Enhancement of fluorescence in anthracene by chlorination: Vibronic coupling and transition dipole moment density analysis

Chemical Physics 430 (2014) 47–55

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Enhancement of fluorescence in anthracene by chlorination: Vibronic coupling and transition dipole moment density analysis Motoyuki Uejima a, Tohru Sato a,b,⇑, Kazuyoshi Tanaka a, Hironori Kaji c a

Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan Unit of Elements Strategy Initiative for Catalysts & Batteries, Kyoto University, Kyoto 615-8510, Japan c Institute for Chemical Research, Kyoto University, Gokasho, Uji, Kyoto 611-0011, Japan b

a r t i c l e

i n f o

Article history: Received 8 November 2013 In final form 24 December 2013 Available online 3 January 2014 Keywords: Anthracene Chloroanthracene Internal conversion Quantum yield Vibronic coupling

a b s t r a c t The vibronic coupling constants and transition dipole moments for the Franck–Condon and adiabatic S1 states of anthracene, 9-chloroanthracene, and 9,10-dichloroanthracene were calculated and analyzed by using the concept of vibronic coupling density (VCD). The transition dipole moments are also analyzed on the basis of the transition dipole moment density (TDMD). The VCD analyses indicate that the vibronic couplings in the Franck–Condon S1 state come from the side rings of anthracene, and introduction of chlorine atoms reduces the vibronic couplings in the side regions and the reorganization energy. The TDMD analyses indicate that the chlorination enhances the transition dipole moment and that the contribution of the chlorine atom to the transition dipole moment is the largest. Finally, we derived a design principle for anthracene derivatives with a high quantum yield: the same long acceptors should be introduced into the two central carbon atoms in the anthracene’s central ring for the derivative to keep the point group to be D2h . Ó 2014 Elsevier B.V. All rights reserved.

1. Introduction Photoluminescence (PL) and electroluminescence (EL) are important phenomena in material chemistry as well as photochemistry, and have attracted much attention for applications such as organic light-emitting diodes (OLEDs) [1–8]. The first modern double-injection OLED was achieved using an anthracene monocrystal [9]. Anthracene is one of the most important materials in the OLED field because its derivatives have high fluorescence quantum yields [10]. Radiative and radiationless processes in anthracene have been theoretically investigated [11,12] and compared with the experimental fluorescence quantum yield (UF  0:3 [13–16]). The fluorescence quantum yield is determined by the competition between radiative and radiationless processes. Internal conversion (IC), vibrational relaxation (VR), and intersystem crossing (ISC) are categorized as radiationless processes. VR gives rise to energy dissipation. On the other hand, IC and ISC suppress a fluorescence process because IC and ISC are main competitive processes. The spectroscopy in superfluid helium droplets suggests the importance of the energy dissipation of VRs. [17]. A theoretical and

⇑ Corresponding author at: Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan. Tel.: +81 75 383 2803; fax: +81 75 383 2555. E-mail address: [email protected] (T. Sato). 0301-0104/$ - see front matter Ó 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.chemphys.2013.12.015

experimental study on oligoacenes has indicated that the small UF for anthracene comes from the high rate of ISCs [11]. Within Pariser–Parr–Pople configuration interaction (PPP-CI) calculations, the energy level for the S1 ð1 B1u Þ state has been shown to lie almost higher than that for the T4 ð3 B2u Þ state, so that the rate of ISC S1 ð1 B1u Þ ! T4 ð3 B2u Þ becomes large. Another semiempirical complete neglect of differential overlap (CNDO) calculation also shows that the rate of the ISCs exceeds that of the fluorescence [12]. The dominant radiationless process has been ascribed to the ISC because the CNDO energy level for the S1 state is higher than that for the T2 state. However, the energy level for the T2 state lies lower than that for the S1 state [18] on the basis of time-dependent density functional theory (TD-DFT) [19]. It should be noted that ISC S1 ð1 B1u Þ ! T1 ð3 B1u Þ is symmetrically forbidden because of the selection rule for spin–orbit couplings. For anthracene, the reported orders of the energy levels are discrepant. In the configuration interaction singles (CIS) [20] and TDDFT [19] calculations, the S1 state was assigned to B1u. On the other hand, the assignment of the S1 state was B2u [21] at the level of the multireference Møller–Plesset (MRMP) theory [22]. However, ultrahigh-resolution fluorescence excitation and dispersed fluorescence spectra showed that the S1 state belongs to B1u with the aid of the symmetry adapted cluster configuration interaction (SAC-CI) [23] calculation [24]. According to previously reported high-resolution spectra of the S1 ð1 B1u Þ S0 ð1 Ag Þ transition of anthracene, the quantum yield UF is lowered from 0.67 to 0.18 by deuteration [25,26]. This is

