J. Phys. Chem. C 2008, 112, 7959–7967
7959
Trends in Electron-Vibration and Electronic Interactions in Bis(dimethylamino) Mixed-Valence Systems: A Joint Experimental and Theoretical Investigation† Chad Risko,‡,| Veaceslav Coropceanu,| Stephen Barlow,| Victor Geskin,⊥ Karin Schmidt,§,| Nadine E. Gruhn,# Seth R. Marder,| and Jean-Luc Bre´das*,| School of Chemistry and Biochemistry, Center for Organic Photonics and Electronics, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, UniVersity of Mons-Hainaut, Laboratory for Chemistry of NoVel Materials, Place du Parc 20, B-7000 Mons, Belgium, and Department of Chemistry, The UniVersity of Arizona, Tucson, Arizona 85721-0041 ReceiVed: December 20, 2007; ReVised Manuscript ReceiVed: February 5, 2008
By using gas-phase ultraviolet photoelectron spectroscopy, vis/NIR spectroscopy, and electronic-structure calculations, we have investigated the electron-vibration and electronic interactions in a series of bisdimethylamino mixed-valence systems: N,N,N′,N′-tetramethyl-p-phenylenediamine, N,N,N′,N′-tetramethylbenzidine, and N,N,N′,N′-tetramethyltolane-4,4′-diamine. Experiment and theory concur to indicate that the electron-vibration coupling in these systems is dominated by interactions with symmetric modes. The results reveal that the strength of both electronic and electron-vibration couplings decreases as the molecular bridge lengthens. The parameters derived for the present compounds have been compared to those of diarylaminobased structural analogs. This comparison underlines that the replacement of the methyl terminal groups with p-anisyl groups has a significant effect on the electronic and electron-vibrational interactions. 1. Introduction Organic mixed-valence (MV) systems have received considerable recent attention as tools for the fundamental study of electron-transfer (ET) processes.1–17 In such systems, the inherent ET properties and patterns of charge (de)localization strongly depend on the interplay and strengths of electronic and vibrational interactions [i.e., transfer integrals (electronic coupling) and intermolecular reorganization energies, respectively]. A characteristic feature of MV compounds is the presence of an absorption band in the visible or near-infrared (NIR). This band, referred to as the intervalence charge-transfer (IVCT) band or, especially in the case of delocalized systems, as the chargeresonance (CR) band, results from transitions within the electron-vibrational manifold generated by electronic interactions among charge-bearing subunits. It is of experimental and theoretical interest18 that this band can be analyzed to provide the values of electronic coupling and reorganization energy. Partly for this reason, organic MV compounds with IVCT bands that are well-separated from other electronic transitions, for instance, bis(triarylamine)s, have been widely investigated. With such compounds, a number of aspectssincluding the influence of the bridge (e.g., the role of the bridge length, topology, and energetics) on the extent of electronic communication between the organic redox sitesshave been well-characterized.6,13,19–29 In this contribution, we describe the electronic and electronvibration couplings in the series of bis-dimethylamino species shown in Figure 1: N,N,N′,N′-tetramethyl-p-phenylenediamine (1), N,N,N′,N′-tetramethyl-benzidine (2), and N,N,N′,N′-tetram† Part of the “Larry Dalton Festschrift”. * Corresponding author. E-mail:
[email protected]. ‡ Present address: Department of Chemistry, Northwestern University, 2145 Sheridan Rd, Evanston, IL 60208. § Present address: Institute of Theoretical and Computational Physics, Graz University of Technology, Petersgasse 16, A-8010 Graz, Austria. | Georgia Institute of Technology. ⊥ University of Mons-Hainaut. # The University of Arizona.
