The impact of molecular stacking interactions on the electronic structure and charge transport properties in distyrylbenzene (DSB-) based D–A complexes: a theoretical study

Abstract

The molecular aggregation structure of three D–A cocrystal complexes based on substituted distyrylbenzenes (DSB) was studied by density functional theory calculations. The influence of molecular stacking on molecular interactions, frontier molecular orbitals, charge transport and photophysical properties has been investigated in depth, by comparison of D1–A1, D2–A2 and D2–A2′ pairs with different substituents in D and A monomers. Our results provide not only a better understanding of the relationship of the D–A configuration and electrical/optical properties, but also the theoretical prediction of novel organic semiconductor materials for the mixed-stack D–A charge-transfer crystal. In particular, the charge-transfer complexes of D1–A1 have been demonstrated as a good ambipolar material, while the complexes of D2–A2 and D2–A2′ should conduct as better n-type organic semiconductor materials.

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Introduction

In the last decades, organic semiconductors are widely studied and used in organic (opto-) electronic devices such as organic light-emitting diodes (OLEDs),^1,2 organic field-effect transistors (OFETs)^3–6 and organic photovoltaics (OPVs),^7,8 with properties such as light weight, low cost, mechanical flexibility, and structural tenability via chemical modification.⁹ To make full use of organic electronic circuitry, many efforts have been made to design charge carrier-transport materials by two major ways: an ambipolar transport material with a single component^10–14 and the combination of p-type and n-type semiconductors with two components.^15–19 Until now, several different approaches have been explored to design and synthesize ambipolar systems with both stable p-type and n-type transport and relatively high charge mobility, such as bridged electron donor(D)–acceptor(A) moieties,^20,21 blended p-/n-channel semiconductor²² and cocrystallized D and A molecules.^23–25 Since the famous discovery of organic conducting charge-transfer (CT) system in tetrathiafulvalene–7,7,8,8-tetracyanoquinodimethane (TTF–TCNQ),^26,27 multicomponent organic systems in particular D–A cocrystal complexes forming CT systems have attracted increased attention.^28,29 Besides, extensive research has also discovered additional intriguing properties in CT systems such as superconductivity,³⁰ ferroelectricity,^31,32 photonicity³³ and photovoltaic characteristics.³⁴

According to the crystal structures or stacking arrangements, D–A complexes with 1 : 1 stoichiometry can be divided into two major stacking modes: segregated- and mixed-stack; that is the D and A molecules are separated D- and A-stacks or the adjacent D and A molecules are alternate along the stacking directions in a face-to-face manner. Recently, the ambipolar features of mixed-stack D–A complexes have been investigated theoretically and experimentally.²³ Especially, Brédas and co-workers³⁵ theoretically predicted remarkable ambipolar charge-transport properties of the mixed-stack D–A CT crystals via quantum chemical calculations, stressing the significance of superexchange along the stacking direction and providing strong theoretical support to the suggestions that CT materials could represent a class of systems with high potential in organic electronics. Therefore, as the progresses made in computational electronic structure and computer technology, such D–A stacking structures with prominent CT interaction could be quantitatively predictable as well as their property. Up to now, organic ambipolar CT systems have been demonstrated mainly based on TTF–TCNQ and its derivatives systems.³⁶ A mixed-stack single-crystalline CT system of distyrylbenzene (DSB-) and dicyanodistyrylbenzene (DCS-) based donor (4M-DSB) and acceptor (CN-TFPA) molecules was designed and synthesized by Gierschner and Park et al.; the efficient luminescence and ambipolar charge-transport properties were reported respectively.³⁷ They also conducted computational analysis for an explanation of relevant structure–property relationships in this unique system. Nevertheless, it is essential to investigate the intermolecular interaction in the D–A CT crystal and then to predict stacking arrangements along the favored charge transport direction by theoretical methods; in most instances, it seems impossible to predict the arrangements in single component building crystals. As the π–π interactions of them could offer stronger driving forces to compel molecules stacking as a cofacial configuration in crystal, the novel designed single-crystalline binary molecular cocrystal system comprising donor (4M-DSB) and acceptor (CN-TFPA) is one-dimensional (1D) densely packed supramolecular arrangement. Moreover, other DSB- and DSC-based molecules have also been investigated, performing different optical and/or photophysical functionality.³⁸

In this article, we introduced these D–A cocrystal complexes (4M-DSB and CN-TFPA, Fig. 1) as a model to study the intermolecular interactions in the donor–acceptor molecular plane (charge transport mainly along the stacking direction) and gain a better understanding on the relationship between the stacking arrangements and the resulting electronic properties at the density functional theory (DFT) level.^39,40 Furthermore, based the experimental data of the crystal structure from X-ray analysis,³⁷ we could confirm computational approach using D1–A1 as a test case to predict two new D–A complexes (D2–A2, D2–A2′, Fig. 2) arrangements without experimental data and corresponding charge transport property. Our theoretical results provide a ground understanding of the molecules stacking in CT crystals and hence provide a strategy for the construction of ambipolar CT systems as novel π-stacking based organic optoelectronic materials.

