Ab initio calculations of structural and electronic properties of crystal solids in density functional and pseudopotential approach in momentum space: Details and examples
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 3, pp. 5-30
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The paper discusses the methods of density functional theory, pseudopotential theory and plane-wave basis set approach. These theories serve as a basis for quantum-chemical study of structural and physical-chemical properties of crystals. Structural and electronic properties of carbon, silicon, germanium and nickel crystals have been calculated. The results of calculations are compared with experimental data.
Keywords: density functional theory, local density approximation, pseudopotential method, plane-wave basis set.
@article{UZKU_2009_151_3_a0,
     author = {V. V. Klekovkina and R. M. Aminova},
     title = {Ab initio calculations of structural and electronic properties of crystal solids in density functional and pseudopotential approach in momentum space: {Details} and examples},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {5--30},
     year = {2009},
     volume = {151},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2009_151_3_a0/}
}
TY  - JOUR
AU  - V. V. Klekovkina
AU  - R. M. Aminova
TI  - Ab initio calculations of structural and electronic properties of crystal solids in density functional and pseudopotential approach in momentum space: Details and examples
JO  - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
PY  - 2009
SP  - 5
EP  - 30
VL  - 151
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/UZKU_2009_151_3_a0/
LA  - ru
ID  - UZKU_2009_151_3_a0
ER  - 
%0 Journal Article
%A V. V. Klekovkina
%A R. M. Aminova
%T Ab initio calculations of structural and electronic properties of crystal solids in density functional and pseudopotential approach in momentum space: Details and examples
%J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
%D 2009
%P 5-30
%V 151
%N 3
%U http://geodesic.mathdoc.fr/item/UZKU_2009_151_3_a0/
%G ru
%F UZKU_2009_151_3_a0
V. V. Klekovkina; R. M. Aminova. Ab initio calculations of structural and electronic properties of crystal solids in density functional and pseudopotential approach in momentum space: Details and examples. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 3, pp. 5-30. http://geodesic.mathdoc.fr/item/UZKU_2009_151_3_a0/

[1] Catlow C. R. A., Price G. D., “Computer modeling of solid-state inorganic materials”, Nature, 347 (1990), 243–248 | DOI

[2] Zhang L., Niu Y., Li Q. et al., “Ab initio prediction of superconductivity in molecular metallic hydrogen under high pressure”, Solid State Commun., 141 (2007), 610–614 | DOI

[3] Mattioli G., Filippone F., Giannozzi P. et al., “Theoretical design of coupled organic-inorganic systems”, Phys. Rev. Lett., 101 (2008), Art. 126805 | DOI

[4] Feng H.-J., Liu F.-M., “First-principles prediction of coexistence of magnetism and ferroelectricity in rhombohedral $\mathrm{Bi}_2\mathrm{Fe}\mathrm{TiO}_6$”, Phys. Lett. A, 372 (2008), 1904–1909 | DOI | Zbl

[5] Zhang L., Wang Y., Cui T. et al., “First-principles study of the pressure-induced rutile-$\mathrm{CaCl}_2$ phase transition in $\mathrm{MgF}_2$”, Solid State Commun., 145 (2008), 283–287 | DOI

[6] An J., Subedi A., Singh D. J., “Ab initio phonon dispersions for PbTe”, Solid State Commun., 148 (2008), 417–419 | DOI

[7] Kheine V., Koen M., Ueir D., Teoriya psevdopotentsiala, Mir, M., 1973, 557 pp.

[8] Zaiman Dzh., Vychislenie blokhovskikh funktsii, Mir, M., 1973, 159 pp.

[9] Singh D. J., Nordstrüm L., Planewaves, Pseudopotentials and LAPW Method, Springer, N.Y., 2006, 134 pp.

