JSEMAT  Vol.4 No.2 , April 2014
Multilevel B-Spline Repulsive Energy in Nanomodeling of Graphenes
ABSTRACT

Quantum energies which are used in applications are usually composed of repulsive and attractive terms. The objective of this study is to use an accurate and efficient fitting of the repulsive energy instead of using standard parametrizations. The investigation is based on Density Functional Theory and Tight Binding simulations. Our objective is not only to capture the values of the repulsive terms but also to efficiently reproduce the elastic properties and the forces. The elasticity values determine the rigidity of a material when some traction or load is applied on it. The pair-potential is based on an exponential term corrected by B-spline terms. In order to accelerate the computations, one uses a hierarchical optimization for the B-splines on different levels. Carbon graphenes constitute the configurations used in the simulations. We report on some results to show the efficiency of the B-splines on different levels.


Cite this paper
Randrianarivony, M. (2014) Multilevel B-Spline Repulsive Energy in Nanomodeling of Graphenes. Journal of Surface Engineered Materials and Advanced Technology, 4, 75-86. doi: 10.4236/jsemat.2014.42011.
References
[1]   Kohn, W. and Sham, L. (1965) Self Consistent Equations Including Exchange Correlation Effects. Physical Review Letters, 140, A1133-A11388. http://dx.doi.org/10.1103/PhysRev.140.A1133

[2]   Harbrecht, H. and Randrianarivony, M. (2011) Wavelet BEM on Molecular Surfaces: Solvent Excluded Surfaces. Computing, 92, 335-364. http://dx.doi.org/10.1007/s00607-011-0147-y

[3]   Randrianarivony, M. (2013) On Space Enrichment Estimator for Nonlinear Poisson-Boltzmann. American Institute of Physics, 1558, 2365-2369.

[4]   Perdew, J. and Wang, Y. (1992) Accurate and Simple Analytic Representation of the Electron-Gas Correlation Energy. Physical Review B, 45, 13244. http://dx.doi.org/10.1103/PhysRevB.45.13244

[5]   Perdew, J. and Zunger, A. (1981) Self-Interaction Correction to Density-Functional Approximation for Many-Electron Systems. Physical Review B, 23, 5048-5079.
http://dx.doi.org/10.1103/PhysRevB.23.5048

[6]   Vosko, S., Wilk, L. and Nusair, M. (1980) Accurate Spin-Dependent Electron Liquid Correlation Energies for Local Spin Density Calculations: A Critical Analysis. Canadian Journal of Physics, 58, 1200-1211.
http://dx.doi.org/10.1139/p80-159

[7]   Stokbro, K., Petersen, D., Smidstrup, S., Blom, A., Ipsen, M. and Kaasbjerg, K. (2010) Semi-Empirical Model for Nano-Scale Device Simulations. Physical Review B, 82, 075420.
http://dx.doi.org/10.1103/PhysRevB.82.075420

[8]   Carbo-Dorca, R. and Bultink, P. (2004) Quantum Mechanical Basis for Mulliken Population Analysis. Journal of Mathematical Chemistry, 36, 231-239.
http://dx.doi.org/10.1023/B:JOMC.0000044221.23647.20

[9]   Cadelano, E., Palla, P., Giordano, S. and Colombo, L. (2009) Nonlinear Elasticity of Monolayer Graphene. Physical Review Letters, 102, 235502. http://dx.doi.org/10.1103/PhysRevLett.102.235502

[10]   Johnson, S. The NLopt Nonlinear-Optimization Package. http://ab-initio.mit.edu/nlopt

 
 
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