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Chemical Physics Letters 633 (2015) 120–125

Contents lists available at ScienceDirect

Chemical Physics Letters

jou rn al h om epa ge: www.elsev ier .com/ locate /cp le t t

rism-C2n carbon dimer, trimer, and nano-sheets: A quantumhemical study

oichi Ohnoa,b,c,∗, Hiroko Satohb,d, Takeaki Iwamotoa

Department of Chemistry, Graduate School of Science, Tohoku University, Aramaki, Aoba-ku, Sendai 980-8578, JapanNational Institute for Informatics (NII), Chiyoda-ku, Tokyo 101-8430, JapanInstitute for Quantum Chemical Exploration, Minato-ku, Tokyo 108-0022, JapanDepartment of Chemistry, University of Zurich, 8057 Zurich, Switzerland

r t i c l e i n f o

rticle history:eceived 10 May 2015

a b s t r a c t

Quantum chemical calculations have predicted the existence of a new carbon family with double-layered

n final form 20 May 2015vailable online 27 May 2015

structures formed by arranging prism-C2n (n = 6, 8, and 12) units. Theoretical explorations of potentialenergy surfaces suggest the lowest barriers of the reaction channels to be ca. 30 kJ mol−1 for a D2h prism-C16 dimer and a D3h prism-C24 trimer. Geometry optimizations under periodic boundary conditions yieldsome prism-C2n sheets composed of CC single bonds of ca. 0.15–0.16 nm. The relative energies per oneatom with respect to graphene are 90–160 kJ mol−1. Van der Waals thickness is estimated to be ca. 0.5 nm.

© 2015 Elsevier B.V. All rights reserved.

. Introduction

In recent years, besides graphite and diamond, new familiesf carbons have been discovered, including fullerenes [1], carbonanotubes [2], and graphenes [3]. These carbon families consistostly of hexagonal rings at their CC bond networks, and fullerenes

nd carbon nanotubes partly contain pentagons in addition toexagons. Considering the various potentialities of hydrocarbontructures, however, one may discover a new class of carbon struc-ures, which consist of different sizes of ring units other than penta-nd/or hexagonal networks, such as cycloalkanes, annulenes, andrismanes [4–6].

Very recently, we have reported a computational study onxploring new carbon structures [7]. As the first results, we haveound prism C2n (n = 6–10, 12, 14, 16, 18, and 20) consisting of n-olygon (hexagon, heptagon, octagon, etc.) rings at the top andottom faces, and of n four-membered rings on the side faces. TheC bond lengths of the prism C2n are ca. 0.144–0.148 nm, which arelearly shorter than the typical single bond of 0.154 nm, and eacharbon atom is surrounded by only three neighboring atoms.

The properties and the shape of the prism C2n appear to be

daptable for forming extensive structures by introducing severalubstances or by connecting the prism units, for example. There-ore, we have made further computational explorations using the

∗ Corresponding author at: Department of Chemistry, Graduate School of Science,ohoku University, Aramaki, Aoba-ku, Sendai 980-8578, Japan.

E-mail address: ohnok@m.tohoku.ac.jp (K. Ohno).

ttp://dx.doi.org/10.1016/j.cplett.2015.05.024009-2614/© 2015 Elsevier B.V. All rights reserved.

prism C2n units and have found another new class of carbons withdouble-layered structures formed by arranging prism-C2n (n = 6, 8,and 12) units. We present here their geometries, bond properties,and energies to discuss the relevance of the prediction. For someof the structures, the lowest barriers of reaction channels havebeen estimated by the explorations on quantum chemical potentialenergy surfaces by using the GRRM (global reaction route mapping)method [8–12].

2. Methods and calculations

All electronic state calculations in the present study were per-formed for the ground singlet states, by using a gaussian 09program package [13].

2.1. Dimer and trimer structures of prism C2n

One series of exploration was performed for dimer and trimerstructures consisting of prism-C16 or prism-C24 units.

