Electronic Structure, Optical Properties, and Hydrogen Adsorption

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Article pubs.acs.org/JPCC

Electronic Structure, Optical Properties, and Hydrogen Adsorption Characteristics of Supercubane-Based Three-Dimensional Porous Carbon K. Srinivasu and Swapan K. Ghosh* Theoretical Chemistry Section, Bhabha Atomic Research Centre, and Homi Bhabha National Institute, Department of Atomic Energy, Mumbai400 085, India S Supporting Information *

ABSTRACT: Three-dimensional porous carbon materials based on supercubane structure are modeled through first principles based density functional theory calculations. The basic supercubane structure is expanded through the insertion of acetylinic and diacetylinic units between both inter- and intracubane C−C bonds leading to more variety of porous carbon materials. The supercubane is found to be an insulator with an indirect band gap of 5.26 eV and the gap is found to decrease on introducing the acetylinic linking groups between the intercubane C−C bonds. The completely carbomerized supercubane structures are also found to be insulators. We have also calculated the phonon dispersion and the variation in free energy with increasing temperature to verify the stability of the materials considered. The calculated free energy profiles are compared with some of the previously studied carbon allotropes to show the possible thermodynamic stability of these 3D carbon systems. The complex frequency-dependent dielectric constant has been calculated for all the designed structures to study the optical properties such as absorption spectra and energy-loss spectra. As these designed structures are associated with high porosity and reactive carbon sites, we have investigated their hydrogen adsorption properties and it is observed that the expanded supercubanes can adsorb hydrogen with a gravimetric density of ∼2.0 wt %.

1. INTRODUCTION Carbon nanomaterials are found to have versatile applications in different fields of science and technology, such as electronics, optics, drug delivery, energy storage, catalysis, etc.1−4 Carbon is known to form a very large number of compounds because of its ability to bond with itself as well as most of the other atoms in the periodic table. Carbon can also form very long chains with multiple C−C bonds which is famously known as the catenation property. Carbon mainly exists as two natural allotropes, namely graphite and diamond, where graphite is composed of all sp2 carbons and diamond with all sp3 carbons. In recent years, there have been tremendous efforts in designing new porous carbon materials which were shown to have very good hydrogen storage capability because of their high surface area and lightweight.5,6 The remarkable discovery of fullerene by Kroto et al.7 in 1985 started the era of synthetic carbon allotropes. The next family of carbon allotrope is the carbon nanotube synthesized in 1991 followed by graphene in 2004 which consists of all sp2 carbon atoms.8,9 In 1978, a unique allotrope of carbon, the body centered cubic (bcc) carbon was reported by Strel'nitskii et al.10 which is also designated as supercubane. Later, Johnston et al.11 carried out detailed theoretical calculations on the proposed super dense C8 through tight-binding approach. In 2008, Liu et al.12 could synthesize the same bcc carbon through a pulsed-laser induced liquid−solid interface reaction. There are © 2012 American Chemical Society

quite a good number of reports on designing new carbon allotropes which are composed of both sp2 and sp, or sp3 and sp hybridized carbons.13,14 Li et al.15 could synthesize graphdiyne, a 2D carbon allotrope composed of sp and sp2 carbons which is proposed for a large number of applications such as nanoelectronics, energy storage, photocatalysis, gas filtration, etc.16,17 Hence the exploration of new possible carbon allotropes with desired structure and property is an important area of research, and still there might be a good number of unexplored forms of carbon yet to be discovered. In the present study, we have modeled different threedimensional bcc carbon allotropes through the expansion of the supercubane by inserting acetylinic and diacetylinic units between both inter- and intracubane C−C bonds. The C−C triple bond, where the carbons are in sp hybridized form, is found to be an important linking group in many of the carbon scaffold and conjugated hydrocarbons. In 1995, Chauvin18 had defined the new kind of molecular systems, carbomers, where, a sp hybridized C2 unit is inserted into each bond resulting in the expansion of the molecular system with similar geometry and symmetry. Later, a large number of carbo-molecular systems were synthesized and found to have interesting properties as compared to the parent molecules.19,20 In 1966, Hoffmann21 Received: October 22, 2012 Published: October 29, 2012 25015

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Figure 1. Optimized unit cell structures of (a) C12, (b) C32, (c) C48, (d) C80, (e) C96, (f) C128, and (g) C144.

