Non Local Corrections to the Electronic Structure of Non Ideal Electron Gases: The Case of Graphene and Tyrosine

Abstract

We introduce a formal definition of a non local functional and show that the non local exchange-correlation potential functional, derived within Density-Functional Theory, is non local in the space of electronic densities. A previously developed non local exchange-correlation potential term, is introduced to approach the exact density-functional potential. With this approach, the electronic structure of the graphene surface and the tyrosine amino acid are calculated.

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Y. García, J. Cuffe, F. Alzina and C. Sotomayor-Torres, "Non Local Corrections to the Electronic Structure of Non Ideal Electron Gases: The Case of Graphene and Tyrosine," Journal of Modern Physics, Vol. 4 No. 4, 2013, pp. 522-527. doi: 10.4236/jmp.2013.44074.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] W. Kohn, “An Essay on Condensed Matter Physics in the Twentieth Century,” Reviews of Modern Physics, Vol. 71, No. 2, 1999, pp. S59-S77. doi:10.1103/RevModPhys.71.S59
[2] P. Hohenberg and W. Kohn, “Inhomogeneous Electron Gas,” Physical Reviews, Vol. 136, No. 3B, 1964, pp. B864-B871. doi:10.1103/PhysRev.136.B864
[3] W. Kohn and L. J. Sham, “Self-Consistent Equations Includeing Exchange and Correlation Effects,” Physical Review, Vol. 140, No. 4A, 1965, pp. A1133-A1138. doi:10.1103/PhysRev.140.A1133
[4] F. M. Bickelhaupt, “Understanding Reactivity with Kohn-Sham MO Theory. The E2-SN2 Mechanistic Spectrum and Other Concepts,” Journal of Computational Chemistry, Vol. 20, No. 1, 1999, pp. 114-128. doi:10.1002/(SICI)1096-987X(19990115)20:1<114::AID-JCC12>3.0.CO;2-L
[5] J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh and C. Fiolhais, “Atoms, Molecules, Solids, and Surfaces: Applications of the Generalized Gradient Approximation for Exchange and Correlation,” Physical Review B, Vol. 46, No. 11, 1992, pp. 6671-6687. doi:10.1103/PhysRevB.46.6671
[6] V. N. Staroverov, G. E. Scuseria, J. Tao and J. P. Perdew, “Comparative Assessment of a New Nonempirical Density Functional: Molecules and Hydrogen-Bonded Complexes,” Journal of Chemical Physics, Vol. 119, No. 23, 2003, pp. 12129-12137. doi:10.1063/1.1626543
[7] R. W. Godby, M. Shluter and L. J. Sham, “Self-Energy Operators and Exchange-Correlation Potentials in Semiconductors,” Physical Review B, Vol. 37, No. 17, 1988, pp. 10159-10175. doi:10.1103/PhysRevB.37.10159
[8] N. Sai, M. Zwolak, G. Vignale and M. Di Ventra, “Dynamical Corrections to the DFT-LDA Electron Conductance in Nanoscale Systems,” Physical Review Letters, Vol. 94, No. 18, 2005, Article ID: 186810. doi:10.1103/PhysRevLett.94.186810
[9] R. K. Nesbet, “Beyond Density Functional Theory: The Domestication of Nonlocal Potentials,” Modern Physics Letters B, Vol. 18, No. 2-3, 2004, pp. 73-82. doi:10.1142/S021798490400669X
[10] J. Jaramillo, G. E. Scuseria and M. Ernzerhof, “Local Hybrid Functionals Based on Density Matrix Products,” Journal of Chemical Physics, Vol. 118, No. 3, 2003, pp. 1068-1073. doi:10.1063/1.1528936
[11] A. D. Becke, “A New Mixing of Hartree-Fock and Local Density-Functional Theories,” Journal of Chemical Physics, Vol. 98, No. 2, 1993, pp. 1372-1377. doi:10.1063/1.464304
[12] T. Yanai, D. P. Tew and N. C. Handy, “A New Hybrid Exchange-Correlation Functional Using the Coulomb-Attenuating Method (CAM-B3LYP),” Chemical Physics Letters, Vol. 393, No. 1-3, 2004, pp. 51-57. doi:10.1016/j.cplett.2004.06.011
