Thienylene Derivatives

Close Packing in Crystals of Cyanophenylene/Thienylene Derivatives

CRYSTAL GROWTH & DESIGN 2006 VOL. 6, NO. 6 1497-1503

William Porzio,* Silvia Destri, Mariacecilia Pasini, Arnaldo Rapallo, and Umberto Giovanella Istituto per lo Studio delle Macromolecole C.N.R., Via E. Bassini 15, 20133 Milano, Italy

Barbara Vercelli Istituto per l’ Energetica e le Interfasi C.N.R., c.o Stati Uniti 4, 35127 PadoVa, Italy

Marcello Campione INFM e Dipartimento di Scienza dei Materiali, UniVersita` di Milano Bicocca, Via Cozzi 53, 20126 Milano, Italy ReceiVed March 7, 2006; ReVised Manuscript ReceiVed March 29, 2006

ABSTRACT: A new molecule, designed as a potential active material in field effect transistor (FET) devices and constituted by p-cyanophenylene and -thienylene residues, has been synthesized and characterized by electrochemical, photophysical, and structural points of view. Its crystal structure, derived from powder XRD data, displays higher close packing as compared with molecular crystals constituted by similar residues. The crystallization aptness has been demonstrated by growing solid films, from 15 nm to 2 µm thick, using high vacuum depositions, casting, and spin coating techniques. AFM investigation shows well formed needles, univocally oriented with respect to the substrate. The HOMO/LUMO levels, matching the electrode working function, the film orientation, and the close packing, suggest its promising use as an active layer in FET devices. Introduction π-Conjugated molecular crystals have shown such relevant optoelectronic properties as to be already on the market, in cases such as light emitting diodes, field effect transistors (FETs), and photodiodes.1 Specifically, the interest in the application of molecular crystals as organic FETs stems from the wide variety of their chemical structures, the appreciable processability allowing an easy device fabrication, and, mostly, the promising results that recently appeared in the literature.2-6 Moreover, the discover of an ambipolar behavior of thin film devices, fabricated by using some molecules6 and polymers,7 further increased the interest. Among the mandatory characteristics to design new molecules suitable for FET applications, close packing, especially π-electron stacking among adjacent molecules, and proper molecular orientation with respect to source and drain electrodes, allowing high charge mobility, are necessary conditions before considering the other requirements.2,3,5,6 For this reason the design of conjugated molecules allowing for H-bond formation and/or smooth contour shape, both suitable for close packing achievement, should be accomplished. Following these guidelines, the molecular design of 5,5′-bis(4-cyanophenyl)-2,2′-bithiophene, hereinafter 1, shown in Scheme 1, largely leads to an expected close packed crystal. Due to the role played by the crystal close packing, a proper computational tool, which takes into account the overlap of the adjacent atomic surfaces, should be adopted, allowing for accurate packing factor (PF) calculation and reliable comparison among selected reference molecules, to gain better insight into the relevance of intrinsic crystal factors, namely, close π-stacking, H-bond presence, and size/form adaptability, to the working of FETs. The peculiar aptness to crystallization of molecule 1 is shown in films of different thickness (from 40 nm up to 1 µm), grown * To whom correspondence should be addressed. Phone: +390223699371. Fax: +3902-70636400. E-mail: [email protected].

Scheme 1: Molecule 1 and Its Isotropic Thermal Parameters (Å2)

