Electronic Properties of 1,5-Diaminonaphthalene:Tetrahalo-1,4

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Electronic Properties of 1,5-Diaminonaphthalene:Tetrahalo-1,4Benzoquinone Donor-Acceptor Cocrystals Rakesh Kumar Behera, Rajesh Goud Nagula, Adam J. Matzger, Jean-Luc Bredas, and Veaceslav Coropceanu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b08360 • Publication Date (Web): 01 Oct 2017 Downloaded from http://pubs.acs.org on October 5, 2017

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The Journal of Physical Chemistry

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Electronic Properties of 1,5-Diaminonaphthalene:Tetrahalo-1,4Benzoquinone Donor-Acceptor Cocrystals

Rakesh Kumar Behera‡, N. Rajesh Goud†, Adam J. Matzger †, Jean-Luc Brédas‡*, and Veaceslav Coropceanu‡*

‡

School of Chemistry & Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, United States † Department of Chemistry and the Macromolecular Science and Engineering Program, University of Michigan, 930 North University Avenue, Ann Arbor, Michigan 48109-1055, United States

*Email: [email protected], [email protected]

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Abstract We have investigated the electronic properties of four charge-transfer (CT) cocrystals involving 1,5-diaminonaphthalene (DAN) as donor and fluoranil (FA), chloranil (CA), bromanil (BA) and iodanil (IA) as acceptors. While DAN-FA, DAN-CA, and DAN-BA crystallized in a mixed-stack fashion, DAN-IA crystallized with segregated-stacks. For the mixed-stack cocrystals, electronic-structure calculations using density functional theory predict large electron-hole couplings with small effective masses, which strongly suggests that these DAN-XA cocrystals are suitable for charge transport applications. Among the four cocrystals, DAN-CA crystallized in a non-centrosymmetric space group; according to our computational analysis, it is predicted to be weakly ferroelectric with a second-order electrical susceptibility ((2)) similar to that of urea. The ionicities (ρ) of the cocrystals calculated using Mulliken population compare well with the experimental results. The couplings between donor and acceptor molecules in DAN-IA are very small, leading to a very small ρ. This is not typical for a system with a segregated-stack packing motif indicating that hydrogen and halogen bondings can have a strong impact on the structureproperty relations in cocrystals.

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INTRODUCTION

Organic semiconductors have received a great attention due to their potential for optoelectronic applications.1 Most of these efforts have dealt with organic semiconductors such as pentacene and rubrene, which are based on a single molecular building block. In the search for new materials with improved performance or new properties, there is increasing interest placed in multi-component

molecular

systems.

For

instance,

tetrathiafulvalene-7,7,8,8-

tetracyanoquinodimethane (TTF-TCNQ)2 consisting of two different molecular species, i.e. TTF acting as donor (D) and TCNQ acting as acceptor (A), exhibits metallic electrical conductivity in contrast to the semiconducting properties of crystalline TTF and TCNQ. Donor-acceptor (D-A) cocrystals can also display technologically relevant properties such as ferroelectricity,3-4 magnetoconductance,5 a memory function,6-7 in addition to their semiconducting properties.8-12 In the case of D-A cocrystals, there is a strong relationship between the crystal geometry and the electronic properties of the system. Cocrystals with 1:1 stoichiometry usually exhibit two types of packing motifs, either segregated-stack or mixed-stack. Cocrystals with a segregated-stack packing motif, in which donor and acceptor molecules locate on adjacent one-dimensional (…-DD-D-… and …-A-A-A-…) stacks, usually display high electrical conductivity.13 TTF–TCNQ is a well-known representative of this class of systems.14 Systems with segregated-stacks typically display a ground-state charge transfer (CT) configuration (

) with a partial ionicity of ρ

~ 0.5. In contrast, systems with a mixed-stack packing motif, in which the donor and acceptor molecules alternate along the stacks (…-D-A-D-A-…), are in general semiconductors with a quasineutral CT configuration (ρ < 0.5) or insulators with a fully ionic (ρ  1) ground state.13 We note that ρ, and subsequently the system properties, strongly depend on two electronic parameters, i.e.

