Quadrupole moments determine the crystal structures of organic semiconductors

Abstract

This study demonstrates that a two-dimensional plot of in-plane quadrupole moments Q in organic semiconductors provides a phase diagram of their crystal structures. When the long- and short-axis Q_xx and Q_yy are positive, the crystal has a herringbone (HB) structure. Introduction of electron-deficient rings makes Q_yy negative, leading to a stacking structure. Terminal electron-deficient moieties make Q_xx negative, which also results in a stacking structure. By contrast, electron-rich groups do not change the HB structure. All these aspects are explained by the various quadrupole moments and the largely different intermolecular distances. The crystal structures of many materials reveal a transition region between the HB and stacking structures, consisting of a HB-like θ-structure with a large dihedral angle of 130°. In alkyl thienoacenes, the alkyl chain extends parallel to the stacking direction in HB crystals, but vertically in θ-structures, though both have the same alkyl orientation within a molecule. The alkyl chain increases Q_xx but decreases Q_yy, which sometimes changes the HB structure to a θ-structure. Side methylthio groups make Q_yy negative, resulting in a stacking structure. Naphthalene tetracarboxylic diimide derivatives have a brickwork structure due to |Q_xx| < |Q_yy|, whereas the perylene analogues have an ordinary stacking structure owing to |Q_xx| > |Q_yy|.

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Introduction

To evaluate the performance of organic semiconductors, we have to understand their crystal structures.^1–7 Conventional materials such as oligothiophene and pentacene have a herringbone (HB) structure (Fig. 1(a)), but many high-performance materials with stacking structures have been reported (Fig. 1(b)).^7–11 It has been pointed out that the quadrupole moments play an important role in determining the crystal structures.¹² The present paper applies this rule to a large number of fundamental aromatic compounds and actual transistor materials,^13,14 and proposes the “phase diagram”. The actual border is not simply determined by the sign of the quadrupole moments but slightly deviated. The structural change induced by the alkylation is explained by the quadrupole moments. The brickwork (BW) structure (Fig. 1(c)) appears when the short-axis moment exceeds the long-axis moment.

Fig. 1 (a) Herringbone (HB, BTBT), (b) stack (PQP), (c) brickwork (BW, Cy6NDI), (d) θ-(TTT), (e) sandwich HB (SHB, perylene), (f) γ-(hexabenzocoronene), and (g) pitched π-stack (Pπ) structures (POOP, viewed from the molecular short axis). (h) C8BTBT. (i) Molecular coordinates.

Desiraju and Gavezzotti have proposed the classification of the crystal structures of aromatic hydrocarbons.³ This study, however, involves compounds containing only C and H, so basic aromatic compounds with S, N, and O have been investigated in my previous paper.¹³ In general, peripheral hydrogen atoms have slight positive charges and are attracted by aromatic carbon atoms with compensating negative charges. The resulting vertical (T-type) molecular arrangement leads to a HB structure with a dihedral angle of θ = 50–60° (Fig. 1(a)).^15–17 However, fused thiophenes do not have peripheral hydrogen atoms, and the HB structure is replaced by a θ-structure with θ = 120–130° (Fig. 1(d)).^13,18 In addition, a sandwich HB (SHB) structure appears specifically in two-leg molecules (Fig. 1(e)), where two-leg means that the width of the molecule corresponds to two aromatic rings. In such a case, the molecular width is approximately twice that of the molecular thickness.

More than three-leg aromatic hydrocarbons have stacking structures,^14,19–21 which Desiraju and Gavezzotti have called γ-structures (Fig. 1(f)).³ Since the molecules in adjacent columns are arranged vertically, this structure is monoclinic and includes the glide (g) intermolecular contact in addition to the stacking (s) interaction. In general, centrosymmetric molecules are located on a lattice point, and the resulting structure has the same symmetry as the HB structure. Even in comparatively isotropic aromatic hydrocarbons, the vertical interaction is formed at the longest edge.¹⁴ Accordingly, the HB structure is regarded as a slim-molecule limit of the γ-structure. When the molecular long side is not straight, the vertical contact is formed at the molecular terminal, leading to a pitched π-stack (Pπ) structure (Fig. 1(g)). This structure has the same symmetry as the HB structure, though the glide interaction is found in the direction of the molecular long axis. Therefore, the HB, θ-, and Pπ structures are regarded as extreme cases of the γ-structure.¹⁴

In the present paper, the crystal structures of a number of fundamental aromatic compounds and actual organic semiconductors are discussed from a plot of the in-plane long-axis and the short-axis quadrupole moments (Q_xx and Q_yy). The resulting phase diagram demonstrates that Q_xx and Q_yy are useful to predict the crystal structure. In addition to fundamental aromatic materials,^13,14 compounds containing a variety of electron-rich and deficient heterocycles are investigated.^22,23 The phase diagram is reproduced by the model using various quadrupole moments with largely different intermolecular distances.

To discuss the effects of alkylation on the quadrupole moments, the structures of alkyl thienoacenes, particularly [1]benzothieno[3,2-b][1]benzothiophene (BTBT) derivatives (Fig. 1(h)), have been investigated.^24,25 Many variations of unsymmetrically substituted alkyl phenyl BTBT have been studied owing to the liquid crystalline properties and the resulting excellent thin films.^26–34 Although alkyl BTBT usually has a HB structure, several alkylated selenium-substituted BTBT derivatives have θ- and stacking structures.^35,36

Naphthalene/perylene tetracarboxylic diimides (NDI/PDI) constitute an important family of n-channel organic semiconductors.³⁷ NDI has a brickwork (BW) structure (Fig. 1(c)), but PDI has a stacking structure; these compounds provide an excellent example of the phase diagram. In addition, compounds with blocking groups such as phenyl and methylthio moieties are discussed. These compounds have been used to realize stacking structures achieving high-performance transistor materials.^7,9–11

Method

To list various molecules, fused aromatic rings are abbreviated as P (phenyl) and T (thiophene), and BTBT (Fig. 1(h)) is designated as PTTP.¹³ Oligomers such as quarterthiophene are represented as 4T. Copolymers are abbreviated as 2P-2T-2P. Similar abbreviations (Fig. 2) are used for selenophene (Se), pyrrole (N), furan (O), thiazole (Tz), thiadiazole (Td), pyrazine (Z), dihydropyrazine (A), pyridine (Y), perfluorophenyl (fP), benzoquinone (Q), quinoxaline (BZ), benzothiadiazole (Bd), and azulene (Az).

Fig. 2 Abbreviations of the units.

Molecular coordinates are defined by placing the origin at the molecular center and taking (X, Y, Z) along the molecular long, short, and vertical axes, respectively (Fig. 1(i)).^13,14 The molecular length L and width W are defined by the difference of the maximum and minimum X and Y values appearing in the molecule (Fig. 1(i)); these values usually come from the terminal and peripheral hydrogen atoms. By using the molecular coordinates, the position of the neighboring molecule is designated as (X_g, Y_g, Z_g) for the glide-connected non-parallel molecule and (X_s, Y_s, Z_s) for the parallel (stacking) molecule (Fig. 1(a)). Owing to the same lattice symmetry, not only the HB but also the θ-, γ-, and Pπ structures have the g and s interactions (Fig. 1). These parameters for the same structure are very similar for entirely different molecules. A largely different parameter indicates an exceptional crystal structure.

When all intralayer molecules are parallel, it is called the stacking structure. Therefore, in addition to the ordinary stacking structure (Fig. 1(b)), the BW structure (Fig. 1(c)) is included in this category. Furthermore, the Pπ structure satisfies this definition (Fig. 1(g)) and is categorized as Type II (IIb).¹³ Molecules in Type I are parallel even in the interlayer direction, among which the BW structure (Fig. 1(c)), designated as Ia, has a large Y_s, whereas the ordinary stacking structure (Fig. 1(b)), labelled as Ib, has practically zero Y_s.

It is somewhat misleading that the parallel interaction in the HB structure is conventionally called a stacking interaction (Fig. 1(a)), because there is practically no molecular overlap due to large Y_s > 5 Å. The γ- and θ-structures have significant “stacking” interactions with reasonably small Y_s = 3.9 and 1.7 Å, respectively. In this paper, these γ- and θ-structures are not called stacking structures. However, the θ-structure is recognized as an intermediate between the HB and stacking structures.

Quadrupole moments were determined by DFT calculations (B3LYP/6-31G) using the molecular coordinates (Tables S2 and S3, ESI†).³⁸ The resulting traceless Q_xx, Q_yy, and Q_zz were oriented along the molecular long, short, and vertical axes (Fig. 1(i)), and the non-diagonal elements were usually negligible.

To compare the stability of various crystal structures, the intermolecular energy was estimated according to the standard 6-exp potential, where the parameters were taken from the MM3 force field (Table S1, ESI†).^13,15,39 To this dispersion energy (V_vdW), electrostatic energy (V_stat) was added (Table S1, ESI†). From the energy of the glide (V_g) and stacking interactions (V_s), the total energy was obtained (V_t = 2V_g + V_s). In general, the dispersion energy is nearly ten times larger than the electrostatic energy.¹³ Nonetheless, the dispersion energy does not depend largely on the molecular orientation because “isotropic” dispersion energy works in proportion to the molecular contact. This is the reason that the electrostatic term represented by the quadrupole moments determines the crystal structure.^15–17 When the θ dependence of V_t is estimated, the HB materials show the minimum around 60°, where the V_stat term plays an important role,¹⁴ whereas materials with a θ-structure show the minimum around 120°. In this study, the θ dependence of V_t (θ-diagram) as well as the parallel movement of the stacked molecule (X_sY_s-diagram) are investigated.

