Design of Novel Generations of Planar Sunflower Molecules

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C: Energy Conversion and Storage; Energy and Charge Transport

Design of Novel Generations of Planar Sunflower Molecules: Theoretical Comparative Study of Electronic Structure and Charge Transport Characteristics Denisa Cagardová, Ján Matúška, Peter Poliak, and Vladimir Lukes J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b05598 • Publication Date (Web): 14 Aug 2019 Downloaded from pubs.acs.org on August 22, 2019

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The Journal of Physical Chemistry

Design of Novel Generations of Planar Sunflower Molecules: Theoretical Comparative Study of Electronic Structure and Charge Transport Characteristics Denisa Cagardová*, Ján Matúška, Peter Poliak, Vladimír Lukeš Department of Chemical Physics, Slovak University of Technology in Bratislava, Radlinského 9, SK-812 37 Bratislava, Slovakia *corresponding author: [email protected]

phone: +421 2 593 25 741, fax: +421 2 593 25751

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ABSTRACT

A series of novel hetero-[n]circulenes of the first, second and the third generation including S and Se heteroatoms for n = 6, 7, 8 and 9 were theoretically designed. Their chemical and electronic structures were investigated using B3LYP based computational method. The interaction energies and electric drift mobilities were evaluated for model parallel-stacked and parallel-slipped dimer configurations at the room temperature using the Marcus theory and the Einstein relation. Based on the calculated properties, the second and third generation of sunflower molecules containing the six-membered central ring are suggested to be perspective candidates for the construction of organic p- and n-type semiconductors, respectively. The obtained results were also compared with the theoretical and published experimental results for reference -sexithiophene, [6]circulene (coronene) and octathio[8]circulene (sulflower) molecules.


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1. INTRODUCTION The circulenes, in general, are the macrocyclic arenes in which a central n-sided polygon is surrounded by fused benzene rings1. Nomenclature within this class of molecules is based on the number of benzene rings surrounding the core which is equivalent to the size of the central polygon. The optimal gas-phase geometries of hydrocarbon [n]circulenes from the [3]circulene to [20]circulene were predicted by Hopf and co-workers2 using the density functional theory (DFT) calculations. They described the strain energy related to enlargement of the [n]circulene structure as compared to the energy associated with [6]circulene (coronene). With respect to the strain energy, the existence of smallest [3]circulene and [4]circulene was considered unfeasible. The strain energy reaches minimum for [6]circulene. Therefore only three pure circulenes without substituents, [5]circulene (corannulene)3,4, [6]circulene (coronene)5 and [7]circulene (pleiadannulene)6 have been prepared to date. The characteristics of their electronic structure, chemical bonding and adsorption spectra were well determined. According to the DFT calculations, the shapes of these circulenes deduced from X-ray structure change from a bowl-shaped [5]circulene through planar [6]circulene to a saddle-shaped [7]circulene. The parent [8]circulene molecule and higher homologues have not yet been synthesized, presumably because of its highly strained structure and instability. On the other hand, the -extended derivatives of [4]circulene (quadrannulene)7 and [8]circulene8 were prepared and their X-ray crystal structures were evaluated. Because of its structure, coronene or [6]circulene can be considered as the smallest molecular approximation of a graphite sheet. It is an important building block for the construction of novel optoelectronic materials and devices9. Although the creation of Organic Field-Effect Transistors (OFETs) from parent coronene is very limited, the discotic liquid crystalline derivatives of hexabenzocoronene have been employed as semiconductors in OFETs. They showed an experimental hole mobility at room temperature up to 0.001 cm2 V−1 s−1 10,11. In the condensed state, [6]coronene and 3 ACS Paragon Plus Environment


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its derivatives form -stacked columns with strong electronic coupling (and facile charge transport) along the column. Charge transfer between the columns is very small or absent, which is responsible for pronounced one-dimensional charge transport12. Incorporation of heteroatoms, such as N, O, S or Se, into the periphery of the circulene core, can induce intercolumnar interactions and improve the charge-carrier mobility in organic semiconductors13. The entire or partial replacing of four fused benzene rings in [8]circulene by heterocyclic five-membered rings results in planar heteropolycyclic compounds with highly -conjugated electronic structures14,15,16,17. In chemical structure of octathio-[8]circulene (C16S8), named as sulflower of first generation, all outer fused benzene rings are replaced by eight fused thiophene rings. In 2006, octathio[8]circulene was synthetized for the first time18. In the solid state and thin films, these planar molecules stacked in columns held together by close S···S contacts (ca 3.25 Å), which could facilitate a threedimensional charge transport. Interestingly, the theoretical calculations of Chernichenko et al.18 showed that the strain energy of fully thiophenyl-circulenes is minimized only for planar molecules containing eight or nine thiophene rings. The applicability of octathio-[8]circulene and its selenium derivative tetraseleno-tetrathio-[8]circulene as organic semiconductor was demonstrated by fabricating thin-film transistors with these materials19. The experimental hole mobility of 9×10−3 cm2 V−1 s−1 and on/off current ratio of 106 at the room temperature was found for sulflower molecule. A rather high threshold voltage ranging from –40 V to – 46 V was measured for these devices. This can be explained (at least partially) by very low energy of highest occupied molecular orbital (HOMO) of –5.7 eV and resulting hole injection barrier at Au electrode (workfunction of 5.1 eV). The octaseleno-[8]circulene (selflower) thin-film transistors show a lower drift hole mobility of about 1×10−3 cm2 V−1 s−1 with much lower threshold voltage of –10 V, in accordance with the higher HOMO energy of –5.2 eV. High device stability and on/off ratio were also observed for these organic semiconductors. It seems that the electric semiconductivity is limited by one4 ACS Paragon Plus Environment

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dimensional growth of studied molecules in thin films. The quantum chemical calculations of electronic structure suggested that the [8]circulene-structure based heteropolycyclic compounds could be perspective candidates for construction of p-type and/or n-type organic semiconductors20,21,22,23. Theoretically predicted electron and hole drift mobilities for the octathio-[8]circulene X-ray structure20 are found to be of 2.6 cm2 V−1 s−1 and 3.5 cm2 V−1 s−1, respectively. The polyaromatic heterocycles exhibit also promising properties enabling the construction of Organic Light Emitting Diodes (OLEDs). In this context, the Fourier transform Infrared spectroscopy (FTIR), Raman, absorption and emission spectra have been measured and theoretically interpreted for various hetero[8]circulenes containing N,O, S, Se, Si and Ge atoms24,25,26,27,28. These studies showed that the benzoannelation is able to improve the emission of the non-fluorescent tetraoxa[8]circulene species28. The alkyl substitution of azaoxa[8]circulene in different positions significantly modulates Raman spectrum25. Recently, Dong et al.29 suggested a new three-step synthesis strategy enabling the potential preparation of next generations of sunflower molecules. They prepared persulfurated coronene (VIb-S12) from the perchlorinated coronene representing second sulflower generation. The DFT calculations show that the periphery of VIb-S12 demonstrates electron-donating properties, particularly at the S–S bonds. The predicted energy gap between the frontier molecular orbitals (2.04 eV) agreed well with the optical results deduced from the UV/Vis absorption spectra. The electrochemical experiments demonstrated that the prepared fully substituted polycyclic aromatic hydrocarbon can represent a promising cathode material for lithium-sulphur batteries. The next interesting question is connected with the possible role of a planar molecular size extension and a variation effect of terminal S and Se atoms on the electronic structure of heterocyclic [6/7/8/9]circulenes representing the second and third generations of sunflower molecules. In this context, we decided to present a systematic theoretical analysis of selected symmetric 43 compounds with different chemical and electronic structure (Figure 1). The partial aims of this study are: (1) to optimize 5 ACS Paragon Plus Environment


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the geometries of electroneutral, cationic and anionic charged states; (2) to calculate energies of the Highest Occupied (HOMO) and Lowest Unoccupied (LUMO) molecular orbitals and (3) to evaluate the reorganization energies by the density functional theory. For the most perspective planar molecules, the charge carrier properties at room temperature were evaluated for model dimers. Finally, the structure modification effect is discussed, and the theoretical results are compared with the available experimental data of reference molecules, i.e. α-sexithiophene and coronene (see Figure 1).

