Electronically Excited States of Higher Acenes up to Nonacene: A

Article pubs.acs.org/JCTC

Electronically Excited States of Higher Acenes up to Nonacene: A Density Functional Theory/Multireference Configuration Interaction Study Holger F. Bettinger,*,† Christina Tönshoff,† Markus Doerr,‡,§ and Elsa Sanchez-Garcia*,‡ †

Institut für Organische Chemie, Universität Tübingen, Auf der Morgenstelle 18, 72076 Tübingen, Baden-Württemberg, Germany Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim/Ruhr, North Rhine-Westphalia, Germany

‡

S Supporting Information *

ABSTRACT: While the optical spectra of the acene series up to pentacene provide textbook examples for the annulation principle, the spectra of the larger members are much less understood. The present work provides an investigation of the optically allowed excited states of the acene series from pentacene to nonacene, the largest acene observed experimentally, using the density functional based multireference configuration method (DFT/MRCI). For this purpose, the ten lowest energy states of the B2u and B3u irreducible representations were computed. In agreement with previous computational investigations, the electronic wave functions of the acenes acquire significant multireference character with increasing acene size. The HOMO → LUMO excitation is the major contributor to the 1La state (p band, B2u) also for the larger acenes. The oscillator strength decreases with increasing length. The 1 Lb state (α band, B3u), so far difficult to assign for the larger acenes due to overlap with photoprecursor bands, becomes almost insensitive to acene length. The 1Bb state (β band, B3u) also moves only moderately to lower energy with increasing acene size. Excited states of B3u symmetry that formally result from double excitations involving HOMO, HOMO−1, LUMO, and LUMO +1 decrease in energy much faster with system size. One of them (D1) has very small oscillator strength but becomes almost isoenergetic with the 1La state for nonacene. The other (D2) also has low oscillator strength as long as it is higher in energy than 1 Bb. Once it is lower in energy than the 1Bb state, both states interact strongly resulting in two states with large oscillator strengths. The emergence of two strongly absorbing states is in agreement with experimental observations. The DFT/MRCI computations reproduce experimental excitation energies very well for pentacene and hexacene (within 0.1 eV). For the larger acenes deviations are larger (up to 0.2 eV), but qualitative agreement is observed.

■

INTRODUCTION Polyacenes 1 (Chart 1) are an important class of polycyclic aromatic hydrocarbons that enjoy considerable attention due to their possible application as active materials in organic electronics.1−11

heptacene were investigated under identical experimental conditions in cryogenic matrices.24,25 The yet larger octacene (n = 8) and nonacene (n = 9) were also generated under such conditions and identified by their absorption spectra.26 It is well-known that the optical spectra of the smaller acenes are dominated by excitations to three excited electronic states, 1 La, 1Lb, or 1Bb according to Platt,27−29 that give rise to band systems that are called p, α, and β according to Clar.15 While the p band is of intermediate intensity, the α band is very weak, and the β band is very strong. As expected based on the experimental data of the smaller acenes,14,15 the p and β bands shift to lower energies (longer wavelengths in the absorption spectra) with increasing size of the acene, in agreement with previous DFT/MRCI30 and subsequently performed timedependent spin−flip DFT computations.31 The deviation from a linear relationship was identified as being indicative of singlet open-shell character of the electronic ground state of higher acenes.31,32 Such a character has some time back been suggested based on the orbital instability of a closed-shell reference function (be it of the Hartree−Fock or the Kohn−

Chart 1. Polyacenes

The absorption spectra of the smaller members, naphthalene (n = 2) to pentacene (n = 5), have been thoroughly studied over many decades.12−17 Experimental investigations of acenes larger than pentacene are much scarcer due to their limited stability.16−21 Heptacene is the first member of the homologous series that cannot be isolated in substance.22 Following the first observation of heptacene (n = 7) by isolation in a PMMA matrix,23 the absorption spectra of pentacene, hexacene, and © 2015 American Chemical Society

Received: July 13, 2015 Published: December 1, 2015 305

DOI: 10.1021/acs.jctc.5b00671 J. Chem. Theory Comput. 2016, 12, 305−312

Article

Journal of Chemical Theory and Computation Sham type),33−35 and it is supported by multireference computations.36−39 While a single-reference coupled-cluster study (CCSD) challenged this view,40 a multireference averaged quadratic coupled-cluster (MR-AQCC) investigation, that also reconsidered the CCSD wavefuntion, confirmed the strong multiradical character of the higher acenes.39 Contrary to earlier predictions based on extrapolation of experimental data,18 the current consensus of computational investigations is that the acenes accessible experimentally in the foreseeable future remain singlet species.41,42 The most notable difference of the optical spectra of octacene and nonacene from those of the smaller members of the series is the presence of an additional strong band at lower energies (longer wavelengths) than the β band.26 Such a new strong band was also observed by Anthony and co-workers in the absorption spectra of kinetically stabilized nonacenes in solution.43 The nature and origin of these bands are not clear, but it was concluded that they are not due to the triplet−triplet transitions based on comparison with absorption spectrum of T1-hexacene.18,26 The purpose of the present work is to compute the excited states of the acenes from pentacene up to and including nonacene using multireference methods in order to assist the ongoing in depth analysis of the experimental spectra. Since the early days of quantum chemistry,44 a large number of theoretical investigations of the excited states of oligoacenes have been reported. Many of them were motivated by performance related issues and were often limited to a few low-lying excited states, mostly 1La and 1Lb.45−61 Notable exceptions are the studies by Tavan and Schulten (up to pentacene),62 Raghu et al.63 and Kawashima et al.64 (up to tetracene), Kurashige and Yanai (up to hexacene),65 the work by Sony and Shukla66 (up to heptacene), and Chakraborty and Shukla42 up to nonacene. Kawashima et al.64 as well as Kurashige and Yanai employed multireference perturbation theories, while the other investigations used configuration interaction (CI) with single and double excitations in a singlereference and multireference framework in conjunction with semiempirical Hamiltonians. The sizes of the systems (nonacene is C38H22 with 248 electrons) that we consider here pose considerable computational challenges that currently preclude highly sophisticated multireference methods. We thus chose the DFT/MRCI method introduced by Grimme and Waletzke.67 The basic idea of the DFT/MRCI method is to take major parts of the dynamic electron correlation into account by DFT, while static correlation effects are included by a short CI expansion.

