J. Phys. Chem. C 2010, 114, 20401–20409
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Charge-Transport Properties of the Tetraphenylbis(indolo[1,2-a])quinoline and 5,7-Diphenylindolo[1,2-a]quinoline Crystals† Lingyun Zhu,‡ Eung-Gun Kim,‡ Yuanping Yi,‡ Eilaf Ahmed,§ Samson A. Jenekhe,§ Veaceslav Coropceanu,*,‡ and Jean-Luc Bre´das*,‡,| School of Chemistry and Biochemistry and Center for Organic Photonics and Electronics, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, Departments of Chemistry and Chemical Engineering, UniVersity of Washington, Seattle, Washington 98195-1750, and Laboratory for Chemistry of NoVel Materials, UniVersity of Mons, B-7000 Mons, Belgium ReceiVed: May 4, 2010; ReVised Manuscript ReceiVed: June 25, 2010
Recently, a single-crystal field-effect hole mobility of about 1.0 cm2/(V s) has been measured for the tetraphenylbis(indolo[1,2-a])quinoline (TPBIQ) crystal. TPBIQ can be considered as almost the dimer of 5,7-diphenylindolo[1,2-a]quinoline (DPIQ), but the experimental hole mobilities differ markedly. Here, based on density functional theory and semiempirical calculations, the charge-transport parameters of TPBIQ crystal are studied and compared to those of the “parent” DPIQ crystal. The results indicate that hole and electron transport in the TPBIQ crystal is significant only along the π-stacking direction, while in DPIQ substantial electronic couplings are also found along other directions. The larger electronic couplings and much smaller reorganization energy calculated for the TPBIQ crystal point to a higher hole mobility in TPBIQ, which is consistent with the experimental observations. Molecular dynamics simulations are also carried out to evaluate the nonlocal electron-phonon couplings. The results suggest that the scattering of the charge carriers is more substantial in DPIQ (especially in the case of electrons) than in TPBIQ, and the relative impact of the phononassisted mechanism is also larger in the case of electrons in DPIQ. 1. Introduction Over the past 20 years, much interest has been devoted to the exploitation of functional organic molecular compounds and polymers as active elements in new generations of plastic (opto)electronic devices such as field-effect transistors,1-3 lightemitting diodes,4-6 or photovoltaic and solar cells.7-9 In particular, oligoacenes10-13 and oligothiophenes14-19 have been very much investigated due to their high charge-carrier mobilities. In spite of significant achievements obtained with these systems, it is desirable to design and synthesize new types of materials to keep improving the performance of organic devices. A detailed understanding of the charge-transport mechanisms in organic semiconductors is of interest from both fundamental and practical points of view.20,21 Recently, two of us22 reported a novel heptacyclic compound, i.e., tetraphenylbis(indolo[1,2-a])quinoline (TPBIQ) (see Figure 1) that exhibits a single-crystal field-effect hole mobility of about 1.0 cm2/(V s). In the present work, we use mainly quantumchemical calculations to elucidate the origin of this large hole mobility. We also report the charge-transport properties of the “parent” 5,7-diphenylindolo[1,2-a]quinoline (DPIQ) system and compare them to those of TPBIQ; note that TPBIQ can be loosely considered as a DPIQ dimer. 2. Methodology Theoretical Models. The relationship between the macroscopic charge-transport properties and the microscopic transport †
Part of the “Mark A. Ratner Festschrift”. * To whom correspondence should be addressed. E-mail: coropceanu@ gatech.edu (V.C.);
[email protected] (J.-L.B.). ‡ Georgia Institute of Technology. § University of Washington. | University of Mons.