ethyltolane-4,4′-diamine (3). The vis-NIR spectroscopy results show that 1+-3+ exhibit a well-separated IVCT band with a finely resolved vibrational structure, a feature that allows for a detailed study of the electron-vibrational interaction. In addition to vis-NIR spectroscopy measurements for 1+-3+, we have also acquired gas-phase ultraviolet photoelectron spectra for 1-3 and performed a series of quantum-chemical calculations. In order to gain further insight into the effects provided by the terminal group substitution on the electronic and electron-vibrational couplings, we compared the results herein to previous analyses of diarylamino-based structural analogs I-III (Figure 1). 2. Experimental and Theoretical Procedures Materials. 1 and 2 were obtained from Acros Organics. 3 was prepared from the Pd0-catalyzed coupling of ArI [Ar ) 4-(dimethylamino)phenyl] with ArC≡CZnCl (which was itself obtained by the coupling of Me3SiC≡CZnCl with ArI, followed by deprotection and metalation). All reactions used standard procedures30 and the 1H NMR spectrum of 3 was in accordance with that reported in the literature.31 Electrochemistry. Cyclic voltammograms were recorded under nitrogen on dry deoxygenated dichloromethane solutions ca. 10-4 M in analyte and 0.1 M in tetra-n-butylammonium hexafluorophosphate using a BAS potentiostat, a glassy carbon working electrode, a platinum auxiliary electrode, and, as a pseudoreference electrode, a silver wire anodized in 1 M aqueous potassium chloride. Potentials were referenced to ferrocenium/ferrocene by using decamethylferrocene as an internal standard (E1/2 ) -0.55 V vs ferrocenium/ferrocene). UV-Vis-NIR Spectroscopy. UV-vis-NIR spectra were recorded in 1-cm cells using a Varian Cary 5E spectrometer. Solutions containing 1+, 2+, and 3+ were generated by the addition of substoichiometric portions of tris(4-bromophenyl)aminium hexafluoroantimonate (Aldrich) to solutions of the appropriate neutral amine in dry solvent. Commercial 1 was
10.1021/jp711954j CCC: $40.75 2008 American Chemical Society Published on Web 04/24/2008
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Risko et al. TABLE 1: Ionization Potentials (in Parentheses) and Widths of the Ionization Bands Derived from the Gas-Phase Photoelectron Spectra of 1-3a 1 2b 3b Ib IIb a
IP1
IP2
∆IP
6.78 (0.74) 6.75 (0.65) 6.81 (0.67) 6.36 (0.59) 6.50 (0.64)
8.36 (0.34) 7.58 (0.54) 7.47 (0.51) 7.05 (0.49) 6.88 (0.62)
1.58 0.83 0.66 0.69 0.38
All values are in electronvolts. b Data from ref 23.
TABLE 2: Electrochemical Half-Wave Potentials (V vs FeCp2+/0, CH2Cl2/0.1 M [nBu4N]+[PF6]-) for for 1-3 and I-III E1/2+/0 E1/22+/+ ∆E1/2
1
2
3
Ia
IIa
IIIa
-0.29 ca. +0.45b ca. 0.74
+0.01 +0.33 0.32
+0.18 +0.39 0.21
-0.15 +0.34 0.49
+0.09 +0.31 0.22
+0.21 +0.36 0.15
a Data from ref 6. b Irreversible; peak potential, Eox, is reported for a scan rate of 50 mVs-1.
Figure 1. Chemical structures of the systems considered in this work.
Figure 2. Gas-phase photoelectron spectra of 1-3.
found to contain colored impurities with absorptions overlapping with the IVCT band of its cation and was therefore purified by sublimation (at 0.15 mmHg and 50 °C, onto a water-cooled probe) before vis-NIR measurements. The stability of solutions of the mixed-valence species decreases in the order 1+ > 2+ > 3+ and, in contrast to bis(diarylamino) species, solutions in acetonitrile are more stable than those in dichloromethane. In the case of 3+, spectra show a feature at ca. 655 nm that can be attributed to a decomposition product whose intensity increases with time, while that of the IVCT decreases.
