Quantum Chemical Calculations of Carbon Nanoscroll Energy Rolled from Zigzag Graphene Nanoribbon
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XVIII INTERNATIONAL SYMPOSIUM “NANOSTRUCTURES: PHYSICS AND TECHNOLOGY”, MINSK, REPUBLIC OF BELARUS, SEPTEMBER, 2020. GRAPHENE
Quantum Chemical Calculations of Carbon Nanoscroll Energy Rolled from Zigzag Graphene Nanoribbon A. I. Siahloa, S. A. Vyrkoa, S. V. Ratkevicha, N. A. Poklonskia,*, A. T. Vlassova, N. N. Hieub,c, and Yu. E. Lozovikd,e a Physics
Department, Belarusian State University, Minsk, 220030 Belarus Institute of Research and Development, Duy Tan University, Da Nang, Vietnam c Faculty of Natural Sciences, Duy Tan University, Da Nang, Vietnam d Institute for Spectroscopy of Russian Academy of Sciences, Troitsk, Moscow, 108840 Russia e Moscow Institute of Electronics and Mathematics, National Research University Higher School of Economics, Moscow, 101000 Russia *e-mail: [email protected] b
Received June 27, 2020; revised July 23, 2020; accepted July 27, 2020
Abstract—Using the semi-empirical quantum chemical PM3 method the energies of carbon nanoscrolls formed from flat zigzag graphene nanoribbons 46zGNR and 70zGNR are calculated. For this purpose a simple algorithm to define the Cartesian coordinates of the atoms of a carbon nanoscroll is proposed. The dependences of the energy of the nanoscrolls relative to the energy of the corresponding flat nanoribbon on the inner radius of nanoscroll obtained using both the quantum chemical calculations and the semi-classical analytical model shows the bistability of the system. This shows promise for nanoscroll-based nanoelectromechanical systems. Keywords: carbon nanoscroll, graphene nanoribbon, Archimedean spiral, Cartesian coordinates DOI: 10.1134/S1063782620120350
1. INTRODUCTION Carbon nanoscroll is a single graphene layer rolled into a scroll [1, 2]. It is known that the structure and energetics of a system which contain up to a few hundred atoms can be calculated using the quantum chemical methods [3]. For example, the calculations of the electronic band structure and the magnetic states of zigzag graphene nanoribbons using the semiempirical method of molecular orbitals PM3 [4], implemented in the MOPAC2016 program [5], were provided in [6]. The atom coordinates in [6] were initially set using translation algorithms and then refined by the full geometry optimization of nanoribbons. In the present work we propose a simple algorithm to define the Cartesian coordinates of the atoms of a carbon nanoscroll to use them in quantum chemical calculations. The purpose of the work is to define the atomic structure of nanoscrolls for quantum chemical calculations using the analytical expressions and to compare the change of nanoscroll energy at process of the nanoscroll rolling from flat graphene nanoribbon obtained by the semi-classical analytical model and by the quantum chemical method.
2. RESULTS AND DISCUSSION The length L of a zigzag graphene nanoribbon nzGNR, that forms a nanoscroll, is equal to L = (3n/2 − 1)aCC, where n is the number of zigzag chains along the length of the nanoribbon (along the x axis in Fig. 1a) and aCC = 0.142 nm is the C–C bond length of
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