Ultrafast Charge Recombination Dynamics in Ternary Electron Donor

8 Nov 2016 - The charge-transfer (CT) state relaxation dynamics of the binary (1:1) and ternary (2:1) benzene/tetracyanoethylene (BZ/TCNE) complexes a...
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Ultrafast Charge Recombination Dynamics in Ternary Electron Donor−Acceptor Complexes: (Benzene)2‑Tetracyanoethylene Complexes Chih-Chung Chiu, Chih-Chang Hung, and Po-Yuan Cheng* Department of Chemistry, National Tsing Hua University, Hsinchu, Taiwan 30043, R. O. C. S Supporting Information *

ABSTRACT: The charge-transfer (CT) state relaxation dynamics of the binary (1:1) and ternary (2:1) benzene/tetracyanoethylene (BZ/TCNE) complexes are reported. Steady-state and ultrafast time-resolved broadband fluorescence (TRFL) spectra of TCNE dissolved in a series of BZ/CCl4 mixed solvents are measured to elucidate the spectroscopic properties of the BZ/TCNE complexes and their CT-state relaxation dynamics. Both steady-state and TRFL spectra exhibit marked BZ concentration dependences, which can be attributed to the formation of two types of 2:1 complexes in the ground and excited states. By combining with the density functional theory (DFT) calculations, it was concluded that the BZ concentration dependence of the absorption spectra is mainly due to the formation and excitation of the sandwich-type 2:1 ternary complexes, whereas the changes in fluorescence spectra at high BZ concentrations are due to the formation of the asymmetric-type 2:1 ternary complex CT1 state. A unified mechanism involving both direct excitation and secondary formation of the 2:1 complexes CT states are proposed to account for the observations. The equilibrium charge recombination (CR) time constant of the 1:1 CT1 state is determined to be ∼150 ps in CCl4, whereas that of the 2:1 DDA-type CT1 state becomes ∼70 ps in 10% BZ/CCl4 and ∼34 ps in pure BZ. The CR rates and the CT1-S0 energy gap of these complexes in different solvents exhibit a correlation conforming to the Marcus inverted region. It is concluded that partial charge resonance occurring between the two adjacent BZs in the asymmetric-type 2:1 CT1-state reduces the CR reaction exothermicity and increases the CR rate.

1. INTRODUCTION Photoexcitation within the charge-transfer (CT) absorption bands in model electron donor−acceptor (EDA) complexes mimics the initial photoinduced charge separation (CS) in many important natural and artificial systems.1−3 As such, the excited-state dynamics of EDA complexes has always been an active research topic continuing to attract attention,4−20 and different CT mechanisms have been discussed for simple molecular EDA complexes18,19 as well as those involving nanocrystals.20 The first CT absorption band of an EDA complex usually corresponds to an excitation from the highestoccupied molecular orbital (HOMO) localized in the donor (D) to the lowest-unoccupied molecular orbital (LUMO) localized in the acceptor (A), resulting in an ion pair, D+-A−, with a high degree of CS.21−23 In liquid solutions, solvation and other relaxation processes rapidly take place to bring the system to an equilibrium CT state, sometimes referred to as the “contact ion pair” (CIP).23 Competing with these relaxations are the charge recombination (CR) and dissociation into free ions. The CR reaction is equivalent to a back electron transfer (ET) and is usually the energy-wasting pathway in light energy harvesting systems.24,25 Different electron transfer mechanisms The series of EDA complexes containing tetracyanoethylene (TCNE) as the acceptor and methyl-substituted benzenes © XXXX American Chemical Society

(MBZ) as the donor have been widely studied as model sytems. 7,26−41 Among them, hexamethylbenzene-TCNE (HMB-TCNE) is probably the most intensively studied MBZ-TCNE system both experimentally31−40 and theoretically.40,42−46 Surprisingly, the smallest member of the series, namely the benzene-TCNE (BZ-TCNE) complex, has not been given much attention. Recently, we have studied the ultrafast CT-state relaxation dynamics of the BZ-TCNE complex in solvents of different polarities with ultrafast broadband time-resolved fluorescence (TRFL) spectroscopy.14 Temporal and spectral evolutions of fluorescence were measured to elucidate various relaxation processes following initial CT excitation. We found that the initial CT-state dynamics is dominated by rapid relaxations along both solvent and vibrational coordinates followed by slower charge recombination reactions. Equilibrium CR time constants for the BZ-TCNE CT state in CH2Cl2 and CCl4 are 29 and 150 ps, respectively, which are generally in line with the expectation for the behavior in the Marcus inverted region.14 Received: October 20, 2016 Revised: November 7, 2016 Published: November 8, 2016 A