UPS. Gas-phase photoelectron spectra for 3 were collected at the Center for Gas-Phase Electron Spectroscopy (Department of Chemistry, The University of Arizona) using an instrument and experimental procedures described in more detail elsewhere.32 3 was sublimed (10-4 Torr) at 140-160 °C with no evidence of contaminants present in the gas phase during data collection. Instrument resolution during data collection was better than 30 meV (measured using the full width at half-height for the 2P3/2 ionization of Ar). Computational Methodology. Minimization of the neutral (S0) and radical-cation (D0) ground states were carried out at the density functional theory (DFT) level using the B3LYP functionals, where Becke’s three-parameter hybrid exchange functional33 is combined with the Lee-Yang-Parr correlation functional;34 a Gaussian atomic orbital basis set of split valence plus polarization quality was used for the evaluations. Excitation energies for the low-lying states of the radical-cation species were calculated at the time-dependent DFT (TDDFT) level. With these results, the lowest-lying radical-cation excited state (D1) was optimized using the recent implementation of analytical gradients in TDDFT.35 Normal-mode analyses were completed for all of the optimized geometries to ensure that the geometries were not at transition states. The vibrational modes were then used to simulate the IVCT band in the framework of the Franck-Condon approach described in detail elsewhere;36 the Huang-Rhys factors contributing to the reorganization energies of the radical cations were obtained using the DUSHIN program of Reimers.37 The usual scaling factor of 0.9613 for the B3LYP frequencies was used to model the experimental spectra. Additional electronic structure calculations were performed at the AM1 level coupled with a complete active space configuration interaction (CAS-CI). All DFT and TDDFT calculations were performed with the TURBOMOLE 5.6 software suite,38 and the AM1 calculations, with Ampac 6.55.39 3. Results and Discussion UPS, Electrochemistry, and Optical Spectra. The photoelectron spectrum of 3 as well as those reported previously23 for 1 and 2 are shown in Figure 2. The vertical ionization potentials, as derived from deconvolutions of the spectra with Gaussian functions, are given in Table 1. The first ionization potentials (IP1) are similar for all three compounds. In contrast
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Figure 3. Vis/NIR spectra of 1+-3+ in CH2Cl2 (solid line) and MeCN (dashed line). Note that the feature observed at ca. 15000 cm-1 for 3+ is due to a decomposition product.
to IP1, the second ionization potentials (IP2) decrease significantly as the bridge lengthens. The ∆IP () IP2 - IP1) is observed to go down from 1.58 to 0.66 eV across 1-3. The UPS data also reveal that although in 2 and 3 the ground and first excited states of the radical cation are well-separated (by over 1 eV) from the second excited state in 1 the energy separation between the first two excited states of the radical cation (corresponding to IP2 and IP3 in Figure 2) is only about 0.4 eV. We note that, according to excited-state calculations, the second excited state of 1+-3+ is dark (dipole-forbidden); therefore, its location cannot be determined from vis-NIR absorption spectra.
J. Phys. Chem. C, Vol. 112, No. 21, 2008 7961 Cyclic voltammetry data are reported in Table 2 for dichloromethane solutions, together with data reported earlier for compounds I-III for comparison; compounds 1-3 are observed to undergo chemically reversible oxidation to their radical cations.40 The ease of oxidation decreases dramatically from 1 to 2 to 3 in contrast to the similarity in IP1 values. Moreover, the replacement of the methyl groups of 1 and 2 with anisyl groups to obtain I and II results in a decrease in IP1, whereas E1/2+/0 shows the opposite behavior. The difference in trends between UPS and electrochemistry is likely related to solvation effects. The separation between the first and second oxidations, ∆E1/2, also decreases from 1-3, although the second oxidation for 1 is not reversible in this solvent.41 ∆E1/2 is not a direct measure of the electronic coupling, V, in the MV species due to other contributing factors;42,43 however, the trends seen in Table 2 are similar to those in Table 5 with experimental estimates of V from both UPS and the CR bands linearly correlating with ∆E1/2 for 1-3. There is also some correlation for I-III, as noted previously by Lambert and No¨ll,6 although the couplings are smaller for a given ∆E1/2 in this series. The vis-NIR absorption spectra for chemically generated 1+, + 2 , and 3+ are presented in Figure 3. The data shown for 1+ and 2+ are consistent with previous reports in the literature,44 whereas, to the best of our knowledge, the absorption of 3+ is reported for the first time. The position and shape of the optical bands show essentially no dependence on solvent polarity. In all three cases, the lowest-lying absorption, which we identify as the CR (IVCT) band, is characterized by a well-defined vibrational structure. It is worth noting that Class-II MV systems are characterized by strong vibronic interactions with both intramolecular and low-frequency solvent vibrations; as a result, their CR bands are broad, Gaussian-shaped, and featureless. In the case of Class-III MV systems, the solvent vibrations are not coupled to ET and the interaction with intramolecular vibrations is generally weaker, leading to narrower and asymmetric CR bands; in a few cases7,45–47 where the vibronic interaction is dominated by high-frequency vibrational modes, the CR bands even exhibit a vibrational structure. Therefore, the observation of a vibrational fine structure in the CR bands of 1+-3+, along with the absence of solvent dependence, strongly points to the assignment of all three radical cations as Robin and Day Class-III (fully delocalized) MV systems.48 Geometric and Electronic Structure. Selected geometric parameters for the ground state of the neutral species (S0) and for the ground (D0) and first-excited (D1) states of the radical cations of 1, 2, and 3, as obtained from DFT and TDDFT, are given in Table 3 (see Figure 4 for bond labeling). The dimethylaminophenyl segments of the S0 states of 1 and 3 are very slightly pyramidal with the bond-angle sums around the nitrogen atoms being slightly less than 360° (356.7° and 359.4° for 1 and 3, respectively). Because of this pyramidal nature, two conformations are possible for the S0 states: one with C2V symmetry, in which all of the methyl groups lie on one side of the phenylene-ring plane, and one belonging to C2h symmetry, in which the methyl groups of the pendant amines lie on opposing sides of the phenylene-ring plane; however, the bond lengths and angles are identical for these energetically quasi-degenerate conformations. For 2, the twist between the phenylene rings of the biphenyl bridge (33°) reduces the molecular symmetry relative to that found in 1 and 3 to C2. The dimethylaminophenyl groups are also slightly pyramidal (358.8°). The bond lengths in the dimethylamino groups and phenylene rings are similar to those of 1.