[10] Ihm J., Zunger A., Cohen M. L., “Momentum-space formalism for the total energy of solids”, J. Phys. C Solid State Phys., 12 (1979), 4409–4422 | DOI

[11] Denteneer P. J. H., van Haeringen W., “The pseudopotential-density-functional method in momentum space: details and test cases”, J. Phys. C Solid State Phys., 18 (1985), 4127–4142 | DOI

[12] Peressi M., Baldereschi A., Baroni S., “Ab initio studies of structural and electronic properties”, Characterization of Semiconductor Heterostructures and Nanostructures, ed. C. Lamberti, Elsevier, 2008, 17–54 | DOI

[13] Jones R. O., Gunnarsson O. P., “The density functional formalism, its applications and prospects”, Rev. Mod. Phys., 61:3 (1989), 689–740 | DOI

[14] Kohn W., Becke A. D., Parr R. G., “Density Functional Theory of Electronic Structure”, J. Chem. Phys., 100 (1996), 12974–12980 | DOI

[15] Nagy Á., “Density functional. Theory and application to atoms and molecules”, Phys. Rep., 298 (1998), 1–79 | DOI

[16] Kohn W., “Nobel Lecture: Electronic structure of matter – wave functions and density functional”, Rev. Mod. Phys., 71:5 (1999), 1253–1266 ; Kon V., “Elektronnaya struktura veschestva – volnovye funktsii i funktsionaly plotnosti”, Usp. fiz. nauk, 172:3 (2002), 336–348 | DOI | DOI

[17] Density Functional Theory, Lecture Notes in Physics, Springer, N.Y., 1983, 301 pp.

[18] Teoriya neodnorodnogo elektronnogo gaza, Mir, M., 1987, 400 pp.

[19] Topics in Current Chemistry: Density Functional Theory, v. I, Functionals and Effective Potentals, Springer, Berlin–Heidelberg, 1996, 224 pp.

[20] Topics in Current Chemistry: Density Functional Theory, v. II, Relativistic and Time Dependent Extensions, Springer, Berlin–Heidelberg, 1996, 209 pp.

[21] Density Functionals: Theory and Applications, Lecture Notes in Physics, Springer, N.Y., 1998, 194 pp.

[22] Hohenberg P., Kohn W., “Inhomogeneous Electron Gas”, Phys. Rev. B, 136:3 (1964), 864–876 | DOI | MR

[23] Highlight of Condensed-Matter Theory, eds. F. Bassani, F. Fumi, M. P. Tosi, Elsevier Science Ltd., 1985, 940 pp.

[24] Levy M., “Electron densities in search of Hamiltonians”, Phys. Rev. A, 24:2 (1982), 1200–1208 | DOI

[25] Physics as Natural Philosophy, Essays in Honor of Laszlo Tisza on his 75th Birthday, eds. A. Shimony, H. Feshbach, MIT Press, Cambridge, Mass., 1982, 448 pp.

[26] Janak J. F., “Proof that $\partial E/\partial n_i=\varepsilon_i$ in density functional theory”, Phys. Rev. B, 18:12 (1978), 7165–7168 | DOI

[27] Von Barth U., Hedin L., “Local-density theory of multplet structure”, Phys. Rev. A, 20:4 (1979), 1693–1703 | DOI

[28] Sousa S. F., Fernandes P. A., Ramos M. J., “General Performance of Density Functional”, J. Phys. Chem. A, 111 (2007), 10439–10452 | DOI

[29] Kohn W., Sham L., “Self-consistent equations including exchange and correlation effects”, Phys. Rev. A, 140:4 (1965), 1133–1138 | DOI | MR

[30] Perdew J. P., Zunger A., “Self-interaction correction to density-functional approximations for many-electron systems”, Phys. Rev. B, 23:10 (1981), 5048–5079 | DOI

[31] Ceperley D. M., “Ground state of the fermion one-component plasma: A Monte-Carlo study in two and three dimension”, Phys. Rev. B, 18:7 (1978), 3126–3138 | DOI

[32] Slater J. C., “Simplification of the Hartree–Fock Method”, Phys. Rev. B, 81:3 (1951), 385–390 | DOI | MR | Zbl

[33] Gunnarsson O., Lundqvist B. I., “Excange and correlation in atoms, molecules, and solids by the spin-density-functional formalism”, Phys. Rev. B, 13:10 (1976), 4274–4298 | DOI

[34] Langreth D. C., Perdew J. P., “Excange-correlation energy of a metallic surface: Wave-vector analysis”, Phys. Rev. B, 15:6 (1977), 2884–2901 | DOI

[35] Evarestov R. A., Kvantovokhimicheskie metody v teorii tverdogo tela, Izd-vo Leningr. un-ta, L., 1982, 280 pp.

[36] Nemoshkalenko V. V., Kucherenko Yu. N., Metody vychislitelnoi fiziki v teorii tverdogo tela. Elektronnye sostoyaniya v neidealnykh kristallakh, Naukova dumka, Kiev, 1986, 296 pp.