Results

Quadrupole moments

T-type arrangement and the resulting HB packing have been explained in terms of the quadrupole moment (eqn (S8), ESI†).^40,41 Negative charges associated with the π-electrons are the origin of the out-of-plane negative quadrupole moment Q_zz (Fig. 3(a) inset), where z corresponds to the molecular vertical direction (Fig. 1(i)). Q_zz pushes down the energy levels of the (face-on) molecule lying on a metal or polar substrate in comparison with the standing (edge-on) molecule.^42–46

Fig. 3 Non-hydrogen atom number N_c dependence of (a) the out-of-plane traceless quadrupole moment Q_z, and (b) in-plane quadrupole moments Q_xx and Q_yy. The insets show the schematic Q_zz, Q_xx, and Q_yy in HB materials. Alignments of Q_yy in the (c) HB and (d) BW structures. (e) In-plane Q_xx and Q_yy of HB acenes and para-phenylenes (red squares), γ-structure aromatic hydrocarbons (black squares), HB thienoacenes (orange triangles), θ-structure thienoacenes (pale blue squares), stacking structures (blue squares), Pπ-structures (violet squares), HB pyrrole compounds (brown triangles), CF₃-containing compounds (yellow squares), fP-containing compounds (light green squares), perfluoroacenes (green squares), CH₃O-containing compounds (pink inverse triangles), and NDI/PDI (pink squares) (Table S2, ESI†). Schematic quadrupole moments in the (f) 4th and (g) 2nd quadrant stacking structures.

As shown in Fig. 3(a), the absolute value of the traceless Q_zz increases with the molecular size in proportion to the number of non-hydrogen atoms, N_c. Thiophene compounds (brown nT and orange PT HB squares) are aligned on the same line as the aromatic hydrocarbons (red acene and pink nP) and the γ-structure large aromatic hydrocarbons (black γ). The negative Q_zz has been considered as the origin of the HB structure.^40,41 However, since the fused thiophenes (pale blue TTT θ) are aligned on the same line, it seems difficult to distinguish the θ-structure from the HB structure using only Q_zz. In general, it is difficult to discuss an offset of a stacking structure only from Q_zz.^47–50

The peripheral hydrogen positive charge of aromatic hydrocarbons makes +–+ alignments along both the molecular long (X) and short (Y) axes, and gives rise to positive Q_xx and Q_yy within the molecular plane (Fig. 3(b) inset). It has been pointed out that this leads to the HB structure as schematically shown in Fig. 3(c).¹² By contrast, when Q_xx and Q_yy have different signs, the Q_yy dominance leads to a BW structure (Fig. 3(d)), whereas the Q_xx dominance results in a stacking structure.⁵¹ Similarly to Q_zz in Fig. 3(a), Q_xx and Q_yy increase with the molecular size (Fig. 3(b)). However, thienoacenes (brown nT and orange PT) have a different slope from acenes (red P and pink nP) and aromatic hydrocarbons (black γ). In addition, Q_xx (squares) and Q_yy (triangles) have different slopes. For the same kind of molecules, the ratios of Q_xx and Q_yy are approximately equal.

Fig. 3(e) shows a plot of Q_xx and Q_yy. Although individual materials will be discussed in the following sections, acenes (red P HB squares) and aromatic hydrocarbons (black) are located in the 1st quadrant (region (1)) due to the positive Q_xx and Q_yy. This is the origin of the HB, SHB, and γ-structures.¹⁴

Oligothiophenes and thienoacenes (orange triangles) are located below the diagonal line. Although some have even negative Q_yy, these compounds maintain the HB structure. Fused thiophenes with a θ-structure (pale blue) are aligned on a line going down and make the border to the stacking structure. Below this pale blue line, the compounds have a stacking or Pπ structure (blue and violet).^52–54 Compounds containing electron-deficient groups have negative Q_yy (Fig. 3(f)) and fall into this category.

Compounds with terminal CF₃ (yellow) and perfluorophenyl (fP, green) groups have negative Q_xx and are located in region (4). Charge distribution as shown in Fig. 3(g) leads to a stacking structure. When Fig. 3(d) is regarded as a structure viewed from the molecular short (Y) axis, this scheme demonstrates that the large Q_xx results in a stacking structure. Here, the diagonal direction designated by the arrow is the stacking direction, and Fig. 3(d) represents a largely tilted stacking structure. In region (8), Q_yy < 0 e Ų but |Q_xx| > |Q_yy|, and still the traceless Q_zz is negative. In region (4), however, Q_zz is positive (Table S1, ESI†). In Fig. 3(a), the absolute values (blue < 0, yellow and green triangles > 0 e Ų) are smaller than those of the region (1) compounds.

Quadrupole moments of individual compounds

In addition to the compounds investigated in my previous paper,^13,14 the Q_xx and Q_yy of fundamental aromatic compounds and actual organic semiconductors are plotted in Fig. 4. The geometrical parameters of the compounds are listed in Tables S4–S6 (ESI†).

Fig. 4 In-plane Q_xx and Q_yy of HB compounds (red and orange), γ-structure aromatic hydrocarbons (black), θ-structure thienoacenes (pale blue), stacking structures (blue), Pπ-structures (violet), and methylthio containing stacking structures (blue triangles) in (a) region (1) and (b) region (8). (c) Molecular structures.

In aromatic hydrocarbons (black and red squares in Fig. 4(a)), both Q_xx and Q_yy are positive owing to the slight positive charges on the hydrogen atoms and the resulting C^δ−–H^δ+ polarization. The Q_yy/Q_xx ratio is nearly one not only in such aromatic hydrocarbons as coronene (>0.95) but also in acenes (red PPP ∼0.8) and para-phenylenes (red nP ∼0.7) because basically Q_yy is a summation of y² over the whole molecule (eqn (S8), ESI†). Accordingly, these compounds are located slightly below the diagonal Q_xx = Q_yy line. These compounds constitute the typical HB and γ-structure compounds.

Compounds containing vinylogue moieties like PvPvP (Fig. S3, ESI†) are basically the same.^55–57 Azulene trimers (Az–Az–Az) have similar quadrupole moments though these compounds have large dipole moments.^58–60 These compounds have the HB structure as well (Tables S4 and S5, ESI†). Phthalocyanine is also located near the diagonal line and categorized as a γ-structure.

The Q_yy of oligothiophenes and thienoacenes (orange triangles) are much smaller and sometimes even negative. Nonetheless, these compounds maintain the HB structure. By extending the molecule, the 4T-6T-8T and 2P–2T–2P–2P–3T–2P–2P–4T–2P series slightly go down (Fig. 4(b)) because the thiophen ring shifts Q_yy to the negative direction. In contrast, the BTBT series, benzothieno[3,2-b]benzothiophene (PTTP)–naphthothieno[3,2-b]naphthothiophene (PPTTPP)–anthrathieno[2,3-d]anthrathiophene (PPPTTPPP), slightly goes up because the P number increases (Fig. 4(a)).

Fused thiophenes (1,4-thiophthene (TT), bisthieno[3,2-b:2′,3′-d]thiophene (TTT), thieno[2′′,3′′:4′,5′]thieno[2′,3′-d]thieno[3,2-b]thiophene (TTTT), and pentathienoacene (TTTTT)) have a θ-structure; the pale blue line goes down. This series forms a slope of (ΔQ_xx, ΔQ_yy) = (3.9, −1.4 e Ų), which is the border to the stacking structure (Fig. 4(a) and (b)). Some other θ-structure compounds such as α,α′-bis(dithieno[3,2-b:2′,3′-d]thiophene) (TTT-TTT) (Fig. 4(b)) and 5,5′-bis(2-thienyl)dithieno[3,2-b:2′,3′-d]thiophene (T-TTT-T) (Fig. 4(a)) are located above the pale blue line due to the existence of the conjugated single bond. Naphtho[2,3-b]naphtho[2′,3′:4,5]thieno[2,3-f][1]benzothiophene (PPTPTPP) and 2,2′-bithieno[3,2-b][1]benzothiophene (PTT-TTP) are situated considerably above the pale blue line, but these compounds have large X_g (>5 Å).¹³ Benzo[1,2-b:4,5-b′]bis(b)benzothiophene (PTPTP) has the HB and θ-polymorphs, but both have large X_g (>5 Å, Table S10, ESI†).

The compounds below the pale blue line have stacking structures (blue squares in Fig. 4(b)). The Pπ structures (violet squares) are included in this category. Quinone (Q), pyrazine (Z), pyridine (Y), and benzothiadiazole (Bd) containing compounds have significantly negative Q_yy, and charge alignment as shown in Fig. 3(f) results in a stacking structure. 2,5-Bis(naphthalen-2-yl)-1,3,4-thiadiazole (PP-Tz-PP) and 2,5-bis(2-naphthyl)thiazolo(5,4-d)thiazole (PP-2Tz-PP) have HB structures, but trans-2,5-bis(2,2′-bithienyl-5-yl)thiazolo (5,4-d)thiazole (2T-TzTz-2T) and 5,5′-bis(4-(thien-2-yl)-2,3,5,6-tetrafluorophenyl)-2,2′-bithiophene (T-fP-2T-fP-T) have stacking structures (Fig. 4(b)).