computations of the excited states, but only the results obtained for the RB3LYP geometries will be discussed in the paper as the resulting excited state energies are closer to experiment. We calculated vertical excitation spectra using the combined density functional multireference configuration interaction (DFT/MRCI) method of Grimme and Waletzke.67 Ten roots in the B2u and B3u irreducible representations with singlet spin multiplicity were calculated for each acene. The SV(P)72 basis set from the Turbomole basis set library was employed, which has been shown to give similar results as the larger TZVP basis set, at considerably lower computational cost.30 All valence electrons were correlated. As described by Grimme and Waletzke,67 the configuration state functions (CSFs) in the MRCI expansion are built up from Kohn−Sham (KS) orbitals of a closed-shell reference state (see Figures S1−S5 for pictorial representations of selected orbitals). Diagonal elements of the effective DFT/MRCI Hamiltonian are constructed from the corresponding Hartree−Fock based expression and a DFT-specific correction term, which contains three empirical parameters. For offdiagonal elements between configurations with the same space part the standard CI expression is used, while for off-diagonal elements with different space parts the standard CI expression is scaled by a factor which depends exponentially on the energy difference between the configurations. By scaling the matrix elements only configurations which are energetically close (those which account for static electron correlation) interact strongly. With this approximation the double counting of electron correlation, which is already included in the diagonal terms, is avoided to a large extent. The scaling factor contains two empirical parameters. All in all, the effective DFT/MRCI Hamiltonian contains five empirical parameters, which depend only on the multiplicity of the excited state, the number of open shells of a configuration, and the density functional employed. Currently, optimized parameter sets for singlet and triplet states are available for the DFT/MRCI Hamiltonian in combination with the BH-LYP functional.69,73−76 The original parameters have been obtained by a least-squares fit of calculated excitation energies to experimental data of a representative set of molecules, including molecules with extended π systems.67,77 We used the new modified set of parameters also developed in the Grimme group78 (p1 = 0.629, p2 = 0.611, pJ = 0.119, p[0] = 8.000, α = 0.503) which is currently only available for singlet electronic states. The required DFT wave functions were generated using Turbomole (version 5.71).79 It has been shown that the DFT/MRCI method gives a satisfying description of the excited states in extended π systems using the standard parameter set. The calculated excitation energies are somewhat too low, but there is no bias to specific states, i.e. the relative order of excited states is well reproduced.30,67,80 In a recent DFT/MRCI study, the new parametrization was used to compute C60 fullerene with very good results.81 Even for other types of challenging systems like transition metal complexes, the DFT/MRCI method was found with both sets of parameters to produce better results than other approaches.82,83 Here, as it is common practice in the DFT/MRCI approach, the CI space was kept moderate by only selecting configurations whose estimated energy is beyond a threshold δEsel above the highest reference space energy. While the usual choice for this parameter is 1.0 hartree, we used a value of 0.8 hartree in our calculations. This was possible due to the modified DFT/MRCI parameter set applied, which improves

■

COMPUTATIONAL DETAILS The geometries of the acenes studied here were fully optimized within the constraint of D2h point group symmetry using the B3LYP68,69 hybrid density functional as implemented70 in the Gaussian 03 program.71 The 6-31G* basis set was employed. It was demonstrated that the spin-unrestricted Kohn−Sham approach produces lower energies for acenes from hexacene onward.34 We have noted earlier that better agreement with the experimental IR spectrum of heptacene is obtained with a RB3LYP rather than with an UB3LYP treatment.25 Lacking experimental or high-level structures of higher acenes, we here performed geometry optimizations at both the RB3LYP and UB3LYP levels. The optimized structures are minima on the corresponding potential energy surfaces. Both sets of geometries, RB3LYP and UB3LYP, were employed for subsequent 306


Article

Journal of Chemical Theory and Computation convergence of the electronic energies with respect to δEsel. Using this combination of δEsel and DFT/MRCI parameters, calculations are sped up by a factor of ≈20, while excitation energies are only slightly changed (in our experience mostly higher by less than 0.1 eV).84 The configurations included in the MRCI reference space were determined iteratively by first performing a DFT/MRCI calculation with a configuration selection threshold δEsel = 0.6 hartree and a reference space that included all configurations contributing to one of the eigenvectors of the initial DFT/ MRCI calculation with a squared coefficient of 0.003 and larger. Further iterations were performed until the energies of all calculated roots were converged to 10−6 Hartree. Figures 1 and 2 were produced from the computed excited state energies using Gaussian broadening with full width at halfmaximum (fwhm) of 0.02 eV.85

Figure 2. Simulated optical absorption spectra for pentacene to nonacene (from top to bottom) up to 2.5 eV computed using DFT/ MRCI and applying Gaussian broadening (fwhm 0.02 eV).

