The Characterization of Charge Transfer in Excited States of Extended

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A: Kinetics, Dynamics, Photochemistry, and Excited States

The Characterization of Charge Transfer in Excited States of Extended Clusters of #-Stacked Donor and Acceptor Complexes in Lock-Arm Supramolecular Ordering Rui-xue Chen, Adelia J. A. Aquino, Andrew Chi-Hau Sue, Thomas A. Niehaus, and Hans Lischka J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b02208 • Publication Date (Web): 03 May 2019 Downloaded from http://pubs.acs.org on May 6, 2019

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The Journal of Physical Chemistry

The Characterization of Charge Transfer in Excited States of Extended Clusters of π-Stacked Donor and Acceptor Complexes in Lock-Arm Supramolecular Ordering Rui-xue Chen,a Adélia J. A. Aquino,a,b Andrew C.-H. Sue,a Thomas Niehausc and Hans Lischkaa,b* a

School of Pharmaceutical Sciences and Technology, Tianjin University, Tianjin 300072, P.R.

China b

Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409,

United States c

Univ Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, 69622

Villeurbanne, France

E-mail: [email protected] † Electronic supplementary information (ESI) available. See DOI:

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Abstract: Lock-arm supramolecular ordering (LASO) cocystals formed by π-stacked material constitute an interesting class of materials which exhibits ferroelectric behavior at room temperature. To characterize the charge transfer in excited states, two complexes with π-stacked donor and acceptor, the 1,5-naphthalene diol (NDI) donor and pyromellitic diimide with diethylene glycol arms (PDIA) acceptor, 5-amino-1-naphthol (AMN) donor and PDIA acceptor, were investigated. The electronic excitations were calculated by using the scaled opposite-spin (SOS) variant of ADC(2), time-dependent density functional theory (TD-DFT) using a long-range corrected (LC) functional (ωB97xD) and the TD-LC approach within density functional based tight-binding (TD-LC-DFTB). Face-to-face mixed stacks and edge-to-face crossed stacks up to hexamers were investigated. The calculations show that the ground state of the complexes does not possess significant CT character. On the other hand, the lowest excited state (S1) shows in all clusters a strong charge transfer. In several cases, the second excited state and also higher excited singlet states possess significant CT character. The orbitals involved in the excitation are mostly well localized and located on adjacent donor/acceptor pairs. Comparing different stacking directions, the vertical excitation energies for the NDI-PDIA crossed stacks are larger than the mixed stacks by 0.2-0.4 eV. In case of the AMN-PDIA system, the energy differences are smaller (~0.1 eV) with mostly the same energetic ordering as for the NDI-PDIA case. Strong red shifts in vertical fluorescence emission transitions have been computed which could even lead to intersection between ground and first excited states which would result in to ultrafast radiationless decay and fluorescence quenching.


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1 Introduction Donor-acceptor (D-A) molecular complexes forming π-stacked structures based on charge transfer (CT) interactions have attracted great interest in developing new organic materials with switchable spontaneous electrical polarization, given its potential application in electronic memory1–3 and optoelectronic fields4,5. Mixed stack charge-transfer complexes are viewed as promising candidates for ferroelectric organic materials,2,6,7 which have similar properties to inorganic ferroelectric materials but with lower cost, reduced toxicity and increased flexibility.8,9 In mixed stacked complexes, the donors (D) and acceptors (A) are arranged in alternate order (···D-A-D-A-···) along a particular direction.10,11 Some mixed stacked complexes are neutral in the ground state, intermolecular charge transfer (CT) occurs by photoinduced processes or by external influences such as temperature or pressure.12–14 Since the discovery of the prototypical TTF-TCNQ system,15,16 more and more organic mixed stack charge-transfer crystals were synthesized. The lock-arm supramolecular ordering (LASO) cocystals7,17,18 are ordered, closely-packed binary cocrystals assembled by electron donors and acceptors extending in one or two dimensions. The governing interactions include charge transfer along the D/A chains and hydrogen-bonding to arrange the supramolecular ordering (Scheme 1a). These cocrystals possess the promising features of ferroelectricity and are characterized by remarkable size and stability which makes them interesting candidates for the next generation of innovative electronic and photonic devices. In the present work, we investigate the nature of the electronic properties of ground and excited states of two different LASO cocystals7. They contain two types of CT systems. One is constructed from the 1,5-naphthalene diol (NDI) as donor and pyromellitic diimide (PDI) with diethylene glycol arms (DGE) attached as acceptor (PDIA), the second one is formed from the 5-amino-1-naphthol (AMN) donor and the PDIA acceptor. The crystal structure (Scheme 1a) shows two kinds of stacking arrangements for the NDI/PDIA system. In the horizontal direction, the arrangement is regular with D-A pairs stacked in a face-to-face manner, called “mixed stack”. In the vertical direction, however, D-A pairs are stacked in an edge-to-face way, denoted as “crossed stack”. The mixed stack and the crossed stack are connected by the lock arms (Scheme 1a). Hydrogen bonds (H-bonds) exist between the hydrogen-bond donors (OH) and hydrogen-bond acceptors (C═O and OCH2CH2). According to the experimental data,18 these two LASO cocrystals display spontaneous 3 ACS Paragon Plus Environment