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M. Uejima et al. / Chemical Physics 430 (2014) 47–55

due to the change in the density of states for the singlet and triplet states, leading to an increase in the rate of ISC [25,26]. If the ISCs are enhanced by deuteration, the Zeeman splitting is expected to be large. However, large Zeeman splitting was not observed in the ultrahigh-resolution spectra [24], indicating that the dominant radiationless process should be ICs. Consequently, it is meaningful to study the intramolecular vibronic couplings for anthracene. Anthracene (A), 9-chloroanthracene (CA), and 9,10-dichloroanthracene (DCA), as shown in Fig. 1, have UF values of 0.33, 0.11, and 0.53, respectively [15]. The fluorescence quantum yield UF for DCA is the largest of the three molecules. This suggests that fluorescence in DCA should be the dominant process rather than IC. Understanding the PL processes for the anthracene derivatives opens up the possibility of developing anthracene derivatives with high quantum yields. Vibronic couplings are the driving force of VRs and ICs. Diagonal vibronic couplings give rise to VRs, which lead to energy loss. In addition, they reduce the Franck–Condon (FC) factors in the vertical electronic transition, because strong diagonal vibronic couplings give rise to a large displacement in the FC state. Small FC factors result in small rate constants of fluorescence. Therefore, small diagonal vibronic couplings are preferable for high efficiency. Off-diagonal vibronic couplings are responsible for ICs. The suppression of off-diagonal vibronic couplings can increase the fluorescence quantum yield. We can reduce the vibronic coupling constants (VCCs) of the molecules by using the concept of vibronic coupling density (VCD) [27–29]. The VCD analysis provides a local picture of a vibronic coupling, so that we can obtain useful information for reducing VCCs. In carrier-transporting molecules, vibronic couplings are responsible for lowering the mobility. By using the VCD concept, we have theoretically designed two molecules with small VCCs for hole/electron-transporting materials, hexaaza½16 parabiphenylophane (HAPBP) [30] and hexaboracyclophane (HBCP) [31]. The VCD analysis can be also applied to an excited state of a molecule [32]. Therefore, we can expect to design fluorescent molecules with small VCCs by using the VCD analysis. A large transition dipole moment can lead to strong fluorescence. We have also proposed the concept of transition dipole moment density (TDMD) [32]. By using both VCD and TDMD analyses, we can control the radiative and radiationless processes of molecules. To design a highly efficient fluorescent molecule, VRs in the FC excited states should be small, and the dominant process should be fluorescence rather than ICs. In this article, we will explain the difference in the UF values for A, CA, and DCA in terms of VCD and

TDMD analyses. The purpose of the present paper is to establish a design principle for molecules with high fluorescence quantum yields. We expound the VCC, VCD, TDMD, and related concepts in Section 2. In Section 3, we explain the method of calculation. In Section 4.1, we show the calculated excitation energies and oscillator strengths for the three molecules in the FC and adiabatic (AD) states, respectively. In Section 4.2, we show the calculated diagonal VCCs in the FC S1 state of the three molecules. In Section 4.3, we describe the diagonal VCDs for the susceptible modes to the chlorinations in the FC S1 state. In Section 4.4, we show the off-diagonal VCCs between the S1 and S0 states of the AD S1 state. In Section 4.5, we describe the off-diagonal VCDs for the susceptible modes to the chlorinations in the off-diagonal VCCs. In Section 4.6, we discuss the differences in the transition dipole moments among the three molecules using the TDMD concept. We summarize the present work and propose the design principle in Section 5. 2. Theory 2.1. Vibronic coupling constant The electronic wave function in the nth excited Sn state of a molecule is defined by Wn ðr; RÞ, which is the eigenfunction of a molecular Hamiltonian Hðr; RÞ. Here, r and R denote sets of electronic coordinates and nuclear coordinates, respectively. The minimum nuclear configuration of the potential surface in the Sn state is denoted as Rn . Consider an absorption in a molecule with configuration R0 in the ground state S0 to excited state Sn. Since the initial state is S0 with the nuclear configuration R0 , the vibronic coupling constant in the final state of FC Sn state is defined with Wn ðr; R0 Þ, where R0 is treated as a fixed parameter. The linear diagonal vibronic coupling constant for Sn with respect to normal mode a is given by Köppel et al. [33]

  +  @Hðr; RÞ    ; W ðr; R Þ  n 0   @Q a R0

* V n;a ¼

Wn ðr; R0 Þ

ð1Þ

where Q a is the normal coordinate of mode a. The diagonal VCC is used in the calculation of the reorganization energy for the VR in the FC state. The off-diagonal VCC is a driving force in the IC Sm ! Sn . Since the IC Sm ! Sn should start from the AD state of Sm, it is reasonable to take Sm state as a reference state. The off-diagonal VCC is defined by

* V mn;a ¼

  +  @Hðr; RÞ    Wn ðr; Rm Þ ;   @Q a Rm

Wm ðr; Rm Þ

ð2Þ

where Q a is the normal coordinate of mode a in the Sm state. In this study, we denote m and n as initial and final states, respectively. We take S0 and S1 as the reference states for the diagonal and off-diagonal VCC calculations, respectively. 2.2. Reorganization Energy The vibronic Hamiltonian in the FC Sn state within the crude adiabatic (CA) approximation [33,34] is given by

Hvib n ¼ En ðR 0 Þ ( X h2 þ  2 a Fig. 1. Chemical structures of chloroanthracenes: anthracene A, 9-chloroanthracene CA, and 9,10-dichloroanthracene DCA.