Figure 1. Chemical structures of TPBIQ and DPIQ.
parameters can be understood by considering the electronic Hamiltonian in a simple tight-binding approximation:23
H)
∑ εmam+am + ∑ tmnam+an m
(1)
m*n
Here, am+ and am denote the creation and annihilation operators, respectively, for an electron on molecular site m, εm is the electron site energy, and tmn is the transfer integral. The two microscopic parameters εm and tmn are in general a function of the vibration (phonon) coordinates; this dependence is referred to as electron-phonon coupling. The modulation of εm by vibrations corresponds to the local electron-phonon coupling, while the modulation of tmn, mostly by intermolecular vibrations, represents the nonlocal coupling.23,24 The local electron-vibration coupling is the key interaction considered in conventional electron-transfer theory and in Holstein’s molecular crystal model.25-28 The overall strength of this coupling is expressed by the relaxation or polaron binding energy Epol, or, in the context of electron-transfer theory, by
10.1021/jp104061c 2010 American Chemical Society Published on Web 07/22/2010
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the reorganization energy λ (≈ 2Epol). It consists of both intraand intermolecular contributions; the former reflects the changes in the geometry of individual molecules, and the latter reflects the changes in the polarization of the surrounding molecules, upon going from the neutral to the charged state and vice versa. The nonlocal coupling constitutes the major interaction considered in the Peierls-type models that have been largely applied to conducting polymers.29 This mechanism, referred to as the non-Condon effect, is also an important player in electrontransfer processes in conventional donor-acceptor systems30 and more complex biological systems.31 We have shown recently32 that the overall strength of this coupling can also be expressed via a microscopic parameter (denoted here as L) that has a physical meaning similar to λ; L also defines the hightemperature limit in the variance of the transfer integral due to thermal fluctuations:32-34
σ2 ) 〈t - 〈t〉〉2 ) 2LkBT
where the subscripts i and j denote the Cartesian coordinates in reciprocal space, E(k) is the band energy, p is the Planck constant, and k is the electron wavevector. The hopping transport can be described as a self-exchange electron transfer reaction from a charged (and relaxed) molecule to a nearby neutral molecule. The carrier mobility can then be expressed as23
µ)
kET ) t2
f(t) )
1
√2πσ2
[
exp -
(t - t0)2 2σ2
]
qτ m
(7)
with ∆G being the free energy difference between reactants and products. The conventional Marcus-type theories do not account for the non-Condon effect (nonlocal coupling). In the nonadiabatic ET limit, this can be done by introducing the following substitution in eq 7:31
(8)
(3)
(4)
where q is the charge, τ the mean free time between collisions (or the mean relaxation time of the band state), and m is the effective mass of the charge carrier. The charge moves coherently in a wave-like manner and is scattered (or relaxed) by phonons from one momentum state to another. The inverse effective mass tensor (mji-1) for a three-dimensional crystal is defined as:38
1 1 ∂2E(k) ) 2 mji p ∂kj∂ki
π exp[-(∆G + λ)2 /4λkBT] λkBTp2
t2 f 〈t2〉 ) 〈t〉2 + σ2 ) t02 + σ2
Here, σ has the same meaning as in eq 2, and t0 is the transfer integral at the equilibrium geometry; f(t) can be then derived as a time average by means of molecular dynamics (MD) simulations.35 Charge transport in molecular crystals represents a very complex problem, and, despite many attempts to develop microscopic models based on Holstein-Peierls-type Hamiltonians,27,28,33,36,37 a comprehensive charge-transport theory for these systems is still missing. Therefore, we focus our discussion in the following on the two limiting transport regimes, namely, the band and hopping regimes. According to band theory, the carrier mobility in wide bands is given by38
µ)
(6)
where kET denotes the electron-transfer (ET) rate, and d is the distance between the two molecules. Viewing each hopping event as a nonadiabatic ET reaction, the rate of charge motion between neighboring molecules in the semiclassical limit can be described as23,24,39
(2)
Here, 〈...〉 represents the statistical average over phonon (vibration) coordinates, kB denotes the Boltzmann constant, and T is the temperature. It is important to note that, when a linear electron-vibration coupling holds (which was assumed in deriving eq 2), L can be obtained from the probability distribution for the transfer integral, f(t). Indeed, in this case, f(t) is given by32
qd2 k kBT ET
(5)