Fig. 1 Chemical structure of 4M-DSB (D1) and CN-TFPA (A1).

Fig. 2 Chemical structure of the new D–A complexes (D2–A2 pair and D2–A2′ pair).

Computational details

All calculations were performed using the Gaussian 09 suite of programs (version D.01). As the well-known B3LYP functional with dispersion correction has been proved to give good descriptions for organic molecular geometry, the ground-state geometries of D and A isolated monomers were optimized at the DFT//B3LYP/6-311G(d) level of theory, imposing C_2h symmetry for purpose of simulating configuration in crystals. In addition, the ground-state geometries with relaxed geometry were also optimized for comparison and the vibrational frequencies analysis showed that the structures were global stable. Stacking configurations for the D–A pairs were constructed in cofacial and parallel-displaced configurations by varying the vertical separation Z between two molecules and the horizontal displacement S (along the long molecular axis) of one molecular center relative to the other, see Fig. S1.† Therefore, the interaction energies, the energies of the highest occupied molecular orbitals (HOMO), the lowest unoccupied molecular orbitals (LUMO) and their energy gaps (ΔH–L) of the D–A pair vary with the intermolecular orientation of the stacking. As density function theory (DFT) including an empirical dispersion-corrected functional (DFT-D)^41,42 can describe long range interactions accurately, ωB97X-D^43,44 has been widely used in recent years to calculate the energy of molecular interaction, which has a significant role in determining the stacked geometry. Thus, in the present work, ωB97X-D functional and basis set 6-311++G(d,p)⁴⁵ with both polarization and diffuse functions were employed for compromising between accuracy and computational costs. The interaction energies were corrected for the basis-set superposition error (BSSE) by the counterpoise correction method.⁴⁶ In search for the energy minimum in the interaction energy curves, the molecular separation, Z values, were ranged from 3.0 Å to 6.0 Å with an increment of 0.2 Å and for each fixed Z values of 3.0–4.0 Å, the S values were changed from zero to 6.0 Å with steps of 0.4 Å. To more accurately characterize the optimized D–A pair conformations, the S values were changed with a step of 0.2 Å for the fixed Z value of 3.4 Å (see further below). The natural bond orbital program (NBO)⁴⁷ has also been used to analyze the charge population at the B3LYP/6-31G(d,p) level of theory. The visualization of intermolecular orbital overlaps and weak interactions was conducted using Multiwfn 2.6 software⁴⁸ in real space. A very recent report has investigated the limitation of TDDFT method for prediction of adiabatic excitation energies and photoemission properties due to its underlying approximations.⁴⁹ The authors found that the two lowest π–π* states predicted by TDDFT for thiophenes and thienoacenes appear in a reversed order (or nearly degenerate) when compared to more accurate post-HF methods, although not for oligothiophene chains. Nowadays, improved TDDFT is still the most effective method for molecular excitation energies and excited state properties calculations, especially for dimer system^40,50 For example, TD-CAM-B3LYP functional is superior to TD-B3LYP for large conjugated system. The TD-CAM-B3LYP functional was proved that it is not sufficient to describe the S₁ and S₂ states accurately for some organic molecular system sometimes, but it could correctly predict the energy ordering of both the states.⁵¹ Whereas the calculations of the optical transitions for monomers and pairs in our paper were performed well with TD-CAM-B3LYP/6-31G (d,p) approach, because it yields a good agreement with experimental data.³⁷

Regardless of charge transport mechanism, charge mobility will decrease with local electron–phonon coupling (charge reorganization energy, λ) and increase with intermolecular electronic coupling (transfer integral, t). Here, we only consider intermolecular electronic coupling as it largely depends on the intermolecular orientation of the interacting molecules. In the case of the complex CT systems, the electronic couplings between the closest donor molecules (or acceptor molecules) actually have superexchange effects, that is, acceptor molecule as “bridge” in the middle of two donor molecules (D–A–D) for hole transport and vice versa for electron transport.^23,35 Therefore, the effective transfer integral can be obtained through molecular orbital splitting method employing the PW91PW91 exchange–correlation functional⁵² and 6-31G(d) basis sets.⁵³ We have also analyzed the influence of the relative orientation of the pairs on the transfer integral. Combined with the interaction energy curves of D1–A1 pair, the charge transfer characters will be also further confirmed (vide infra) from comparison of theoretical and experimental results as a test case. Notably, the D1–A1 arrangement in experiment is S ≈ 3.33 Å, Z ≈ 3.33 Å obtained from X-ray analysis.³⁷ Hence, the arrangement of D2–A2 and D2–A2′ pairs could be reliably predicted by employing the same computational protocol.

