The electronic absorption study of imide anion radicals in terms of time dependent density functional theory

Spectrochimica Acta Part A 61 (2005) 2029–2032

The electronic absorption study of imide anion radicals in terms of time dependent density functional theory Marcin Andrzejak, Mariusz Sterzel, Marek T. Pawlikowski∗ Department of Theoretical Chemistry, Faculty of Chemistry, Jagiellonian University, 30-060 Krakow, Ingardena 3, Poland Received 21 May 2004; accepted 12 August 2004

Abstract The absorption spectra of the N-(2,5-di-tert-butylphenyl) phthalimide (1− ), N-(2,5-di-tert-butylphenyl)-1,8-naphthalimide (2− ) and N-(2,5di-tert-butylphenyl)-perylene-3,4-dicarboximide (3− ) anion radicals are studied in terms of time dependent density functional theory (TDDFT). For these anion radicals a large number electronic states (from 30 to 60) was found in the visible and near-IR regions (5000–45000 cm−1 ). In these regions the TD/B3LYP treatment at the 6–1+G* level is shown to reproduce satisfactorily the empirical absorption spectra of all three anion radicals studied. The most apparent discrepancies between purely electronic theory and the experiment could be found in the excitation region corresponding to D0 →D1 transitions in the 2− and 3− molecules. For these species we argue that the structures seen in the lowest energy part of the absorptions of the 2− and 3− species are very likely due to Franck–Condon (FC) activity of the totally symmetric vibrations not studied in this Letter. © 2004 Elsevier B.V. All rights reserved. Keywords: Imide anion radicals; Time dependent density functional theory; Electronic structure

1. Introduction In the series of recent papers [1–8] we have studied the electronic and vibronic structures of cationic, anionic and neutral species in their low energy states. From these experiences we learned that the complete active space (CASSCF) [9] technique may offer one of the best methodology to deal with the electronic structures of moderately large molecules. However, CASSCF technical problems grow very fast with the numbers of heavy atoms, especially when a debate addresses the electronic structures of highly excited electronic states of large molecules [10]. In such cases the CASSCF approach is sometimes replaced by other more efficacious and less time devouring computational techniques. There is a wide class of molecules for which physically acceptable results can be relatively easily achieved within formally less sophisticated but very practical treatments based on the density functional theory (DFT) [4–7]. The ∗

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monoanionic and monocationic species with the extended ␲ systems belong to that class of molecules. The aromatic imides and diimides anion radicals, like these derivable from the perylene-3,4-dicarboximide and the perylene-3,4:9,10tetracarboxydimide [11–13], may serve as specific examples. Very recently these important electron acceptors were experimentally investigated and their good quality electronic spectra were reported in the broad energy range from 5000 to 45000 cm−1 [14]. The large number of electronic states detected in that energy excitation region has encouraged us to challenge these spectra in terms of time dependent density functional theory (TDDFT), naturally oriented to study the excited electronic states of the large open shell systems. In this Letter we are going to present the preliminary theoretical studies of N-(2,5-di-tert-butylphenyl) phthalimide (1− ), N-(2,5-di-tert-butylphenyl)-1,8-naphthalimide (2− ) and N-(2,5-di-tert-butylphenyl)-perylene-3,4-dicarboximide (3− ) anion radicals. To this end we examine TDDFT applied at the level of Becke’s three-parameter hybrid method with a Lee-Yang-Parr correlation functional (B3LYP). The

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basic utility of that functional was already demonstrated in the absorption and the resonance Raman (RR) studies of the relatively small PMDA monoanion [4]. In this Letter we will not consider the vibrational degrees of freedom, i.e., the electronic rather than vibronic transitions are interested for us in the absorption spectra of 1, 2 and 3 anion radicals. The consequences of that simplification are briefly discussed in this Letter.

2. Method and computational details The geometrical structures of the anion radicals studied are schematically depicted in Fig. 1. The orientation of the Cartesian axes applied in the computations are also sketched in Fig. 1. Due to presence of tert-butyl fragments all three chemical compounds belong to C1 point group. The low symmetry complicates the model computations because the symmetry arguments cannot be applied as a simplification factor. Moreover, due to possible rotations of the methyl fragments every tert-butyl fragment is structurally very flexible making the standard geometry optimization processes very inefficient in practice. Fortunately, the tert-butyl groups have no ␲ electrons, which might contribute to the optical transitions in the visible and near-IR excitation regions. Hence, for purposes of the model computations, the tert-butyl groups were brushed away and replaced by the hydrogen atoms. At this level the 1− , 2− and 3− molecules can be treated as species that belong to the C2v or C2 point groups. The consequences of that simplification will be discussed in some detail in the subsequent section. For the “reduced” 1− , 2− and 3− molecules the geometry optimization led us to the ground electronic state of the 2 A2 symmetry. This and the other results reported in this Letter were obtained in the series of computations based on the time dependent density functional theory. Specifically, Backe’s