We used GRRM14 [12] for geometry optimization calculationswith adequate cares for tightness of minimization, updating timingof Hessians, and ultra-fine grids in density functional calculations.Harmonic vibrational modes were calculated to confirm stableequilibrium structures with no imaginary frequencies as well as

to perform zero-point vibrational energy (ZPVE) corrections. Ini-tial minimization calculations for the dimer 1 (Figure 1a) andtrimer 2 (Figure 2) structures were done at the level of B3LYP/6-31G(d) starting from two D8h prism-C16 units and from three D12h

K. Ohno et al. / Chemical Physics L

Figure 1. A D2h prism-C16 dimer 1. (a) Two prism-C16 units are connected to eachother via four joint CC single bonds in a cuboid bridge. The bond lengths are listedin Table 1. (b) Bondpaths and bond critical points obtained from the bond-criticalpoint analyses by the quantum theory of atoms in molecules (QTAIM). A bondpathwith a bond-critical point is shown as a red ball. A ring-critical point (RCP) is markeda

paTCbtcpoea

Ff

s a yellow ball. A cage critical point (CCP) is marked as a green ball.

rism-C24 units, respectively, by placing them in parallel to face onenother at their four-membered rings with a distance of 0.157 nm.o prepare the initial structure for the trimer (2), three D12h prisim-24 units were arranged to be trigonal, joining each other via cuboidridges at a three-fold symmetry. The equilibrium geometries ofhese structures obtained by further geometrical re-optimizationalculations at higher levels of B3LYP/6-311++G(2d,2p), B3LYP/cc-VDZ, and B3LYP/cc-pVTZ were found to be very similar to thosebtained at the level of B3LYP/6-31G(d). The chemical bond prop-rties in those equilibrium structures were well reproduced even

t lower levels, such as RHF/STO-3G and RHF/3-21G.

igure 2. A D3h prism-C24 trimer 2. Any pair of three prism-C24 units is connected byour joint CC single bonds in a cuboid bridge. The bond lengths are listed in Table 2.

etters 633 (2015) 120–125 121

2.2. Bond-critical point analysis

The chemical bonding was confirmed by bond-critical pointanalyses for the electronic wave function of the prism-C2n dimer(n = 8) at the level of B3LYP/6-31G(d) by the quantum theory ofatoms in molecules (QTAIM) [14]. Bondpaths and bond criticalpoints of various types were obtained with using AIM2000 [15].

2.3. Barrier-height calculations along reaction pathways

In order to know the thermal stability of the equilibrium struc-tures of the prism-C2n dimer 1 and trimer 2, the barrier heightsalong reaction pathways surrounding the equilibrium geometrieswere studied by the anharmonic downward distortion following(ADDF) algorithm incorporated in the GRRM method [8–12] at thelevels of B3LYP/6-31G(d) and B3LYP/cc-pVDZ. The ZPVE correctionswere made for both of the equilibrium and transition structures.For reducing computation time, the large ADDF (LADD) and theFirstOnly options in GRRM14 [12] were used; the LADD option lim-its ADDF to larger anharmonic downward distortions for cuttingoff high energy pathways, and the FirstOnly option limits the ADDFsearch only around the started equilibrium structure [11].

2.4. Periodic prism-C2n sheets

Another exploration was made for double-layered carbon sheetstructures by arranging the prism-C2n (n = 6, 8, and 12) units in sev-eral ways. The sheet structures were optimized with using periodicboundary conditions (PBC) of gaussian 09 [13]. To reduce compu-tational demands, all PBC optimized structures of the prism carbonsheets were obtained at the level of RHF/STO-3G. For the prism-C12 and C16 sheets, PBC optimization calculations at the level ofRHF/3-21G were also done. The unit cell contains one prism struc-ture initiated from a regular polygon prism with CC bond lengths of0.144 nm at the polygons and of 0.150 nm at the vertical side bonds.Initial two-dimensional (2D) translation vectors were set to be at anangle of 60◦ or 90◦ with a nearest distance of 0.157 nm between theprism-C2n units. In the PBC calculations, all coordinates were opti-mized through repeated procedures. During the PBC calculations,energy levels of the highest occupied crystal orbital (HOCO) and thelowest unoccupied crystal orbital (LUCO) were traced to estimatethe band gaps. Relative energies with respect to the graphene sheetwere estimated at the same calculation level. The relative ener-gies were normalized per one carbon atom to compare betweendifferent sizes of carbon unit-cell.

