Three-Dimensional Carbon Allotropes Comprising Phenyl Rings and Acetylenic Chains in sp+sp2 Hybrid Networks

We here identify by ab initio calculations a new type of three-dimensional (3D) carbon allotropes that consist of phenyl rings connected by linear acetylenic chains in sp+sp2 bonding networks. These structures are constructed by inserting acetylenic or diacetylenic bonds into an all sp2-hybridized rhombohedral polybenzene lattice, and the resulting 3D phenylacetylene and phenyldiacetylene nets comprise a 12-atom and 18-atom rhombohedral primitive unit cells in the symmetry, which are characterized as the 3D chiral crystalline modification of 2D graphyne and graphdiyne, respectively. Simulated phonon spectra reveal that these structures are dynamically stable. Electronic band calculations indicate that phenylacetylene is metallic, while phenyldiacetylene is a semiconductor with an indirect band gap of 0.58 eV. The present results establish a new type of carbon phases and offer insights into their outstanding structural and electronic properties.

porous aromatic frameworks (PAFs) via inserting rigid phenyl rings into all the C-C bonds of diamond was reported [33][34][35] . These studies open a new approach to constructing 3D covalent carbon network structures.
In this work we report ab initio total-energy and phonon calculations [36][37][38][39][40][41] that predict a new type of 3D carbon phases in R m 3 (D d 3 5 ) symmetry constructed by inserting linear acetylenic chains into an sp 2 -hybridized rh6 polybenzene lattice 3 . The resulting 3D network structures of phenylacetylene and phenyldiacetylene consist of benzene rings bonding together with acetylene or diacetylene, which topologically correspond to 2D graphyne and graphdiyne, respectively. They are energetically more favorable than the sp-hybridized 1D carbyne chains and the recently reported sp+ sp 3 -hybridized 3D diamondyne, and they are all dynamically stable. Moreover, 3D-phenylacetylene is metallic and 3D-phenyldiacetylene is semiconductor with an indirect band gap of 0.58 eV, in contrast to the semimetallic nature of graphite. These results provide new insights for the development of novel carbon allotropes.

Results and Discussion
We first present the structural characterization of the simplest 3D phenylacetylene network constructed by inserting triple (-C≡ C-) yne-bonds into the rh6 polybenzene lattice (see Fig. 1a), as well as the so-called 2D graphyne by inserting triple yne-bonds into an expanded graphene sheet 21 . This new carbon phase has a R m 3 (D d 3 5 ) symmetry as that of rh6 polybenzene 3 and topologically corresponds to 2D γ-graphyne 24 . In the hexagonal representation, it has a 36-atom hexagonal unit cell (see Fig. 1b) with lattice parameters a = 11.6050 Å, c = 3.6443 Å, occupying the 18h1 (0.8579, 0.9289, 0.4849) and 18h2 (0.8617, 0.7233, 0.6021) Wyckoff positions. The carbon atoms on the 18h1 sites form three benzene rings, as in rh6 carbon, with aromatic sp 2 hybridization, while the carbon atoms on the 18h2 sites form nine triple yne-bonds located between the benzene rings with an ethyne-type sp-hybridization. As in rh6 carbon 3 , this structure also can be regarded as a three-dimensional chiral crystalline modification of carbyne connected via zigzag benzene rings with alternating single, triple and aromatic carbon-carbon bonds. It contains three distinct carbon-carbon bond lengths, a longer bond of 1.433 Å (C 1 -C 1 ) in the benzene rings and two shorter bonds of 1.389 Å (C 1 -C 2 ) and 1.232 Å (C 2 -C 2 ) associated with the single and triple bond in carbyne chains, respectively. Meanwhile, there are three different bond angles, 171.13° for ∠C 1 -C 2 -C 2 along the carbyne chains, 119.39° for ∠C 1 -C 1 -C 1 inside and 120.21° for ∠C 1 -C 1 -C 2 out of the zigzag benzene rings, respectively. On the other hand, in the rhombohedral representation, it has a 12-atom primitive unit cell with equilibrium lattice parameters a = 6.8094 Å, α = 116.889°, occupying the 6 h (0.3428, 0.5560, 0.5560) and 6 h (0.4638, 0.4638, 0.8788) position, thus this 3D-phenylacetylene is also termed as rh12 carbon.