Fig. 1. The geometrical structures of the 1− , 2− and 3− anion radicals and the orientations of the Cartesian axes used in the computations. X-axis is perpendicular to the plane of the imide fragments.

three-parameter hybrid approach with the Lee-Yang-Parr correlation functional was used [15]. The appropriate quantum chemical procedures of the TD/B3LYP method were taken from the GAUSSIAN 98 package [16] and the 6–1+G* basis set was mainly employed. Some other basis set(s), such as 6–11+G*, was also tested to control the quality of computational results. All three radicals were found to have a large number of electronic states in the visible and near-IR excitation regions. For example the 60 doublets were detected in the absorption spectrum of the two anion radical below the experimental cutoff at 40000 cm−1 [14]. For a few low-energy D0 →Dn transitions the excitation energies and the oscillatory strengths are listed in Table 1. The description of the electronic states in terms of electron promotions within the manifold of Kohn–Sham orbitals are also given in Table 1. The absorption spectra discussed in the next section were calculated from the expression: I(Ω) =


ΓX | A2 |D|X |2 √ · π (Ω − E(X))2 + ΓX2 X

(1)

where the transition dipole moments A2 |D|X could be extracted from the oscillatory strength computed for the 2 A2 → 2 X transitions. Γ X is a linewidth of the X-th electronic state, which is the only adjustable parameter in our model calculations.

3. Results and discussion Fig. 2 shows the experimental (top) absorption spectra of the 1− , 2− and 3− species and their theoretical reconstructions (bottom) gained under assumption that the tert-butyl fragments can be ignored in the computations. The ␦-function absorption spectra are also given for the sake of comparison in Fig. 2. The empirical spectra were taken from reference [14]. The theoretical curves were obtained from Eq. (1) applied for linewidths: Γ X = 1200, 1000 and 800 cm−1 for the 1, 2 and 3 anion radicals, respectively. These values of Γ X are apparently too large when confronted with the typical excited state linewidths due to radiative damping process. It suggests that the substantial contributions to Γ X may arise from non-radiative and inhomogeneous effects. A look at Fig. 2 allows us to state that the agreement between the theory and experiment is generally quite good for all anion radicals studied. In particular, from Fig. 2 one can see that not only the calculated excitation energies but also the intensity distributions are reasonably well reproduced in framework of TD/B3LYP method applied at 6-31+G* level. For all three radicals the computed transition energies miss the corresponding experimental values only by ca. ±1600 cm−1 on an average. This is a typical “inaccuracy” expected within entirely electronic TDDFT treatment, i.e., when the vibrational modes are not taken into account in the computations. However, we wish to note that the agreement

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Table 1 The vertical excitation energies (cm−1 ), oscillatory strengths (f) and the state descriptions of 1− and 2− and 3− chemical compounds State

Descriptiona

Ever (f)

0.97 (S→L) − 0.18 (S→L+4) − 0.13 (H−2→S) 0.98 (S→L+2) 0.88 (S→L+1) + 0.48 (S→L+3) −0.48 (S→L+1) + 0.88 (S→L+3) 0.98 (S→L+4) 0.89 (S→L+6) + 0.45 (S→L+5) −0.45 (S→L+6) + 0.89 (S→L+5) 0.92 (S→L+7) − 0.35 (S→L+8) 0.94 (S→L+10) − 0.23 (H−4→S) + 0.20 (H−2→L) 0.35 (S→L+7) + 0.92 (S→L+8)

10002 (0.0061) 17229 (0.0004) 17350 (0.0000) 17898 (0.0000) 18745 (0.0002) 21318 (0.0037) 22496 (0.0001) 22972 (0.0000) 25819 (0.0938) 26714 (0.0000)

1− D1 (12 B1 ) D2 (22 A2 ) D3 (12 A1 ) D4 (22 A1 ) D5 (22 B1 ) D6 (12 B2 ) D7 (22 B2 ) D8 (32 A1 ) D9 (32 A2 ) D10 (42 A1 ) 2− D1 D2 D3 D4 D5 D6 D7 D8