Chart 2. Orientation of the Acene Molecules Used Throughout This Work

Table 1. Selected Pentacene Singlet State Excitation Energies (E, in eV), Oscillator Strengths, Dominant Contributions to the Electronic Wavefunction, and Their Weights (above 0.1) As Computed with the DFT/MRCI Methoda

Figure 1. Simulated optical absorption spectra for pentacene to nonacene (from top to bottom) generated from the ten lowest energy excited states in the B2u and B3u irreducible representations computed using DFT/MRCI and applying Gaussian broadening (fwhm 0.02 eV). A close-up of the p band (1La) region is given in Figure 2.

state

■

RESULTS AND DISCUSSION 1. General Considerations. The UV/vis spectra of the smaller members of the acene series including hexacene have been thoroughly investigated previously.12−17 The 1A → 1La transition (p band) is polarized along the short axis and falls into the B2u irreducible representation (see Chart 2 for orientation adopted in the present work). This transition is primarily due to an excitation from HOMO to LUMO. For ease of representation in Tables 1−5 (and Tables S1−S5 that include the full set of computed excited states), we label HOMO, HOMO−1, HOMO−2, etc. as 1, 2, 3 and LUMO, LUMO+1, LUMO+2, ... as 1′, 2′, 3′, .... Thus, the HOMO → LUMO excitation corresponds to 1 → 1′. The α (1Lb) and β (1Bb) bands originate from transitions that are polarized along the long molecular axis and are thus of B3u character in the orientation (Chart 2) used throughout this work. For the

E/eV

osc strength

GS 1 1B2u (1La, p) 1 1B3u (1Lb, α)

2.16 2.95

0.097 0.008

2 1B3u (D1)

3.50

0.000

3 1B3u (1Bb, β)

4.27

4.111

6 1B3u (D2)

5.37

0.029

a

dominant contributions

wt

(6)2 (5)2 (4)2 (3)2 (2)2 (1)2 1 → 1′ 3 → 1′ 1 → 3′ 2,1 → 1′,1′ 1,1 → 1′,2′ 1 → 3′ 3 → 1′ 1,1 → 1′,2′ 2,1 → 1′,1′ 8 → 1′

0.87 0.86 0.43 0.36 0.36 0.29 0.46 0.38 0.23 0.10 0.14

See Table S1 for the full set of states.

smaller acenes, the 1Lb and 1Bb states result from HOMO−1 → LUMO (2 → 1′) and its alternancy symmetry conjugate, i.e., HOMO → LUMO+1 (1 → 2′).64,86 The α bands usually are the weakest (log ε ≈ 2−3), followed by the p bands (log ε = 4). The β bands lie in the UV region, and being the strongest absorptions (log ε ≈ 4−6), they dominate the electronic spectra.15,86 307


Article

Journal of Chemical Theory and Computation Note that for kinetically stabilized heptacenes and nonacenes the β band could not be measured in all instances due to overlap with solvent. Cryogenic matrix isolation techniques provide a larger spectroscopic window routinely to 200 nm, and hence the very strong β bands can be observed. These strong bands provide a point of reference, and for the present discussion we focus on the low-energy excited electronic states up to and including the β bands. With increasing acene length, a number of states drop faster in energy than the β band and hence lie at lower energy than the β band for nonacene. Those states are also discussed for the smaller acenes to elucidate the development of the electronic spectra with length. 2. Nature of Excited States of Polyacenes. In this section the most important excited states of the polyacenes are discussed. Molecular orbitals and all computed excited states of the acenes are provided in the Supporting Information (Figures S1−S5, Tables S1−S5). Graphical representations of the optical spectra generated from computed excited states are given in Figure 1 and up to an energy of 2.5 eV in Figure 2. Pentacene (Table 1, Table S1, and Figures 1 and 2). The reference configuration is (2b2g)2 (1b3g)2 (1au)2 (3b1u)2 (2b3g)2 (3b2g)2 (2au)2 (3b3g)2 (4b1u)0 (4b2g)0 (3au)0 (5b1u)0 (4b3g)0 (5b2g)0 (6b1u)0 (4au)0, and its weight in the electronic ground state is 87%. Among the excited states of B2u symmetry, 11B2u (1La) is dominated (86%) by a 1 → 1′ excitation. This state corresponds to the well-known p band of pentacene. The most intense band in the absorption spectrum, the β band, is due to excitation into the 31B3u (1Bb) state. Due to a switch in the order of occupied molecular orbitals, the state no longer arises from 2 → 1′/1 → 2′ as for the smaller acenes64 but from 3 → 1′/1 → 3′ excitations (84%). The other state that is dominated (79%) by the 3 → 1′/1 → 3′ singly excited configurations is 11B3u, and this corresponds to the weak α band (1Lb). It is noteworthy that the 21B3u state is composed to about 65% of a linear combination that involves the excitation of two electrons from the HOMO and HOMO−1 into the LUMO and the alternancy symmetry conjugate, i.e. two electrons from HOMO into LUMO and LUMO+1 (2,1 → 1′,1′/1,1 → 1′,2′). As this corresponds to doubly excited configurations, it is labeled D1 for the remainder of this paper. The importance of doubly excited configurations in the lowenergy excited states of acenes was previously noted by Tavan and Schulten62 using D-CI and by Kawashima et al.64 The latter group found an excited state (21B3u) of similar composition in their MRMP2 investigation of tetracene. The other linear combination of these excitations, labeled D2 for convenience, contributes 33% to the 61B3u state of pentacene. Another state that has a large contribution (35%) of a linear combination of two-electron excitations is the 41B3u state (6,1 → 1′,1′/1,1 → 1′,6′). Transitions to the 21B3u and 41B3u states have negligible oscillator strengths. Hexacene (Table 2, Table S2, and Figures 1 and 2). The reference configuration (1b3g)2 (3b1u)2 (1au)2 (2b3g)2 (3b2g)2 (2au)2 (4b1u)2 (3b3g)2 (3au)2 (4b2g)0 (5b1u)0 (4b3g)0 (5b2g)0 (4au)0 (6b1u)0 (6b2g)0 (7b1u)0 (5b3g)0 has a weight of 87% in the ground state. The 11B2u state (1 → 1′) shifts to lower energies and loses oscillator strength. The most noteworthy change compared to pentacene is the switch of state ordering within the B3u species. The 11B3u state is now dominated by the twoelectron excitations D1 (2,1 → 1′,1′/1,1 → 1′,2′), while the 21B3u state is due to 3 → 1′/1 → 3′ single excitations and corresponds to the α band (1Lb state). The 31B3u state (1Bb, 1 → 3′/3 → 1′) still corresponds to the β band. Its oscillator