by different techniques, such as casting, spin-coating, and highvacuum (HV) depositions. As shown by XRD, AFM, and optical microscopy, the film orientations and morphologies are essentially the same, regardless of the growing method and of their thickness. Moreover, molecule 1 shows some similarities to other molecular crystals employed in FET fabrication: the presence of both thienylene and phenylene moieties, often used in p-type devices, with cyano groups, typically present in n-type active molecules.8,9 Finally, this paper reports on the synthesis and the electrochemical and optical properties of the compound here presented. All the results indicate molecule 1 is a promising candidate as the active layer component in FET devices, eventually functioning in ambipolar mode.6 Experimental Section The synthesis of molecule 1 was performed according to a standard Suzuki heterocupling reaction with the procedure reported below. 5,5′-Bis(4-cyanophenyl)-2,2′-bithiophene. 4-Bromobenzonitrile (93.3 mg, 0.51 mmol), 5,5′-bis(4,4,5,5-tetramethyl-1,3,2-dioxaborolan-2-yl)2,2′-bithiophene9 (100 mg, 0.24 mmol), Pd(PPh3)4 (18 mg, 0.015 mmol), and a catalytic amount of TEBA were dissolved in a mixture of THF (4 mL) and aqueous 2 M K2CO3 (2 mL) under nitrogen atmosphere. The solution was refluxed for 25 h and monitored with TLC (hexane/ ethyl acetate, 7:3 as eluent). Finally, the mixture was poured into slightly acidic (HCl) water, giving a yellow and insoluble powder, which was filtered off into a Buckner funnel and washed several times with water and CHCl3. No further purification was required: yield (63%). Mp:

10.1021/cg060126t CCC: $33.50 © 2006 American Chemical Society Published on Web 05/05/2006

1498 Crystal Growth & Design, Vol. 6, No. 6, 2006

Figure 1. Cyclovoltammetry of molecule 1. 291 °C. MS (APCI): m/z ) 369 [M + H]+. 1H NMR (270 MHz, CDCl3, ppm): 7.58 (br, 8H, phenyl protons), 7.27 (d, 2H, thienyl protons, J ) 3.85 Hz), 7.16 (d, 2H thienyl protons, J ) 3.85 Hz). Elemental analysis for C22H12N2S2 (%): calculated C 71.72, H 3.28, S 17.40, N 7.60; found C 71.80, H 3.38, S 17.11, N 7.66. DSC experiments were performed on a Perkin-Elmer Pyris 1 apparatus under nitrogen flux. Temperature XRD experiments on both powders and films of molecule 1 were performed with an Anton-Parr camera, under nitrogen flux with a control on the working temperature within (1 °C, using a Siemens D-500 apparatus with Soller slits (2° wide), narrow receiving windows (0.3° wide), and a graphite monochromator, along the [0 0 2] direction, allowing pure Cu KR radiation in a Bragg-Brentano geometry. The HV depositions were carried out in a chamber kept at basic vacuum of 2 × 10-7 mbar; to maintain the growing rate at 0.6 nm/s, the crucible temperature was maintained at 360 °C; other deposition details are described in ref 10. Cast films were obtained by slow evaporation of a 10 mg/mL tetrachloroethane (TCE) solution. Spincoated films were obtained from a 4 mg/mL CHCl3 solution, and the spin rate was 1500 rpm. The thickness of the films, as derived by AFM and profilometer measurements, ranges from 15 nm up to 40 nm and from 0.5 µm up to 2 µm for HV-deposited and cast or spin-coated films, respectively. Molecular modeling calculations, crystal structure resolution, and packing energy minimizations were performed using the MATSTUDIO package, release 3.0, developed by Accelrys.11 AFM images were collected in tapping mode with silicon cantilevers with a Nanoscope IIIa (Digital Instruments).

Results and Discussion Electronic Characterization. A cyclovoltammetric study of a film of molecule 1 was performed in acetonitrile + 0.1 M Bu4NClO4 (scan rate: 0.1 V s-1) as shown in Figure 1. The analysis showed a complete reversible behavior of 1. Indeed, the measurement on a film deposited on ITO glass indicated a reversible oxidation process at the onset potential of 1.0 V and a quasireversible reduction process at the onset potential of -2.0 V. Consequently, IP and EA values of 5.62 and 2.69 eV, respectively, were derived from the onset values considering that the energy level of Ag/Ag+ is 4.39 eV below the vacuum level.12 Moreover, an Eg value of ∼2.93 eV is comparable with the optical gap of ∼2.85 eV.13 The good match of both IP and EA values with the working functions of commonly used source/drain (S/D) electrodes, namely Pt (5.6 V) and Al (3.2 V) for p- and n-type FET devices, respectively, constitutes a notable prerequisite to consider molecule 1 as a proper candidate. Optical Characterization. In Figure 2 the absorption and photoluminescence (PL) spectra of a dilute CHCl3 solution (s ) and a 15 nm thick (‚‚‚) evaporated film of 1 are reported. The CHCl3 solution absorption maximum, centered at 400 nm, is

Porzio et al.