Results and discussion

Exploration of D1–A1 pair: to test and verify

Geometries and frontier molecular orbitals of D1/A1 molecule. The optimized geometries of D1 and A1 isolated monomers were obtained with the relaxed (C₁) and constrained (C_2h) geometry. The differences between optimized geometries and the experimental values based on the crystal structures were summarized in Table S1.† The selected important bond lengths of the optimized D1 and A1 molecules are in good agreement with the experimental values, especially for D1, and the main disparity is the torsion angles. The torsion angle of A1 calculated for the isolated molecule has a slightly larger discrepancy against experimental data than that of D1. Due to the π–π stacking effects and other intermolecular interactions between adjacent molecules in the crystal lattice, the molecule structures in experiment are tend to be planar. Apparently, the bond lengths of the fully relaxed geometry are nearly identical with the constrained geometry, the same case as the further calculated HOMO/LUMO energy levels and electronic density contours plotted in Fig. S2.† Note that both of the HOMOs and LUMOs of D1 and A1 molecules nearly spread over the whole π-conjugated backbones, and the HOMO orbitals generally show bonding character whereas the LUMO orbitals exhibit antibonding character. By comparison of the frontier orbitals of D1 and A1 molecules, we found that the bonding–antibonding pattern of the orbitals is nearly the same, which indicates modifying DSB/DSC by disubstitution with dimethyl or trifluoromethyl hardly changes the electronic characteristics. The difference of the potential energy (ΔE) between the relaxed and the constrained geometry is also evaluated and listed. The results show that the potential energy of the molecules with the constrained geometry is much higher for A1 than D1, mainly due to the rotation of C–C single bond. In view of the discussed above, we have confidence in the calculated geometries with C_2h symmetry and then estimate the stacking arrangements in the crystal primarily determined by the intermolecular interactions.⁵⁴

Intermolecular interaction energies of D1–A1 pair. As we know, the intermolecular interaction energy could be used to measure the relative stability of the aggregation, and thus tune the molecular solid-state arrangements.⁵⁵ In this part, we investigated the relationship between intermolecular interaction energies and intermolecular relative orientation of D1–A1 pair (which is the smallest element and has the strangest interaction in the crystal lattice). The interaction energies were computed as a function of the vertical separation Z and horizontal displacement S, as shown in Fig. 3. Since the rod-like molecular shape, rotation models were not considered here. When one molecule is shifted vertically or horizontally relative to the other, the interaction energies between two molecules exhibit energy minima both in the range of Z and S. Note that the eclipsed (S = 0 Å) molecular stacking is of the highest energy due to π–π repelling interactions making the D1–A1 pair less stable, and the energy decreasing with S values is more obvious for smaller Z value. In search for the energy minimum and to specify the interactions in the stacking, the S values changed with a step of 0.2 Å for the fixed Z values of 3.4 Å are calculated and illustrated in Fig. 3(c). It can be seen that the global minimum with the strongest binding interaction energy is obtained when two monomers shift about 3.2 Å relative to each other at the vertical distance of 3.4 Å. The visualization of the interactions between D1 and A1 molecules was drawn by VMD software using gradient isosurface method which is widely employed to study the signature of non-covalent interactions in real space based on electron density.⁵⁶ As shown in Fig. 4, the gradient isosurface with a scale running from −0.01(min) to 0.01(max) reveals that the D1–A1 pair at the optimal configuration has a continuous wave function overlap, mainly dominated by van der waals interaction and followed by weak electronic attraction and repulsion effect in some areas. However, the gradient isosurface at the situation of S = 0 Å is discontinuous, and the molecular interaction is localized between the face-to-face atoms, which exhibits the dominant repulsion effect (in accord with the calculated interaction energies). Fig. 5 shows that the optimal configuration possesses the geometry with the central benzene ring of one molecule overlapping the C=C double bond of the other one. In a word, the molecular stacking with the energy minimum is consistent with the crystal structure of D–A complexes in experiment (Fig. S3†).

Fig. 3 Evolution of the calculated interaction energy curves for D1–A1 pair (a) as a function of the horizontal displacement S for each fixed vertical separation Z from 3.2 Å to 3.6 Å and from 3.0 Å to 4.0 Å (shown in the inset), (b) as a function of the Z values changed with a step of 0.2 Å for the fixed S values of 0 Å and (c) as a function of the S values changed with a step of 0.2 Å for the fixed Z values of 3.4 Å, respectively.