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polarization at room temperature, which indicated that there is substantial charge transfer interaction in both the face-to-face and edge-to-face orientations. However, it should be mentioned that in investigations on PDIA/1,5-diaminonaphtalene cocrystals17,19 other experimental investigations were interpreted as essentially neutral systems20. Previous theoretical studies concentrated on the prediction of the remnant polarization and on phase transitions in LASO cocrystals.2,21,22 In addition, quantum chemical calculations on selected π-stacked dimers were performed23,24 to study the electronic aspects of the CT processes. However, in these latter investigations the attention was focused on dimer structures only. To further elucidate the CT mechanism in LASO cocrystals, it is necessary to investigate significantly more extended systems in order to show details of the CT states with increasing cluster size and to analyze the electronic transitions with respect to the degree of delocalization in larger aggregates. a

b

1,5-naphthalene diol (NDI)

5-amino-1-naphthol (AMN) O

O

N O

N O

OH

O

O HO


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pyromellitic diimide (PDI)

pyromellitic diimide-DGE (PDIA)

Scheme 1. (a)Mixed and crossed stack arrangements of NDI/PDIA based on the crystal structure7. (b) The different donor (top) and acceptor (bottom) compounds. To calculate non-bonded interactions and obtain a balanced description of electronic CT excitations is a challenging task, particularly for larger supramolecular aggregates of stacked πsystems. Currently, time-dependent density functional theory (TD-DFT) is most widely used to study electronic excitations including CT states. However, many functionals tend to largely overestimate the stability of CT states25,26 due to the deficiency in the description of long-range electron correlations.27,28 This problem has been addressed by the development of long-range corrected functionals (LC)29–31. Several functionals are available, such as LC-ωPBE30,32, Coulombattenuated CAM-B3LYP33 and the ωB97 family34,35. Ab initio methodologies are also well suitable to describe CT excitations since they are not prone to the afore-mentioned artifacts concerning CT. However, these methods are usually computationally much more demanding as compared to TDDFT.36 In view of the extended molecular sizes in realistic molecular models for the LASO structures discussed above, methods like the approximate coupled cluster singles-and-doubles model (CC2)37 and the second-order algebraic diagrammatic construction (ADC(2))38,39 method in combination with the resolution-of-the-identity (RI) approach40 have been proven as reliable and cost-effective methods for the calculation of excited states and CT processes in particular.23,24,41,42 Concerning methods with increased cost efficiency beyond DFT, density functional based tight-binding (DFTB)43 can be considered as a useful alternative. Particularly, electronic excitations can be calculated with the time-dependent approach (TD-DFTB)44 in linear response for which long-range corrected (LC) functionals provide a significant improvement for the description of state localization and charge transfer excitations.45–47 Several studies46–49 have applied TD-LC-DFTB to the description of exciton and charge transfer excitations in extended systems with low computational cost and reliable results. Previous theoretical studies on CT in π-stacked dimers have been performed on complexes between tetracyanoethylene (TCNE) and aromatic donors using ADC(2) in combination with the scaled opposite-spin (SOS) correction50 and on several complexes containing PDI/1,5diaminonaphthalene, para-chloranil/tetramethyl-para-phenylenediamine and tetracyanobenzene/ 1,2-di(4-pyridyl)ethylene using TDDFT with the LC-B97xD functional and SOS-ADC(2).24 5 ACS Paragon Plus Environment


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Together with other good experience with this method,51 they provide a good theoretical reference for studying other stacked π-donor-acceptor complexes. The goal of our present work is to perform investigations on both afore-mentioned stacking types, the face-to-face orientation (mixed stack) and the edge-to-face orientation (crossed stack). To show the character and spatial extent of the CT states with increasing cluster sizes, systems in the range of up to hexamers were investigated. For generating reference results, SOS-ADC(2) calculations were performed for dimers and trimers. Subsequently, calculations with TD-DFT, based on the ωB97xD functional, and the TD-LC-DFTB method were performed. The latter calculations are especially of interest for the evaluation of costeffective options for the calculation of excited states of the larger clusters. Environmental effects were also included in some of the computational models by means of polarizable continuum models.