DOI: 10.1021/acs.jpcb.6b10593 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B During our previous study, we noticed that the CT absorption and fluorescence behaviors strongly depend on the donor concentration in solutions. As suggested by several previous studies,47−53 these phenomena can be attributed to secondary quenching as well as formation of higher-order complexes, i.e., those containing two or more donor molecules. In order to avoid these interferences, we have used the lowest donor concentrations possible in our previous study and have checked the donor concentration dependence to ensure the detection of the 1:1 BZ-TCNE complex only.14 Nevertheless, the fluorescence behaviors observed at higher donor concentrations are important in their own right. In fact, these higher order complexes can serve as models to some extended systems found in nature and solid-state devices. As such, a few groups47−53 have studied the formation and spectroscopic properties of the 2:1 ternary complexes (D2A). For example, Mataga’s group50−52 has investigated 1,2,4,5-tetracyanobenzene (TCNB) in several methyl-substituted benzene solutions using ultrafast transient absorption spectroscopy and has observed the formation kinetics of 2:1 CIP. However, there are still important issues remaining unanswered; most importantly, how the presence of additional donors in the complex affects the CR dynamics. In this work, we aim at addressing these issues by extending our previous studies to solutions containing higher donor concentrations. Combining with the density functional theory (DFT) calculations, the present study provides some new insights to the nature of the ternary-complex CT states and their relaxation dynamics.

Figure 1. (A) BZ concentration dependence of normalized CT absorption spectra of BZ/TCNE complexes measured in a series of CCl4 solutions containing TCNE and BZ. The initial BZ mole fractions were varied from 0.15% to 100% (pure BZ), while the initial TCNE concentration was kept constant at 1.5 × 10−3 M in all cases. (B) BZ concentration dependence of the maximum absorbance (path length =1 mm) of the spectra shown in (A). The solid line is the best fit of the data (red circles) to a binary/ternary complexes equilibrium model described in the text. The inset shows the dependence in the low BZ concentrations region.

2. EXPERIMENTAL SECTION The ultrafast time-resolved broadband fluorescence spectrometer used in this work is based on the optical Kerr gating and has been described in detail in our previous report.14,54 The setup includes an amplified femtosecond laser system that provides excitation and gating pulses at 383 and 766 nm, respectively. To measure the time-resolved fluorescence (TRFL) spectra, fluorescence arising from excitation of sample solutions was collected and directed through an optical Kerr shutter and detected by a spectrograph/CCD camera combination. The details of the experimental setup are given in the Supporting Information (SI). All TRFL measurements reported in this work were carried out with an effective temporal instrument response function (IRF) of about 0.35− 0.5 ps in width (see SI). TCNE solutions were prepared in mixed solvents of BZ and CCl4 with the BZ mole fraction varied between 0.15% and 100% (pure BZ). In all solutions, the initial concentration of TCNE was kept at 1.5 × 10−3 M. Sample solutions were freshly prepared before each experiment. TCNE was purchased from Aldrich (98%) and was sublimed twice before use. BZ (Merck, Uvasol grade) was used as received, while CCl4 (Showa, 99.5%) was fractionally distilled under dry nitrogen before use. All experiments were carried out at a room temperature of 23 °C.

gradually shifts to the blue and the bandwidth slightly broadens. Notice that the red-edge shoulder near 450 nm does not noticeably grow in until BZ concentration becomes greater than ∼50%. The blue shift is quite modest, such that even for xBZ = 100%, i.e., TCNE dissolved in pure BZ, the shift is only about 10 nm. The CT absorbance increases monotonically with increasing BZ concentrations and gradually saturates at high concentrations, as shown in Figure 1B, suggesting that the spectral change observed in Figure 1A is not due to solvatochromism. In order to account for these observations at higher BZ concentrations, the formation of TCNE complexes with more than one BZ molecules must be considered.47,48,55,56 It has been suggested55,56 that in systems where [D]0 ≫ [A]0, the EDA complex compositions can be described by the following binary/ternary complexes equilibrium:

3. RESULTS AND DATA ANALYSES 3.1. BZ Concentration Dependence of Steady-State Absorption Spectra. Figure 1A displays the BZ concentration dependence of CT absorption spectra of TCNE dissolved in BZ/CCl4 mixed solvents with the TCNE initial concentration kept at 1.5 × 10−3 M. Below ∼1.0% of BZ mole fraction (xBZ), the CT absorption spectral profiles remain nearly constant. As the BZ concentration increases, the CT absorption maximum

D + A ⇄ DA; K1

(1)

DA + D ⇄ D2 A; K 2

(2)

where K1 and K2 are the formation equilibrium constants for the 1:1 DA binary and 2:1 D2A ternary complexes, respectively. Contributions from higher-order complexes are assumed to be negligible. This presumption is supported by the much smaller K2 than K1 as well as the results from our DFT calculations, as discussed below. Combinations of the Beer’s law and the stoichiometry of eqs 1 and 2 yields eq 3, which relates the measured absorbance (Abs) to the initial concentrations ([D]0 B

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The Journal of Physical Chemistry B and [A]0), the two K values, and the molar absorptivities of DA (ε1) and D2A (ε2). Abs =

(ε1K1[D]0 [A]0 + ε2K1K 2[D]0 2 [A]0 ) (1 + K1[D]0 + K1K 2[D]0 2 )

(3)

The data shown in Figure 1B were fit with eq 3 with [A]0 fixed at 0.0015 mol L−1, and the parameters obtained (at T = 23 °C) are K1= 1.0 ± 0.1 L mol−1; K2 = 0.1 ± 0.02 L mol−1, and ε1 = 2000 ± 100 L mol−1cm−1; ε2 = 3200 ± 100 L mol−1cm−1. These values agree quite well with previously reported results.55 According to this model, K2 is found to be about 10 times smaller than K1, suggesting that the formation constants for higher order complexes must be even smaller. 3.2. BZ Concentration Dependence of Steady-State Fluorescence Spectra. In contrast to the marginal changes in the CT absorption spectral profile, the fluorescence spectra of TCNE in BZ/CCl4 solutions with 383 nm excitation are much more sensitive to the BZ concentration, as shown in Figure 2.

Figure 3. Comparison of steady-state absorption (dashed lines) and fluorescence (solid lines) spectra of BZ/TCNE complexes measured in TCNE (1.5 × 10−3 M) solutions of three BZ/CCl4 mixed solvents with xBZ = 0.35 (blue lines), 10 (green lines), and 100% (red lines). All spectra are displayed in wavenumber (cm−1) scale.

report14 and have been assigned to the absorption and fluorescence spectra of the 1:1 BZ-TCNE complex in nearly pure CCl4. Table 1 summarizes some important spectral characteristics of the BZ/TCNE systems measured in different solvents. 3.3. BZ Concentration Dependence of Fluorescence Decay. Figure 4 shows the BZ concentration dependence of fluorescence transients excited at 383 nm and measured at 635 nm. Between 0.15 and 0.35% of BZ, the fluorescence transients are nearly independent of BZ concentrations and decay with a time constant of ∼150 ps, which mainly reflect the CT state relaxation dynamics of the 1:1 BZ-TCNE complex in pure CCl4. However, when the BZ concentration increases, the fluorescence decay gradually becomes faster, reaching as fast as a few picoseconds in pure BZ. Multiple decay components are noticeable in transients of high BZ concentrations. These observations immediately suggest that there exists additional spectral relaxation and quenching mechanisms due to the increase of BZ concentrations. Details of the fluorescence decay dynamics are examined more closely for three BZ concentrations, xBZ = 0.35, 10, and 100%, with the TRFL experiments described below. 3.4. TRFL Spectra of BZ/TCNE Complexes. We have measured TRFL spectra of BZ/TCNE complexes in TCNE solutions of three BZ/CCl4 mixed solvents with xBZ = 0.35, 10, and 100% (pure BZ) at 383 nm excitation. The results after spectral-sensitivity and time corrections using the procedures described in our previous report are displayed in Figure 5A, D, and G. For the sake of clarity, only TRFL spectra at some representative delay times are shown. Sharp spectral features due to Raman scattering have been removed from these spectra. The data for the xBZ = 0.35% solution are those taken from our previous report for 1:1 BZ-TCNE complex in CCl4.14 These corrected TRFL spectra are also displayed as falsecolored contour plots in Figures 5B, E, and H. Note that the time scales of these contour plots are different for each case. The time dependence of fluorescence intensity, i.e., the fluorescence transients, at various emission wavelengths derived from the TRFL spectra are shown in Figure 5C, F, and I. These transients were obtained by summing the fluorescence counts within a ∼ 16 nm spectral window at the specified emission wavelength at each delay time. The variations of the transients