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TABLE 3: Selected Unique Bond Lengths (Å) and Angles (deg) for the S0, D0, and D1 States of 1, 2, and 3 at the DFT/TDDFT Levels of Theory (see Figure 4 for bond labeling) 1+
1
2+
2
3+
3
state molecular symmetry
S0 C2V
D0 D2h
D1 D2h
S0 C2
D0 D2
D0 D2h
D1 D2h
S0 C2V
D0 D2h
D1 D2h
1 2 3 4 5 6 7 angle sum N
1.446 1.399 1.413 1.395
1.465 1.357 1.433 1.375
1.448 1.413 1.414 1.399
1.447 1.389 1.417 1.394 1.408 1.484
1.462 1.359 1.431 1.378 1.426 1.451
1.462 1.359 1.431 1.377 1.427 1.452
1.456 1.382 1.422 1.389 1.415 1.492
356.7
360.1
360.0
358.8
360.0
360.1
360.1
1.449 1.385 1.419 1.391 1.412 1.426 1.222 359.4
1.462 1.359 1.433 1.377 1.427 1.397 1.234 360.0
1.458 1.377 1.426 1.386 1.418 1.422 1.225 360.1
Upon oxidation to the D0 state, the molecular symmetry of both 1 and 3 transforms to D2h as the dimethylaminophenyl groups lose their pyramidal nature. The CmethylsN bonds lengthen, while the N-Cphenylene bonds shorten significantly. Within the phenylene rings, the bond-length alternation (BLA) increases significantly, while the acetylene bridge of 3 undergoes a decrease in BLA; these structural changes mark the expected progression toward a more quinoidal structure upon oxidation. The calculated geometries of 1 and 1+ are comparable to the previous computational results (B3LYP/6-31G*) of Brouwer49 and the crystallographic results of de Boer and Vos50 and of Ikemoto et al.51 Oxidation of 2 to the D0 state planarizes the dimethylaminophenyl units, as in the case of 1+ and 3+ described above, and thus increases the molecular symmetry. From the DFT calculations, two possible geometric structures of very similar energy and having D2 [twisted biphenylene (∼15°)] and D2h [planar biphenylene (0°)] molecular symmetry are possible (the D2h geometry has been used in all subsequent calculations). Similar results have been obtained in earlier work, from both DFT calculations and time-resolved resonance Raman spectroscopy.52,53 As in the other compounds, the CmethylsN bonds lengthen, the N-Cphenylene bonds shorten, the C-C bonds within the phenylene units of the biphenylene bridge take on a more quinoidal-like structure, and the central biphenylene C-C bond shortens considerably with respect to the neutral molecule. The TDDFT transition energies and transition dipole moments for 1+-3+ are included in Table 4. The calculated energies of the first optical transition are somewhat overestimated; however, the experimental variation in peak position among the compounds is well-reproduced. The molecular orbitals of the radical cations are very similar to those of the corresponding neutral species, with the singly occupied orbitals of the radical ions corresponding to the HOMOs of the neutral species, which are shown in Figure 5. Using the nomenclature of the neutral molecules, the TDDFT results indicate that the lowest energy transitions for the radical-cation species are predominantly HOMO-1 to HOMO in nature. In each case, the HOMO and HOMO-1 are of opposite parity and can be regarded as inphase or out-of-phase linear combinations of two amine-based orbitals dominated by p-like nitrogen orbitals with considerable contributions from the π orbitals of the bridge. The present orbital pictures closely resemble those reported for delocalized bis(diarylamino) radical cations,21,26,28,29 suggesting that the lowest optical band in both groups of compounds have comparable IVCT character.