[1,2,5]Thiadiazolo[3′,4′:5,6]naphtho[1,2-c][1,2,5]thiadiazole (Bd′Bd′), 5H,11H-[1,2,5]thiadiazolo[3′,4′:6,7]anthra[2,3-c][1,2,5]thiadiazole-5,11-dione (BdQBd), and [1,2,5]thiadiazolo[3′,4′:5,6]anthra[1,2-c][1,2,5]thiadiazole-6,12-dione (Bd′QBd′) (Fig. 4(c)) have different Q_xx and Q_yy signs in agreement with the stacking (Ib) structure (Fig. 4(b) and 5(a)). 4,7-Bis(pyridyl)-2,1,3-benzothiadiazoles, oY-Bd-oY, mY-Bd-mY, and pY-Bd-pY, have largely different moments depending on the o-, m-, and p-pyridine, but the o- and p-compounds are correctly located in the stacking structure region (Fig. 4(b)). Indigo and quinacridone are also included in this region. These molecules have hydrogen bonds and additional intermolecular interactions, but the resulting crystal structures do not conflict with the quadrupole moments.

Fig. 5 In-plane Q_xx and Q_yy in (a) region (4) and (b) electron-rich and TPT/TOT materials.

Terminal CF₃ and perfluorophenyl (fP) groups make Q_xx negative, and the charge distribution as shown in Fig. 3(g) results in a stacking structure. A large number of CF₃ and fP containing compounds (yellow and green) have a stacking structure in region (4) (Fig. 5(a)).

Electron-rich pyrrole (N) compounds (carbazole (PNP), 5,10-dihydroindolo[3,2-b]indole (PNNP), 6H-dibenzo[b,h]carbazole (PPNPP), and 2,7-diphenyl-9H-carbazole (P-PNP-P)) have positive Q_yy larger than Q_xx (Fig. 5). These compounds maintain the HB structure because both Q_xx and Q_yy are positive. The HB structure is observed even at negative Q_xx in PNP and PNNP. In a similar way, dihydrophenazine compounds (yellow 5,10-dihydrophenazine (PAP), 5,12-dihydrobenzo[b]phenazine (PAPP), and 6,13-dihydrodibenzo[b,i]phenazine (PPAPP) in Fig. 5(b)) are electron-rich and have a HB structure. By contrast, pyrazine is electron-deficient, and the corresponding dehydro compounds (yellow phenazine (PZP), benzo[b]phenazine (PZPP), and dibenzo[b,i]phenazine (PPZPP)) have negative Q_yy (region (8) in Fig. 5(b)), forming a stacking structure.

Terminal electron donating CH₃O groups increase Q_xx, but Q_xx remains positive. Accordingly, these compounds maintain the HB structure (pink inverse triangles in Fig. 5(b)). The terminal amino groups have the same effect, and N,N,N′,N′-tetramethylbenzidine ((CH₃)₂N–2P–N(CH₃)₂) has a HB structure. The absolute magnitudes of Q_zz in Fig. 3(a) (pink inverse triangles) are larger than those of the standard HB compounds.

Compounds with outermost thiophenes (benzo[1,2-b:4,5-b′]dithiophene (TPT), naphtho[2,3-b:6,7-b′]dithiophene (TPPT), and anthra[2,3-b:6,7-b′]dithiophene (TPPPT)) are located in the 1st quadrant (red squares in Fig. 5(b)) in agreement with the observed HB structure. However, the nondiagonal Q_xy is larger than Q_xx (Table S3, ESI†). In these compounds, two molecules are crystallographically independent, and the molecular long axes are not perfectly parallel. Furthermore, the thiophene S positions are disordered in TPPT and TPPPT. The low symmetry and the disorder seem to be associated with the large nondiagonal Q_xy. Both Q_xx and Q_yy are negative in TPTPT (Fig. 5(b)), and this compound has an unusual stacking (IIa) structure. TPTTP is located in the bordering region between the HB and θ-structures (brown square in Fig. 4(a)), but actually has a SHB structure in spite of the one-leg character. TTPTT and 4O are situated in the HB/θ transition region (Fig. 5(b)), but have a characteristic stacking (III) structure, where molecules not only in the interlayer direction but also within the layer are orthogonal.¹³ In these materials, the large Q_xx seems to be the major driving force to make the Pπ-like structure. 6O has similar moments (Fig. 5(b)), but exhibits a HB structure. Since the HB structures are found at larger Q_xx, the crystal structure may depend on the magnitude of Q.

OPO is located near TPT (Fig. 5(b)) and has a similar HB structure. POOP appears near PTTP, but has a Pπ structure. PPOPP is also near PPTPP, but has a Pπ structure. The calculated electron-deficient character of a furan ring is not largely different from a thiophene ring, but the former seems underestimated, and the latter is overestimated.⁶¹ These compounds have significant O⋯H contacts (2.83 Å in 4O and 2.62 Å in POOP) on the molecular side. These factors induce the Pπ structure in the furan compounds. It is difficult to predict the Pπ structure distinguished from the stacking structure. When Q_yy is negative and the molecular terminal has C–H groups (Q_xx > 0 e Ų), a Pπ structure is likely. For compounds with terminal CF₃ and fP groups, a Pπ structure is unlikely.

Perfluoropentacene (fPPPPP) and perfluoroanthracene (fPPP) have a HB-like structure (Fig. 6(a) inset),^62,63 but because θ is large (88.5° and 90.0°) and V_s is larger than V_g, these compounds are considered to have γ-structures (Table S5, ESI†). The attracting charges between the negative F and the positive C are opposite to the ordinary aromatic hydrocarbons. Accordingly, both Q_xx and Q_yy are negative (Fig. 5(a)), which lead to a HB-like γ-structure. Since the fluorine atom has a large negative charge (−0.2), the electrostatic energy (V_stat) is even larger than the dispersion energy (V_vdW in Fig. 6(a)). When a stacked molecule is moved parallel to the molecular plane, the potential minimum appears at a very large Y_s = 3.8 Å (Fig. 6(b)). Then, fPPPPP is unlikely to form an ordinary stacking (Ib) structure with an X_s offset. In addition to the bulk γ-phase, a thin-film phase has a BW structure (Table S5, ESI†).⁶⁴ This phase actually has large Y_s (2.86 and 5.19 Å). A BW phase has also been reported in fPPP (Fig. S4, ESI†).⁶² The BW arrangement is a structure avoiding the electrostatic repulsion in the stacking. In these compounds, |Q_yy| is slightly larger than |Q_xx|, also suggesting the existence of BW polymorphs. In Fig. 3(a), the positive Q_zz (green squares) is scaled by the same slope as the ordinary HB materials.

Fig. 6 (a) θ-dependent potential curves of perfluoropentacene (fPPPPP) and the crystal structure, viewed from X. (b) X_sY_s-map of stacked fPPPPP V_s at Z_s = 3.45 Å. The red points designate the actual molecular geometry in the thin-film phase.

Recently, 3,7-dihydrobenzo[1,2-b:4,5-b′]difuran-2,6-dione (BDF, Fig. 4(c)) has attracted attention because the polymer exhibits high n-type conductivity (2000 S cm⁻¹).⁶⁵ The monomer as well as another type of the monomer unit, 3-(2-oxo-1-benzofuran-3(2H)-ylidene)-1-benzofuran-2(3H)-one (BFD),⁶⁶ has a Pπ structure (Table S6, ESI†). The minimum of the X_sY_s-map of BDF appears at (2.2, 0.8 Å) (Fig. S8, ESI†), which agrees with the actual geometry (2.37, 0.99 Å). These compounds have different signs of Q_xx and Q_yy, where BDF appears in region (4) (Fig. 5(a)) and BFD appears in region (8) (Fig. 4(b)). The C=O parts make Q_xx negative in BDF, but Q_xx negative in BFD. This is in complete agreement with the Pπ structure.

Herringbone and θ-structures in alkyl compounds

Alkylation is extensively used in organic semiconductors,¹ but structural analyses of long alkyl compounds are not easy in the conventional method. Recently, however, the crystal structures of many benzothienobenzothiophene (BTBT) derivatives (Fig. 1(g)) have been examined due to the excellent transistor performance.^4,24,25 To discuss the impact of alkylation in quadrupole moments, the structures of alkyl thienoacenes are listed in Tables 1 and 2. When both terminals are alkylated, dioctyl-BTBT is abbreviated as C8PTTP. Monoalkyl is represented as mC4PTTP, whereas the alkyl phenyl substitution is represented as C8PTTP-P. Thiophene sulfur is assumed to appear alternately up and down, and the alkyl substitution is at the 2-position of P (meta position of the sulfur atom). Another isomer is indicated as P or P′. Lattice constants are converted to b < a < c (Fig. 1(a)), where b is the monoclinic unique axis and c is the interlayer direction. The orientation of the alkyl chain is defined by the difference of the coordinates between the terminal carbon atom and the root core carbon atom for even alkyl carbon n, or the root alkyl carbon atom for odd n.