Fig. 4 Visualization of the weak interactions for D1–A1 pair (top view) in real space at the configuration of (a) S = 0 Å (b) S = 3.2 Å with fixed Z = 3.4 Å. The scale runs from −0.01(min) to 0.01(max).

Fig. 5 Structure of top view for the strongest binding interaction energy.

Frontier molecular orbitals (FMOs) of D1–A1 pair. The relative orderings of HOMO and LUMO energies generally provide a reasonable qualitative indication of chemical stability; and they are important parameters for organic semiconductor used in electronic devices. Fig. S4† presents the evolution of the HOMO, LUMO energy levels, and energy gaps (ΔH–L) as a function of S values for fixed Z of 3.2 Å, 3.4 Å and 3.6 Å. The first important observation is that the HOMO/LUMO energy levels exhibit several local energy minima and maxima in the total range of S with obvious fluctuation. For the HOMO energy levels, the local maxima implying the instability correspond to the displacement of one molecule relative to the other for about one ring (S ≈ 2.4 Å) and two rings (S ≈ 4.8 Å), whereas the local minima implying the stability correspond to the displacement of a half ring (S ≈ 1.2 Å) and central benzene ring overlapping the C=C double bond (S ≈ 3.4 Å); in contrast, an opposite tendency is shown for the LUMO levels and therefore the energy gaps have the same trends with the LUMO levels. Moreover, the energy levels fluctuate more markedly for smaller Z values. For this phenomenon, it is mainly because of the alternate arrangement along the long molecular axis of the HOMO orbitals and LUMO orbitals as well as their similar distribution for both D1 and A1 monomers (see Fig. S2†). When the global overlap between the π-orbitals is maximized, the calculated HOMO levels are the highest and LUMO levels are the lowest, which indicates the instability with strong electronic repulsion. From Fig. 6, we found that the HOMO orbital is almost localized on D1, whereas the LUMO orbital is almost localized on A1, implying that D1 is responsible for hole transport and A1 for electronic transport. Considering both the interaction energies and FMOs of D1–A1 pair, we can confirm our calculation of the optimal configuration (S ≈ 3.4 Å, Z ≈ 3.4 Å, this values are in accord with the experiment), which, to some extent, contributes to predicting the configuration of D–A pair like these. As to the optimal configuration of D1–A1 pair, it can be seen from Fig. 7 that the alternate distribution of HOMO and LUMO orbital overlaps between D1 and A1 molecules. Obviously, the more LUMO orbital overlap than HOMO implies the more easily electron transfers along the molecular stacking.

Fig. 6 Electronic density contours of the LUMO (a) and HOMO (b) for D1–A1 pair at the optimal configuration.

Fig. 7 Visualization of intermolecular orbital (HOMO and LUMO) overlap between D1 and A1 molecules. Green/blue isosurface refers to the overlap in the way of same/opposite phase.

The influence of intermolecular orientation on transfer integral. Charge transfer integral (t) is the main factor determining the charge mobility for carrier (hole or electron) in organic semiconductors as Marcus charge transfer theory expressed, which largely depends on the relative orientation of interacting molecules. Therefore, an in-depth understanding of the influence of the molecular stacking arrangements (relative orientation) on the intermolecular transfer integral is of extreme importance to design the novel organic semiconductors materials.

Several methods have been proposed to evaluate the transfer integral, such as orbital energy level splitting method, site-energy correction method and direct evaluation method.⁵⁷ Recently, energy-splitting approach has been proved to be accurate for mixed-stack systems,³⁵ hence we evaluate the t_e (electron transfer integral) and t_h (hole transfer integral) values obtained by Koopmans' theorem (KT) method:

t_h = (E_HOMO − E_HOMO−1)/2

t_e = (E_LUMO+1 − E_LUMO)/2

where E_HOMO (E_HOMO−1) is the energy of the HOMO (HOMO−1) levels taken from the neutral trimer of D–A–D for calculating the hole transfer integral, and E_LUMO+1 (E_LUMO) is the energy of the LUMO+1 (LUMO) levels taken from the neutral trimer of A–D–A for calculating the electron transfer integral. The evolution of transfer integral (t) as a function of horizontal displacement S within the range from zero to 6 Å in the interval of 0.2 Å for each fixed Z of 3.2 Å, 3.4 Å and 3.6 Å is depicted in Fig. 8. Note that a small displacement can lead to a significant change in the amplitude of the transfer integral. The overall attenuation of the oscillation patterns with horizontal displacement indicates that the intermolecular orbital overlap is progressively reduced as the degree of translation increases. As many studies have reported,^58,59 the charge transfer integral values, for both hole and electron, decay significantly as the intermolecular vertical separation is increased. It is fascinating that there are translations for which the t_e value is larger than t_h (thereby potentially favoring electron mobility over hole mobility),^50,52,54,56 though t_h value is generally larger than t_e in the range of S values. For example, for the horizontal displacement of 1.2 Å with fixed vertical separation of 3.4 Å, t_h and t_e are 0.011 eV and 0.04 eV, respectively. Apparently, the calculated evolution is directly related to the bonding–antibonding pattern of the frontier orbitals of D1 and A1 molecules (see Fig. S2†). The t_h and t_e values are the largest when the global overlap between the π-orbitals is maximized, but when there occurs reduction in global overlap, these values reach minimum. Therefore, the charge transfer integral is closely related to the electron coupling of π-orbitals between two molecules. Combined with the earlier discussion about the intermolecular interaction energies and frontier molecular orbitals of D1–A1 pair, it can be found that at the optimal configuration of Z = 3.4 Å and S = 3.4 Å, the t_h and t_e values are 0.017 eV and 0.029 eV, respectively. These indicates that the D–A cocrystal complexes potentially possess higher electron mobility than hole mobility, which is in accord with the experimental results. In the meantime, it should be noted that there is a cross point of t_h and t_e curves between S = 3.2 Å and S = 3.4 Å, which suggests it should act as good ambipolar material. Encouragingly, it can reach the same conclusion if the vertical separation of two monomers changes a little in real solid state.

Fig. 8 Evolution of the charge transfer integral values (t_h/t_e refers to the hole/electron transfer integral) for D1–A1 pair as a function of the vertical separation Z (Å) and horizontal displacement S (Å) obtained by the KT method.

Exploration of D2–A2 pair and D2–A2′ pair: to predict and compare

Geometries and frontier molecular orbitals of D2/A2/A2′ molecule. All the optimized geometries of D2, A2 and A2′ isolated monomers were also calculated with the relaxed (C₁) and constrained (C_2h) geometry. From the vibrational frequencies analysis, it can be found that the ground state structure of D2 molecule possesses C_2h symmetry. The main geometric parameters of different optimized geometries are list in Table S2.† The selected corresponding bond lengths and torsion angles of the optimized D2 and A2 are very close to D1 and A1, respectively, while the HOMO levels and LUMO levels of D2 (A2) are both higher than those of D1 (A1) molecule. These indicate that the mono-substituted phenyl makes little difference in geometry, but increases the molecular activity or instability compared with the disubstituted one. From the comparison of A2 and A2′, as the change of the position of cyano group, A2′ possesses shorter bond 3, 6 and larger bond 2, 5 than A2. Moreover, the HOMO and LUMO levels of A2′ are also higher than those of A2. Fig. S5† shows the electronic density contours of HOMOs and LUMOs for D2, A2 and A2′. Apparently, the distribution of all orbitals is nearly identical with that of D1 and A1, implying a similar electronic characters of them.

Intermolecular interaction energies curves and frontier molecular orbitals of D2–A2 and D2–A2′ pairs. To predict the stacking arrangements of D2–A2 and D2–A2′ complexes in solid state, intermolecular interaction energies and frontier molecular orbitals of D2–A2 and D2–A2′ pairs have been investigated as a function of the vertical separation Z and horizontal displacement S as well. As shown in Fig. 9, the interaction energy curves between two molecules consist of several local energy minima and maxima with the horizontal displacement S, in sharp contrast with that of D1–A1 pair. Coincidentally, the local maxima of the energy correspond to the displacement of about one ring (S ≈ 2.4 Å) and two rings (S ≈ 4.4 Å), while the local minima correspond to the displacement of a half ring (S ≈ 1.2 Å) and central benzene ring overlapping the C=C double bond (S ≈ 3.2 Å). Moreover, for both D2–A2 pair and D2–A2′ pair, a lower energy minima with the strongest binding have been seen at a horizontal displacement of a half ring (S ≈ 1.2 Å) and a vertical separation of 3.6 Å between two molecules. It also can be predicted that the configuration with S ≈ 3.2 Å and Z ≈ 3.6 Å might be achieved by tuning the crystal growth conditions. The larger separation caused by the mono-substituted phenyl in DSB than the disubstituted one is largely because of the reduced electron-withdrawing/electron-donating effect of –CF₃/–CH₃; thus the electrostatic interaction decreasing, which causes the proportion of exchange repulsion interaction increasing in the π–π interaction. Therefore, the potential energies at the optimal configuration of D2–A2 and D2–A2′ are higher than D1–A1 (see Fig. 10). Compared with D2–A2 pair, D2–A2′ pair possesses a little lower energy, implying the position of cyano group has little influence on the intermolecular interaction energies.