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the electronic coupling (transfer integral) between donor and acceptor ( t D  A ) and the energy gap , where IP is the ionization potential of the donor and EA, the electron affinity of the acceptor. Several mixed-stack cocrystals were found to display a neutral-to-ionic phase transition (NIT) with TTF-chloranil (TTF-CA) being one the best-characterized NIT systems.15-16 Thus, TTF-CA is neutral at room temperature (ρ  0.3) and experiences a transition to an ionic state with ρ  0.7 around T = 81 K. An additional interesting characteristic of the NIT is the structural instability of the (…-D-A-D-A-…) stacks against dimerization and therefore the formation of polar configurations which results in the system becoming ferroelectric.17 Other D-A cocrystals formed by TTF and various substituted benzoquinones have been developed and investigated.18 These studies indicate that a minor change in the chemical structure of the acceptor can lead to major changes in the system properties. For instance, TTF-bromanil (TTF-BA) is nearly ionic (ρ < 0.95) in the whole temperature range and displays a paramagnetic-to-nonmagnetic phase transition at about 53 K.3 In recent work,19 some of us have synthesized four D-A cocrystals involving 1,5diaminonaphthalene (DAN) as the donor and substituted benzoquinone XA (XA = fluoranil (FA), chloranil (CA), bromanil (BA), and iodanil (IA)) as acceptors (see Figure 1). The computed IP of the DAN molecule is larger than that of TTF only by 0.2 eV, as a consequence, the energy gaps in the DAN-XA cocrystals should be similar to those of their TTF-XA counterparts. It is, therefore, of great interest to investigate the structure-property relationships in DAN-XA cocrystals. Here, we focus on the electronic-structure properties of the recently synthesized DANFA, DAN-CA, DAN-BA, and DAN-IA cocrystals.

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Figure 1. Chemical structures of the donor (D) and acceptor (A) molecules: tetrathiafulvalene (TTF), 1,5-diaminonaphthalene (DAN), fluoranil (FA), chloranil (CA), bromanil (BA) and iodanil (IA).

Methodology The electronic-structure calculations on DAN-XA systems were performed by means of density functional theory (DFT) using the B3LYP functional and the 6-31G basis set. The experimental crystal geometries were used in all DFT calculations. The Brillouin zone was sampled using an 8 x 8 x 6, 8 x 8 x 4, 8 x 4 x 8 and 4 x 4 x 4 Monkhorst−Pack k-point mesh for DAN-FA, DAN-CA, DAN-BA, and DAN-IA cocrystals, respectively. The effective mass (mij) of charge carriers are calculated by means of Eq.1: 1

1

1

Here, E is the band energy; , the Planck’s constant; k, the electron wave vector; and i and j denote the Cartesian coordinates in reciprocal space. The diagonalization of the inverse effective mass 5



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tensor (mij−1) generates the principal components and their orientations. The inverse effective mass tensor is calculated by means of Sperling’s centered difference method with dk = 0.06/bohr. We have also investigated the ferroelectric and second order non-linear properties of the DAN-CA cocrystal. The ferroelectric polarization was estimated using the Berry phase approach.20-21 Since only the non-centrosymmetric experimental structure is available, a pseudocentrosymmetric structure needed for these calculations was generated as shown in the first section of the supplementary information (SI, see also Tables S1-S2 and Figure S1). The atomic coordinates used to estimate the polarization in DAN-CA cocrystal at 85 K is reported in Tables S3 - S5, while Figure S2 illustrates the experimental non-centrosymmetric vs. centrosymmetric DA distance variation in the 15 K and 105 K TTF-CA structures to validate our pseudocentrosymmetric structure generation. The static second order non-linear susceptibility ((2)) of DAN-CA was evaluated by using the Coupled Perturbed Hartree-Fock/Kohn-Sham (CPHF/KS) method.22 All DFT calculations with periodic boundary condition were carried out using the CRYSTAL14 package.23-24 The transfer integrals between donor-acceptor, donor-donor, and acceptor-acceptor molecules of the DAN-XA systems were calculated using the nearest neighbor pairs extracted from the experimental geometries. A fragment orbital approach with a basis set orthogonalization procedure was used for these calculations.25 In addition, the effective couplings between donor molecules eff eff (t D-D ) or acceptor molecules (t A-A ) along the stacking direction were obtained using the energy-

splitting approach by considering the energy levels of D-A-D or A-D-A triads.26 These calculations were performed with the B3LYP functional and the 6-311G(d,p) basis set, using the Gaussian 09 package.27

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RESULTS AND DISCUSSION Crystal structure The crystal structures measured at 85 K19 indicate that DAN-FA, DAN-CA, DAN-BA, and DAN-IA crystallize in P21/c, Pn, P21/n and C2/c space group, respectively (Table S6). All systems are characterized by a 1:1 stoichiometry with DAN-FA, DAN-CA, and DAN-BA exhibiting mixed-stack arrangements while DAN-IA exhibits a segregated-stack packing motif (see Figure S3 for more details).19 Structural analysis of DAN-CA at 85 K reveals two distinct centroid-tocentroid distances (dc-c) between the donor and acceptor molecules along the stack (3.883 Å and 3.958 Å) that resembles the polar phase of TTF-CA with two distinct D-A distances along the stack (3.511 Å and 3.690 Å) (Table 1, Table S1, Figures S1 and S2).15, 28 In order to examine the impact of temperature on the donor-acceptor distance anisotropy along the mixed-stacking direction, single crystal X-ray data were collected on the same crystal of DANCA at 85 K, 185 K, 285 K and 385 K. A systematic analysis of these variable temperature DANCA structures leads to the following observations. First, the positive thermal expansion of the lattice was found to be anisotropic (Table 1 and Figure S4) in all three directions. Comparing the lattice parameters between 85 K and 385 K, the a-axis shows ~0.8% expansion while the b- and c-axes expand by ~2.3% and 1.7%, respectively, which corresponds to a ratio of ~1:3:2 along a-, b-, and c-axes, emphasizing the anisotropy. The largest expansion is observed along the stacking direction (along b). The coefficients of linear thermal expansion (αl) for heating the sample from 85 K till 385 K is observed to be all positive with magnitude < 80 MK-1 (27 MK-1 < a < 33 MK1