U

1.753

u1

S

1.732

1.755

S

s1

S

T

S

t1 1.754

S

1.755

1.755

S

T

S

U

S

6T 1.879/ 1.972

B

X

b1

A

S A

X X

s1

a1

X

B S A b1

s1

a1

X

*VI (D6h)

1.825/ 1.950

X

X

X

a1

X

*VIa-S6 (D6h)/ *VIa-S3 (D3h)/ *VIa-Se3 (D3h) *VIa-Se6 (D6h)

Figure 1. Schematic structure of selected studied molecules and the bond notation of central ring. The bonds a1-a9 (b1-b6; c1-c6; d1-d6; s1-s5; t1-t5; u1-u5) are ordered in a clockwise direction. The asterisk symbol (*) indicates the electroneutral planar B3LYP geometry. Symmetry of studied electroneutral molecules is written in parentheses. The selected single and double B3LYP bond lengths of neutral molecules are in Angströms. Sulfur and selenium analogues are distinguishable by X atom corresponding to S or Se atoms, respectively.


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1.776/ 1.919 X

X

X

X

B A

b1

X

X

a1

X

X

X

X X

X

*VIb-S12 (D6h)/ *VIb-Se12 (D6h) 1.648/ 1.916 1.788/ 1.939

1.802/ 1.942 X X

S

1.648/ 1.921

B A b1

a1

X

X

1.648/ 1.816

X

1.788/ 1.935

X

X

s1

X

x

X

X X

1.788/ 1.934

X

X

*VIa-S3-S6 (C2v) / *VIa-Se3-Se6 (C2v)

X

VIb-S6 (C6v)/ VIb-Se6 (C6v)

Figure 1. (continued) Schematic structure of selected studied molecules and the bond notation of central ring. The bonds a1-a9 (b1-b6; c1-c6; d1-d6; s1-s5; t1-t5; u1-u5) are ordered in a clockwise direction. The asterisk symbol (*) indicates the electroneutral planar B3LYP geometry. Symmetry of studied electroneutral molecules is written in parentheses. The selected single and double B3LYP bond lengths of neutral molecules are in Angströms. Sulfur and selenium analogues are distinguishable by X atom corresponding to S or Se atoms, respectively.



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1.712/ 1.862 X

1.744/ X 1.899

X

X X

C D B c1

X

b1

d1

X

X

X

A

a1 X

X

X

X

X

X X

X

X

*VIc-S18 (D6h)/ *VIc-Se18 (D6h) Figure 1. (continued) Schematic structure of selected studied molecules and the bond notation of central ring. The bonds a1-a9 (b1-b6; c1-c6; d1-d6; s1-s5; t1-t5; u1-u5) are ordered in a clockwise direction. The asterisk symbol (*) indicates the electroneutral planar B3LYP geometry. Symmetry of studied electroneutral molecules is written in parentheses. The selected single and double B3LYP bond lengths of neutral molecules are in Angströms. Sulfur and selenium analogues are distinguishable by X atom corresponding to S or Se atoms, respectively.


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1.756/ 1.886

T

B

b1

X

1.763/ 1.892 s1

S A C B C T

1.785/ 1.913

t1

X X

X

a1

c1

X

X

a1

X

1.756/ 1.886

S A

1.787/ 1.910

s1

X

1.757/ 1.880

X X

B T S A T C S B b1

X

t1

X

1.769/ 1.895

s1

X

a1

1.772/ 1.898

c1

X

VIIa-S7 (C7v)/

*VIIa-S3 (C2v)/*VIIa-Se3 (C2v)

*VIIa-Se7 (D7h)

*VIIa-S4 (C2v)/*VIIa-Se4 (C2v)

VII (C2) 1.652/ 1.814 X

1.657/ 1.820

X

b1

T S T A C B S t1

X

1.780/ 1.905

B

X

1.740/ 1.869

1.745/ 1.887

X

s1

X

a1

c1

X

X

1.743/ 1.877

b1

X

t1

X

X

X

s1

X 1.654/

X

1.655/ 1.915 X

1.920

X

1.747/ 1.880

1.739/ 1.888

a1

c1

X X

X

B T S C A B C T

1.744/ 1.881 1.654/ 1.815

X

1.715/ 1.860

X

1.691/ 1.853

*VIIa-S4-S6 (Cs)/ *VIIa-Se4-Se6 (Cs) *VIIa-S3-S8 (C2v) / VIIa-Se3-Se8 (C2) Figure 1. (continued) Schematic structure of selected studied molecules and the bond notation of central ring. The bonds a1-a9 (b1-b6; c1-c6; d1-d6; s1-s5; t1-t5; u1-u5) are ordered in a clockwise direction. The asterisk symbol (*) indicates the electroneutral planar B3LYP geometry. Symmetry of studied electroneutral molecules is written in parentheses. The selected single and double B3LYP bond lengths of neutral molecules are in Angströms. Sulfur and selenium analogues are distinguishable by X atom corresponding to S or Se atoms, respectively.



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1.730/ 1.875

1.765/ 1.878 X X

S s1

X

S

X

a1

X

s1

A

X

X

X

b1

B

X

a1

A

X

X

X

*VIIIa-S8 (D8h)/ *VIIIa-S4 (D4h)/ VIII (C2)

*VIIIa-Se8 (D8h) VIIIa-Se4 (D2d) 1.651/ 1.921 X

1.721/ 1.878 X X

X

b1

S s1

B

X X

a1

A

X

X X

X

X

X

VIIIa-S4-S8 (D2d) / VIIIa-Se4-Se8 (D2d) Figure 1. (continued) Schematic structure of selected studied molecules and the bond notation of central ring. The bonds a1-a9 (b1-b6; c1-c6; d1-d6; s1-s5; t1-t5; u1-u5) are ordered in a clockwise direction. The asterisk symbol (*) indicates the electroneutral planar B3LYP geometry. Symmetry of studied electroneutral molecules is written in parentheses. The selected single and double B3LYP bond lengths of neutral molecules are in Angströms. Sulfur and selenium analogues are distinguishable by X atom corresponding to S or Se atoms, respectively.


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1.748/ 1.894

1.750/ 1.896 X

X

1.743/ 1.888

1.737/ 1.856

X

1.742/ 1.888

X

X

S

X

X

s1

1.743/ 1.892

X

a1

A

X

X

1.744/ 1.891

X X

X

X

X X

1.743/ 1.892

IX (C2) X

1.645/ 1.917 X

1.722/ 1.893

X

1.725/ 1.882

X

X X

1.726/ 1.886

X

X

1.648/ 1.925

1.647/ 1.919 X

X

1.722/ 1.892

1.648/ 1.919

X

1.648/ X 1.919

x

X

X X X

1.687/ 1.847 X

1.715/ 1.861

x X

1.724/ 1.869

IXa-S4 (C2) / IXa-Se4 (C2) IXa-S5 (Cs) / IXa-Se5 (Cs)

*IXa-S9 (D9h) / *IXa-Se9 (D9h) 1.649/ 1.922

X

X

1.753/ 1.895

1.728/ 1.882

X

1.734/ 1.883

1.654/ 1.921

1.721/ 1.893 X

X

X

X

1.715/ 1.875

X

X

1.751/ 1.893

IXa-S5-S8 (Cs) / IXa-Se5-Se8 (Cs) IXa-S4-S10 (Cs) / IXa-Se4-Se10 (Cs) Figure 1. (continued) Schematic structure of selected studied molecules and the bond notation of central ring. The bonds a1-a9 (b1-b6; c1-c6; d1-d6; s1-s5; t1-t5; u1-u5) are ordered in a clockwise direction. The asterisk symbol (*) indicates the electroneutral planar B3LYP geometry. Symmetry of studied electroneutral molecules is written in parentheses. The selected single and double B3LYP bond lengths of neutral molecules are in Angströms. Sulfur and selenium analogues are distinguishable by X atom corresponding to S or Se atoms, respectively.