@2 @Q 2a

!  V n;a Q a þ

) 1 2 xn;a Q 2a þ    ; 2

ð3Þ

where xn;a denotes the frequency of mode a. The adiabatic potential ECA n ðRÞ within the CA approximation is given by

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M. Uejima et al. / Chemical Physics 430 (2014) 47–55

9 8 !2 2 = X<1 V V n; a a n; CA En ðRÞ ¼ En ðR0 Þ þ x2n;a Q a  2  ; 2 :2 xn;a 2xn;a ; a

2.4. Transition dipole moment density

ð4Þ

where we take the directions of the normal modes so that the coefficients of the first-order Q a are negative. Within the CA approximation, the reorganization energy in the FC Sn state DECA n is defined by

DECA n

¼

X

kn;a

a

X V 2n;a ¼ ; 2 a 2xn;a

ð5Þ

V 2n;a : 2x2n;a

ð6Þ

We can examine the validity of the CA approximation by comparing the reorganization energy using the Born–Oppenheimer (BO) approximation. Within the BO approximation, the adiabatic potential is

EBO n ðRÞ ¼ hWn ðr; RÞjHe ðr; RÞjWn ðr; RÞi þ U nn ðRÞ;

ð7Þ

where He is the electronic Hamiltonian, and U nn is the nuclear–nuclear potential. Since the electronic wave function depends on the nuclear coordinates, calculations for various nuclear configurations R are required to obtain the BO potential. The reorganization energy within the BO approximation is given by

DEBO n

¼ En ðRn Þ  En ðR0 Þ:

ð8Þ

The validity of the CA approximation for the present systems can be CA checked by the following condition: DEBO n  DEn . The change in the fluorescence quantum yields caused by deuteration suggests that the BO approximation breaks with the vibronic couplings in the S1 state [24,25,35]. 2.3. Vibronic coupling density The diagonal VCD [27–29] gn;a ðxÞ in the FC Sn state is defined by

gn;a ðxÞ ¼ Dqn ðxÞv a ðxÞ;

ð9Þ

where Dqn is the electron-density difference at R0 between the electron density in the Sn state, qn , and that in the ground state, q0 :

Dqn ðxÞ ¼ qn ðxÞ  q0 ðxÞ:

ð10Þ

The potential derivative v a is defined as the derivative of the nuclear-electronic potential for single electron uðxÞ with respect to Q a :

v a ðxÞ ¼

  @uðxÞ : @Q a R0

ð11Þ

The spatial integral of gn;a is equal to the diagonal VCC V n;a :

V n;a ¼

Z

gn;a ðxÞd3 x:

ð12Þ

The diagonal VCD enables us to discuss the diagonal VCC in the FC Sn state in terms of electronic and vibrational structures. The off-diagonal VCD gmn;a ðxÞ between Sm and Sn states is given by Sato et al. [32]

gmn;a ðxÞ ¼ qmn ðxÞv a ðxÞ;

ð13Þ

where qmn denotes the overlap density (transition density) at Rm between the Sm and Sn states. The integral of gmn;a yields

V mn;a ¼

Z

gmn;a ðxÞd3 x:

lmn ¼ hWm ðr; Rm Þjl^ jWn ðr; Rm Þi;

ð15Þ

^ denotes the electric dipole moment operator given by where l

X

l^ ¼ 

eri :

ð16Þ

i

where kn;a represents the reorganization energy for mode a, given by

kn;a ¼

The transition dipole moment lmn for the Sm ! Sn transition is given by

ð14Þ

The off-diagonal VCD analysis allows us to tune the off-diagonal element of vibronic couplings.

The transition dipole moment density [32] is defined by a density form of the transition dipole moment as a function of the spatial coordinate x ¼ ðx; y; zÞ:

smn ðxÞ ¼ ex qmn ðxÞ:

ð17Þ

Note that we can set the origin of the position vector x for a transition dipole moment anywhere, though smn depends on the choice of the origin. This is because the transition dipole moment is invariant with respect to the choice of the origin. We set the origin of x at the center of the charges. The integral of smn is equal to the transition dipole moment, given by

lmn ¼

Z

smn d3 x ¼

Z

3

ex qmn ðxÞ d x:

ð18Þ

We can capture the features of the transition dipole moment via the TDMD analysis. A widespread distribution of overlap density leads to a large dipole moment. 3. Method of calculation The structures of A, CA, and DCA in the S0 state were optimized at the B3LYP/cc-pVTZ level of theory. The optimized structures of the molecules were confirmed to be minima by using vibrational analyses. We used TD-DFT for the calculation of the S1 states. In order to confirm whether the TD-B3LYP calculation is appropriate or not, we also calculated using the complete active space self-consistent field (CASSCF) and CASSCF plus second-order perturbation theory (CASPT2) [36]. The structure of A in the S0 state was optimized at the CASSCF level. The state-averaged CASSCF was performed using the (12,12) active space, employing the ccpVDZ basis set. The six occupied p orbitals and six unoccupied p orbitals that are the same as in the previous study [21] were used for the active space. Furthermore, single-state CASPT2 (SSCASPT2) and multi-state CASPT2 (MS-CASPT2) were performed. We calculated the forces in the FC S1 states at the TD-B3LYP/ccpVTZ level. The diagonal VCCs in the FC S1 states were calculated by using the matrix elements of the force matrices and normal modes obtained from vibrational analyses. We adopted the normal modes with strong VCCs that are greatly changed by the chlorination for the VCD analyses in the FC S1 states. These modes are called susceptible modes, hereafter. We also obtained the AD S1 state from the geometrical optimization for the S1 states at the TD-B3LYP/cc-pVTZ level. To calculate the off-diagonal VCCs and VCDs at the R1 nuclear configuration, we obtained the normal modes by using vibrational analyses for the S1 state. We calculated the off-diagonal VCCs between the S1 and S0 states at R1 . VCD analyses between the S1 and S0 states were applied for the susceptible normal modes to the chlorinations. We calculated the TDMD between the S1 and S0 states of the optimized structures of the S1 state. The TD-B3LYP calculation was performed using the Gaussian 09 program [37]. The CASSCF and CASPT2 calculations were carried out using the MOLCAS [38]. We employed our codes for the VCC, VCD, and TDMD calculations.