2 Computational Details The initial structures for the optimization were taken from crystal x-ray structures7. Scheme 1b shows the donors and acceptors used in the clusters investigated in the present work. For the dimer and trimer structures, the geometry optimizations of ground state geometries was performed using (i) DFT with the hybrid functional PBE052 and the D3 dispersion corrections53 (PBE0-D3) with the cc-pVDZ54basis set and (ii) the self-consistent-charge (SCC)43 density functional tight binding (DFTB) method with 3rd order correction (DFTB3)55 with the 3ob-3-1 Slater-Koster (SK) set56 which is part of the third-order parametrization for organic and biological systems. In the DFTB calculations, the dispersion interactions were included via a Lennard-Jones potential57 with parameters adopted from the universal force field (UFF)58. The electronic excitations were computed using the following methods: (i) SOS-ADC(2) in combination with the RI approach, (ii) the TD-ωB97xD and (iii) the TD-LC-DFTB with 2nd order correction (TD-LC-DFTB2). The excited states calculations were based on the structures optimized in the ground state by the PBE0D3 method. Excited-state geometry optimizations for the first singlet excited state were performed using the SOS-ADC(2) and TD-ωB97xD methods. Furthermore, fluorescence emission energies were computed as vertical transitions from the S1 minimum to the ground state. In addition to the vertical transitions, the adiabatic excitation energies from the minimum (ground state) to the minimum (excited state) were also computed. For the excited states calculations using the DFTB method the ob2-1-1-base SK set59 designed for LC-DFTB2 was used. For the SOS-ADC(2) and 6 ACS Paragon Plus Environment

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DFT calculations, the correlation consistent polarized double zeta basis set cc-pVDZ was applied. For the larger systems (tetramer and hexamer), the ground state was optimized with PBE0-D3/ccpVDZ. Considering the computational cost, only the TD-ωB97XD and TD-LC-DFTB2 methods were used in these cases to calculate the electronic excitations. The environmental effects were taken into account on the basis of the polarizable continuum model (PCM)60. Excited state solvation was treated for the TD-DFT method using linear response (LR) and state-specific (SS) approaches.61–65 The conductor-like screening model (COSMO)66 was used in combination with SOS-ADC(2).67 We chose dichloromethane (CH2Cl2), a solvent of medium polarity, as an example to include environmental effects. The parameters for the dielectric constant ε and the refractive index n (ε = 10.7, n = 1.4268) were chosen. Equilibrium solvation was used in the ground states optimization. The calculation of charge transfer in the electronic ground state was analyzed by means of the natural population (NPA)69. The value of charge transfer from fragment A to fragment B for excited states using the descriptor q(CT)70 for a given electronic transition was analyzed by means of transition density matrices D0 n ,[ AO ] defining the descriptor 𝛺𝑛𝐴𝐵 as 𝛺𝑛𝐴𝐵 =

1 ∑ (𝐷0𝑛,[𝐴𝑂]𝑆[𝐴𝑂])𝑎𝑏(𝑆[𝐴𝑂]𝐷0𝑛,[𝐴𝑂])𝑎𝑏 2𝑎 ∈ 𝐴

(1)

𝑏∈𝐵

where n labels the electronic state and S[AO] is the AO orbital overlap matrix.  nAB represents the contribution of charge transfer from fragment A to fragment B (for A≠B), and the contributions of the same-fragment excitations (for A = B). The total CT character for a system with multiple fragments is given by: 1

𝑞(𝐶𝑇) = Ω𝑛∑𝐴∑𝐵 ≠ 𝐴Ω𝑛𝐴𝐵

(2)

𝛺𝑛represents the total sum of the charge transfer numbers for all pairs of A and B. If q(CT)=1e, a complete charge transfer of one electron has occurred while for q(CT) = 0 the transition is a locally excited or Frenkel excitonic state. The ADC(2) and PBE0-D3 calculations were carried out with the TURBOMOLE 7.2 program71. The Gaussian 09 package (Rev.E.01)72 was used for the ωB97xD calculations. The DFTB calculations were performed with a development version of the DFTB+ program73. The 7 ACS Paragon Plus Environment


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charge-transfer analysis and natural transition orbitals (NTO’s)74of the excited states was performed with the program package Theodore.70,75,76