3. Results and discussion

3.1. Dimer and trimer of Prism-C16 and -C24

The dimer 1 was optimized to a D2h symmetry (Figure 1a),where the carbon atoms are numbered clockwise starting from anatom on the joint bridge for the upper-plane, and the carbons inthe lower plane are numbered in the same manner with a primesymbol. C1–C8, C1′–C8′, C9–C16, and C9′–C16′ are components ofan octagon ring, respectively, in the original prisms. Four new CCbonds (C1–C16, C8–C9, C1′–C16′, and C8′–C9′) are formed betweenthe two octagon prisms, which compose a cuboid bridge (C1, C8,C9, C16, C1′, C8′, C9′, and C16′).

Table 1 shows the energies and bond lengths of D2h prism-C16dimer 1 optimized at the four kinds of level. The CC-bond lengths inthe cuboid bridge are slightly longer than the typical CC single bond

of 0.154 nm: The bond lengths of the four new joint bonds (C1–C16,C8–C9, C1′–C16′, and C8′–C9′) and the four vertical bonds (C1–C1′,C8–C8′, C9–C9′, and C16–C16′) are ca. 0.158 nm. The rest of the CCbonds of the cuboid bridge, which are merged with the octagon

122 K. Ohno et al. / Chemical Physics Letters 633 (2015) 120–125

Table 1Optimized energiesa and bond lengthsb of D2h prism-C16 dimer 1.

B3LYP/6-31G(d) B3LYP/6-311++G(2d,2p) B3LYP/cc-pVDZ B3LYP/cc-pVTZ

Total energy −1217.69165 −1217.95012 −1217.77549 −1218.02243C1–C2 0.15104 0.15087 0.15139 0.15070C2–C3 0.14114 0.14068 0.14151 0.14054C3–C4 0.14101 0.14057 0.14142 0.14045C4–C5 0.15054 0.15057 0.15097 0.15036C1–C8 0.16085 0.16058 0.16103 0.16052C1–C16 0.15822 0.15802 0.15847 0.15786C1–C1′c 0.15768 0.15758 0.15804 0.15747C2–C2′c 0.14700 0.14664 0.14753 0.14666C3–C3′c 0.16016 0.16077 0.16089 0.16053C4–C4′c 0.14656 0.14616 0.14699 0.14611

a

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Energies are in Hartree.b Bond lengths are shown in nm for only one of the symmetrically equivalent bonc Vertical connection with the primed numbering atom.

ings, (C1–C8, C9–C16, C1′–C8′, and C9′–C16′) are ca. 0.161 nm inength.

The prisms in the dimer are slightly deformed from the D8heometry of the original prism-C16 structure (0.143 nm on thectagon, and 0.153 nm on the side) [7]: from the joint bridge, theertical CC bond lengths on the side faces are 0.158 nm, 0.147 nm,.161 nm, and 0.147 nm for C1–C1′, C2–C2′, C3–C3′, and C4–C4′,espectively, and the horizontal CC bond lengths on the octagonsre 0.161 nm, 0.151 nm, 0.141 nm, 0.141 nm, and 0.151 nm for1–C8, C1–C2, C2–C3, C3–C4, and C4–C5, respectively. The ratherhorter bond lengths (0.141 nm) of C2–C3 and C3–C4 in the rangef unsaturated CC bonds give a hint of further extension to therism-C16 sheets, which will be described in the next subsection.