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M. Uejima et al. / Chemical Physics 430 (2014) 47–55

experiment. In contrast, CA has the lowest UF in the experiment while the calculated f10 for CA is larger than for A. This suggests that radiationless processes also play an important role.

4. Results and discussion 4.1. Excitation energy and oscillator strength Vertical transition energies E, transition dipole moments jlmn j and oscillator strengths fmn in the FC Sn (n = 1–3) and AD S1 states are listed in Table 1. The vertical transition energies for the FC S1 states (S1 S0) of A, CA, and DCA are in agreement with experimental absorption wavelengths [15,39]. The observed absorption wavelengths and fluorescence quantum yields in gas phase and those in condensed phase are almost identical, and therefore, the difference in the phase does not matter in this system. The calculated excitation energies E and oscillator strengths f0n for Sn states (n = 1–3) of A are consistent with the previous TD-DFT calculation [18]. However, the excitation energies for the S1 states of A, CA, and DCA obtained from the CIS calculations [16] are larger than those from the present TD-B3LYP calculations. The vertical transition energies (Sn S0) obtained from the TD-B3LYP, CASPT2 calculations are summarized in Table S1 in the Supporting Information as well as those obtained from the previously reported MRMP [21], SAC-CI [24] calculations, and experiments [24,40– 46]. The S1 state was shown to be B2u for A [21] on the basis of the MRMP calculation [22]. However, the excitation energies at the MRMP level are slightly smaller than those at the SS-CASPT2 level. According to the ultrahigh-resolution spectra with the analysis of the Zeeman splittings [24], the 11 B2u state was assigned to S2 that lies 0.16 eV higher than the 11 B1u (S1) state. This is consistent with the SAC-CI calculation [24] and the other experiments [40,42,43,45]. The excitation energies obtained from the TDB3LYP calculations are also consistent with the experiments [24,40–46]. Therefore, we employed the results of the TD-B3LYP calculations for the further analyses. The calculated f01 (S1 S0) values fall in the order A < CA < DCA. The differences in the oscillator strengths between the FC state f01 and AD state f10 (S1 ! S0 ) are small so that the order of f10 in the AD S1 state remains the same as that in the FC S1 state: A < CA < DCA. The fact that DCA has the largest f10 of the three molecules is consistent with the fact that it exhibited the largest UF in the Table 1 Vertical transition energies E (eV), oscillator strengths f, transition dipole moments Molecule

a b c d e f g h i j

c

Fig. 3(b1)–(b3) shows the potential derivatives v a with respect to the susceptible modes to the chlorinations for A, CA, and DCA. The distributions of v a for the molecules are similar because the susceptible modes to the chlorinations are almost the same. The electron-density differences Dq1 are depicted in Fig. 5(a1)–(a3). The electron-density differences Dq1 are distributed on the side rings of the molecules, especially in the regions along the C2–C3 and C6–C7 bonds. The negative Dq1 around the C9 atom is large in CA and that around the C9 and C10 atoms is large in DCA.

l (a.u.), and experimental fluorescence quantum yields UF . CISb

Experiment

l

f

E

f

E

E (UF )

3.21 3.84 4.50

0.04 0.00 0.00

4.0352

(0.30d, 0.31e) 3.48d, 3.43f, 3.47g

3.2138 3.8714 4.5521 2.7677

0.8160 (z) 0.0747 (y) – 0.8939 (z)

0.0524 0.0005 – 0.0542

CA S1 S2 S3 S1 !

S0 S0 S0 S0

3.1064 3.8209 4.4870 2.6730

0.9582 0.0237 0.0530 1.0363

0.0700 0.0001 0.0003 0.0700

Ref. Ref. The Ref. Ref. Ref. Ref. Ref. Ref. Ref.

4.3. Diagonal vibronic coupling density analysis

E S0 S0 S0 S0

S0 S0 S0 S0

Fig. 2 shows the diagonal VCCs in the FC S1 state. The normal modes 48, 48, and 49 indicated by the arrows in the figures represent the second strongest coupling modes for A, CA, and DCA, respectively. They are susceptible to the chlorinations: Chlorination leads to the decrease in the VCCs for these normal modes. Fig. 3(a1–a3) shows the susceptible modes to the chlorinations for A, CA, and DCA. These modes correspond to C–C stretchings. It is found that the modes are almost the same. The reorganization energies for the normal modes, k1;a , are shown in Fig. 4. The reduction in the VCC for the susceptible mode to the chlorinations gives rise to the decrease in the total reorganization energy DE1 . The reorganization energies within the CA and BO approximations and the experimental Stokes shifts are summarized in Table 2. Reorganization energies within the CA approximation, DECA 1 , were calculated with the frequencies in the S0 state instead of those in the S1 state. Reorganization energies DECA 1 agree well with reorganization energies within the BO approximation, DEBO 1 . This indicates that the CA approximation which the VCD concept is based on can be applied for the present systems.

TD-B3LYPa

Present work

A S1 S2 S3 S1 !

DCA S1 S2 S3 S1 !

4.2. Vibronic coupling constant in the Franck–Condon S1 state

3.0001 3.7664 4.4135 2.5799

(z) (y) (y) (z)

1.2308 (z) 0.1118 (y) – 1.1853 (z)

0.0905 0.0012 – 0.0889

[18], TD-B3LYP/6–311G (d,p). [16], CIS/6–311G⁄⁄. directions of the transition dipole moments are given in the parentheses. [15]. [48]. [39]. [43]. [49]. [50]. [51].