3 Results and Discussions 3.1 Ground states The ground states were optimized using two methods, one was PBE0-D3 with the cc-pVDZ basis set and for the other one DFTB3 with dispersion included via UFF. Figure 1 shows the geometries of the NDI-PDI and AMN-PDI dimers in mixed stack and crossed stack arrangements and trimers consisting of one mixed stack and one crossed stack feature. When considering pure mixed stack complexes, the lock arms have been removed for computational efficiency leading to the core acceptor structures (Scheme 1a-b). Since they reach to another chain, they have only a negligible influence on the spectroscopic properties as will be shown further below. In case of crossed stack structures and trimers, the lock arms interact via hydrogen bond with the NDI and AMN donors, respectively, and were, therefore, included in the calculations. Terminal lock arm atoms were kept fixed at the experimental positions since they would have moved around otherwise and created new hydrogen bonds not existing in the crystal. In addition, two atoms of the donor were frozen across the diagonal for crossed stack complexes to avoid the face-to-edge direction changing. To characterize their geometries, two distances between donor and acceptor were selected: for dimers, the intermolecular distance (Dint) between one of the C atoms of the donor and a corresponding one of the acceptor (Figure 1); the distance DOH which is the closest cro OH distance between D and A. For trimers, the intermolecular distances 𝐷mix int and 𝐷int were

chosen to characterize the distances in mixed stack and crossed stack structures, respectively. Interaction energies Eint are calculated as the energy differences between the complex and the separated systems. a) Mixed stack dimer


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NDI-PDI

AMN-PDI b) Crossed stack dimer

NDI-PDIA

AMN-PDIA c) Trimer

NDI-PDIA-PDIA

AMN-PDIA-PDIA

Figure 1. The geometries of D-A complexes in mixed and crossed stack. (a) NDI-PDI and AMN-PDI dimer in mixed stack. (b) Dimers with PDIA acceptor in crossed stack. (c) Trimers with PDIA acceptor. For the PDI acceptor of crossed-stack structures the D-A complexes and trimers, the DGE arm is included. Figure 1 shows that there is good overlap between donor and acceptor in the mixed stack. For crossed stack complexes, The optimized intermolecular distances are shown in Table 1. For the NDI-PDI and AMN-PDI dimers in the mixed stack, the Dint values of PBE0-D3 optimized structures are about 0.2 Å smaller than DFTB3-UFF results. The DOH values differ much more (~1 Å). These differences are due to a torsion of the parallel sheets. The absolute values of Eint 9 ACS Paragon Plus Environment


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obtained with PBE0-D3 are larger than the DFTB3-UFF ones by about 4 kcal/mol. For the crossed stack dimers, the donor is approximately perpendicular to the acceptor and does not show a good overlap. However, it is noted that a hydrogen bond exists between the hydrogen of the donor and the oxygen of the lock arm which enhances the interaction. The Dint distances are much larger than in the mixed stack case. For the trimers, both types of stacking, mixed stack and crossed stack, occur. The interaction energies are always stronger binding by 3.0~6.0 kcal/mol than the sum of the interaction energies of the respective mixed stacked and cross-stacked dimers at the same level. Slight translation and rotation also occurred in comparison to the crystal structures. However, it should be noted that the structures of the cocrystals include side groups, stacking effects and the interaction with other units that are all missing in the dimer and trimer structures. Charge transfer values of q(CT) given in Table 1 are all less than 0.1 e for the investigated structures, which indicates that the ground state of the complexes does not possess significant CT character. Environmental effects on the computed ground state structures of the investigated complexes are also considered using the PBE0-D3 method. Compared with the respective data of isolated system, the COSMO Dint distances are quite similar. As before, the DOH values show a larger variation. However, interaction energies (Eint) are more affected by the environmental effects. The magnitudes of the Eint values were reduced by 3.0~5.0 kcal/mol in the dimers and by ~12.4 kcal/mol in the trimers in solvent compared to that in gas phase. Table 1. Selected bond distances (Å) for the complexes, interaction energies Eint (kcal/mol) and charge transfer q(CT) in e of the ground state structures Dint (Å) DOH (Å) Mixed stack NDI-PDI dimer Isolated system PBE0-D3 DFTB3-UFF COSMO PBE0-D3 AMN-PDI dimer Isolated system PBE0-D3 DFTB3-UFF COSMO PBE0-D3

Eint

q(CT)

3.30 3.53

2.36 3.38

-19.0 -14.8

0.07 0.02

3.33

3.01

-13.6

0.06

3.27 3.51

2.35 3.28

-19.7 -15.4

0.08 0.03

3.30

2.85

-14.4

0.08 10

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Crossed stack NDI-PDIA dimer Isolated system PBE0-D3 DFTB3-UFF

