Optoelectronic Properties of Polycyclic Aromatic Hydrocarbons of Various Sizes and Shapes: A DFT Study

Polycyclic aromatic hydrocarbons (PAHs) can be considered as graphene nanoflakes in which the edges are hydrogenated. Zigzag and armchair-edged PAHs possessing circular, parallelogram, rectangular and triangular shapes have been studied using M06L/6-31+G(d) level of density functional theory (DFT). Molecular electrostatic potential (MESP) analysis of the PAHs is done to characterize their electron distribution while the time-dependent DFT (TD-DFT) analysis was used for the absorption spectral analysis. MESP analysis clearly showed Clar’s sextet like electronic arrangement in armchair-edged systems whereas zigzag-edged ones showed significant electron localization towards the edges. TD-DFT analysis casts light upon the absorption features of these systems, which followed a linear trends in absorption maximum (max) for most of the armchair-edged systems with respect to the number of π-electrons. MESP analysis on the electron rich and electron deficient features of PAH systems led to the design of donor-spacer-acceptor type PAH-π-PAH systems (D-π-A systems) 2 wherein a conjugated diene moiety functions as the π-spacer. Though these systems behaved weakly as D-π-A systems, with the introduction of electron donating functional group NMe2 on one PAH and electron withdrawing group COOH on the other led to the formation of strong D-π-A systems. The MESP features, frontier molecular orbital (FMO) distribution, and absorption spectral features supported their strong D-π-A character. Among the different shapes studied, the rectangular PAH moiety showed the most efficient tuning of HOMO-LUMO gap. The optical and electronic data of PAH, PAH-π-PAH and functionalized PAH-π-PAH systems shed light upon possible tuning of their optoelectronic properties for practical applications. Introduction The field of molecular materials flourished in the 21 century after the isolation of graphene by Nobel Prize winners Geim and Novoselov, even though the pioneering theoretical work was done by P. Wallace in the year 1947. By definition, graphene is a polycyclic aromatic hydrocarbon (PAH) which is a flat monolayer of sp carbon atoms packed into a two dimensional -conjugated system, having exceptional electronic, thermal and mechanical properties. Despite being one atom thick, graphene can be optically visualized. Together with this visibility, other remarkable optical properties like hot luminescence, saturable absorption, and broadband applicability renders graphene an ideal photonic and optoelectronic material. Figure 1. Different types of periphery and edges in PAHs. 3 Large flakes of graphene in which every ring are different from the other are termed nanographene, the properties of which are largely influenced by the size and edge shape. As the size of the PAH increases, the number of isomers possible also increases. Graphene nanoflakes are stable than carbon nanotubes of similar size, but less stable than the corresponding fullerenes. In addition, large flakes have almost zero bandgap whereas small ones are semiconductors or insulators. Graphene nanoflakes tend to show new and unexpected electronic, optical, vibrational and magnetic properties based on the size and geometry. 24,25,30-35 For example, triphenylene and tetracene are made of four aromatic rings, the absorption maximum of former is at 265 nm and the same for latter is 471 nm, a much higher value. In addition, triphenylene is quite stable against oxidation whereas tetracene is easily oxidized. On the basis of resonance structures of PAH, Clar proposed the sextet rule which predicts the largest number of disjoint benzene-like -conjugated moieties one can draw for a PAH. According to Clar’s rule, triphenylene having three sextet rings is more aromatic and more stable than the isomer tetracene having only one sextet. Two types of periphery (zigzag and armchair) and three types of edges (the bay, the cove and the fjord) are observed for PAHs, (Figure 1). PAHs with armchair periphery are more resonance stabilized compared to those with the zigzag periphery, making zigzag ones more reactive so that larger PAHs with zigzag periphery is instantaneously converted to quinine in the air. 31 It is already proven that the HOMO-LUMO band gap engineering can be done by changing the size and the shape of graphene nanoflakes. Large PAHs are present naturally, but graphene nanoflakes are very difficult to synthesize and are not found naturally. Syntheses of nanoflakes are done, but the growth and nucleation trends are yet to be understood. Both topdown and bottom-up approaches are adopted for synthesis. Extensive theoretical research on graphene nanoflakes have been done by various groups. 4 Here we consider PAH molecules of various sizes and shapes as potential candidates for the design of donor or acceptor part of a donor-()spacer-acceptor (D--A) system. MESP analysis is used to evaluate the electron rich/deficient feature of a particular shape or size of the PAH. The electron rich PAH will be proposed suitable for the design of donor while a relatively electron deficient PAH will be suggested for the design of acceptor. Further, functionalization of the donor PAH is considered with NMe2 substituent while an acceptor moiety COOH is proposed to improve the accepting ability of the acceptor PAH. Computational Methods All the molecules are optimized using Gaussian16 suite of programs, using the DFT method M06L/6-31+G(d). The optimized geometries are confirmed as energy minima by vibrational frequency analysis. The electron density generated using M06L/631+G(d) method is used for molecular electrostatic potential (MESP) calculations. Using time-dependent density functional theory (TD-DFT) technique at the same level of theory, the absorption and molecular orbital features of every set of molecules are derived. Results and Discussion PAH systems: structure The PAHs are categorized into six groups on the basis of the overall shape of the molecule and the shape of their zigzag and armchair edges. A circular and parallelogram-shaped PAH can have armchair and zigzag edges. Armchair edged triangular-shaped PAH is also considered whereas a zigzag edged triangular shape is