Computational Methods. The molecular geometries and normal modes of the neutral and radical-ion states were obtained at the density functional theory (DFT) level with the B3LYP functional and 6-31G(d,p) basis set, as implemented in the Gaussian 03 program.40 The vertical ionization potentials (IPs) [electron affinities (EAs)] were calculated at the same level of theory. The evaluation of the intramolecular components to the reorganization energy λi and their decomposition into the contributions from each vibrational mode were carried out with the approach described in detail in our previous work.20,41-43 The effective transfer integrals for nearest-neighbor molecular pairs were evaluated by using the fragment orbital approach44 in combination with a basis set orthogonalization procedure.45 These calculations were also performed at the DFT-B3LYP/ 6-31G(d,p) level of theory. The modulations of the electronic transfer integrals due to thermal fluctuations were derived by combining MD simulations and quantum-chemical calculations.32,35,43,46,47 For both compounds, a supercell with 144 molecules was initially created via a 3 × 4 × 3 replica of the crystal unit cell. The MD simulations were carried out with the Discover module of the Materials Studio package using the COMPASS force field.48 Each system was equilibrated for 150 ps using an Anderson thermostat in the NVT ensemble at 298 K and a time step of 1 fs. After equilibration, a simulation of 150 ps was run, and 5000 frames were extracted by taking a snapshot every 30 fs along the trajectory. The calculations of the transfer integrals were performed in this case at the semiempirical intermediate neglect of differential overlap (INDO) level. Optimizations of the crystal structures were performed at the DFT-B3LYP/6-31G(d) level with the CRYSTAL06 package;49 the positions of the atoms in the unit cell were relaxed while
Charge-Transport Properties of TPBIQ and DPIQ Crystals
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Figure 2. B3LYP/6-31G(d,p)-calculated bond-length changes (in Å) upon oxidation (going from the neutral to the cation state) and reduction (going from the neutral to the anion state) in TPBIQ and DPIQ. The bond indices are labeled on the molecular structures.
TABLE 1: IPs and EAs for Isolated TPBIQ and DPIQ Molecules at the B3LYP/6-31G (d,p) Level IP (eV) molecule
vertical
Koopmans
TPBIQ DPIQ
5.70 6.13
4.67 4.83
a
EA (eV) exp.
c
5.19d (5.14)e 5.12f
vertical
Koopmansb
exp.c
-0.88 -0.19
-1.91 -1.53
-2.60d (-2.79)e -2.42f
a Negative of the highest occupied molecular orbital (HOMO) energy. b Lowest unoccupied molecular orbital (LUMO) energy. voltammetry measurements. d In solution; ref 22. e In thin film; ref 22. f In solution; see Supporting Information.
the cell parameters were kept fixed at the experimental values. The electronic band structures and density of states (DOS) were calculated using the optimized crystal structures. Uniform 4 × 4 × 4 and 4 × 8 × 4 Monkhorst-Pack k-point meshes were employed for the TPBIQ and DPIQ crystals, respectively. The inverse effective mass tensor was calculated by means of Sperling’s centered difference method with dk ) 0.01/Bohr for TPBIQ and 0.02/Bohr for DPIQ. Subsequent diagonalization of mji-1 provided the principal components and their orientations. Experimental Details. The synthesis and characterization of DPIQ along with the details of device fabrication and chargetransport measurements are described in the Supporting Information. 3. Results and Discussion Molecular Properties. The geometry optimizations show that the fused rings in the TPBIQ [DPIQ] molecule (red part in Figure 1) are mostly coplanar and that the phenyl rings twist
c
Cyclic
by 46.6° [47.4°] and 55.9° [57.5°], in good agreement with the experimental crystal structures (42° [44°] and 50° [53°]).22 The geometry modifications occurring upon oxidation and reduction of the TPBIQ and DPIQ molecules are shown in Figure 2. The bond relaxations upon oxidation and reduction are found to occur over the entire molecule and are more pronounced within the fused rings. There are also large modifications in the twist angles between the phenyl rings and the central part (see Table S1 in the Supporting Information). The geometry changes that take place after reduction are significantly larger than those occurring upon oxidation; this indicates that the reorganization energy for electrons is substantially larger than that for holes in both TPBIQ and DPIQ. The vertical IPs and EAs derived from self-consistent field (∆SCF) calculations and at the Koopmans’ theorem level50 are collected in Table 1. The Koopmans’ theorem values point to a decrease in IP by 0.2 eV and an increase in EA by 0.4 eV when going from DPIQ to TPBIQ; the respective changes
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Figure 3. B3LYP/6-31G(d)-optimized TPBIQ and DPIQ crystal structures (the hydrogen atoms are not shown for the sake of clarity). The labeling of the molecular pairs as used in the calculations of the transfer integrals is also shown.