The construction of 3D-phenylacetylene can also be applied to design a 3D-phenyldiacetylene network (see Fig. 1c) by inserting butadiyne (-C≡ C-C≡ C-) segments between the benzene rings in the rh6 polybenzene lattice. The resulting structure has a 54-atom hexagonal unit cell with an equilibrium lattice parameters a = 16.0963 Å, c = 4.1987 Å, occupying the 18h1 (0.1023, 0.0511, 0.5065), 18h2 (0.1008, 0.8992, 0.4507), and 18h3 (0.1435, 0.8565, 0.3755) Wyckoff positions. The carbon atoms on the 18h1 sites form three benzene rings, while the carbon atoms on the 18h2 and 18h3 sites form nine diyne-bonds. This 3D network structure has a R m 3 symmetry as in rh6 carbon, and topologically corresponds to 2D graphdiyne 24 , thus there are four distinct carbon-carbon bond lengths, a longer bond of 1.427 Å (C 1 -C 1 ) is associated with the carbon atoms in the benzene rings and three shorter bonds of 1.395 Å (C 1 -C 2 ), 1.233 Å (C 2 -C 3 ), and 1.338 Å (C 3 -C 3 ) are along the chains between the benzene rings. Note that the carbon chains are not perfectly linear with the bond angles of 172.54° for ∠C 1 -C 2 -C 3 and 180° for ∠C 2 -C 3 -C 3 . In the rhombohedral representation, it has an 18-atom primitive unit cell, thus it also termed as rh18 carbon. The two new structures introduced here represent a new type of carbon allotropes that consist of phenyl rings connected by linear acetylenic chains in sp+ sp 2 bonding networks.
The total energies of rh12 phenylacetylene and rh18 phenyldiacetylene as a function of volume are shown in Fig. 2 in comparison with the results for diamond, graphite, rh6 carbon, carbyne, and diamondyne. Our calculated energetic data establish the stability sequence: diamondyne < carbyne < rh18 < rh12 < rh6. It is clearly seen that the rh12 and rh18 polybenzene-ynes are located between the energy range for rh6 carbon and carbyne, with an energy gain of about 0.07 eV per atom, while the diamondyne is out of the energy range, and even less favorable than carbyne.
By fitting the calculated total energy as a function of volume to Murnaghan's equation of state 42 , we obtain the bulk modulus (B 0 ) of rh12 and rh18 carbon as 195 and 129 GPa, respectively. The atomic densities are estimated to be 2.50, 1.69, and 1.14 g/cm 3 for rh6, rh12, and rh18 carbon, respectively, which are considerably different from 3.51 g/cm 3 for diamond and 2.27 g/cm 3 for graphite. We can see that with increasing of the acetylenic chain length, the atomic density and bulk modulus are decreasing to a level even lower than those of graphite. The calculated equilibrium structural parameters, total energy, and bulk modulus for diamond, rh6 polybenzene, rh12-phenylacetylene, rh18-phenyldiacetylene, and graphite are listed in Table 1 and compared to available experimental data 43 .
We next examine the dynamic stability of the 3D sp+ sp 2 bonding networks by phonon mode analysis. Figure 3a shows the phonon band structures and density of state (DOS) for the 3D phenylacetylene. The obtained phonon eigenvalues can be explained well by considering the bonding nature of the phenyl and triple carbon-carbon bonds. The vibrational modes due to the triple yne-bond can be observed clearly around 2150 cm −1 with the carbon-carbon bond length of 1.232 Å (C 2 -C 2 ) and the vibrational modes due to the phenyl bonds are distributed around 1500 cm −1 with the carbon-carbon bond length of 1.433 Å (C 1 -C 1 ). The combination modes of phenyl and triple bonds of carbon atoms can be seen clearly below 730 cm −1 . No imaginary frequencies were observed throughout the entire phonon band structures, thus confirming the dynamic stability of the 3D-phenylacetylene. Meanwhile, there is a large phonon band gap in the frequency range of 1500

Structure
Method Diamond and 2100 cm −1 . Similar dynamic stability and vibrational modes are also confirmed for 3D phenyldiacetylene as shown in Fig. 3b. However, in the latter case there are two yne-modes around 2148 and 2193 cm −1 due to the diyne bonds related to the C 2 and C 3 carbon atoms.