Table 1 Structural parameters of HB and θ-structures in alkyl compounds

Compound^a	μ max (cm^2 V^−1 s^−1)	a (Å)	b (Å)	θ (°)	V g (kJ mol^−1)	V s (kJ mol^−1)	α (°)	φ 1/φ2 (°)	l	δ (°)	CCDC	Ref.
a mCnPTTP: monoalkyl-PTTP, Cn’: the alkyl chain is substituted at the para (3-) position of the sulfur (otherwise meta (2-) position). C10PTTP′-P: the phenyl group is substituted at the para (3-) position of the sulfur (otherwise meta (2-) position). C10TPTPT*: all sulfur atoms are aligned on the same side (Table S10, ESI). b Two crystallographically independent molecules. c Field-effect hole mobility. d //a−c. e Alternate HB and stacking patterns. The in-plane (φ2 = 0°) alkyl groups are associated with the odd number of thiophene rings. f C10TPTPT* see Table S10 (ESI).
HB
PTTP		7.9331	5.8622	56.4	−26.66	−19.55	11.6				975935	67
C2PTTP		8.3402	7.8271	64.8	−35.77	−22.76		3/24	(0.35, 0.63, 0.70)		1525673	27
C8PTTP	2.9	7.88	5.927	56.4	−69.99	−48.54	4.9	30/18	(0.04, 0.49, 0.87)	30	679293	24
C10PTTP	2.7	7.838	5.923	55.5	−80.78	−54.94	5.2	30/18	(0.03, 0.55, 0.83)	33	679294	24
C12PTTP	3.9	7.74	5.864	55.2	−93.31	−62.61	5.0	30/17	(0.03, 0.50, 0.86)	30	677772	25
mC2PTTP		9.1532	6.0178	56.1	−32.58	−21.94	35.5	22/32	(0.71, 0.54, 0.45)		1525677	27
mC3PTTP		7.5942	6.0321	54.6	−26.21	−23.39	1.2	24/30	(0.26, 0.58, 0.77)		1525678	27
mC4PTTP		8.191	5.8764	58.1	−36.83	−25.48	10.8	10/26	(0.11, 0.26, 0.96)	16	1525679	27
mC9PTTP		7.9219	5.9762	63.9	−45.19	−34.18	4.8	30/16	(0.02, 0.52, 0.86)	31	1525680	27
C3PTTP-P^b		7.8648	5.9541	54.9	−30.96	−30.96	4.7	16/28	(0.23, 0.49, 0.84)	29	1400438	28
				54.2	−32.21	−32.21		24/27	(0.23, 0.49, 0.84)	30
C4PTTP-P		8.357	5.95	53.8	−26.08	−26.08	20.5	24/28	(0.18, 0.51, 0.84)	33	1400439	28
C5PTTP-P		7.8111	6.0866	51.5	−31.77	−31.77	3.7	31/20	(0.09, 0.53, 0.84)	33	1400440	28
C6PTTP-P		7.8022	6.0957	51.3	−33.51	−33.51	5.1	32/17	(0.05, 0.50, 0.87)	30	1400441	28
C8PTTP-P		7.804	6.0861	51.0	−63.53	−38.15	5.5	30/16	(0.04, 0.45, 0.89)	27	1400442	28
C9PTTP-P		7.8515	6.1099	51.2	−65.55	−39.24	4.7	27/25	(0.02, 0.54, 0.84)	32	2233289	33
C10PTTP-P	14.7	7.7568	6.0471	50.2	−69.55	−41.66	4.0	32/16	(0.03, 0.50, 0.87)	30	1017499	29
C6PTTPP-P		7.801	6.065	51.2	−63.86	−41.81	6.7	33/19	(0.06, 0.50, 0.86)	30	1866226	30
C10′PTTP′-P	0.26	7.391	7.029	31.3	−48.85	−31.50	23.7	60/17	(0.04, 0.66, 0.75)	41	1866227	30
C10′PTTPP′-P	2.8	7.406	6.931	42.0	−75.79	−33.80	25.3	58/21	(0.04, 0.66, 0.75)	41	1866225	30
C5PTTP-PC1		9.1167	5.9715	54.2	−47.17	−35.32	32.2	29/21	(0.26, 0.54, 0.80)	37	2233290	33
C6PTTP-PC1		9.1363	5.9272	55.0	−56.25	−41.55	31.9	27/27	(0.41, 0.53, 0.75)	41	2233291	33
C7PTTP-PC1		9.1572	5.9434	55.0	−56.05	−42.55	32.1	30/20	(0.32, 0.54, 0.78)	39	2233292	33
C8PTTP-PC1		9.0903	5.9152	55.1	−56.64	−46.84	31.3	30/16	(0.42, 0.55, 0.73)	43	2233293	33
C9PTTP-PC1	7.2	7.806	5.9079	53.9	−68.80	−45.29	5.2	30/16	(0.03, 0.51, 0.86)	30	2233294	33
C10PTTP-PC1	6.3	7.7655	5.9285	53.4	−69.75	−46.72	3.7	30/16	(0.03, 0.52, 0.85)	31	2233295	33
C11PTTP-PC1	8.6	7.8152	5.9147	54.3	−71.07	−48.86	2.2	31/16	(0.02, 0.55, 0.84)	33	2233296	33
C12PTTP-PC1	8.0	7.7398	5.9093	53.3	−75.48	−50.45	3.7	30/16	(0.03, 0.52, 0.86)	31	2233297	33
C13PTTP-PC1	10.2	7.852	5.9208	54.6	−77.89	−52.42	4.7	31/16	(0.02, 0.51, 0.86)	31	2233298	33
C14PTTP-PC1	6.7	7.7178	5.9024	53.1	−81.88	−54.07	5.9	32/15	(0.02, 0.52, 0.86)	31	2233299	33
mC8PTTPP^b	1.43	7.8788	6.0191	54.0	−57.91	−39.61	6.7	33/19	(0.02, 0.50, 0.86)	30	2023249	31
					−48.75	−39.75		34/18	(0.07, 0.50, 0.87)	30
mC8PPTTP^b	1.54	7.8705	6.0098	53.8	−53.75	−36.27	6.8	34/18	(0.02, 0.50, 0.87)	30	2023252	31
					−54.31	−36.26		33/19	(0.07, 0.49, 0.87)	29
mC8′PTTPP^b	0.031	8.0009	6.0576	54.9	−55.04	−40.42	7.9	17/13	(0.08, 0.46, 0.89)	27	2023251	31
					−54.84	−40.62		17/12	(0.04, 0.45, 0.89)	27
mC8′PPTTP^b	0.34	7.948	6.1144	53.2	−53.33	−37.52	5.7	21/13	(0.06, 0.45, 0.89)	27	2023255	31
					−50.04	−37.50		20/14	(0.10, 0.44, 0.89)	27
C6′PTTPT-P	0.036	7.827	12.88/2	47.2	−58.34	−40.00	25.0	45/29	(0.14, 0.48, 0.86)	30	2270804	34
C10′PTTPT-P	0.041	7.74	12.95/2	51.3	−59.08	−34.10	23.8	54/21	(0.01, 0.64, 0.77)	40	2312364	34
C6′PTTP'T-P	8.7	7.8737	6.1043	53.4	−59.45	−41.47	3.9	16/14	(0.13, 0.38, 0.91)	24	2297468	34
C10′PTTP′T-P	9.0	7.8735	6.0743	52.9	−70.78	−48.45	4.1	12/56	(0.06, 0.45, 0.89)	27	2088582	34
C10PPTTPP	1.0	7.6164	5.9945	51.1	−100.27	−63.41	8.6	35/18	(0.03, 0.58, 0.81)	36	2128319	68
C10PTPTP-P	0.3	7.8042	6.1357	51.0	−75.22	−46.89	5.9	26/13	(0.05, 0.52, 0.85)	35	1964820	32
C10PPTPTPP	16	7.7106	6.1265	46.2	−106.57	−68.53	1.0	33/15	(0.03, 0.58, 0.81)	36	980612	69
C10PPTPP	1.0	7.8143	6.0863	42.2	−92.04	−58.11	7.9	30/10	(0.09, 0.56, 0.82)	35	886144	70
C6′PPTPP	9.5	7.9123	6.1104	46.1	−69.31	−47.44	0.0	26/15	(0.07, 0.50, 0.86)	30	886146	70
C10′PPTPP	6.5	7.8143	6.0863	45.3	−91.03	−61.12	0.0	28/13	(0.03, 0.53, 0.85)	32	886145	70
C1TPPPT	0.41	7.407	7.026	51.1	−43.51	−30.67		6/1	(0.09, 0.72, 0.69)	47	891039	71
C2P-2T-P		9.109	5.7272	52.5	−53.84	−38.39	35.6	17/29	(0.05, 0.49, 0.87)	29	634487	72
C6P-2T-P	0.02	9.274	5.666	52.9	−64.19	−61.02	27.0	27/16	(0.05, 0.32, 0.95)^d	19^a	600832	73
C6T-PPP-T	0.4	7.395	5.866	50.1	−81.01	−56.12	4.2	19/16	(0.05, 0.46, 0.89)	28	265820	74
C6-2T-PPP-2T		12.50	5.837	46.1	−87.47	−73.85		30/16	(0.62, 0.53, 0.58)	39	1956922	75
C8P-TTT-P	10.2	7.333	5.822	40.1	−91.94	−50.42	0.0	28/13	(0.04, 0.52, 0.86)	31	922123	76
C12P-TTT-P	1.8	7.391	5.846	40.1	−114.54	−64.70	0.0	28/12	(0.03, 0.51, 0.86)	30	922124	76
C8PP-TTT-PP	0.54	7.445	5.903	41.1	−111.77	−66.42	0.0	28/14	(0.05, 0.52, 0.85)	32	963347	77
C4-4T	0.002	7.854	6.04	61.3	−60.89	−48.47	26.0	10/2	(0.08, 0.52, 0.85)	31	826820	78
C6-4T	0.005	7.814	6.049	61.8	−67.42	−51.31	25.0	8/4	(0.03, 0.58, 0.82)	35	255049	79
C6T-TTT-T^e	7 × 10^−5	7.496	5.653	57.8	−75.83	−47.95	11.8	14/0	(0.11, 0.24, 0.96)	15	655866	80
C7T-TTT-T^e		7.161	5.5128	58.8	−77.68	−53.57	2.5	18/0	(0.13, 0.28, 0.95)	18	969085	81
C10TPTPT*^f	6.2	7.6675	6.1022	34.1	−50.18	−46.95	4.7	20/34	(0.23, 0.49, 0.84)	33	1503965	82
θ
C10PTPTP	1	10.814	4.2983	109.1	−60.63	−116.12	1.2	24/19	(0.54, 0.02, 0.84)	32	1964819	32
C6PTTTP	8.8	11.09	4.12	118.4	−41.08	−90.02	0.0	28/19	(0.58, 0.04, 0.81)	35	830987	83
C8PSeSeP	0.066	11.1892	4.1874	113.5	−41.35	−99.26	0.4	32/22	(0.63, 0.03, 0.78)	39	730254	36
C12PSeSeP	0.23	10.6926	4.4014	105.5	−62.00	−118.75	5.9	22/23	(0.50, 0.02, 0.87)	30	730256	36