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2. COMPUTATIONAL DETAILS The quantum chemical calculations were made using Gaussian 09 program package30. The initial geometries of studied molecules were optimized by DFT method with B3LYP (Becke’s three parameter Lee–Yang–Parr) functional31,32 without any constraints (energy cut-off of 10−5 kJmol−1, final RMS energy gradient under 0.01 kJmol−1A−1). All calculations of open-shell (ionized) states used the unrestricted formalism (UB3LYP) and the spin contamination was less than 0.01. The SVP/FitSVP basis set of atomic orbitals was applied for all atoms33,34. In the case of sulfur and selenium atoms, the basis set was augmented with diffuse s- and p- functions which were taken from non-relativistic ma-def2-SVP basis set35.The interaction energies for selected molecular dimers were corrected on Basis Set Superposition Error (BSSE)36 using the counterpoise method37,38 and the empirical dispersion corrections were also included. For the B3LYP functional, we have used the Grimme´s dispersion correction with Becke-Johnson damping function (GD3BJ)39. This approach was previously tested as effective for evaluating the dimer interactions40. The molecules and molecular orbitals were vizualized using the Molekel program package41. The starting geometries were symmetrized, and corresponding point group symmetry was used for geometry optimization of electroneutral states.

2.1 Aromaticity indices As a structure-based measure, we have expressed the geometrical changes of C–C, C–S and C–Se aromatic bond lengths with respect to the chemical structure using the modified Harmonic Oscillator Model of Electron Delocalization (HOMED) index42,43

1m 2 HOMED  1   XY  R(XY) ref  R(XY)i   m  i 1 


(1)

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where m represents the number of bonds considered in investigated aromatic ring and R(XY)i is the actual bond length between X and Y atoms. The appropriate reference aromatic bond lengths Rref were determined from the B3LYP calculations of benzene, thiophene and selenophene molecules. The proposed Rref values for the used basis set are of 1.3988 Å for C–C, 1.7326 Å for C–S and 1.8737 Å for C–Se bonds. The normalization  constants were calculated by equation44



 XY  2  R(XY) ref  R(XY)sin    R(XY) ref  R(XY)doub  2



2 1

(2)

where the reference single bonds Rsin and reference double bonds Rdoub were estimated from ethane and ethene (CC bonds), CH3–S–CH3 and H2C=S molecules (CS bonds)45. For carbon-selenium bond lengths, we have used analogues of sulphur molecules, i.e. CH3–Se–CH3 and H2C=Se. The calculated B3LYP Rsin bond lengths are of 1.5277 Å (C–C), 1.8213 Å (C–S) and 1.9633 Å (C–Se). The reference double bonds Rdoub are shorter than Rsin, i.e. of 1.3330 Å (C=C), 1.6163 Å (C=S) and 1.7553 Å (C=Se). Based on these bond lengths, the normalization constants for corresponding bonds are CC = 95.57 Å–2,

CS = 93.47 Å–2 and CSe = 90.78 Å–2.

2.2 Hole and electron drift mobilities In order to investigate the charge transport properties, the hopping model was used. The hopping mechanism supposes that the hole and electron carriers can jump between the adjacent molecules. The charge-transport rate k between two selected moieties is given by the Marcus formula46,47,48 1/2

khole/electron  t

2 eff, hole/electron

   ( r G 0    /  )2   exp    2  /  4  /  kBT   h k B T  

(3)

where teff represents an effective intermolecular charge transfer integral between interacting molecular sites, h is the reduced Planck constant, kB is the Boltzmann constant, T is the thermodynamic temperature and +/– represents the reorganization energy for hole/electron owing to the geometric 13 ACS Paragon Plus Environment


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relaxation accompanying charge transfer and ΔrG0 is the overall reaction free energy, which is zero in the present charge self-exchange reactions49. The reorganization energy is usually described as the sum of internal reorganization and external polarization λe. The latter term λe describes the electronic polarization change of the surrounding molecules. The external contribution to the reorganization λe is difficult to evaluate theoretically, and thus is normally neglected during discussion49. The internal reorganization energy +/– refers to the energy required for a geometry relaxation upon going from an electroneutral to charged molecular state and vice versa. This energy46,50,51 is obtained from the adiabatic potential energy surface method and it is given by the equation

  /   1 /   2 /    E /  (QN )  E /  (Q /  )    EN (Q /  )  EN (QN ) 

(4)

where E+/–(QN) is the total energy of the charged state in the neutral geometry, E+/–(Q+/–) is the total energy of the charged state in the charged state geometry, EN(Q+/–) is the total energy of the electroneutral state in the charged state geometry, and EN(QN) is the total energy of the neutral state in the neutral geometry50. In case of charge transfer integral calculations, the direct evaluation method was used52 0,site-i $|  0,site-j ti , j ; hole/electron  HOMO/LUMO |F HOMO/LUMO

where

(5)

0,site-i 0,site-j and HOMO/LUMO are the highest occupied/lowest unoccupied molecular orbitals HOMO/LUMO

HOMOs/LUMOs of the two adjacent molecules i and j when no intermolecular interaction is present.

$is the Fock operator and its density matrix F is constructed from non-interacting molecular Symbol F orbitals

F  SCεC1 .


(6)

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In this equation, S is the atomic orbital overlap matrix, C and  are matrices of molecular orbital coefficients and energies from one-step diagonalization without iteration, respectively. The calculations were simplified by considering the geometry of the electroneutral dimer. The generalized or effective charge transfer integral teff is defined in terms of charge transfer integral ti,j, spatial overlap integral Si,j and site energies εi and εj as

 j  teff,i , j  ti , j  Si , j  i   2 

(7)

where εi and εj are the energies of a charge when it is localized at ith and jth molecules, respectively53. Because of its simplicity, the Koopmans’ theorem together with the Energy-Splitting-in-Dimer54 approach is currently the most frequently used method for the estimation of transfer integrals in organic semiconductors. Under the fixed temperature, the electric hole/electron drift mobility hole/electron can be calculated from Einstein–Smoluchowski relation55,56

hole/electron 

e khole/electron d 2 2nkBT

(8)

where e is the elementary charge. The length of hopping pathway d is defined as the centroid-tocentroid distance. The symbol n stands for the space dimensionality which is of 2 in our case and khole/electron is hole/electron charge transfer rate.

3. RESULTS AND DISCUSSION 3.1 Chemical structure The optimal gas-phase geometries of all studied molecules are dependent on the size of central ring as well as number of heterocyclic units. The first generation of these compounds (denoted by a) is characteristic by the central [n]membered core surrounded by [n] aromatic rings, e.g. only fused 15 ACS Paragon Plus Environment


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heterorings - thiophenes and selenophenes or combination of fused heterorings with the benzene units (see Figure 1). Molecules of a second generation (b in the notation) are the derivatives of coronene, which is the first approximation of graphite sheet. Structure of the third-generation molecules (c) contains circumcoronene unit and heteroatoms bounded on the outer sphere. These molecules are much more suitable for organic semiconductors construction, because of circumcoronene π-electron distribution characterising the next level of graphite sheet approximation. The obtained geometries for all studied molecules are bowl-shaped, saddle-shaped or planar and possess twelve types of point group symmetry (see Figure 1). As it is shown in Figure S1 for electroneutral states, smaller molecules VIbS6, VIb-Se6 and VIIa-S7 exhibit the bowl-shaped geometry. Interestingly, in comparison with VIIa-S7 molecule, selenium analogue VIIa-Se7 is planar and probably this planarity is caused by the steric effect of bulk selenium atoms. The saddle-shaped structures were found for the pure [7]coronene (VII), [8]coronene (VIII), [9]coronene (IX) and derived hetero-circulenes containing the five-membered heteroring condensed with six-membered benzene rings. Planar VIIIa-S4 molecule represents only one exception, where the strain energy is zero due to the presence of less bulky sulphur atoms resulting in molecular planarity. Excluding above-mentioned distorted VIb-S6 and VIb-Se6 molecules, the reference [6]coronene (VI) and its remaining studied derivatives with [6]-sided inner ring are planar. In agreement with published DFT study of Chernichenko et al.18, VIIIa-S8, and IXa-S9 molecules are planar. The molecular planarity is also predicted for structural selenium analogues VIIIa-Se8 and IXaSe9. The key properties for high charge mobility of π-conjugated organic molecules are high stability, planarity, symmetric structure and appropriate π-electron delocalization. Thus, evaluation of aromaticity indices of studied compounds gives us significant awareness about their electronic properties. The obtained B3LYP HOMED indices of individual aromatic rings for studied planar molecules are collected in Table 1. 16 ACS Paragon Plus Environment