Å−1. The Brillouin zone has been sampled using the automatically generated 4 × 4 × 4 Monkhorst−Pack set of k points.28 As it is known from the literature that the band gap calculated from pure DFT is underestimated, we have also used the hybrid functional B3LYP29 as implemented in Crystal0630 to calculate the band structures. For calculating the hydrogen adsorption in the systems considered here, we have included the dispersion correction as the nature of bonding is weak van der Waals interactions.31 The phonon dispersion along the high symmetry k-path is obtained using the open source package Phonopy.32 The initial geometries and all reported structures have been obtained using the graphic software MOLDEN33 and XCrySDen.34 The hydrogen adsorption energy in these porous carbons (PC) is calculated using eq 1.

proposed novel all-carbon allotropes, cyclo[n]carbons, with a different number of sp hybridized carbons. The cyclo[18] carbon annulene was synthesized by Diederich et al.22 in the year 1989. Though there are many two-dimensional annulenes with CC as a linking group, the 3D structures are rare. Diederich and co-workers23 have synthesized the expanded cubane where they could introduce diacetylinic fragments between all C−C single bonds of the C8 cubane which resulted in a C56 cube. Later, Bachrach24 had carried out a detailed electronic structure calculations on the ethynyl-expanded cubane and found that there is a relaxation in the strain due to the expansion of the cubane bond angle from 90° to 107.5°. We have considered here different cubane based systems, viz. C8, C32, C56 with 0, 1, and 2 −CC− units inserted between each intracubane C−C bond, respectively. We have considered the intercubane C−C bond as well and inserted acetylinic and diacetylinic groups to construct porous carbon allotropes with varying porosity and density. A detailed study on the electronic structure, optical properties, and hydrogen adsorption characteristics has been carried out. To the best of our knowledge, ours is the first density functional theory (DFT)-based study on supercubane-based three-dimensional porous carbon materials and will definitely create interest in the experimental community for synthesizing these porous materials which can have a wide range of applications from catalysis to gas storage.

BE H2 = 1/n{E(PC − (H 2)n ) − [E(PC) + nE(H 2)]} (1)

The imaginary part of the complex dielectric constant is calculated using the relation εαβ 2(ω) =

4π 2e 2 1 limq → 0 2 Ω q

∑ 2Wkδ(εc k − ενk − ω) c ,ν ,k

× ⟨uc k + eαq|uν k ⟩⟨uc k + eβq|uν k ⟩*

where the indices c and v refer to conduction and valence band states, respectively. The real part of the dielectric constant is calculated using the Kramers−Kronig relation as

2. COMPUTATIONAL DETAILS Periodic density functional theory (DFT)-based electronic structure calculations are used for all the studies using the first principles based Vienna ab initio Simulation Package (VASP).25 Projector augmented wave (PAW)26 potentials with a kinetic energy cutoff of 550 eV were employed for all the elements. The exchange-correlation energy density functional, Exc[ρ] has been treated using the generalized gradient approximation (GGA) of Perdew−Burke−Ernzerhof (PBE).27 In all these calculations, the convergence criteria for total energy in the selfconsistent field iteration was set to 1 × 10−6 eV, and the optimizations have been carried out until the Hellmann− Feynman force component on each atom is less than 0.01 eV

εαβ1(ω) = 1 +

2 P π

∫0

∞

εαβ 2(ω′)ω′ ω′2 − ω 2 + iη

dω′

where P denotes the principle value. The loss function, L(ω) is calculated as −Im (1/ε(ω)).

3. RESULTS AND DISCUSSION We have considered different possible three-dimensional carbon allotropes ranging from 16 to 144 carbon atoms per unit cell and all with bcc lattice. In the present work, we have 25016

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along the symmetric k-path of the first Brillouin zone,35 P-Γ-H using PBE as well as B3LYP functionals and the corresponding results are reported in Table 2. The calculated band structures