Figure 2. BZ concentration dependence of normalized steady-state fluorescence spectra of BZ/TCNE complexes excited at 383 nm in a series of CCl4 solutions containing TCNE and BZ. The initial BZ mole fractions were varied from 0.15 to 100% (pure BZ), while the initial TCNE concentrations were kept constant at 1.5 × 10−3 M in all cases. Sharp spectral features due to Raman scattering at ∼475 nm have been removed.

At xBZ < 0.35%, the fluorescence spectrum peaking at ∼580 nm is nearly independent of BZ concentration and can be assigned to the emission of 1:1 BZ-TCNE complex in nearly pure CCl4, as have been discussed in our previous report.14 However, as the BZ concentration increases the emission maximum gradually shifts to the red, reaching at ∼740 nm when pure BZ is used as the solvent. At moderate BZ concentrations (xBZ = 1−11%), a new emission spectral feature begins to appear in the red spectral region (700−750 nm). It is important to emphasize here that the spectra do not simply shift to the red; instead, the 580 nm band remains nearly unchanged while the red emission band grows in. Indeed, between ∼5−11%, it appears that both bands are concurrently present, making the entire spectra substantially broader. These observations immediately indicate that the spectral change is not due to increase of solvation upon addition of BZ; instead, it is more likely due to a newly formed species that emits at a much lower frequency. At even higher concentrations, the 580 nm band gradually fades and the red emission band keeps growing. For easy comparison, the steady-state absorption and fluorescence spectra of TCNE dissolved in xBZ = 100 (pure BZ), 10, and 0.35% BZ/CCl4 mixed solvents are shown together in Figure 3. The ones with xBZ = 0.35% are taken from our previous C

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The Journal of Physical Chemistry B Table 1. Solvent Properties and Spectral Characteristics of BZ/TCNE Complexes and C153 in Different Solvents steady-state characteristicsc properties of the major solvent solvents

a

CH2Cl2 Pure BZ 10% BZ/CCl4 CCl4

b

μ

ε

π*

ETN

1.14 0.00

8.9 2.3

0.73 0.55

0.309 0.111

0.00

2.3

0.21

0.052

BZ/TCNE

e

time-dependent characteristicsd C153

f

BZ/TCNEe

C153

νabs

νem

δν

δν

ν(0)

ν(∞)

Δν0∞

Δν0∞

25700 26100 25950 25700

13000 13000 14500 16930

12700 13100 11450 8770

5060 4770

20300 20200 20100 20000

13000 13100 14500 16500

7300 7100 5600 3500

1110 720

4160

300

a

For BZ/TCNE measurements in CH2Cl2, cTCNE = 0.02 M and cBZ = 0.2 M (xBZ = 1.28%); in CCl4, cTCNE = 0.0015 M and cBZ = 0.037 M (xBZ = 0.35%). In both solutions, the 1:1 BZ-TCNE complex predominates. bDipole moments (μ) in Debye and static dielectric constants (ε) are for 25 °C. The solvatochromic polarity scales π* values are from refs 74 and 75, and ENT values are from ref 73. cνabs and νem are peak frequencies of the steady-state absorption and emission spectra. δν is the Stoke shift. All frequencies are in cm−1. dν(0) is the mean emission frequency near time zero derived from the observed TDFSS data; ν(∞) is the mean emission frequency at long delay time where spectral relaxation ceases; Δν0∞ is the magnitude of the dynamics Stokes shift defined as ν(0) − ν(∞); Δνt0∞, taken from ref 72, is the estimate of the magnitude of dynamic Stokes shifts of C153. All frequencies are in cm−1. eSpectral characteristics of BZ/TCNE complexes in TCNE solutions of different mixed solvents containing BZ. Data in CH2Cl2 and CCl4 are from ref 14. fAll C153 data in pure CH2Cl2, BZ, and CCl4 are from ref 72.

