References

Books

[1] Attila Szabo and Neil S. Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory (Dover Publications , 1996).

[2] Robert G. Parr and Weitao Yang. Density-Functional Theory of Atoms and Molecules. Oxford University Press. 1989.

[3] Wolfram Koch and Max C. Holthausen. A Chemist's Guide to Density Functional Theory, Second Edition. Wiley-VCH. 2000.

[4] Andrew R. Leach. Molecular Modelling: Principles and Applications, Second Edition. Prentice-Hall. 2001.

[5] Jos M. Thijssen, Computational Physics (Cambridge University Press , 1999); The example programs can be obtained online at http://www.cp.tn.tudelft.nl/people/thijssen/book/progdir.html.

[6] John P. Lowe, Quantum Chemistry, 2nd Edition (Academic Press, San Diego , 1993).

[7] Ira N. Levine, Quantum Chemistry, 4th Edition (Prentice-Hall, New Jersey , 1991).

[8] Peter William Atkins, Molecular Quantum Mechanics, Second Edition (Oxford University Press , 1983).

[9] Richard L. Liboff, Introductory Quantum Mechanics (Holden-Day, Oakland, CA , 1980).

[10] Stephen Gasiorowicz, Quantum Physics (John Wiley & Sons, New York , 1974).

[11] Leonard I. Schiff, Quantum Mechanics, Third Edition (McGraw-Hill, New York , 1968).

[12] Gordon Baym, Lectures on Quantum Mechanics (Benjamin-Cummings, Menlo Park,CA , 1973).

[13] Ramamurti Shankar, Principles of Quantum Mechanics, 2nd Edition (Plenum Press, New York , 1994).

[14] J.J. Sakurai, Modern Quantum Mechanics (Benjamin-Cummings, Menlo Park, CA , 1985).

[15] J.J. Sakurai, Advanced Quantum Mechanics (Addison-Wesley, Redwood City,CA , 1967).

[16] David S. Saxon, Elementary Quantum Mechanics (Holden-Day, San Francisco, CA , 1968).

[17] John W. Negele and Henri Orland, Quantum Many-Particle Systems (Addison-Wesley, Reading, MA , 1988).

[18] Alexander L. Fetter and John Dirk Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, New York , 1971).

[19] Claude Itzykson and Jean-Bernard Zuber, Quantum Field Theory (McGraw-Hill, New York , 1980).

[20] Siegfried Flügge, Practical Quantum Mechanics (Springer-Verlag, Berlin , 1970).

[21] George Arfken, Mathematical Methods for Physicists, 3rd Edition, International Edition (Academic Press, Orlando , 1985).

[22] Herbert Goldstein, Classical Mechanics, 2nd Edition (Addison-Wesley , 1980).

[23] Robert Geroch, Mathematical Physics (University of Chicago Press , 1985).

[24] Garrett Birkoff and Saunders MacLane, A Survey of Modern Algebra, 4th Edition (MacMillan Publishing, New York , 1977).

[25] J.P. Elliott and P.G. Dawber, Symmetry in Physics, Volume 1: Principles and Simple Applications (Oxford University Press, Oxford , 1979).

[26] J.P. Elliott and P.G. Dawber, Symmetry in Physics, Volume 2: Further Applications (Oxford University Press, Oxford , 1979).

[27] Peter F. Bernath, Spectra of Atoms and Molecules (Oxford University Press, Oxford , 1995).

[28] Hermann Haken and Hans Christoph Wolf, Molecular Physics and Elements of Quantum Chemistry: Introduction to Experiments and Theory (Springer-Verlag, Berlin , 1995).

[29] Walter S. Struve, Fundamentals of Molecular Spectroscopy (John Wiley & Sons, New York , 1989).

[30] Hélène Lefebvre-Brion and Robert W. Field, The Spectra and Dynamics of Diatomic Molecules: Revised and Enlarged Edition (Academic Press, New York , 2004). ISBN: 0124414567.

[31] John M. Brown and Alan Carrington, Rotational Spectroscopy of Diatomic Molecules (Cambridge Molecular Science) (Cambridge University Press, Cambridge , 2003). ISBN: 0521530784.

[32] Gerhard Herzberg, Molecular Spectra and Molecular Structure, Reprint Edition (Krieger Publishing, Melbourne, Florida , 1992). ISBN: 0-89464-789-X.

[33] John C. Slater, Quantum Theory of Atomic Structure, Volume I, International Series in Pure and Applied Physics (McGraw-Hill, New York , 1960).

[34] John C. Slater, Quantum Theory of Atomic Structure, Volume II, International Series in Pure and Applied Physics (McGraw-Hill, New York , 1960).

[35] E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra (Cambridge University Press , 1967).

[36] I.M. Mills, T. Cvitas, K. Homann, N. Kallay, and K. Kuchitsu, Quantities, Units and Symbols in Physical Chemistry, Second Edition, International Union of Pure and Applied Chemistry (Blackwell Scientific Publications, Oxford , 1993).