Table 2. Selected Hexacene Singlet State Excitation Energies (E, in eV), Oscillator Strengths, Dominant Contributions to the Electronic Wavefunction, and Their Weights (above 0.1) As Computed with the DFT/MRCI Methoda state

a

E/eV

osc strength

GS 1 1B2u 1 1B3u

1.80 2.63

0.077 0.003

2 1B3u

2.88

0.010

3 1B3u

3.99

4.421

5 1B3u

4.48

0.004


wt

(6)2 (5)2 (4)2 (3)2 (2)2 (1)2 1 → 1′ 2,1 → 1′,1′ 1,1 → 1′,2′ 3 → 1′ 1 → 3′ 1 → 3′ 3 → 1′ 1,1 → 1′,2′ 2,1 → 1′,1′

0.82 0.85 0.31 0.26 0.37 0.29 0.37 0.30 0.29 0.24


strength is increased, and it is shifted to lower energy by 0.3 eV compared to pentacene. The higher energy state that is dominated by the two-electron excitations 1,1 → 1′,2′/2,1 → 1′,1′ (D2) drops much more in energy (0.89 eV), and it is the major contributor to 51B3u (it was 61B3u in pentacene). Heptacene (Table 3, Table S3, and Figures 1 and 2). The reference configuration is (3b2g)2 (2b3g)2 (2au)2 (4b1u)2 (3b3g)2 Table 3. Selected Heptacene Singlet State Excitation Energies (E, in eV), Oscillator Strengths, Dominant Contributions to the Electronic Wavefunction, and Their Weights (above 0.1) As Computed with the DFT/MRCI Methoda state

E/eV

osc strength

GS

a

1 1B2u 1 1B3u

1.57 2.08

0.057 0.001

2 1B3u

2.80

0.020

4 1B3u

3.65

3.696

6 1B3u

3.97

1.772


wt

...(5)2 (4)2 (3)2 (2)2 (1)2 1,1 → 1′,1′ 1 → 1′ 2,1 → 1′,1′ 1,1 → 1′,2′ 3 → 1′ 1 → 3′ 1,1 → 1′,2′ 2,1 → 1′,1′ 1 → 3′ 3 → 1′ 1 → 3′ 3 → 1′ 1,1 → 1′,2′ 2,1 → 1′,1′

0.74 0.10 0.83 0.35 0.30 0.42 0.31 0.22 0.19 0.14 0.10 0.32 0.25 0.09 0.08


(4b2g)2 (3au)2 (4b3g)2 (5b1u)0 (5b2g)0 (4au)0 (6b1u)0 (5b3g)0 (6b2g)0 (7b1u)0 (5au)0; and its weight in the electronic ground state is 74%, while that of the doubly excited configuration 1,1 → 1′,1′ is 10%. Compared to hexacene, the 11B2u state drops further in energy and loses oscillator strength but remains strongly dominated by the 1 → 1′ excitation. Within the B3u irreducible representation, the 11B3u (2,1 → 1′,1′/1,1 → 1′,2′) and 21B3u (3 → 1′/1 → 3′) states have lower excitation energies but do not change their character. The heptacene 41B3u state results from configuration interaction of the doubly excited configurations (2,1 → 1′,1′/1,1 → 1′,2′; 41%) with the singly excited configurations (1 → 3′/3 → 1′; 24%) that are associated with the 1Bb state (β band) in the 308


Article

Journal of Chemical Theory and Computation smaller acenes. The other state involving configuration interaction of these doubly (17%) and singly excited configurations (57%) is 61B3u. The configuration interaction of the very weakly absorbing doubly excited and the strongly absorbing singly excited (1Bb) states produces two states with large oscillator strengths of f = 3.7 (41B3u) and f = 1.8 (61B3u). Octacene (Table 4, Table S4, and Figures 1 and 2). The weight of the reference configuration (2b3g)2 (4b1u)2 (2au)2

Table 5. Nonacene Singlet State Excitation Energies (E, in eV), Oscillator Strengths, Dominant Contributions to the Electronic Wavefunction, and Their Weights (above 0.1) As Computed with the DFT/MRCI Methoda state

Table 4. Octacene Singlet State Excitation Energies (E, in eV), Oscillator Strengths, Dominant Contributions to the Electronic Wavefunction, and Their Weights (above 0.1) As Computed with the DFT/MRCI Methoda state

E/eV

osc strength

GS 1 1B2u 1 1B3u 1

a

1.43 1.64

0.038 0.001

2 B3u

2.79

0.032

4 1B3u

3.19

2.620

6 1B3u

3.80

3.425


weight

...(5)2 (4)2 (3)2 (2)2 (1)2 1,1 → 1′,1′ 1 → 1′ 2,1 → 1′,1′ 1,1 → 1′,2′ 4 → 1′ 1 → 4′ 1,1 → 1′,2′ 2,1 → 1′,1′ 1 → 4′ 4 → 1′ 1 → 4′ 4 → 1′ 1,1 → 1′,2′ 2,1 → 1′,1′

0.63 0.16 0.80 0.34 0.29 0.40 0.29 0.28 0.25 0.03 0.02 0.41 0.30 0.02 0.01

E/eV

osc strength

GS

a

1 1B2u 1 1B3u

1.34 1.31

0.023 0.001

3 1B3u

2.76

0.080

4 1B3u

2.81

2.849

5 1B3u

2.85

0.001

10 1B3u

3.76

2.920


weight

...(5)2 (4)2 (3)2 (2)2 (1)2 1,1 → 1′,1′ 1 → 1′ 2,1 → 1′,1′ 1,1 → 1′,2′ 4 → 1′ 1 → 4′ 1,1 → 1′,2′ 2,1 → 1′,1′ 4 → 1′ 1 → 4′ 1 → 4′ 4 → 1′