; 56 MK-1 < b < 78 MK-1; and 35 MK-1 < c < 58 MK-1). In most organic molecular crystals, the

positive coefficient of linear thermal expansion is generally < 20 x 10-6 K-1 or 20 MK-1. 29-32 Second, the asymmetry in the distance between donor and acceptor molecules increases with temperature 7



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while maintaining the same Pn space group (Table 1). This trend suggests that there is no possible higher symmetry phase transitions in DAN-CA with increasing temperature as is observed for ferroelectric crystals (e.g., TTF-CA) where the asymmetry in the donor and acceptor distance changes to a symmetric distribution beyond the Curie temperature (Pn to P21/n above Tc).15

Table 1: Effect of temperature on the cell parameters, linear expansion coefficient (αl) and D-A distance of DAN-CA cocrystal. The distances are measured from centroid to centroid (dc-c) with the centroid estimated as a positional average of all atoms in the molecule. Temp

a

b

c

β

Volume

αl

dDA

dAD

(K)

(Ǻ)

(Ǻ)

(Ǻ)

(°)

(Ǻ3)

(x10-6/K or MK-1)

(Ǻ)

(Ǻ)

3.883

3.958

a

b

c

85

6.5307

7.8401

15.0342

98.552

761.21

185

6.5481

7.8841

15.0861

98.582

770.11

27

56

35

3.902

3.983

285

6.5733

7.9444

15.1496

98.591

782.25

33

67

38

3.932

4.013

385

6.5850

8.0232

15.2960

98.760

798.70

28

78

58

3.968

4.056

Electronic properties The electronic band structures of mixed-stack DAN-FA, DAN-CA, and DAN-BA and the segregated-stacked DAN-IA based on experimental crystal geometries derived at 85 K are presented in Figures 2 and 3, respectively.

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Figure 2. Electronic band structures and densities of states (DOS) of mixed-stack (a) DAN-FA, (b) DAN-CA, and (c) DAN-BA cocrystals in the structures measured at 85 K as calculated at the B3LYP/6-31G level. The points of high symmetry in the first Brillouin zone are in crystallographic coordinates:  = (0, 0, 0), X = (½, 0, 0), Y =(0, ½, 0), Z = (0, 0, ½), V = (½, ½, 0), U = (½, 0, ½), and T = (0, ½, ½). The zero value of energy is taken as the top of the valence band (VB). The lables given to donor and acceptor molecules are used to describe the electronic couplings.

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Figure 3. Electronic band structure and densities of state (DOS) of the segregated-stack DAN-IA cocrystal in the structures measured at 85 K calculated at the B3LYP/6-31G level. The points of high symmetry in the first Brillouin zone are in crystallographic coordinates:  = (0, 0, 0), X = (1/4 , 0, 0), Y =(0,1/4, 0), Z = (0, 0,1/4), V = (1/4, 1/4, 0), U = (1/4, 0, 1/4), and T = (0, 1/4, 1/4). The primitive unit cell used here was obtained by a linear transformation of the original unit cell (see SI).

The estimated valence band (VB) and conduction band (CB) widths of the crystals are summarized in Table 2. Among the mixed-stack systems, DAN-FA displays the largest bandwidth (803 meV) for the VB and the smallest bandwidth (268 meV) for the CB. DAN-CA also exhibits a larger VB width (638 meV) than CB width (319 meV). In the case of DAN-BA, the widths of the valence (561 meV) and conduction (406 meV) bands show the same trend but are more comparable. In the segregated DAN-IA cocrystal, the widths of both valence (144 meV) and conduction (100 meV) bands are significantly smaller than in the case of mixed-stack DAN-XA systems. We note that a large bandwidth generally results in a small charge carrier effective mass (as described later) and is, therefore, an indication of good charge transport properties. As seen from Figure 2, in the DAN-FA, DAN-CA, and DAN-BA cocrystals, both VB and CB show a 10