v ̅ (t ) =

∫ v·I(v , t )dv ∫ I(v , t )dv

(4)

where I(ν, t) represents the measured TRFL spectra after spectral-sensitivity and time corrections. The time-dependent fluorescence dynamic Stokes shift (TDFSS) is then defined as δν(t) = ν(t) − ν(∞). A portion of the BZ/TCNE fluorescence appears in region beyond the red edge of the spectral detection window. In order to estimate the spectra in the undetected region, we extrapolated the observed TRFL spectra by fitting them to log-normal line shape functions.14 The evaluation of ν(t) was then performed with the results obtained from the lognormal function fittings. A procedure suggested by Gutavaason et al.57 was employed to partially remove the temporal broadening effect by fitting ν(t) with a multiple-exponential model function. The results of these fittings are shown in Figure 6 for TCNE dissolved in solvents of three BZ concentrations; and the obtained time constants and magnitudes are summarized in Table 1. In the case of the 0.35% BZ/CCl4 solution, the two faster relaxation components (0.4 and 0.9 ps) observed in ν(t) relaxation have been attributed to rapid solvation in response to sudden dipole moment change upon CT excitation of the 1:1 BZ-TCNE complex, whereas the slower component (14 ps) has been assigned to vibrational relaxation.14 Within the first few picoseconds, the ν(t) relaxation observed in the 10% BZ/ CCl4 solution is quite similar to that of the 1:1 complex in nearly pure CCl4. On the other hand, the relaxation observed in pure BZ exhibits a much greater relaxation within the first few picoseconds, followed by slower relaxations that are similar to those observed in very low BZ concentrations. We also evaluate the total fluorescence intensity of the TRFL spectra with cubic-frequency correction, P(t), using the following expression:

Figure 4. BZ concentration dependence of fluorescence transients obtained by exciting BZ/TCNE complexes in a series of CCl4 solutions containing TCNE and BZ. The initial BZ mole fractions were varied from 0.15 to 100% (pure BZ), while the initial TCNE concentrations were kept at 1.5 × 10−3 M in all cases. The excitation wavelength was 383 nm, and the fluorescence was measured at 635 ± 10 nm.

with the emission wavelengths reflect the temporal evolutions of spectral characteristics. However, various processes, such as solvation, vibrational relaxation, and electronic transitions, occur concurrently and all contribute to the fluorescence transient at a particular wavelength. Some of them occur in very similar time scales, making it difficult to identify these entangled temporal components from the fluorescence transients. For this reason, we will focus on evaluating the temporal evolution of spectral characteristics of TRFL spectra as a whole. Overall, the results shown here in Figure 5 clearly reveal that when TCNE is dissolved in pure BZ the fluorescence undergoes a rapid and strong spectral relaxation within the first picosecond, whereas the spectral relaxation is slower and weaker in the other two solutions of lower BZ concentrations. 3.5. Time-Dependent Mean Emission Frequency and Total Fluorescence Intensity P(t). To unveil the dynamical information contained in the TRFL spectra, we examined the time dependence of some spectral properties. The timedependent mean emission frequency (the first moment) was evaluated with

P(t ) =

∫ I(v ,v3t )dv

(5)

where I(ν, t) is the observed TRFL spectra after spectralsensitivity and time corrections. Again, P(t) was evaluated with the results obtained from log-normal-function fittings of the measured I(ν, t). This function approximately reflects the temporal evolution of the product of the total excited-state population and the square of the emission electronic transition moment.34,58−60 Temporal components due to pure spectral D