0.50 0.23 0.77 0.32 0.28 0.13 0.08 0.27 0.24 0.25 0.18 0.30 0.26


addition to the 11B3u state that drops by 0.33 eV compared to octacene, a large number of states within the B3u irreducible representation drop in energy, and hence the two strongly allowed states are 41B3u (f = 2.8) and 101B3u (f = 2.9). The former one is still dominated by the two-electron excitation 1,1 → 1′,2′/2,1 → 1′,1′ (51%), while the latter is singly excited involving 1 → 4′/4 → 1′ (56%). This state thus resembles the 1 Bb state (β band) of the smaller acenes. Note that there are 17 states within B2u and B3u with lower energy than the β band. Most of these have very small oscillator strengths, but eight of them (11B2u, 21B2u, 61B2u, 31B3u, 41B3u, 61B3u, 71B3u) could be observable by conventional absorption spectroscopy. 3. Evolution of the Excitation Energies with Increasing Acene Length. The DFT/MRCI computations show that the most prominent excited states of the acenes, 1La (p band), 1 Lb (α band), 1Bb (β band), shift to lower energies as expected based on the behavior of the well investigated shorter congeners (see Figure 3). The multireference treatment in addition reveals that there are two states that involve twoelectron excitations, named D1 and D2 for now, from HOMO−1 and HOMO to LUMO and its alternancy symmetry conjugate. These states drop more quickly in energy with acene size than the aforementioned ones. As a consequence, D1 is lower in energy than the α band from hexacene on, and it is very close to the p band for nonacene; while D2 is lower in energy than the β band from heptacene onward. Both D1 and D2 have very small oscillator strengths for acenes smaller than heptacene, and this does not change for D1 over the entire acene series studied here. However, in heptacene D2 strongly interacts with 1Bb and gains significant intensity that is kept also in octacene and nonacene, despite the fact that the contribution of 1Bb to D2 quickly becomes small. In summary, once D2 drops below 1Bb in energy, the two configurations D2 and 1Bb mix. A consequence of this interaction is a significant gain in oscillator strength of the states in octacene and nonacene that are dominated by the D2 configurations. 4. Comparison with Experiment. In the spectra of pentacene and hexacene the 1La, 1Lb, and 1Bb bands were assigned previously.17,18,25 For comparison with our computations (Table 6) we mostly take data obtained in argon matrix as this environment has only a small influence on the absorption


(4b2g)2 (3b3g)2 (5b1u)2 (3au)2 (4b3g)2 (4au)2 (5b2g)0 (6b1u)0 (6b2g)0 (5b3g)0 (7b1u)0 (5au)0 (7b2g)0 (8b1u)0 (8b2g)0 decreases to 63%, and that of the doubly excited configuration (1,1 → 1′,1′) increases to 16%. The 11B2u state remains dominated by the 1 → 1′ transition, but it becomes again less intense. The two states with large oscillator strengths within the B3u irreducible representation remain the 41B3u ( f = 2.62) and 61B3u (f = 3.43). The 41B3u state is dominated by the doubly excited configurations 1,1 → 1′,2′/2,1 → 1′,1′ (53%), while the contribution of the singly excited configurations 1 → 4′/4 → 1′ (no longer 1 → 3′/3 → 1′ due to switch in orbital ordering) is reduced to 5%. On the other hand, the 61B3u state is largely of single excitation character (1 → 4′/4 → 1′, 71%) as the weight of the two-electron excitation 1,1 → 1′,2′/2,1 → 1′,1′ is only 3%. Nonacene (Table 5, Table S5, and Figures 1 and 2). The reference configuration (2b3g)2 (2au)2 (4b2g)2 (3b3g)2 (5b1u)2 (3au)2 (5b2g)2 (4b3g)2 (4au)2 (5b3g)2 (6b1u)0 (6b2g)0 (7b1u)0 (5au)0 (7b2g)0 (6b3g)0 (8b1u)0 (8b2g)0 (6au)0 (9b1u)0 has a weight of 50%, while the 1,1 → 1′,1′ doubly excited configuration contributes about 23% to the ground state of nonacene. Note that the small weight of the reference configuration is indicative of a significant polyradical character as discussed previously in the literature.36,39,41 The 11B2u state is largely dominated by the 1 → 1′ excitation (77%), but the contribution of this excitation is smallest for all acenes studied here. Also, the oscillator strength of the 11B2u state of nonacene is smallest among all acenes considered here. Most remarkable, the 11B3u state that is dominated by doubly excited configurations (2,1 → 1′,1′/1,1 → 1′,2′, 60%) is computed to be even lower in energy than 11B2u by 0.03 eV. In 309


Article

Journal of Chemical Theory and Computation

Figure 3. Change of the excitation energy to selected excited states in the acene series as computed with the DFT/MRCI method. Lines are there to guide the eye.

Table 6. Comparison between Experimental and Computed (DFT/MRCI) Excitation Energies for Selected Excited States of the Higher Acenes 5ac state 1

La Lb 1 Bb D1 D2 1

theor 2.16 2.95 4.27 3.50 5.37

6ac a

exp.

2.21 2.94 4.25 n.a. n.a.

theor 1.80 2.88 3.99 2.63 4.48

7ac exp.

a

1.89 2.81b 3.99 n.a. n.a.

8ac a

theor

exp.

c

1.57 2.80 3.97 2.08 3.65

1.70 n.a. 3.77c n.a. n.a.

theor 1.43 2.79 3.80 1.64 3.19

9ac d

theor

exp.d

e

1.34 2.76 3.76 1.31 2.81

1.43e n.a. 3.66e n.a. 2.97e

exp.

