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Journal articles on the topic 'Kohn-Sham equation'

Author: Grafiati

Published: 4 June 2021

Last updated: 12 February 2022

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1

GÁL, TAMÁS. "TREATMENTS OF THE EXCHANGE ENERGY IN DENSITY-FUNCTIONAL THEORY." International Journal of Modern Physics B 22, no. 14 (2008): 2225–39. http://dx.doi.org/10.1142/s0217979208039344.

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Following a recent work [Gál, Phys. Rev. A64, 062503 (2001)], a simple derivation of the density-functional correction of the Hartree–Fock equations, the Hartree–Fock–Kohn–Sham equations, is presented, completing an integrated view of quantum mechanical theories, in which the Kohn–Sham equations, the Hartree–Fock–Kohn–Sham equations and the ground-state Schrödinger equation formally stem from a common ground: density-functional theory, through its Euler equation for the ground-state density. Along similar lines, the Kohn–Sham formulation of the Hartree–Fock approach is also considered. Further, it is pointed out that the exchange energy of density-functional theory built from the Kohn–Sham orbitals can be given by degree-two homogeneous N-particle density functionals (N = 1, 2, …), forming a sequence of degree-two homogeneous exchange-energy density functionals, the first element of which is minus the classical Coulomb-repulsion energy functional.

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2

Li, Tiecheng, and Yanmin Li. "Kohn-Sham equation for time-dependent ensembles." Physical Review A 31, no. 6 (1985): 3970–71. http://dx.doi.org/10.1103/physreva.31.3970.

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3

E, Weinan, and Jianfeng Lu. "The Kohn-Sham equation for deformed crystals." Memoirs of the American Mathematical Society 221, no. 1040 (2012): 1. http://dx.doi.org/10.1090/s0065-9266-2012-00659-9.

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4

Kato, Tsuyoshi, Katsuyuki Nobusada, and Shinji Saito. "Inverse Kohn–Sham Equations Derived from the Density Equation Theory." Journal of the Physical Society of Japan 89, no. 2 (2020): 024301. http://dx.doi.org/10.7566/jpsj.89.024301.

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5

Staroverov, Viktor N. "Contracted Schrödinger equation and Kohn–Sham effective potentials." Molecular Physics 117, no. 1 (2018): 1–5. http://dx.doi.org/10.1080/00268976.2018.1463470.

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6

Watanabe, Naoki, and Masaru Tsukada. "Efficient algorithm for TD-Schrödinger equation and TD-Kohn–Sham equation." Computer Physics Communications 142, no. 1-3 (2001): 255–58. http://dx.doi.org/10.1016/s0010-4655(01)00335-6.

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7

Soba, A., E. A. Bea, and G. Houzeaux. "Resolution of the Kohn-Sham equation using real space discretization with finite elements." Anales AFA 23, no. 1 (2013): 182–84. http://dx.doi.org/10.31527/analesafa.2013.23.1.182.

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8

Dagviikhorol, Naranchimeg, Munkhsaikhan Gonchigsuren, Lochin Khenmedekh, Namsrai Tsogbadrakh, and Ochir Sukh. "Imaginary-Time Time-Dependent Density Functional Calculation of Excited States of Atoms Using CWDVR Approach." Solid State Phenomena 323 (August 30, 2021): 14–20. http://dx.doi.org/10.4028/www.scientific.net/ssp.323.14.

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We have calculated the energies of excited states for the He, Li, and Be atoms by the time dependent self-consistent Kohn Sham equation using the Coulomb Wave Function Discrete Variable Representation CWDVR) approach. The CWDVR approach was used the uniform and optimal spatial grid discretization to the solution of the Kohn-Sham equation for the excited states of atoms. Our results suggest that the CWDVR approach is an efficient and precise solutions of excited-state energies of atoms. We have shown that the calculated electronic energies of excited states for the He, Li, and Be atoms agree with the other researcher values.

