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Quantum chemical exploration of dimeric forms of polycyclic aromatic hydrocarbons, naphthalene, perylene, and coronene
Chemical Physics Letters 716 (2019) 147–154
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Research paper
Quantum chemical exploration of dimeric forms of polycyclic aromatic hydrocarbons, naphthalene, perylene, and coronene
T
⁎
Koichi Ohnoa,b, , Hiroko Satohb,c,d, Takeaki Iwamotoa a
Department of Chemistry, Graduate School of Science, Tohoku University, Aramaki, Aza-Aoba, 6-3, Aoba-ku, Sendai 980-8578, Japan Institute for Quantum Chemical Exploration, Kaigan 3-9-15, Minato-ku, Tokyo 108-0022, Japan c Department of Chemistry, University of Zurich, 8057 Zurich, Switzerland d Research Organization of Information and Systems (ROIS), Tokyo 105-0001, Japan b
H I GH L IG H T S
aromatic hydrocarbon dimers were obtained by geometry optimization. • Polycyclic PAH molecules placed in parallel were directly bonded between them. • Two structures with four-membered rings on the side faces were constructed. • Cage dimers were found to be located in sufficiently deep potential energy wells. • PAH • PAH dimers were found to have massive energies larger than two isolated molecules.
A B S T R A C T
We have found dimeric forms of polycyclic aromatic hydrocarbon (di-PAH) molecules by quantum chemical calculations. Geometry optimization starting from short distances of ca. 0.15 nm between two PAH molecules placed in parallel gave cage structures of di-PAH with CC bond connections forming four-membered rings between the PAH molecules. The di-PAH molecules are located in sufficiently deep potential energy wells surrounded by high energy barriers, although their energies are much higher than those of the isolated two PAH molecules.
1. Introduction A carbon atom can be bonded with several atoms to yield various sizes of chains, rings, and cages, which have interesting structures and valuable properties. Many of hydrocarbon and carbon structures, such as benzene, cyclohexane, adamantane, graphene, and diamond, are composed of stable six-membered rings. In some other cases, such as azulene, corannulene, fullerenes, and nano tubes, their carbon skeletons include five-membered rings or seven membered rings. Besides these intensively studied structures with five-, six-, or seven membered rings, another type of structures also with four- or three-membered rings has been explored. For example, hydrocarbons called prismanes C2nH2n, formed by two parallel regular n-gons connected by n rectangular faces, are to be noted due to their peculiar cage structures and high chemical energies [1–6]. Although some prismanes, such as prismane C6H6 [1], cubane C8H8 [2], and pentaprismane C10H10 [3] were really synthesized, many other systems, such as hexaprismane C12H12 [5,6] and the larger analogues have been studied only by theoretical calculations. In connection with hexaprismane C12H12, various benzene ⁎
dimers (C6H6)2 have been studied by quantum chemical calculations [7–10]. Computational explorations revealed fifteen isomeric forms of benzene dimers [8], which include four types of synthesized dimers. Recently, a systematic exploration for the benzene isomers C6H6 on the ground-state potential energy surface (PES) by quantum chemical calculations found numerous numbers, more than two thousand, of isomeric forms [11,12]. In the view of these studies, the search for further new types of hydrocarbon is still challenging. Possible structures for carbon skeletons in hydrocarbon molecules can be related to those for carbons. Carbon structures were classified on the basis of known structures [13], for instance, various fullerene types, prisms, spiral chains, zigzag tubes, double layers, and diamond-like structures. More recently, quantum chemical calculations suggested the existence of a new class of carbon allotropes with four-membered rings [14–17]: A prism-C2n series (n = 8–10, 12, 14, 16, 18 and 20) like hamster wheels [14] can be related to the [n]-prismanes C2nH2n (n = 3–10) [6]. The prism-C2n structures can connect to each other by facing at four-membered rings to give various sheet structures called the prism-C2n sheets (n = 6, 8, and 12) [15]. The prism-C12 sheet
Corresponding author at: Department of Chemistry, Graduate School of Science, Tohoku University, Aramaki, Aza-Aoba 6-3, Aoba-ku, Sendai 980-8578, Japan. E-mail address: [email protected] (K. Ohno).
https://doi.org/10.1016/j.cplett.2018.12.034 Received 8 November 2018; Received in revised form 4 December 2018; Accepted 12 December 2018 Available online 26 December 2018 0009-2614/ © 2018 Elsevier B.V. All rights reserved.
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Fig. 1. Hexagonal carbon skeletons of polycyclic aromatic hydrocarbons (PAHs). (a) Naphthalene C10H8, (b) perylene C20H12, (c) coronene C24H12. Carbon atoms are conventionally numbered so as to be common in the three cases.
representative PAH with fully convex perimeters. The study on acene dimerization [28] investigated various dimers, which have two bonds in between, for naphthalene, anthracene, pentacene, and heptacene, but no study on the dimers with more than two bonds has been yet reported. As will be shown, our quantum chemical calculations predicted that those structures have high energy but can exist in a deep potential energy well surrounded by high energy barriers.
corresponds to a honeycomb shaped double carbon layers with covalent CC-bond connections between two graphene sheets [13], and it may be related to face-fused poly-hexaprismanes. The prism-Cn tubes are carbon allotropes with four-membered rings on the side faces and axially piled up n-membered carbon polygons (n = 3–8, 10, 12, 14, 16, 18, and 20) [16]. The prism-Cn tubes can be related to poly[n]prismanes (n = 3–6) [5]. The wavy carbons with condensed four-membered rings were also found by quantum chemical calculations [17]. In connection with the above studies, interactions between two benzene molecules [10] should be noted. Intermolecular π/π interactions between two benzene molecules cause weak attraction due to van der Waals forces at interplane distances of ca. 0.37 nm. In shorter distance around 0.25–0.30 nm, the exchange repulsion between the two aromatic molecules rises. However, once they come much closer at ca. 0.16 nm, strong covalent interactions take over, which yield cyclodimers of benzenes [10]. Considering the existence of the covalent bonds between polygons in [n]-prismanes and prism-C2n, covalent interactions between polycyclic aromatic hydrocarbon (PAH) molecules are also expected to obtain at such a short distance. Regarding computational methods, automatic explorations on PES for all the possible isomeric structures and transition state structures, as well as reaction pathways had been a significantly difficult issue. In recent two decades, a global exploration of equilibrium structures (EQ), transition state structures (TS), and dissociation channels (DC) on PES for a given chemical composition became possible by the global reaction route mapping (GRRM) techniques [18–23]. Based on the GRRM techniques, many studies concerning explorations on PES [11,12,14–17,24–27] were performed. The GRRM techniques are useful not only to list up EQ, TS and DC but also to determine the lowest energy barrier from an EQ, which gives essential information on the stability of the EQ. The capability accomplishing these tasks is a notable advantage of the GRRM techniques. In this study, we have explored hydrocarbon structures with fourmembered rings in a cage form by using the GRRM program [23]. They consist of a pair of PAH structures placed in parallel, which have many bonds between them. We have investigated dimers of naphthalene C10H8 as the smallest PAH in polyacene systems, perylene C20H12 as a typical PAH with concave perimeters, and coronene C24H12 as a