3.12d 3.9436

(0.11d, 0.083f, 0.13h) 3.37d, 3.34f, 3.16h

3.8485

(0.53d, 0.55e, 0.58f, 0.51h, 0.56i) 3.27d, 3.22f, 3.07h, 3.07j

3.01d, 2.97h

2.90d, 2.88h

M. Uejima et al. / Chemical Physics 430 (2014) 47–55

(a)

(b)

51

(c)

Fig. 2. Vibronic coupling constants in the Franck–Condon S1 state: (a) anthracene A, (b) 9-chloroanthracene CA, and (c) 9,10-dichloroanthracene DCA. The peaks indicated by the arrows show the second strongest coupling modes, which are susceptible to the chlorinations.

Fig. 3. The susceptible modes to the chlorinations (a1–a3) and derivatives of the electronic-nuclear potentials with respect to their modes v a (b1–b3): (a1, b1) A (x48 ¼ 1427:55 cm1), (a2, b2) CA (x48 ¼ 1420:09 cm1), and (a3, b3) DCA (x49 ¼ 1409:13 cm1). The isovalue for v a is 1  102 a.u. White regions are positive; blue regions are negative. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

(a)

(b)

(c)

Fig. 4. Reorganization energies for the active modes in the Franck–Condon S1 state, k1;a : (a) A, (b) CA, and (c) DCA.

Table 2 Reorganization energies in the Sn state, DEn , calculated within the crude adiabatic (CA) and Born–Oppenheimer (BO) approximations, and Stokes shifts ESt in eV.

DE1 (S1)

A CA DCA a

DE0 (S0)

ESt

CA

BO

CA

BO

CA

BO

Exp.a

0.2332 0.2275 0.2211

0.2268 0.2189 0.2141

0.2126 0.2059 0.1995

0.2193 0.2127 0.2061

0.4459 0.4334 0.4206

0.4461 0.4316 0.4202

0.367 0.359 0.374

Ref. [15].

The diagonal vibronic coupling densities g1;a are shown in Fig. 5(b1–b3). One can see that g1;a on the chlorine atoms is small.

DCA has a large positive g1;a around the C9 and C10 atoms because Dq1 is large in the same region. This positive g1;a contributes to the reduction in the VCC. The positive g1;a appears on the C2, C3, C6, and C7 atoms with the chlorination because the positive Dq1 s are distributed on the atoms in the chlorinated anthracenes. The positive g1;a on the C2, C3, C6, and C7 atoms also reduces the VCC. For this reason, the VCCs for the susceptible modes become small with the chlorination. The VCCs are decomposed into atomic vibronic coupling constants (AVCCs) [32]. The diagonal AVCCs for the susceptible modes are also shown in Fig. 5(b1–b3). The AVCCs for the C2, C3, C6, and C7 atoms are the largest in A and DCA, and the AVCCs for the C2 and C7 atoms are the largest in CA. This is consistent with the

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M. Uejima et al. / Chemical Physics 430 (2014) 47–55

Fig. 5. Electron-density differences between the S1 and S0 states, Dq1 (a1–a3) and diagonal vibronic coupling densities in the Franck–Condon S1 state for the susceptible normal modes to the chlorinations, g1;a (b1–b3): (a1, b1) A, (a2, b2) CA, and (a3, b3) DCA. Atomic vibronic coupling constants in 105 a.u. are shown in (b1–b3). Large AVCC values are shown in red and those reduced significantly by chlorinations are shown in blue. The isovalues for Dq1 and g1;a are 2  103 and 1  105 in atomic units, respectively. White regions are positive; blue regions are negative. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

distributions of g1;a . The AVCCs for the C2, C3, C6, and C7 atoms become small because of the positive g1;a . To suppress the VCCs and DE1 for anthracene, Dq1 localized on the edge carbon atoms should be reduced. This finding can be helpful for designing molecules with a low energy loss in VR.

4.4. Off-diagonal vibronic coupling constant between the S1 and S0 states Off-diagonal vibronic couplings give rise to an IC, which is responsible for the radiationless transitions. The off-diagonal VCCs between the S1 and S0 states are shown in Fig. 6. The order of the sums of the absolute values of the off-diagonal P VCCs over normal mode a jV 10;a j, with their values in 104 atomic units, are as follows: DCA (1.24) < A (1.30) < CA (1.69), indicating that the off-diagonal VCCs for DCA are reduced and those for CA are increased. This is because CA has about twice as many active modes as A and DCA, owing to a lower degree of symmetry than A and DCA. A and DCA belong to the D2h point group whereas CA belongs to the C 2v point group. The irreducible representations (irrep) for the

electronic state S1 of A, CA, and DCA correspond to B1u ; A1 , and B1u , respectively. According to the selection rule for vibronic couplings, the B1u ; A1 , and B1u modes are vibronically active between the S1 and S0 states in A, CA, and DCA, respectively. The inactive Ag modes in the higher D2h symmetry correspond to the active A1 modes in the lower C 2v , according to the compatibility relations between C 2v and D2h :

B1u # C 2v ¼ A1 ;

Ag # C 2v ¼ A1 :

ð19Þ

A and DCA have 11 active modes of B1u :

CðD2h Þ ¼ 12Ag þ 4B1g þ 6B2g þ 11B3g þ 5Bu þ 11B1u þ 11B2u þ 6B3u :

ð20Þ

In contrast, CA has 23 active modes of A1 :

CðC 2v Þ ¼ 23A1 þ 9A2 þ 12B1 þ 22B2 :

ð21Þ

For this reason, CA has about twice as many active modes as A and DCA. This suggests that CA has the lowest UF because of the large number of the coupling channels. Our goal is to establish the design principle for molecules with high quantum yields, and we found out the second principle by

Fig. 6. Off-diagonal vibronic coupling constants between the S1 and S0 states: (a) A, (b) CA, and (c) DCA. The peaks indicated by the arrows show the second strongest coupling modes, which are susceptible to the chlorinations.