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9

Yang, Lei. "An Implicit Solver for the Time-Dependent Kohn-Sham Equation." Numerical Mathematics: Theory, Methods and Applications 14, no. 1 (2021): 261–84. http://dx.doi.org/10.4208/nmtma.oa-2020-0040.

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10

Romanowski, Zbigniew. "Adaptive solver of a Kohn–Sham equation for an atom." Modelling and Simulation in Materials Science and Engineering 17, no. 4 (2009): 045001. http://dx.doi.org/10.1088/0965-0393/17/4/045001.

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11

Fang, Jun, Xingyu Gao, and Aihui Zhou. "A Kohn–Sham equation solver based on hexahedral finite elements." Journal of Computational Physics 231, no. 8 (2012): 3166–80. http://dx.doi.org/10.1016/j.jcp.2011.12.043.

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12

Persson, Clas, and Claudia Ambrosch-Draxl. "A full-band -method for solving the Kohn–Sham equation." Computer Physics Communications 177, no. 3 (2007): 280–87. http://dx.doi.org/10.1016/j.cpc.2007.02.111.

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13

Chávez, Victor H., and Adam Wasserman. "Towards a density functional theory of molecular fragments. What is the shape of atoms in molecules?" Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales 44, no. 170 (2020): 269–79. http://dx.doi.org/10.18257/raccefyn.960.

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In some sense, quantum mechanics solves all the problems in chemistry: The only thing one has to do is solve the Schrödinger equation for the molecules of interest. Unfortunately, the computational cost of solving this equation grows exponentially with the number of electrons and for more than ~100 electrons, it is impossible to solve it with chemical accuracy (~ 2 kcal/mol). The Kohn-Sham (KS) equations of density functional theory (DFT) allow us to reformulate the Schrödinger equation using the electronic probability density as the central variable without having to calculate the Schrödinger wave functions. The cost of solving the Kohn-Sham equations grows only as N3, where N is the number of electrons, which has led to the immense popularity of DFT in chemistry. Despite this popularity, even the most sophisticated approximations in KS-DFT result in errors that limit the use of methods based exclusively on the electronic density. By using fragment densities (as opposed to total densities) as the main variables, we discuss here how new methods can be developed that scale linearly with N while providing an appealing answer to the subtitle of the article: What is the shape of atoms in molecules?

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14

Yamada, Shunsuke, Masashi Noda, Katsuyuki Nobusada, and Kazuhiro Yabana. "First-principles method for propagation of ultrashort pulsed light in thin films." EPJ Web of Conferences 205 (2019): 01003. http://dx.doi.org/10.1051/epjconf/201920501003.

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We develop a first-principles method to simulate the propagation of intense and ultrashort pulsed light in crystalline thin films solving the Maxwell equations for light electromagnetic fields and the time-dependent Kohn-Sham equation for electrons simultaneously using common spatial and temporal grids. As a demonstration, we apply the method to silicon thin films.

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15

Cohen, Or, Leeor Kronik, and Achi Brandt. "Locally Refined Multigrid Solution of the All-Electron Kohn–Sham Equation." Journal of Chemical Theory and Computation 9, no. 11 (2013): 4744–60. http://dx.doi.org/10.1021/ct400479u.

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16

Bauernschmitt, Rüdiger, and Reinhart Ahlrichs. "Stability analysis for solutions of the closed shell Kohn–Sham equation." Journal of Chemical Physics 104, no. 22 (1996): 9047–52. http://dx.doi.org/10.1063/1.471637.

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17

Shen, Yedan, Yang Kuang, and Guanghui Hu. "An Asymptotics-Based Adaptive Finite Element Method for Kohn–Sham Equation." Journal of Scientific Computing 79, no. 1 (2018): 464–92. http://dx.doi.org/10.1007/s10915-018-0861-0.