Figure 4. Bond labeling scheme.
Although the DFT geometries obtained for 1+-3+ are symmetrical, suggesting assignment to Class III, it should be noted that DFT methods often lead to overdelocalization54 and, therefore, may erroneously suggest a symmetric Class-III structure for a Class-II species.24 However, these methods have previously been found to give good agreement with structural and spectroscopic features when applied to species determined experimentally to belong to Class III.7,20,21,26 Therefore, the agreement between the trends in the TDDFT and experimental transition energies does provide further support for the assignment of the 1+-3+ species to class III. Electronic Coupling. On the basis of the experimental and theoretical results presented above, the degree of electronic coupling between the two amine redox sites can be assessed via several methods. The first is based on the energy of the absorption spectra and the assumption that 1+-3+ are delocalized Class-III MV systems; the electronic coupling can then be derived from V ) Eop/2, where Eop is the energy of the CR peak. The second experimental estimate is based on the ionization potentials; in this approach, the electronic coupling is obtained as V ) (IP2 - IP1)/2.23 Theoretical estimates of V were derived in the same way from the TDDFT energies for the first optical transition and, in the framework of Koopmans’ theorem55 (KT), as half of the difference between the HOMO and HOMO-1 energies. These estimates of electronic couplings for 1+-3+ are given in Table 5; for the sake of comparison, results derived previously for I+-III+ are also given. Both the UPS and vis-NIR results reveal that the electronic coupling is almost halved on going from 1+ to 2+ and decreases much less significantly between 2+and 3+. We note that estimates of V based on UPS are smaller than those derived from the optical spectra; the principal difference between the two sets of data is related to the fact that UPS data are acquired at the geometry of the neutral molecule while CR data are determined at the geometry of the radical cation. TDDFT overestimates the electronic coupling to some extent. At the KT level, the best theoretical agreements with experiment are obtained for the values derived from AM1 calculations; overall, the calculated electronic-structure results are in good qualitative agreement with the experimental estimates. Electron-Vibrational Coupling. To gain insight into the electron-vibration couplings, we derived the relaxation energy and normal modes of the first excited states of 1+-3+ by means of TDDFT calculations.38 The geometry of the lowest excited state of each of the three species (Table 3) belongs to the D2h symmetry group. In the D1 state of 1+, the Cmethyl-N bonds shorten to lengths very similar to those observed in the neutral ground state, while the N-Cphenylene bonds lengthen to distances longer than those observed in both the S0 (by 0.014 Å) and D0 (by 0.056 Å) ground states. The phenylene ring adjusts back to
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Figure 5. Pictorial representations of the B3LYP/6-31G** HOMO and HOMO-1 molecular orbitals in 1, 2, and 3.
TABLE 4: TDDFT Vertical Excitation Energies and Transition Dipole Moments (µ) of Compounds 1+-3+ Obtained at the UB3LYP/6-31G** Radical-Cation Geometrya 1+ 2+ 3+
a
TABLE 6: Vibrational Mode Frequencies (ν, cm-1) and Huang-Rhys Factors (S) for Transition into the First Excited State of 1+-3+ 1+
2+
3+
Eop/eV
µ/D
configuration
ν
S
ν
S
ν
S
2.32 2.58 1.54 2.30 1.39 2.41 2.41 2.45 2.48
4.69 0.00 7.82 0.07 9.75 0.00 0.04 0.00 0.00
HOMO-1 f HOMO (91.2%) HOMO-2 f HOMO (97.7%) HOMO-1 f HOMO (93.1%) HOMO-2 f HOMO (98.0%) HOMO-1 f HOMO (93.1%) HOMO-3 f HOMO (97.7%) HOMO-4 f HOMO (97.7%) HOMO-2 f HOMO (90.6%) HOMO-5 f HOMO (99.3%)
306 543 929 1122 1197 1289 1401 1443 1602
0.28 0.07 0.10 0.18 0.08 0.16 0.01 0.02 0.35
212 930 1143 1204 1243 1345 1450 1586
0.29 0.01 0.05 0.07 0.02 0.04 0.01 0.14
181 1114 1189 1343 1452 1584 2159
0.34 0.07 0.01 0.02 0.01 0.07 0.04
The molecular orbital labels refer to the neutral states.