1.53 n.a. 3.78e n.a. 3.28e

a Experimental data (Ar matrix, 15 K, band system maxima) taken from Mondal et al.25 unless noted otherwise. bCyclohexane/benzene (9:1) at room temperature, Nijegorodov et al.17 cBand split for unknown reason, absorption maximum given (see text). dExperimental data (Ar matrix, 30 K, band system maxima) taken from Tönshoff and Bettinger.26 eTentative assignment based on band position and intensity.

energies.17,18,25 Note that in the previous matrix isolation study, we could not assign the 1Lb band of the larger acenes due to its weakness and due to overlap with the n → π* transition of the α-diketone photo precursor. We hence will not discuss the 1Lb state in any detail here. Furthermore, assignment of p and β band systems is problematic for heptacene experimentally as, in contrast to expectations based on the smaller members, weaker longer wavelength features are observed for those bands in solid argon and xenon,25 as well as in the PMMA matrix where only the p band could be studied.23 The origin of these splittings is not clear, but matrix effects due to the presence of incompletely planarized molecules could be responsible.25 Intrinsic electronic effects, however, cannot be excluded. The investigation of the absorption and fluorescence spectra of heptacene is ongoing in our laboratory to clarify this point. For now, we give the energy of the most intensive absorption of the p (1La) and β (1Bb) band systems in Table 6. For octacene and nonacene we previously identified a large number of absorptions that could not yet be assigned in detail. Only the longest wavelength features were assigned to the respective p band systems based on expectations. Here we focus on these as well as on the few strong ones that we tentatively assign to the 1Bb and D2 states discussed in depth above, based on band positions and intensities. The agreement between experiment and theory is very good for all bands assigned in the pentacene and hexacene spectra, with deviations of less than 0.1 eV. The theoretical 1La energy is in agreement with experiment within 0.1 eV for all acenes except heptacene where the deviation amounts to 0.13 eV.

The 1Bb energies of pentacene and hexacene deviate by only 0.02 eV from experiment, but for heptacene the computed value is 0.2 eV too high. This indicates that our computations possibly overestimate the interaction between 1Bb and D2 such that the former may be too high and the latter too low in energy. Finally, as the D1 band remains weak over the entire acene series investigated so far experimentally, it is expected that it cannot be observed easily by conventional absorption spectroscopy. The D2 band, on the other hand, gains significant intensity either in heptacene or in octacene. While an additional feature is observed for heptacene at lower energy (3.66 eV) than the β band (which is at 3.77 eV), it is not clear if this is indeed due to D2 (calc. 3.65 eV). The additional strong bands observed in the experimental spectra of octacene and nonacene are tentatively assigned to D2 based on the present computations, as DFT/MRCI arrives at an additional strong absorption at lower energy than the β band. It should be noted that in the experiments the higher energy band is always more intense. In the computations the oscillator strengths differ such that at strong configuration interaction (as in heptacene) the lower energy state is more strongly absorbing. With increasing size of the systems this is reversed and hence in agreement with the experimental observations.

■

CONCLUSIONS The computational study of the ten lowest excited states in the optically allowed B2u and B3u irreducible representations of the acenes from pentacene to nonacene can be summarized as follows: 310


Journal of Chemical Theory and Computation

■

ACKNOWLEDGMENTS The work in Tübingen was supported by the Deutsche Forschungsgemeinschaft (DFG). E.S.-G. acknowledges the support of the Fonds der Chemischen Industrie (Liebig Stipend) and the DFG (Cluster of Excellence RESOLV (EXC 1069) and Collaborative Research Center SFB1093). We thank Reinhold Fink and Rachel Crespo-Otero for helpful discussions.

1. The weight of the reference configuration drops quickly with acene length and approaches only 50% for nonacene. Although the present work focuses on the optically allowed transitions, it is likely that the two-electron excited state 21Ag (1,1 → 1′,1′) becomes the S1 state for the higher acenes. This is to be studied in future work. 2. The energy of the well-known excited states of the acene series, 1La (p band), 1Lb (α band), and 1Bb (β band) decreases with increasing system length. 3. There are a number of excited states that are dominated by two-electron and even three-electron excitations based on the reference configuration. Most of these states have very small or negligible oscillator strengths and thus may be difficult to detect experimentally. 4. Exceptions are excitations involving HOMO−1, HOMO, LUMO, and LUMO+1. This gives rise to two states (named D1 and D2 here for convenience) that both decrease in energy much faster than the traditional one-electron excited states (1La, 1 Lb, 1Bb). Once D2 is lower in energy than 1Bb, both states strongly interact, and D2 acquires intensity from 1Bb. As a consequence, two strongly absorbing excited states are obtained for heptacene up to nonacene. Such excited states were also computed by Chakraborty and Shukla with PPP-MRSDCI based on idealized structures (CC distances of 1.400 Å, 120° bond angles).42 5. D1 also decreases quickly in energy with acene length and becomes the lowest optically allowed state for nonacene, but it remains very weakly absorbing. 6. The agreement with experiment is very good for pentacene and hexacene (within 0.1 eV). The prediction of two strongly absorbing states for octacene and nonacene is in agreement with experiment, but the overall deviation becomes larger (up to 0.2 eV). The DFT/MRCI method predicts that the additional strongly absorbing state should be detectable for heptacene, but the experimental data available does not yet allow a conclusive assignment. The present computational investigation of the excited states of the higher acenes is expected to provide data for further analysis and experimental investigations of the optical spectra of the acenes to be conducted at Tübingen.