2. Methods and calculations 2.1. Calculation methods All the electronic state calculations in this study were performed for the ground singlet states, by using the Gaussian 09 program package [29]. The energy minimization procedures were performed at a very tight level by using the GRRM program (GRRM14) [23]. The ultrafine grids were used for density calculations. At the minimum point, all the Hessian eigenvalues were confirmed to be positive. We employed the density functional theory (DFT) with the B3LYP exchange-correlation functional based on our experiences in quantum chemical explorations of H3CNO3 [24], formaldehyde clusters [25], and prism-carbon structures [14–17]. Through the comparative studies with thirty-eight levels of the HF, DFT, MP2, and CCSD(T) methods, the computed molecular structures were well confirmed to be acceptable, and the geometry at B3LYP, BLYP, and MP2 was found to be fairly similar even with different basis sets [30], although subtle differences of energies between isomers by DFT were observed. This is because of insufficient interactions due to dispersion forces [30]. We coped with the problem by using the DFT-D3 method for dispersion corrections, which was developed by Grimme and co-workers to remove the drawback of DFT [31,32] and was confirmed to yield very good agreement with the CCSD(T)/CBS benchmark data [33]. The DFT(B3LYP)-D3 method gave also sufficient results in the study of formaldehyde clusters [25]. DFT calculations can sometimes give insufficient results especially for radical pair regions of PES. As far as our experiences of PES-searches, non-radical characters of H3CNO3 were thoroughly and efficiently searched with B3LYP calculations [24]. Therefore, we decided to use the DFT (B3LYP) method supplemented 148
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We assumed that the formation of separated benzene rings in the capsule form should be due to insufficient interactions between the central rings at the distance of 0.150 nm. Therefore, we carried out further geometry optimization starting with an initial vertical distance 0.140 nm and obtained the fully bonded di-coronene, [24]-di-coronene (4) (Fig. 2) as expected. All of the optimized structures with the D3-dispersion corrections were similar to those obtained without dispersion corrections. The geometrical structures obtained at the B3LYP-D3/cc-pVDZ level were also fairly the same as those obtained at the B3LYP-D3/6-31G(d) level. The interatomic distances and the HOMO/LUMO levels obtained at the B3LYP-D3/cc-pVDZ level were summarized in Table 1. The geometry optimization for 1 was done also at the B3LYP-D3/ccpVTZ and B3LYP-D3/aug-cc-pVTZ levels. Slight differences were found in the energy, but the geometrical structures at the levels of B3LYP-D3/ cc-pVTZ and B3LYP-D3/aug-cc-pVTZ were found to be nearly the same within three digits as those at the level of B3LYP-D3/cc-pVDZ, as can be seen in Table S1 of Supplementary data. Thus, we decided that the geometry optimization at the level of B3LYP-D3/cc-pVDZ would give relevant geometrical structures also for the larger systems of di-perylene and di-coronene. All of the CC bond lengths for the fully-bonded di-PAHs (1, 2, 4) are in the range of 0.154–0.159 nm, which correspond to a CC single bond. All of the carbon atoms in 1, 2, and 4 are bonded with four atoms. However, the carbon atoms in the central hexagonal rings of [18]-dicoronene (3) (C4, C5, C6, C19, C20, C11, C4′, C5′, C6′, C19′, C20′, and C11′) are bonded to three C atoms with bond length of 0.142 nm (e.g. C4-C5 in Table 1), and there are no bond between Cn and Cn′ (n = 4, 5, 6, 19, 20, and 11). As can be seen in Table 1, the distance C4-C4′ 0.286 nm is longer than the CC single bonds of C1-C2, C2-C3, C3-C4, C1-C1′, and C3-C3′ (0.151–0.166 nm) and the CC bond of C4-C5 (0.142 nm). This C4-C4′ distance of 0.286 nm is similar to the typical interatomic distance for a non-bonded carbon atom pair at the para position of benzene ring and is much shorter than the typical van der Waals CC distance of 0.335 nm between adjacent graphene layers in graphite. The electron density analysis of 3 showed bond critical points with electron densities of ca 0.19–0.25 au for CC single bonds and rather higher electron density of ca. 0.29 au for the CC bonds at the central hexagonal rings (C4-C5) (Table 1), whereas no bond critical point was obtained for C4-C4′ between two central rings. The results of the electron density analysis with QTAIM can be referred in Fig. S1 of Supplementary data. As can be seen in Table 1, the energy gaps between the HOMO and LUMO levels for fully bonded di-PAHs decrease from 5.885 eV (1) to 3.634 eV (4) associated with the system sizes increasing. However, the HOMO-LUMO gap of 3 (4.089 eV) is much larger than that of 4 (3.634 eV), which reflects the larger stabilization of HOMO (−1.267 eV) with respect to the case of LUMO (−0.812 eV) in 3 in comparison with that of 4. The shapes of the HOMO and LUMO of 3 can be seen in Fig. S2 of Supplementary data. The electron densities for the HOMO and LUMO at the outer part of the central hexagonal rings exhibit characteristic shapes of the respective π orbitals of benzene, although some electron distributions can be seen along the CC skeletons due to through-bond interactions.
with the dispersion corrections (D3) to investigate the PAH dimers concerned with non-radical systems. 2.2. Geometry optimizations of PAH dimers Fig. 1 shows the carbon skeletons of naphthalene, perylene, and coronene with their numbering. Geometry optimization calculations were started from a pair of PAH molecules that are placed in parallel with a vertical distance of 0.150 nm. The distance of 0.150 nm was chosen, because the CC bond lengths connecting two polygon carbon rings were found to be ca. 0.146–0.161 nm in the previous studies of carbon allotropes [14–17,26]. The initial CC and CH bond lengths and all of the bond angle were set to be 0.144 nm, 0.110 nm, and 120°, respectively. 2.3. Explorations of the lowest energy barrier In order to know the stability of each of the minimum structures, we have explored the lowest energy barrier from the structure on the PES. To find the lowest energy barrier, reaction pathways leading to TS and DC around the respective EQ need to search. The search of such vast regions of PES is usually a highly time-consuming task, but the anharmonic downward distortion following (ADDF) method [18–21], which is one of the GRRM techniques implemented in the GRRM program [23], allows us to do this efficiently: One of the notable functions of the ADDF method is to find a neighboring EQ structure via a TS at the lowest energy barrier. This function works by following large anharmonic downward distortion (LADD option) to avoid tracing energetically high barriers and by focusing only on finding the neighboring minima (FirstOnly option). We set LADD = 3 to select only three ADD routes from the largest one. Examples of input data using the above options of the GRRM program were listed in Supplementary data. All of the reactions were explored as the intrinsic reaction coordinate (IRC) pathways. The B3LYP-D3/6-31G(d) level was used for the estimation of the lowest energy barriers. For the small systems of naphthalene and perylene dimers, the heights of the energy barrier were refined at the B3LYP-D3/cc-pVDZ level. We determined the energy for the molecules including the zero-point energy (ZPE) correction. 2.4. Electron density analysis We confirmed chemical bonds by electron density analysis in the scheme of the quantum theory of atoms in molecules (QTAIM) [34], which is implemented in the AIM2000 software [35]. The bond critical points on the bond paths were obtained by the electron density analysis at the level of B3LYP/cc-pVDZ. 3. Results and discussion 3.1. Di-PAH molecules The initial trials of the geometry optimization of the PAH dimers of naphthalene, perylene, and coronene at the B3LYP/6-31G(d) level successfully gave dimers (di-PAHs), in which all of the perimeter carbon atoms are bonded between the two PAH molecules. We name these dimers [10]-di-naphthalene (1), [20]-di-perylene (2), and [18]-di-coronene (3), respectively (Fig. 2), where the number in each of the square brackets indicates the number of the CC bonds between the two PAH molecules. Namely, [10]-di-naphthalene (C10H8)2 and [20]-di-perylene (C20H12)2 means that all of the carbon atoms in one PAH connect to the corresponding carbon atoms in the counterparts. In [18]-di-coronene (C24H12)2, eighteen pairs of carbon atoms at the perimeters connect to each other between the PAH sheets, but the rest of six pairs of carbons at the central hexagonal rings do not connect, which makes a capsulelike space between the PAH structures.