Fig. 9 Evolution of the calculated interaction energy curves for D2–A2 pair (a) and D2–A2′ pair (b) as a function of the horizontal displacement (S, Å) for each fixed vertical separation (Z, Å).

Fig. 10 Comparison of the variation of intermolecular interaction energies of D1–A1 pair, D2–A2 pair and D2–A2′pair each at the optimal vertical separation (Z = 3.4 Å for D1–A1 pair, Z = 3.6 Å for D2–A2 pair and D2–A2′ pair).

The visualization of the interactions between D2 and A2 (A2′) molecules at the eclipsed (S = 0 Å) configuration and the optimal configuration (S = 1.2 Å) was drawn in Fig. S6.† The gradient isosurfaces of D2–A2 and D2–A2′ pairs also show a continuous wave function overlap with nearly all the van der waals interaction at their optimal configurations. However, compared with D2–A2 (A2′) pair, the D1–A1 pair at the same horizontal displacement (S = 0 Å and S = 1.2 Å) exhibits stronger repulsion effect (larger red area has been shown). Thus, it can explain the relative stability (shown in Fig. 10) of these pairs at S = 0 Å, S = 1.2 Å and S = 3.2 Å, respectively.

From Fig. S7,† we found that the values and variation trend of the frontier molecular orbitals for both D2–A2 pair and D2–A2′ pair possess small change and are both similar to that of D1–A1 pair. It can be seen that the lowest HOMO level and the highest LUMO level of D2–A2 and D2–A2′ pairs correspond to the horizontal displacement of 1.2 Å. Hence, combined with the interaction energies analysis, the predicted optimal configurations in solid state of D2–A2 and D2–A2′ pairs are nearly identical (Z ≈ 3.6 Å, S ≈ 1.2 Å). To clarify the difference of these three molecule pairs, the comparison of their frontier molecular orbitals is also presented in Fig. 11. Obviously, the pairs with mono-substituted phenyl in DSB increase both the HOMO and LUMO level; but the inner-cyano substituted (A2′) DSC can only largely increase the LUMO level in contrast to the outer–cyano substituted (A2) one, since their HOMO levels are very close to each other. In a word, we have found the difference in optimal configuration of these three pairs caused by the change of substitution, i.e. the number of substitution on phenyl and the position of cyano group in the vinylene unit.

Fig. 11 Comparison of the evolution of HOMO energies (a) and LUMO energies (b) for D1–A1 pair, D2–A2 pair and D2–A2′ pair each at the optimal vertical separation (Z = 3.4 Å for D1–A1 pair, Z = 3.6 Å for D2–A2 pair and D2–A2′ pair).

The visualization of intermolecular orbital overlaps for D2–A2 pair and D2–A2′ pair with optimal configurations is shown in Fig. S8.† We also found the alternate distribution of HOMO and LUMO orbital overlap and the more LUMO orbital overlap as well. However, on account of the larger vertical separation of D2–A2 and D2–A2′ pairs, the total values of orbital overlap are lower than D1–A1 pair. In spite of the larger overlapping area between D2 and A2 (A2′) molecules (the smaller horizontal displacement), their overlap degree of the orbitals decreases compared with D1–A1 pair.

The influence of intermolecular orientation on transfer integral for D2–A2 pair and D2–A2′ pair. To investigate the difference of these three pairs in charge transport properties, the evolution of transfer integral values as a function of the horizontal displacement S for D2–A2 pair and D2–A2′ pair is depicted in Fig. 12 each at the optimal vertical separation. Fig. 13 displays the evolution of hole and electron transfer integral of these two new pairs in comparison with D1–A1 pair. Obviously, both the hole and electron transfer integral values of D2–A2 and D2–A2′ pairs are similar. Besides, t_e values are found to be larger than t_h values around their optimal configurations (Z ≈ 3.6 Å, S ≈ 1.2 Å), which indicates that the electron mobility is expected to be higher than hole mobility; and they both could act as n-type organic semiconductor materials. Surprisingly, when the configuration with S ≈ 3.2 Å and Z ≈ 3.6 Å achieved by tuning the crystal growth conditions, D2–A2 and D2–A2′ cocrystal complexes could also act as good ambipolar materials similar to D1–A1 complexes. It is clearly showed in Fig. 13 that, both the hole and electron transfer integral values for D1–A1 pair are larger than those for D2–A2 and D2–A2′ pairs, mainly because of the larger optimal vertical separation between D2 and A2 (A2′) molecules. Moreover, not only the little difference between D2–A2 and D2–A2′ pairs in the evolution of charge transfer integral, but the values are almost equal at their optimal configuration, i.e. t_h (t_e) values are 0.005 eV (0.022 eV) and 0.006 eV (0.022 eV) for D2–A2 and D2–A2′, respectively. Therefore, we can conclude that the influence of intermolecular orientation on the transfer integral for the pairs with mono-substituted phenyl in DSB is similar to those with disubstituted one; nevertheless, they should possess different charge transfer properties according to the charge transfer integral at their optimal configurations.

