JMP  Vol.4 No.4 , April 2013
Non Local Corrections to the Electronic Structure of Non Ideal Electron Gases: The Case of Graphene and Tyrosine

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.

Cite this paper
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.
[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.

[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