(12 B1 ) (22 B1 ) (12 A1 ) (22 A1 ) (22 A2 ) (12 B2 ) (32 A2 ) (32 B1 )

0.97 (S→L) − 0.13 (H−2→S) − 0.10 (H→L+4) 0.97 (S→L+4) + 0.24 (S→L+6) 0.99 (S→L+3) 0.99 (S→L+1) 0.98 (S→L+2) 1.00 (S→L+5) 0.79 (H→S) − 0.68 (S→L+9) 0.96 (S→L+6) − 0.23 (S→L+4)

11400 (0.0288) 15833 (0.0008) 17987 (0.0000) 18334 (0.0000) 18640 (0.0042) 20214 (0.0009) 20270 (0.0001) 20326 (0.0141)

3− D1 D2 D3 D4

(22 A2 ) (12 B1 ) (22 B1 ) (32 A2 )

0.85 (H→S) + 0.62 (S→L+1) 0.98 (S→L) 0.98 (S→L+2) 0.74 (S→L+1) − 0.49 (H→S) + 0.16 (H−3→L)

12978 (0.0067) 14648 (0.0442) 16237 (0.0007) 18132 (0.5462)

a

H, S and L indicate the highest doubly occupied, the singly occupied and the lowest empty Kohn–Sham orbitals, respectively.

Fig. 2. The experimantal (top) and the theoretical (bottom) absorption spectra: (a) 1− , (b) 2− and (c) 3− molecules. The linewidths are Γ X =1200 cm−1 , Γ X = 1000 cm−1 and Γ X = 800 cm−1 for the 1, 2 and 3 anion radicals, respectively. The sticks represent the ␦-function spectra. The experimental absorptions from reference [14].

between the theory and the experiment, albeit quite good, is not perfect and some minor shortcomings can be noticed in the theoretical spectra. In our opinion, these discrepancies reflect the model simplifications rather than the insufficient quality of the TD/B3LYP method. In particular, it is possible to consider that the computations done with and without tertbutyl groups could lead us to slightly different ground state

nuclear geometries of the radicals studied. In series of tests we checked that a small departure from C2v symmetry, e.g., due to rotation of the imide and phenyl planes, does not affect much the absorption of the 2− and 3− molecules. Somewhat larger effect could be only noticed in the absorption spectrum of the one anion radical. We could also verify that a rotation of the phenyl and imide fragments has virtually no effect on

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the shape of the absorption spectrum of the three anion. It allows us to conclude that nearly all electronic transitions in the 3− molecule have a “local” character, i.e., their transition dipole moments are localized on the imide moiety. The discrepancies of another kind can be detected when the onsets of theoretical spectra of 2− and 3− molecules are compared to their experimental counterparts. For the 2− molecule TD/B3LYP treatment situates the lowest energy D1 (12 B1 ) state at 11400 cm−1 (Table 1), whereas two other much weaker D2 (22 B1 ) and D3 (12 A1 ) states could be found at 15833 and 17987 cm−1 , respectively. Since the energy differences E(22 B1 ) − E(12 B1 ) and E(12 A1 ) − E(12 B1 ) are larger than typical vibrational energy quanta, it is plausible to deliberate that two peaks separated by ca. 1400 cm−1 in the empirical spectrum near 12000 cm−1 are due to activity of the totally symmetric mode(s) in the D0 (12 A2 ) → D1 (12 B1 ) transition. The similar arguments arise when viewing the empirical absorption of the 3 monoanion near 13000 cm−1 . For this molecule the TD/B3LYP computations yields two electronic states D1 (22 A2 ) and D2 (12 B1 ) located in the narrow energy range from 12000 to 15000 cm−1 (Table 1). Therefore, it is reasonable to consider that the “quartet” conspicuous near 13000 cm−1 in the empirical spectrum of the 3− (insert in Fig. 2c) reveals FC activities of totally symmetric mode(s) in one of two or both D0 (12 A2 )→D1 (22 A2 ) and D0 (12 A2 )→D1 (12 B1 ) electronic transitions. Unfortunately, not much is still known about the electronic structures of anion radicals studied and even less can be said about the vibronic activities of different modes in the excited states of the radicals studied. Therefore, we can conclude that more experimental and theoretical work has to be done in order to shed light on the vibronic problem(s) alluded in this Letter. The work on that problem is now in progress in our group.

Acknowledgments The computations were done in Academic Computer Center “Cyfronet” (KBN/SGI2800/UJ/022/2001) and Wroclaw Centre for Networking and Supercomputing.

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