening a new path to designing highly efficient singlet fission materials through the phonon-bath engineering.

TOC graphic


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Singlet fission, where a singlet exciton generated by light irradiation splits into two triplet excitons, is a promising photophysical process that could improve photo-current conversion efficiency of photovoltaic cells1-4 and that could realize a ultrafast photoswitching by drastic change in nonlinear optical properties.5

In spite of strong curiosity to reveal the

mechanism as well as to construct design guidelines for efficient singlet fission, the mechanism of singlet fission is still not sufficiently clarified.

It was predicted that energy

matching conditions4,6,7 for the related singlet and triplet excited states of monomer as well as electronic coupling4 between monomers are important for efficient singlet fission.

On the

other hand, recent experimental studies using transient spectroscopy have shed light on the existence of strong vibronic coupling (VC) and coherent nuclear vibration in singlet fission process.8

In addition, electronic structure calculations and quantum dynamical simulations

have illuminated significant roles of vibronic coupling in singlet fission.9–16

Nevertheless,

the detailed microscopic origin and structure-property relationships of VC in singlet fission have not been elucidated.

In 2006, Sato et al. have developed a useful tool for analyzing the

vibronic coupling, that is, the vibronic coupling density (VCD).17

They have defined VCD

for both Holstein (HC) and Peierls (PC) couplings,18 where the former and the latter modulate the excited state energy and the electronic coupling, respectively, through molecular vibration. Since the spatial integral of VCD gives the corresponding HC or PC, the VCD enables us to reveal a microscopic origin and a spatial contribution to the VC.

As the first step of

revealing these VC effects on singlet fission, we investigate a microscopic origin of the HCs and PCs related to singlet fission in a model tetracene dimer, a typical singlet fission system, by using the VCD analysis.

The present results will clarify the structure – VCs relationships,

which contribute to paving a new path to designing the VCs, that is, bath engineering, for efficient singlet fission.



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Scheme 1. Tetracene dimer model (a) and five diabatic electronic states (b) essential for singlet fission

The spin-flip time-dependent density functional theory with the Tamm-Dancoff approximation19 together with the collinear approximation20 using the 6-311G* basis set21 and the BHHLYP xc-functional (50% Hartree-Fock exchange and 50% Becke exchange22 with Lee-Yang-Parr correlation23) is employed in the geometry optimization procedure and normal mode analysis in accordance with a previous study.24

Note here that the geometry

optimization is performed not in a dimer but in an isolated monomer. After the geometry optimization of tetracene monomer, we form a slip-stack configuration of two tetracenes, which has an intermolecular distance of 4.0 Å with 0.5 Å shift in the lateral direction (x direction) as shown in Scheme 1a.

Although such model configuration does not correspond

to real tetracene crystal structures, it is often employed in theoretical studies on the relationships between the dimer configuration and electronic coupling,4,25,26 which predict a moderate electronic coupling for the present slip-stack configuration.

In this study, we

consider five diabatic excited electronic states as in previous studies: two Frenkel-type one-electron excited states (FE1 (hA lA)) and FE2 (hB lB)), two charge-transfer excited states (CT1 (hB lA) and CT2 (hA lB)) and a double-triplet state (TT ((hA, hB) (lA, lB))), where, for example, (hA lB) and ((hA, hB) (lA, lB)) indicate the one-electron excitation configuration from orbital h (= Highest Occupied Molecular Orbital (MO)) of monomer A to 4 ACS Paragon Plus Environment

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orbital l (= Lowest Unoccupied MO) of monomer B, and a two-electron excitation configuration from (hA, hB) to (lA, lB), respectively.

These excited electronic states are

assumed to be described well by the above spin-adapted configurations. representations of these diabatic electronic states are shown in Scheme 1b.

Schematic The (frozen)

monomer orbitals, hA, hB, lA and lB, are obtained at the restricted Hartree-Fock (RHF)/cc-pVDZ27 level of theory.

The zero-overlap approximation between MOs belonging

to different molecules is employed as widely used in previous studies.4,13,16,25,26

In VC

calculation in the dimer system, we examine two ways of the superposition of each monomer vibration mode, that is, “in-phase” and “out-of-phase” superposition in the dimer.

The linear

VCs are evaluated from the numerical integration of the corresponding VCDs.