---

Table 2 Structural parameters of stacking structures in alkyl compounds

Compound	μ max (cm^2 V^−1 s^−1)	a (Å)	b (Å)	X s1 (Å)	Y s1 (Å)	Z s1 (Å)	V s1 (kJ mol^−1)	θ//X^b (°)	φ 1/φ2 (°)	CCDC	Ref.
a CnPPTTPP*: Fig. S10 (ESI). b θ in the interlayer direction. The non-zero θ//X indicates a Pπ-like arrangement.
Stack Ia (BW)
C8POOP	0.076	5.53	5.02	3.01	2.22	3.35	−64.65	0	48/9	1840602	88
Stack Ib
C12TPT	0.01	5.900	4.187	1.62	1.16	3.68	−117.59	0	33/9	684276	89
C8TOPOT		8.177	6.657	7.93	1.29	3.52	−87.61	0	26/1	1526539	90
β-C10TTTT		9.1811	8.2512	7.24	1.80	3.53	−88.75	0	25/2	639115	91
C3PTTP		7.453	4.6827	2.99	0.24	3.60	−66.41	0	12/35	1525674	27
C4PTTP		7.6517	4.6426	2.95	0.19	3.58	−72.72	0	13/36	1525675	27
C5PTTP		8.6807	4.7594	2.94	0.14	3.59	−83.32	0	3/38	1525676	27
C4PTPTP	0.01	9.223	4.584	3.04	0.02	3.43	−81.38	0	12/39	667691	92
C6TTPTT	1.7	6.3989	5.3344	3.80	0.86	3.86	−82.15	0	41/15	717515	93
C4PPTTPP*^a	0.16	7.9484	4.8135	3.21	0.86	3.49	−94.64	0	1/31	1995852	94
C6PPTTPP*	0.0016	7.2092	8.5332	7.76	0.61	3.50	−90.98	0	11/1	1995853	94
C8PPTTPP*	2.7	7.7923	6.5695	5.48	0.98	3.49	−114.73	0	7/6	1995854	94
C10PPTTPP*	3.5	7.7947	11.0524	10.42	0.94	3.55	−112.41	0	4/1	1995855	94
Stack IIa (BW)
C10PSeSeP	0.18	7.2956	5.6136	5.78	2.58	3.63	−101.34	59.7	23/2	730255	36
C14PSeSeP	0.16	7.3316	5.5648	6.12	1.76	3.64	−130.91	59.6	14/2	730257	36

---

The arrangements of the core parts in the HB compounds (Table 1) are very similar to those of the unsubstituted compounds (Table S8, ESI†), and the intermolecular geometry (Y_g, Z_g, Y_s, and Z_s) follows the standard relations (eqn (S2)–(S5), ESI†) of the HB structure (Fig. 7(a)).¹³ Accordingly, the a and b values (Table 1) are not largely different from those of the unsubstituted compound (PTTP). In unsubstituted materials, X_g is sometimes as large as 2 Å,¹³ whereas in alkyl materials, X_g is close to zero; the exceptions are several short alkyl materials (Table S8, ESI†).

Fig. 7 (a) Intermolecular geometry of alkyl compounds in Table 1 with the standard relations of the HB structure (eqn (S2)–(S5), ESI†). (b) Top and side views of C8PTTP and C12PTTP. (c) Molecular packing of C8PTTP viewed from a and (d) from c. (e) Molecular packing and (f) top and side views of C6-4T. (g) Molecular packing and (h) top and side views of C10PTPTP.

From the molecular coordinates, the in-plane angle φ₁ of the alkyl group with respect to the X axis (Fig. 7(b)) is estimated together with the out-of-plane angle φ₂ with respect to the molecular plane (Table 1). In addition, the orientation unit vector l of the alkyl group with respect to the crystallographic axes is evaluated (Fig. 7(c)). In the representative compounds such as C8PTTP, l is approximated as (0, sin δ, cos δ), which means that the alkyl chain is tilted by δ from the c axis within the bc plane, extending in the vertical direction (Fig. 7(d)). This is a requirement to make all chains parallel to each other in the monoclinic crystal. As a result, φ₁ is about 30° in many cases and is approximately equal to δ. In addition, φ₂ is related to θ/2, practically a little smaller than θ/2. C8PTTP and C12PTTP are depicted in the same graph in Fig. 7(b) using the respective molecular coordinates. Owing to the same orientation of the alkyl chains, these molecules entirely overlap with each other.

Compounds with short alkyl chains (C2PTTP, mCnPTTP (n = 2–4), and CnPTTP-P (n = 3–4)) do not follow these restrictions, and the orientation of the alkyl chains is not related to the crystallographic axes. The alkyl chain is usually substituted at the 2-position (meta position of the sulfur atom). Even when the alkyl chain is at the 3-position (para position of the sulfur atom; examples are mC8′PTTPP, mC8′PPTTP, C6′PTTP′T-P, and C10′PTTP'T-P), φ₁ and δ are about 20°. However, when a phenyl group is substituted at the 3 (para)-position of the sulfur (C10′PTTP′-P and C10′PTTPP′-P), together with C6'PTTPT-P and C10′PTTPT-P, a large value of φ₁ ≈ 60° is observed. In such a case, the angle α of the core long axis (X) from the c axis (Fig. 7(c)) is large (25°), and δ (40°) is not largely different from the other cases. Owing to the tilted core packing, however, X_g (∼1.3 Å) and X_s (∼2.9 Å) are large (Table S8, ESI†).

The alkyl chains of the quarterthiophene derivatives (C4-4T and C6-4T) extend parallel to the core part (Fig. 7(e) and (f)), where both φ₁ and φ₂ are small (<10°). However, not only δ but also α are around 30°. In general, an alkyl chain extends straight from a thiophene terminal (φ₁ and φ₂ ≈ 0°), though that from a phenyl group extends to the 30° (or 60°) direction.

The selenium analogues of PTTP (C8PSeSeP and C12PSeSeP) have a θ-structure, though the unsubstituted PSeSeP has an ordinary HB structure. In the θ-compounds, Y_g, Z_g, Y_s, and Z_g satisfy the standard relations (Fig. 7(a)). As shown in Table 1, the orientation vector l of the θ-structure materials is approximated as (sin δ, 0, cos δ), where the alkyl chain is tilted by δ from the c axis within the ac plane (Fig. 7(g)). The alkyl chain extends in the horizontal direction in the flat (small b) crystal lattice.

In C8PTTP, the plane of the zig-zag alkyl chain is tilted by 42° from the bc plane, forming another HB structure. Polyethylene oligomers have a HB structure analogous to the alkyl part of the present compounds.^84–86 The area a × b = 41 Ų of polyethylene is 88% of the area of the present compounds, 47 Ų (Table S7, ESI†), which is not largely different from the unsubstituted compound.¹³ One alkyl chain is almost sufficient to realize the molecular fastener effect in the one-leg compounds.⁸⁷

Stacking structures in alkyl compounds

Table 2 lists compounds with a stacking structure. The lattice constants are converted to b < a < c, where c is the interlayer direction (Fig. 8(a)). Here, s1 represents the stacking direction (Table 2), s is the side molecule (Table S9, ESI†), and s2 designates the intermediate direction (Fig. 8(a)).

Fig. 8 Crystal structures of stacking structure alkyl materials. (a) Molecular packing and (b) molecular structure of C8POOP. (c) Molecular packing and (d) molecular structure of C4PTTP. (e) Molecular packing and (f) molecular structure of C10PSeSeP.

In Table 2, only C8POOP is listed as BW (Ia) (Fig. 8(a)) not only due to the relatively large Y_s1 but also due to V_s2 (Table S8, ESI†) comparable to V_s1. The first four compounds in Table 2 have comparatively large Y_s1, where φ₂ is close to 0°, and the alkyl chain extends approximately parallel to the core plane (Fig. 8(b)).