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Table 1. Selected planar B3LYP HOMED indices for A, B, C, D benzene rings and HOMED for S, T, U heteroaromatic thiophene or selenophene rings of selected studied molecules in the electroneutral state. Notation of rings is descripted in Figure 1. Molecule/HOMED(ring) 6T VI VIa–S3 VIIa–S3 VIIa–S4 VIIIa–S4 VIa–S6 VIIIa–S8 IXa–S9 VIa–S3–S6 VIIa–S3–S8 VIIa–S4–S6 VIb–S12 VIc–S18 VIa–Se3 VIIa–Se3 VIIa–Se4 VIa–Se6 VIIa–Se7 VIIIa–Se8 IXa–Se9 VIa–Se3–Se6 VIIa–Se4–Se6 VIb–Se12 VIc–Se18

HOMED(A) – 0.907 0.989 0.833 0.909 0.528 0.986 0.927 0.693 0.990 0.859 0.900 0.967 0.935 0.982 0.727 0.799 0.992 0.908 0.670 0.172 0.977 0.813 0.923 0.887

HOMED(B) – 0.931 0.967 0.988 0.993 0.910 – – – 0.967 0.662 0.612 0.967 0.950 0.988 0.974 0.984 – – – – 0.988 0.778 0.943 0.908

HOMED(C)

HOMED(D)

– – – 0.922 0.987 – – – – – 0.920 0.622 – 0.918 – 0.899 0.974 – – – – – 0.768 – 0.896 17 ACS Paragon Plus Environment

– – – – – – – – – – – – – 0.911 – – – – – – – – – – 0.861

HOMED(S) 0.970 – 0.675 0.926 0.908 0.821 0.075 0.939 0.938 0.675 0.989 0.983 – – 0.781 0.909 0.892 0.580 0.906 0.933 0.821 0.781 0.967 – –

HOMED(T) 0.969 – – 0.914 0.899 – – – – – 0.956 0.950 – – – 0.889 0.922 – – – – – 0.959 – –

HOMED(U) 0.961 – – – – – – – – – – – – – – – – – – – – – – – –


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In the case of reference linear α-sexithiophene 6T, the HOMED of all rings are practically identical, i.e. of 0.97. These values are slightly higher than HOMED of 0.95 obtained from optimal thiophene structure. As it is shown in Figure 1, the calculated bond lengths C–S for individual aromatic rings in 6T are of 1.755/1.755 Å (in central S rings), 1.755/1.753 Å (in T rings) and 1.754/1.732 Å (in lateral U rings). The coronene molecule VI exhibits lower aromaticity indices comparing to the benzene molecule where HOMED = 1. The HOMED(A) is of 0.907 and HOMED(B) is of 0.931. The interesting situation occurs for the sunflower molecules of the first generation. The highest aromaticity occurs for the central ring of VIa-S6 molecule (HOMED(A) of 0.986) where the condensed thiophene rings have the very low aromaticity character, i.e. HOMED(B) is of 0.075. Within the [n]hetero-[n]circulenes group of molecules, the higher number of condensed fivemembered heteroaromatic rings causes aromaticity increase of thiophene/selenophene rings and decrease the value of HOMED(A). Molecule VIa-S6 and its selenium analogue VIa-Se6 have the highest aromaticity HOMED(A) index of central ring of 0.986 and 0.992, respectively, depending mostly on the bond lengths in central rings (see Table S1). Moreover, in IXa-S9 and IXa-Se9 molecules, nine heteroaromatic rings cause significant decrease of central ring aromaticity (HOMED(A) values of 0.693 and 0.172, respectively). Probably, this fact relates to the decrease of C–S bond lengths within the first generation of studied molecules, i.e. of 1.879 Å for VIa-S6, 1.785 Å for non-planar VIIa-S7, 1.765 Å for VIIIa-S8 and 1.737 Å for IXa-S9 molecule. The C– S bond length in IXa-S9 is very close to the value obtained for optimal geometry of thiophene (1.733 Å). The identical trends occur for the selenium analogues of studied derivatives, where C–Se varies from 1.972 Å for VIa-Se6 through 1.913 Å for VIIa-Se7 and 1.878 Å for VIIIa-Se8 and 1.856 Å for IXa-Se9. The relevant bond length in the optimal selenophene molecular structure is of 1.874 Å. The highest HOMED values for all individual aromatic rings are indicated for the second generation of hetero-[n]circulenes, e.g. VIb-S12, where HOMED(A)/HOMED(B) are of 0.967. Interestingly, selenium atoms slightly decrease the aromaticity. For VIb-Se12 molecule, HOMED(A) and 18 ACS Paragon Plus Environment

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HOMED(B) aromaticity indices are of 0.923 and 0.943, respectively. In the case of molecular structures, where fused benzene and heteroaromatic rings are present, aromaticity index of central ring HOMED(A) and benzene rings HOMED(B) are significantly higher than HOMED of present heterorings HOMED(S), which are in some cases very low (e.g. in molecule VIa-S3-S6, HOMED(A), HOMED(B) and HOMED(S) are of 0.990, 0.967 and 0.675, respectively). The aromaticity analysis of hetero[8]circulenes based on Nucleus Independent Chemical Shifts (NICS) and Gauge-Including Magnetically Induced Currents (GIMIC) methods indicate the non-aromatic or antiaromatic character of eight-membered cycle57,58. In agreement with the evaluated structural HOMED indices for VIIIa-S8 and VIIIa-Se8, the presence of selenium atoms globally decreases the molecular aromaticity59. As it is shown in Figure 1, the influence of central ring size on the C=S and C=Se double bond lengths in outer benzene rings is minimal. Two different C=S and C=Se bond lengths were obtained for the largest molecules of the third generation corresponding to two types of benzene rings C and D. For the VIc-S18 molecule, the C=S bond length is of 1.712 Å at the C ring and of 1.744 Å at the D ring. Corresponding C=Se bond lengths in VIb-Se12 are of 1.862 Å and 1.899 Å at C and D benzene rings, respectively (see Figure 1).

