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Chin. Phys. B, 2022, Vol. 31(12): 126101    DOI: 10.1088/1674-1056/ac873a
Special Issue: SPECIAL TOPIC — The third carbon: Carbyne with one-dimensional sp-carbon
SPECIAL TOPIC—The third carbon: Carbyne with one-dimensional sp-carbon Prev   Next  

Accurate theoretical evaluation of strain energy of all-carboatomic ring (cyclo[2n]carbon), boron nitride ring, and cyclic polyacetylene

Tian Lu(卢天)1,†, Zeyu Liu(刘泽玉)2, and Qinxue Chen(陈沁雪)1
1 Beijing Kein Research Center for Natural Sciences, Beijing 100024, China;
2 School of Environmental and Chemical Engineering, Jiangsu University of Science and Technology, Zhenjiang 212100, China
Abstract  Cyclocarbon fully consists of sp-hybridized carbon atoms, which shows quite unusual electronic and geometric structures compared to common molecules. In this work, we systematically studied strain energy (SE) of cyclocarbons of different sizes using regression analysis method based on electronic energies evaluated at the very accurate DLPNO-CCSD(T)/cc-pVTZ theoretical level. In addition, ring strain of two systems closely related to cyclocarbon, boron nitride (BN) ring, and cyclic polyacetylene (c-PA), is also explored. Very ideal relationships between SE and number of repeat units ($n)$ are built for cyclo[2$n$]carbon, B$_{n}$N$_{n}$, and [2$n$]c-PA as ${\rm SE} = 555.0\cdot n^{-1}$, 145.1$\cdot n^{-1}$, and 629.8$\cdot n^{-1}$ kcal$\cdot $mol$^{-1}$, respectively, and the underlying reasons of the difference and similarity in their SEs are discussed from electronic structure perspective. In addition, force constant of harmonic potential of C-C-C angles in cyclocarbon is derived based on SE values, the result is found to be 56.23 kcal$\cdot $mol$^{-1}\cdot $rad$^{-2}$. The possibility of constructing homodesmotic reactions to calculate SEs of cyclocarbons is also explored in this work, although this method is far less rigorous than the regression analysis method, its result is qualitatively correct and has the advantage of much lower computational cost. In addition, comparisons show that $\omega $B97XD/def2-TZVP is a good inexpensive alternative to the DLPNO-CCSD(T)/cc-pVTZ for evaluating energies used in deriving SE, while the popular and very cheap B3LYP/6-31G(d) level should be used with caution for systems with global electron conjugation such as c-PA.
Keywords:  strain energy      ring strain      cyclo[18]carbon      boron nitride ring      cyclic polyacetylene      quantum chemistry  
Received:  10 June 2022      Revised:  27 July 2022      Accepted manuscript online:  05 August 2022
PACS:  61.46.Np (Structure of nanotubes (hollow nanowires))  
  71.15.Mb (Density functional theory, local density approximation, gradient and other corrections)  
  82.20.Wt (Computational modeling; simulation)  
Corresponding Authors:  Tian Lu     E-mail:

Cite this article: 

Tian Lu(卢天), Zeyu Liu(刘泽玉), and Qinxue Chen(陈沁雪) Accurate theoretical evaluation of strain energy of all-carboatomic ring (cyclo[2n]carbon), boron nitride ring, and cyclic polyacetylene 2022 Chin. Phys. B 31 126101