M. Uejima et al. / Chemical Physics 430 (2014) 47–55

analyzing the off-diagonal vibronic couplings. As discussed in the previous subsection, the first principle is reduction in Dq1 on the edge carbon atoms. The second principle that we obtain here is as follows: The symmetry of a molecular structure should be kept as high as possible. For the anthracene derivatives, D2h symmetry is desirable to suppress the increase in the number of the coupling channels for the IC. From Fig. 6 it is found that VCC for the second strongest coupling mode becomes large as the number of chlorine atoms increases. These modes are susceptible to the chlorinations in the off-diagonal vibronic couplings. The susceptible modes for A, CA, and DCA are shown in Fig. 7(a1)–(a3). One can see that the normal mode is localized on the C9–C14 atoms. We analyze the offdiagonal VCCs for the susceptible normal modes to the chlorinations in terms of the off-diagonal VCD.

4.5. Off-diagonal vibronic coupling density between the S1 and S0 States The potential derivatives with respect to the susceptible normal modes to the chlorinations are shown in Fig. 7(b1)–(b3). Because the normal mode is localized on the central ring, v a s on the central C9–C14 atoms become large. The overlap densities q10 are depicted in Fig. 8(a1)–(a3). Small q10 s appear on the chlorine atoms for CA and DCA. These small q10 s do not contribute to the decrease in the VCCs because of the symmetric distributions. However, the distribution enhances the TDMD, as described in the following subsection. The overlap densities q10 on the C9 and C10 atoms are also symmetrically distributed. The off-diagonal vibronic coupling densities g10;a on the C9 and C10 atoms cancel in the spatial integration. The vibronic coupling densities g10;a are depicted in Fig. 8(b1)– (b3). Because of the large v a s around the carbon atoms in the central ring, g10;a s on the C9–C14 atoms become large. As mentioned above, cancellations occur on the C9 and C10 atoms in the spatial integration of g10;a . It is naturally understood that the g10;a s on the chlorine atoms are small because q10 s are small.

53

The off-diagonal AVCCs between the S1 and S0 for A, CA, and DCA are also shown in Fig. 8(b1)–(b3). The magnitudes of the AVCCs are consistent with the distributions of g10;a . The AVCCs for C9 and C10 atoms are small, and those for the C11–C14 atoms are large. It is found that the AVCCs for C11–C14 atoms increase with the chlorination. The VCD analysis showed that q10 on the atoms of the central ring in anthracene should be reduced in order to avoid the unpreferable increase in VCCs with substitutions. 4.6. Transition dipole moment density analysis of the S1 and S0 states A large transition dipole moment enhances the radiative process. As shown in Table 1, DCA has the largest transition dipole moment l10 . To clarify why DCA has the largest l10 , we use the TDMD concept. The overlap densities q10 on the chlorine atoms enhance the z component of l10 , as shown in Fig. 8(a1)–(a3). The z components of the transition dipole moments between the S1 and S0 states, s10;z , are shown in Fig. 9. Because the chlorine atoms are positioned a long distance from the center of the charges, and because q10 s are localized on the chlorine atoms, the s10;z s become large on the chlorine atoms. Thus, we have discovered that the small portion of the overlap density on the chlorine atoms enhances the transition dipole moment. The overlap density q10 can be expressed as a linear combination of orbital overlap densities:

q10 ¼

X

C ij wi wj ;

ð22Þ

ij

where wi and wj indicate the molecular orbitals, and C ij denotes the expansion coefficient. The main contribution of the orbital overlap densities to q10 is ascribed to the overlap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). Fig. 10 shows the HOMOs and LUMOs with their energy levels for A, CA, and DCA. The small portion of q10 on the chlorine atoms comes from the small molecular orbital coefficients of the chlorine atoms in the HOMOs. In other words, the chlorine atoms withdraw q10 .

Fig. 7. The susceptible modes to the chlorinations in the adiabatic S1 states (a1–a3) and derivatives of the electronic-nuclear potentials with respect to their modes v a (b1– b3): (a1, b1) A (x42 ¼ 1291:08 cm1), (a2, b2) CA (x44 ¼ 1289:63 cm1), and (a3, b3) DCA (x45 ¼ 1277:36 cm1). The isovalue for v a is 1  102 a.u. White regions are positive; blue regions are negative. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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M. Uejima et al. / Chemical Physics 430 (2014) 47–55

Fig. 8. Overlap densities between the S1 and S0 states, q10 (a1–a3) and off-diagonal vibronic coupling densities between S1–S0 states and the susceptible modes to the chlorinations, g10;a (b1–b3): (a1, b1) A, (a2, b2) CA, and (a3, b3) DCA. Atomic vibronic coupling constants in 105 a.u. are shown in (b1–b3). Large AVCC values are shown in red and those reduced significantly by chlorinations are shown in blue. The isovalues for q10 and g10;a are 5  103 and 5  105 in atomic units, respectively. White regions are positive; blue regions are negative. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