mainly studied the (i) electronic structure and stability, (ii) optical properties, and the effect of the extent of conjugation on the frequency-dependent dielectric function, and (iii) hydrogen adsorption properties of these carbon allotropes. First, we look at the electronic structure of the considered structures, calculated by using the first-principles-based DFT-based approach as implemented in VASP code. As a starting member for this study, we considered the bcc C8 cubane which is also known as supercubane with 16 carbon atoms per unit cell as shown in Figure 1a. The calculated cell parameter using the PBE functional is found to be 4.877 Å corresponding to a density of 2.75 g/cm3 which is in good agreement with the earlier report.11 The C−C bond lengths of the intracubane bonds are found to be 1.586 Å and that of the intercubane bonds are found to be 1.476 Å. Similar to the graphyne structure, where each C6 ring is connected to six C6 rings through CC linking groups, we connected each C8 cube with other eight such cubes by inserting one CC between each intercubane C−C bond of the supercubane as shown in Figure 1b, and this structure can be called as supercubyne. We have also modeled a supercubdiyne similar to graphdiyne with a diacetylinic unit as linking groups as shown in Figure 1c. The optimized cell parameters for supercubyne and supercubdiyne with 32 and 48 carbon atoms per unit cell are found to be 7.860 and 10.835 Å and the corresponding densities are calculated to be 1.31 and 0.75 g/cm3, respectively. In the case of next member of the series considered, we have inserted acetylinic units between all the C−C (both inter- and intracubane) bonds of the supercubane structure as shown in Figure 1d and this can be considered as the complete carbomerization of the supercubane. The optimized cell parameters of this structure is found to be 10.026 Å with a density of 0.72 g/cm3. The C−C bond length of the acetylinic unit is found to be 1.21 Å which is very close to the carbon− carbon triple bond length while the C(sp3)−C(sp) inter- and intracubane bond lengths are 1.475 and 1.486 Å, respectively. More interestingly, the CCC bond angle at the corner of the cubane is found to expand to 105.93° from 90° in the supercubane. This expansion indicates a relaxation in the strain associated with the supercubane due to the highly compressed 90° angle instead of the sp3 bond angle of 109.5°. The next structure considered consists of 96 carbon atoms per unit cell where the cubane unit is with 32 carbons and diacetylinic unit inserted between the inter cubane C−C bonds as shown in Figure 1e. The optimized cell parameter is found to be 16.004 Å and the corresponding density is calculated to be 0.47 g/cm3. The intra- and intercubane CC bond lengths are found to be 1.210 and 1.218 Å respectively. In the next structure studied, diacetylinic unit is inserted into the intracuabne C−C bonds resulting into a C56 cubane unit and the acetylinic unit is inserted into the intercubane C−C bonds. The optimized cell parameters of this structure with 128 carbon atoms per unit cell are found to be around 18.14 Å and the calculated density is 0.43 g/cm3. The CCC cubane corner bond angle is found to get expanded further to 107.3° leading to the strain relaxation. In the case of the final structure considered, both inter- and intracubane C−C bonds are sandwiched by diacetylinic units as shown in Figure 1f with a total of 144 carbon atoms per unit cell. The optimized cell parameters are found to be around 21.12 Å and its density is calculated to be 0.3 g/cm3. Electronic Structure. The electronic band structure calculations are carried out for all the bcc structures considered

Table 1. Calculated Formation Energies Per Atom, Cell Parameters, Densities and CCC Cubane Corner Bond Angles of the Different Supercubane Based Carbon Materials number of carbon atoms per unit cell

formation energy/atom (eV)

cell parameter (Å)

density (gm/ cm3)

CCC corner bond angle (deg)

16 32 48 80 96 128 144

−8.46 −8.28 −8.25 −8.03 −8.05 −8.09 −8.09

4.877 7.860 10.835 13.026 16.004 18.145 21.129

2.75 1.31 0.75 0.72 0.47 0.43 0.30

90 90 90 105.93 105.95 107.26 107.26

Table 2. Energy of Valence Band Maxima (VBM), Conduction Band Minima (CBM) and the Band Gap Values Calculated Using PBE and B3LYP Functionals for All the Modeled 3D-Carbon Materials. All Energy Values Are Reported in eV energy of VBM