All the

quantum chemistry calculations are performed by using GAMESS2012,28 except for RHF calculation, which is done by Gaussian09.29 program.30

All the densities are sketched using the VMD

A brief summary of the theory of VCD analysis is given in the Supporting

Information.



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Figure 1.

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Holstein couplings of FE1 (a), CT1 (b), and TT (c), and Peierls couplings of

FE1-CT1 (d), FE1-CT2 (e) and CT1-TT (f).

The blue and red lines indicate “in-phase” and

“out-of-phase” vibration contributions, respectively.

The purple, green, and grey numbers

indicate the frequencies (the values in parentheses indicate the vibronic coupling amplitudes) of out-of-plane bending modes, of the ring-breathing modes, and of the C-C stretching modes, respectively.

The calculated VCs, that is, HCs and PCs, of FE1, CT1, CT2, and TT states are shown in Figure 1 (FE1 (a), CT1 (b), and TT (c) for HCs; FE1-CT1 (d), FE1-CT2 (e), and CT1-TT (f) for PCs).

These values indicate amplitudes of VCs (see eqs s2 and s3, and Table

S1–S4 in the Supporting Information).

Selected vibration modes indicated by arrows in

Figure 1 are discussed in detail as examples (see also Figure S3 in the Supporting Information).

Hereafter, “in-phase” and “out-of-phase” modes are represented by adding “i”

and “o” superscripts on the frequency, respectively, for example, a term “100i cm–1 mode”


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represents the vibration mode of dimer, which is composed of the “in-phase” superposition of the vibrational modes (100 cm-1) of two monomers.

A term “100i, o cm–1 mode” is used

when we mention both superpositions, that is, “in-phase” and “out-of-phase” superpositions, of the two monomer vibration modes in the dimer.

First, we examine the HC spectra.

Figure 1a-c show significant differences in overall amplitudes and characteristic frequencies giving large HCs, both of which depend on the electronic states and the relative phase (“in-phase” or “out-of-phase”) of vibrational motion in each monomer. dependence is observed for CT1 and TT states, while not for FE1 state.

The latter

In FE1 state, we

observe three largest HC peaks (263 meV, 268 meV, and 267 meV), which correspond to a ring-breathing mode (1271i,o cm–1), and two carbon-carbon (C-C) stretching modes (1455i,o cm–1 and 1651i,o cm–1), respectively.

In CT1 state, three largest HC peaks (721 meV, 1411

meV, and 1005 meV) correspond to an out-of-plane bending mode (60.5i cm–1) and two ring-breathing modes (328o cm–1 and 794o cm–1), respectively.

In TT state, three largest HC

peaks are observed at the same frequencies as those in FE1 state, though they are observed only in in-phase modes.

The HC intensities of TT state are found to be twice the FE1 ones,

that is, 526 meV (TT) vs. 263 meV (FE1) at 1271i cm-1, 535 meV (TT) vs. 268 meV (FE1) at 1455i cm-1, and 533 meV (TT) vs. 267 meV (FE1) at 1651i cm–1. Next, we investigate the PC spectra.

Figure 1d-f show the PC of each mode

related to vibrational modulation of the electronic couplings between these electronic states, that is, FE1-CT1, FE1-CT2 and CT1-TT couplings.

The PCs related to FE1-CT1 and

FE1-CT2 couplings are shown to have the largest peaks, 43 and 40 meV, respectively, at 60.5o cm–1 (out-of-plane bending mode) as well as two smaller peaks, 32 and 36 meV, respectively, at 328i cm-1 (ring-breathing mode), and 16 and 23 meV, respectively, at 794i cm–1 (ring-breathing mode).

On the other hand, the PC spectra related to CT1-TT coupling show

large peaks with 17 and 32 meV at two out-of-plane bending modes, 60.5o and 202o cm–1,



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respectively.

Figure 2. Difference densities of FE1 (a), CT1 (b), and TT (c), and the transition densities for FE1-TT (d), FE1-CT2 (e), and CT1-TT (f).

The white and blue surfaces indicate positive

and negative isosurfaces (±9x10–4 a.u. for difference densities, and ±5x10–5 a.u. for transition densities), respectively.

In order to obtain an insight into the microscopic origin of the VCs, the vibronic coupling density (VCD) analysis is performed.