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18

Hu, Guanghui, Hehu Xie, and Fei Xu. "A multilevel correction adaptive finite element method for Kohn–Sham equation." Journal of Computational Physics 355 (February 2018): 436–49. http://dx.doi.org/10.1016/j.jcp.2017.11.024.

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19

Uemoto, Mitsuharu, Kazuhiro Yabana, Shunsuke A. Sato, Yuta Hirokawa, and Taisuke Boku. "A first-principles simulation method for ultra-fast nano-optics." EPJ Web of Conferences 205 (2019): 04023. http://dx.doi.org/10.1051/epjconf/201920504023.

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We develop a computational approach for ultrafast nano-optics based on first-principles time-dependent density functional theory. Solving Maxwell equations for light propagation and time-dependent Kohn-Sham equation for electron dynamics simultaneously, intense and ultrashort laser pulse interaction with a dielectric nano-structure is described taking full account of nonlinear effects. As an illustrative example, irradiation of a pulsed light on silicon nano-sphere system is presented.

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20

Bao, Gang, Guanghui Hu, and Di Liu. "Towards Translational Invariance of Total Energy with Finite Element Methods for Kohn-Sham Equation." Communications in Computational Physics 19, no. 1 (2016): 1–23. http://dx.doi.org/10.4208/cicp.190115.200715a.

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AbstractNumerical oscillation of the total energy can be observed when the Kohn- Sham equation is solved by real-space methods to simulate the translational move of an electronic system. Effectively remove or reduce the unphysical oscillation is crucial not only for the optimization of the geometry of the electronic structure, but also for the study of molecular dynamics. In this paper, we study such unphysical oscillation based on the numerical framework in [G. Bao, G. H. Hu, and D. Liu, An h-adaptive finite element solver for the calculations of the electronic structures, Journal of Computational Physics, Volume 231, Issue 14, Pages 4967–4979, 2012], and deliver some numerical methods to constrain such unphysical effect for both pseudopotential and all-electron calculations, including a stabilized cubature strategy for Hamiltonian operator, and an a posteriori error estimator of the finite element methods for Kohn-Sham equation. The numerical results demonstrate the effectiveness of our method on restraining unphysical oscillation of the total energies.

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21

Hu, Yang Kuang &. Guanghui. "On Stabilizing and Accelerating SCF Using ITP in Solving Kohn–Sham Equation." Communications in Computational Physics 28, no. 3 (2020): 999–1018. http://dx.doi.org/10.4208/cicp.oa-2019-0024.

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22

Manby, F. R., P. J. Knowles, and A. W. Lloyd. "The Poisson equation in density fitting for the Kohn-Sham Coulomb problem." Journal of Chemical Physics 115, no. 20 (2001): 9144–48. http://dx.doi.org/10.1063/1.1414370.

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23

Yang, Chao, Juan C. Meza, and Lin-Wang Wang. "A Trust Region Direct Constrained Minimization Algorithm for the Kohn–Sham Equation." SIAM Journal on Scientific Computing 29, no. 5 (2007): 1854–75. http://dx.doi.org/10.1137/060661442.

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24

Bao, Gang, Guanghui Hu, and Di Liu. "Real-time adaptive finite element solution of time-dependent Kohn–Sham equation." Journal of Computational Physics 281 (January 2015): 743–58. http://dx.doi.org/10.1016/j.jcp.2014.10.052.

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25

Ospadov, Egor, Jianmin Tao, Viktor N. Staroverov, and John P. Perdew. "Visualizing atomic sizes and molecular shapes with the classical turning surface of the Kohn–Sham potential." Proceedings of the National Academy of Sciences 115, no. 50 (2018): E11578—E11585. http://dx.doi.org/10.1073/pnas.1814300115.