obtained from ∆SCF calculations are about 2 times as large. The experimental cyclic voltammetry measurements in solution indicate similar trends; however, the differences between the experimental IPs and EAs of these two molecules are much smaller than the DFT estimates, likely due to the polarization by the solvent in the experiment. Crystal Properties. The TPBIQ crystal belongs to the monoclinic space group C2/c (a ) 18.8616 Å, b ) 13.9296 Å, c ) 12.4295 Å, and β ) 95.464°) with two molecules per primitive unit cell, while the DPIQ crystal belongs to the P21/c monoclinic space group (a ) 15.958 Å, b ) 7.035 Å, c ) 22.523 Å, and β ) 132.189°) with four molecules per unit cell. The optimized crystal structures of TPBIQ and DPIQ are shown in Figure 3. Overall, the molecular geometries obtained from the optimization of crystal structures are very similar to those obtained for isolated molecules. In the case of TPBIQ, the molecules are arranged along the c direction into a slipped cofacial motif (π-stacking) with a distance of about 3.60 Å between the N atoms of two adjacent molecules. In the DPIQ crystal, the π-stacking direction corresponds to the b-axis (see Figure 3). In this case, there are two different dimers along the π-stacking direction with the N-N distances between two adjacent molecules of 4.11 Å and 4.68 Å, respectively. Transfer Integrals. The largest transfer integrals calculated for nearest-neighbor pairs of TPBIQ and DPIQ molecules along various crystal directions are collected in Table 2. In the case of TPBIQ, we find significant electronic couplings for both electrons and holes only along the π-stacking direction; they are 43 meV for holes and 49 meV for electrons. These values
TABLE 2: Transfer Integrals (t0) Calculated for TPBIQ and DPIQ with the B3LYP/6-31G (d, p) Method system TPBIQ DPIQ
pair 1 2 3 1 2 3 4 5
(along c-axis) (along b-axis) (along b-axis) (in ac plane)
t0 (holes)/meV
t0 (electrons)/meV
-43 2 5 -20 -58 1 7 -3
49 -4 1 -16 -17 -16 3 4
are almost twice smaller than those in pentacene43 (85 and 81 meV for holes and electrons along the diagonal directions within the ab-plane, respectively). There is also significant electronic coupling along the π-stacking direction in the case of DPIQ; as mentioned above, there are two nonequivalent dimers along the π-stacking direction in this crystal: the corresponding electronic couplings for the two dimers are very different in the case of holes, but are rather similar in the case of electrons. In DPIQ, in contrast to TPBIQ, non-negligible electronic couplings can be found along directions other than the π-stacking direction. For instance, the coupling for electrons in pair 3 is similar to that along the π-stacking direction; there is also a moderate coupling of about 7 meV for holes in pair 4. As seen from Table 2, the transfer integrals for electrons in TPBIQ are significantly larger than those in DPIQ. In the case of holes, the transfer integrals along the π-stacking direction in TPBIQ fall between those of the two nonequivalent dimers present along the π-stacking direction in DPIQ. However, as we discussed
Charge-Transport Properties of TPBIQ and DPIQ Crystals
J. Phys. Chem. C, Vol. 114, No. 48, 2010 20405 TABLE 3: Hole and Electron Effective Masses mii (In Units of the Electron Mass at Rest, m0) at the Band Extrema of the TPBIQ and DPIQ Crystals system TPBIQ
a
holes at ∆L (0.3673,0.3673,0) holes at La electrons at ΛLb (0.0918, 0.0918,0)
DPIQ
holes at B electrons at ΛBA (0.5, 0.2449, 0)
m/m0
parallel to
3.44
c + 0.179a - 0.179b
6.91 12.5 3.53 5.72 -20.2 1.43
a - b - 0.275c a+b c + 0.361a - 0.361b a - b - 0.725c a+b c + 0.190a - 0.190b - b - 0.302c +b + 0.666c
7.16 20.0 2.59 5.40 77.3 3.81
a a a b a a
4.21 13.3
c - 0.098a (|c) b
- 0.972c + 0.502c (⊥c)
a Either A or L is not the energy maximum; ∆E(∆L - A) ) 6.82 meV and ∆E(∆L - L) ) 1.30 meV. b The Γ-point is not the energy minimum; ∆E(ΛL - Γ) ) 0.30 meV.