energy of CBM

number of C

PBE

B3LYP

PBE

B3LYP

PBE

band gap B3LYP

16 32 48 80 96 128 144

−2.54 −3.70 −3.85 −5.01 −4.92 −4.60 −4.60

−3.03 −4.19 −4.30 −5.73 −5.58 −5.18 −5.18

1.11 −1.51 −2.12 −1.27 −1.16 −1.64 −1.56

2.23 −0.63 −1.35 −0.32 −0.28 −0.83 −0.74

3.65 2.19 1.73 3.74 3.76 2.96 3.04

5.26 3.56 2.95 5.41 5.30 4.35 4.44

along with the density of states (DOS) plotted for the first three systems with 16, 32, and 48 carbon atoms per unit cell are shown in Figure 2. In the case of C16, the indirect band gap calculated through the PBE functional is found to be 3.01 eV which is considerably less as compared to the earlier reported value.11 This can be because of the well-known drawback of the pure density functionals which are known to underestimate the band gaps. However, the band gap calculated for the same structure using the hybrid functional, B3LYP is found to be 5.26 eV which is in good agreement with the earlier reported band gap of 5.5 eV.11 The systems supercubyne and supercubdiyne are found to have direct band gaps of 3.56 and 2.95 eV respectively along the Gamma point as calculated through B3LYP functional. This shows that the insertion of acetylinic groups in-between the intercubane C−C bonds decreases the band gap of the supercubane. The band decomposed charge density plots of the supercubyne, reported in Supporting Information, Figure S1 shows that the highest valence band is contributed by (C− C)sp3 and (C−C)sp bonds whereas the lowest conduction band arises from the Csp-Csp3 bonds. Completely carbomerized supercubane is again found to be an insulator with a direct band gap of 5.41 eV along the gamma point as calculated through B3LYP method. The band decomposed charge density given in Supporting Information, Figure S2 shows that both the highest valence band and lowest conduction band are coming from the intracubane acetylinic π bonds. Upon introduction of one more acetylinic units in between the intercubane C−C bonds, the band gap is found to decrease slightly, i.e. from 5.41 to 5.30 eV. 25017

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Figure 2. Calculated band structure along with the density of states (DOS) through PBE functional (a, b, and c) and phonon dispersion plots (d, e, and f) of C16, C32, and C48, respectively .

In case of the system with the diacetylinic unit between the intracubane C−C bonds and acetylinic unit between the intercubane C−C units, the band gap is 4.35 eV, whereas the structure with diacetylinic units inserted between all C−C bonds of cubane shows a band gap of 4.44 eV. These band structure results indicate that wherever the intercubane acetylinic units contribute to the higher valence band and lower conduction band, the band gaps come down. In the case of the structures, where the intracubane acetylinic units are contributing to the top of valence band and bottom of conduction band, the band gaps are found to be high and the systems are insulating. It is required to check the stability of the materials modeled here, by calculating the phonon dispersion because of the high porosity and low density associated with these materials. Except for the C144 unit cell, we calculated the phonon frequencies for all the systems using the density functional perturbation theory as implemented in VASP. The calculated phonon dispersion plots along the high symmetry k-path of the first Brillouin zone for C16, C32 and C48 are shown in Figure 2, whereas the corresponding plots for C80, C96 and C128 are reported in Supporting Information, Figure S3. These phonon dispersion plots indicate the stability of the expanded supercubane structures. We have also calculated the formation energy per carbon atom to verify the thermodynamic stability of the proposed systems and results are reported in Table 1. Though the calculated formation energies per carbon are less as compared to that of graphene (−9.26 eV), diamond (−9.10 eV), and graphite (−9.25 eV), these are comparable to the formation energies of the recently explored carbon allotropes, namely, graphdiyne (−8.49 eV), planar T graphene (−8.78 eV), and buckled T graphene36 (−8.41 eV), and are even higher than that of T carbon37 (−7.95). These formation energies further indicate the possible thermodynamic stability of the proposed porous carbon allotropes. In addition, we have also calculated the variation of free energy with temperature and compared it with the previously explored two-dimensional carbon systems, viz. graphene, graphyne, and graphdiyne in Figure 3. From the free energy plot one can observe that though the thermody-

Figure 3. Variation of free energy of different carbon allotropes as a function of temperature.

namic stability of these systems is less than that of graphene, at least for the less porous systems like C16, C32, and C48, it is comparable with that of the recently synthesized carbon allotrope graphdiyne. As we have considered different expanded supercubanes consisting of varying number of acetylinic units, they are expected to have interesting optoelectronic properties. To calculate the optical absorption spectra of all these supercubane-based structures, we have calculated the frequencydependent dielectric constant. The absorption spectra and energy-loss spectra of C80 and C144 with acetylinic and diacetylinic units between all the supercubane C−C bonds, respectively, are given in Figure 4, and for all other systems the spectra are given in Supporting Information (Figures S4 and S5). In the case of a simple supercubane, the absorption spectrum shows a broad fine structure starting from around 3.5 eV with maxima at 8.9 eV which can be attributed to direct transitions between the valence band and conduction band (σ→σ*). The energy-loss spectrum of supercubane shows a broad plasmon resonance peak centered around 29 eV. In the case of the C32 system, the absorption maxima is found to be located at around 5.1 eV and the energy-loss spectra show one 25018

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Figure 4. Plots of imaginary and real parts of the complex dielectric function of (a) C80 and (b) C144 and the energy-loss function of (c) C80 and (d) C144.