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The Kohn–Sham potential veff(r) is the effective multiplicative operator in a noninteracting Schrödinger equation that reproduces the ground-state density of a real (interacting) system. The sizes and shapes of atoms, molecules, and solids can be defined in terms of Kohn–Sham potentials in a nonarbitrary way that accords with chemical intuition and can be implemented efficiently, permitting a natural pictorial representation for chemistry and condensed-matter physics. Let ϵmax be the maximum occupied orbital energy of the noninteracting electrons. Then the equation veff(r)=ϵmax defines the surface at which classical electrons with energy ϵ≤ϵmax would be turned back and thus determines the surface of any electronic object. Atomic and ionic radii defined in this manner agree well with empirical estimates, show regular chemical trends, and allow one to identify the type of chemical bonding between two given atoms by comparing the actual internuclear distance to the sum of atomic radii. The molecular surfaces can be fused (for a covalent bond), seamed (ionic bond), necked (hydrogen bond), or divided (van der Waals bond). This contribution extends the pioneering work of Z.-Z. Yang et al. [Yang ZZ, Davidson ER (1997) Int J Quantum Chem 62:47–53; Zhao DX, et al. (2018) Mol Phys 116:969–977] by our consideration of the Kohn–Sham potential, protomolecules, doubly negative atomic ions, a bond-type parameter, seamed and necked molecular surfaces, and a more extensive table of atomic and ionic radii that are fully consistent with expected periodic trends.

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26

Kusakabe, Koichi. "A Rigorous Extension of the Kohn-Sham Equation for Strongly Correlated Electron Systems." Journal of the Physical Society of Japan 70, no. 7 (2001): 2038–48. http://dx.doi.org/10.1143/jpsj.70.2038.

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27

LI, YANLING, and ZHI ZENG. "FIRST-PRINCIPLES STUDY OF THE STRUCTURAL, ELECTRONIC AND OPTICAL PROPERTIES OF MgSiO3 AT HIGH PRESSURE." International Journal of Modern Physics C 20, no. 07 (2009): 1093–101. http://dx.doi.org/10.1142/s0129183109014242.

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The high-pressure behavior of perovskite ( MgSiO 3) is studied based on density functional simulations within generalized gradient approximation (GGA). All calculations are performed by using the linear augmented plane waves plus local orbital (LAPW+lo) method to solve the scalar-relativistic Kohn-Sham equations. The static calculations predict a perovskite (pnma phase) — post-perovskite (Cmcm phase) transition occurring at 86 gigapascals (GPa). The similar bulk modulus values, differing only 3 GPa, are given by using three kinds of equation of states. The electronic structure and optical properties of MgSiO 3 at phase transition pressure are also discussed.

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28

Repisky, Michal, Lukas Konecny, Marius Kadek, et al. "Excitation Energies from Real-Time Propagation of the Four-Component Dirac–Kohn–Sham Equation." Journal of Chemical Theory and Computation 11, no. 3 (2015): 980–91. http://dx.doi.org/10.1021/ct501078d.

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29

Ku, Jonas, Aditya Kamath, Tucker Carrington, and Sergei Manzhos. "Machine Learning Optimization of the Collocation Point Set for Solving the Kohn–Sham Equation." Journal of Physical Chemistry A 123, no. 49 (2019): 10631–42. http://dx.doi.org/10.1021/acs.jpca.9b09732.

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30

Romanowski, Zbigniew. "A B-spline finite element solution of the Kohn–Sham equation for an atom." Modelling and Simulation in Materials Science and Engineering 16, no. 1 (2007): 015003. http://dx.doi.org/10.1088/0965-0393/16/1/015003.

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31

Zavodinsky, Victor G., and Olga A. Gorkusha. "A Simple Quantum Mechanics Way to Simulate Nanoparticles and Nanosystems without Calculation of Wave Functions." ISRN Nanomaterials 2012 (August 29, 2012): 1–3. http://dx.doi.org/10.5402/2012/531965.