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Figure 5. (A, D, G) Time and spectral-sensitivity corrected TRFL spectra of BZ/TCNE complexes excited at 383 nm in TCNE (1.5 × 10−3 M) solutions of three BZ/CCl4 mixed solvents with xBZ = 0.35, 10, and 100% (pure BZ). Only spectra at representative delay times are shown for the sake of clarity. Spectral features due to Raman scatterings have been removed. (B, E, H) Early time portions of false color contour plots of the TRFL spectra shown above. (C, F, I) Fluorescence transients extracted from the TRFL spectra shown above. Each trace is the average of data over a ∼ 16 nm spectral window centered at the specified wavelength. The colored solid lines are the best fits of a multiexponential model function convoluted with the IRF to the data (colored circles).

included with the polarizable continuum model using the integral equation formalism variant (IEFPCM).64 All calculations were performed using the Gaussian 09 program.65 4.1. Ground-State Structures and Energetics. The ground-state (S0) structures of the three complexes in CCl4 were first optimized at the ωB97XD/aug-cc-pVTZ level of theory with IEFPCM (solvent = CCl4) for solvation, and the results are shown in Figure 8. Details of the optimization procedures and molecular structures are given in the SI. For the 1:1 BZ-TCNE complex, only the lowest-energy “Y conformer”,14 which belongs to the C2V point group, is shown here. For the sandwich-type DAD 2:1 complex, it is found that the most stable configuration assumes the D2h geometry with the second BZ residing on the other side of TCNE symmetrically. On the other hand, the DDA-type 2:1 complex has a structure in which the two BZs are nearly parallel but displaced laterally. As expected, the symmetric DAD-type 2:1 complex exhibits a vanishing ground-state dipole moment (see

relaxation processes that do not alter excited-state populations, e.g., solvation and vibrational relaxation, are expected to be greatly suppressed in this function. Figure 7 displays the P(t)’s obtained from TCNE solutions with three BZ concentrations along with the best fits with the kinetics model described below.

4. ELECTRONIC STRUCTURE CALCULATIONS We have also carried out electronic structure calculations to provide theoretical insights into the structures and energetics of relevant complexes. Three types of BZ/TCNE complexes are calculated here, namely the 1:1 BZ-TCNE, the 2:1 sandwichtype BZ-TCNE-BZ, and the 2:1 asymmetric-type BZ-BZTCNE complexes, hereafter referred to as the DA, DAD, and DDA complexes, respectively. We carried out density functional theory (DFT) calculations with the ωB97XD functional, which has been shown to give good performances for noncovalent bonded molecular complexes61,62 and CT excitation energy with time-dependent (TD) calculations.63 Solvent effects are E

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Figure 6. Temporal evolutions of mean emission frequency, ν(t), of BZ/TCNE complexes excited at 383 nm in three BZ/CCl4 mixed solvents. (triangles) xBZ = 0.35%, (circles) xBZ = 10%, and (squares) xBZ = 100%. The solid lines are the deconvoluted results using the procedures described in ref 57.

Figure 8. (A−C) Optimized ground-state structures of the binary and ternary BZ/TCNE complexes at the ωB97XD/aug-cc-pVTZ level of theory. (D−F) Optimized structures of the first single CT state (1CT1) of the three BZ/TCNE complexes at the TD-ωB97XD/ccpVDZ level of theory. The calculated dipole moments (in Debye) and the net charges (q) residing on each moiety evaluated by NPA are also indicated for each case. The CT1-state dipole moments are those calculated with a larger basis set (aug-cc-pVTZ) at the optimized structures.

structure of the two BZ molecules and the binding energy of the DDA-type complex are very similar to those of the parallel displaced configuration of benzene dimers in the gas phase,66,67 suggesting that the second BZ mainly interacts with the first BZ and the CT contribution is not important in this case. The nearly identical dipole moment also supports this notion. An important conclusion reached here is that the DAD-type 2:1 complex is much more stable than the DDA-type in nonpolar solvents and should be predominant in solutions of higher BZ concentrations. 4.2. Vertical Excitation Energies. Vertical excitation energies of the first few singlet excited states of these complexes at the ground-state optimized structures in CCl4 were calculated at the TD-ωB97XD/aug-cc-pVTZ level of theory with IEFPCM (solvent = CCl4) for solvation. The results are summarized in Table 2. The first two nearly degenerate singlet excited states of the 1:1 BZ-TCNE complex correspond to HOMO and HOMO−1 to LUMO excitations. The energy difference between these two CT states is only ∼725 cm−1 in the Franck−Condon (FC) region. This is well understood because the HOMO and HOMO−1 in the complex originate from the doubly degenerate HOMOs in isolated BZ, which are split into two closely lying MOs due the influence of TCNE in the complex. Under a strict C2v geometry, the transition from S0 to the first singlet CT excited state (CT1) is forbidden by symmetry, whereas the transition to the second singlet CT state (CT2) is allowed and carries most of the oscillator strength.