Fig. 12 Evolution of the charge transfer integral values for D2–A2 pair (a) and D2–A2′ pair (b) as a function of horizontal displacement S (Å) at the vertical separation Z of 3.6 Å.

Fig. 13 Comparison of the charge transfer integral values for D1–A1 pair, D2–A2 pair and D2–A2′ pair as a function of horizontal displacement S (Å) each with the fixed optimal vertical separation (Z = 3.4 Å for D1–A1 pair, Z = 3.6 Å for D2–A2 pair and D2–A2′ pair), (a) and (b) for holes and electrons respectively.

As to the mixed-stack D–A complex, the adjacent D and A molecules should possess efficient charge separation and transport, related to their different ability in electron attraction or repulsion. Therefore, the natural bond orbital (NBO) analysis was employed to investigate the population charge distributions of these D–A pairs. Fig. 14 shows the evolution of the population charge distribution of the A molecule in pair as a function of horizontal displacement (S) for comparison. Interestingly, the trend of the charge variation with S is similar to the interaction energies, implying that the electrostatic interaction is the major contribution to the interaction energies. As we known, the electron capacity of A in pair is better than D, then the negative charge distribution in A should benefit the stable interactions of the pairs. Note that all their optimal configurations have significant charge separation characters, although the maximum charge distribution for D2–A2 pair and D2–A2′ pair is not at their optimal configurations. We found that the larger charge separation have been shown at the smaller vertical separation (Z = 3.4 Å). In addition, the charge distribution is more sensitive to the variation of Z for D1–A1 compared with D2–A2 (A2′), mainly because of the ability in electron attraction or repulsion is larger for disubstituted phenyl than mono-substituted one in DSB. Moreover, the trend of the charge variation with S for D2–A2 and D2–A2′ is nearly the same, indicating that D2–A2 and D2–A2′ almost have the same charge transfer characters.

Fig. 14 Evolution of the population charge distribution of A in pairs as a function of horizontal displacement S (Å). The horizontal line points to the zero, indicating there is no charge separation in D–A pair.

The influence of intermolecular orientation on electronic structure. As organic functional materials, it is essential to investigate the condensed-state photophysical behaviors theoretically. The UV-vis absorption spectra of the monomers and pairs have been calculated. Here, we reproduced the calculation on D1–A1 pair, which have also been done in ref. 37. From the absorption spectra of D1 and A1 monomers with C₁ and C_2h geometry in Fig. S9,† it can be found that the absorption peaks have small bathochromic shift when the geometry from relaxed (C₁) to restrained (C_2h), revealing the increased potential energy of the planar molecules. The maximum absorption peaks of D–A pairs mainly caused from D molecules are around 345 nm, primarily attributable to the HOMO → LUMO+1 transition from the S₀ to S₃ state, as shown in Fig. 15(a) and (b). Obviously, the strength of the absorption is enhanced for the aggregation. As to the absorption peaks of monomers and pairs (Fig. 15(c) and (d)), D2/A2 monomer has small bathochromic shift compared with D1/A1 monomer, respectively; D2–A2 pair has small bathochromic shift, while D2–A2′ pair has small hypochromic shift compared with D1–A1 pair. Moreover, D2–A2 and D2–A2′ pairs exhibit stronger absorption than D1–A1 pair.

Fig. 15 Computed UV-vis absorption spectra of (a) D1, A1 monomer and D1–A1 pair at the optimal configuration (b) D2, A2 monomer and D2–A2 pair at the optimal configuration (c) D1, A1, D2, A2 monomer for comparison (d) D1–A1 pair, D2–A2 pair and D2–A2′ pair at their optimal configuration for comparison.