Atomic and Molecular Spectroscopy

[37] C.J.H. Schutte, J.E. Bertie, P.R. Bunker, Jon T. Hougen, I.M. Mills, J.K.G. Watson, and B.P. Winnewisser, “Notations and conventions in molecular spectroscopy: Part 1. General spectroscopic notation”, Pure & Appl. Chem. 69 1633-1639 (1997); For a list of other IUPAC Recommendations see, http://www.iupac.org/reports/

[38] C.J.H. Schutte, J.E. Bertie, P.R. Bunker, Jon T. Hougen, I.M. Mills, J.K.G. Watson, and B.P. Winnewisser, “Notations and conventions in molecular spectroscopy: Part 2. Symmetry notation”, Pure & Appl. Chem. 69 1641-1649 (1997); For a list of other IUPAC Recommendations see, http://www.iupac.org/reports/

[39] P.R. Bunker, C.J.H. Schutte, Jon T. Hougen, I.M. Mills, J.K.G. Watson, and B.P. Winnewisser, “Notations and conventions in molecular spectroscopy: Part 3. Permutation and permutation-inversion symmetry notation”, Pure & Appl. Chem. 69 1651-1657 (1997); For a list of other IUPAC Recommendations see, http://www.iupac.org/reports/

[40] Jon T. Hougen, “The Calculation of Rotational Energy Levels and Rotational Line Intensities in Diatomic Molecules”, NBS Monograph 115 (1970); http://physics.nist.gov/Pubs/Mono115/contents.html

[41] E.E. Nikitin and R.N. Zare, “Correlation diagrams for Hund's coupling cases in diatomic molecules with high rotational angular momentum”, Molecular Physics 82, 85-100 (1994).

[42] E.R. Cohen and P. Giacomo, “IUPAP, Symbols, Units, Nomenclature and Fundamental Constants in Physics, 1987 Revision, Document IUPAP-25 (SUNAMCO 87-l)”, Physica 146A, 1-68 (1987).

[43] F.A. Jenkins, “Report of Subcommittee 𝒻 (Notation for the Spectra of Diatomic Molecules)”, Journal of the Optical Society of America 43, 425-426 (1953).

[44] R.S. Mulliken, “Report on Notation for the Spectra of Polyatomic Molecules (Joint Commission for Spectroscopy of IUPAP and IAU 1954)”, J. Chem. Phys. 23, 1997 (1955).

Internet Resources

[45] “ IUPAC Recommendations & Reports: http://www.iupac.org/reports/. ” •Parameters and Symbols for Use in Nuclear Magnetic Resonance, •4.5 physical quantities: atoms, molecules and spectroscopy, •Glossary of terms used in theoretical organic chemistry.

[46] W. C. Martin and W. L. Wiese, “ Atomic Spectroscopy: A Compendium of Basic Ideas, Notation, Data, and Formulas. ” http://physics.nist.gov/Pubs/AtSpec/.

[47] Eric W. Weisstein, “ From MathWorld―A Wolfram Web Resource: http://mathworld.wolfram.com, ” Clebsch-Gordan Coefficient, Racah V-Coefficient, Racah W-Coefficient, Wigner 3j-Symbol Wigner 6j-Symbol Wigner 9j-Symbol.

[48] Marianne Breinig, “ A Web-Based Quantum Mechanics Course with In-Class Tutorials. Physics 522, Quantum Mechanics II, Spring 2001, The University of Tennessee, Department of Physics and Astronomy. ” http://electron6.phys.utk.edu/qm2/modules/m4/wigner.htm.

[49] Site description:"While not itself an introduction to density-functional theory (DFT), this page is intended to provide the information necessary for a novice to get started in the complicated world of density functionals."― . Mark Casida. http://www-ledss.ujf-grenoble.fr/PERSONNEL/LEDSS7/casida/CompChem/DFT.html.

[50] CLRC Quantum Chemistry Group density-functional Repository, CLRC Daresbury Laboratory, Daresbury, Cheshire, WA4 4AD United Kingdom. Contact Huub van Dam (h.j.j.vandam@dl.ac.uk) or Paul Sherwood for further information . (http://www.cse.clrc.ac.uk/qcg/dft/).

[51] Particle Data Group: . http://pdg.lbl.gov/2004/reviews/clebrpp.pdf..

[52] Basis sets were obtained from the Extensible Computational Chemistry Environment Basis Set Database, Version 6/19/03, as developed and distributed by the Molecular Science Computing Facility, Environmental and Molecular Sciences Laboratory which is part of the Pacific Northwest Laboratory, P.O. Box 999, Richland, Washington 99352, USA, and funded by the U.S. Department of Energy. The Pacific Northwest Laboratory is a multi-program laboratory operated by Battelle Memorial Institute for the U.S. Department of Energy under contract DE-AC06-76RLO 1830. Contact David Feller or Karen Schuchardt for further information. (http://www.emsl.pnl.gov/forms/basisform.html. European mirror: http://www.cse.clrc.ac.uk/qcg/basis/).