3.2 Frontier molecular orbitals The energy levels of Highest Occupied (HOMO) and Lowest Unoccupied (LUMO) Molecular Orbitals are key parameters for assessing the p-type and n-type carrier injection ability and stability of the material, respectively. These energies should be close to work function (WF) of electrodes in vacuum resulting to improve their charge transport ability. In many technical situations60, the calcium (WF ranges from 2.87 to 2.90 eV) and magnesium (WF = 3.68 eV) electrodes are preferred for ntype organic semiconductors. Therefore, too low LUMO energy of organic molecules causes also the decrease of chemical stability of compounds on the air. Reportedly the LUMO energies of n-type organic semiconductors should be optimally higher than 3.0 eV but lower than 4.4 eV61,62,63. On the 19 ACS Paragon Plus Environment


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other hand, gold (WF = 5.10 to 5.47 eV) or ITO (WF = 4.80 eV) electrodes are one of the best electrodes used as organic p-type semiconductors. As it was reported by Filo et al.64, the optimal interval of energy levels of HOMO for typical p-type semiconducting molecules is from –4.9 to – 5.5 eV, because the standard counterpart metallic hole injecting electrodes have comparable ionization potentials. Based on the optimized structures of electroneutral states, the energy levels of HOMOs and LUMOs were calculated and depicted in Figure 2. The B3LYP HOMO energies calculated for the reference linear α-sexithiophene (6T) and coronene (VI) are of –5.15 eV and –5.70 eV, respectively. These values are close to the electrochemical measurements data (−5.20 eV 65 and −5.72 eV 66). The HOMO energies of thio-circulenes vary from –6.59 eV for VIa-S3-S6 to –5.35 eV for VIbS12 and the interval of LUMO energies ranges from –5.33 eV for VIIa-S3-S8 molecule to –1.36 eV for IXa-S9. The replacement of sulfur atoms by selenium atoms causes increase of HOMO energies. The lowest HOMO energy level (–5.86 eV) was found to be for VIa-Se6 and maximal value was reached at –5.21 eV for VIb-Se12. The highest (–4.54 eV) and lowest (–1.43 eV) LUMO energies are predicted for VIa-Se3-Se6 and IXa-Se9 molecule, respectively. Inspection of the data in Figure 2 shows that the HOMO energies of VIb-S12, IXa-Se9, VIb-Se12 and VIc-Se18 molecules could support a p-type semiconduction, because these energy levels are within the pink bar characterising optimal HOMO energy range for potential p-type semiconductors. On the other hand, optimal setting of LUMO energies is important for n-type semiconductors construction. Suitable LUMO energy levels were found for VIa-S6, VIIa-Se4-Se6, VIb-Se12, VIc-Se18 and VIc-S18 (Figure 2). In case of inorganic semiconductors, atoms are strongly bound by covalent interactions. However, in comparison to that, molecules in semiconductors built by organic molecules are held together by weak interactions between moieties resulting in a necessity of narrow bandwidth67.


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(a)

(b)

Figure 2. Energy diagram of B3LYP frontier molecular orbitals for the studied electroneutral planar derivatives of sulflower (a) and selflower (b) molecules. The HOMO–LUMO energy gaps Eg are in eV. The blue and pink bars indicate the optimal range of energies for the n- and p-type semiconductors, respectively.



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If we consider minimal HOMO–LUMO bandwidth Eg as an important criterion for appropriate properties for p- or n-type semiconduction, one can exclude IXa-Se9 and VIa-S6 molecule because of its high calculated energy gap of 3.96 eV and 2.59 eV, respectively. In case of IXa-Se9, it is more than twice as high as the HOMO–LUMO energy gaps of remaining selected molecules. By decreasing of LUMO energy, an instability on the air increase relating to inappropriate range of work functions and it could be a problem in practical optoelectronic usage of VIIa-Se4-Se6 molecule. The local and global aromaticity of studied molecules influences the shape of frontier molecular orbitals. The shapes of HOMOs and LUMOs for all planar molecules are depicted in Figure S2. In the case of planar hetero-[n]circulenes of the first generation VIa-S6/VIa-Se6, VIIa-Se7, VIIIaS8/VIIIa-Se8 and IXa-S9/IXa-Se9, the lobes of HOMOs are radially oriented along Cα-C bonds in thiophene or selenophene rings. For the smallest VIa-S6/VIa-Se6 and VIIa-Se7 molecules, the LUMOs are delocalized only over the lateral S or Se and carbon Cα atoms. In the case of larger molecules, another electron cloud occurs over the carbon atoms of central ring (e.g. see IXa-S9 in Figure 3). If there is combination of fused benzene and thiophene/selenophene rings around the central ring in molecule, the electrons in LUMOs are less populated over the heteroatoms (e.g. see VIIa-S4 in Figure 3). For the persulfurated or perselenorated second generation of selected circulenes (e.g. see VIb-S12 in Figure 3), ion pairs of electrons from heteroatoms do not contribute uniformly to the frontier molecular orbitals. Nevertheless, the electron clouds in HOMOs are dominantly delocalized over the major part of molecular plane. The LUMOs are not delocalized over the carbon framework but entirely localized on and in between the sulphur atoms. The significant differences in the shape of HOMOs exhibit the largest investigated hetero-circulenes of the third generation VIc-S18 and VIc-Se18 (see Figure 3). It seems that shape of HOMO for VIc-Se18 molecule does not have -electron character and it is very similar to the LUMO ones for VIb-S12 and VIb-Se12. On the other hand, LUMOs of both VIc-S18 and VIc-Se18 molecules possess electrons delocalization over the outer atoms in the hetero-aromatic rings. 22 ACS Paragon Plus Environment

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HOMO

Molecule

LUMO

IXa-S9

VIIa-S4

VIb-S12

Figure 3. B3LYP/SVP shapes of HOMO and LUMO of selected studied molecules. The depicted isosurface value is of 0.025 a.u.



HOMO

Molecule

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LUMO

VIc-S18

VIc-Se18

Figure 3. (continued) B3LYP/SVP shapes of HOMO and LUMO of selected studied molecules. The depicted iso-surface value is of 0.025 a.u. Finally, the combination of fused thiophene/selenophene ring and quinoidal aromatic rings containing two C=S and C=Se double bonds lead to two possible electron distributions depending on even or odd number of sides in the central ring. In case of VIa-S3-S6 with 6-membered central ring, the electron clouds of HOMOs are delocalized dominantly over all C=S and LUMOs are delocalised mainly on the heteroatoms. On the other hand, if there is odd number of sides in central ring, delocalization is populated over one side of molecular plane (e.g. see VIIa-S4-S6 and VIIa-Se4-Se6 24 ACS Paragon Plus Environment

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in Figure S2). From this point of view, a minimal or non-equal distribution of -electrons over the molecular ring will not create preconditions for the charge transport between the neighbouring molecules.

3.3 Ionization potentials, electron affinities and reorganization energies The reorganization energy +/– is an important quantity determining the charge mobility and reflects geometrical changes upon electric charging. If the reorganization energy of a system is low, molecule exhibits a high rate of charge hopping. The calculated values of +/– for both charged cationic and anionic states are listed in Table 2. The B3LYP hole reorganization energy of the reference 6T and VI molecules connected with the formation of cationic state (+) are of 292 meV and 127 meV, respectively. Hole reorganization energies are quite low and vary in a range from 50 meV (VIIa-Se4-Se6) to 186 meV (VIIa-S4). Exceptions were found for VIIa-Se4 molecule, VIaS3-S6 and its selenium analogue VIa-Se3-Se6, which have relatively large + values due to a large distortion of their cationic state, e.g. 262 meV (VIIa-Se4), 479 meV (VIa-S3-S6) and 780 meV (VIa-Se3-Se6). The highest values of electron reorganization energies (−) were found for VIb-S12 (602 meV) and VIb-Se12 (483 meV) molecules. Remaining theoretical − values for studied heterocirculenes range from 49 meV / 66 meV (VIIIa-Se8 / VIIIa-S8) and 49 meV / 62 meV (VIcSe18 / VIc-S18) to 249 meV / 256 meV (VIIa-S4 / VIIa-Se4). These values are comparable with the published DFT values of typical p-type or n-type organic semiconductors, e.g. pentacene (+ = 98 meV

68,69),

N,N,’-diphenyl-N,N’-bis(3-methylphenyl)-(1,1’-biphenyl)-4,4’-diamine (TPD)

with hole reorganization energy + = 290 meV

48,

C60 fullerene (− varies from 22 meV to 56

meV) 70, donor-acceptor 1,8-naphthalimide derivatives (− = 216 to 283 meV and + = 212 to 247 meV) 71, fluorinated pentacene (− = 246 meV) 72 or tris(8-hydroxyquinolinato)aluminum (− = 296 meV) 73. The third generation of sunflower molecules (VIc-S18 and VIc-Se18) have the