Figure 7. (A) Long-time scale and (B) short-time scale temporal evolution of the total fluorescence intensity with cubic frequency correction, P(t), as defined in the text for BZ/TCNE complexes excited at 383 nm in three BZ/CCl4 mixed solvents. (green circles) xBZ = 0.35%, (blue circles) xBZ = 10%, and (red circles) xBZ = 100%. The solid lines are the best fits of the kinetics model (convoluted with the IRF) described in the text to the data.

Figure 8), while the asymmetric DDA-type has a dipole moment (1.46 D) nearly identical to that of the 1:1 DA complex (1.45 D). The binding energy of the 1:1 DA complex is calculated to be 0.36 eV, which is in good agreement with a recent result of 0.371 eV calculated at a higher level of theory (CCSD(F12*)(T)/cc-pVDZ-F12).41 The binding energies between the second BZ and a 1:1 DA complex are 0.352 and 0.157 eV for the DAD and DDA type complexes, respectively. Apparently, binding of the second BZ onto the other side of TCNE is much stronger than to the first BZ. In fact, the local F

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localized on TCNE is raised upward due the interaction with the second BZ, while the energies of the occupied HOMO’s on the two BZs remain similar to those in 1:1 DA complex. For the DDA-type 2:1 complex, only two CT states are found in the energy region of interest, the other two CT states occurs in a much higher energy region ( ∼ 50%, may suggest some minor presence of the DDA-type interaction at very high BZ concentrations.

localized within a D−A pair, and the second BZ acts more like a perturbing solvent. The net charges residing on each moiety evaluated by natural population analysis (NPA) indeed show a distribution consistent with the above description. This notion is further supported by the electron density difference between the CT1 and S0 states calculated at the CT1-state minimum (see Figure 9). The vertical transition energy between the CT1 and S0 states at the CT1-state minimum is predicted to be 2.10 eV (∼590 nm), which is 0.14 eV higher than the corresponding energy in the 1:1 complex. This indicates that the DAD-type 2:1 complex emission, if observed, should be blue-shifted with respect to that of the 1:1 DA complex. For the DDA-type 2:1 complex, the CT1-state optimized structure contains a local DA geometry similar to that found in the 1:1 complex. The dipole moment at CT1-state minimum (14.4 D) is noticeably larger than those found in the 1:1 and the DAD-type 2:1 complexes, suggesting a higher degree of charge separation in this case. Indeed, the electron density difference between the CT1 and S0 at the CT1-state optimized structure does reveal a very small fraction of charge transferred from the second BZ, and the charge distribution evaluated by NPA indicates a small net positive charge residing on the second BZ. The vertical transition energy between the CT1 and S0 states at the DDA-type CT1-state minimum is predicted to be 1.79 eV (∼693 nm), which is ∼0.17 eV lower than the corresponding energy in the 1:1 complex. This suggests that the DDA-type 2:1 complex emission is red-shifted with respect to that of the 1:1 DA complex. The relevant energetics of the ground and CT states calculated for the three complexes are schematically summarized in Figure 10 for easy comparisons.

Figure 10. Schematic energetic diagram of some relevant states of binary and ternary BZ/TCNE complexes from DFT calculations. Horizontal lines denote the minima of the ground (S0) and CT1 states. Blue upward arrows represent the vertical excitation from the S0-state minima to the FC region of the first allowed CT states. Red downward arrows denote the vertical emission from the CT1-state minima to S0. Horizontal dashed lines represent the FC states of corresponding transitions. The relative and transition energies (in eV) are indicated accordingly, and the CT1-S0 energy gaps are also highlighted (green vertical lines).

5. DISCUSSION 5.1. CT Absorption Spectra and the Formation of 2:1 Complexes. The results presented in Sections 3.1 and 3.2 show that, at the lowest concentrations (