Figure 2. Absorption and photoluminescence spectra of a dilute CHCl3 solution (s) and a thin (15 nm) (‚‚‚) evaporated film of molecule 1.

unstructured except for a small shoulder at 430 nm, while structured profiles at 455 and 480 nm are observed in the emission spectrum, indicating a more planar molecule upon excitation. Absorption spectra of the evaporated thin film show peaks at 414, 446, and 484 nm; PL emission peaks are at 490 and 520 nm with a shoulder at 550 nm. A solution-like contribution is present in solid-state absorption spectra; its band intensity, peaked around 400 nm, is a function of an increased thickness of the film, mapping the unaggregated or disordered part of the film. The small Stokes shift (0.16 eV), defined as the distance between the absorption and emission maxima, can be responsible for the reabsorbing phenomena, hiding the solution spectral contribution in solid-state PL. Moreover, the overlap between solution emission and solidstate absorption requisite is satisfied, and a resonant energy transfer process could take place. Therefore, in agreement with XRD patterns (see below), the 15 nm film displays a large amount of ordered-packing domains, while with increasing number of layers (over 60 layers), defects are created, and the emission contains both crystals and features attributable to less ordered parts. The shift of the absorption edge of the solid state with respect to that of the solution can be related to the aggregation energy of molecules, being larger than that in the case of oligothiophenes14 and meaning an even higher tendency to close crystal packing of molecule 1. Crystal Structure Determination from Powder XRD Data. DSC observations revealed the presence of only one endothermic peak in the heating trace and only an exothermic peak in the cooling trace, in agreement with melting of the 3D phase studied in the following. Crystal structure determination from XRD data was accomplished by means of the MATSTUDIO package.11 The unit cell was determined from the experimental XRD pattern; two different unit cells, a monoclinic and a triclinic one, could match all the observed peaks, but the last one could not agree with any reasonable model, and therefore, the cell with P21/c symmetry was considered in a preliminary attempt at crystal structure solution. Concerning the structure reconstruction, since the considered molecule is constituted by 26 non-hydrogen atoms, it was possible to apply neither the trial-error method15 nor the “directspace” method.16,17 We therefore resorted to Monte Carlo (MC) simulated annealing.18 The optimization of the isolated molecule was performed using the condensed-phase optimized molecular potentials for atomistic simulation studies (COMPASS) of the MATSTUDIO package.11 The MC simulated-annealing method was adopted using the Powder Solve program11 to estimate the

Crystals of Cyanophenylene/Thienylene Derivatives

Crystal Growth & Design, Vol. 6, No. 6, 2006 1499

Table 1. Working Conditions and Refined Parameters of Molecule 1 with Estimated Standard Deviations in Parentheses Cu KR radiation/power 2θ range dmin step size (time) zero corrections (deg)a

1.541 84 Å/40 kV x 40 mA 10-50° (1.82 Å) 0.04° (80 s) -0.0413(14) T1 ) 0.020(4) T2 ) 0.050(4) Na ) 0.05(4) Nb ) 0.019(2) U ) 0.81(16) V ) 0.18(40) W ) 0.04(4) P ) 0.24(7) P2 ) 0.18(4) P3 ) -0.57(13) P4 ) -0.41(9) R ) 46(3) β ) 916(340) γ ) 3484(2700) A ) 0.02(1) B ) 0.11(13) C ) 1.37(9) Rwp ) 0.0587 Rbck wp ) 0.1016 Rp ) 0.0399 a ) 0.754 (5) b ) 1.176 (9) c ) 1.153(10) nm β ) 122.89(4)° P21/c (no. 14), Z ) 2 dcalc ) 1.425 g cm-3 dobs ) 1.43 g cm-3 11.7

pseudo-Voigt profile parametersb

asymmetryc

crystallite size (Å)d lattice straind disagreement factors

unit cell parameters

space group crystal and exptl densities thienylene-phenylene torsion anglee

Rwpf )