Figure 2 shows the difference densities of

FE1 (a), CT1 (b) and TT (c) concerning HCs, and the transition densities for FE1-CT1 (d), FE1-CT2 (e) and CT1-TT (f) concerning PCs. These densities multiplied by the potential derivatives with respect to the corresponding normal mode coordinate provide the VCDs, the spatial integral of which gives the corresponding VCs17,18 (see the Supporting Information for the corresponding vibration modes).

The difference and transition densities are related to

their excitation characters: the difference density is proportional to the difference between the unoccupied and occupied MO densities concerning the excitation, while the transition density


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is proportional to the product of those MOs.

Figure 3. Potential derivative maps of in-phase vibrational motions, 60.5 cm–1 (a), 202 cm–1 (b), 328 cm–1 (c) and 1455 cm–1 (d), as well as of out-of-phase vibrational motions, 60.5 cm–1 (e), 202 cm–1 (f), 328 cm–1 (g) and 1455 cm–1 (h).

The white and blue surfaces represent the

isosurfaces ±0.05 a.u., respectively.



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Figure 4. Vibronic coupling densities: HCs [60.5i cm–1 mode for CT1 state (a), 328o cm–1 mode for CT1 state (b), 1455i cm–1 mode for TT state (c)] and PCs [60.5o cm–1 mode for FE1-CT1 (d), 328i cm–1 mode for FE1-CT1 (e) and 202o cm–1 for CT1-TT (f)].

The white

and blue surfaces represent the isosurfaces ±5x10–5 a.u., respectively.

First, we analyze the difference densities, potential derivatives, and VCD for HCs. As seen from Figure 2a-c, the difference densities of FE1 and TT states show negative distributions for the C-C double bonds due to their π-π* (bonding orbital to anti-bonding orbital) excitation nature typically seen in alternant hydrocarbons, though in TT state, the same difference density distribution is observed in both molecules due to its two-electron excitation nature.

On the other hand, the difference density of CT1 state shows positive and

negative distributions on the upper and the lower molecules, respectively, due to its charge transfer nature.

We here analyze the overlap distributions between these densities and

potential derivatives (see Figure 3a-d for in-phase and 3e-h for out-of-phase).

The potential


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derivative of the C-C stretching mode at 1455i cm–1 (Figure 3d) shows that alternating positive and negative distribution between each C-C bond well overlaps with the difference density of TT state in a common distribution region, leading to the large HC of TT state. Similar difference density distribution in monomer is observed in FE1 and TT states (Figure 2a and c), excepting that FE1 and TT have the distribution in only the upper monomer and in both monomers, respectively.

For in-phase vibrations, therefore, the HC peak intensities of

TT state (Figure 1c) are found to be almost twice those of FE1 state (Figure 1a).

On the

other hand, for out-of-phase vibrations, the HC densities of each molecule for TT state are predicted to be canceled out each other and thus HCs for out-of-phase vibrations are shown to almost vanish (Figure 1c).

The large HCs of TT, which are twice the HCs of FE1, imply that

such high-frequency C-C stretching modes (1271i, 1455i, 1651i cm–1) reduce the energy difference between FE1 and TT states and make them near-degenerate, close to conical intersection, through nuclear motion along these modes and thus can be effective reaction coordinates for FE1-to-TT transition in singlet fission, especially when the in-phase vibration mode is excited.

These reaction coordinates have already been suggested without

considering relative phase of vibration.10

Such vibration is expected to be possible because

the photo-excited states of acenes can be highly delocalized.9

Indeed, the recent observation

of vibronic coherence in ultrafast timescale8 is predicted to be in conformity with the above discussion.

Such effective reaction coordinates would never be found unless one considers

state-dependent VCs, as discussed above. On the HCs of CT1 state, the out-of-phase ring-breathing mode at 328o cm–1 is found to have widely distributed positive (negative) potential derivative in the region around the upper (lower) molecule especially in the middle ring region (Figure 3g), causing a large overlap with the difference density distribution of CT1 state, where positive and negative distributions are separately distributed in the upper and lower molecules, respectively (Figure



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2b).

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As a result, we obtain extended positive distributions of the VCD above and below the

molecular planes (Figure 4b), which lead to a large HC of 1411 meV at 328o cm–1 in CT1 state.