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It is shown that the variation principle can be used as a practical way to find the electron density and the total energy in the frame of the density functional theory (DFT) without solving of the Kohn-Sham equation. On examples of diatomic systems Si2, Al2, and N2, the equilibrium interatomic distances and binding energies have been calculated in good comparison with published data. The method can be improved to simulate nanoparticles containing thousands and millions atoms.

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32

Bylaska, Eric J., Michael Holst, and John H. Weare. "Adaptive Finite Element Method for Solving the Exact Kohn−Sham Equation of Density Functional Theory." Journal of Chemical Theory and Computation 5, no. 4 (2009): 937–48. http://dx.doi.org/10.1021/ct800350j.

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33

Zhou, Yunkai, James R. Chelikowsky, and Yousef Saad. "Chebyshev-filtered subspace iteration method free of sparse diagonalization for solving the Kohn–Sham equation." Journal of Computational Physics 274 (October 2014): 770–82. http://dx.doi.org/10.1016/j.jcp.2014.06.056.

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34

NICHOLSON, D. M. C., G. M. STOCKS, Y. WANG, W. A. SHELTON, Z. SZOTEK, and W. M. TEMMERMAN. "LOCAL DENSITY CALCULATIONS FOR LARGE SYSTEMS USING MULTIPLE SCATTERING THEORY." Surface Review and Letters 02, no. 01 (1995): 71–79. http://dx.doi.org/10.1142/s0218625x95000078.

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The accuracy of energy differences calculated from first principles within the local density approximation (LDA) has been demonstrated for a large number of systems. Armed with these energy differences researchers are addressing questions of phase stability and structural relaxation. However, these techniques are very computationally intensive and are therefore not being used for the simulation of large complex systems. Many of the methods for solving the Kohn-Sham equations of the LDA rely on basis set methods for solution of the Schrodinger equation. An alternative approach is multiple scattering theory (MST). We feel that the locally exact solutions of the Schrodinger equation which are at the heart of the multiple scattering method give the method an efficiency which cannot be ignored in the search for methods with which to attack large systems. Furthermore, the analytic properties of the Green function which is determined directly in MST result in computational shortcuts.

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35

Ekuma, E. C., L. Franklin, G. L. Zhao, J. T. Wang, and D. Bagayoko. "Local density approximation description of electronic properties of wurtzite cadmium sulfide (w-CdS)." Canadian Journal of Physics 89, no. 3 (2011): 319–24. http://dx.doi.org/10.1139/p11-023.

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We present calculated, electronic, and related properties of wurtzite cadmium sulfide (w-CdS). Our ab initio, nonrelativistic calculations employ a local density functional approximation (LDA) potential and the linear combination of atomic orbitals (LCAO). Following the Bagayoko, Zhao, and Williams (BZW) method, we solved self-consistently both the Kohn–Sham equation and the equation giving the ground-state density in terms of the wave functions of the occupied states. Our calculated, direct band gap of 2.47 eV at the Γ point is in excellent agreement with experiment. So are the calculated density of states and the electron effective mass. In particular, our results reproduce the peaks in the conduction band density of states, within experimental uncertainties.

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36

Ullrich, CA, and EKU Gross. "Density Functional Theory of Normal and Superconducting Electron Liquids: Explicit Functionals via the Gradient Expansion." Australian Journal of Physics 49, no. 1 (1996): 103. http://dx.doi.org/10.1071/ph960103.

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The basic idea of density functional theory is to map an interacting many-particle system on an effective non-interacting system in such a way that the ground-state densities of the two systems are identical. The non-interacting particles move in an effective local potential which is a functional of the density. The central task of density functional theory is to find good approximations for the density dependence of this local single-particle potential. An overview of recent advances in the construction of this potential (beyond the local-density approximation) will be given along with successful applications in quantum chemistry and solid state theory. We then turn to the extension of density functional theory to superconductors and first discuss the Hohenberg-Kohn-Sham-type existence theorems. In the superconducting analogue of the the normal-state Kohn-Sham formalism, a local single-particle potential is needed which now depends on two densities, the ordinary density n(r) and the anomalous density △(r,r/). As a first step towards the construction of such a potential, a gradient expansion technique for superconductors is presented and applied to calculate an approximation of the non-interacting kinetic energy functional Ts[n, △]. We also obtain a Thomas-Fermi-type variational equation for superconductors.