{

[

f Rw/o-bck ) wp

∑w (cY i

sim

{

∑w (cY

[

∑w (I i

i

exp

(2ϑi) - Y back(2ϑi))2

}

(2ϑi) - I exp(2ϑi) + Y back(2ϑi))2]

i

}

(2ϑi) - I exp(2ϑi) + Y back(2ϑi))2]

i

sim

i

∑w (I i

exp

(2ϑi))2

i

1/2

∑|cY

1/2

Rpf )

sim

(2ϑi) - I exp(2ϑi) + Y back(2ϑi)|

i

∑|I

exp

(2ϑi)|

i

a According to the Bragg-Brentano geometry; see ref 19. b According to Caglioti et al.20 c According to ref 21. d According to ref 22. e The value (deg) is in reference to the scheme. The esd is ∼1°. f Where wi ) 1/Iexp(2qi is a weighting function, c is a constant scaling factor optimized to obtain the lowest value of Rwp, Iexp(2qi) is the measured experimental spectrum, and Yback(2qi) is the background intensity of the measured spectrum.

crystal packing. To this aim, a rigid-body whole-molecule approach, involving 6 degrees of freedom (3 for translations and 3 for rotations) plus two torsion angles, along the central thienylene-thienylene and thienylene-phenylene bonds, was taken, and for each model five cycles of 2 000 000 MC steps were performed. The results converged toward a molecular position close to the inversion center at position (0.5; 0.5; 0.5). Hence, a subsequent minimization was performed constraining half the molecule to be linked to centrosymmetry, i.e., Z ) 2, so that all the translations and the central torsion angle were kept fixed, allowing only the three rotations and the thienylenephenylene torsion to change. Rietveld refinement promptly converged to the final arrangement with a minimum disagreement factor and no significant preferred orientation. In Table 1 the refined parameters and working conditions are reported, while Figure 3 shows the final profiles of both calculated and observed XRD patterns. Isotropic thermal parameters of non-hydrogen atoms (Uiso/ Å2) were treated as indicated in Scheme 1 to prevent convergence failure during the refinement.

Structure Description and Film Orientation. The crystal and molecular structure of molecule 1 is shown in Figure 4, as viewed along the short axis (top) and perpendicular to that (bottom). The molecule lies in the inversion center and is essentially planar, and the largest torsion angle between thiophene and phenylene residues is close to 11°, consistent with both acceptable intramolecular contacts, i.e., H-H and S-H, and reasonable van der Waals contacts with adjacent molecules. The close packing is determined by a quite short CN- - -NC contact (∼0.26 nm) of adjacent molecules, shown by a red bar in Figure 4 (top), while other C-C or S-C contacts exceed 0.335 or 0.365 nm, respectively. It should be noted that such a N-N contact implies another short contact between an N-atom and the phenyl H-atom in the R position of the adjacent molecule (0.26 nm). Nevertheless, a true hydrogen-bond formation is hampered by the too bent angle N‚‚‚H-C (∼127°); suitable values have always been observed to be over 150°.23 Indeed, in a selected series of best solved crystal structures, containing cyano groups,8,9,24-28 a H-bond involving an N-atom with


Figure 3. Final results of Rietveld refinement of molecule 1. The simulated spectrum (‚‚‚) is shifted by 10 units for clarity, vertical bars indicate the reflections involved, and the difference spectrum is reported on the bottom.

Figure 4. Crystal structure of molecule 1 as viewed along the short axis (top) and perpendicular to that (bottom). The short N- - -N distance (∼0.26 nm) is indicated by a red bar (top), while green dotted bars display the π-stacking of closer molecular segments (bottom).

distance ranging from 0.215 nm up to 0.27 nm is found whenever the N‚‚‚H-C angle exceeds 150°. Moreover, in the same structures, the short CN- - -NC contact, unobserved only in molecules with bulky side groups, such as ethylenedioxythiophene and butyl,9,28 ranges from 0.28 nm up to 0.31 nm, indicating strong packing closeness (PC) for molecule 1, as below discussed in terms of packing factor (PF).29 It should be noted that the π-stacking between adjacent molecules is achieved by the alignment of the thiophenephenylene-cyano sequence with the same segment of the adjacent molecules of the nearest cells, along the a axis, at an average distance below 0.36 nm. Such segment overlap is shown in Figure 4 (top), as well as in Figure 4 (bottom) by green dotted bars. The mean molecular axis of the almost planar molecule is perpendicular to the a axis, while the π-conjugated residues are essentially parallel to the (4 0 -2) plane (see Figure 4 (bottom)). Thin films grown by HV evaporation, spin-coating from CHCl3 solution, and casting from TCE solution onto polar

Porzio et al.