CnPTTP for n = 3–5 has a standard stacking (Ib) structure with practically zero Y_s1 (Fig. 8(c)). The φ₁ value is small, indicating that the alkyl chain extends vertically in analogy with the HB compounds (Fig. 8(d)).

C10PSeSeP and C14PSeSeP have the BW (IIa) arrangement.¹³ These compounds have small φ₂, and the alkyl chain extends horizontally within the molecular plane (Fig. 8(e) and (f)). This is the same as the θ-structure C8PSeSeP and C12PSeSeP (Table 1), where the alkyl chains are again horizontal. This is in contrast to CnPTTP, which forms HB and stacking structures, but the alkyl chains are always vertical.

Potential curves of alkyl compounds

To understand the observed structures, intermolecular potentials are investigated as a function of θ similarly to unsubstituted compounds.^13,14 The core part is rotated around the axis connecting the root carbon atoms with changing the lattice constants (eqn (S4) and (S5), ESI†), while the alkyl chains are fixed to the vertical or horizontal direction (Fig. 7). Alternatively, the core part is rotated around the longest crystal axis (c), but practically the same results are obtained. The lattice constants a and b are estimated using the molecular contact conditions (eqn (S4) and (S5), ESI†), and Y_g, Z_g, X_s, Y_s, and Z_s are evaluated using eqn (S2)–(S3) (ESI†). Then, the positions of adjacent molecules and the intermolecular energy V_g and V_s are estimated, and finally, a, b, and X_g are optimized so as to minimize V_t. Owing to the irregular shape of the molecules, the potential curves are not entirely smooth (Fig. 9); when the alkyl part collides with another part, the potential curve tends to change abruptly.

Fig. 9 θ-Diagrams of alkyl (a) PTTP and (b) PSeSeP compounds with vertical (solid) and horizontal (dashed) alkyl chains. The core and alkyl contributions are from C12PTTP and C12PSeSeP.

For C12PTTP, the core–core and the alkyl–alkyl potentials are depicted independently (Fig. 9(a)). The core–core potential (black) slightly prefers the low-angle (HB) structure, but the vertical alkyl–alkyl potential (blue) is evidently stable at low angles. As a result, the total potential prefers the HB arrangement. The potential minimum of the vertical alkyl arrangement (solid curves) appears around 50°, indicating HB packing, whereas the minimum of the horizontal alkyl arrangement (dashed curves) appears around 120°. Therefore, the HB structure is always associated with the vertical alkyl arrangement, while the θ-structure appears together with the horizontal alkyl chains.

In the selenium analogues, the horizontal arrangement becomes comparatively stable (Fig. 9(b)). These compounds actually form θ-structures (n = 8 and 12), and the n = 10 and 14 compounds have BW structures with horizontal alkyl chains (Table 2). The HB structure is evidently stable in monoalkyl- and alkyl/phenyl-substituted compounds (Fig. S5, ESI†).

Quadrupole moments in alkyl compounds

As shown in Fig. 10, alkylation increases Q_xx and decreases Q_yy; the position in the Q_xxQ_yy-diagram moves to the lower right. Here, compounds with the same core parts are connected by lines. The unsubstituted and alkyl PTTP (black squares) have a HB structure. The phenyl compound (C8PTTP-P) is situated above the line of the pure alkyl compounds, preferring the HB structure. However, it is difficult to explain the stacking structure of short alkyl compounds such as C3PTTP from this diagram.

Fig. 10 Influence of alkylation in the Q_xxQ_yy-phase diagram.

The unsubstituted PSeSeP (pink square) is HB, but θ-(C8 and C12) PSeSeP and stacking (C10 and C14) PSeSeP appear below the pale blue line of the TTT θ-structure. Since the shift (ΔQ_xx, ΔQ_yy) = (9, −6 e Ų) is steeper than the pale blue θ line (3.9, −1.4 e Ų), alkylation sometimes changes the HB structure to the θ- and stacking structures. The shift is, however, not proportional to the alkyl chain length because the electrostatic energy becomes constant for long alkyl chains (Fig. S6, ESI†), though the ordinary dispersion energy increases in proportion to the alkyl length. Then, C12PTTP is located at the left of C8PTTP, and the difference between the θ-(C8 and C12) PSeSeP and the stacking (C10 and C14) PSeSeP is not due to the alkyl chain length.

Such compounds as PTTP, PPTTPP, PPTPP, P-TTT-P, and 4T maintain the HB structure in both the unsubstituted and alkyl compounds (Table S8, ESI†). There are several examples in which the unsubstituted and the alkyl compounds have different structures (Table S10, ESI†). The unsubstituted PTPTP has HB and θ-polymorphs, but C10PTPTP has a θ-structure (Fig. 7(g)). PTTTP changes from a HB structure to a θ-structure. In Fig. 10, the resulting alkyl compounds (orange and violet right ends) are located below the pale blue line, and the transformation from HB to θ is understandable from the quadrupole moments. However, the θ-structure sometimes appears considerably above the pale blue line owing to large X_s > 5 Å. In such a case, the transformation from θ to HB takes place (PPTPTPP and T-TTT-T in Fig. S7(d), ESI†), because alkyl compounds are restricted to X_s = 0 Å.

The horizontal alkyl part of the θ-structure has the same orientation as the vertical alkyl group of the HB structure with φ₁/φ₂ = 30/18° and has the same quadrupole moments. The vertical and horizontal alkyl chains in the stacking molecules are different from this arrangement. The alkyl orientation dependence of the quadrupole moments is usually small (Fig. S7(e), ESI†), but the in-plane alkyl orientation (φ₁/0°) exhibits the largest Q_xx shift in general.

Stacking structures of NDI and PDI compounds

The structural parameters of naphthalene tetracarboxylic diimides (NDI) and perylene tetracarboxylic diimides (PDI) are listed in Table 3. These molecules are important n-channel transistor materials,^22,37 and a large number of compounds have been prepared. The molecular width W = 6.5 Å is typical of two-leg compounds (for example, perylene: 6.87 Å), where the O–O width (4.5 Å) is smaller than the H–H width. Nonetheless, these compounds do not form a SHB structure like perylene but universally have a stacking structure.