In the in-phase out-of-plane bending modes at 60.5i cm–1, the vibrational motion of

the lower molecule significantly affects the potential derivative distribution near the upper molecule (and vice versa) (see Figure 3a), so that a large HC of CT1 state is observed at this out-of-plane mode (see Figure 2b for the difference density, Figure 4a for the VCD, and the Supporting Information for further discussion). Since a nuclear motion in the intermolecular direction is expected, out-of-plane bending, that is, translational or acoustic modes, which modulate the intermolecular distance in condensed phase, could cause similar effect on that in the case of CT1 state. Thus, long-range HCs induced by such vibrations are predicted to largely oscillate CT state energy and significantly affect the singlet fission dynamics in condensed phase.

These kinds of vibrations should have very low frequencies and should be

easily excited by thermal activation; therefore, the temperature dependence of singlet fission rate in a sort of systems such as crystalline tetracene,31 might be related to the VCs of these vibrations.

Although the previous quantum dynamical simulation studies13,15,16 investigated

such acoustic-mode-like low-frequency mode effect, they focused on only the effect of such low-frequency mode of PCs, not of HCs.

Tao14 addressed the effect of HCs at

low-frequency modes on the singlet fission dynamics, assuming state-independent HCs, though state-dependence is predicted to be crucial especially for such HCs of CT states.

In

this regard, as we have discussed above, HCs of CT states are predicted to be related not only to the high-frequency mode intramolecular vibronic interaction but also to the low-frequency mode intermolecular vibronic interaction. Next, we analyze the PCs in the same manner.

The transition density between FE1

and CT1 (Figure 2d) is shown to have positive distribution between the two molecules because that is proportional to the product of hA and hB.

As seen from Figure 4d, the VCD


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of out-of-plane bending mode at 60.5o cm–1 for FE1-CT1 coupling has larger distributions (with negative sign) in the intermolecular region of the middle rings than in that of the terminal rings (with positive sign), which lead to the large amplitude of the VC, owing to the large distributions of the transition density and potential derivative in this region.

On the

other hand, the potential derivative of a ring-breathing mode at 328i cm–1 is also shown to be largely positive in a wide intermolecular region, causing significant distribution of the related VCD for FE1-CT1 coupling.

The largest CT1-TT coupling in an out-of-plane bending mode

at 202o cm–1 is related to the phase of the transition density and potential derivative.

As seen

from Figure 2f, the transition density between CT1 and TT states is proportional to the product of hA and lB, so that the “moment” of its positive and negative distribution lies in the lateral direction of the molecules.

Figure 3b and f show that the potential derivative of the

202i,o cm–1 mode is positive on the one side of the upper molecule in the lateral direction, while negative on the other side.

Thus, the product of the transition density (Figure 2f) and

potential derivative (Figure 3f) distributions is found to give widely distributed positive VCD in the intermolecular region as shown in Figure 4f. Although we have discussed the dimer in a slip-stack configuration, most our results are expected to be valid for other molecular configurations with some exceptions. Namely, as long as the dimer is put with zero or small displacement in slip-stack configuration, our results are predicted to be applicable.

In a configuration with larger

displacement than a half of the molecular size along the lateral axis, large PC peak modes would be different from those obtained in this study due to the change in the relative phase of molecular orbitals.

Other parts of VCs, not related to the relative phase, are expected to be

similar to those in this study since potential derivatives are localized around a monomer for most vibration modes. Indeed, a recent study on similar molecules in the condensed phase, crystalline pentacene, has clarified the characteristic frequency 1380 cm–1 of vibrations



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mainly contributing to the VC in steady-state spectrum,32 which is similar to the frequencies of large HC modes (1250–1650 cm–1) for the dipole-allowed FE state of the tetracene dimer model in the present study.

This also supports the validity of the above discussion in the

condensed phase. Finally, we speculate a possible way of enhancing singlet fission rate from a bath engineering point of view based on the electron-phonon interaction.

As is well known,

adding or subtracting energy quantum to the bath occurs through a phonon creation or annihilation when an electronic state energy oscillates (HC) or electronic transition occurs (PC).

In this regard, the energy difference |E(FE) – E(TT)| and vibration frequency are

desired to be matched in the case of considering energy conserving terms only.

Indeed, as

shown in the present result, tetracene has a large HC at high frequency (~1500 cm–1 = 0.19 eV), which accidentally nearly matches the energy difference |E(FE) – E(TT)| ~ 0.1–0.2 eV of tetracene or pentacene,4 resulting in their efficient singlet fission. singlet fission would be more attenuated.