To further examine the thermal stability, we have also performed ab initio molecular dynamics simulations using a 1 × 1 × 2 hexagonal supercell, which contains 6 primitive cells. After being heated at room temperature (300 K) and 1000 K for 3 ps with a time step of 1 fs, no structural changes occurred for both rh12 and rh18 carbon. These results show that rh12 and rh18 carbon are viable carbon allotrope for experimental synthesis. . Results for rh12 phenylacetylene (a) and rh18 phenyldiacetylene (b). The spectra due to the triple bonds and phenyl bonds occur around 2150 cm −1 and 1500 cm −1 , respectively. A clearer picture for the low vibrational modes is given in Fig. S1 in Supplementary Information. Figure 4 shows the calculated electronic band structures and projected density of states (PDOS) by using the hybrid functionals (HSE06) 39 . The calculated band gap for diamond is about 5.36 eV, which is closed to the experimental data of 5.47 eV 43 , indicating the validity of the HSE06 method in predicting the band gaps for diamond and related sp 3 bonded carbon structures. For 3D-phenylacetylene, as shown in Fig. 4a, there are three bands around the A, K and M points across the Fermi level, resulting in the metallic nature of the system. Meanwhile, for 3D-phenyldiacetylene, as shown in Fig. 4b, the conduction band minimum and valence band maximum are located at the L and Γ point, respectively, showing a semiconductor character with an indirect band gap of 0.58 eV. Moreover, from the PDOS, we can see that the states around the Fermi level are mainly coming from the 2p orbitals, which define the metallic nature for phenylacetylene and the band gap for phenyldiacetylene.
To understand the bonding nature of electrons in both rh12 and rh18 carbon, the electron density difference (EDD) and electron localization function (ELF) maps are illustrated in Fig. 5. The EDD maps represent the variation of electron density in terms of chemical bonding. One can make an EDD plot by subtracting the overlapping  [44][45][46] , which was initially proposed by Becke and Edgecombe 45 based on Hartree-Fock theory, and generalized by Savin et al. 46 based on density functional theory. From the EDD maps shown in Fig. 5a,b, we can be seen that there is a larger gain of electron density between triple bonded carbons. Meanwhile, from the ELF maps shown in Fig. 5c,d, we can see that the electrons are well localized along the carbon chain, and the enhanced localization between triple bonded carbons can be seen clearly, which is more than the localization between the single and aromatic bonded carbons. These results show the strong triple bonding nature in the sp+ sp 2 hybrid networks. Furthermore, to understand the aromaticity in the phenyl rings, the nuclear-independent chemical shift NICS(0) at the center of the phenyl rings are calculated using the gauge-including atomic orbital (GIAO) method at the B3LYP/6-311 + G(d,p) level 47 . The NICS(0) values are estimated to be − 8.16 ppm for benzene, − 5.23 ppm for rh12 carbon, and − 6.57 ppm for rh18 carbon. These results show that the aromaticity in phenyl rings of rh12 and rh18 carbon are smaller than the aromaticity in benzene.