Table 3 Structural parameters of NDI and PDI compounds

Compound	μ max (cm^2 V^−1 s^−1)	θ (°)	W (Å)	X s1 (Å)	Y s1 (Å)	Z s1 (Å)	V s1 (kJ mol^−1)	X s2 (Å)	Y s2 (Å)	Z s2 (Å)	V s2 (kJ mol^−1)	φ 1/φ2^c (°)	CCDC	Ref.
a C1P-NDI: tolyl-NDI, C7*NDI: 1-methylhexyl-NDI, C4OPNDI: n-butoxyphenyl-NDI, FPC2NDI: p-fluorophenylethyl-NDI, DCF3PC1NDI: di(trifluoromethyl)benzyl-NDI, Cy5: cyclopentyl, PC2PDI#: phenylethyl-diaza-PDI, PCH3C2PDI: 2,2-methylphenylethyl-PDI, fPC2PDI: perfluorophenylethyl-PDI, C2OC2PDI: ethoxyethyl-PDI, and C5*PDI: 1-methylbutyl-PDI. b Field-effect electron mobility. c φ 1/φ2 in phenyl-containing compounds is estimated from the terminal C and N atoms. d s1 = s2 due to the crystal symmetry. e Exceptional HB-like arrangement. f Alternate BW and γ patterns. g The second interaction is in the X direction with large Xs2. h C8NDTI: dioctylnaphthodithiophene diimide (Table S11, ESI).
θ											V g
θ-NDI		143.3	6.57	1.29	3.07	3.16	−43.17	5.26	4.99	2.47	−11.38		1905853	95
C1P-NDI^a		100.6	6.81	1.79	2.33	3.54	−82.19	1.44	4.18	6.48	−25.02		161262	96
PDI		124.6	6.55	3.38	1.11	3.34	−79.02	6.53	4.82	4.81	−11.55		264109	97
C1PDI		166.9	6.49	0.91	1.61	3.40	−92.63	9.15	4.32	3.40	−15.87		1140279	98
Stack Ia (BW)										V s2
NDI			6.47	1.70	2.56	3.29	−40.27	5.79	4.04	2.92	−17.58		2041062	99
C2NDI			6.48	1.00	3.53	3.20	−51.18	5.66	4.35	3.03	−25.16	6/38	937648	100
C4NDI			6.53	1.42	3.84	3.24	−54.96	5.92	4.09	3.11	−28.44	3/74	819749	101
C5NDI			6.49	0.86	3.76	3.22	−61.63	6.26	4.11	3.12	−48.94	27/6	238148	102
C6NDI	0.7		6.45	1.15	3.40	3.33	−72.29	6.31	4.39	3.08	−48.55	18/6	671518	8
C7*NDI^a			6.50	0.95	3.69	3.96	−65.96	1.02	4.43	2.87	−65.87	21/20	630806	101
C8NDI	0.16		6.50	1.82	2.84	3.39	−88.69	2.48	5.06	3.31	−54.81	4/34	1972223	103
C10NDI			6.50	1.71	2.88	3.37	−99.63	2.36	5.15	3.29	−65.52	8/38	1972224	103
C12NDI			7.23	1.60	2.80	3.29	−114.58	2.61	5.09	3.27	−77.41	9/35	819750	101
C14NDI			8.65	1.58	2.82	3.33	−125.31	2.61	5.14	3.30	−90.36	10/35	230429	104
CH3SC3NDI			6.49	0.87	3.64	3.22	−66.12	6.14	4.19	3.09	−50.88	26/7	1919395	105
C4OPNDI^a			6.49	1.09	2.56	3.33	−108.86	4.43	4.43	5.19	−37.82	5/13	1497523	106
P-NDI	10^−5		6.49	0.56	3.75	3.46	−63.01	5.07	4.16	3.68	−34.08	1/6	296236	107
FPC2NDI^a	0.068		6.49	0.96	3.59	3.19	−75.73	5.79	4.29	3.09	−49.99	11/0	726747	108
DCF3PC1NDI^a	0.57		7.71	1.08	3.35	3.18	−108.11	11.38	5.80	0.81	−32.86^f	11/49	697036	109
Cy5NDI^a	0.011		6.42	1.13	3.94	3.27	−59.70	2.88	4.05	3.44	−44.11	38/2	939278	110
Cy6NDI^d	6.2		6.45	0.82	4.19	3.34	−62.40	0.82	4.19	3.34	−62.40	22/0	671519	8
Cy7NDI	0.019		6.39	0.92	3.97	3.29	−70.75	2.92	3.98	3.77	−54.99	3/6	939279	110
Cy8NDI^d^e	0.018	15.9	6.45	2.07	4.47	2.89	−65.64	1.60	3.61	4.13	−65.64	41/2	939280	110
C8PDI	1.7		6.68	1.51	2.95	3.35	−115.60	2.65	5.17	3.35	−68.26	6/33	1938481	111
PC2PDI#^a	3.0		7.06	1.13	3.64	3.27	−96.24	5.34	4.54	3.20	−61.91	14/5	1938483	111
PCH3C2PDI^a			6.57	1.17	3.48	3.37	−113.37	7.10	4.66	3.39	−63.03	11/2	1140275	98
fPC2PDI^a	1.1		6.42	1.04	3.45	3.27	−113.81	5.63	4.70	3.16	−65.36	9/1	2034087	112
Cy6PPPDI^f		72.8	4.70	0.04	4.19	3.09	−69.62	6.36	2.00	4.79	−44.06	21/1	2348426	113
Cy6PZPDI	0.099		4.74	1.15	3.91	3.15	−67.33	3.94	2.98	3.69	−57.74	22/12	2348427	113
Stack Ib
C3NDI			6.45	0.57	0.78	3.35	−66.58	3.77	7.41	2.30	−10.28	2/32	1029340	114
C5PDI			6.53	3.09	1.30	3.37	−116.80	5.98	6.56	2.61	−40.12	6/43	1140273	98
C2OC2PDI^a			6.54	3.21	1.28	3.38	−111.42	5.47	6.54	2.64	−47.30	6/62	1140271	98
C1OC3PDI			6.52	3.13	0.67	3.48	−111.82	5.74	7.02	2.54	−39.67	22/19	1140272	98
C2OC3PDI			6.53	3.05	1.28	3.41	−121.39	5.84	6.53	2.89	−48.79	8/39	1140274	98
CH3OPC1PDI			6.52	2.67	0.35	3.47	−140.62	6.04	7.39	2.30	−26.46	3/70	1140280	98
C4F7PDI	0.67		6.51	3.35	1.16	3.40	−117.65	5.72	6.72	2.56	−37.52	2/43	719790	115
PC2PDI			6.53	3.19	0.45	3.48	−134.36	6.66	7.69	1.88	−30.25	7/11	1140276	98
Stack IIb (Pπ)
C4PDI		135.5	6.53	3.13	1.03	3.40	−113.84	5.73	6.93	2.72	−29.00	8/57	1140278	98
C5*PDI^a		95.5	6.52	5.44	0.97	3.43	−109.96	3.42	6.87	2.76	−35.44	12/27	1140277	98
Stack III											V g
PC1PDI		87.6	6.53	3.07	1.15	3.43	−123.54	5.16	6.76	3.62	−20.72	2/55	1140281	98
γ											V g
C8F15NDI^g	0.05	74.2		1.21	3.98	3.15	−87.58	1.35	1.14	6.29	−53.53	5/22	161260	96
C8NDTI^h	0.051	82.4		0.60	3.78	3.35	−104.62	5.70	3.41	6.70	−34.45	5/29	988064	116

---

In particular, CnNDI compounds usually have a BW (Ia) structure with large Y_s1 (>2.5 Å), where Y_s1 is larger than X_s1. Not only Z_s1 but also Z_s2 correspond to the interplanar spacing (3.2 Å). V_s2 is smaller than V_s1, indicating imbalance, but usually V_s2 amounts to more than half of V_s1.

Many compounds have small φ₁ < 10°, indicating that the alkyl chain extends vertically to the molecular core (Fig. 11(a)). Some others have small φ₂ < 10°, where the alkyl chain is approximately parallel (horizontal) to the core plane (Fig. 11(b)). Several compounds have large X_s2 (>5 Å) with a serious long-axis offset. Cycloalkane (Cyn) extends in the vertical direction (X_s1 < 1 Å), realizing balanced BW structures. In particular, Cy6NDI forms an ideal BW structure (Fig. 1(g)); due to the C2/m space group, Y_s1 and Y_s2 are exactly the same (4.19 Å) and half of a = 8.541 Å. Cy8NDI is regarded as HB with θ = 15.9°, which is an intermediate between the HB and BW structures (Fig. 11(c)).

Fig. 11 Crystal structures of (a) C8NDI with vertical alkyl chains, (b) C6NDI with horizontal alkyl chains, and (c) Cy8NDI.

By contrast, CnPDI usually has an ordinary stacking (Ib and IIb) structure with small Y_s1 (<1.5 Å). Here, Y_s2 is as large as W, and V_s2 is significantly smaller than V_s1. These compounds are triclinic, and the alkyl orientation is not restricted. Nevertheless, it is remarkable that the Ib compounds have vertical (small φ₁) alkyl groups.

The X_sY_s-map of NDI in Fig. 12(a) has minima separated to the Y_s direction. This indicates that NDI prefers the BW structure; most NDI compounds in Table 3 are included in the BW (Ia) category. To realize the BW arrangement, the actual Y_s1 > 2.5 Å is larger than Y_s1 = 1.8 Å at the potential minimum. In general, the X_sY_s-maps of most compounds show an X_s offset (Fig. S8, ESI†); exceptions are para-phenylenes (nP) and acenes. Therefore, the X_sY_s-maps are not very useful to predict the crystal structures. The Y_s offset is a token of polar molecules. C=O is oppositely polarized to C–H, and the ordinary HB (and SHB) packing does not seem to be attractive. In addition, NDI is a two-leg molecule. In such a case, the BW structure is likely.

Fig. 12 X _s Y _s-maps of stacked molecules V_s at Z_s = 3.45 Å for (a) NDI and (b) PDI, where the minimum appears at (X_s, Y_s) = (1.0, 1.8 Å) and (1.8, 0.0 Å), respectively. X_sY_s-maps of stacked molecules for (c) Cy6PPPDI and (d) Cy6PZPDI. (e) In-plane Q_xx and Q_yy in NDI and PDI. (f) Stack (Ib long-axis BW) structure of TIPS-pentacene and (g) Pπ-stacking structure of rubrene. Molecular structures of (h) α-2CH₃T-TPT, (i) β-2CH₃T-TPT, and (j) 4CH₃T-pyrene.

By contrast, the X_sY_s-map of PDI in Fig. 12(b) is elongated in the X_s direction, and PDI prefers a simple stack (Ib) structure. The PDI compounds are involved in the stack (Ib) group with Y_s1 < 1.5 Å in Table 3. In general, X_s2 is large, and V_s2 is less than half of V_s1.

In these NDI and PDI compounds, the molecules are usually parallel also in the interlayer direction, and categories II and III are rare. C₈F₁₄NDI has non-parallel intercolumnar contacts, which is categorized as a γ-structure (Table 3). Unsubstituted NDI (stack Ia top) forms an exceptional BW structure, in which the long axes are non-parallel in the stacking direction. Unsubstituted PDI forms a θ-like structure, and recently a similar θ-like polymorph of NDI has been reported. There are hydrogen bonds using the terminal hydrogen atoms: N–H⋯O/H⋯O = 2.87/2.01, 2.88/2.03 Å for stacking NDI, 2.89/1.94 Å for θ-NDI, and 2.91/2.00 Å for PDI. This is related to the extraordinary molecular packing.

NDI makes Q_yy negative (pink squares in Fig. 12(e)), and because of |Q_xx| < |Q_yy|, NDI exhibits a BW structure. In PDI, however, Q_xx is negative (blue lines), and |Q_xx| > |Q_yy| realizes a stacking structure. Owing to the molecular size, the C=O negativity mainly works along the Y axis in NDI, but along the X axis in PDI.

The one-leg anthracene diimide (Cy6PPPDI, Fig. 12(c)) has alternate BW and γ-patterns, whereas the pyrazine derivative (Cy6PZPDI) has a BW structure. When the Cy6 units are removed, the X_sY_s-maps show two minima in the X_s and Y_s directions. The X_s minimum is slightly more stable in Cy6PPPDI, but the Y_s minimum is stable in Cy6PZPDI. These compounds are located on the border between the X_s and Y_s offset materials. In Fig. 12(e), the slightly |Q_xx| < |Q_yy| character (light green squares) suggests preference to the BW structure.