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substantial dispersion along directions other than the stacking directions. As a result, the VB and CB widths along the stacking directions, in particular the VB widths for DAN-FA and DAN-CA, are substantially smaller than the total bandwidth, which confirms that there exist significant electronic couplings along other directions as well. Table 2. Comparison of band gaps and band widths (valence - VBW and conduction - CBW) of DAN-XA cocrystals in the structures measured at 85 K and TTF-CA cocrystals. All energies reported are in meV. Cocrystal

Band Gap

VBW

CBW

DAN-FA

1310

803

268

DAN-CA

1240

638

319

DAN-BA

1169

561

406

DAN-IA

1349

144

100

TTF-CA (centrosymmetric)

470

550

620

TTF-CA (non-centrosymmetric)

1020

300

430

Overall, the estimated band widths are large and comparable to those in other cocrystals based on TCNQ derivatives investigated earlier,26,

33

such as BZ-TCNQ (BZ = benzidine/4,4′-

diaminobiphenyl), DBTTF-TCNQ (DBTTF = dibenzotetra-thiafulvalene), DMQtT−F4TCNQ (DMQtT = dimethylquaterthiophene), and STB-F4TCNQ (STB = stilbene), which show VB and CB widths in the range of 380 - 690 meV and 340 - 860 meV, respectively. For the sake of comparison, we also computed the band structure of TTF-CA (see Figure S5). The estimated widths of the VB are 550 and 300 meV in the centrosymmetric and the non-centrosymmetric TTFCA structures, respectively; both values are actually smaller than those in the mixed-stack DAN-

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XA systems (see Table 2). However, the widths of the CB (620 meV and 430 meV, in the centrosymmetric and non-centrosymmetric structures, respectively) in TTF-CA are significantly larger than those of the DAN-XA crystals. The band gap of the non-centrosymmetric TTF-CA is only 0.2 eV smaller than that of DAN-CA which is consistent with the trend in the

values.

The bandwidths in the DAN-FA, DAN-CA, and DAN-BA cocrystals are also comparable to those in well-known oligocenes such as pentacene34-35 where the VB and CB widths, computed at the same level of theory, are 610 and 590 meV, respectively. In order to gain a deeper understanding of the band-structure results, we also evaluated the electronic couplings along possible transport pathways (Table 3) including the couplings between D-A, D-D, and A-A pairs. The electronic couplings along the stacking directions are supereff exchange in nature, i.e., the electronic coupling for holes (t D-D ) results from the mixing of the

frontier orbitals of two closest donor molecules with the orbitals of the "bridging" acceptor eff molecule, and vice-versa for electrons (t A-A ).7 For instance, in the case of DAN-CA, assuming in

the weak coupling limit that only the electronic coupling between the HOMO of a donor and the LUMO of the adjacent acceptor along the stacking direction contributes to the super-exchange mechanism,26, 33, 36-37 the effective transfer integrals for a hole transfer between two closest donors eff 12 27 ( D1-A2-D7, see Figure 2b) are given by: t D-D = (t D-A x t A-D ) /ΔEDA. The effective transfer eff eff integrals for electrons (t A-A ) can be obtained in a similar way. In this t D-D formulation, we took

into account that for DAN-CA the adjacent D-A (D1-A2 and A2-D7) pairs along the stacking direction are inequivalent. However, when all D-A pairs along the stacking direction are equivalent, eff eff as in the case of DAN-FA and DAN-BA (Table S6), the effective couplings t D-D [or t A-A ] can be

also estimated beyond the weak coupling limit by means of the energy-splitting approach using

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the energy levels of a D–A–D [or A–D–A] triad.26 As seen from Table 3, both approaches yield comparable values of the effective transfer integrals. Large electronic couplings can also occur along other stacking directions due to direct overlap of the frontier orbitals of two closest donor molecules (tD-D) or acceptor molecules (tA-A). The computed tD-D and tA-A values along different directions are listed in Table 3 for all systems. eff eff and t A-A (effective Table 3. Electronic properties estimated for the 85 K DAN-XA cocrystals: t D-D 12 transfer integrals for holes and electrons, respectively), t D-A (electronic coupling between HOMO of donor and LUMO of acceptor), tD-D (electronic coupling between HOMO of donors), and tA-A (electronic coupling between LUMO of acceptors). The numbers associated with the electronic couplings refer to the molecule labels in Figures 2 and 3. Energies are in meV. The effective coupling values in parentheses are estimated using the super-exchange mechanism.

Cocrystal

t

t

t

t

t

t

t

DAN-FA

56 (63)

45 (63)

534

80

22

5

1

DAN-CA

- (52)

- (52)

464

79

4

18

10

DAN-BA

46 (49)

44 (49)

453

57

Electronic Properties of 1,5-Diaminonaphthalene:Tetrahalo-1,4

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