4.48 4.37

1.87 1.94

-18.7 -10.5

0.03 0.02

COSMO PBE0-D3

4.48

1.87

-15.6

0.04

AMN-PDIA dimer Isolated system PBE0-D3

4.38

2.00

-16.0

0.03

4.80

2.22

-7.2

0.01

-12.4

0.03

Eint

q(CT)

DFTB3-UFF COSMO PBE0-D3

NDI-PDIA-PDIA Isolated system PBE0-D3 DFTB3-UFF COSMO PBE0-D3 AMN-PDIA-PDIA Isolated system PBE0-D3 DFTB3-UFF COSMO PBE0-D3

4.37 2.00 Trimer 𝐷mix 𝐷cro int (Å) int (Å) 3.36 3.60

4.43 4.48

-66.3 -40.2

0.07 0.02

3.28

4.45

-53.9

0.07

3.54 3.58

4.51 4.77

-50.6 -34.3

0.05 0.02

3.50

4.47

-38.2

0.04

a) Mixed stack

TetramerNDI-PDI

TetramerAMN-PDI



HexamerNDI-PDI

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HexamerAMN-PDI b) Crossed stack

TetramerNDI-PDI

TetramerAMN-PDI

HexamerNDI-PDI

HexamerAMN-PDI

Figure 2. The optimized geometries of tetramer and hexamer using PBE0-D3/cc-pVDZ. (a) mixed stack; (b) crossed stack. The values on the dotted lines show the intermolecular distance (Å). Tetramers and hexamers were optimized using the PBE0-D3/cc-pVDZ method. In terms of the optimized tetramer and hexamer structures in the mixed stack (Figure 2a), donor and accepter are staggered face to face. The intermolecular distance Dint between donor and accepter remains at values ~3.3 Å, which is same as the mixed stack dimer. For the crossed stack tetramer and hexamer (Figure 2b), the system with NDI-PDIA has a similar intermolecular distance (~4.4 Å) as the crossed stack dimer. However, the cross-stacked tetramer and hexamer of the AMN-PDIA system show some difference to the dimer, because PDIA makes small in-plane rotations leading to 12 ACS Paragon Plus Environment

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variations of 0.1-0.2 Å in the intermolecular distance compared with the dimer. Nevertheless, the AMN-PDIA units are still arranged face-to-edge. Concerning the intermolecular distances in the experimental crystal data, Dint values are for the mixed stack are 3.47 Å (NDI-PDIA) and 3.45 Å (AMN-PDIA), and for the crossed stacks 4.44 Å (NDIA-PDIA) and 4.42 Å (AMN-PDI). Thus, there are differences of about 0.1~0.2 Å for the mixed stack system and ~0.1 Å for the crossed stack system based on PBE0-D3 results. 3.2 Electronical Excitations: CT States The focus of this work is laid on the characterization of charge transfer in excited states, especially for extended clusters. For dimers and trimers, SOS-ADC(2) , TD-DFT/B97xD, and TD-LC-DFTB2 methods were used. For mixed stack tetramers and hexamers, considering computational cost, only the TD-B97xD and TD-LC-TDFB2 methods were applied. In Table S1 of the Electronic Supplementary Information (ESI), a comparison is made between the excitation energies for the PDI-NDI mixed dimer and PDIA-NDI with lock arms. This comparison shows that the results are almost the same within 0.04 eV. Therefore, the lock arms were not included in the structures of mixed dimer excited state calculations. For the mixed stack NDI-PDI dimer (Table 2), the S1 excitation energy calculated with the SOS-ADC(2) method is largest (3.41 eV) as compared to TD-DFT/B97xD (2.90 eV) and TDLC-DFTB2 (2.78 eV). For the AMN-PDI dimer the situation is similar. In case of the calculations including solvent effects, PBE0-D3/COSMO optimized structures were used for all excited state calculations. Inclusion of the solvent effect reduces the excitation energy of the S1 state in the range of 0.1 to 0.2 eV at both the SOS-ADC(2)/COSMO and TD-SS-B97xD/PCM levels. At the LR level, increases in the excitation energy as well as decreases are found. The q(CT) values given in Table 2 for the NDI-PDI and AMN-PDI dimers for the isolated complexes indicate that the lowest excited state has a strong CT character with almost a full charge transferred to the PDI acceptor. This CT is confirmed by all methods used. With the TD-ωB97XD method, the S2 state also has substantial CT character which is still enhanced by the SS solvation model. The lowest transition is always given by a HOMO-LUMO excitation with the HOMO located on the donor and the LUMO on the acceptor part of the complex (Figure S1). Extended results including more excited singlet states are given in Tables S2.