■

■

REFERENCES

(1) Würthner, F. Angew. Chem., Int. Ed. 2001, 40, 1037−1039. (2) Bendikov, M.; Wudl, F.; Perepichka, D. F. Chem. Rev. 2004, 104, 4891−4945. (3) Würthner, F.; Schmidt, R. ChemPhysChem 2006, 7, 793−797. (4) Anthony, J. E. Chem. Rev. 2006, 106, 5028−5048. (5) Anthony, J. E. Angew. Chem., Int. Ed. 2008, 47, 452−483. (6) Bettinger, H. F. Pure Appl. Chem. 2010, 82, 905−915. (7) Zade, S. S.; Bendikov, M. Angew. Chem., Int. Ed. 2010, 49, 4012− 4015. (8) Watanabe, M.; Chen, K.-Y.; Chang, Y. J.; Chow, T. J. Acc. Chem. Res. 2013, 46, 1606−1615. (9) Suzuki, M.; Aotake, T.; Yamaguchi, Y.; Noguchi, N.; Nakano, H.; Nakayama, K.-i.; Yamada, H. J. Photochem. Photobiol., C 2014, 18, 50− 70. (10) Ye, Q.; Chi, C. Chem. Mater. 2014, 26, 4046−4056. (11) Ortmann, F.; Radke, K. S.; Günther, A.; Kasemann, D.; Leo, K.; Cuniberti, G. Adv. Funct. Mater. 2015, 25, 1933−1954. (12) Clar, E. Ber. Dtsch. Chem. Ges. B 1936, 69, 607−614. (13) Clar, E. Chem. Ber. 1949, 82, 495−514. (14) Klevens, H. B.; Platt, J. R. J. Chem. Phys. 1949, 17, 470−481. (15) Clar, E. Polycyclic Hydrocarbons; Academic Press: London and New York, 1964; Vol. 1, pp 50−69. (16) Biermann, D.; Schmidt, W. J. Am. Chem. Soc. 1980, 102, 3163− 3173. (17) Nijegorodov, N.; Ramachandran, V.; Winkoun, D. P. Spectrochim. Acta, Part A 1997, 53, 1813−1824. (18) Angliker, H.; Rommel, E.; Wirz, J. Chem. Phys. Lett. 1982, 87, 208−212. (19) Watanabe, M.; Chang, Y. J.; Liu, S.-W.; Chao, T.-H.; Goto, K.; IslamMd, M.; Yuan, C.-H.; Tao, Y.-T.; Shinmyozu, T.; Chow, T. J. Nat. Chem. 2012, 4, 574−578. (20) Bettinger, H. F.; Tönshoff, C. Chem. Rec. 2015, 15, 364−369. (21) Tönshoff, C.; Bettinger, H. F. Top. Curr. Chem. 2013, 349, 1− 30. (22) Einholz, R.; Bettinger, H. F. Angew. Chem., Int. Ed. 2013, 52, 9818−9820. (23) Mondal, R.; Shah, B. K.; Neckers, D. C. J. Am. Chem. Soc. 2006, 128, 9612−9613. (24) Bettinger, H. F.; Mondal, R.; Neckers, D. C. Chem. Commun. 2007, 5209−5211. (25) Mondal, R.; Tönshoff, C.; Khon, D.; Neckers, D. C.; Bettinger, H. F. J. Am. Chem. Soc. 2009, 131, 14281−14289. (26) Tönshoff, C.; Bettinger, H. F. Angew. Chem., Int. Ed. 2010, 49, 4125−4128. (27) Platt, J. R. J. Chem. Phys. 1949, 17, 484−495. (28) Moffitt, W. J. Chem. Phys. 1954, 22, 320−333. (29) Hohlneicher, G.; Boersch-Pulm, B. Ber. Bunsen-Ges. Phys. Chem. 1987, 91, 929−941. (30) Marian, C. M.; Gilka, N. J. Chem. Theory Comput. 2008, 4, 1501−1515. (31) Minami, T.; Ito, S.; Nakano, M. J. Phys. Chem. A 2013, 117, 2000−2006. (32) Dias, J. R. J. Phys. Chem. A 2013, 117, 4716−4725. (33) Baldo, M.; Piccitto, G.; Pucci, R.; Tomasello, P. Phys. Lett. A 1983, 95, 201−203. (34) Bendikov, M.; Duong, H. M.; Starkey, K.; Houk, K. N.; Carter, E. A.; Wudl, F. J. Am. Chem. Soc. 2004, 126, 7416−7417. (35) Jiang, D.; Dai, S. J. Phys. Chem. A 2008, 112, 332−335.

ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jctc.5b00671. Kohn−Sham molecular orbitals of acenes, full tables with B2u and B3u excited state energies and configurations for pentacene to nonacene, and Cartesian coordinates of the acenes (PDF)

■

Article

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (H.F.B.). *E-mail: [email protected] (E.S-.G.). Present Address

́ Grupo de Bioquimica Teórica, Universidad Industrial de Santander, Cra 27, Calle 9, Bucaramanga, Colombia. §