TABLE 5: Electronic Coupling (eV) as Determined from UPS and CR Band Measurements and TDDFT, KT-DFT, and KT-AM1 Calculations 1+ 2+ 3+ I+c II+ III+
UPS
CRa
TDDFTb
KT-DFT
KT-AM1b
0.79 0.42 0.32 0.35 0.19
1.00 0.60 0.49 0.59 0.39 0.38
1.16 0.77 0.69 0.57 0.43 0.41
0.92 0.45 0.47 0.48 0.29 0.28
0.87 0.41 0.37 0.42 0.26 0.21
a Calculated assuming the cations to be class-III systems using V ) Eop/2 for data acquired in CH2Cl2 (1+-3+) or CH2Cl2/0.1 M [nBu4N][PF6] (I+-III+). b On the basis of calculated Eop/2 for DFT optimized geometries. c Data for I+-III+ are taken from ref 24.
the more aromatic-like structure of the S0 state with a BLA of only 0.015 Å. For the first excited state of 2+, the methyl-nitrogen bond lengths fall in between those found for the neutral and radical-cation ground states, while the nitrogen-phenylene bonds are closer in length to those observed for the neutral structure. The bond lengths in the phenylene units within the bridge fall between the observed bond lengths for the neutral and radical-cation ground states but are closer to those observed in the neutral structure; the central single bond of the biphenyl unit lengthens considerably versus the radical-cation ground state. For 3+, the structure of the first excited state also resembles that of the neutral ground state more closely.
The geometric changes after the IVCT transition lead to moderate intramolecular relaxation energies. The results derived from direct self-consistent field calculations of the adiabatic potential energy surfaces yield relaxation energies, λrel, of 0.36, 0.14, and 0.10 eV in 1+, 2+, and 3+, respectively. As in the case of the electronic couplings, there is a much sharper drop between the relaxation energy values of 1+ and 2+ than between those of 2+ and 3+. The contribution of each vibrational mode to the relaxation energy has been obtained by expanding the potential energies of the ground and excited states in a power series of the normalmode coordinates. In the harmonic approximation, the relaxation energy, λrel, can be written as
∑ λi ) ∑ pωiSi
(1)
ki λi ) ∆Qi2, Si ) λi ⁄ pωi 2
(2)
λrel )
Here, the summations run over all vibrational modes; ∆Qi represents the displacement along normal mode i between the TABLE 7: AM1/CAS Mulliken Excess Positive Charges (in |e|) for the Various Segments of 1+-3+ and I+-III+ terminal groups amino N atoms bridging group
1+
2+
3+
I+
II+
III+
0.48 0.20 0.32
0.40 0.16 0.44
0.36 0.12 0.52
0.48 0.26 0.26
0.40 0.24 0.36
0.36 0.24 0.40
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Figure 6. Pictorial representation of the prominent vibrational modes contributing to the relaxation energy upon IVCT excitation.