[13] Y. Garcia and J. C. Sancho-Garcia, “On the Role of the Nonlocal Hartree-Fock Exchange in Ab-Initio Quantum Transport: H2 in Pt Nanocontacts Revisited,” Journal of Chemical Physics, Vol. 129, No. 3, 2008, Article ID: 034702.
[14] A. Nitzan and M. A. Ratner, “Electron Transport in Molecular Wire Junctions,” Science, Vol. 300, No. 5624, 2003, pp. 1384-1389. doi:10.1126/science.1081572
[15] N. Mohanty and V. Berry, “Graphene-Based Single-Bacterium Resolution Biodevice and DNA Transistor: Interfacing Graphene Derivatives with Nanoscale and Microscale Biocomponents,” Nano Letters, Vol. 8, No. 12, 2008, pp. 4469-4476. doi:10.1021/nl802412n
[16] C. Lu, H. Yang, C. Zhu, X. Chen and G. Chen, “A Graphene Platform for Sensing Biomolecules,” Angewandte Chemie International Edition, Vol. 48, No. 26, 2009, pp. 4785-4787. doi:10.1002/anie.200901479
[17] A. W. Ghosh and S. Datta, “Molecular Conduction: Paradigms and Possibilities,” Journal of Computational Electronics, Vol. 1, No. 4, 2002, pp. 515-525. doi:10.1023/A:1022961608941
[18] J. P. Perdew and A. Zunger, “Self-Interaction Correction to Density-Functional Approximations for Many-Electron Systems,” Physical Review B, Vol. 23, No. 10, 1981, pp. 5048-5079. doi:10.1103/PhysRevB.23.5048
[19] J. Da-Chai and M. Head-Gordon, “Long-Range Corrected Hybrid Density Functionals with Damped Atom-Atom Dispersion Corrections,” Physical Chemistry Chemical Physics, Vol. 10, No. 44, 2008, pp. 6615-6620. doi:10.1039/b810189b
[20] G. Vignale and W. Kohn, “Current-Dependent Exchange-Correlation Potential for Dynamical Linear Response Theory,” Physical Review Letters, Vol. 77, No. 10, 1996, pp. 2037-2040. doi:10.1103/PhysRevLett.77.2037
[21] C. Adamo and V. Barone, “Towards Reliable Adiabatic Connection Models Free from Adjustable Parameters,” Chemical Physics Letters, Vol. 274, No. 1-3, 1997, pp. 242-250. doi:10.1016/S0009-2614(97)00651-9
[22] A. D. Becke, “Density-Functional Thermochemistry. III. The Role of Exact Exchange,” Journal of Chemical Physics, Vol. 98, No. 7, 1993, pp. 5648-5651. doi:10.1063/1.464913
[23] F. M. Bickelhaupt and E. J. Baerends, “Kohn-Sham Density Functional Theory: Predicting and Understanding,” Reviews of Computational Chemistry, Vol. 15, 2000, pp. 1-86. doi:10.1002/9780470125922.ch1
[24] W. Schattke, M. A. Van Hove, F. J. G. de Abajo, R. Diez Muino and N. Mannella, “Solid-State Photoemission and Related Methods: Theory and Experiment,” Wiley-VCH, Berlin, 2003. doi:10.1002/9783527602506
[25] M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Nor- mand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, A. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski and D. J. Fox, “Gaussian 09, Revision A.1,” Gaussian, Inc., Wallingford, 2009.
[26] J. P. Perdew and Y. Wang, “Accurate and Simple Density Functional for the Electronic Exchange Energy: Generalized Gradient Approximation,” Physical Review B, Vol. 33, No. 12, 1986, pp. 8800-8802. doi:10.1103/PhysRevB.33.8800
[27] Protein data bank. www.pdb.org
[28] Y. Yu, Y. Zhao, S. Ryu, L. E. Brus, K. S. Kim and P. Kim, “Tuning the Graphene Work Function by Electric Field Effect,” Nano Letters, Vol. 9, No. 10, 2009, pp. 3430-3434. doi:10.1021/nl901572a
[29] F. J. Owens, “Electronic and Magnetic Properties of Armchair and Zigzag Graphene Nanoribbons,” Journal of Physical Chemistry, Vol. 128, No. 19, 2008, pp. 194701-194704. doi:10.1063/1.2905215

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