Figure 5. XRD patterns of molecule 1 films on plasma-etched silica: (‚‚‚) spin coated (50 nm thick) film; (-) high-vacuum evaporated (40 nm thick) film.

substrates, specifically on both plasma etched and untreated silica, have been investigated by XRD; irrespective of the growth method, the patterns are quite similar, and in Figure 5 an example of thin film (40/50 nm thick) XRD patterns is reported. The unique peak detected (0.588 nm) indicates an anambiguous orientation along the [0 1 0] crystallographic direction, i.e., the vertical one in Figure 4 (top), in agreement with both AFM observations (see below) and optical microscopy findings (unpresented). Hence, the molecular axis is parallel to the substrate, while π-conjugated residues are edge on, allowing for a suitable charge mobility between S/D electrodes. Also in this regard, the use of this molecule as active layer in FET devices is quite promising. Moreover, line profile analysis30 on XRD patterns (Bragg-Brentano mode) of samples of thickness up to 50 nm, measured with a quartz thickness monitor, reveals that the coherence along the [0 1 0] direction persists over the whole film thickness. Close Packing Analysis. As mentioned above, one of the relevant parameters to increase the performance of FET devices is the PC, clearly affecting the charge mobility in the film. PC in a crystal structure is inadequately represented by crystal density,31 because it does not take into account four major factors contributing to PC, namely, (1) the crystal symmetry, which reduces the intermolecular distances, (2) the chemical nature of the molecule, which determines the strength of the intermolecular interactions, (3) the reciprocal orientation of the adjacent molecules, which guarantees efficient π-stacking, and (4) the size/form adaptability, which affects the smoothness of the surface contours of the molecule. PF is known to be a well-representing quantity of the PC of molecular crystals, so some care should be paid to its evaluation. A brief review of the method adopted for PF calculation is reported in the Appendix. Indeed, Figure 6 shows selected π-conjugated molecules, crystallizing in close packed arrangements, i.e., PF values 0.7 or larger, and in Table 2 PF and crystal density values are reported. The choice has been addressed by considering cyanogroup presence, heavy atom presence, H-bond formation, and FET behavior. Data in Table 2 supply evidence that PC is not adequately described by the crystal density, the range of which is quite wide as compared to the PF values. As a matter of fact, the density ranking follows the relative weight of heavier chemical species constituting the molecule. Contrarywise, PF values strictly map the crystal compactness.


Crystal Growth & Design, Vol. 6, No. 6, 2006 1501

Figure 6. Selected close packed molecules. The ball colors map the atomic species: H (white), C (gray), N (blue), O (red), S (yellow), Cl (green). H indicates H-bond formation in the crystal, while F denotes FET behavior. Table 2. Density and Packing Factor Values for the Molecules Shown in Figure 6 molecule

density (g‚cm-3)

PFa

H-bond

ref

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

1.425 1.228 1.235 1.364 1.450 1.646 1.322 1.507 1.553 1.349 1.322 1.820 1.460 1.407 1.395

0.745 0.705 0.736 0.725 0.694 0.750 0.701 0.716 0.739 0.761 0.752 0.779 0.768 0.711 0.716

n y y y y y n y n n n n y n n

this paper 24 25 26 27 8 9 28 15 32 33 34 31 35 35

a

PF values larger than the one calculated for molecule 1 are indicated in italics.