equilibrium positions of the ground and excited states; ki and ω are the corresponding force constants and vibrational frequencies; Si denotes the Huang-Rhys factor (electron-vibration coupling constant). Intramolecular relaxation energies estimated from the normalmode calculations (the results are collected in Tables 6 and 7) agree remarkably well (0.37, 0.14, and 0.10 eV for 1+, 2+, and 3+, respectively) with those obtained from the adiabatic potential energy surfaces. As seen from Table 6, the geometry relaxation upon IVCT transition in 1+ is dominated by one low-frequency mode at 306 cm-1 with a Huang-Rhys factor S ) 0.28 and one high-frequency mode at 1602 cm-1 with S ) 0.35; modes at 929, 1122, 1197, and 1289 cm-1 do also contribute. When increasing the bridge by one phenylene unit to form 2+, the relaxation upon IVCT excitation is dominated by one low-frequency mode (212 cm-1, S ) 0.29) and one high-frequency mode (1586 cm-1, S ) 0.14). However, as can be seen from comparison of the Huang-Rhys factors, the role of the high-frequency mode is severely diminished versus that displayed in 1+. In the relaxation process of 3+, as in the case of the other two systems, there is a strong interaction with a lowfrequency mode (181 cm-1, S ) 0.34). However, the interaction with a high-frequency mode around 1600 cm-1 completely disappears; however, it is worth noting that there is some increase in interactions with several high-frequency modes around 1400 cm-1 with an overall (summed) Huang-Rhys factor of S ) 0.14. The significant decrease in electron-vibration interaction with a high frequency mode at ∼1600 cm-1 in 2+ and 3+ with respect to that in 1+ can be rationalized in terms of orbital vibronic constants.56–58 As seen from Figure 6, this vibration essentially represents a deformation of the phenylene rings. In the case of 1+, the two molecular orbitals (HOMO and HOMO-1) involved in the description of the electronic configuration of the first excited state show a significant electron density on the phenylene rings (see Figure 5). Therefore, distortion of 1+ along the 1600 cm-1 mode strongly affects the energy of both HOMO and HOMO-1, indicating that these orbitals have large orbital vibronic constants; as a consequence, the overall vibronic coupling of this mode to the first excited state is also large. In 2+ and 3+, because of the change in electron density pattern,
the HOMO-1 energy is less affected by distortions along this mode; as a result, the strength of the corresponding vibrational interaction is strongly diminished. The IVCT bands of 1+, 2+, and 3+, modeled from the results of the normal-mode calculations, are shown in Figure 7. Excellent agreement with the experimental bands is found for all three species. The decrease in the contribution of the highfrequency modes to the relaxation energy leads to a narrowing of the IVCT band when going from 1+ to 3+. Thus, both the experimental data and the theoretical results obtained from the normal-mode calculations and the subsequent simulations of the IVCT bands demonstrate that the electron-vibration coupling in 1+-3+ is dominated by interactions with symmetric modes; this interaction, as expected, decreases as the size of the molecule increases. Comparisons with Bis(diarylamino) Analogs. We now turn to a comparison of the electronic and electron-vibration couplings in 1+-3+ with those of the diarylamino-based structural analogs I+-III+ (Figure 1).6,20–25 The electronic couplings of 1+-3+ and I+-III+ systems are compared in Table 5. We note that the IVCT estimates of V in this table were obtained as V ) Eop/2, an approach that can strictly be used only for Class-III systems. Because we do not rule out the possibility of symmetry breaking to lead to Class-II species in I+-III+ (indeed, IR data26 support the assignment of III+ to Class II), the IVCT estimates of 0.59, 0.39, and 0.38 eV for I+, II+, and III+, respectively, should be treated as upper limits. For the same reason, the TDDFT results given in Table 5 also overestimate V in I+-III+. These estimates, along with the UPS results, indicate that the electronic couplings in I+-III+ are about twice as small as those in 1+-3+. As in the case of 1+-3+, a significant drop in V occurs between I+ and II+, while the electronic couplings between II+ to III+ are similar. A comparison of the IVCT bands of I+-III+ with those of + 1 -3+ is given in Figure 8. In contrast to 1+-3+, the IVCT transitions in I+-III+ are structureless and demonstrate a moderate solvatochromic effect that increases with length of the bridge. For instance, the IVCT maxima in DMSO/0.1 M [nBu4N][PF6] are blue-shifted relative to CH2Cl2/0.1 M
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Figure 8. IVCT bands in CH2Cl2 or CH2Cl2/0.1 M [nBu4N][PF6] for: (a) 1+-3+; and (b) I+-III+. For the sake of comparison, the centers of the IVCT bands have been shifted and their intensities normalized.
Figure 7. Experimental (in CH2Cl2, solid line) and theoretically simulated (gas-phase, dashed line) IVCT band for 1+-3+.