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For isolated mixed stack tetramers (Table S2), the first three excited states show strong charge transfer character. From the distribution of the CT location on individual monomers given in the table one can see that the CT locations at the edges (D1A1, D2A2) characterize the two lowest states whereas the inner CT (D2A1) belongs always to the third state (Figures S2-S3). LR solvation leaves this picture unchanged, while SS solvation induces stronger changes by which the inner CT is removed from the list of lower states. For the hexamer with NDI and AMN donors, respectively (Table 3), the first five excited states have strong charge transfer. In case of the isolated NDI donor complex, CT processes in the edge monomers are accompanied by those in the inner part (Figure S4). This happens with both the DFTB and B97xD methods. This situation remains about the same with the LR solvation model. With SS solvation only the lowest two states could be converged in which edge CT states are favored. The energy spacing between different CT states is rather narrow, mostly well below 0.1 eV. For the AMN containing hexamer, CT in the inner segments occurs also starting with S3, both for the isolated system and LR solvation. With SS solvation only two CT states were available again and both have edge CT character. The natural transition orbitals involved in S1 are shown for the NDI-PDI dimer and hexamer in Figure 3a. The figure illustrates the localized character of the orbitals which is in some cases extended by the inclusion of a second acceptor location (NDI hexamer). Density difference plots between S0 and S1 are shown in Figure 3b for comparison. They give a very similar picture as obtained from the NTO plots. Complete information on calculated transition energies, oscillator strengths, CT values and transition orbitals are shown in Tables S2-S4 and Figures S1-S5. The absorption spectra of the cocrystals in the mixed stack have been reported.18 The strongest absorption bands are observed at 476 nm (2.60 eV) for NDI-PDIA-PDIA and 490 nm (2.53 eV) for AMN-PDIA-PDIA. These bands have been attributed to the CT interactions between face-toface D-A complexes. The PCM TD-SS-B97xD excitation energies of 2.81 eV (NDI-PDI) and 2.60 eV (AMN-PDI) for the hexamer (Table 3) come quite close to the experimental results. A second band system has been observed experimentally at lower energies, 530 nm (2.34 eV) for NDI-PDIA-PDIA and 595 nm (2.08 eV) for AMN-PDIA-PDIA. Table 2. Vertical excitation energies Eexc (eV), oscillator strengths (f) and charge transfer values q(CT) in e for the mixed stack dimer. NDI-PDI AMN-PDI 14 ACS Paragon Plus Environment

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State Eexc

f

q(CT)

Eexc

f

q(CT)

Isolated system SOS-ADC(2) TD-B97xD TD-LC-DFTB2

S1 S2 S1 S2 S1 S2

3.41 4.17 2.90 3.91 2.78 3.29

0.08 0.01 0.07 0.00 0.04 0.00

0.96 0.22 0.94 0.65 0.98 0.01

3.17 4.06 3.01 3.92 2.61 3.29

0.07 0.03 0.04 0.00 0.04 0.00

0.80 0.39 0.96 0.95 0.79 0.36

S1 S2 S1 S2 S1 S2

3.26 4.17 3.01 4.02 2.73 3.85

0.08 0.03 0.07 0.00 0.07 0.00

0.97 0.12 0.95 0.57 0.94 0.78

2.97 4.00 2.78 3.82 2.53 3.53

0.08 0.01 0.08 0.00 0.07 0.01

0.80 0.81 0.94 0.73 0.94 0.94

PCM/COSMO SOS-ADC(2) TD-LRB97xD TD-SS-B97xD

Table 3. Vertical excitation energies Eexc (eV), charge transfer values q(CT) in e and the distribution of the CT location (locCT) for the mixed stack hexamer. HexamerNDI-PDI HexamerAMN-PDI State Eexc q(CT) locCT Eexc q(CT) locCT Isolated system S1 2.88 0.74 2.73 0.98 D1 A1 D1 A1, A2, A3 D2A2 S2 3.09 0.96 2.88 0.98 D3A3 D3A3 TD-LC-DFTB2 S3 3.13 0.93 D2, D3A1, A2, A3 2.98 0.98 D2A2 S4 3.16 0.94 D2, D3A1, A2, A3 3.13 0.98 D3A2 S5 3.20 0.76 D2, D3A1, A2, A3 3.16 0.98 D2A1 S1 S2