The influence of intermolecular orientation on the excited states was explored as a function of horizontal displacement S with the fixed vertical separation at 3.4 Å and 3.6 Å. Fig. 16 shows the evolution of the excitation energy of the two lowest excited states (S₁, S₂) of these pairs. The trend of the excited state of S₁ and S₂ with the horizontal displacement S also exhibits several local energy minima and maxima. It can be detected that the S₁ state is primarily attributable to HOMO (localize in D) → LUMO (localize in A) and the S₂ state is HOMO−1 → LUMO. Here, we also compared the difference between FMOs and the lower excited states. The energy gap (HOMO–LUMO) of the D1–A1 pair at the optimal configuration calculated from the ground state is 5.44 eV, while the energy difference between S₀ and S₁ energy states is 2.70 eV. Similarly, the LUMO and LUMO+1 energy gap is 1.20 eV, while the difference between S₁ and S₂ energy states is 0.53 eV. Surprisingly, the energy difference of orbitals nearly doubles of the difference between S₁ and S₂ lower energy states, and the variation of the excited states S₁ is similar to that of the energy gap (HOMO–LUMO). However, LUMO/LUMO+1 orbitals and the lower excited states S₁/S₂ are still different in essential. Thus, the LUMO or LUMO+1 orbitals were not employed as approximation for the lower excited states.

Fig. 16 Evolution of the excitation energy of the lowest two excited states of (a) D1–A1 pair (b) D2–A2 pair as a function of horizontal displacement S with the fixed vertical separation at 3.4 Å and 3.6 Å (c) D1–A1 pair, D2–A2 pair and D2–A2′pair as a function of horizontal displacement S at the fixed vertical separation at 3.6 Å (d) D1–A1 pair, D2–A2 pair and D2–A2′pair as a function of horizontal displacement S each at the fixed optimal vertical separation (Z = 3.4 Å for D1–A1 pair, Z = 3.6 Å for D2–A2 pair and D2–A2′ pair).

Furthermore, for these pairs, the larger vertical separation shows higher excitation energy. The smaller energy gap is localized at S = 1.2 Å and S = 3.2 Å, indicating the higher activity at their optimal configuration once motivated. From the comparison of the excited states in Fig. 16(c) and (d), D1–A1 pair has lower excitation energy, while D2–A2′ pair has higher excitation energy. Moreover, the deviation of excitation energy is evident for S₁ state; whereas for S₂ state, D1–A1 pair and D2–A2 pair is closed to each other. Thus, it should be concluded that the order of the activity is D1–A1 < D2–A2 < D2–A2′ once motivated.

Conclusions

In this work, we have investigated the geometric and electronic structures of five studied monomers as well as their intermolecular interaction energies, frontier molecular orbitals and charge transfer properties of three D–A models influenced by intermolecular relative orientation. By comparison of the calculated results and the experimental data of the crystal structure from X-ray analysis for D1 and A1, we can gain confidence in the theoretical approach to calculate the geometries and the intermolecular interactions. And then, the stacking arrangements of D2–A2 and D2–A2′ complexes in solid state were predicted. In view of the difficulty in predicting the molecular stacking of single component, the transfer integral values are mostly obtained based on the molecular dimers taken from experimental measurement and then the evaluated charge mobility often contains notable error.⁵⁷ With respect to the mixed stacked D–A CT crystals, the favoured charge transport direction coincides with the stacking direction, and thus the intermolecular orientation of the stacking direction basically determines the charge transport properties. Through the comparison and analysis of the three molecular pairs, the results can be summarized as follows: the number of substituents at phenyl and the different position of cyano group in the vinylene unit exert almost no influence on the geometric and electronic structures of DSB cores; the former could effectively tune the molecular stacking and resultant charge transfer properties. The intermolecular electrostatic interactions caused by electron-withdrawing/electron-donating effect of –CF₃/–CH₃ play a major role in π-stacking, which directly influence on molecular stacking arrangements of D–A crystals. The CT complexes of D1–A1 have been demonstrated as good ambipolar materials, while the complexes of D2–A2 and D2–A2′ should act as n-type organic semiconductor materials by the calculation in this work. Moreover, they could also act as good ambipolar materials similar to D1–A1 complexes by tuning the crystal growth conditions. The features of the D1–A1′ complexes were not being considered in this work, because the similar results from the discussion on D2–A2′ complexes by analogy can be gained. It is practical to design and synthesis various types of organic semiconductor materials by tuning the substituents of DSB core for mixed stacked D–A complexes.

In a word, this article opens a new route toward prediction of molecular stacking and charge transfer properties in mixed-stack D–A CT crystals by theoretical calculation. Besides, better understanding of the relation of intermolecular relative orientation to intermolecular interaction energies and transfer integral provides D–A complexes based DSB molecules with a bright future of development. It is our expectation that our findings would facilitate the future design and preparation of novel organic semiconductor materials.

Acknowledgements

This work was supported by the Natural Science Foundation of China (Grant 21203071 and 21003057) and the State Key Development Program for Basic Research of China (Grant no. 2013CB834801) and the Jilin Provincial Natural Science Foundation (Grant no. 201215031).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ra06497j

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