[37] Fundamental Materials Research: Electronic Properties of Solids Using Cluster Methods, Kluwer Academic, N.Y., 2002, 202 pp.

[38] Kittel Ch., Kvantovaya teoriya tverdykh tel, Nauka, M., 1967, 491 pp.

[39] Louie S. G., Ho K. M., Cohen M. L., “Self-consistent mixed-basis approach to the electronic structure in solids”, Phys. Rev. B, 19:4 (1979), 1774–1782 | DOI

[40] Singh D., “Ground-state properties of lanthanum: Treatment of extended-core states”, Phys. Rev. B, 43:8 (1991), 6388–6392 | DOI

[41] Evarestov R. A., Quantum Chemistry of Solids. The LCAO First-Principles Treatment of Crystals, Springer, Berlin–Heidelberg, 2007, 571 pp.

[42] Bandura A. V., Evarestov R. A., Neempiricheskie raschety kristallov v atomnom bazise (s ispolzovaniem Internet-saitov i parallelnykh vychislenii), Izd-vo S.-Peterb. un-ta, SPb., 2004, 232 pp.

[43] Evarestov R. A., Smirnov P. M., Metody teorii grupp v kvantovoi khimii tverdogo tela, Izd-vo Leningr. un-ta, L., 1987, 375 pp.

[44] Chadi D. J., Cohen M. L., “Special Points in the Brillion Zone”, Phys. Rev. B, 8:12 (1973), 5747–5753 | DOI | MR

[45] Baldereschi A., “Mean-Value Point in the Brillion Zone”, Phys. Rev. B, 7:12 (1973), 5212–5215 | DOI

[46] Monkhorst H. J., Pack J. D., “Special points for Brillion-zone integrations”, Phys. Rev. B, 13:12 (1976), 5188–5192 | DOI | MR

[47] Gill P. E., Murray W., Wright M. H., Practical Optimization, Acad. Press, London–N.Y., 1981, 417 pp. | MR

[48] Gillan M. J., “Calculation of the vacancy formation energy in aluminium”, J. Phys. Condens. Matter., 1 (1989), 689–711 | DOI

[49] S̆tich I., Car R., Parrinello M., Baroni S., “Conjugate gradient minimization of the energy functional: A new method for electronic structure calculation”, Phys. Rev. B, 39:8 (1989), 4997–5004 | DOI

[50] Teter M. P., Payne M. C., Allan D. C., “Solution of Schrödinger's equation for large systems”, Phys. Rev. B, 40:18 (1989), 12255–12263 | DOI

[51] Payne M. C., Teter M. P., Allan D. C. et al., “Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients”, Rev. Mod. Phys., 64:4 (1992), 1046–1096 | DOI

[52] Holzschuh E., “Convergence of momentum space, pseudopotential calculations for Si”, Phys. Rev. B, 28:12 (1983), 7346–7348 | DOI

[53] Pickett W. E., “Pseudopotential methods in condenced matter applications”, Computer Phys. Rep., 9 (1989), 115–197 | DOI

[54] Austin B. J., Heine V., Sham L. J., “General Theory of Pseudopotentials”, Phys. Rev., 127:1 (1962), 276–282 | DOI | Zbl

[55] Hellmann H., “A new approximation method in the problem of many electrons”, J. Chem. Phys., 3 (1935), 61–63 | DOI

[56] Gombás P., “Über die metallische Bindung”, Z. Phys., 94 (1935), 473–475 | DOI

[57] Slater J. C., “Wave functions in a Periodic Potential”, Phys. Rev., 51 (1937), 846–851 | DOI | Zbl

[58] Herring C., “A New Method for Calculating Wave Functions in Crystals”, Phys. Rev., 57 (1940), 1169–1177 | DOI | Zbl

[59] Preuss H., “Untersuchungen zum kombinierten Näherungsverfahren”, Z. Naturf. A, 10 (1955), 365–367

[60] Phillips J. C., “Energy-Band Extrapolation Scheme Based on Pseudopotentials”, Phys. Rev., 112:3 (1958), 685–695 | DOI

[61] Phillips J. C., Kleinman L., “New Method for Calculating Wave Functions in Crystals and Molecules”, Phys. Rev., 116:2 (1959), 287–294 | DOI | Zbl