[nBu4N][PF6] by 600, 1180, and 1550 cm-1 for I+, II+, and III+, respectively.6 Additionally, although the IVCT band in 1+-3+ narrows upon increasing the length of the conjugated bridge, the trend for the I+-III+ series turns out to be quite different as the IVCT band first narrows on going from I+ to II+ and then broadens when going from II+ to III+.13 Finally, as the π-conjugation path lengthens in I+-III+, the IVCT bands become more symmetric, a trend that also contrasts with 1+-3+. These results indicate that the replacement of the methyl terminal
groups with p-anisyl groups has a significant effect on the nature of the electron-vibrational coupling. First, the bulky anisyl groups add new low-frequency vibrational modes that are presumably coupled to the ET process and thus contribute to the loss of vibrational structure in the optical bands. However, the shape of the IVCT bands in I+-III+ cannot be solely explained by assuming a simple increase in the number of vibrational modes. Previous vibronic coupling simulations24 have shown that a good agreement with experiment in these systems can be reached only when, in addition to the interaction with symmetric vibrations, the interaction with antisymmetric vibrations is taken into account. The strength of electron-vibration interactions with antisymmetric modes, in contrast to interactions with symmetric vibrations, increases as the length of the central bridge increases.24 We have also investigated the adiabatic potential energy surfaces in both 1+-3+ and I+-III+ at the AM1-CAS level. We found that the AM1-CAS geometries are essentially the same as those obtained from DFT calculations, as far as the potential minima are concerned. As in the case of the DFT calculations, symmetry breaking was not observed in any of the systems. However, the differences in terminal groups can lead to significant consequences. The replacement of methyl groups with anisyl groups results in a marked decrease of positive charge density in the bridge (see Table 7). The AM1/
7966 J. Phys. Chem. C, Vol. 112, No. 21, 2008 CAS Mulliken excess positive charges are 0.32, 0.44, and 0.52 |e| on the bridge in 1+-3+ versus 0.26, 0.36, and 0.40 in their anisyl analogs. This result is in line with the decrease in electronic coupling in bis(diarylamino) systems. The bulky anisyl groups also introduce additional structural degrees of freedom for the bis(diarylamino) species because the three phenylenes surrounding the nitrogen atom cannot be coplanar; their tilt angles, in turn, influence both conjugation through the nitrogen atoms and charge localization/delocalization. Although no symmetry breaking was found, analyses of the AM1-CAS results reveal that symmetry-broken conformations in I+-III+ lie within 0.1-0.2 eV above the optimized symmetric structures. We conclude that the presence of donor anisyl end groups makes bis(diarylamino) radical cations more prone to symmetry breaking than the bis(dimethylamino) analogs studied here. We also note that the symmetry-broken geometry, even if it is not the ground state for an isolated molecule, could be stabilized by the environment, for example, through solvent interactions. 4. Conclusions In this work, we have investigated the properties of three bis(dimethylamino) mixed-valence systems, 1+-3+. Our results strongly point to the assignment of all three radical cations to Robin and Day’s Class-III (fully delocalized) MV systems. Both experiment and theory also point to a ∼50% decrease in electronic coupling when the phenylene bridge is replaced by biphenylene. However, an additional increase in bridge length via insertion of a triple bond between the phenylene units (tolane bridge) only leads to a modest further change in electronic coupling. The IVCT band in these systems shows a wellresolved vibrational structure. We have shown that the IVCT band can be very well described in the framework of a linear vibronic coupling model, using the electron-vibration constants derived by means of TDDFT calculations. The comparison of the results obtained for the bis(dimethylamino) species with those reported previously for bis(diarylamino)-based structural analogs underlines that the replacement of methyl end groups with anisyl groups leads to a significant reduction in electronic coupling and has a marked effect on the nature of the electron-vibrational interactions. Although the IVCT bands in the bis(dimethylamino) compounds can be modeled by assuming interactions with only symmetric vibrations, to reach a good agreement between theory and experiment for bis(diarylamino) systems requires that the interactions with antisymmetric vibrations also be included. These results indicate that the electronic and electron-vibrational couplings can be tuned efficiently not only by modifications of the bridge but also by modifications of the terminal groups. Acknowledgment. We are indebted to J. Reimers for kindly providing his DUSHIN program and to H. Ro¨ckel for supplying a sample of compound 3. This work has been partly supported by the National Science Foundation (through the STC Program under Award Number DMR-0120967 and the CRIF Program under Award CHE-0443564) and the Georgia Tech “Center on Organic Photonics and Electronics (COPE)”. The work in Mons has been supported by the Interuniversity Attraction Pole IAP 6/27 Program of the Belgian Federal Government “Functional Supramolecular Systems (FS2)”. References and Notes (1) Launay, J. P. Chem. Soc. ReV. 2001, 30, 386–397. (2) Lahlil, K.; Moradpour, A.; Bowlas, C.; Menou, F.; Casoux, P.; Bonvoisin, J.; Launay, J. P.; Dive, G.; Dehareng, D. J. Am. Chem. Soc. 1995, 117, 9995–10002.
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