[1] Segawa Y, Yagi A, Ito H and Itami K 2016 Org. Lett. 18 1430
[2] Guo Q H, Qiu Y Y, Wang M X and Fraser Stoddart J 2021 Nat. Chem. 13 402
[3] Li Y M, Kono H, Maekawa T, Segawa Y, Yagi A and Itami K 2021 Acc. Mater. Res. 2 681
[4] Lewis S E 2015 Chem. Soc. Rev. 44 2221
[5] Spitler E L, Johnson C A and Haley M M 2006 Chem. Rev. 106 5344
[6] Mirzaei S, Castro E and Hernández Sánchez R 2021 Chem.-Eur. J. 27 8642
[7] Watanabe K, Segawa Y and Itami K 2020 Chem. Commun. 56 15044
[8] Bachrach S M 1990 J. Chem. Educ. 67 907
[9] George P, Trachtman M, Bock C W and Brett A M 1976 Tetrahedron 32 317
[10] Wiberg K B, Bader R F W and Lau C D H 1987 J. Am. Chem. Soc. 109 1001
[11] Hoffmann R 1966 Tetrahedron 22 521
[12] Haley M M 2019 Chem. 5 2517
[13] Kaiser K, Scriven L M, Schulz F, Gawel P, Gross L and Anderson H L 2019 Science 365 1299
[14] Fang S and Hu Y H 2021 Carbon 171 96
[15] Zou W L, Tao Y W and Kraka E 2020 J. Chem. Phys. 152 154107
[16] Arulmozhiraja S and Ohno T 2008 J. Chem. Phys. 128 114301
[17] Remya K and Suresh C H 2016 RSC Adv. 6 44261
[18] Dai C S, Chen D D and Zhu J 2020 Chem.-Asian J. 15 2187
[19] Hou L, Hu H M, Yang G W and Ouyang G 2021 Phys. Status Solidi-R. 15 2000582
[20] Seenithurai S and Chai J D 2020 Sci. Rep. 10 13133
[21] Nandi A, Solel E and Kozuch S 2020 Chem.-Eur. J. 26 625
[22] Chen J L, Sun L and Zhang R Q 2021 Phys. Chem. Chem. Phys. 23 17545
[23] Raeber A E and Mazziotti D A 2020 Phys. Chem. Chem. Phys. 22 23998
[24] Liu Z Y, Lu T and Chen Q X 2020 Carbon 165 468
[25] Wang X, Liu Z Y, Yan X F, Lu T, Zheng W L and Xiong W W 2022 Chem.-Eur. J. 28 e202103815
[26] Liu Z Y, Lu T and Chen Q X 2020 Carbon 165 461
[27] Wang X, Liu Z Y, Yan X F, Lu T, Wang H W, Xiong W W and Zhao M D 2022 Phys. Chem. Chem. Phys. 24 7466
[28] Liu Z Y, Lu T, Yuan A H, Wang X, Chen Q X and Yan X F 2021 Chem.-Asian J. 16 2267
[29] Liu Z Y, Lu T and Chen Q X 2021 Chem.-Asian J. 16 56
[30] Liu Z Y, Lu T and Chen Q X 2021 Carbon 171 514
[31] Lu T, Liu Z Y and Chen Q X 2021 Mat. Sci. Eng. B 273 115425
[32] Liu Z Y, Lu T and Chen Q X 2021 J. Mol. Model. 27 42
[33] Lu T and Chen Q X 2021 ChemPhysChem 22 386
[34] Liu Z Y, Wang X, Lu T, Yuan A H and Yan X F 2022 Carbon 187 78
[35] Lu T, Chen Q X and Liu Z Y 2019 ChemRxiv DOI: 10.26434/chemrxiv.11320130
[36] Pichierri F 2020 Chem. Phys. Lett. 738 136860
[37] Raeber A E and Mazziotti D A 2020 Phys. Chem. Chem. Phys. 22 23998
[38] Miao Z H, Gonsales S A, Ehm C, Mentink-Vigier F, Bowers C R, Sumerlin B S and Veige A S 2021 Nat. Chem. 13 792
[39] Lu T 2021 J. Mol. Model. 27 263
[40] Chai J D and Head-Gordon M 2008 Phys. Chem. Chem. Phys. 10 6615
[41] Weigend F, and Ahlrichs R 2005 Phys. Chem. Chem. Phys. 7 3297
[42] Szczepanik D W, Solá M, Andrzejak M, Pawełek B, Dominikowska J, Kukułka M, Dyduch K, Krygowski T M and Szatylowicz H 2017 J. Comput. Chem. 38 1640
[43] Vikramaditya T and Lin S T 2019 J. Comput. Chem. 40 2810
[44] Frisch M J, Trucks G W, Schlegel H B, et al. 2016 Gaussian 16 A.03, Wallingford, CT
[45] Riplinger C, Pinski P, Becker U, Valeev E F and Neese F 2016 J. Chem. Phys. 144 024109
[46] Dunning J T H 1989 J. Chem. Phys. 90 1007
[47] Neese F, Wennmohs F, Becker U and Riplinger C 2020 J. Chem. Phys. 152 224108
[48] Lu T and Chen F W 2012 J. Comput. Chem. 33 580
[49] Lu T, and Chen F W 2011 Acta Phys. -Chim. Sin. 27 2786
[50] Becke A D and Edgecombe K E 1990 J. Chem. Phys. 92 5397
[51] Lu T and Chen Q X 2018 Acta Phys. -Chim. Sin. 34 503
[52] Lu T and Chen Q X 2020 Theor. Chem. Acc. 139 25
[53] Lu T and Chen F 2013 J. Phys. Chem. A 117 3100
[54] Stephens P J, Devlin F J, Chabalowski C F and Frisch M J 1994 J. Phys. Chem. 98 11623
[55] Hariharan P C and Pople J A 1973 Theor. Chem. Acc. 28 213
[56] Brédas J L 2017 Chem. Mater. 29 477
[57] Wannere C S, Sattelmeyer K W, Schaefer Iii H F and Schleyer P V R 2004 Angew. Chem. Int. Ed. 43 4200
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