More surprising is the fact that whenever a molecule displays an H-bond, its corresponding PF value is not necessarily larger than the value of molecule 1 (see molecules 2, 4, 5, and 8), irrespective of the presence of light (C, N, O) or heavy (S, Cl) chemical species. On the contrary, as somehow expected, large PF values are observed in molecular crystals constituted by fused-ring molecules (10-12), likely due to the best-match of both size/form adaptability and π-stacking. Molecule 1 presents neither fused rings nor H-bond formation. It is remarkable that with the exception of pentacene (10), which

Figure 7. (a) 10 × 10 µm2 AFM image (error signal) of the surface of a high-vacuum deposited thin film of 1 (40 nm thick). Crystalline needles a few microns long appear in bright contrast. The bright rectangular area (2 × 1 µm2) at the center of the image is viewed in a magnified AFM image in part b (height image) and part c (error signal). From the height image needles are observed to be about 80 nm thick, and from the error signal their faceted morphology is apparent. (d) 2 × 2 µm2 AFM 3D image of the surface of a spin-coated film of 1 on silicon oxide. Crystalline aggregates appear in bright contrast.

can reach a higher PF value without heavy atom or H-bond presence, in all the other molecules having PF values higher than that found in 1, namely 6, 11, 12, and 13, two conditions are verified: (1) a higher weight fraction of heavy atoms with respect to 1 (namely in 6, 11, and 12) and (2) H-bond formation (namely in 6 and 13). On the basis of these considerations, compound 1 displays a typical close packing aptness, based on π-stacking interactions only; it is therefore reasonable to believe that such a molecule constitutes a quite promising candidate for application to active layer films in FET devices, also from crystal packing analysis. AFM Analysis. The results of an AFM analysis of the surface of high-vacuum sublimated, 50 nm thick films of 1 are reported in Figure 7. The film surface is characterized by the presence


of needlelike crystals covering about 40% of the substrate surface (Figure 7a). Needles are a few microns in size and up to 100 nm in thickness, as deduced from the height image reported in Figure 7b. Their crystalline nature is well evidenced in Figure 7c, where the contrast of the error signal points out the faceted morphology of the needles. The needlelike morphology is a signature of the arrangement of the molecules with their axes parallel to the substrate surface (see e.g. ref 36 and references therein). As indeed detected by XRD, the contact plane of crystallites is the (0 1 0) plane, which contains the molecular axes. With this orientation, molecules interact strongly in a direction parallel to the substrate plane through the π-stacking of phenyl and thiophene rings (which is in turn parallel to the a-axis; see Figure 4 (bottom)); this confers the elongated shape of the crystallites. From Figure 4, molecular layers with spacing of b/2 ) 0.588 nm along the [0 1 0] direction can be observed in the crystal structure. Due to the film orientation, these layers might be, in principle, resolved with AFM; however, under our growth conditions, the mechanism of nucleation of these films is 3D, and then, crystallites are bound by flat faces instead of showing the terraced pyramidlike morphology typical of a layer-by-layer type of growth. Figure 7d reports on the morphology of a thin film of 1 obtained with the spin-coating technique from CHCl3 solution. Crystalline aggregates of 1 are clearly visible and well separated from one another. This observation demonstrates that, despite the kinetic conditions of this technique, the molecules maintain a strong tendency to diffuse and aggregate. In both AFM and optical microscopy (unreported) investigations on high-vacuum evaporated and spin-coated films, a quite relevant aptness to crystallization is revealed. These peculiarities are widely desirable in the context of FET devices. Conclusions A molecule based on the sequence of p-cyanophenylene and thienylene moieties has been designed in view of FET applications. The solid-state molecular properties, according to crystal structure from powder XRD data, have been investigated by electrochemistry, optical absorption and emission, powder/film XRD, crystal packing, and AFM, indicating the following: (1) derived IP and EA values well-matching with the working function of S/D electrodes, (2) quite close crystal packing, due neither to fused-ring presence nor to H-bond formation but rather to the efficient π-stacking, through a short NsN intermolecular contact, (3) peculiar crystal compactness, as compared with selected related molecules constituted by similar moieties, e.g., thienylene, cyano, acenes, etc., all exhibiting PF > 0.7, and in some cases large charge mobilities, i..e. up to 1 cm2 V-1 s-1, (4) aptness to aggregate observed in thin films (whose thicknesses range from 5 nm up to 1 µm) obtained by casting, spincoating, and HV evaporation from optical and AFM analyses, and (5) proper unique molecular orientation with respect to both the substrate and S/D electrodes from XRD and AFM studies. All data contributed to conceive molecule 1 as a promising candidate for FET behavior. In fact, FET device fabrication is in progress. Acknowledgment. We thank the Italian Cariplo foundation project “TESEO” and European project, Research Training Network EUROFET, Contract No. HPRN-CT-2002-00327, for partial support of this work. Appendix: Close Packing Analysis The van der Waals volume of a molecule (Vm) is the volume of the union of overlapping spheres representing the molecule’s