peak at around 6.7 eV corresponding to interband transitions and other broad plasmon resonance peak centered around 22.5 eV arising from the excitation of core electrons. The absorption spectrum of C48 shows a peak with maxima at 3.5 eV coming from the excitation of valence electron to the lower conduction levels and the energy loss spectrum shows interband transitions at 5.6 eV, whereas the plasmon resonance peak is centered around 19.4 eV. In the case of a completely carbomerized supercubane, the absorption maxima is found to be located at around 5.38 eV, as shown in Figure 4. The energy-loss function shows a first peak at 7.7 eV and the broad peak around 18.5 eV. Systems with 96 and 124 carbons per unit cell are found to have the absorption maxima at 4.2 and 3.7 eV, respectively. The final structure with increased conjugation is found to have a sharp absorption peak at 3.7 eV which can be attributed to the π→π* transitions. The energy-loss function shows a sharp peak at 5.1 eV and a broad peak centered around 15.5 eV. From C80 to C144 the absorption maximum is found to decrease from 5.38 to 3.7 eV which can be attributed to the increased conjugation while moving from one acetylinic group to two acetylinic groups. These supercubane based materials modeled here can be expected to adsorb molecular hydrogen because of their highly porous nature and the presence of more electronegative sp carbon atoms. To explore the hydrogen storage properties, we have studied the molecular hydrogen adsorption in two of the seven model systems. In the first case, we have considered the C32 unit cell, and four molecules of hydrogen are allowed to interact near the acetylinic groups as shown in Figure 5, left side, and the corresponding gravimetric density based on adsorbed hydrogen is calculated to be 2.04 wt %. The hydrogen adsorption energy per H2 molecule, as calculated through the dispersion corrected PBE method is found to be −2.5 kcal/mol.

Figure 5. Optimized unit cell and 2 × 2 × 2 supercell structures of hydrogenated C32 with four and six molecular hydrogens per unit cell.

In the same C32 unit cell, we have then allowed six H2 molecules to be adsorbed as shown in Figure 5, right side, and the calculated binding energy is found to be just −1.4 kcal/ mol per H2 which shows a large drop in the adsorption energy at higher hydrogen loading. The next member studied for hydrogen adsorption is the largest one considered, with 144 carbon atoms per unit cell. In this case, initially we have studied the adsorption of eighteen H2 molecules per unit cell as shown in Figure 6a with a gravimetric density of 2.1 wt % and the 25019

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Figure 6. Optimized unit cell structures of C144 with (a) 18 and (b) 24 hydrogen molecules per unit cell.

interaction energy per H2 is calculated to be just −0.9 kcal/mol. The number of hydrogen molecules is then increased from 18 to 24 to check the hydrogen adsorption capacity of the material and the optimized structure is shown in Figure 6b. The calculated hydrogen adsorption energy is found to be −0.7 kcal/mol with a gravimetric density of 2.7 wt %. These results indicate that the materials with medium porosity can hold hydrogen more effectively as compared to the highly porous materials like C144 systems considered here. However, as these results are based on one possible structure considered and the system can have complicated potential energy surface, there can be another minima which can give still higher adsorption energies. Because of the high surface areas and availability of acetylinic groups, it may be further possible to modify the systems, for example through metal doping which is shown to be effective in improving the hydrogen adsorption in many of the carbon materials studied earlier.

that porous materials with medium size pores are preferred for better hydrogen storage.

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ASSOCIATED CONTENT

S Supporting Information *

Band decomposed charge density plots, phonon dispersion plots, and additional figures. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the BARC computer center for providing the high performance parallel computing facility. This work has been supported by the INDO-EU project HYPOMAP, in the area of Computational Materials Science. The work of S.K.G. is also supported through Sir J.C. Bose Fellowship from the Department of Science and Technology, India.

4. CONCLUSIONS In summary, we have modeled different three-dimensional carbon materials with varying numbers of carbon atoms starting from C8 cubane unit to an expanded C56 cubic unit and also with different intercubane C−C linking units. The band structure calculations show that the band gaps from PBE functionals are underestimated and the B3LYP results are close to the existing results. The simple supercubane is an insulator and the introduction of acetylinic units between the intercubane C−C bonds reduces the band gap. The calculated phonon frequencies and the free energy profiles show the possible stability of these considered porous carbon materials. The optical absorption spectra show that on moving from C80 to C144, the energy corresponding to the absorption maximum decreases from 5.38 to 3.7 eV because of the increased conjugation. The energy-loss spectra show interband transition in the low energy region and a broad plasmon resonance peak in the range 18−29 eV. The expanded supercubane, C32 is found to adsorb hydrogen with a gravimetric density of 2 wt % and adsorption energy of −2.5 kcal/mol. However, at higher hydrogen densities and in the case of highly porous systems like C144, the hydrogen adsorption energies are very low indicating

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REFERENCES

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The Journal of Physical Chemistry C

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dx.doi.org/10.1021/jp3104479 | J. Phys. Chem. C 2012, 116, 25015−25021