The results of bond critical point (BCP) analyses for the prism-16 dimer 1 are shown in Figure 1b. A BCP connecting carbontoms by bondpaths is shown as a red ball in between. Electronensities on the BCPs are all 0.217 au at the four joint bonds and.202–0.291 au at the prisms. These values are considered as nor-al values for ordinal chemical bonds. This result confirmed the

elevancy of the chemical bonds drawn in Figure 1a. Electron den-ities on the other points are much smaller: For the ring criticaloint (RCP), which is marked as a yellow ball, the electron densi-ies are ca. 0.07–0.11 au at the centers of the squares and 0.004 aut the centers of the octagon rings. For the cage critical point (CCP),

hich is marked as a green ball, the electron density is 0.028 au

t the body center of the cuboid bridge and 0.004 au at the bodyenters of the prisms.

able 2ptimized energiesa and bond lengthsb of D3h prism-C24 trimer 2.

RHF/STO-3G RHF/3-21G

Total energy −2688.80404 −2706.48557C1–C2 0.15841 0.15983

C2–C3 0.15307 0.15257

C3–C4 0.13895 0.13952

C4–C5 0.14136 0.14086

C5–C6 0.14948 0.14970

C6–C7 0.13541 0.13515

C1–C12 0.15609 0.15555

C12–C13 0.15718 0.15822

C11–C14 0.15882 0.15917

C1–C1′c 0.15573 0.15730

C2–C2′c 0.15843 0.16207

C3–C3′c 0.14418 0.14423

C4–C4′c 0.16211 0.16934

C5–C5′c 0.14405 0.14458

C6–C6′c 0.15582 0.15963

a Energies are in Hartree.b Bond lengths are shown in nm for only one of the symmetrically equivalent bonds.c Vertical connection with the primed numbering atom.

The trimer 2 was optimized to D3h symmetry (Figure 2). Table 2shows optimized energies and bond lengths of 2 at the four kinds oflevel. The CC bond lengths of the new 10 joint bonds (e.g., C12–C13and C11–C14) are 0.157–0.159 nm, those of the decagon rings (e.g.,C1–C2 and C2–C3) are 0.135–0.159 nm, and those of the verticalbonds at the side faces (e.g., C1-C1′ and C2–C2′) are 0.144–0.162 nm.According to the bond lengths, all of the CC bonds on the threecuboid bridges (e.g., C1–C1′, C1–C2, and C1–C2) are considered tobe single bonds as those of the prism-C16 dimer 1 are. The lengthsof some of the bonds in the dodecagon rings, C3–C4, C4–C5, andC6–C7, are shorter (0.135–0.141 nm), which are in agreement withthose of unsaturated CC bonds. This gives a hint of further extensionto the prism-C24 sheets.

Exploration on the potential energy surfaces using GRRMrevealed that the height of the lowest energy barrier from the D2hprism-C16 dimer 1 is 34.3 kJ mol−1 at the level of B3LYP/6-31G(d)and 33.4 kJ mol−1 at the level of B3LYP/cc-pVDZ. The barrier is for areaction where a bond disconnection of a pair of adjacent verticalCC bonds in the cuboid bridge occurs on either of the prism-C16structures (e.g., a pair of C1–C1′ and C8–C8′, or a pair of C16–C16′

and C9–C9′). The reaction product is a deformed structure, show-ing 632.5 (625.8) kJ mol−1 lower than 1, where the cc-pVDZ valueis in the parenthesis. The GRRM exploration for the D3h prism-C24trimer 2 revealed that there is a pathway with a barrier height

of 30.3 kJ mol−1, producing a 583.4 kJ mol−1 lower structure. Thisis also a bond disconnection reaction for a pair of adjacent verti-cal CC bonds in the cuboid bridge but occurs between two prisms