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lowest reorganization energies for both electrons and holes, thus they are suitable for both charge transfer types and could be promising p- or n-type semiconductors. Table 2. B3LYP vertical ionization potentials (VIPs), adiabatic ionization potentials (AIPs), vertical electron affinities (VEAs), adiabatic electron affinities (AEAs), reorganization energies for hole and electron transfer (+ and ) of the selected planar electroneutral molecules. All energies are in eV. Molecule

VIP

VEA

AIP

AEA





VI

7.09

0.33

7.02

0.41

0.127

0.168

VIa-S3

7.44

0.26

7.37

0.37

0.134

0.230

VIIa-S3

7.08

0.54

7.03

0.65

0.100

0.230

VIIa-S4

7.03

0.61

7.18

0.73

0.186

0.249

VIIIa-S4

7.17

0.98

7.10

1.08

0.128

0.199

VIa-S6

7.79

2.33

7.70

2.40

0.180

0.141

VIIIa-S8

7.29

0.15

7.23

0.18

0.122

0.066

IXa-S9

6.95

0.17

6.89

0.20

0.135

0.057

VIa-S3-S6

8.08

4.10

7.14

4.15

0.479

0.107

VIIa-S3-S8

7.17

4.26

7.15

4.34

0.053

0.165

VIIa-S4-S6

7.63

3.73

7.56

3.81

0.157

0.168

VIb-S12

6.45

2.24

6.40

2.53

0.114

0.602

VIc-S18

6.74

3.59

6.70

3.63

0.085

0.062

6T

6.15

1.37

5.99

1.52

0.292

0.260

VIa-Se3

7.20

0.23

7.15

0.34

0.111

0.236

VIIa-Se3

6.87

0.54

6.83

0.66

0.083

0.239

VIIa-Se4

6.94

0.59

6.77

0.71

0.262

0.256

VIa-Se6

7.24

1.69

7.17

1.75

0.137

0.125

VIIa-Se7

7.07

0.69

7.01

0.75

0.113

0.129

VIIIa-Se8

6.80

0.26

6.75

0.29

0.109

0.049

IXa-Se9

6.56

0.30

6.51

0.37

0.119

0.141

VIa-Se3-Se6

6.98

3.34

6.57

3.43

0.780

0.190


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Table 2. (continued) B3LYP vertical ionization potentials (VIPs), adiabatic ionization potentials (AIPs), vertical electron affinities (VEAs), adiabatic electron affinities (AEAs), reorganization energies for hole and electron transfer (+ and ) of the selected planar electroneutral molecules. All energies are in eV. Molecule

VIP

VEA

AIP

AEA





VIIa-Se4-Se6

6.89

3.31

6.94

3.40

0.050

0.194

VIb–Se12

6.26

2.78

6.21

3.01

0.093

0.483

VIc–Se18

6.33

3.49

6.29

3.52

0.081

0.049

Ionization potential (IPs) and electron affinities (EAs) reflect geometrical changes upon the electron abstraction or addition. In practice, it was found that the gas-phase frontier molecular orbital energy analysis using DFT often reaches agreement with experimental solid-state estimations of ionization energies and electron affinities, even though the former obviously do not account for solidstate effects. According to the tuning procedure, which is based on the ionization potential theorem, the negative HOMO energy in exact Kohn−Sham DFT is equal to the vertical ionization potential corresponding to a difference in total energy between the electroneutral and positively-charged (cationic) systems for a fixed geometry74. These calculated gas-phase B3LYP quantities for studied molecules are collected in Table 2. The adiabatic ionization potentials (AIPs) for model selected molecules are found to be from 6.21 eV for VIb-Se12 to 7.70 eV for VIa-S6. The adiabatic electron affinity (AEA) increases from 0.18 eV for VIIIa-S8 to 4.26 eV for VIIa-S3-S8. The corresponding vertical IP values are higher than the adiabatic ones and reflect geometrical changes of monocation and monoanion geometries comparing to electroneutral states. The available experimental VIP value for coronene VI is of 7.29 ± 0.03 eV75 and AEA is of 0.470 ± 0.090 eV76, which is in very good agreement with our theoretical VIP and AEA ones of 7.09 eV and 0.41 eV, respectively. The comparison of these experimental energies with predicted results indicates reasonable chemical accuracy of applied functional and basis set. 27 ACS Paragon Plus Environment


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The type of semiconduction of pure intrinsic organic semiconductors can be changed by doping with a strong electron acceptor (from n- to p-type) or doping with a strong electron donor (from pto n-type). In this context we would like to note that the balance between the shape and energies of frontier molecular orbitals, optical band gaps, IPs and EAs of potential organic semiconductors (OSC) and dopants is very important for the estimation of energetic structure in the p-n homojunction or heterojunction devices77,78. In principle, a p-type molecular dopant is a molecule with the LUMO deep enough to extract an electron from the HOMO of organic semiconductor. Likewise, an n-type molecular dopant is a molecule with the HOMO shallow enough to donate an electron to the LUMO of organic semiconductor. Neutral molecular dopants can interact with organic semiconductors by the ion pair formation and the charge-transfer complex (CTC) formation79. For example, Si3N4 can be used avoiding oxygen during thermally activated deposition caused by oxidation which arises from the organic molecule. In some cases, wider band gap of the insulator far from the frontier MOs energies is chosen, so that it eliminates charge injection into these levels. It is often stated that ion pair formation occurs if EA(dopant) is higher than IE(OSC) and the n-type doping should only happen if IE(dopant) is lower than EA(OSC). An important consequence of the charge-transfer formation is that the lower energy CTC state (the “bonding” or local HOMO state) contains both of the HOMO level electrons from the donor, while the higher energy CTC state (the “antibonding” or local LUMO state) remains empty80. Interestingly, if both the IE and EA of the n-type layer are larger than the ptype layer, heterojunctions can allow for stable p–n junctions in organic photovoltaic devices, such as diodes, lasers and solar cells81.

3.4 Model -stacking dimers and electron drift mobility simulations Macroscopic electric properties of semiconducting materials are determined also by mutual intermolecular interaction, morphology and molecular arrangement in the active layer. Intrinsic properties of organic semiconductors could be followed by using their single crystals. In comparison to inorganic crystals, organic ones offer highly ordered crystal structures, minimized traps and they 28 ACS Paragon Plus Environment

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are free from grain boundaries82. The corresponding X-ray structures available for reference 6T83, VI84 and VIIIa-S885 molecules provide the monoclinic molecular crystal structure (see Figure S3). For a detailed characterization and understanding of the distribution of molecules with different dimeric arrangements in the X-ray structure, we have calculated the molecular distribution function describing the radial packing of the molecules in a given crystal structure. We have considered a supercell of the 3×3×3 unit cell dimension with a cut-off distance of 15 Å. Within α-sexithiophene 6T crystal, each molecule is surrounded by five neighbors. The selected parallel-slipped stacking arrangement of two 6T molecules represents the first dimer (P) with centroid-to-centroid distance of 6.03 Å with the relatively high occurrence (see Figure 4a).

(a) Figure 4. Dependence of the number of dimer configurations on the intermolecular centroid-tocentroid distance between moieties in the dimer configurations of X-ray structures of 6T83 (a), VIIIaS885 (b) and VI84 (c), molecules in 3 x 3 x 3 supercell. Letters characterize notation of parallel (P), longitudinal (L) and transversal (T) dimer configurations.



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(b)

(c) Figure 4. (continued) Dependence of the number of dimer configurations on the intermolecular centroid-to-centroid distance between moieties in the dimer configurations of X-ray structures of 6T83 (a), VIIIa-S885 (b) and VI84 (c), molecules in 3 x 3 x 3 supercell. Letters characterize notation of parallel (P), longitudinal (L) and transversal (T) dimer configurations.