3.2. Structural stabilities Figs. 3–6 show the energy profiles associated with the reaction from the respective di-PAH to a deformed structure via the lowest TS for each of the optimized di-PAHs (1–4). The absolute energy in Hartree and the energy relative to the lowest ones in kJ mol−1 are shown without the ZPE corrections. The relative path lengths along the IRCs are shown with respect to the TSs. The energy profiles for 1 and 2 were obtained at the level of B3LYP-D3/cc-pVDZ, whereas those for 3 and 4 were obtained at the level of B3LYP-D3/6-31G(d) to reduce the computation 149
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Fig. 2. Dimerized PAHs 1–4. (1) [10]-di-naphthalene (C10H8)2 (D2h), (2) [20]-di-perylene (C20H12)2 (D2h), (3) [18]-di-coronene (C24H12)2 (D6h), (4) [24]-di-coronene (C24H12)2 (D6h). Table 1 Interatomic distances and HOMO/LUMO levels of di-PAHs 1–4.a,b [10]-di-naphthalene 1 C1-C2 C2-C3 C3-C4 C4-C5 C5-C10 C1-C10 C4-C11 C1-H1 C2-H2 C3-H3 C1-C1′ C2-C2′ C3-C3′ C4-C4′ C5-C5′ C10-C10′ HOMO LUMO
0.156 0.157 0.156 0.155 0.156 0.155
(0.231) (0.226) (0.231) (0.231) (0.222) (0.231)
0.110 0.110 0.110 0.159 0.156 0.156 0.159 0.156 0.156 −4.970 0.915
(0.270) (0.271) (0.271) (0.221) (0.234) (0.234) (0.221) (0.249) (0.249)
[20]-di-perylene 2 0.156 0.157 0.156 0.157 0.156 0.155 0.157 0.110 0.110 0.110 0.159 0.156 0.159 0.156 0.158 0.156 −4.148 0.410
(0.228) (0.227) (0.227) (0.222) (0.224) (0.221) (0.221) (0.270) (0.272) (0.272) (0.221) (0.227) (0.222) (0.248) (0.243) (0.249)
[18]-di-coronene 3
[24]-di-coronene 4
0.154 0.154 0.151 0.142 0.151 0.154 0.142 0.110 0.110
(0.242) (0.241) (0.250) (0.291) (0.250) (0.241) (0.291) (0.271) (0.271)
0.157 0.156 0.154 0.155 0.154 0.156 0.155 0.110 0.110
(0.224) (0.227) (0.227) (0.228) (0.227) (0.227) (0.228) (0.274) (0.274)
0.157 0.157 0.166 0.286 0.286 0.166 −5.103 −1.014
(0.227) (0.227) (0.193)
0.159 0.159 0.156 0.158 0.158 0.156 −3.836 −0.202
(0.226) (0.226) (0.250) (0.246) (0.246) (0.250)
(0.193)
a
Interatomic distances are given in nm, and orbital energies are given in eV for the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). Electron densities at bond critical points are given in parentheses in the atomic unit. b C-atom is labelled as Cn for the upper one or Cn′ for the lower one, with the numbering n in Fig. 1. H-atom is labelled as Hn, where n is for Cn in the respective CH bond.
time. The ADDF method can find DCs if they exist, but no DCs lower than the respective TS in Figs. 3–6 were found. The lowest height of the barrier around 1 is ca. 118 kJ mol−1 after the ZPE correction. The barrier of 100 kJ mol−1 gives a Boltzmann factor (BF) of 3.9 × 10−18 at 300 K, therefore, thermal decomposition of 1 is considered to be improbable at the ambient temperature of ca. 300 K. When BF increases to 2.4 × 10−3 at 2000 K, 1 may be isomerized into a deformed structure [9]-di-naphthalene (5) in Fig. 3,
which shows bond breaking at C1-C1′. The reverse barrier from 5 to 1 is only 10.1 kJ mol−1 (BF = 0.017 at 300 K), therefore, 5 would easily go back to 1. Further exploration of the reaction pathways around 5 gave the lowest barrier of 1.3 kJ mol−1 leading to [6]-di-naphthalene (Cs), which is much more stable than 1. We did not go further exploration in this study, but it is technically possible to explore further deformation reactions by using the ADDF method as shown in the study on C16 isomers [27]. 150
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Fig. 3. Energy profile of the reaction pathway of [10]-di-naphthalene 1 to a deformed form [9]di-naphthalene 5 via the lowest energy barrier TS. The vertical dotted line indicates the position of the barrier (TS). The barrier height from 1 to TS is 127.5 kJ mol−1 (117.7 kJ mol−1 with ZPE correction), and the reverse barrier height from 5 to TS is 8.4 kJ mol−1 (10.1 kJ mol−1 with ZPE correction).
respect to 4 (Fig. 6). The deformed structure 8 is a form of [20]-dicoronene, which has four less bonds by breaking at C6-C6′, C5-C5′, C4C4′, and C11-C11′ between the upper and the lower parts of 4. Such a large structural deformation makes many kinks in the energy profile from the TS to 8 in Fig. 6. It is noteworthy that the deformed structure 8 still keeps two CC bonds at C19-C19′ and C20-C20′. Thus, 8 is expected to deform further to [18]-di-coronene (3) with large release of energy of 730.9 kJ mol−1. This indicates that 3 is much more stable than 4 with a very large decrease in energy of 1894.6 kJ mol−1.
The energy profile for 2 (Fig. 4) shows also a high barrier from 2 to a deformed structure [19]-di-perylene (6) (164.1 kJ mol−1) and a low barrier from 6 to 2 (6.8 kJ mol−1), which indicates that 2 is stable enough to exist in the equilibrium geometry at the ambient temperature of ca. 300 K. The deformed structure 6 shows a bond breaking at C2-C2′ between the upper and the lower parts. Contrary to the cases of 1 and 2, the both barriers from 3 to its deformed structure 7 (250.6 kJ mol−1) and from 7 to 3 (217.9 kJ mol−1) are considerably high (Fig. 5). The deformed structure 7 shows bond breakings at C1-C10 and C1′-C10′. The capsule structure 3 is thus expected to be highly stable. [24]-di-coronene 4 shows a sufficiently high energy barrier (127.8 kJ mol−1), which would not be easily surmounted at the ambient temperature of ca. 300 K, whereas the deformed structure 8 is located at a substantially low energy level (−1163.7 kJ mol−1) with
3.3. Stored chemical energy The energies of di-PAHs are higher than those of the isolated two PAHs, that means, di-PAHs store higher chemical energy. As listed in Table 2, the larger the size of PAH becomes, the larger the relative Fig. 4. Energy profile of the reaction pathway of [20]-di-perylene 2 to a deformed form [19]-diperylene 6 via the lowest energy barrier TS. The vertical dotted line indicates the position of the barrier (TS). The barrier height from 2 to TS is 173.9 kJ mol−1 (164.1 kJ mol−1 with ZPE correction), and the reverse barrier height from 6 to TS is 5.5 kJ mol−1 (6.8 kJ mol−1 with ZPE correction).