3.05 3.09

0.79 0.91

S3

3.18

0.87

S4

3.33

0.93

S5

3.37

0.78

S1

3.00

0.91

S2

3.05

0.82

S3

3.12

0.84

S4

3.26

0.92

TD-B97xD

D1A1 D3A3 D2A2 D2A1 D3A3 D3A2 D2A2 D2A1

2.85 2.88

0.96 0.96

3.02

0.96

D1A1 D3A3 D2A2

3.30

0.96

D3A2

3.31

0.95

D2A1

2.80

0.96

D3A3

2.87

0.96

2.96

0.95

3.13

0.95

D1A1 D2A2 D2A1 D3A2

PCM/COSMO

TD-LR-B97xD

D2A2 D3A3 D1A1 D2A2 D2A1 D3A3



TD-SS-B97xD

S5

3.31

0.83

S1 S2

2.81 2.82

0.98 0.96

D3A2 D2A2 D2A1 D1A1 D3A3

Page 16 of 30

3.16

0.94

D2A2 D2A1

2.60 2.67

0.95 0.94

D3A3 D1A1

a) Natural transition orbitals

DimerNDI-PDI

HexamerNDI-PDI b) Density difference plots

DimerNDI-PDI

HexamerNDI-PDI

Figure 3. Natural transition orbitals (NTO) plots and isodensity plots of the density difference between the ground state and the S1 state for the NDI-PDI dimer and hexamer, using the B97xD method. The value above the arrow represents weight of these configurations. The isodensity values are 0.001e/Å3. Blue indicates depletion and red increase of electron density.


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Table 4 displays the vertical excitation energies for different sizes of isolated crossed stack D-A complexes with edge-to-face orientation (Figure 2b). Comparing with the vertical excitation energies for mixed stacked complexes, the vertical excitation energies of S1 in crossed stack are larger by 0.2~0.4 eV for the NDI-PDIA complexes. In case of the AMN-PDIA complexes, the vertical S1 excitation energies for crossed stack hexamer and tetramer structures are similar to the mixed stacks, the differences lie within in 0.1 eV at LC-TD-DFTB2 level. For the dimer, however, the ordering depends on the computational method; at TD-ωB97XD level, for example, the order of the ordering is even reversed. For both the NDI-PDIA and AMN-PDIA crossed stack dimers, the excitation energies of S1 calculated by SOS-ADC(2) are larger by 0.3~0.6 eV than those computed with the other two methods. For the tetramers and hexamers, the vertical excitation energies of S1 are very similar to the dimer with differences within 0.05 eV. The q(CT) data show that the lowest excited state possesses also for the crossed stack conformation a strong CT character which is located in the edge D/A monomers (Figure 4). It should be mentioned that more CT states at higher excitation energies (Table S7) were also found for the NDI-PDIA hexamer. Not only S1 to S3 have a strong CT character, but also S7 and S8 show CT character (Table S7). These states have similar vertical excitation energies differing only by less than 0.1 eV. The CT locations with lower vertical excitation energies tend to be at the edges (D1A1, D3A3) between adjacent D/A stacks. Table 4. Vertical excitation energies Eexc (eV), charge transfer values q(CT) and the distribution of the CT location (locCT) for isolated crossed stack complexes. DimerNDI-PDIA State Eexc q(CT) locCT S1 3.69 1.00 DA SOS-ADC(2) S2 4.20 0.01 S1 3.09 1.00 DA TD-B97xD S2 4.02 0.00 S1 3.15 1.00 DA TD-LC-DFTB2 S2 3.21 0.00 TetramerNDI-PDIA State Eexc q(CT) locCT S1 3.20 0.91 D2A2 S2 3.21 0.00 TD-LC-DFTB2 S3 3.23 1.00 D1A1 3.24 0.00 S4 S5 3.26 0.89 D2A1 Method

DimerAMN-PDIA Eexc q(CT) locCT 3.11 0.99 DA 4.04 0.79 DA 2.56 0.99 DA 3.73 0.99 DA 2.79 1.00 DA 3.19 0.00 TetramerAMN-PDIA Eexc q(CT) locCT 2.76 1.00 D2A2 2.78 1.00 D1A1 2.95 1.00 D2A1 3.18 0.00 3.21 0.00 17

ACS Paragon Plus Environment


HexamerNDI-PDIA State Eexc q(CT) locCT S1 3.10 1.00 D3A3 S2 3.17 1.00 D1A1 TD-LC-DFTB2 S3 3.19 1.00 D3A2 S4 3.22 0.00 S5 3.24 0.00

Page 18 of 30

HexamerAMN-PDIA Eexc q(CT) locCT 2.79 1.00 D3A3 2.84 1.00 D1A1 2.87 1.00 D2A2 2.97 1.00 D3A2 2.97 1.00 D2A1