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37

Kadek, Marius, Lukas Konecny, Bin Gao, Michal Repisky, and Kenneth Ruud. "X-ray absorption resonances near L2,3-edges from real-time propagation of the Dirac–Kohn–Sham density matrix." Physical Chemistry Chemical Physics 17, no. 35 (2015): 22566–70. http://dx.doi.org/10.1039/c5cp03712c.

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38

Zhu, Ying, and John M. Herbert. "Self-consistent predictor/corrector algorithms for stable and efficient integration of the time-dependent Kohn-Sham equation." Journal of Chemical Physics 148, no. 4 (2018): 044117. http://dx.doi.org/10.1063/1.5004675.

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39

Bao, Gang, Guanghui Hu, and Di Liu. "Numerical Solution of the Kohn-Sham Equation by Finite Element Methods with an Adaptive Mesh Redistribution Technique." Journal of Scientific Computing 55, no. 2 (2012): 372–91. http://dx.doi.org/10.1007/s10915-012-9636-1.

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40

BANG*, Junhyeok. "A Self-Consistent Crank-Nicolson Method for Solving Time-Dependent Kohn-Sham Equation in a Localized Atomic Orbital Basis Set." New Physics: Sae Mulli 70, no. 8 (2020): 646–51. http://dx.doi.org/10.3938/npsm.70.646.

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41

Scheiner, Andrew C., Jon Baker, and Jan W. Andzelm. "Molecular energies and properties from density functional theory: Exploring basis set dependence of Kohn?Sham equation using several density functionals." Journal of Computational Chemistry 18, no. 6 (1997): 775–95. http://dx.doi.org/10.1002/(sici)1096-987x(19970430)18:6<775::aid-jcc4>3.0.co;2-p.

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42

BANG*, Junhyeok. "Erratum: A Self-Consistent Crank-Nicolson Method for Solving Time-Dependent Kohn-Sham Equation in a Localized Atomic Orbital Basis Set." New Physics: Sae Mulli 70, no. 10 (2020): 908. http://dx.doi.org/10.3938/npsm.70.908.

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43

Faber, C., P. Boulanger, C. Attaccalite, I. Duchemin, and X. Blase. "Excited states properties of organic molecules: from density functional theory to the GW and Bethe–Salpeter Green's function formalisms." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372, no. 2011 (2014): 20130271. http://dx.doi.org/10.1098/rsta.2013.0271.

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Many-body Green's function perturbation theories, such as the GW and Bethe–Salpeter formalisms, are starting to be routinely applied to study charged and neutral electronic excitations in molecular organic systems relevant to applications in photovoltaics, photochemistry or biology. In parallel, density functional theory and its time-dependent extensions significantly progressed along the line of range-separated hybrid functionals within the generalized Kohn–Sham formalism designed to provide correct excitation energies. We give an overview and compare these approaches with examples drawn from the study of gas phase organic systems such as fullerenes, porphyrins, bacteriochlorophylls or nucleobases molecules. The perspectives and challenges that many-body perturbation theory is facing, such as the role of self-consistency, the calculation of forces and potential energy surfaces in the excited states, or the development of embedding techniques specific to the GW and Bethe–Salpeter equation formalisms, are outlined.

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44

SONODA, KOHJI, FUYUKI SHIMOJO, KOZO HOSHINO, and MITSUO WATABE. "SIZE AND DENSITY DEPENDENCES OF THE SCREENING EFFECT IN METAL CLUSTERS." Surface Review and Letters 03, no. 01 (1996): 329–34. http://dx.doi.org/10.1142/s0218625x96000607.