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Fig. 5. Energy profile of the reaction pathway of [18]-di-coronene 3 to a deformed form 7 via the lowest energy barrier TS. The vertical dotted line indicates the position of the barrier (TS). The barrier height from 3 to TS is 266.2 kJ mol−1 (250.6 kJ mol−1 with ZPE correction), and the reverse barrier height from 7 to TS is 222.9 kJ mol−1 (217.9 kJ mol−1 with ZPE correction).
parts and the existence of the shorter CC bonds with the unsaturated character in the middle parts of the capsule structure of 3.
energies with respect to the isolated two PAH molecules get. To see more details, the chemical energies stored in 1–4 are normalized with the number of carbon atoms. The normalized chemical energy per carbon atom was found to increase from 1 (55 kJ mol−1) to 4 (185 kJ mol−1). Such large amount of normalized chemical energy is comparable to those of carbon allotropes with four-membered ring structures (100–350 kJ mol−1) [14–17,26]. The high amount of chemical energy mainly comes from atypical sp3 bond angles at the tetravalent carbon atoms, where the CH bonds are much less strained in comparison with the CC bonds that rigidly forms the carbon skeletons. The ordering of the normalized chemical energies of the fully-bonded di-PAHs (1, 2, 4) is 1 < 2 < 4, which corresponds to the number of the CH bonds, which are expected to reduce the strain of the cage structures. The large difference of the normalized chemical energies between 3 and 4 can be ascribed to the loss of the highly strained CC bonds between the upper and the lower
3.4. Partly bonded dimers We have scanned the outcome of the structure optimization starting from different distances between two naphthalene molecules from 0.16 to 0.30 nm at the level of B3LYP-D3/cc-pVDZ. The results were: (1) the initial distance of 0.16 nm gave the same outcome [10]-di-naphthalene as that started from 0.15 nm; (2) the initial distances of 0.17–0.24 nm gave partly bonded dimers, such as [2]-dimer, [4]-dimer, [6]-dimer, [8]-dimer and [10]-dimer; (3) the initial distances of 0.25 and 0.30 nm gave no covalent-dimers but van der walls dimers ([0]-dimer). The detailed data are contained in Table S2 of Supplementary data. We did not perform the scanning for the larger systems of perylene or coronene dimers in this study but assume that they would give a similar Fig. 6. Energy profile of the reaction pathway of [24]-di-coronene 4 to a deformed form [20]-dicoronene 8 via the lowest energy barrier TS. The vertical dotted line indicates the position of the barrier (TS). The barrier height from 4 to TS is 138.4 kJ mol−1 (127.8 kJ mol−1 with ZPE correction), and the reverse barrier height from 8 to TS is 1319.8 kJ mol−1 (1291.5 kJ mol−1 with ZPE correction).
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Table 2 Energies of di-PAHs 1–4.a
Electronic energy/Hartree
b
−1c
Relative energy/kJ mol Normalized chemical energy per one carbon atom/kJ mol−1d a b c d
[10]-di-naphthalene 1
[20]-di-perylene 2
[18]-di-coronene 3
[24]-di-coronene 4
−771.438065 (−771.854291) 1092.802 54.640
−1537.920850 (−1538.958866) 2725.310 68.133
−1842.534306 (−1843.971681) 3773.828 78.621
−1840.593881 (−1843.971681) 8868.413 184.759
Energies calculated at the level of B3LYP-D3/cc-pVDZ without the ZPE corrections. Energies for isolated pair of respective PAH molecules are listed in parentheses Relative energies with respect to the isolated pair of respective PAH molecules. Relative energies normalized with the number of carbon atoms.
Hayashi, at Wakayama University for technical advises to use AIM2000. H.S. and K.O. were supported by “Challenging Exploratory Research Projects for the Future” grant from ROIS (Research Organization of Information and Systems), Japan.
tendency. 3.5. Possibility of existence Our calculations suggested that the dimerized PAH molecules 1–4 have 1093–8868 kJ mol−1 higher energy relative to the isolated two PAH molecules but can exist stably enough in an energy well, which is deeper than 100 kJ mol−1. Aromatic hydrocarbon molecules are so stable that its dimerization reaction requires a certain amount of positive energy from the outside as an endothermic reaction. A typical example is a dimerization of benzene molecules that produces 6-prismane and some others [9]. The reaction requires energy absorption of 170 – 480 kJ mol−1. The intermolecular force between aromatic hydrocarbon molecules in short distance had been considered to be repulsive, however, this study on diPAHs 1–4 suggests that attractive force can take over the repulsive force under high pressure. The repulsive force between two naphthalene molecules at distances of 0.15–0.25 nm is estimated to be ca. 4 × 10−8 N, which corresponds to ca. 60 GPa for the molecular area of ca. 7 × 10−19 m2. The Gibbs energy change from the naphthalene dimer 1 to TS (Fig. 3) calculated at the B3LYP-D3/cc-pVDZ level was 112.57 kJ mol−1 at 298.15 K 1 atm and 97.03 kJ mol−1 at 1000 K 100 atm. These large values indicate that 1 can exist at the high-temperature and highpressure condition. In the mechanical point of view, the carbon skeletons of the PAH dimer molecules are formed with tough covalent CC single bonds like diamonds, which are often used as a pressing tool to make ultra-high pressure. Therefore, PAH dimers 1–4 are expected to stably exist not only at an ambient condition but also at a high-temperature and high-pressure atmosphere.
Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.cplett.2018.12.034. References [1] T.J. Katz, N. Acton, Synthesis of prismane, J. Am. Chem. Soc. 95 (1973) 2738. [2] P.E. Eaton, T.W. Cole Jr., The cubane system, J. Am. Chem. Soc. 86 (1964) 962. [3] P.E. Eaton, Y.S. Or, S.J. Branca, Pentaprismane, J. Am. Chem. Soc. 103 (1981) 2134. [4] P.E. Eaton, Cubanes: Starting materials for the chemistry of the 1990s and the new century, Angew. Chem. Int. Ed. Engl. 31 (1992) 1421. [5] R.M. Minyaev, V.I. Minkin, T.N. Gribanova, A.G. Starikov, R. Hoffmann, Poly[n] prismanes: a family of stable cage structures with half-planar carbon centers, J. Org. Chem. 68 (2003) 8588. [6] T.N. Grivanova, R.M. Minyaev, V.I. Minkin, Structural stability of [n]-prismanes and [n]-asteranes: a quantum-chemical study, Doklady Chem. 411 (Pt 1) (2006) 193. [7] R. Engelke, P.J. Hay, D.A. Kleier, W.R. Wadt, Theoretical study of dimeric forms of ground-state benzene molecules, J. Am. Chem. Soc. 106 (1984) 5439. [8] G.W. Schriver, D.J. Gerson, Energies and isomerization of (CH)12 hydrocarbons, J. Am. Chem. Soc. 112 (1990) 4723. [9] A.Y. Rogachev, X.-D. Wen, R. Hoffmann, Jailbreaking benzene dimers, J. Am. Chem. Soc. 134 (2012) 8062. [10] Y.-F. Wang, Z.-R. Li, F.-F. Wang, C.