Compounds with blocking groups

High-performance transistor materials have been achieved in compounds with blocking groups such as phenyl and methylthio moieties.^7,9–11 Representative materials are listed in Table S12 (ESI†). TIPS-pentacene (TIPS: triisopropylsilylethynyl) has a stacking (Ib) structure (Fig. 12(f)), where the molecular plane is largely tilted from the stacking axis. This structure is sometimes regarded as a long-axis BW structure; this is a stacking structure in which Fig. 3(d) is regarded as a scheme of the molecular long-axis quadrupole moments viewed from the molecular short axis. Q_xx and Q_yy are both positive (Fig. 12(e)), suggesting a HB structure. However, the HB structure is impossible due to the presence of the TIPS groups.

Rubrene has a Pπ structure (Fig. 12(g)). Since Q_xx is negative and Q_yy is positive (Fig. 12(e)), the observed Pπ structure is reasonable. It is characteristic that the interlayer V_c is not much smaller (0.72) than the stacking V_s1 (Table S12, ESI†).

Following the same principle, recently high-performance organic semiconductors have been developed on the basis of pyrene and perylene with methylthio blocking groups. These compounds also have a long-axis brickwork structure.^9–11 When methylthio (CH₃T–) groups are attached to the terminal α-position of TPT (α-2CH₃T-TPT in Fig. 12(h)), Q_xx and Q_yy are positive (Fig. 12(e)), and the HB structure is maintained. By contrast, when the side (β-position) is substituted by methylthio groups (β-2CH₃T-TPT in Fig. 12(i)), Q_yy becomes negative (Fig. 12(e)) because the methylthio groups are weakly electronegative,¹¹⁷ and the θ- or stacking structures are realized. Many polymorphs (Table S14, ESI†) have been obtained when the methylthio groups are replaced by methoxy (CH₃O–) and methylseleno (CH₃Se–) groups. In high-mobility 4CH₃T-pyrene (Fig. 12(j)),⁹Q_yy is negative (Fig. 12(e)), and pyrene forms a long-axis BW structure similar to TIPS-pentacene. In the same way, CH₃T compounds have been prepared based on perylene, PPPP, TPPT, TPPPT, and TTTT (Table S12, ESI†). The CH₃T part makes Q_yy negative (Fig. 12(e)), consistent with the stacking structures. Although it seems strange to attribute the impact of CH₃T to Q_yy, CH₃T destroys the side C–H polarization and the T-type molecular arrangement. As a consequence, Q_xx realizes a stacking structure.

Quadrupole interaction

The quadrupole–quadrupole interaction energy has been obtained in an analytical form for the axial moments (Q_xx = Q_yy = −Q_zz/2).¹¹⁹ The orthogonal arrangement is most stable, which leads to a T-type arrangement (HB A(yz) in Fig. 13). However, the molecular quadrupole is not always axial, but changes to biaxial (Q_xx = −Q_yy, Q_zz = 0) and to more general values. Owing to the relation Q_xx + Q_yy + Q_zz = 0 e Ų, all three components are defined on the Q_xxQ_yy-diagram. The quadrupole interaction rapidly decreases with the inter-quadrupole distance R; the interaction decays in proportion to R⁻⁵ (Fig. S11(b), ESI†). Since the molecular thickness Z₀, width W, and length L are largely different, interactions including L do not appear in the actual crystal structures.

Fig. 13 Largest quadrupole–quadrupole interactions in the Q_xxQ_yy-diagram for Y_g = Z₀.

Placing point charges Q_xx/2 on the unit length x = ±1.0 Å and similarly in the y and z directions, the electrostatic Coulomb energy is calculated. In addition to the axial T-type interaction, the bipolar B(xz) arrangement represents the stacking (Ib) interaction (Fig. 13), and B(yz) corresponds to the BW interaction. A diagram for Y_g = Z₀ is shown in Fig. 13. In the 1st quadrant, large negative Q_zz leads to a HB structure. When Q_yy becomes negative, Q_zz and Q_xx form a stacking structure, B(xz). This is replaced by the BW structure when |Q_yy| becomes large. This is basically in agreement with the empirically obtained phase diagram. The diagram is centrosymmetric.

Fig. 13 shows a plot of the largest interaction, but the actual structure consists of different interactions. In particular, the θ-structure is represented by a combination of the T-type and stacking interactions. It is also noteworthy that the phase boundary depends on the R parameters. When Y_g > Z₀ is used, the HB region decreases (Fig. S11(d), ESI†). In the two-leg molecules, the large Y_g enhances the BW structure.

Accordingly, the crystal structures are attributed to the variety of quadrupole moments together with the remarkably anisotropic intermolecular distances.

Conclusion

A two-dimensional plot of Q_xx and Q_yy in organic semiconductors provides a “phase diagram” of the crystal structures. Compounds with positive Q_xx and Q_yy have axial Q and HB structures in one-leg molecules, SHB structures in two-leg materials, and γ-structures in more than three-leg compounds.^13,14 Electron-deficient groups such as Tz, Q, Y, and Bd make Q_yy negative, and the resulting biaxial Q leads to stacking or Pπ structures. Introduction of terminal CF₃ and fP groups makes Q_xx negative, leading to stacking structures as well. Accordingly, the stacking structure is found in many n-channel organic semiconductors. However, introduction of electron-rich units does not change the HB structure. Stacking structures of such compounds as indigo, quinacridone, BdQBd, and BDF are also in agreement with the different signs of Q_xx and Q_yy. When investigating a number of materials, the HB structure is maintained even at negative Q_yy, and the θ-structure appears in the transition region.

Since X is the molecular long axis and Y is the short axis, most compounds satisfy |Q_xx| > |Q_yy|. As a result, the stacking structure is universally observed. However, exceptional |Q_xx| < |Q_yy| cases lead to a BW structure. NDI derivatives have a BW structure owing to |Q_xx| < |Q_yy|, but PDI has an ordinary stacking structure due to |Q_xx| > |Q_yy|. When both Q_xx and Q_yy are negative, a HB-like γ-structure is realized as exemplified by fPPP and fPPPPP. Due to the slight |Q_xx| < |Q_yy| character, however, these compounds have BW polymorphs. In the X_sY_s-map, most compounds show an X_s offset, but the BW compounds have a characteristic Y_s offset. It is reasonable that many compounds satisfy |Q_xx| > |Q_yy| and are located in regions (1), (4), and (8). There are comparatively fewer examples in other regions.

In alkyl thienoacenes, the alkyl chain extends in the vertical direction when the core part is HB, but in the horizontal direction when the core has a θ-structure. This is a requirement to make all chains parallel to each other in a monoclinic crystal. However, these two have the same alkyl orientation (φ₁/φ₂ = 30/18°) within a molecule. In the stacking structure, the alkyl chain is usually vertical to the molecular plane (φ₁ ≈ 0°), whereas in the BW structure, the alkyl chain sometimes extends parallel to the molecular plane in the horizontal direction (φ₂ ≈ 0°). Alkylation increases Q_xx and decreases Q_yy, which moves the compound lower right in the Q_xxQ_yy-diagram. Since the effect is slightly steeper than the θ-structure border, this sometimes causes a HB compound to adopt a θ- or stacking structure. When P is inserted within the fused T, the HB and θ-structure regions are overlapped due to large X_g. This explains the polymorphs of PTPTP. However, X_g is restricted to nearly zero (<1 Å) in alkyl compounds.¹³ Such a case leads to the transformation from θ to HB.

The Q_xxQ_yy-diagram is an empirical rule coming from the mapping of the actual crystal structures, but provides a good starting point for understanding the crystal structures. The phase diagram is reproduced by considering various quadrupole moments and largely different intermolecular distances. In principle, the crystal structures of unknown compounds are predicted by calculating the quadrupole moments. However, furan realizes an exceptional stacking structure within the HB region due to the extra side O⋯H interaction. Thienoacenes with outermost thiophene rings have large nondiagonal Q_xy, which is associated with the low symmetry and disorder. Some conjugated rings are not coplanar and realize two different structures within a crystal. There are a few cases in which the actual crystal structures do not simply follow the Q_xxQ_yy-diagram, but the individual additional factors are important. In general, the Q_xxQ_yy-diagram is useful in S-, N-, and F-containing materials, but insufficient in furan containing materials.

Out-of-plane Q_zz has been used to account for the HB structure and the interfacial energy level shift.^40–46 However, Q_zz is simply scaled by the molecular size (N_c), and the θ-structure fused thiophenes are located on the same line as the HB compounds (Fig. 3(a)). Since Q_xx and Q_yy are also scaled by the molecular size (Fig. 3(b)), the orientation from the origin in the Q_xxQ_yy-diagram or the Q_yy/Q_xx ratio is of fundamental importance. However, regions (8) and (4) exhibit different properties, and alkylation adds a different slope to the original compound. It is remarkable that even the impact of alkylation and methylthio substitution is understandable in terms of the quadrupole moments. The charge distributions of molecules have been investigated using Hirshfeld surfaces,^120,121 but the present method simplifies the discussion using a few numbers. Quadrupole moments must be potentially useful to understand the interfacial and nanoscale phenomena.

Conflicts of interest

There are no conflicts to declare.

Data availability

Software for molecular geometry calculations is available from http://indigo1026.la.coocan.jp/lib/exp.html.

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Footnote

† Electronic supplementary information (ESI) available: Additional information for parameters of potential energy, structural parameters, crystal structures, and quadrupole moments. See DOI: https://doi.org/10.1039/d5tc01794g

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