[62] Hamann D. R., Shlüter M., Chiang C., “Norm-Conserving Pseudopotentials”, Phys. Rev. Lett., 43:20 (1979), 1494–1497 | DOI

[63] Bachelet G. B., Hamann D. R., Shlüter M., “Pseudopotential that work: From H to Pu”, Phys. Rev. B, 26:8 (1982), 4199–4228 | DOI

[64] Kerker G. P., “Non-singular atomic pseudopotentials for solid state applications”, J. Phys. C Solid St. Phys., 13 (1980), L189–L194 | DOI

[65] Vanderbilt D., “Soft self-consistent pseudopotentials in a generalized eigenvalue formalism”, Phys. Rev. B, 41:11 (1990), 7892–7895 | DOI

[66] Laasonen K., Car R., Lee C., Vanderbilt D., “Implementation of ultrasoft pseudopotentials in ab initio molecular dynamics”, Phys. Rev. B, 43:8 (1991), 6796–6799 | DOI

[67] Laasonen K., Pasquarello, Car R., Lee Ch., Vanderbilt D., “Car-Parrinello molecular dynamics with ultrasoft pseudopotentials”, Phys. Rev. B, 47:16 (1993), 10142–10153 | DOI

[68] Gonze X., Stumpf R., Scheffler M., “Analysis of separable potentials”, Phys. Rev. B, 44:16 (1991), 8503–8513 | DOI

[69] Goedecker S., Teter M., Hutter J., “Separable dual-space Gaussian pseudopotentials”, Phys. Rev. B, 54:3 (1996), 1703–1710 | DOI

[70] Pseudopotentials Database, svobodnyi dostup http://www.pwscf.org/pseudo.php

[71] Scandolo S., Giannozzi P., Cavazzoni C., de Gironcoly S. et al., “First-principles codes for Computational Crystallography in the Quantum-ESPRESSO package”, Z. Kristallogr., 220 (2005), 574–579 | DOI

[72] Giannozzi P. et al., Quantum ESPRESSO, ver. 4.0.4, svobodnyi dostup , 2008 http://www.quantum-espresso.org

[73] Vychislitelnye metody v teorii tverdogo tela, Mir, M., 1975, 400 pp.

[74] Sleter Dzh., Metody samosoglasovannogo polya dlya molekul i tverdykh tel, Mir, M., 1978, 662 pp.

[75] Kittel Ch., Vvedenie v fiziku tverdogo tela, Nauka, M., 1978, 791 pp.

[76] Gonze X., “First-principles responses of solids to atomic displacements and homogeneous electric fields: Implementation of a conjugate-gradient algorithm”, Phys. Rev. B, 55:16 (1997), 10337–10354 | DOI

[77] Gonze X., Lee C., “Dynamical matrices, Born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory”, Phys. Rev. B, 55:16 (1997), 10355–10368 | DOI

[78] Dal Corso A., Pasquarello A., Baldereschi A., “Density-functional perturbation theory for lattice dynamics with ultrasoft pseudopotentials”, Phys. Rev. B, 56:18 (1997), 369–372

[79] Dal Corso A., “Density-functional perturbation theory with ultrasoft pseudopotentials”, Phys. Rev. B, 64 (2001), Art. 235118

[80] Baroni S., de Gironcoli S., Dal Corso A., Giannozzi P., “Phonons and related crystal properties from density-functional perturbation theory”, Rev. Mod. Phys., 73 (2001), 516–562 | DOI

[81] Giannozzi P., Baroni S., “Density-Functional Perturbation Theory”, Handbook of Materials Modeling, Springer, N.Y., 2005, 195–214 | DOI

[82] Giannozzi P., de Gironcoli S., Pavone P., Baroni S., “Ab initio calculation of phonon dispersions in semiconductors”, Phys. Rev. B, 43:9 (1991), 7231–7242 | DOI

[83] Martin R. M., “Lattice vibrations in silicon: microscopic dielectric model”, Phys. Rev. Lett., 21:8 (1968), 536–539 | DOI

[84] Martin R. M., “Dielectric Screening Model for Lattice Vibrations of Diamond-Structure Crystals”, Phys. Rev., 186:3 (1969), 871–884 | DOI

[85] Palevsky H., Hughes D. J., Kley W. et al., “Lattice vibrations in silicon by scattering of cold neutrons”, Phys. Rev. Lett., 2:6 (1959), 258–259 | DOI