-C. Sun, The inter-ring σ/(π/π) covalent interactions of cyclodimes of benzenes, Phys. Chem. Chem. Phys. 11 (2009) 455. [11] H. Tokoyama, H. Yamakado, S. Maeda, K. Ohno, Exploration of isomers of benzene by GRRM/SCC-DFTB, Chem. Lett. 43 (2014) 702. [12] H. Tokoyama, H. Yamakado, S. Maeda, K. Ohno, Isomers of benzene on its global network of reaction pathways, Bull. Chem. Soc. Jpn. 88 (2015) 1284. [13] E.A. Belenkov, A. Greshnyakov, Classification of structural modifications of carbon, Phys. Solid Stat. 55 (2013) 1754. [14] K. Ohno, H. Satoh, T. Iwamoto, A prism carbon molecule C20, Chem. Lett. 44 (2015) 712. [15] K. Ohno, H. Satoh, T. Iwamoto, Prism-C2n carbon dimer, trimer, and nano-sheets: a quantum chemical study, Chem. Phys. Lett. 633 (2015) 120. [16] K. Ohno, H. Tokoyama, H. Yamakado, A quantum chemical study of novel carbon structures: prism carbon tubes, Chem. Phys. Lett. 635 (2015) 180. [17] K. Ohno, H. Satoh, T. Iwamoto, H. Tokoyama, H. Yamakado, Wavy carbon: a new series of carbon structures explored by quantum chemical calculations, Chem. Phys. Lett. 639 (2015) 178. [18] K. Ohno, S. Maeda, A scaled hypersphere search method for the topography of reaction pathways on the potential energy surface, Chem. Phys. Lett. 384 (2004) 277. [19] S. Maeda, K. Ohno, Global mapping of equilibrium and transition structures on potential energy surfaces by the scaled hypersphere search method: Application to ab initio surfaces of formaldehyde and propyne molecules, J. Phys. Chem. A 109 (2005) 5742. [20] K. Ohno, S. Maeda, Global reaction route mapping on potential energy surfaces of formaldehyde, formic acid, and their metal substituted analogues, J. Phys. Chem. A 110 (2006) 8933. [21] S. Maeda, K. Ohno, K. Morokuma, Systematic exploration of the mechanism of chemical reactions: Global reaction route mapping (GRRM) strategy by the ADDF and AFIR methods, Phys. Chem. Chem. Phys. 15 (2013) 3683. [22] K. Ohno, Study of potential energy surfaces towards global reaction route mapping, Chem. Rec. 16 (2016) 2198. [23] S. Maeda, Y. Harabuchi, Y. Osada, T. Taketsugu, K. Morokuma, K. Ohno, GRRM14, http://iqce.jp/GRRM/index_e.shtml (accessed date: 1 December 2018). [24] K. Ohno, N. Kishimoto, T. Iwamoto, S. Satoh, Global exploration of isomers and
4. Concluding remarks We have demonstrated the possibility of the existence of the dimerized PAH molecules based on quantum chemical calculations. The investigations of di-PAH structures 1–4 suggested that the stored chemical energies per carbon atom of 1–4 are 55–185 kJ mol−1, which are much larger than those of benzene-dimers (ca. 14–40 kJ mol−1). It is assumed that the same type of dimers can be further explored other than the naphthalene-, perylene-, and coronene-basis ones. Our study suggests that the preferred distance between the monomers would be about 0.14–0.16 nm in the initial structure for geometry optimizations. We would mention an interesting capsule structure that was found in [18]-di-coronene (3). There is a space of ca. 0.3 nm between the upper and lower benzene rings with π-character. Intramolecular excimer-like states can be expected in the excited state of the capsule form. Further investigation of this aspect is also interesting to design a new type of π electron networks based on the di-PAH structures. Acknowledgments The authors thank Professor Waro Nakanishi and Dr. Satoko 153
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Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Research paper
Quantum chemical exploration of dimeric forms of polycyclic aromatic hydrocarbons, naphthalene, perylene, and coronene
T
⁎
Koichi Ohnoa,b, , Hiroko Satohb,c,d, Takeaki Iwamotoa a
Department of Chemistry, Graduate School of Science, Tohoku University, Aramaki, Aza-Aoba, 6-3, Aoba-ku, Sendai 980-8578, Japan Institute for Quantum Chemical Exploration, Kaigan 3-9-15, Minato-ku, Tokyo 108-0022, Japan c Department of Chemistry, University of Zurich, 8057 Zurich, Switzerland d Research Organization of Information and Systems (ROIS), Tokyo 105-0001, Japan b
H I GH L IG H T S
aromatic hydrocarbon dimers were obtained by geometry optimization. • Polycyclic PAH molecules placed in parallel were directly bonded between them. • Two structures with four-membered rings on the side faces were constructed. • Cage dimers were found to be located in sufficiently deep potential energy wells. • PAH • PAH dimers were found to have massive energies larger than two isolated molecules.
A B S T R A C T
We have found dimeric forms of polycyclic aromatic hydrocarbon (di-PAH) molecules by quantum chemical calculations. Geometry optimization starting from short distances of ca. 0.15 nm between two PAH molecules placed in parallel gave cage structures of di-PAH with CC bond connections forming four-membered rings between the PAH molecules. The di-PAH molecules are located in sufficiently deep potential energy wells surrounded by high energy barriers, although their energies are much higher than those of the isolated two PAH molecules.
1. Introduction A carbon atom can be bonded with several atoms to yield various sizes of chains, rings, and cages, which have interesting structures and valuable properties. Many of hydrocarbon and carbon structures, such as benzene, cyclohexane, adamantane, graphene, and diamond, are composed of stable six-membered rings. In some other cases, such as azulene, corannulene, fullerenes, and nano tubes, their carbon skeletons include five-membered rings or seven membered rings. Besides these intensively studied structures with five-, six-, or seven membered rings, another type of structures also with four- or three-membered rings has been explored. For example, hydrocarbons called prismanes C2nH2n, formed by two parallel regular n-gons connected by n rectangular faces, are to be noted due to their peculiar cage structures and high chemical energies [1–6]. Although some prismanes, such as prismane C6H6 [1], cubane C8H8 [2], and pentaprismane C10H10 [3] were really synthesized, many other systems, such as hexaprismane C12H12 [5,6] and the larger analogues have been studied only by theoretical calculations. In connection with hexaprismane C12H12, various benzene ⁎
dimers (C6H6)2 have been studied by quantum chemical calculations [7–10]. Computational explorations revealed fifteen isomeric forms of benzene dimers [8], which include four types of synthesized dimers. Recently, a systematic exploration for the benzene isomers C6H6 on the ground-state potential energy surface (PES) by quantum chemical calculations found numerous numbers, more than two thousand, of isomeric forms [11,12]. In the view of these studies, the search for further new types of hydrocarbon is still challenging. Possible structures for carbon skeletons in hydrocarbon molecules can be related to those for carbons. Carbon structures were classified on the basis of known structures [13], for instance, various fullerene types, prisms, spiral chains, zigzag tubes, double layers, and diamond-like structures. More recently, quantum chemical calculations suggested the existence of a new class of carbon allotropes with four-membered rings [14–17]: A prism-C2n series (n = 8–10, 12, 14, 16, 18 and 20) like hamster wheels [14] can be related to the [n]-prismanes C2nH2n (n = 3–10) [6]. The prism-C2n structures can connect to each other by facing at four-membered rings to give various sheet structures called the prism-C2n sheets (n = 6, 8, and 12) [15]. The prism-C12 sheet
Corresponding author at: Department of Chemistry, Graduate School of Science, Tohoku University, Aramaki, Aza-Aoba 6-3, Aoba-ku, Sendai 980-8578, Japan. E-mail address: [email protected] (K. Ohno).
https://doi.org/10.1016/j.cplett.2018.12.034 Received 8 November 2018; Received in revised form 4 December 2018; Accepted 12 December 2018 Available online 26 December 2018 0009-2614/ © 2018 Elsevier B.V. All rights reserved.
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Fig. 1. Hexagonal carbon skeletons of polycyclic aromatic hydrocarbons (PAHs). (a) Naphthalene C10H8, (b) perylene C20H12, (c) coronene C24H12. Carbon atoms are conventionally numbered so as to be common in the three cases.
representative PAH with fully convex perimeters. The study on acene dimerization [28] investigated various dimers, which have two bonds in between, for naphthalene, anthracene, pentacene, and heptacene, but no study on the dimers with more than two bonds has been yet reported. As will be shown, our quantum chemical calculations predicted that those structures have high energy but can exist in a deep potential energy well surrounded by high energy barriers.