Notes

The authors declare no competing financial interest. 311


Article

Journal of Chemical Theory and Computation (36) Hachmann, J.; Dorando, J. J.; Avilés, M.; Chan, G. K.-L. J. Chem. Phys. 2007, 127, 134309. (37) Casanova, D.; Head-Gordon, M. Phys. Chem. Chem. Phys. 2009, 11, 9779−9790. (38) Qu, Z.; Zhang, D.; Liu, C.; Jiang, Y. J. Phys. Chem. A 2009, 113, 7909−7914. (39) Plasser, F.; Pašalić, H.; Gerzabek, M. H.; Libisch, F.; Reiter, R.; Burgdörfer, J.; Müller, T.; Shepard, R.; Lischka, H. Angew. Chem., Int. Ed. 2013, 52, 2581−2584. (40) Hajgato, B.; Szieberth, D.; Geerlings, P.; De Proft, F.; Deleuze, M. S. J. Chem. Phys. 2009, 131, 224321. (41) Horn, S.; Plasser, F.; Müller, T.; Libisch, F.; Burgdörfer, J.; Lischka, H. Theor. Chem. Acc. 2014, 133, 1511. (42) Chakraborty, H.; Shukla, A. J. Phys. Chem. A 2013, 117, 14220− 14229. (43) Purushothaman, B.; Bruzek, M.; Parkin, S. R.; Miller, A.-F.; Anthony, J. E. Angew. Chem., Int. Ed. 2011, 50, 7013−7017. (44) Coulson, C. A. Proc. Phys. Soc. London 1948, 60, 257−269. (45) Schug, J. C.; Brewer, D. A. J. Phys. Chem. 1977, 81, 167−171. (46) Heinze, H. H.; Görling, A.; Rösch, N. J. Chem. Phys. 2000, 113, 2088−2099. (47) Grimme, S.; Parac, M. ChemPhysChem 2003, 4, 292−295. (48) Dierksen, M.; Grimme, S. J. Phys. Chem. A 2004, 108, 10225− 10237. (49) Kadantsev, E. S.; Stott, M. J.; Rubio, A. J. Chem. Phys. 2006, 124, 134901. (50) Sotoyama, W.; Sato, H.; Matsuura, A.; Sawatari, N. J. Mol. Struct.: THEOCHEM 2006, 759, 165−169. (51) Wang, Y.-L.; Wu, G.-S. Int. J. Quantum Chem. 2008, 108, 430− 439. (52) Dorando, J. J.; Hachmann, J.; Chan, G. K.-L. J. Chem. Phys. 2007, 127, 084109. (53) Peach, M. J. G.; Benfield, P.; Helgaker, T.; Tozer, D. J. J. Chem. Phys. 2008, 128, 044118. (54) Knippenberg, S.; Starcke, J. H.; Wormit, M.; Dreuw, A. Mol. Phys. 2010, 108, 2801−2813. (55) Wong, B. M.; Hsieh, T. H. J. Chem. Theory Comput. 2010, 6, 3704−3712. (56) Lopata, K.; Reslan, R.; Kowalska, M.; Neuhauser, D.; Govind, N.; Kowalski, K. J. Chem. Theory Comput. 2011, 7, 3686−3693. (57) Richard, R. M.; Herbert, J. M. J. Chem. Theory Comput. 2011, 7, 1296−1306. (58) Kuritz, N.; Stein, T.; Baer, R.; Kronik, L. J. Chem. Theory Comput. 2011, 7, 2408−2415. (59) Wiberg, K. B. J. Org. Chem. 1997, 62, 5720−5727. (60) Malloci, G.; Mulas, G.; Cappellini, G.; Joblin, C. Chem. Phys. 2007, 340, 43−58. (61) Filatov, M.; Huix-Rotllant, M. J. Chem. Phys. 2014, 141, 024112. (62) Tavan, P.; Schulten, K. J. Chem. Phys. 1979, 70, 5414−5421. (63) Raghu, C.; Anusooya Pati, Y.; Ramasesha, S. Phys. Rev. B: Condens. Matter Mater. Phys. 2002, 66, 035116. (64) Kawashima, Y.; Hashimoto, T.; Nakano, H.; Hirao, K. Theor. Chem. Acc. 1999, 102, 49−64. (65) Kurashige, Y.; Yanai, T. Bull. Chem. Soc. Jpn. 2014, 87, 1071− 1073. (66) Sony, P.; Shukla, A. Phys. Rev. B: Condens. Matter Mater. Phys. 2007, 75, 155208. (67) Grimme, S.; Waletzke, M. J. Chem. Phys. 1999, 111, 5645−5655. (68) Becke, A. D. J. Chem. Phys. 1993, 98, 5648−5652. (69) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B: Condens. Matter Mater. Phys. 1988, 37, 785−789. (70) Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. J. Phys. Chem. 1994, 98, 11623−11627. (71) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao,

O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, Revision E.01; Gaussian, Inc.: Wallingford, CT, 2004. (72) Schäfer, A.; Horn, H.; Ahlrichs, R. J. Chem. Phys. 1992, 97, 2571−2577. (73) Dirac, P. A. M. Proc. R. Soc. London, Ser. A 1929, 123, 714. (74) Slater, J. C. Phys. Rev. 1951, 81, 385. (75) Becke, A. D. Phys. Rev. A: At., Mol., Opt. Phys. 1988, 38, 3098. (76) Becke, A. D. J. Chem. Phys. 1993, 98, 1372−1377. (77) Grimme, S. Chem. Phys. Lett. 1996, 259, 128−137. (78) Gerenkamp, M. Entwicklung und Anwendung quantenchemischer Methoden zur Berechnung komplexer chemischer Systeme. Ph.D. Dissertation, Universität Münster, Münster, 2005. (79) Ahlrichs, R.; Bär, M.; Häser, M.; Horn, H.; Kölmel, C. Chem. Phys. Lett. 1989, 162, 165−169. (80) Silva-Junior, M. R.; Schreiber, M.; Sauer, S. P. A.; Thiel, W. J. Chem. Phys. 2008, 129, 104103. (81) Sen, K.; Crespo-Otero, R.; Weingart, O.; Thiel, W.; Barbatti, M. J. Chem. Theory Comput. 2013, 9, 533−542. (82) Escudero, D.; Thiel, W. J. Chem. Phys. 2014, 140, 194105. (83) Crespo-Otero, R.; Barbatti, M. J. Chem. Phys. 2011, 134, 164305. (84) Parac, M.; Doerr, M.; Marian, C. M.; Thiel, W. J. Comput. Chem. 2010, 31, 90−106. (85) Petrenko, T.; Neese, F. J. Chem. Phys. 2007, 127, 164319. (86) Klessinger, M.; Michl, J. Excited States and Photochemistry of Organic Molecules; VCH Publishers: New York, 1989; pp 71−74.

312


Electronically Excited States of Higher Acenes up to Nonacene: A

Recommend Documents