I present the continuation of a study on Laplacian Level Kinetic Energy (KE) functionals applied to metallic nanosystems. The development of novel Kinetic Energy functionals is an important topic in density functional theory (DFT). The nanoparticles are patterned using gelatin spheres of different sizes, background density and number of electrons. To reproduce the correct kinetic and potential energy density of the various nanoparticles, the use of semilocal descriptors is necessary. Need an explicit density functional expression for the kinetic energy of electrons, including the first e second functional derivative, i.e. the kinetic potential and the kinetic kernel, respectively. The exact explicit form of the non interacting kinetic energy, as a functional of the electron density, is known only for the homogeneous electron gas (HEG), i.e., the Thomas-Fermi (TF) local functional and for 1 and 2 electron systems, i.e., the von Weizsacker (VW) functional. In between these two extreme cases, different semilocal or non local approximations were developed in recent years. Most semilocal KE functionals are based on modifications of the second-order gradient expansion (GE2) or fourth-order gradient expansion (GE4). I find that the Laplacian contribute is fundamental for the description of the energy and the potential of nanoparticles. I propose a new LAP2 semilocal functional which, better than the previous ones, allows us to obtain fewer errors both of energy and potential. More details of the previous calculations can be found in my 2 previous works which will be cited in the text.
| Published in | International Journal of Systems Science and Applied Mathematics (Volume 9, Issue 2) |
| DOI | 10.11648/j.ijssam.20240902.12 |
| Page(s) | 30-36 |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Density Functional Theory, Kinetic Energy Functionals, Jellium
| [1] | Engel E., Dreizler R. M. Density functional theory. Springer; 2013, https://doi.org/10.1007/978-3-642- 14090-7 |
| [2] | Wang Y. A., Carter E. A. Orbital-free kinetic-energy density functional theory. In Theoretical Methods in Condensed Phase Chemistry, edited by S. D. Schwartz. Netherlands, Dordrecht: Springer; 2002, 117-184. |
| [3] | Wesolowski T. A., Wang Y. A. Recent progress in orbital- free density functional theory, Vol. 6. World Scientific; 2013. |
| [4] | Bruus H., Flensberg K. Many-body quantum theory in condensed matter physics: an introduction. Oxford university press; 2004. |
| [5] | Thomas L. H. In Mathematical Proceedings of the Cambridge Philosophical Society. Vol. 23, Cambridge University Press; 1927, 542-548. |
| [6] | Percus J. K. The role of model systems in the few- body reduction of the N-fermion problem. International Journal of Quantum Chemistry. 1978, 13(1), 89-124. https://doi.org/10.1002/qua.560130108 |
| [7] | Pope T., Hofer W. Exact orbital-free kinetic energy functional for general many-electron systems. Frontiers of Physics. 2020, 15, 23603. https://doi.org/10.1007/s11467-019-0948-6 |
| [8] | Kohn W., Sham L. J. Self-Consistent Equations Including Exchange and Correlation Effects. Physical Review Journals Archive. 1965, 140(4A), A1133-A1138. https://doi.org/10.1103/PhysRev.140.A1133 |
| [9] | Neugebauer J. Couplings between electronic transitions in a subsystem formulation of time- dependent density functional theory. The Journal of Chemical Physics. 2007, 126(13), 134116. https://doi.org/10.1063/1.2713754 |
| [10] | Karasiev V. V., Jones R. S., Trickey S. B., Harris F. E. Properties of constraint-based single- point approximate kinetic energy functionals. Phys. Rev. B. 2009, 80(24), 245120-245136. https://doi.org/10.1103/PhysRevB.80.245120 |
| [11] | Laricchia S., Fabiano E., Constantin L., Della Sala F. Generalized Gradient Approximations of the Noninteracting Kinetic Energy from the Semiclassical Atom Theory: Rationalization of the Accuracy of the Frozen Density Embedding Theory for Nonbonded Interactions. Journal of chemical theory and computation. 2011, 7(8), 2439-2451. https://doi.org/10.1021/ct200382w |
| [12] | Lembarki A., Chermette H. Obtaining a gradient- corrected kinetic-energy functional from the Perdew- Wang exchange functional. Phys. Rev. A. 1994, 50(6), 5328-5331. https://doi.org/10.1103/PhysRevA.50.5328 |
| [13] | Thakkar A. J. Comparison of kinetic-energy density functionals. Phys. Rev. A. 1992, 46(11), 6920-6924. https://doi.org/10.1103/PhysRevA.46.6920 |
| [14] | Burke K. Perspective on density functional theory. The Journal of Chemical Physics. 2012, 136(15), 150901. https://doi.org/10.1063/1.4704546 |
| [15] | Perdew J. P., Wang Y. Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B. 1992, 45(23), 13244-13249. https://doi.org/10.1103/PhysRevB.45.13244 |
| [16] | Yang W. Gradient correction in Thomas-Fermi theory. Physical Review A. 1986, 34(6), 4575. https://doi.org/10.1103/PhysRevA.34.4575 |
| [17] | Laricchia S., Constantin L. A., Fabiano E., Della Sala F. Laplacian-Level Kinetic Energy Approximations Based on the Fourth-Order Gradient Expansion: Global Assessment and Application to the Subsystem Formulation of Density Functional Theory. Journal of chemical theory and computation. 2014, 10(1), 164-179. https://doi.org/10.1021/ct400836s |
| [18] | Urso V. Development of novel kinetic energy functional for orbital-free density functional theory applications. International Journal of Modern Physics C. 2021, 33(04), 2250044. https://doi.org/10.1142/S0129183122500449 |
| [19] | Urso V. Development of novel kinetic energy functional for orbital-free density functional theory applications II. London Journals Press. 2022, 22(12), 1-8. DDC Code: 530.41 LCC Code: QC176.8.E4. |