corresponds to a honeycomb shaped double carbon layers with covalent CC-bond connections between two graphene sheets [13], and it may be related to face-fused poly-hexaprismanes. The prism-Cn tubes are carbon allotropes with four-membered rings on the side faces and axially piled up n-membered carbon polygons (n = 3–8, 10, 12, 14, 16, 18, and 20) [16]. The prism-Cn tubes can be related to poly[n]prismanes (n = 3–6) [5]. The wavy carbons with condensed four-membered rings were also found by quantum chemical calculations [17]. In connection with the above studies, interactions between two benzene molecules [10] should be noted. Intermolecular π/π interactions between two benzene molecules cause weak attraction due to van der Waals forces at interplane distances of ca. 0.37 nm. In shorter distance around 0.25–0.30 nm, the exchange repulsion between the two aromatic molecules rises. However, once they come much closer at ca. 0.16 nm, strong covalent interactions take over, which yield cyclodimers of benzenes [10]. Considering the existence of the covalent bonds between polygons in [n]-prismanes and prism-C2n, covalent interactions between polycyclic aromatic hydrocarbon (PAH) molecules are also expected to obtain at such a short distance. Regarding computational methods, automatic explorations on PES for all the possible isomeric structures and transition state structures, as well as reaction pathways had been a significantly difficult issue. In recent two decades, a global exploration of equilibrium structures (EQ), transition state structures (TS), and dissociation channels (DC) on PES for a given chemical composition became possible by the global reaction route mapping (GRRM) techniques [18–23]. Based on the GRRM techniques, many studies concerning explorations on PES [11,12,14–17,24–27] were performed. The GRRM techniques are useful not only to list up EQ, TS and DC but also to determine the lowest energy barrier from an EQ, which gives essential information on the stability of the EQ. The capability accomplishing these tasks is a notable advantage of the GRRM techniques. In this study, we have explored hydrocarbon structures with fourmembered rings in a cage form by using the GRRM program [23]. They consist of a pair of PAH structures placed in parallel, which have many bonds between them. We have investigated dimers of naphthalene C10H8 as the smallest PAH in polyacene systems, perylene C20H12 as a typical PAH with concave perimeters, and coronene C24H12 as a
2. Methods and calculations 2.1. Calculation methods All the electronic state calculations in this study were performed for the ground singlet states, by using the Gaussian 09 program package [29]. The energy minimization procedures were performed at a very tight level by using the GRRM program (GRRM14) [23]. The ultrafine grids were used for density calculations. At the minimum point, all the Hessian eigenvalues were confirmed to be positive. We employed the density functional theory (DFT) with the B3LYP exchange-correlation functional based on our experiences in quantum chemical explorations of H3CNO3 [24], formaldehyde clusters [25], and prism-carbon structures [14–17]. Through the comparative studies with thirty-eight levels of the HF, DFT, MP2, and CCSD(T) methods, the computed molecular structures were well confirmed to be acceptable, and the geometry at B3LYP, BLYP, and MP2 was found to be fairly similar even with different basis sets [30], although subtle differences of energies between isomers by DFT were observed. This is because of insufficient interactions due to dispersion forces [30]. We coped with the problem by using the DFT-D3 method for dispersion corrections, which was developed by Grimme and co-workers to remove the drawback of DFT [31,32] and was confirmed to yield very good agreement with the CCSD(T)/CBS benchmark data [33]. The DFT(B3LYP)-D3 method gave also sufficient results in the study of formaldehyde clusters [25]. DFT calculations can sometimes give insufficient results especially for radical pair regions of PES. As far as our experiences of PES-searches, non-radical characters of H3CNO3 were thoroughly and efficiently searched with B3LYP calculations [24]. Therefore, we decided to use the DFT (B3LYP) method supplemented 148
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We assumed that the formation of separated benzene rings in the capsule form should be due to insufficient interactions between the central rings at the distance of 0.150 nm. Therefore, we carried out further geometry optimization starting with an initial vertical distance 0.140 nm and obtained the fully bonded di-coronene, [24]-di-coronene (4) (Fig. 2) as expected. All of the optimized structures with the D3-dispersion corrections were similar to those obtained without dispersion corrections. The geometrical structures obtained at the B3LYP-D3/cc-pVDZ level were also fairly the same as those obtained at the B3LYP-D3/6-31G(d) level. The interatomic distances and the HOMO/LUMO levels obtained at the B3LYP-D3/cc-pVDZ level were summarized in Table 1. The geometry optimization for 1 was done also at the B3LYP-D3/ccpVTZ and B3LYP-D3/aug-cc-pVTZ levels. Slight differences were found in the energy, but the geometrical structures at the levels of B3LYP-D3/ cc-pVTZ and B3LYP-D3/aug-cc-pVTZ were found to be nearly the same within three digits as those at the level of B3LYP-D3/cc-pVDZ, as can be seen in Table S1 of Supplementary data. Thus, we decided that the geometry optimization at the level of B3LYP-D3/cc-pVDZ would give relevant geometrical structures also for the larger systems of di-perylene and di-coronene. All of the CC bond lengths for the fully-bonded di-PAHs (1, 2, 4) are in the range of 0.154–0.159 nm, which correspond to a CC single bond. All of the carbon atoms in 1, 2, and 4 are bonded with four atoms. However, the carbon atoms in the central hexagonal rings of [18]-dicoronene (3) (C4, C5, C6, C19, C20, C11, C4′, C5′, C6′, C19′, C20′, and C11′) are bonded to three C atoms with bond length of 0.142 nm (e.g. C4-C5 in Table 1), and there are no bond between Cn and Cn′ (n = 4, 5, 6, 19, 20, and 11). As can be seen in Table 1, the distance C4-C4′ 0.286 nm is longer than the CC single bonds of C1-C2, C2-C3, C3-C4, C1-C1′, and C3-C3′ (0.151–0.166 nm) and the CC bond of C4-C5 (0.142 nm). This C4-C4′ distance of 0.286 nm is similar to the typical interatomic distance for a non-bonded carbon atom pair at the para position of benzene ring and is much shorter than the typical van der Waals CC distance of 0.335 nm between adjacent graphene layers in graphite. The electron density analysis of 3 showed bond critical points with electron densities of ca 0.19–0.25 au for CC single bonds and rather higher electron density of ca. 0.29 au for the CC bonds at the central hexagonal rings (C4-C5) (Table 1), whereas no bond critical point was obtained for C4-C4′ between two central rings. The results of the electron density analysis with QTAIM can be referred in Fig. S1 of Supplementary data. As can be seen in Table 1, the energy gaps between the HOMO and LUMO levels for fully bonded di-PAHs decrease from 5.885 eV (1) to 3.634 eV (4) associated with the system sizes increasing. However, the HOMO-LUMO gap of 3 (4.089 eV) is much larger than that of 4 (3.634 eV), which reflects the larger stabilization of HOMO (−1.267 eV) with respect to the case of LUMO (−0.812 eV) in 3 in comparison with that of 4. The shapes of the HOMO and LUMO of 3 can be seen in Fig. S2 of Supplementary data. The electron densities for the HOMO and LUMO at the outer part of the central hexagonal rings exhibit characteristic shapes of the respective π orbitals of benzene, although some electron distributions can be seen along the CC skeletons due to through-bond interactions.