Porzio et al. Table 3. Average Molecular Volumes of Molecule 1 and Standard Deviations for Different Finenesses of the Grid Nθ × NO Nθ × N φ

〈Vm〉 (Å3)

σ (Å3)

40 × 80 100 × 200 5000 × 10000

319.83 319.75 319.76

0.16 0.07 0.02

constitutive atoms. Within this work, each atom k was provided with a specific van der Waals radius Fk as given in ref 37, irrespective of the particular molecule it belonged to. The general molecular surface area determinations and volume calculations, which can be viewed as tightly connected problems, are not trivial due to the unavoidable overlap of the surface contours of different atoms. Considerable effort has been devoted to these problems in the solid geometry, and both numerically29,38,39 and analytically40-42 efficient computational methods appear in the literature for facing them. Due to the relevance of the packing factor in assessing the suitability of a certain molecule for FET applications, a home-made computer program was prepared for its evaluation, aiming at numerical accuracy rather than at computational efficiency. This program discretizes the molecular surface in terms of suitable grid points on the atomic spheres. For each atom k a local reference frame centered at the corresponding nucleus is defined, having a random orientation with respect to the laboratory’s one for avoiding certain systematic errors which can stem from overor underestimation of the exposed portion of the atomic surface at the intersections of neighboring atoms. With reference to these frames, a spherical coordinate system is employed for locating the points over the van der Waals atomic spheres. The ranges (0;π) for angle θ and (0,2π) for angle φ are discretized in Nθ and Nφ points, respectively, this defining a partition of the atomic spheres in portions of area: ∆Ai,jk ) 2Fk2∆φ sin(θi) sin(∆θ/ 2).The program, then, probes for the exposure of each point on each atom in the molecule and collects every contribution of this type into the measure of the molecular surface area. The computation of the molecular volume V can be carried out within this scheme by exploiting the divergence theorem which connects the flux of a vector b V through a closed surface S to the integral over the volume contained in the surface, of the divergence of the same vector. The vector flux can be easily calculated while the surface is being evaluated. If b V is chosen as b V ) xıˆ + yjˆ + zkˆ , with ˆı, ˆj, and kˆ being the unit vectors along the X, Y, and Z axes of a reference frame centered at some point in the interior of the surface, its divergence is constant and equal to 3, so that the vector flux yields three times the Vm. For obtaining high accuracy in the volumes estimation, different evaluations of the flux were performed with respect to different reference frames centered at the nuclei of the molecule’s atoms, and the average of the computed fluxes was taken as the estimate of the true vector flux. Indeed, from a mathematical point of view, the total flux does not depend on the particular reference frame with respect to which it is calculated, but due to the discretization of the surface and the numerical accumulation of partial contributions to the total flux, such a dependence on the particular reference frame artificially appears. Moreover, also the fineness of the grid over the atomic spheres contributes to the overall quality of the results, as shown in Table 3. In Table 3 the average molecular volume of molecule 1 and the standard deviation σ is given for different finenesses of the grid Nθ × Nφ. It can be noted that though the standard deviation is higher when the number of grid points is small, the value of the average does not dramatically change, indicating that


averaging over the different results obtained from XYZ frames centered at different nuclei is a good practice and yields the necessary accuracy for reliable packing closeness evaluation. All the calculations in this work were carried out with the finest grid 5000 × 10000. Supporting Information Available: CIF data are available free of charge via the Internet at http://pubs.acs.org.

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