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We employ a jellium sphere as a model for a metal cluster and calculate the change in the electronic states when an extra positive point charge is introduced at its center, by solving the Kohn–Sham equation in the local-density approximation and in the local-spin-density approximation with the self-interaction correction, and by solving the Hartree–Fock equation. The screening charge density around the extra charge is estimated by subtracting the charge induced near the cluster surface from the total induced charge density. It is found that, even for small clusters with the number of atoms N=20, 40, and 58, the screening effect is similar to that in the bulk jellium and that the screening charge distributions for larger clusters with N=92 almost coincide with that in the bulk. The density dependence of the screening charge is also investigated by calculating the screening charge for rs=3.0, 4.0, and 5.0. It is shown that the period of oscillation of these screening charge distributions can almost be scaled by rs and it is close to that of the Friedel oscillation. The results obtained by three methods are compared with special attention to the effect of the self-interaction.

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45

Abdulkareem, Aawzad A., Sarkawt A. Sami, and Badal H. Elias. "Structural, Electronic and Optical Properties of Cubic Perovskite Cspbx3 (X= Br, Cl and I)." Science Journal of University of Zakho 8, no. 1 (2020): 23–28. http://dx.doi.org/10.25271/sjuoz.2020.8.1.632.

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Plane waves with norm conserving pseudopotentials (PW-PP) method in conjunction with density functional theory (DFT) frame work have been used to investigate structural, electronic and optical properties of lead-halide cubic perovskite CsPbX3 (X=Br, Cl and I). The generalized gradient approximation (GGA), specifically Perdew-Burke-Ernzerhof (PBE) flavor, has been chosen to treat the exchange correlation term of Kohn-Sham equation. Structural parameters are comparable with other theoretical and experimental studies. In spite of good agreement of our band gap values with other theoretical works, however, they were not comparable when compared to the experimental values due to the well-known problem of Eg value underestimation of DFT. To update the value, we have used GW method as a self-consistent quasiparticle method on energies and wave functions and indeed they have been improved. Optical properties have been calculated using density functional perturbation theory (DFPT). Our results show that CsPbX3 (X=Br, Cl, I) has maximum response to the electromagnetic spectrum at low energies (visible region) but minimum response at high energies.

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46

Trinh, Lang Hoang, Tao Van Chau, Chien Hoang Le, Hong Thi Yen Huynh, and Tram Ngoc Huynh. "Positron annihilation rate in single atom with slater type orbital approximation." Science and Technology Development Journal 16, no. 4 (2013): 43–51. http://dx.doi.org/10.32508/stdj.v16i4.1595.

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A theoretical approximation for the structure of many-positron and manyelectron atoms in bound states is presented. The purpose of this theory is to permit the calculation of positron lifetimes from annihilation enhancement factor which is directly estimated by pair correlation function for each element atom, but not analytical form of correlation functions which depend upon homogeneous electron gas Monte– Carlo simulation data. We therefore used a modified orbital approximation for the electrons and positron. The orbital modification consisting of explicit electronpositron and electron-electron correlation in each elec-tronic orbital was used for the electrons and positron wave functions. The kinetic energies of the electrons and positron were treated on the same footing, and the Born-Oppenheimer approximation was applied to the nuclei. In this paper we treated only those systems for the valance electrons in the real spatial coordinate of the atom or molecule. The complex of many-particle problem was solved by the Schrongdinger of one particle equation which is derived by Kohn–Sham approximation and single particle wave function of Slater type orbital. As a result of this model, the positron annihilation rate and lifetime in some atoms, Ti, Zn and Zr, were calculated.

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Chen, Duan, and Guo-Wei Wei. "Quantum Dynamics in Continuum for Proton Transport I: Basic Formulation." Communications in Computational Physics 13, no. 1 (2013): 285–324. http://dx.doi.org/10.4208/cicp.050511.050811s.