with the dispersion corrections (D3) to investigate the PAH dimers concerned with non-radical systems. 2.2. Geometry optimizations of PAH dimers Fig. 1 shows the carbon skeletons of naphthalene, perylene, and coronene with their numbering. Geometry optimization calculations were started from a pair of PAH molecules that are placed in parallel with a vertical distance of 0.150 nm. The distance of 0.150 nm was chosen, because the CC bond lengths connecting two polygon carbon rings were found to be ca. 0.146–0.161 nm in the previous studies of carbon allotropes [14–17,26]. The initial CC and CH bond lengths and all of the bond angle were set to be 0.144 nm, 0.110 nm, and 120°, respectively. 2.3. Explorations of the lowest energy barrier In order to know the stability of each of the minimum structures, we have explored the lowest energy barrier from the structure on the PES. To find the lowest energy barrier, reaction pathways leading to TS and DC around the respective EQ need to search. The search of such vast regions of PES is usually a highly time-consuming task, but the anharmonic downward distortion following (ADDF) method [18–21], which is one of the GRRM techniques implemented in the GRRM program [23], allows us to do this efficiently: One of the notable functions of the ADDF method is to find a neighboring EQ structure via a TS at the lowest energy barrier. This function works by following large anharmonic downward distortion (LADD option) to avoid tracing energetically high barriers and by focusing only on finding the neighboring minima (FirstOnly option). We set LADD = 3 to select only three ADD routes from the largest one. Examples of input data using the above options of the GRRM program were listed in Supplementary data. All of the reactions were explored as the intrinsic reaction coordinate (IRC) pathways. The B3LYP-D3/6-31G(d) level was used for the estimation of the lowest energy barriers. For the small systems of naphthalene and perylene dimers, the heights of the energy barrier were refined at the B3LYP-D3/cc-pVDZ level. We determined the energy for the molecules including the zero-point energy (ZPE) correction. 2.4. Electron density analysis We confirmed chemical bonds by electron density analysis in the scheme of the quantum theory of atoms in molecules (QTAIM) [34], which is implemented in the AIM2000 software [35]. The bond critical points on the bond paths were obtained by the electron density analysis at the level of B3LYP/cc-pVDZ. 3. Results and discussion 3.1. Di-PAH molecules The initial trials of the geometry optimization of the PAH dimers of naphthalene, perylene, and coronene at the B3LYP/6-31G(d) level successfully gave dimers (di-PAHs), in which all of the perimeter carbon atoms are bonded between the two PAH molecules. We name these dimers [10]-di-naphthalene (1), [20]-di-perylene (2), and [18]-di-coronene (3), respectively (Fig. 2), where the number in each of the square brackets indicates the number of the CC bonds between the two PAH molecules. Namely, [10]-di-naphthalene (C10H8)2 and [20]-di-perylene (C20H12)2 means that all of the carbon atoms in one PAH connect to the corresponding carbon atoms in the counterparts. In [18]-di-coronene (C24H12)2, eighteen pairs of carbon atoms at the perimeters connect to each other between the PAH sheets, but the rest of six pairs of carbons at the central hexagonal rings do not connect, which makes a capsulelike space between the PAH structures.
3.2. Structural stabilities Figs. 3–6 show the energy profiles associated with the reaction from the respective di-PAH to a deformed structure via the lowest TS for each of the optimized di-PAHs (1–4). The absolute energy in Hartree and the energy relative to the lowest ones in kJ mol−1 are shown without the ZPE corrections. The relative path lengths along the IRCs are shown with respect to the TSs. The energy profiles for 1 and 2 were obtained at the level of B3LYP-D3/cc-pVDZ, whereas those for 3 and 4 were obtained at the level of B3LYP-D3/6-31G(d) to reduce the computation 149
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Fig. 2. Dimerized PAHs 1–4. (1) [10]-di-naphthalene (C10H8)2 (D2h), (2) [20]-di-perylene (C20H12)2 (D2h), (3) [18]-di-coronene (C24H12)2 (D6h), (4) [24]-di-coronene (C24H12)2 (D6h). Table 1 Interatomic distances and HOMO/LUMO levels of di-PAHs 1–4.a,b [10]-di-naphthalene 1 C1-C2 C2-C3 C3-C4 C4-C5 C5-C10 C1-C10 C4-C11 C1-H1 C2-H2 C3-H3 C1-C1′ C2-C2′ C3-C3′ C4-C4′ C5-C5′ C10-C10′ HOMO LUMO
0.156 0.157 0.156 0.155 0.156 0.155
(0.231) (0.226) (0.231) (0.231) (0.222) (0.231)
0.110 0.110 0.110 0.159 0.156 0.156 0.159 0.156 0.156 −4.970 0.915
(0.270) (0.271) (0.271) (0.221) (0.234) (0.234) (0.221) (0.249) (0.249)
[20]-di-perylene 2 0.156 0.157 0.156 0.157 0.156 0.155 0.157 0.110 0.110 0.110 0.159 0.156 0.159 0.156 0.158 0.156 −4.148 0.410
(0.228) (0.227) (0.227) (0.222) (0.224) (0.221) (0.221) (0.270) (0.272) (0.272) (0.221) (0.227) (0.222) (0.248) (0.243) (0.249)
[18]-di-coronene 3
[24]-di-coronene 4
0.154 0.154 0.151 0.142 0.151 0.154 0.142 0.110 0.110
(0.242) (0.241) (0.250) (0.291) (0.250) (0.241) (0.291) (0.271) (0.271)
0.157 0.156 0.154 0.155 0.154 0.156 0.155 0.110 0.110
(0.224) (0.227) (0.227) (0.228) (0.227) (0.227) (0.228) (0.274) (0.274)
0.157 0.157 0.166 0.286 0.286 0.166 −5.103 −1.014
(0.227) (0.227) (0.193)
0.159 0.159 0.156 0.158 0.158 0.156 −3.836 −0.202
(0.226) (0.226) (0.250) (0.246) (0.246) (0.250)
(0.193)
a
Interatomic distances are given in nm, and orbital energies are given in eV for the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). Electron densities at bond critical points are given in parentheses in the atomic unit. b C-atom is labelled as Cn for the upper one or Cn′ for the lower one, with the numbering n in Fig. 1. H-atom is labelled as Hn, where n is for Cn in the respective CH bond.
time. The ADDF method can find DCs if they exist, but no DCs lower than the respective TS in Figs. 3–6 were found. The lowest height of the barrier around 1 is ca. 118 kJ mol−1 after the ZPE correction. The barrier of 100 kJ mol−1 gives a Boltzmann factor (BF) of 3.9 × 10−18 at 300 K, therefore, thermal decomposition of 1 is considered to be improbable at the ambient temperature of ca. 300 K. When BF increases to 2.4 × 10−3 at 2000 K, 1 may be isomerized into a deformed structure [9]-di-naphthalene (5) in Fig. 3,
which shows bond breaking at C1-C1′. The reverse barrier from 5 to 1 is only 10.1 kJ mol−1 (BF = 0.017 at 300 K), therefore, 5 would easily go back to 1. Further exploration of the reaction pathways around 5 gave the lowest barrier of 1.3 kJ mol−1 leading to [6]-di-naphthalene (Cs), which is much more stable than 1. We did not go further exploration in this study, but it is technically possible to explore further deformation reactions by using the ADDF method as shown in the study on C16 isomers [27]. 150
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Fig. 3. Energy profile of the reaction pathway of [10]-di-naphthalene 1 to a deformed form [9]di-naphthalene 5 via the lowest energy barrier TS. The vertical dotted line indicates the position of the barrier (TS). The barrier height from 1 to TS is 127.5 kJ mol−1 (117.7 kJ mol−1 with ZPE correction), and the reverse barrier height from 5 to TS is 8.4 kJ mol−1 (10.1 kJ mol−1 with ZPE correction).
respect to 4 (Fig. 6). The deformed structure 8 is a form of [20]-dicoronene, which has four less bonds by breaking at C6-C6′, C5-C5′, C4C4′, and C11-C11′ between the upper and the lower parts of 4. Such a large structural deformation makes many kinks in the energy profile from the TS to 8 in Fig. 6. It is noteworthy that the deformed structure 8 still keeps two CC bonds at C19-C19′ and C20-C20′. Thus, 8 is expected to deform further to [18]-di-coronene (3) with large release of energy of 730.9 kJ mol−1. This indicates that 3 is much more stable than 4 with a very large decrease in energy of 1894.6 kJ mol−1.