B3LYP/6-31G(d) B3LYP/cc-pVDZ

−2739.78285 −2739.967930.15916 0.159390.15030 0.150600.13981 0.140240.14222 0.142630.14682 0.147190.13852 0.138940.15480 0.155050.15814 0.158300.15921 0.159400.15683 0.157260.16248 0.162950.14682 0.147260.16137 0.161890.14664 0.147050.15466 0.15515

ysics Letters 633 (2015) 120–125 123

(3btCb

3

olugFsCwtaertb3tlO

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Figure 3. Two types of the prism-C12 sheet. (a) A D6h prism-C12 sheet 3. The prism-C12 units are condensed forming a hexagonal sheet of equivalent carbon atomsbonded with four adjacent carbon atoms. (b) A D2h prism-C12 sheet 4. The prism-

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K. Ohno et al. / Chemical Ph

e.g., a pair of C11–C11′ and C14–C14′). The energy barrier of ca.0 kJ mol−1 (ca. 2500 cm−1) is corresponding to the range of theinding energies of hydrogen bonds (1–155 kJ mol−1). Accordingo these calculation results, it is predicted that this series of prism-2n structures are stable enough to observe at low temperaturesut are thermally metastable at high temperatures.

.2. Prism carbon sheets

Since we obtained a hint of extensive structures from the resultsf the dimer and the trimer, we explored the possibility of double-ayered carbon sheets by arranging several sizes of prism-C2nnits. The geometry optimization calculations with the 2D PBCsave several types of periodic array of prism carbons as shown inigures 3–5: a D6h prism-C12 sheet 3 (Figure 3a), a D2h prism-C12heet 4 (Figure 3b), a D4h prism-C16 sheet 5 (Figure 4), a D6h prism-24 sheet 6 (Figure 5a), and a D4h prism-C24 sheet 7 (Figure 5b),here lattices cut at certain ranges are visualized, though calcula-

ions were done for infinite systems. Translation vectors a and bre shown by arrows. In Table 3, optimized energies, the relativenergies per one atom with respect to graphene, the minimum indi-ect energy gaps between HOCO and LUCO, bond lengths, and theranslation vector components are listed. All of the data that wille shown are those calculated at the RHF/STO-3G level, besides, for–5, the data calculated at the RHF/3-21G level is also shown inhe parenthesis. As will be described below, according to the bondengths, all of the bonds in 3–6 are considered to be single bonds.nly in 7, both single- and double bond lengths are observed.

All carbon atoms of the D6h prism-C12 sheet 3 (Figure 3a) arequivalent. Each carbon atom has four bonds: three hexagonal CConds of 0.1566 (0.1566) nm and one vertical CC bond of 0.15620.1583) nm in length. The structure of 3 is composed of double-arallel-layers of a graphene-like sheet, which are connected eachther by vertical CC bonds. However, considering the bond lengths,ll of the hexagons are made of single bonds. This suggests that the

rism sheet 3 has a different property of the electron system fromhe � electron conjugation system of graphene.

There are two types of carbon atoms in the D2h prism-C12 sheet (Figure 3b): one is of the cuboid bridges, and the other is of the

C12 structures are connected by cuboid bridges in the y-direction and by rectanglebridges in the x-direction. Bond lengths are listed in Table 3. The components of thetranslation vectors a and b are also listed in Table 3.

able 3ptimized energiesa and bond lengthsb of prism-C2n sheet obtained by periodic boundary calculations at the level of RHF/STO-3G (values at the level of RHF/3-21G are shown

n the parenthesis).

D6h prism-C12 (3) D2h prism-C12 (4) D4h prism-C16 (5) D6h prism-C24 (6) D4h prism-C24 (7)

Total energy −448.63218 (−451.45170) −448.47968 (−451.31503) −597.92448 (−601.69124) −896.77919 −896.67305Relative energyc 95.65 129.02 136.97 148.73 160.34Minimum energy gapd 14.69 (10.52) 13.08 (10.08) 13.99 (9.85) 13.15 11.69C1–C2 0.1566 (0.1566) 0.1568 (0.1565) 0.1558 (0.1553) 0.1561 0.1532C2–C3 0.1566 (0.1566) 0.1575 (0.1585) 0.1577 (0.1591) 0.1579 0.1532C3–C4 0.1566 (0.1566) 0.1568 (0.1565) 0.1558 (0.1553) 0.1561 0.1583C1–ae 0.1566 (0.1566) 0.1569 (0.1564) 0.1577 (0.1591) 0.1578 0.1583C2–bf 0.1566 (0.1566) 0.1580 (0.1598) 0.1577 (0.1591) 0.1578C3–bf 0.1580 (0.1598) 0.1577 (0.1591) 0.1578 0.1583C1–C1′g 0.1562 (0.1583) 0.1580 (0.1607) 0.1568 (0.1590) 0.1567 0.1574C2–C2′g 0.1562 (0.1583) 0.1561 (0.1579) 0.1568 (0.1590) 0.1567 0.1327Tvah x