Introduction
The field of molecular materials flourished in the 21 st century after the isolation of graphene by Nobel Prize winners Geim and Novoselov, 1 even though the pioneering theoretical work was done by P. Wallace in the year 1947. 2 By definition, graphene is a polycyclic aromatic hydrocarbon (PAH) which is a flat monolayer of sp 2 carbon atoms packed into a two dimensional -conjugated system, [3][4][5] having exceptional electronic, thermal and mechanical properties. 1,6 Despite being one atom thick, graphene can be optically visualized. 7,8 Together with this visibility, other remarkable optical properties like hot luminescence, saturable absorption, and broadband applicability renders graphene an ideal photonic and optoelectronic material. [9][10][11][12][13][14][15][16][17]  3 Large flakes of graphene in which every ring are different from the other are termed nanographene, 3,[18][19][20][21][22][23] the properties of which are largely influenced by the size and edge shape. [24][25][26][27][28] As the size of the PAH increases, the number of isomers possible also increases. 29 Graphene nanoflakes are stable than carbon nanotubes of similar size, but less stable than the corresponding fullerenes. In addition, large flakes have almost zero bandgap whereas small ones are semiconductors or insulators. Graphene nanoflakes tend to show new and unexpected electronic, optical, vibrational and magnetic properties based on the size and geometry. 24,25,[30][31][32][33][34][35] For example, triphenylene and tetracene are made of four aromatic rings, the absorption maximum of former is at 265 nm and the same for latter is 471 nm, a much higher value. In addition, triphenylene is quite stable against oxidation whereas tetracene is easily oxidized. On the basis of resonance structures of PAH, Clar proposed the sextet rule which predicts the largest number of disjoint benzene-like -conjugated moieties one can draw for a PAH. According to Clar's rule, triphenylene having three sextet rings is more aromatic and more stable than the isomer tetracene having only one sextet. [36][37][38][39] Two types of periphery (zigzag and armchair) and three types of edges (the bay, the cove and the fjord) are observed for PAHs, (Figure 1). 24 PAHs with armchair periphery are more resonance stabilized compared to those with the zigzag periphery, making zigzag ones more reactive so that larger PAHs with zigzag periphery is instantaneously converted to quinine in the air. 24 31 It is already proven that the HOMO-LUMO band gap engineering can be done by changing the size and the shape of graphene nanoflakes. 40 Large PAHs are present naturally, but graphene nanoflakes are very difficult to synthesize and are not found naturally. 41 Syntheses of nanoflakes are done, [42][43][44][45] but the growth and nucleation trends are yet to be understood. Both topdown [46][47][48][49][50] and bottom-up 43,51 approaches are adopted for synthesis. Extensive theoretical research on graphene nanoflakes have been done by various groups. 52-57 4 Here we consider PAH molecules of various sizes and shapes as potential candidates for the design of donor or acceptor part of a donor-()spacer-acceptor (D--A) system. MESP analysis is used to evaluate the electron rich/deficient feature of a particular shape or size of the PAH. The electron rich PAH will be proposed suitable for the design of donor while a relatively electron deficient PAH will be suggested for the design of acceptor. Further, functionalization of the donor PAH is considered with NMe2 substituent while an acceptor moiety COOH is proposed to improve the accepting ability of the acceptor PAH.