The energy profile for 2 (Fig. 4) shows also a high barrier from 2 to a deformed structure [19]-di-perylene (6) (164.1 kJ mol−1) and a low barrier from 6 to 2 (6.8 kJ mol−1), which indicates that 2 is stable enough to exist in the equilibrium geometry at the ambient temperature of ca. 300 K. The deformed structure 6 shows a bond breaking at C2-C2′ between the upper and the lower parts. Contrary to the cases of 1 and 2, the both barriers from 3 to its deformed structure 7 (250.6 kJ mol−1) and from 7 to 3 (217.9 kJ mol−1) are considerably high (Fig. 5). The deformed structure 7 shows bond breakings at C1-C10 and C1′-C10′. The capsule structure 3 is thus expected to be highly stable. [24]-di-coronene 4 shows a sufficiently high energy barrier (127.8 kJ mol−1), which would not be easily surmounted at the ambient temperature of ca. 300 K, whereas the deformed structure 8 is located at a substantially low energy level (−1163.7 kJ mol−1) with
3.3. Stored chemical energy The energies of di-PAHs are higher than those of the isolated two PAHs, that means, di-PAHs store higher chemical energy. As listed in Table 2, the larger the size of PAH becomes, the larger the relative Fig. 4. Energy profile of the reaction pathway of [20]-di-perylene 2 to a deformed form [19]-diperylene 6 via the lowest energy barrier TS. The vertical dotted line indicates the position of the barrier (TS). The barrier height from 2 to TS is 173.9 kJ mol−1 (164.1 kJ mol−1 with ZPE correction), and the reverse barrier height from 6 to TS is 5.5 kJ mol−1 (6.8 kJ mol−1 with ZPE correction).
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Fig. 5. Energy profile of the reaction pathway of [18]-di-coronene 3 to a deformed form 7 via the lowest energy barrier TS. The vertical dotted line indicates the position of the barrier (TS). The barrier height from 3 to TS is 266.2 kJ mol−1 (250.6 kJ mol−1 with ZPE correction), and the reverse barrier height from 7 to TS is 222.9 kJ mol−1 (217.9 kJ mol−1 with ZPE correction).
parts and the existence of the shorter CC bonds with the unsaturated character in the middle parts of the capsule structure of 3.
energies with respect to the isolated two PAH molecules get. To see more details, the chemical energies stored in 1–4 are normalized with the number of carbon atoms. The normalized chemical energy per carbon atom was found to increase from 1 (55 kJ mol−1) to 4 (185 kJ mol−1). Such large amount of normalized chemical energy is comparable to those of carbon allotropes with four-membered ring structures (100–350 kJ mol−1) [14–17,26]. The high amount of chemical energy mainly comes from atypical sp3 bond angles at the tetravalent carbon atoms, where the CH bonds are much less strained in comparison with the CC bonds that rigidly forms the carbon skeletons. The ordering of the normalized chemical energies of the fully-bonded di-PAHs (1, 2, 4) is 1 < 2 < 4, which corresponds to the number of the CH bonds, which are expected to reduce the strain of the cage structures. The large difference of the normalized chemical energies between 3 and 4 can be ascribed to the loss of the highly strained CC bonds between the upper and the lower
3.4. Partly bonded dimers We have scanned the outcome of the structure optimization starting from different distances between two naphthalene molecules from 0.16 to 0.30 nm at the level of B3LYP-D3/cc-pVDZ. The results were: (1) the initial distance of 0.16 nm gave the same outcome [10]-di-naphthalene as that started from 0.15 nm; (2) the initial distances of 0.17–0.24 nm gave partly bonded dimers, such as [2]-dimer, [4]-dimer, [6]-dimer, [8]-dimer and [10]-dimer; (3) the initial distances of 0.25 and 0.30 nm gave no covalent-dimers but van der walls dimers ([0]-dimer). The detailed data are contained in Table S2 of Supplementary data. We did not perform the scanning for the larger systems of perylene or coronene dimers in this study but assume that they would give a similar Fig. 6. Energy profile of the reaction pathway of [24]-di-coronene 4 to a deformed form [20]-dicoronene 8 via the lowest energy barrier TS. The vertical dotted line indicates the position of the barrier (TS). The barrier height from 4 to TS is 138.4 kJ mol−1 (127.8 kJ mol−1 with ZPE correction), and the reverse barrier height from 8 to TS is 1319.8 kJ mol−1 (1291.5 kJ mol−1 with ZPE correction).
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Table 2 Energies of di-PAHs 1–4.a
Electronic energy/Hartree
b
−1c
Relative energy/kJ mol Normalized chemical energy per one carbon atom/kJ mol−1d a b c d
[10]-di-naphthalene 1
[20]-di-perylene 2
[18]-di-coronene 3
[24]-di-coronene 4
−771.438065 (−771.854291) 1092.802 54.640
−1537.920850 (−1538.958866) 2725.310 68.133
−1842.534306 (−1843.971681) 3773.828 78.621
−1840.593881 (−1843.971681) 8868.413 184.759
Energies calculated at the level of B3LYP-D3/cc-pVDZ without the ZPE corrections. Energies for isolated pair of respective PAH molecules are listed in parentheses Relative energies with respect to the isolated pair of respective PAH molecules. Relative energies normalized with the number of carbon atoms.
Hayashi, at Wakayama University for technical advises to use AIM2000. H.S. and K.O. were supported by “Challenging Exploratory Research Projects for the Future” grant from ROIS (Research Organization of Information and Systems), Japan.
tendency. 3.5. Possibility of existence Our calculations suggested that the dimerized PAH molecules 1–4 have 1093–8868 kJ mol−1 higher energy relative to the isolated two PAH molecules but can exist stably enough in an energy well, which is deeper than 100 kJ mol−1. Aromatic hydrocarbon molecules are so stable that its dimerization reaction requires a certain amount of positive energy from the outside as an endothermic reaction. A typical example is a dimerization of benzene molecules that produces 6-prismane and some others [9]. The reaction requires energy absorption of 170 – 480 kJ mol−1. The intermolecular force between aromatic hydrocarbon molecules in short distance had been considered to be repulsive, however, this study on diPAHs 1–4 suggests that attractive force can take over the repulsive force under high pressure. The repulsive force between two naphthalene molecules at distances of 0.15–0.25 nm is estimated to be ca. 4 × 10−8 N, which corresponds to ca. 60 GPa for the molecular area of ca. 7 × 10−19 m2. The Gibbs energy change from the naphthalene dimer 1 to TS (Fig. 3) calculated at the B3LYP-D3/cc-pVDZ level was 112.57 kJ mol−1 at 298.15 K 1 atm and 97.03 kJ mol−1 at 1000 K 100 atm. These large values indicate that 1 can exist at the high-temperature and highpressure condition. In the mechanical point of view, the carbon skeletons of the PAH dimer molecules are formed with tough covalent CC single bonds like diamonds, which are often used as a pressing tool to make ultra-high pressure. Therefore, PAH dimers 1–4 are expected to stably exist not only at an ambient condition but also at a high-temperature and high-pressure atmosphere.
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4. Concluding remarks We have demonstrated the possibility of the existence of the dimerized PAH molecules based on quantum chemical calculations. The investigations of di-PAH structures 1–4 suggested that the stored chemical energies per carbon atom of 1–4 are 55–185 kJ mol−1, which are much larger than those of benzene-dimers (ca. 14–40 kJ mol−1). It is assumed that the same type of dimers can be further explored other than the naphthalene-, perylene-, and coronene-basis ones. Our study suggests that the preferred distance between the monomers would be about 0.14–0.16 nm in the initial structure for geometry optimizations. We would mention an interesting capsule structure that was found in [18]-di-coronene (3). There is a space of ca. 0.3 nm between the upper and lower benzene rings with π-character. Intramolecular excimer-like states can be expected in the excited state of the capsule form. Further investigation of this aspect is also interesting to design a new type of π electron networks based on the di-PAH structures. Acknowledgments The authors thank Professor Waro Nakanishi and Dr. Satoko 153
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