y0.4698 (0.4698)−0.0003 (−0.0003)

0.4926 (0.4922)0.0000 (0.0000)

0.5357 (0.5378)0.0000 (0.0000)

0.64370.3718

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Tvb h xy

0.2349 (0.2349)0.4069 (0.4068)

0.0000 (0.0000)0.4153 (0.4176)

0.0000 (0.0000)0.5357 (0.5378)

0.6439−0.3718

0.00000.7487

a Energies are in Hartree.b Bond lengths are shown in nm for some representative bonds.c Relative energy per one carbon atom with respect to graphene in kJ mol−1.d Minimum indirect energy gap between HOCO and LUCO in eV.e Horizontal connection with the adjacent atom generated with the translation vector a.f Horizontal connection with the adjacent atom generated with the translation vector b.g Vertical connection with the primed numbering atom.h Translation vector components in nm.

124 K. Ohno et al. / Chemical Physics L

Figure 4. A D4h prism-C16 sheet 5. Prism-C16 units are connected by cuboid bridgesin both of the x- and y-directions. The bond lengths are listed in Table 3. The com-ponents of the translation vectors a and b are also listed in Table 3.

Figure 5. Two types of the prism-C24 sheet. (a) A D6h prism-C24 sheet 6. (b) A D4h prismThe bond lengths are listed in Table 3. The components of the translation vectors a and b

etters 633 (2015) 120–125

rectangular bridges. The bond length of the vertical bonds at therectangular bridges is 0.1580 (0.1607) nm, which is slightly longerthan the length of the vertical bonds at the cuboid bridges of 0.1561(0.1579) nm. Thus, the shape of the sheet is uneven slightly with ca.0.002–0.003 nm difference of up (at the rectangular bridges) anddown (at the cuboid bridges). The horizontal bond lengths rangebetween 0.156 and 0.160 nm.

The D4h prism-C16 sheet 5 (Figure 4) adopts an even shape withthe same length vertical CC bonds between the layers of 0.1568(0.1590) nm. Two different lengths of CC bonds appear in the sheetlayers: 0.1577 (0.1591) nm for the bonds on the bridges and 0.1558(0.1553) nm for the others. The cuboid bridges in 5 are approxi-mately cubic with almost the same length of twelve CC bonds of0.1568–0.1577 (0.1590–0.1591) nm.

The structure of the D6h prism-C24 sheet 6 (Figure 5a) is com-posed of dodecagon prisms connected to each other by the jointCC bonds of 0.1578 nm in the cuboid bridges. The shape of 6 iseven with the same length vertical CC bonds between the lay-

ers of 0.1567 nm. The bond lengths of the dodecagon rings are0.1561–0.1579 nm, which are slightly deformed from a regular D12hstructure.

-C24 sheet 7. In both 6 and 7, the prism-C24 units are connected by cuboid bridges. are also listed in Table 3.

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The shape of the do decagon prisms in the D4h prism-C24 sheet (Figure 5b) is considerably deformed from the regular dodecagonrism. The vertical CC bonds in the cuboid bridges (e.g., C1–C1′) givehe single bond length (0.1574 nm), whereas the other vertical CConds (e.g., C2–C2′) are very much shorter (0.1327 nm), which is ingreement with the double bond length. The double bond propertys observed only on the vertical part of the cuboid bridges, and theonds in the horizontal part (e.g., C3–C4) show single bond property0.1532–0.1583 nm).