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The second and third dimers belong to the transversal orientations (T1 and T2), where the distance between the centers of mass is ca 1 Å shorter than in P-dimer configuration. The corresponding interaction energies are of –86 kJmol–1 for T-dimers and of –64 kJmol–1 for parallel-slipped Pdimers. Moreover, longitudinal (L) orientations of two moieties are also identified in X-ray structures of the VI and VIIIa-S8 crystals. As it is shown in Figure 4c, the most significant distribution of molecules arises at molecular separations with centroid-to-centroid distance of 4.67 Å, 10.04 Å, 8.33 Å for P-, L- and T-dimer configuration of VI moieties, respectively. Within X-ray structure of VIIIaS8, significant distribution is present for transversal T2 / T1-, parallel P- and longitudinal L-dimer configurations with corresponding centroid-to-centroid distances of 10.07 Å / 10.22 Å, 3.87 Å and 11.14 Å, respectively. Interestingly, significant distribution was obtained also for mass-centers distance of 7.80 Å, which is twice as high as distance in case of P-dimer arrangement. It occurs when three parallel-slipped molecules within columnar layer are present. The corresponding interaction energies for longitudinal VIIIa-S8(L) and transversal VIIIa-S8(T1/T2) dimer configurations range from –16 kJmol–1 to –20 kJmol–1. The VIIIa-S8(P) dimer occurring in the columnar layer is stabilized by the weak non-covalent C···C as well as C···S contacts. The corresponding interaction energy is of –129 kJmol–1 in comparison with the interaction energy for VI(P) dimer (–84 kJmol– 1).

For these reference molecules providing p-type semiconduction, we presented shapes of HOMO, HOMO–1, HOMO–2 and HOMO–3 for selected parallel P-, transversal T- and longitudinal L- dimer configurations for crystal structure of coronene VI (Figure S4), octathio-[8]circulene VIIIa-S8 (Figure S5) and α-sexithiophene 6T (Figure S6). To understand the -stacking ability of the second and third generation of perspective sunflower molecules, we have performed the full geometry optimization of two different model basic configurations (parallel-stacked and parallel-slipped). The perfectly stacked sandwich arrangement is represented by the D1 configuration where the central cores have mutual parallel orientation (see 31 ACS Paragon Plus Environment


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Figure 5). The second model D2 configuration consists of two parallel-slipped molecules. The initial geometries consisted of one monomer molecule which was symmetrically and constantly slipped by about one aromatic ring along the longest x axis. Obtained geometrical parameters of interacting monomers (perpendicular distance R, the longitudinal shift along x axis (r) and distance between centers of mass d (see Figure 5) are collected in Table 3.


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D1

D2 VIIIa-S8

D1

D2 VIb-S12

Figure 5. Structures of studied model dimers: side and top views of perfect sandwich D1 configuration and parallel-slipped D2 configuration along the x-axis of VIIIa-S8, VIb-S12 and VIc-Se18 molecules. The definition of R, r and d distances. 33 ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

D1

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D2

VIc-Se18 Figure 5 (continued). Structures of studied model dimers: side and top views of perfect sandwich D1 configuration and parallel-slipped D2 configuration along the x-axis of VIIIa-S8, VIb-S12 and VIc-Se18 molecules. The definition of R, r and d distances.


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Table 3. Distances (in Å) between the molecular centers d, minimal normal distance between the molecular planes R, the mutual shift along the x axis r, interaction energies Eint (in kJmol−1), electron/hole–transport rate between two adjacent molecular sites kelectron/hole (in 1014 s–1), absolute values of effective electron/hole transfer integral teff, electron/hole (in meV) and electron/hole drift mobilities electron/hole (in cm2V−1s−1) calculated for the selected ideal sandwich dimers (D1) in their optimal centroid–to–centroid distance r and the parallel-shifted dimer-configurations (D2). Molecule

d

R

r

Eint

khole

teff, hole

hole

VI(D1)

3.62

3.62

–

–70.00

10.59

277.9

13.51

VI(D2)

3.70

3.36

1.54

–94.96

5.66

203.2

7.54

VIIIa–S8(D1)

3.74

3.74

–

–100.02

9.42

253.4

12.83

VIIIa-S8(D2)

3.79

3.45

1.54

–128.87

1.17

89.2

1.63

VIb–S12(D1)

3.44

3.44

–

–168.69

10.97

258.4

12.63

VIb-S12(D2)

3.77

3.45

1.51

–223.03

1.21

85.8

1.67

VIb–Se12(D1)

3.48

3.48

–

–196.49

19.68

297.3

23.19

VIb–Se12(D2)

3.92

3.42

1.92

–268.88

0.00

2.6

0.00

VIc-S18(D1)

3.69

3.69

–

–345.41

22.62

299.3

29.97

VIc-S18(D2)

4.33

3.42

2.67

–435.30

2.04

89.9

3.72

VIc–Se18(D1)

3.83

3.83

–

–399.09

0.57

45.8

0.81

VIc–Se18(D2)

3.83

–

–

–526.62

–

–

–



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Table 3 (continued). Distances (in Å) between the molecular centers d, minimal normal distance between the molecular planes R, the mutual shift along the x axis r, interaction energies Eint (in kJmol−1), electron/hole–transport rate between two adjacent molecular sites kelectron/hole (in 1014 s–1), absolute values of effective electron/hole transfer integral teff, electron/hole (in meV) and electron/hole drift mobilities electron/hole (in cm2V−1s−1) calculated for the selected ideal sandwich dimers (D1) in their optimal centroid–to–centroid distance r and the parallel-shifted dimer-configurations (D2). Molecule

d

R

r

Eint

kelectron

teff, electron

electron

VIb–Se12(D1)

3.48

3.48

–

–196.49

0.01

74.3

0.01

VIb–Se12(D2)

3.92

3.42

1.92

–268.88

0.00

23.7

0.00

VIc–S18(D1)

3.69

3.69

–

–345.41

29.17

280.6

38.6

VIc-S18(D2)

4.33

3.42

2.67

–435.30

1.73

68.3

3.15

VIc–Se18(D1)

3.83

3.83

–

–399.09

56.27

346.9

80.2

VIc-Se18(D2)

3.83

–

–

–526.62

–

–

–


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The predicted interaction energies increase with the molecular size, i.e. from –70.0 kJ·mol–1 for VI(D1) to –526.6 kJ·mol–1 for VIc-Se18(D2). The corresponding distances between the molecular centres change from 3.62 Å to 3.83 Å. Considering comparison with the X-ray P-dimer configurations of corresponding molecules, interaction energies for gas-phase model VI(D1) (– 70.0 kJ·mol–1) and VI(D2) (–95.0 kJ·mol–1) dimers are similar to that of VI(P) (–84.1 kJ·mol–1) dimer in crystal structure (see Table 4). For VIIIa-S8 molecule, the gas-phase parallel-slipped dimer VIIIa-S8(D2) exhibits interaction energy of –128.9 kJ·mol–1, which is in excellent agreement with X-ray parallel dimer configuration VIIIa-S8(P) providing interaction energy of –129.2 kJ·mol–1. For the sake of comparison, we would like to note that the stacking interaction energy for VIIIa-S8 is ca 2.5 times higher than the total energy of intermolecular interactions estimated by Espinosa’s equation86. Moreover, the distances between centers of mass for VIIIa-S8(D2) (3.79 Å) and VIIIaS8(P) (3.87 Å) are very similar, too. Interestingly, the gas-phase geometries of monomers in D1 dimer configuration have slightly perturbated planarity (see Figure 5). Planarity of third generation persulfurated molecule VIc-S18 is perturbed lightly. On the other hand, in case of D2 dimer configuration, structure of its selenium analogue (VIc-Se18) is perturbed significantly and exhibits a saddle-shaped structure (see Figure 5), thus it is not further investigated. The macroscopic electric drift mobilities are determined by the local drift mobilities coming from the individual molecular dimers. The calculated hole mobilities for X-ray dimers of studied 6T, VI and VIIIa-S8 molecules are summarized in Table 4. For linear reference 6T molecule, the contributions from parallel P- and transversal T-dimers are practically identical, i.e. of 0.01 cm2∙V−1∙s−1 and 0.02 cm2∙V−1∙s−1. The experimental hole mobilities for the room temperature available in the literature change between 10–2 cm2∙V−1∙s−1 and 0.2 cm2∙V−1∙s−1.