Figure 4. B3LYP/6-31G(d)-calculated band structures and DOS for the geometry-optimized TPBIQ (top panel) and DPIQ (bottom panel) crystals. Points of high symmetry in the first Brillouin zone are labeled as follows: (TPBIQ) Γ ) (0,0,0), A ) (0.5, 0, 0), Z ) (0, 0.5, 0.5), L ) (0.5, 0.5, 0), M ) (0.5, 0.5, 0.5), and V ) (0, 0, 0.5); (DPIQ) B ) (0.5,0,0), Y ) (0,0.5,0), Z ) (0,0,0.5), C ) (0, 0.5, 0.5), D ) (0.5, 0, 0.5), A ) (0.5, 0.5, 0), and E ) (0.5, 0.5, 0.5), all in crystallographic coordinates. The Fermi energy is taken as the origin of the energy axis.
elsewhere,51 we note that, in the case of alternating dimers, charge transport along the corresponding direction is determined by the smaller transfer integral rather than the average of the two (this is valid in both hopping and band-like regimes). This means that the effective electronic coupling for holes is actually larger in TPBIQ. Band Structure. The electronic band structures of the TPBIQ and DPIQ crystals are displayed in Figure 4. The conduction and valence bands of TPBIQ consist of two sub-bands that arise from the presence of two molecules in the primitive unit cell. The overall widths of the valence and conduction bands are 199 and 218 meV, respectively. These values are only slightly larger than the values that would be derived from a onedimensional tight-binding model (along the c-axis: 4th ) 174
meV; 4te ) 199 meV). For the sake of comparison, we note that the valence bandwidth in rubrene obtained from similar band-structure calculations is about 400 meV.52 The largest valence and conduction band dispersions occur, as expected, along the π-stacking direction (Γ-Z). Very small band dispersions are observed along the other directions. These results are consistent with the results of the transfer integral calculations on molecular pairs. In the case of DPIQ, the conduction and valence bands consist of four sub-bands since four inequivalent molecules are present in the unit cell. As a consequence of the presence of alternating dimers along the π-stacking direction, the valence band splits into two groups of sub-bands with bandwidths of 86 and 65 meV, respectively. A one-dimensional tight-binding model that accounts only for the couplings along the b-axis yields a bandwidth of 157 meV, which is slightly smaller than the full valence bandwidth of 187 meV derived from the band-structure calculations. In the case of electrons, in contrast to holes, the inequivalent dimers display similar couplings; as a result, the two-by-two splitting observed for the valence band does not occur in the conduction band. The DFT-estimated conduction bandwidth is about 145 meV. Effective Mass. The calculated effective masses are reported in Table 3. In the TPBIQ crystal, the smallest effective mass for both holes and electrons, as expected, is found along the π-stacking direction: about 1.37m0 for electrons and 3.44m0 for holes, which is almost twice larger than the effective masses for holes in pentacene53 (estimated to be 1.7m0). In the case of DPIQ, the smallest hole effective mass is 2.59m0, approximately along the diagonal direction in the ac-plane; for electrons, it is 3.81m0, along a direction nearly perpendicular to the c-axis in the ac-plane. We note that the effective mass is defined not only by the electronic coupling but also by the intermolecular distance, d. For instance, in a one-dimensional tight-binding model, the effective mass is given by38
m)
p2 2td2
(9)
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TABLE 4: B3LYP/6-31G(d, p)-Calculated Reorganization Energies λ (in eV) for Hole and Electron in TPBIQ and DPIQ TPBIQ DPIQ pentacene rubrene a
λh
λe
0.125 0.250 0.097a 0.159b
0.286 0.425 0.132a 0.192c
References 54 and 55. b Reference 52. c Present work.
