Effects of basis set superposition error on DFT model of C$_2$N/graphene bilayer

D. V. Babailova   ; K. V. Alantev   ; M. V. Kaplun   ; E. V. Anikina   ; T. Yu. Nikonova

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 15 (2023) no. 3, pp. 62-69

Résumé

We investigated the structural and energetic properties of the C$_2$N/graphene bilayer using the electron density functional theory. We compared two approaches for wave function decomposition: plane waves (PW) and localized pseudoatomic orbitals (PAOs). We showed that for the weakly bonded bilayer, it is essential to consider correction to the basis set superposition error in binding energy calculations and geometry optimization. Otherwise, the interlayer binding energy and layer separation could be overestimated by 45–90 % and underestimated by 4–12 %, respectively. Also, to have the quantitative agreement between PAOs and PW results, the atomic-like basis set should be optimized. Overall, calculated with dispersion corrections, the interlayer binding energy (0,17–0,22 J/m$^2$) is of the van der Waals nature.

Détail

Keywords: C$_2$N/graphene bilayer, density functional theory, local pseudoatomic orbitals (PAOs), plane waves (PW), basis set superposition error (BSSE).

Bibliographie

[1] Sang M., Shin J., Kim K., Yu K.J., “Electronic and Thermal Properties of Graphene and Recent Advances in Graphene Based Electronics Applications”, Nanomaterials, 9:3 (2019), 374 | DOI

[2] Andrei E.Y., MacDonald A.H., “Graphene Bilayers with a Twist”, Nat. Mater., 19: 12 (2020), 1265–1275 | DOI

[3] Yankowitz M., Ma Q., Jarillo-Herrero P., LeRoy B.J., “Van der Waals Heterostructures Combining Graphene and Hexagonal Boron Nitride”, Nat. Rev. Phys., 1:2 (2019), 112–125 | DOI

[4] Mahmood J., Lee E.K.,. Jung M, Shin D., Jeon I.-Y., Jung S.-M., Choi H.-J., Seo J.-M., Bae S.-Y., Sohn S.-D., Park N., Oh J.H. Shin, H.-J., Baek J.-B., “Nitrogenated holey two-dimensional structures”, Nat. Commun. Nature Publishing Group, 6 (2015), 6486 | DOI

[5] Guan Z., Ni S., “NiInsights from First Principles Graphene/g-C$_2$N Bilayer: Gap Opening, Enhanced Visible Light Response and Electrical Field Tuning Band Structure”, Appl. Phys. A, 123:11 (2017), 678 | DOI

[6] Lee K., Yu J., Morikawa Y., “Comparison of Localized Basis and Plane-Wave Basis for Density-Functional Calculations of Organic Molecules on Metals”, Phys. Rev. B, 75:4 (2007), 045402 | DOI | MR

[7] Ferre-Vilaplana A., “Numerical Treatment Discussion and Ab Initio Computational Reinvestigation of Physisorption of Molecular Hydrogen on Graphene”, J. Chem. Phys., 122:10 (2005), 104709 | DOI

[8] Artacho E., Anglada E., Diéguez O., Gale J.D., Garcia A., Junquera J., Martin R.M., Ordejón P., Pruneda J.M., S?nchez-Portal D., Soler J.M., “The SIESTA Method; Developments and Applicability”, J. Phys. Condens. Matter, 20:6 (2008), 064208 | DOI

[9] Kresse G., Furthmüller J., “Efficient Iterative Schemes for Ab Initio Total-Energy Calculations using a Plane-Wave Basis Set”, Phys. Rev. B, 54:16 (1996), 11169–11186 | DOI

[10] Abinit's Fritz-Haber-Institute (FHI) pseudo database, (data obrascheniya: 20.01.2023) https://departments.icmab.es/leem/SIESTA_MATERIAL/Databases/Pseudopotentials/periodictable-intro.html

[11] Perdew J.P., Burke K., Ernzerhof M., “Generalized Gradient Approximation Made Simple”, Phys. Rev. Lett., 77:18 (1996), 3865–3868 | DOI

[12] Grimme S., “Semiempirical GGA-Type Density Functional Constructed with a Long-Range Dispersion Correction”, J. Comput. Chem., 27:15 (2006), 1787–1799 | DOI

[13] Dion M., Rydberg H., Schr?der E., Langreth D.C., Lundqvist B.I., “Van der Waals Density Functional for General Geometries”, Phys. Rev. Lett., 92:24 (2004), 246401 | DOI

[14] Berland K., Hyldgaard P., “Exchange Functional that Tests the Robustness of the Plasmon Description of the Van Der Waals Density Functional”, Phys. Rev. B, 89:3 (2014), 035412 | DOI | MR

[15] Anikina E.V., Beskachko V.P., “Basis Set Parameter Optimization for Hydrogen Adsorption on Carbon Metananotubes Simulation in SIESTA Package”, Scientific search, Proc. IX scientific conference of graduate and doctoral students (Chelyabinsk, 2017), Izdatel'skiy tsentr YuUrGU, Chelyabinsk, 2017, 126–134 (in Russ.)

[16] Alant'ev K.V., Anikina E.V., “Monolayer C$_2$N as a promising material for hydrogen storage: DFT modeling”, Proc. XXII All-Russian School-seminar on the problems of condensed matter physics in memory of M.I. Kurkin, SPFKS-22 (Yekaterinburg, November 24 - December 1, 2022), IFM UrO RAS Publ., Yekaterinburg, 2022, 301 pp. (in Russ.)

[17] Kaplun M.V., Anikina E.V., Beskachko V.P., “Ab Initio Modelling of a Bilayer Graphene”, Bulletin of the South Ural State University. Series of “Mathematics. Mechanics. Physics”, 14: 2 (2022), 64–71 | DOI

[18] Boys S.F., Bernardi F., “The Calculation of Small Molecular Interactions by the Differences of Separate Total Energies. Some Procedures with Reduced Errors”, Mol. Phys., 19:4 (1970), 553–566 | DOI

[19] D. Wang, D. Han, L. Liu, L. Niu, “Structure and Electronic Properties of C$_2$N/Graphene Predicted by First-Principles Calculations”, RSC Adv. Royal Society of Chemistry, 6:34 (2016), 28484–28488 | DOI

[20] Liu Z., Liu J. Z., Cheng Y., Li Z., Wang L., Zheng Q., “Interlayer binding energy of graphite: A mesoscopic determination from deformation”, Phys. Rev. B - Condens. Matter Mater. Phys., 85:20 (2012), 205418 | DOI

[21] Bilenko R.V., Dolganina N. Yu., Ivanova E.V., Rekachinsky A.I., “High-performance Computing Resources of South Ural State University”, Bulletin of the South Ural State University. Series of “Computational Mathematics and Software Engineering”, 11:1 (2022), 15–30 | DOI