| [20] | Mahan G. D., Subbaswamy K. Local density theory of polarizability. New York: Springer; 1990. |
| [21] | Loos P.-F., Gill P. M. W. The uniform electron gas. Wiley Interdisciplinary Reviews: Computational Molecular Science. 2016, 6. https://doi.org/10.1002/wcms.1257 |
| [22] | Fiolhais C., Almeida L. M. Surface energies of simple metals from slabs: Comparison of exchange- correlation density functionals. International Journal of Quantum Chemistry. 2005, 101(6), 645-650. https://doi.org/10.1002/qua.20321 |
| [23] | Lehtola S., Steigemann C., Oliveira M. J., Marques M.A. Recent developments in libxc - A comprehensive library of functionals for density functional theory. SoftwareX. 2018, 7, 1-5. |
APA Style
Urso, V. (2024). New Functional Orbital-free Within DFT for Metallic Systems. International Journal of Systems Science and Applied Mathematics, 9(2), 30-36. https://doi.org/10.11648/j.ijssam.20240902.12
ACS Style
Urso, V. New Functional Orbital-free Within DFT for Metallic Systems. Int. J. Syst. Sci. Appl. Math. 2024, 9(2), 30-36. doi: 10.11648/j.ijssam.20240902.12
AMA Style
Urso V. New Functional Orbital-free Within DFT for Metallic Systems. Int J Syst Sci Appl Math. 2024;9(2):30-36. doi: 10.11648/j.ijssam.20240902.12
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Download@article{10.11648/j.ijssam.20240902.12,
author = {Vittoria Urso},
title = {New Functional Orbital-free Within DFT for Metallic Systems},
journal = {International Journal of Systems Science and Applied Mathematics},
volume = {9},
number = {2},
pages = {30-36},
doi = {10.11648/j.ijssam.20240902.12},
url = {https://doi.org/10.11648/j.ijssam.20240902.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20240902.12},
abstract = {I present the continuation of a study on Laplacian Level Kinetic Energy (KE) functionals applied to metallic nanosystems. The development of novel Kinetic Energy functionals is an important topic in density functional theory (DFT). The nanoparticles are patterned using gelatin spheres of different sizes, background density and number of electrons. To reproduce the correct kinetic and potential energy density of the various nanoparticles, the use of semilocal descriptors is necessary. Need an explicit density functional expression for the kinetic energy of electrons, including the first e second functional derivative, i.e. the kinetic potential and the kinetic kernel, respectively. The exact explicit form of the non interacting kinetic energy, as a functional of the electron density, is known only for the homogeneous electron gas (HEG), i.e., the Thomas-Fermi (TF) local functional and for 1 and 2 electron systems, i.e., the von Weizsacker (VW) functional. In between these two extreme cases, different semilocal or non local approximations were developed in recent years. Most semilocal KE functionals are based on modifications of the second-order gradient expansion (GE2) or fourth-order gradient expansion (GE4). I find that the Laplacian contribute is fundamental for the description of the energy and the potential of nanoparticles. I propose a new LAP2 semilocal functional which, better than the previous ones, allows us to obtain fewer errors both of energy and potential. More details of the previous calculations can be found in my 2 previous works which will be cited in the text.},
year = {2024}
}
TY - JOUR T1 - New Functional Orbital-free Within DFT for Metallic Systems AU - Vittoria Urso Y1 - 2024/08/04 PY - 2024 N1 - https://doi.org/10.11648/j.ijssam.20240902.12 DO - 10.11648/j.ijssam.20240902.12 T2 - International Journal of Systems Science and Applied Mathematics JF - International Journal of Systems Science and Applied Mathematics JO - International Journal of Systems Science and Applied Mathematics SP - 30 EP - 36 PB - Science Publishing Group SN - 2575-5803 UR - https://doi.org/10.11648/j.ijssam.20240902.12 AB - I present the continuation of a study on Laplacian Level Kinetic Energy (KE) functionals applied to metallic nanosystems. The development of novel Kinetic Energy functionals is an important topic in density functional theory (DFT). The nanoparticles are patterned using gelatin spheres of different sizes, background density and number of electrons. To reproduce the correct kinetic and potential energy density of the various nanoparticles, the use of semilocal descriptors is necessary. Need an explicit density functional expression for the kinetic energy of electrons, including the first e second functional derivative, i.e. the kinetic potential and the kinetic kernel, respectively. The exact explicit form of the non interacting kinetic energy, as a functional of the electron density, is known only for the homogeneous electron gas (HEG), i.e., the Thomas-Fermi (TF) local functional and for 1 and 2 electron systems, i.e., the von Weizsacker (VW) functional. In between these two extreme cases, different semilocal or non local approximations were developed in recent years. Most semilocal KE functionals are based on modifications of the second-order gradient expansion (GE2) or fourth-order gradient expansion (GE4). I find that the Laplacian contribute is fundamental for the description of the energy and the potential of nanoparticles. I propose a new LAP2 semilocal functional which, better than the previous ones, allows us to obtain fewer errors both of energy and potential. More details of the previous calculations can be found in my 2 previous works which will be cited in the text. VL - 9 IS - 2 ER -
Department of Basic and Applied Sciences for Engineering, Sapienza University, Rome RM, Italy; Department of Physics, University of Modena and Reggio Emilia, Modena MO, Italy
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