In DPIQ, the distance between adjacent molecules in the ac plane is over 3 times larger than along the b-axis. Consideration of eq 9 rationalizes why, in this crystal, the smallest effective mass for holes is found within the ac plane, although the transfer integral for holes along the b-axis is 6 times as large as that in the ac plane. Local Electron-Vibration Coupling. The intramolecular reorganization energies of the TPBIQ and DPIQ molecules are collected in Table 4 along with those of rubrene and pentacene. The data show that, when going from TPBIQ to the parent DPIQ, λ increases by a factor of 2 and 1.5 for holes and electrons, respectively. In both compounds, the reorganization energy of the holes is about twice as small as that for electrons. As seen from Table 4, λ for holes in TPBIQ falls between the values derived at the same level of theory for pentacene54,55 and rubrene.52 The decompositions of the reorganization energies into the contributions from the normal modes are illustrated in Figure 5. The reorganization energy for the hole is dominated by highenergy normal modes above 1200 cm-1, which account for 71% and 65% of λ in TPBIQ and DPIQ, respectively. They are associated with normal modes due to both the phenyl rings and the central fused rings (see Figures S4 and S5 in the Supporting Information). In the case of electrons, the contribution of the high-frequency vibrations above 1200 cm-1 to the reorganization energy is 55% in TPBIQ and only 40% in DPIQ. As seen from Figure 5, low-frequency modes below 200 cm-1 interact more strongly with electrons than with holes; this indicates that the temperature effects on charge transport in both systems due to interactions with intramolecular vibrations are larger for electrons than for holes. As mentioned above, in addition to the intramolecular (innersphere) contribution to the reorganization energy, there is a second (outer-sphere) contribution that reflects the changes in
the polarization of the surroundings. When a hole or an electron is localized on a given molecule, its energy is modified by the electronic polarization P that results from the interaction of the excess charge with both permanent and induced multipoles in the surrounding molecules. Coupling with phonons takes place through changes in P as a result of intermolecular geometric relaxations. In the case of nonpolar molecules, the outer-sphere part of the reorganization energy was shown to be much smaller than its intramolecular counterpart.56,57 We expect, therefore, that the overall reorganization energies in TPBIQ for both holes and electrons are only slightly larger than the values given in Table 4. The situation is likely different in the case of DPIQ since this molecule, in contrast to TPBIQ, has a significant dipole moment (1.6 D, i.e., equivalent to that of the water molecule); we can thus anticipate that in DPIQ the reorganization energies are substantially larger than the values given in Table 4. Nonlocal Electron-Vibration Coupling. We now turn to nonlocal coupling (a detailed discussion can be found in our recent work32). The probability distributions of the transfer integrals related to the π-stacking directions are shown in Figure 6; the relaxation energies, thermal averaged values of the transfer integrals, and their standard deviations derived from these distributions are collected in Table 5. As seen from Figure 5, the transfer-integral distributions display a Gaussian shape, and the average values of the transfer integrals are very close to the values derived at equilibrium geometries. These findings suggest that both the harmonic approximation for the vibration manifold and the linear approximation for nonlocal coupling, which have been assumed in deriving eqs 2 and 3, hold very well for the present systems. There are noticeable differences between the transfer integrals shown in Table 2 and in Table 5 that can be attributed to the differences in DFT and COMPASS optimized crystal geometries. As seen from Table 5, the relaxation energies related to nonlocal coupling are larger for holes than for electrons, a trend opposite to that found for local couplings. The nonlocal coupling has a dual effect on charge transport. On one hand, as a scattering mechanism, it works toward decreasing the carrier mobility. On the other hand, it leads to an effective increase in the squared transfer integrals that results in an additional, so-called phonon-assisted (non-Condon), contribution to the mobility.33 The relaxation time due to scattering processes induced by the nonlocal coupling depends
Figure 5. Contributions of the vibrational modes to the polaron binding energy (relaxation energy) in TPBIQ and DPIQ.
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Figure 6. Normalized probability distributions of the transfer integrals for holes and electrons along the TPBIQ and DPIQ π-stacking directions; the average values 〈t〉 and the standard deviations σ are reported in Table 5. The red lines represent Gaussian fits, and the vertical lines correspond to the transfer integrals (t0) obtained from the equilibrium geometry at the COMPASS molecular mechanics level.