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AbstractProton transport is one of the most important and interesting phenomena in living cells. The present work proposes a multiscale/multiphysics model for the understanding of the molecular mechanism of proton transport in transmembrane proteins. We describe proton dynamics quantum mechanically via a density functional approach while implicitly model other solvent ions as a dielectric continuum to reduce the number of degrees of freedom. The densities of all other ions in the solvent are assumed to obey the Boltzmann distribution. The impact of protein molecular structure and its charge polarization on the proton transport is considered explicitly at the atomic level. We formulate a total free energy functional to put proton kinetic and potential energies as well as electrostatic energy of all ions on an equal footing. The variational principle is employed to derive nonlinear governing equations for the proton transport system. Generalized Poisson-Boltzmann equation and Kohn-Sham equation are obtained from the variational framework. Theoretical formulations for the proton density and proton conductance are constructed based on fundamental principles. The molecular surface of the channel protein is utilized to split the discrete protein domain and the continuum solvent domain, and facilitate the multiscale discrete/continuum/quantum descriptions. A number of mathematical algorithms, including the Dirichlet to Neumann mapping, matched interface and boundary method, Gummel iteration, and Krylov space techniques are utilized to implement the proposed model in a computationally efficient manner. The Gramicidin A (GA) channel is used to demonstrate the performance of the proposed proton transport model and validate the efficiency of proposed mathematical algorithms. The electrostatic characteristics of the GA channel is analyzed with a wide range of model parameters. The proton conductances are studied over a number of applied voltages and reference concentrations. A comparison with experimental data verifies the present model predictions and validates the proposed model.

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Komorovský, Stanislav, Michal Repiský, Olga L. Malkina, Vladimir G. Malkin, Irina Malkin Ondík, and Martin Kaupp. "A fully relativistic method for calculation of nuclear magnetic shielding tensors with a restricted magnetically balanced basis in the framework of the matrix Dirac–Kohn–Sham equation." Journal of Chemical Physics 128, no. 10 (2008): 104101. http://dx.doi.org/10.1063/1.2837472.

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Nagy, Á. "Kohn-Sham equations for multiplets." Physical Review A 57, no. 3 (1998): 1672–77. http://dx.doi.org/10.1103/physreva.57.1672.

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Majumdar, Sangita, and Amlan K. Roy. "Shannon Entropy in Confined He-Like Ions within a Density Functional Formalism." Quantum Reports 2, no. 1 (2020): 189–207. http://dx.doi.org/10.3390/quantum2010012.

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Shannon entropy in position ( S r ) and momentum ( S p ) spaces, along with their sum ( S t ) are presented for unit-normalized densities of He, Li + and Be 2 + ions, spatially confined at the center of an impenetrable spherical enclosure defined by a radius r c . Both ground, as well as some selected low-lying singly excited states, viz., 1sns (n = 2–4) 3S, 1snp (n = 2–3) 3P, 1s3d 3D, are considered within a density functional methodology that makes use of a work function-based exchange potential along with two correlation potentials (local Wigner-type parametrized functional, as well as the more involved non-linear gradient- and Laplacian-dependent Lee-Yang-Parr functional). The radial Kohn-Sham (KS) equation is solved using an optimal spatial discretization scheme via the generalized pseudospectral (GPS) method. A detailed systematic analysis of the confined system (relative to the corresponding free system) is performed for these quantities with respect to r c in tabular and graphical forms, with and without electron correlation. Due to compression, the pattern of entropy in the aforementioned states becomes characterized by various crossovers at intermediate and lower r c regions. The impact of electron correlation is more pronounced in the weaker confinement limit and appears to decay with the rise in confinement strength. The exchange-only results are quite good to provide a decent qualitative discussion. The lower bounds provided by the entropic uncertainty relation hold well in all cases. Several other new interesting features are observed.

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