Relative energies of the prism-C2n sheets 3–7 were estimatedith respect to the graphene sheet at the same level of the

BC calculations; the normalized relative energies per one carbontom are 3: 96.65 kJ mol−1, 4: 129.02 kJ mol−1, 5: 136.97 kJ mol−1,: 148.73 kJ mol−1, and 7: 160.34 kJ mol−1. These values indicatehat the prism carbon sheets are not very stable thermodynami-ally compared with the graphene sheet. However, as consideringhe typical CC bond energies (348 kJ mol−1, 614 kJ mol−1, and39 kJ mol−1 for a CC single-, double-, and triple bonds, respectively16]), the relative energies are small to break the arrayed carbonetworks by disconnecting a CC bond. It is thus assumed that therism sheets are still stable enough to retain the carbon networks.

In order to discuss the band gaps sufficiently, a higher calcu-ation level is necessary to determine the precise band structures.evertheless, we will try to discuss the band gaps using the data at

he RHF/STO-3G level done in the present calculations, which mayive a crude estimation. The gap separations between HOCO andUCO are 3: 14.69 eV (10.52 eV), 4: 13.08 eV (10.08 eV), 5: 13.99 eV10.52 eV), 6: 11.69 eV, and 7: 13.15 eV, where the values at theHF/3-21G level are shown in the parenthesis. Even taking intoccount that the gap separation values tend to decrease with thearger basis set, they are considered to be still large enough, whichndicates that the prism carbon sheets would be insulators withoutolor under the visible light.

The thickness of the prism carbon sheets can be estimated toe 0.49–0.50 nm from the lengths of the longest vertical CC bonds0.15–0.16 nm) and the standard van der Waals radius of carbontom (0.17 nm). Therefore, this class of carbons can be also a carbonano-sheet family.

. Concluding remarks

In the present work, we discussed the possibility of a new classf carbon structures composed of prism-C2n units, which haveeen predicted with quantum chemical calculations. The units areonnected each other by the CC single bond formation, which com-oses of a cuboid bridge or a rectangular bridge. The lowest barriereights of reaction channels estimated by the GRRM exploration forhe dimer 1 and the trimer 2 (ca. 30 kJ mol−1) suggest that they aretable enough to observe in experiments at lower temperatures.uch a metastable character together with the energy gap to theroduct via the lowest energy barrier can be useful for an alterna-ive purpose, like for storing energy to use as an energy-reservoir,or example. If the prism-C2n sheet compounds undergo the same

ype of reaction channels as those found for 1 and 2, it is predictedhat the prism sheets can supply energy through simple isomeriza-ion reactions (e.g., the disconnection of the vertical bonds), whichelease chemical energy of ca. 100–160 kJ mol−1 per one carbon

[[[

etters 633 (2015) 120–125 125

atom without any substance production that can contaminatethe environments. The prism-C2n sheets are predicted to possessnano-size thickness and colorless insulator property. We believethat further detailed investigations from several angles, includ-ing the formation mechanisms, electronic structures, and property,will figure out clearer characters of this new prism-C2n carbonfamily.

The prism-C2n molecules and their derivatives such as thepresent prism carbon sheets may be challenging synthetic targetsin the context of synthesis of strained molecules, such as prismane[17], cubane [18], pentaprismane [19], and polymerized fullerenes[20], of which total syntheses have been successfully achieved.

Acknowledgments

The authors thank Professor Waro Nakanishi at Wakayama Uni-versity for technical advises to use AIM2000. H.S. was supportedby a Grant-in-Aid for Challenging Exploratory Research (Grant No.25540017) from the Japan Society for the Promotion of Science.H.S. and K.O. were supported by the Grant from the Data CentricScience Research Commons Project of the Research Organizationof Information and Systems (ROIS), Japan.

References

[1] H. Kroto, J.E. Fischer, D.E. Cox (Eds.), The Fullerenes, Pergamon Press, Oxford,1993.

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