If not such matching, the

Namely, a bath engineering, that is, molecular

design of vibronic coupling, so as to match the vibronic coupling peak frequency with the energy difference |E(FE) – E(TT)| would be a promising way of improving the singlet fission rate.

Such vibronic coupling design could be achieved through chemical modifications

based on the VCD analysis.

Indeed, very recent experimental study33 has revealed a crucial

role of VC in efficient singlet fission of pentacene derivatives using ultrafast two-dimensional electronic spectroscopy, which further encourages us to investigate and design VC, that is, bath engineering, for efficient singlet fission. The present study has demonstrated using a model tetracene dimer that the VCs related to the singlet fission strongly depend on both the excited electronic states, that is, intramolecular (FE) and intermolecular (CT and TT) excited states, and vibrational modes such as out-of-plane bending, ring-breathing and C-C stretching modes.

These


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state-dependent vibronic couplings considering intermolecular excitation nature of CT and TT states have not been examined in dynamical simulation of singlet fission, though they are speculated to make a strong impact on singlet fission where a conical intersection may play an important role.8

These characteristics and their physico-chemical origin has been analyzed

by using VCD in detail.

The VCD analysis has clarified (i) that the relative phase of

vibration on each monomer plays an important role on the HCs of CT and TT states due to their intermolecular excitation nature, (ii) that large HCs of FE and TT states in high-frequency C-C stretching mode tend to be observed in π-π* excited state of typical alternant hydrocarbons, (iii) that these C-C stretching modes cause large HC of TT state only in in-phase vibration, so that vibronic coherence in ultrafast time scale8 is possibly generated by this doubly excited nature of TT state and is also possibly a key to be effective reaction coordinates for these modes, (iv) that long-range vibronic coupling induced by the low-frequency out-of-plane and possibly acoustic mode of spatially separated molecules could significantly stabilize or de-stabilize CT states and thus could be a cause of the temperature dependence of singlet fission,31 and (v) that the PCs are primarily caused by the out-of-plane bending and ring-breathing modes owing to the wide distributions of their potential derivatives, which overlap with the transition densities in the intermolecular region. These findings pave a new path to the fundamental understanding of singlet fission mechanism as well as to building rational design principles for highly efficient singlet fission materials from the viewpoint of VC together with VCD,34 though these findings should be combined with quantum dynamics for full understanding of the VC effect on singlet fission dynamics.

Furthermore, more accurate estimation of VCs related to singlet fission in

moderate size systems remains a challenge in the quantum chemistry research in the future. They are in progress in our laboratory.



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AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS This work is supported by JSPS Research Fellowship for Young Scientists (No. 02604505), a Grant-in-Aid for Scientific Research (A) (No. 25248007) from JSPS, a Grant-in-Aid for Scientific

Research

on

Innovative

Areas

“Stimuli-Responsive

Chemical Species”

(A24109002a), “π-System Figuration” (15H00999), “Photosynergetics” (A26107004a), MEXT, the Strategic Programs for Innovative Research (SPIRE), MEXT, and the Computational Materials Science Initiative (CMSI), Japan.

Theoretical calculations are

partly performed using Research Center for Computational Science, Okazaki, Japan.

Supporting Information Available: A brief summary of the theory of vibronic coupling density.

Molecular normal mode vibrations.

low-frequency out-of-plane modes.

Intermolecular vibronic coupling in

Tables of vibronic couplings.