(a)

(b)

(c)

Fig. 9. Transition dipole moment densities between the S1 and S0 states in the z direction, s10;z , for (a) A, (b) CA, and (c) DCA. The isovalue is 1  102 a.u. White regions are positive; blue regions are negative. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

If long acceptors are introduced into the C9 and C10 atoms, a widespread overlap density on the substituents can be expected, in addition to a large transition dipole moment. The introduction of the acceptors also makes it possible to reduce the overlap density on the carbon atoms in the central ring and the electron-density difference at the sides of the anthracene. The high D2h symmetry has advantage of the suppression in the IC, as discussed in Section 4.5. Therefore, the design principle for a molecule with a high quantum yield is as follows: the same long acceptors should be introduced into the C9 and C10 atoms along the C9–C10 axis for the derivative to retain the point group to be D2h . 5. Conclusion

Fig. 10. Energy levels of the HOMO and LUMO for chloride anthracenes. The isovalue for the molecular orbitals in this figure is 5  102 a.u. White regions are positive; blue regions are negative. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

We calculated the VCCs and transition dipole moments for the S1 states of anthracene A, 9-chloroanthracene CA, and 9,10-dichloroanthracene DCA at the TD-B3LYP/cc-pVTZ level of theory. The effect of the chlorinations on the vibronic couplings and transition dipole moments was analyzed by using the VCD and TDMD concepts, respectively.

M. Uejima et al. / Chemical Physics 430 (2014) 47–55

The calculated reorganization energy for DCA is the smallest. This is consistent with the experimentally verified fact that the largest UF is found in DCA [15]. The reorganization energy becomes small with the chlorination because the diagonal VCCs decrease with the chlorination. By using the VCD concept, we found that the vibronic couplings in the FC states mainly come from the sides of the anthracene because the electron density difference Dq1 is localized on the side of the molecule. It is found that Dq1 s on the carbon atoms on the sides become small with the chlorination. The off-diagonal vibronic couplings between the S1 and S0 states of the structures of the AD S1 states originate from the center ring because of the large overlap densities Dq10 in the central region. Furthermore, CA has the largest number of vibronically active modes because CA has the lowest symmetry, C 2v , of the three molecules. This suggests the large rate of IC (S1 ! S0 ) and small UF in CA. The transition dipole moments are enhanced with the chlorination. From the TDMD analysis, we have found that the small portion of the overlap density q10 on the chlorine atom leads to the large s10;z on chlorine atoms and large transition dipole moment. The small portion of q10 results from the fact that the chlorine atoms withdraw q10 . DCA has the smallest reorganization energy, the smallest number of active modes, and the largest transition dipole moment. Thus, DCA has the highest UF . The similar behavior was found in chloronaphthalene [47] and the TDMD and VCD analyses can explain this. To confirm whether the present theory is generally applicable or not, the application of the TDMD and VCD analyses to the chloronaphthalene will be reported. Finally, the design principle for anthracene derivatives with high fluorescence quantum yields is as follows: The same long acceptors into the C9 and C10 atoms should be introduced along the C9–C10 axis for the derivative to keep the point group to be D2h . On the basis of this principle, we have succeeded in experimentally achieving a high fluorescence quantum yield in an anthracene derivative, and will report in the near future.

[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]

Acknowledgement Numerical calculations were performed partly at the Supercomputer Laboratory of Kyoto University and the Research Center for Computational Science, Okazaki, Japan. This research was partly supported by the Japan Society for the Promotion of Science (JSPS) through its Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST Program). Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.chemphys.2013. 12.015. References [1] C.W. Tang, S.A. VanSlyke, Appl. Phys. Lett. 51 (1987) 913. [2] C. Adachi, T. Tsutsui, S. Saito, Appl. Phys. Lett. 55 (1989) 1489. [3] R.H. Friend, R.W. Gymer, A.B. Holmes, J.H. Burroughes, R.N. Marks, C. Taliani, D.D.C. Bradley, D.A.D. Santos, J.L. Brédas, M. Löglund, W.R. Salaneck, Nature 397 (1999) 121.

[38]

[39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51]