Computational Methods
All the molecules are optimized using Gaussian16 suite of programs, 58 using the DFT method M06L/6-31+G(d). 59 The optimized geometries are confirmed as energy minima by vibrational frequency analysis. The electron density generated using M06L/6-31+G(d) method is used for molecular electrostatic potential (MESP) calculations.
Using time-dependent density functional theory (TD-DFT) 60-63 technique at the same level of theory, the absorption and molecular orbital features of every set of molecules are derived.

PAH systems: structure
The PAHs are categorized into six groups on the basis of the overall shape of the molecule and the shape of their zigzag and armchair edges. A circular and parallelogram-shaped PAH can have armchair and zigzag edges. Armchair edged triangular-shaped PAH is also considered whereas a zigzag edged triangular shape is 5 not included in the study due to the requirement of odd number of C-H bonds to complete the shape (odd electron system). The sixth category belongs to rectangularshaped PAHs. For such a shape, one side has to be zigzag edged while the adjacent side has to be armchair edged. In every set of molecules, 4 systems are analyzed in the present study, which are designated as XyN, where X = C, T, P or R denoting circular, triangular, parallelogram and rectangular shaped structures respectively and y = z, a or h standing for zigzag, armchair and hybrid morphology, respectively. The notation N is used as a serial number (1)(2)(3)(4) for the smallest to the largest system studied in each category. A representative set of molecules from each category is given in Figure 2. For the PAH systems, the number of π-electrons and number of π-electrons per CC bonds (nπ) are given in Table 1. The nπ can be used as a simple measure to assess the π-electron density in every molecule. In every category, nπ decreases as the size of the system increases because the number of CC bonds monotonically increases.
The CxN systems show the lowest nπ value.

PAH systems: MESP analysis
To understand the electronic characteristics of every PAH systems, the most negative valued MESP (Vmin) in the molecules is determined. 64,65 MESP has been successfully demonstrated as an effective tool in studying PAH and other related systems, especially to interpret Clar's aromatic sextet theory. [36][37][38] Figure 3 shows MESP features of a representative set of systems (the smallest member in every category). See supporting information for MESP isosurface for all the systems. The black dot in the MESP isosurface denotes the deepest Vmin and their values are given in Table 2 (cf. Figure S1 for MESP isosurface plots). A gradual decrease in the absolute value of the Vmin is observed with increase in the size of the PAH which indicates the diminishing electron richness due to the enhancement of electron delocalization.  N=2 -12.5 -11.9 -13.1 -13.0 -13.5 -13.4 N=3 -11.8 -11.7 -12.4 -12.3 -12.9 -13.0 N=4 -11.0 -11.3 -11.9 -12.1 -12. 6 -12.7 Plots showing the correlation between nπ values and the corresponding Vmin values are given in Figure 4. The good linear relationships indicate that in a specific series, the πelectronic features gradually decrease with increase in the size of the molecule. The circular shaped systems (red dots in Figure 4) show the highest rate of decrease in πelectron density while the rectangular RhN systems (green dots) display the lowest.  The sextet localization of electrons in the rings is the lowest for such mixed systems.