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REFERENCES (1) Nozik, A. J.; Ellingson, R. J.; Micic, O. I.; Blackburn, J. L.; Yu, P.; Murphy, J. E.; Beard, M. C.; Rumbles, G. Proceedings of the 27th DOE Solar Photochemistry Research Conference, June 6-9, 2004, Airline Conference Center, Warrenton, VA; 2004; pp 63-66. (2) Michl, J.; Chen, X.; Rana, G.; Popović, D. B.; Downing, J.; Nozik, A. J.; Johnson, J. C.; Ratner, M. A.; Paci, I. Book of Abstracts, DOE Solar Program Review Meetings, Denver, CO, October 24–28, 2004; U.S. Department of Energy: Washington, DC, 2004; p 5. (3) Hanna, M. C.; Nozik, A. J. Solar Conversion Efficiency of Photovoltaic and Photoelectrolysis Cells with Charge Multiplication Absorbers. J. Appl. Phys. 2006, 100, 074510/1–074510/8. (4) Smith, M. B.; Michl, J. Singlet Fission. Chem. Rev. 2010, 110, 6891–6936. (5) Liu, Y.; Chang, C.; Wang, R.; Chang, B.; Tan, Z.; Wang, X.; Xiao, M. Large Optical Nonlinearity by Singlet Fission in Pentacene Films. Angew. Chem. Int. Ed. 2015, 54, 1–6. (6) Minami, T.; Nakano, M. Diradical Character View of Singlet Fission. J. Phys. Chem. Lett. 2012, 3, 145−150. (7) Nakano, M., Excitation Energies and Properties of Open-Shell Singlet Molecules. Applications to a New Class of Molecules for Nonlinear Optics and Singlet Fission; Springer; 2014. (8) Musser, A. J.; Liebel, M.; Schnedermann, C.; Wende, T.; Kehoe, T. B.; Rao, A.; Kukura, P. Evidence for Conical Intersection Dynamics Mediating Ultrafast Singlet Exciton Fission. Nat. Phys. 2015, 11, 352–357. (9) Zimmerman, P. M.; Bell, F.; Casanova, D.; Head-Gordon, M. Mechanism for Singlet Fission in Pentacene and Tetracene: From Single Exciton. J. Am. Chem. Soc. 2011, 133, 19944–19952. (10) Casanova, D. Electronic Structure Study of Singlet Fission in Tetracene Derivatives. J.



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Chem. Theory Comput. 2014, 10, 324–334. (11) Zeng, T.; Hoffmann, R.; Ananth, N. The Low-lying Electronic States of Pentacene and Their Roles in Singlet Fission. J. Am. Chem. Soc. 2014, 136, 5755–5764. (12) Berkelbach, T. C.; Hybertsen, M. S.; Reichman, D. R. Microscopic Theory of Singlet Exciton Fission. I. General Formulation J. Chem. Phys. 2013, 138, 114102/1–114102/16. (13) Berkelbach, T. C.; Hybertsen, M. S.; Reichman, D. R. Microscopic Theory of Singlet Exciton Fission. II. Application to Pentacene Dimers and the Role of Superexchange. J. Chem. Phys. 2013, 138, 114103/1–114103/12. (14) Tao, G. Bath Effect in Singlet Fission Dynamics. J. Phys. Chem. C 2014, 118, 27258–27264. (15) Tamura, H.; Huix-Rotllant, M.; Burghardt, I.; Olivier, Y.; Beljonne, D. First-Principles Quantum Dynamics of Singlet Fission: Coherent vs Thermally Activated Mechanisms Governed by Molecular π Stacking. Phys. Rev. Lett. 2015, 115, 107401/1–107401/5. (16) Renaud, N.; Grozema, F. C. Intermolecular Vibrational Modes Speed Up Singlet Fission in Perylenediimide Crystals. J. Phys. Chem. Lett. 2015, 6, 360–165. (17) Sato, T.; Tokunaga, K.; Tanaka, K. Vibronic Coupling in Cyclopeantadienyl Radical: A Method for Calculation of Vibronic Coupling Constant and Vibronic Coupling Density Analysis. J. Chem. Phys. 2006, 124, 024314/1–024314/12. (18) Sato, T.; Uejima, M.; Iwahara, N.; Hatura, N.; Shizu, K; Tanaka, K. Vibronic Coupling Density and Related Concepts. J. Phys.: Conf. Ser., 2013, 428, 012010/1–012010/19. (19) Hirata, S.; Head-Gordon, M. Time-Dependent Density Functional Theory within the Tamm-Dancoff Approximation. Chem. Phys. Lett. 1999, 314, 291−299. (20) Shao, Y.; Head-Gordon, M.; Krylov, A. I. The Spin-Flip Approach with Time-Dependent Density Functional Theory: Theory and Applications to Diradicals. J. Chem. Phys. 2003, 118, 4807–4818.