Finally, we plot in Fig. 6a simulated x-ray diffraction (XRD) patterns for graphite, diamond, rh6 polybenzene, rh12 phenylacetylene, rh18 phenyldiacetylene and and fcc C 60 , compared to the experimental data for chimney soot and detonation soot 48 . It is shown that the main (101) peak at 30° for rh6 should shift to 26° for rh12 and 22.4° for rh18 carbon. The main (101) peak at 26° for rh12 is very close to the main (002) peak at 26.5° for graphite, thus rh12 carbon may coexist with graphite in the detonation soot (see Fig. 6b and the Fig. 2 in ref. 48). On the other hand, for chimney soot, as shown in Fig. 6b, there is a sharp peak at 29.8°, which is fit well by the rh6 (101) diffraction peak, while a broad diffraction around 23°, which matches the rh18 (101) diffraction peak. These results suggest that rh12 and rh18 carbon as well as rh6 carbon may be present in chimney soot, carbon black or detonation soot 48 .

Conclusions
In conclusion, we have identified by ab initio calculations a new type of three-dimensional carbon allotropes that consist of phenyl rings connected by linear acetylenic chains in sp+ sp 2 bonding networks. The resulting 3D phenylacetylene and phenyldiacetylene network structures in R m 3 (D d 3 5 ) symmetry are topologically corresponding to 2D graphyne and graphdiyne, respectively, and they are energetically more favorable than the sp-hybridized 1D carbyne chains and the recently reported sp+ sp 3 -hybridized 3D diamondyne. Phonon calculations show that these newly predicted structures are all dynamically stable. Electronic band and density of states calculations indicate that 3D-phenylacetylene with acetylenic yne-bonds is metallic, while 3D-phenyldiacetylene with diacetylenic yne-bonds is a semiconductor with an indirect band gap of 0.58 eV. Moreover, a detailed XRD analysis shows that phenylacetylene and phenyldiacetylene 3D network structures as well as rh6 polybenzene match the experimental diffraction peaks seen in the carbon black, diesel soot or chimney soot 48 . Our findings suggest a novel strategy in constructing carbon framework structures that may help solve the structures of the newly discovered but unidentified carbon phases seen in recent detonation experiments.

Methods
Our calculations are carried out using the density functional theory as implemented in the Vienna ab initio simulation package (VASP) 36 . The generalized gradient approximation (GGA) developed by Armiento-Mattsson (AM05) 37 were adopted for the exchange-correlation potential. The all-electron projector augmented wave (PAW) method 38 was adopted with 2s 2 2p 2 treated as valence electrons. A plane-wave basis set with a large energy cutoff of 800 eV was used. Forces on the ions are calculated through the Hellmann-Feynman theorem allowing a full geometry optimization. The energy minimization is done over the atomic and electronic degrees of freedom using the conjugate gradient iterative technique. Convergence criteria employed for both the electronic self-consistent relaxation and the ionic relaxation were set to 10 −8 eV and 0.01 eV/Å for energy and force, Figure 6. X-ray diffraction (XRD) patterns. (a) Simulated XRD patterns for graphite, diamond, rh6 polybenzene, rh12 phenylacetylene, rh18 phenyldiacetylene, and fcc C 60 . (b) Experimental XRD patterns for chimney soot and detonation soot 48 . The black, green, and red arrows indicate the XRD peaks corresponding to the main peak for rh6, rh12, and rh18 carbon, respectively. X-ray wavelength is 1.5406 Å with a copper source.
Scientific RepoRts | 6:24665 | DOI: 10.1038/srep24665 respectively. A hybrid density functional method based on the Heyd-Scuseria-Ernzerhof scheme (HSE06) 39 has been used to calculate electronic properties. Phonon calculations are performed using the phonopy code 40 based on the supercell approach 41 with a (1 × 1 × 2) 72-atom hexagonal supercell for rh12 and a (1 × 1 × 2) 108-atom hexagonal supercell for rh18 carbon. Ab initio molecular dynamics simulations under constant temperature (300 K and 1000 K) and volume (NVT) were performed to check thermal stability with a time step of 1 fs up to 3 ps. The nuclear-independent chemical shift NICS(0) at the center of the phenyl rings are calculated using the gauge-including atomic orbital (GIAO) method at the B3LYP/6-311 + G(d,p) level 47 as as implemented in Gaussian03.