55

M.A. Baldo, M.E. Thompson, S.R. Forrest, Nature 403 (2000) 750. L.S. Hung, C.H. Chen, Mater. Sci. Eng. R 39 (2002) 143. B.W. D’Andrade, S.R. Forrest, Adv. Mater. 16 (2004) 1585. C.C. Wu, Y.T. Lin, K.T. Wong, R.T. Chen, Y.Y. Chien, Adv. Mater. 16 (2004) 61. R.J. Tseng, R.C. Chiechi, F. Wudl, Y. Yang, Appl. Phys. Lett. 88 (2006) 093512. W. Helfrich, W.G. Schneider, Phys. Rev. Lett. 14 (1965) 229. S.-K. Kim, B. Yang, Y. Ma, J.-H. Lee, J.-W. Park, J. Mater. Chem. 18 (2008) 3376. N. Nijegorodov, V. Ramachandran, D.P. Winkoun, Spectrochim. Acta Part A 53 (1997) 1813. Y.F. Pedash, O.V. Prezhdo, S.I. Kotelevski, V.V. Prezhdo, J. Mol. Struct. Theor. 585 (2002) 49. G. Weber, F.W.J. Teale, Trans. Faraday Soc. 53 (1957) 646. W.R. Dawson, M.W. Windsor, J. Phys. Chem. 72 (1968) 3251. S. Atesß, A. Yildiz, J. Chem. Soc. Faraday Trans. I (79) (1983) 2853. W. Sotoyama, H. Sato, A. Matsuura, N. Sawatari, J. Mol. Struct. Theor. 759 (2006) 165. D. Pentlehner, A. Slenczka, J. Chem. Phys. 138 (2013) 024313. E.S. Kadantsev, M.J. Stott, J. Chem. Phys. 124 (2006) 134901. R. Bauernschmitt, R. Ahlrichs, Chem. Phys. Lett. 256 (1996) 454. J.B. Foresman, M. Head-Gordon, J.A. Pople, M.J. Frisch, J. Phys. Chem. 96 (1992) 135. Y. Kawashima, T. Hashimoto, H. Nakano, K. Hirao, Theor. Chem. Acc. 102 (1999) 49. K. Hirao, Chem. Phys. Lett. 190 (1992) 374. H. Nakatsuji, Chem. Phys. Lett. 59 (1978) 362. M. Baba, M. Saitoh, K. Taguma, K. Shinohara, K. Yoshida, Y. Semba, S. Kasahara, N. Nakayama, H. Goto, T. Ishimoto, U. Nagashima, J. Chem. Phys. 130 (2009) 1345. S. Okajima, B.E. Frosch, E.C. Lim, J. Phys. Chem. 87 (1983) 4571. A. Amirav, C. Horwitz, J. Jortoner, J. Chem. Phys. 88 (1988) 3092. T. Sato, K. Tokunaga, K. Tanaka, J. Phys. Chem. A 112 (2008) 758. T. Sato, K. Shizu, T. Kuga, K. Tanaka, H. Kaji, Chem. Phys. Lett. 458 (2008) 152. T. Sato, K. Tokunaga, N. Iwahara, K. Shizu, K. Tanaka, The Jahn–Teller Effect: Fundamentals and Implications for Physics and Chemistry, Springer–Verlag, Berlin and Heidelberg, 2009 (p. 99). K. Shizu, T. Sato, K. Tanaka, H. Kaji, J. Mater. Chem. 21 (2011) 6375. K. Shizu, T. Sato, K. Tanaka, H. Kaji, Appl. Phys. Lett. 97 (2010) 142111. T. Sato, M. Uejima, N. Iwahara, N. Haruta, K. Shizu, K. Tanaka, J. Phys: Conf. Ser. 428 (2013) 012010. H. Köppel, W. Domcke, L.S. Cederbaum, Adv. Chem. Phys. 57 (1984) 59. G. Fischer, Vibronic Coupling: The Interaction Between the Electronic and Nuclear Motions, Academic Press, London, 1984. E.C. Lim, J.D. Laposa, J. Chem. Phys. 41 (1964) 3257. K. Andersson, P. Malmqvist, B.O. Roos, A.J. Sadlej, K. Wolinski, J. Phys. Chem. 94 (1990) 5483. M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G.A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H.P. Hratchian, A.F. Izmaylov, J. Bloino, G. Zheng, J.L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J.A. Montgomery, Jr., J.E. Peralta, F. Ogliaro, M. Bearpark, J.J. Heyd, E. Brothers, K.N. Kudin, V.N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J.C. Burant, S.S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J.M. Millam, M. Klene, J.E. Knox, J.B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, R.L. Martin, K. Morokuma, V.G. Zakrzewski, G.A. Voth, P. Salvador, J.J. Dannenberg, S. Dapprich, A.D. Daniels, Ö. Farkas, J.B. Foresman, J.V. Ortiz, J. Cioslowski, D.J. Fox, Gaussian 09 Revision B.1, Gaussian Inc, Wallingford, CT, 2009. G. Karlström, R. Lindh, P.-Å. Malmqvist, B.O. Roos, U. Ryde, V. Veryazov, P.-O. Widmark, M. Cossi, B. Schimmelpfennig, P. Neogrady, L. Seijo, Comput. Mater. Sci. 28 (2003) 222. S. Hirayama, Y. Iuchi, F. Tanaka, K. Shobatake, Chem. Phys. 144 (1990) 401. A. Bergman, J. Jortner, Chem. Phys. Lett. 15 (1972) 309. B. Dick, G. Hohlneicher, Chem. Phys. Lett. 83 (1981) 615. H.B. Klevens, J.R. Platt, J. Chem. Phys. 17 (1949) 470. W.R. Lambert, P.M. Syage, A.H. Zewail, J. Chem. Phys. 81 (1984) 2195. L.E. Lyons, G.C. Morris, J. Mol. Spectrosc. 4 (1960) 480. R.P. Steiner, J. Michl, J. Am. Chem. Soc. 100 (1978) 6861. H. Suzuki, Electronic Absorption Spectra and Geometry of Organic Molecules, Academic, New York, 1967. B.A. Jacobson, J.A. Guest, F.A. Novak, S.A. Rice, J. Chem. Phys. 87 (1989) 269. M. Sonnenschein, A. Amirav, J. Jortoner, J. Phys. Chem. 88 (1984) 4214. N. Nijegorodov, W.S. Downey, Spectrochim. Acta Part A 51 (1995) 2335. E. Bowen, J. Shau, J. Chem. Phys. 63 (1959) 4. R.G. Bennet, P.J. McCartin, J. Chem. Phys. 44 (1966) 1969.