Page 19 of 26

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(21) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. Self-Consistent Molecular Orbital Methods. XX. A Basis Set for Correlated Wavefunctions. J. Chem. Phys. 1980, 72, 650–654. (22) Becke, A. D. Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior. Phys. Rev. A 1998, 38, 3098−3100. (23) Lee, C.; Yang, W.; Parr, P. G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785−789. (24) Minami, T.; Ito, S.; Nakano, M. Signature of Singlet Open-Shell Character on the Optically Allowed Singlet Excitation Energy and Singlet-Triplet Energy Gap. J. Phys. Chem. A 2013, 117, 2000–2006. (25) Smith, M. B.; Michl, J. Recent Advances in Singlet Fission. Annu. Rev. Phys. Chem. 2013, 64, 361–386. (26) Wang, L.; Olivier, Y.; Prezhdo, O. V.; Beljonne, D. Maximizing Singlet Fission by Intermolecular Packing. J. Phys. Chem. Lett. 2014, 5, 3345–3353. (27) Dunning Jr. T. H. Gaussian Basis Sets for Use in Correlated Moleculer Calculations. I. The Atoms Boron through Neon and Hydrogen. J. Chem. Phys. 1989, 90, 1007–1023. (28) Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S. J.; et al. General Atomic and Molecular Electronic Structure System. J. Comput. Chem. 1993, 14, 1347–1363. (29) 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 09, Revision B.01; Gaussian, Inc.: Wallingford, CT, 2010. (30) Humphrey, W.; Dalke, A; Schulten, K. VMD – Visual Molecular Dynamics J. Molec. Graphics, 1996, 14, 33–38. (31) Piland, G. B.; Bardeen, C. J. How Morphology Affects Singlet Fission in Crystalline Tetracene. J. Phys. Chem. Lett. 2015, 6, 1841–1846.



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(32) Hestand, N. J.; Yamagata, H.; Xu, B.; Sun, D.; Zhong, Y.; Harutyunyan, A. R.; Chen, G.; Dai, H.-L.; Rao, Y.; Spano, F. C. Polarized Absorption in Crystalline Pentacene: Theory vs Experiment. J. Phys. Chem. C 2015, 119, 22137–22147. (33) Bakulin, A. A.; Morgan, S. E.; Kehoe, T. B.; Wilson, M. W. B.; Chin, A. W.; Zigmantas, D.; Egorova, D.; Rao, A. Real-Time Observation of Multiexcitonic States in Ultrafast Singlet Fission

Using

Coherent

2D

Electronic

Spectroscopy.

Nat.

Chem.

2015,

DOI:10.1038/NCHEM.2371. (34) Uebe, M.; Ito, A.; Kameoka, Y.; Sato, T.; Tanaka, K. Fluorescence Enhancement of Non-Fluorescent Triphenylamine: A Recipe to Utilize Carborane Cluster Substitutents. Chem. Phys. Lett. 2015, 633, 190–194.


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(a) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(b)

1271 cm–1

794 cm–1 (1005 meV)

1651 cm–1 1455 cm–1

328

cm–1

Frequency [cm–1]

Frequency [cm–1]

(e)

60.5 cm–1

1455 cm–1 1651 cm–1 1271 cm–1

328 cm–1 (1411 meV) 60.5 cm–1

Frequency [cm–1]

(d)

(c)

(f)

60.5 cm–1 328 cm–1

60.5 cm–1 202 cm–1

794 cm–1

794 cm–1

Frequency [cm–1]

ACS Paragon Plus Environment –1

Frequency [cm ]

Frequency [cm–1]


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Difference density (a)

(b)

FE1

(c)

CT1

TT

Transition density (d)

(f)

(e)

FE1-CT1

FE1-CT2

ACS Paragon Plus Environment

CT1-TT

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Potential derivative (a)

In-phase (c)

(b)

60.5i cm-1

(e)

202i cm-1

328i cm-1 Out-of-phase (g)

(f)

60.5o cm-1

(d)

202o cm-1

(h)

328o cm-1


1455i cm-1

1455o cm-1


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Holstein coupling density (a)

(b)

CT1 60.5i cm–1

(c)

CT1 328o cm–1

TT 1455i cm–1

Peierls coupling density (d)

(f)

(e)

FE1-CT1 60.5o cm–1

FE1-CT1 328i cm–1 ACS Paragon Plus Environment

CT1-TT 202o cm–1

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a)

(b)

z

A

lA

lB

hA

hB

A

B

FE2

FE1

4.0 Å B

x 0.5 Å

CT1


CT2

TT


Vibronic Couplings in Singlet Fission Vibronic coupling!

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CT!

TT!

FE! ω"


Density Analysis of Intra- and Intermolecular Vibronic Couplings

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