S1 D3 A3 (1.00) HOMO-1

LUMO

Figure 4. Molecular orbitals involved in the S1 transition in NDI-PDI crossed stack hexamer obtained at the TD-LC-DFTB2 level. The value in parentheses represents weight of these configurations. To complete the study of the CT character in excited states, clusters of π-stacked donor and acceptor complexes combined in mixed stack and crossed stack directions were studied for the NDI-PDIA-PDIA and AMN-PDIA-PDIA trimers. As to be expected, the two lowest excited states of the complexes (Table 5) have pronounced CT character (except S2, LC-TDDFTB2). The charge transfer in the S1 state from donor to acceptor occurred in the mixed stack arrangements. For isolated NDI-PDIA-PDIA trimers, the vertical excitation energies of S1 are similar to the results of NDI-PDI dimers obtained for the mixed stack alone within 0.1 eV. Charge transfer in the crossed stack direction occurred for S2 at TD-ωB97xD level, whereas for the TD-LC-DFTB2 method it is found only in the S4 state (Table S8). Compared to the results of the crossed stack NDI-PDIA dimer at the same computational level, the vertical excitation energies are larger by ~0.3 eV . Crossed stack charge transfer states have been observed in the S2 state of the isolated AMN-PDIA-PDIA trimer also. Compared to the crossed stack AMN-PDIA dimer, there is only a small variation of about 0.1~0.2eV in terms of the vertical excitation energies. Besides, several higher states also have a strong charge transfer character in the mixed stack direction for both trimers (Table S5). Figure 5 shows the NTOs involved in the charge-transfer transition of the NDI18 ACS Paragon Plus Environment

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PDIA-PDIA (S1, S2) at the TD-B97xD level. Considering solvation effects, we found in case of the SS approach that the vertical excitation energies decrease 0.2~0.5eV for the two lowest states. In terms of the LR method, the vertical energy changed much less.,. Table 5 Vertical excitation energies Eexc (eV) and charge transfer values q(CT) and the distribution of the CT location (locCT) for the two lowest CT states of each trimer investigated. NDI-PDIA-PDIA State Eexc q(CT) locCT

AMN-PDIA-PDIA Eexc q(CT) locCT

Isolated system TD-B97xD TD-LC-DFTB2 PCM TD-LRB97xD TD-SS-B97xD Mix

S1 S2 S1 S2

2.81 3.43 2.72 3.23

0.94 0.99 0.98 0.02

Mix Cross Mix -

2.65 2.71 2.76 2.98

0.96 0.99 0.98 1.00

Mix Cross Mix Cross

S1 S2 S1 S2

2.84 3.45 2.66 2.91

0.95 0.99 0.94 0.99

Mix Cross Mix Cross

2.71 2.94 2.40 2.48

0.96 0.99 0.99 0.95

Mix Cross Mix Cross

Mixed stack direction. Cross Crossed stack direction.

D

D

A2

A1

D

A1

A2

S1 D A1 0.99

S2 D A2 0.97

A2

A1

D

A2

A1

Figure 5. Natural transition orbitals (NTO) for the two lowest energy charge transfer 19 ACS Paragon Plus Environment


Page 20 of 30

excitations of isolated NDI-PDIA-PDIA trimer using the B97xD method. The value above of arrow is represents the weight of the configuration. 3.3 Fluorescence Energies Comparison of the ground-state intermolecular distances Dint (Table 1, PBE0) with the corresponding distances for the optimized S1 state of the mixed dimers and trimers (Table 6, TDωB97XD), shows relatively small changes by 0.1 Å. The fluorescence energies are computed as the vertical emission energies to the ground state starting from the optimized S1 geometries for the isolated complexes of mixed stacks (Table 6). Vertical absorption and adiabatic absorption energies are given in this table for the purpose of comparison as well. The structural relaxation in S1 leads to a significant energetic stabilization by ~0.7 eV for SOS-ADC(2) and 0.5~0.7 eV at the TD-B97xD level. It has been shown for similar dimer calculations that environmental effects will reduce the emission energy of the CT states further. Thus, the interesting situation could occur that the energy surfaces of ground and first excited states intersect which would give rise to ultrafast radiationless deactivation and fluorescence quenching. Since NTO plots for the geometryoptimized S1 state (Figure S9, NDI-PDIA-PDIA, TD-B97xD) show a similar shape as those reported for the vertical excitation using the ground state geometry (Figure 5), the character of the transition did not change significantly in spite of the large decrease of the S1/S0 energy difference by 1.1 eV in comparison to the vertical excitation. Solvent effects reduce the fluorescence energies by less than

The Characterization of Charge Transfer in Excited States of Extended

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