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Table 4. The distances between the molecular centers d (in Å), interaction energies Eint (in kJmol−1), hole–transport rate between two adjacent molecular sites khole (in 1012 s–1), absolute values of effective hole transfer integral teff, hole (in meV) and hole drift mobilities hole (in cm2V−1s−1) calculated for the dimers selected from the X–ray structure of VI84, VIIIa–S885 and 6T83 molecules. The closest parallel (P), longitudinal (L) and transversal (T) dimer configurations were selected (see Figure 4 and Figure S3). Molecule(dimer)

d

Eint

khole

teff, hole

hole

VI(P)

4.67

–84.10

6.85

22.4

0.15

VI(L)

10.04

–16.49

2.96

14.7

0.29

VI(T)

8.33

–18.16

0.00

0.0

0.00

VIIIa–S8(P)

3.87

–129.24

213.32

120.6

3.10

VIIIa–S8(L)

11.14

–16.23

0.05

1.9

0.01

VIIIa–S8(T1)

10.22

–20.17

0.13

3.0

0.01

VIIIa–S8(T2)

10.07

–19.41

0.04

0.3

0.00

6T(P)

6.03

–63.89

0.20

10.4

0.01

6T(T1)

4.92

–86.36

0.68

19.3

0.02

6T(T2)

4.98

–86.32

0.91

22.4

0.02


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The evaluated hole drift mobility for parallel coronene dimer VI(P) is of 0.29 cm2V−1s−1, which is the most significant contribution (approximately 70 percent of overall hole-transport rate). Interestingly, parallel configuration hole mobility is twice as high as in the transversal dimer (0.15 cm2∙V−1∙s−1). These predicted values agree well with the experimental charge carrier mobility for coronene at room temperature (0.2 cm2V−1s−1)87. The main influence on the hole mobility in the VIIIa-S8 crystal is provided by the parallel dimer of VIIIa-S8(P) where the calculated hole mobility is of 3.10 cm2∙V−1∙s−1. This arrangement will be probably less populated in thin films because the corresponding experimental hole mobility for thin film transistor in combination with Au electrodes and SiO2 gate-dielectrics with a threshold gate voltage of −45 V is of 9 × 10−3 cm2∙V−1∙s−1 12. Lower occurrence of VIIIa-S8(P) in crystal structure is obvious also from Figure 4 showing higher counts of different dimer configurations with centroid-to-centroid distance more than 10 Å and very low hole-transfer rate constant. In the case of perfect gas-phase sandwich D1 dimers, the evaluated drift mobilities of the selected studied molecules are approximately ten-times larger than the values obtained for the full optimized parallel-slipped D2 dimers (see Table 3 and Table 4). Hole drift mobilities for VIIIa-S8(D1) and VIIIa-S8(D2) are of 12.83 cm2∙V−1∙s−1 and 1.63 cm2∙V−1∙s−1, respectively. Parallel dimer configuration D1 represents a sandwich with optimal displacement. On the other hand, more probable displacement in crystal structure is a parallel-slipped one, thus D2 dimer configuration is suitable for modelling electronic properties based on a comparison with an X-ray structure. Among the D2 model dimers, the highest values of hole drift mobilities were obtained for the reference coronene VI (7.54 cm2∙V−1∙s−1), which is a well-known p-type semiconductor. The B3LYP/SVP theoretical hole mobility for VIb-S12(D2) is of 1.67 cm2∙V−1∙s−1 and it is very close to hole for VIIIa-S8(D2) (1.63 cm2∙V−1∙s−1). The third-generation molecule VIc-S18 provides significantly high hole mobility of 3.72 cm2∙V−1∙s−1 and 29.97 cm2∙V−1∙s−1 for D2 and D1 model dimers, respectively. In comparison with the hole-transport, electron mobility has a significant meaning only in case of VIc-S18(D2) 39 ACS Paragon Plus Environment


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molecule (3.15 cm2∙V−1∙s−1), see Table 3, which is similar to its hole carrier mobility. Thus, VIcS18 is suitable for ambipolar semiconductors construction. The dependences of drift mobilities on the intermolecular distance from 3.5 to 6.0 Å for selected studied model dimers D1 with ideal sandwich displacement, for reference 6T, VI and perspective VIb-S12, VIb-Se12, VIc-S18 and VIc-Se18 molecules are illustrated in Figure 6 The obtained dependences have exponential character for the R distance range and are characterized by equation

  A exp( BR)

(9)

The fitted optimal A and B parameters are collected in Table S2. For hole mobilities, the lowest B exponent exhibit the reference coronene molecule. The VIc-S18 molecule has comparable parameters for hole as well as electron drift mobility. On the other hand, the largest selenium analogue (VIc-Se18 molecule) is promising n-type semiconductor.

Figure 6. The theoretical dependence of drift mobilities on the centroid-to-centroid distance d in model optimal sandwich dimers (D1) of VIb-S12, VIb-Se12, VIc-S18 and VIc-Se18 molecules. Drift mobilities of coronene VI and α-sexithiophene 6T served as references.


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4. CONCLUSIONS We have theoretically designed a series of novel symmetric hetero-[n]circulenes including S and Se heteroatoms for [n] from 6 to 9. The bowl-shaped optimal geometry was obtained for three smaller molecules, i.e. VIb-S6, VIb-Se6 and VIIa-S7. Mostly the hetero-[n]circulenes containing fivemembered heteroring condensed with benzene rings as well as the pure VIII and IX [n]coronenes provide a saddle-shaped structure. Our calculations also indicated the different effect of bulk selenium atom on the molecular geometry. For the VIIa-Se7 molecule, selenium atoms support the planarity in comparison with bowl-shaped VIIa-S7. In case of the saddle-shaped VIIIa-Se4, the planarity is suppressed while VIIIa-S4 molecule is planar. For planar molecules, the local aromaticity of individual molecular rings was described using the HOMED aromaticity indices. This analysis of the first generation of sunflower molecules showed that the highest aromaticity occurs in the fused thiophene rings with the antiaromatic character, where enhancement of the central ring changes the local ring aromaticity. The highest HOMED values for all individual aromatic rings are indicated for the second and third generation of hetero-[n]circulenes. The potential role of intermolecular bonds stabilizing the stacking structures in a real bulk was estimated by the mutual comparison of interaction energies for the model parallel-stacked (D1) and the parallel-slipped dimer configurations (D2). The electron drift mobilities were evaluated for the model dimers at room temperature using the Marcus theory and the Einstein relation. Based on the reorganization energies and charge transport characteristics, the second generation of sunflowers VIb-S12 and VIb-Se12 could possess p-type semiconduction. Our simulations showed that the third generation of sunflower molecules could have higher drift mobilities comparing to the reference αsexithiophene and coronene molecules. The VIc-S18 molecule could be suitable for the construction of ambipolar organic semiconductors while the VIc-Se18 molecule exhibits better n-type of semiconduction.



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SUPPORTING INFORMATION Optimal geometries of non-planar molecules, point group symmetry and shapes of frontier molecular orbitals for optimized molecules and dimer configurations from crystal structure, molecular packing diagrams obtained from X-ray structures, aromaticity HOMED indices for central ring and corresponding bond lengths, parameters for electron drift mobility dependence on centroid-tocentroid distance

ACKNOWLEDGMENT The work has been supported by Slovak Research and Development Agency (APVV-15-0053). The authors would like to thank for financial contribution from the STU Grant scheme for Support of Young Researchers (1619). We are grateful to the HPC centre at the Slovak University of Technology in Bratislava, which is a part of the Slovak Infrastructure of High Performance Computing (SIVVP project, ITMS code 26230120002, funded by the European region development funds, ERDF) for the computational time and resources made available.


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Design of Novel Generations of Planar Sunflower Molecules

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