TABLE 5: Values of L, Average of the Transfer Integrals 〈t〉, and Standard Deviation σ for Representative Dimers (Pair 1 in TPBIQ and Pairs 1 and 2 in DPIQ, See Figure 3)a dimers
σh
〈th〉
Lh
σe
TPBIQ
1
26.5
-64.7
13.7
DPIQ
1 2
30.3 25.0
-3.0 -55.2
17.8 12.2
a
〈te〉
Le
21.1
44.4
8.7
13.6 21.4
-10.9 7.9
3.6 8.9
All values in meV.
on the dimensionless parameter t0/L.58 Thus, our results suggest that the scattering of the charge carriers due to the interaction with optical vibrations (phonons) is more intense in DPIQ (especially in the case of electrons) than in TPBIQ. The ratio
between the phonon-assisted contribution (non-Condon) and conventional (Condon) contribution to the charge transport is given, according to eqs 7 and 8, by σ2/t02. The relative impact of the phonon-assisted mechanism is also larger in the case of electrons in DPIQ. In the case of TPBIQ, we also checked the effect of the nonlocal interaction on the electronic couplings along directions other than the π-stacking direction (see Supporting Information). The results indicate that the nonlocal interactions do not lead to any substantial increase in electronic couplings along these directions; this points to the fact that charge transport in this system is quasi-one-dimensional (favorable only along the π-stacking direction).
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4. Conclusions We have investigated by means of DFT and semiempirical INDO calculations the charge-transport parameters of the TPBIQ crystal and compared them to those of the parent DPIQ crystal. The band-structure calculations underscore that hole and electron transport in the TPBIQ crystal is favorable only along the π-stacking direction, while in DPIQ significant electronic couplings are also found along other directions. The effective electronic couplings are calculated to be larger in TPBIQ than in DPIQ, while the intramolecular reorganization energies are lower. In addition, since the DPIQ molecule has a significant dipole moment, a larger external contribution to the reorganization energy is expected in this crystal. Thus, we anticipate that the activation energy for both electron and hole transfer is substantially higher in DPIQ. These results suggest that charge transport at high (i.e., room) temperature in DPIQ should take place in a hopping regime. The larger electronic couplings and much smaller λ and t0/L values in TPBIQ than in DPIQ suggest that the intrinsic charge transport in TPBIQ could take place in a band-like or intermediate regime. Further clarification of this issue could be obtained from temperaturedependent measurements of mobility and modeling of charge transport in the framework of more elaborate polaron models. Our findings are consistent with the experimental data. Fieldeffect mobility measurements in the TPBIQ single crystal indicate that the hole mobility along the π-stacking direction is about 1.0 cm2/(V s). In DPIQ, the hole mobility (see Supporting Information) is very small, ∼10-5 cm2/(V s) (note, however, that the field-effect transistors in the latter case were based on thin films of DPIQ, and the lower performance could be partly attributed to a lower structural quality of the material). In any event, our results underline that the observed difference in charge-transport properties is largely a reflection of the intrinsic electronic properties of these materials. Acknowledgment. The authors would like first to acknowledge the profound influence that Professor Mark Ratner has had on their work over the past several decades; we are most grateful for the many stimulating collaborations in which Mark invariably offered deep insight and infectious enthusiasm. The Georgia Tech-Washington collaboration is partly supported by the STC Program of the National Science Foundation (under Award DMR-0120967) and by Solvay. S.A.J. also acknowledges partial support from the NSF (DMR-0805259), and J.-L.B. acknowledges support from the NSF MRSEC Program (under Award DMR-0819885). Supporting Information Available: Synthesis, cyclic voltammetry measurements, charge-transport properties, device fabrication and characterization of DPIQ, and X-ray crystallographic data in CIF format for DPIQ; B3LYP/6-31G(d,p)optimized bond lengths in the neutral TPBIQ and DPIQ molecules and singly charged cation and anion state; B3LYP/ 6-31G(d,p) local electron-vibration couplings in TPBIQ and DPIQ from the adiabatic potential (AP) surfaces and from a normal-mode (NM) analysis; illustration of the normal-mode leading to strong vibronic coupling in cationic and anionic TPBIQ and DPIQ; and nonlocal electron-vibration coupling along various directions in TPBIQ. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Garnier, F.; Hajlaoui, R.; Yassar, A.; Srivastava, P. Science 1994, 265, 1684.
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