PAH-π-PAH systems: structure
Only the first member from each category of molecules (Cz1, Ca1, Pz1, Pa1, Ta1 and Rh1) is selected to design the PAH-π-spacer-PAH systems (PAH-π-PAH). The selected π-spacer is t-butadiene moiety. These systems thus designed are named as Ta1-Pa1, Pa1-Rh1, and Ta1-Rh1. Naming is done in such a manner that the PAH system having the highest negative Vmin value is given first, followed by the name of the second PAH moiety. The most electron rich carbon of the PAH systems as seen in MESP topography (the carbon that appears nearest to the

PAH-π-PAH systems: MESP analysis
These systems are analyzed for their electronic features using the tool of MESP and the Vmin values on different parts of the systems are given in Table 3. The notations in Table 3 are color coded; the PAH moiety showing more electron rich character than

Functionalized PAH-π-PAH systems: structure
The PAH-π-PAH systems show only minor variations in the electron density distribution at various parts of the system meaning that the donor-π-acceptor (D-π-A) character is very weak in PAH-π-PAH. Hence to force a more significant electronic rearrangement on the PAH moieties, an electron withdrawing group COOH and electron releasing group NMe2 are introduced in the system. NMe2 is introduced at the relatively more electron rich PAH portion (donor) while COOH is attached with the other PAH unit (acceptor). Seven such functionalized PAH-π-PAH systems (f_PAH-π-PAH) are considered here which showed the difference 0.5 kcal/mol between the Vmin values of the constituting PAH parts. These systems in abbreviated names are f_Pa1-Cz1, f_PAH-π-PAH systems (f_Ta1-Cz1 and f_Rh1-Ca1) are given in Figure 8.

Functionalized PAH-π-PAH systems: MESP analysis
The Vmin values on different parts of the systems (donor, acceptor and spacer) are given in Table 4. The MESP topography is significantly modified when the system is functionlized using electron donating and withdrawing groups. kcal/mol is reduced to -12.0 kcal/mol for the functionalized f_Pa1-Ca1 system. The MESP features confirm that the functionalized systems are more like a true D-π-A system. The visual representation of MESP for PAH-π-PAH (Ta1-Ca1) and f_PAH-π-PAH (f_Ta1-Ca1) systems is given in Figure 9, where the isosurface (in pink color) is

Frontier molecular orbital analysis
The change in the size and shape of any PAH system will contribute towards the HOMO-LUMO gap modulation. 40 The HOMO energy (EHOMO), LUMO energy (ELUMO) and the corresponding HOMO-LUMO energy gap (E) of every systems are given in   For PAH-π-PAH systems, the energies EHOMO, ELUMO and E are given in Table 6 Figure 13. Frontier molecular orbitals of f_Ta1-Cz1 system.

Optical properties
The calculated optical properties include absorption maxima (λmax), oscillator strength The optical properties of the PAH systems are given in Table 8 and Table 9. Table 8 lists The absorption spectra of representative PAH systems are illustrated in Figure   14. For all the systems in CzN, single λmax values are observed with an exception Cz4.  600-640 nm. Ca1 system (hexabenzocoronene) has λmax at 397 nm and a shoulder at 341 nm. The experimental λmax for this system is centred around 350nm. 67 Ca2 shows λmax at 619 nm and a shoulder at 413nm. Ca3 has λmax at 754 and shoulder at 552 nm, whereas the largest system analysed Ca4 has λmax at 1122 nm and shoulder at 764 nm.

Conclusions
The Armchair edged PAH system are found to be more resonance stabilised, which is supported by the Clar's aromatic sextet like MESP isosurface arrangement in the entire structure. For zigzag periphery systems, the electron cloud is localised more towards the edges and these classes of systems might be very useful for donor-acceptor type electronic applications. Rectangular shaped PAH systems having both armchair and zigzag edges in same molecule are electronically very dense which has a characteristic very low HOMO-LUMO gap even when number of rings constituting is less. This effect is verified by comparing with other systems of much higher number of constituting rings. In summary, the theoretical study on PAH, PAH-π-PAH and f_PAH-π-PAH systems provide new insight on the design and development of efficient light harvesting molecules that are derived from graphene nanoflakes of different sizes and shapes.

Supporting Information
MESP figures, HOMO and LUMO representations, Absorption spectra, and Optimized nuclear coordinates of all the structures.