[53] The General Atomic and Molecular Electronic Structure System (GAMESS) is a general ab initio quantum chemistry package. (GAMESS:http://www.msg.ameslab.gov/GAMESS/gamess.html). GAMESS-UK is a package of ab initio programs written by M.F. Guest, J.H. van Lenthe, J. Kendrick, K. Schoeffel, P. Sherwood, and R.J. Harrison, with contributions from R.D. Amos, R.J. Buenker, H. van Dam, M. Dupuis, N.C. Handy, I.H. Hillier, P.J. Knowles, V. Bonacic-Koutecky, W. von Niessen, A.P. Rendell, V.R. Saunders, A. Stone and D. Tozer. The package is derived from the original GAMESS code due to M. Dupuis, D. Spangler and J. Wendoloski, NRCC Software Catalog, Vol. 1, Program No. QG01 (GAMESS), 1980.. (GAMESS-UK:http://wserv1.dl.ac.uk/CFS/).

[54] Peter David Haynes, Linear-scaling methods in ab initio quantum-mechanical calculations (Cambridge University Ph.D. Dissertation , 1998); Can be viewed at http://www.tcm.phy.cam.ac.uk/~pdh1001/thesis/thesis.html.

[55] , UniChem on-line documentation (Oxford Molecular, Ltd. , 1996); Can be viewed at http://www.cesup.ufrgs.br/unichem/uc_help.html.

Density functionals and their implementations

[56] P. Hohenberg and W. Kohn, “Inhomogeneous Electron Gas”, Phys. Rev. 136, B864-B871 (1964).

[57] ☎ N. David Mermin, “Thermal Properties of the Inhomogeneous Electron Gas”, Phys. Rev. 137, A1441-A1443 (1965).

[58] W. Kohn and L. J. Sham, “Self-Consistent Equations Including Exchange and Correlation Effects”, Phys. Rev. 140, A1133-A1138 (1965).

[59] Walter Kohn, Axel D. Becke, and R. G. Parr, “Density Functional Theory of Electronic Structure”, J. Phys. Chem. 100, 12974-12980 (1996).

[60] Walter Kohn, “Nobel Lecture: Electronic structure of matter―wave functions and density functionals”, Rev. Mod. Phys. 71, 1253-1266 (1999).

[61] R.O. Jones and O. Gunnarsson, “The density functional formalism, its applications and prospects”, Rev. Mod. Phys. 61, 689-746 (1989).

[62] John P. Perdew and Karla Schmidt, “Jacob's ladder of density functional approximations for the exchange-correlation energy”, in Density Functional Theory and Its Application to Materials: Antwerp, Belgium, 8-10 June 2000 (Aip Conference Proceedings, 577), pp. 1-20, edited by V. Van Doren, C. Van Alsenoy, and P. Geerlings, (American Institute of Physics, New York , 2001); http://proceedings.aip.org/dbt/dbt.jsp?KEY=APCPCS&Volume=577&Issue=1

[63] U. von Barth and L. Hedin, “A local exchange-correlation potential for the spin polarized case”, J. Phys. C: Solid State Phys. 5, 1629-1642 (1972).

[64] ☎ M.M. Pant and A.K. Rajagopal, “Theory of inhomogeneous magnetic electron gas”, Sol. State Commun. 10, 1157-1160 (1972).

[65] ♪ A.K. Rajagopal and J. Callaway, “Inhomogeneous Electron Gas”, Phys. Rev. B 7, 1912-1919 (1973).

[66] ☎ J. Harris and R.O. Jones, “The surface energy of a bounded electron gas”, J. Phys. F: Met. Phys. 4, 1170-1186 (1974).

[67] O. Gunnarsson and B.I. Lundqvist, “Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism”, Phys. Rev. B 13, 4274-4298 (1976); Phys. Rev. B 15, 6006 (1976).

[68] ☎ David C. Langreth and John P. Perdew, “Exchange-correlation energy of a metallic surface: Wave-vector analysis”, Phys. Rev. B 15, 2884-2901 (1977).

[69] D. Ceperley, “Ground state of the fermion one-component plasma: A Monte Carlo study in two and three dimensions”, Phys. Rev. B 18, 3126-3138 (1978).

[70] J. F. Janak, “Proof that ∂E/∂n_i= epsilon in density-functional theory”, Phys. Rev. B 18, 7165-7168 (1978).

[71] D.M. Ceperley and B.J. Alder, “Ground State of the Electron Gas by a Stochastic Method”, Phys. Rev. Lett. 45, 566-569 (1980).

[72] S.H. Vosko, L. Wilk, and M. Nusair, “Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis”, Can. J. Phys. 58, 1200 (1980).

[73] ♪ Mel Levy, “Universal Variational Functionals of Electron Densities First Order Density Matrices, and Natural spin-orbitals and Solution of the v-Representability Problem”, Proc. Natl. Acad. Sci. USA 76, 6062 (1979).

[74] ☎ Mel Levy, “Electron densities in search of Hamiltonians”, Phys. Rev. A 26, 1200-1208 (1982).

[75] ☎ E. Lieb, “Density functionals for Coulomb systems”, in Physics as Natural Philosophy: Essays in Honor of Laszlo Tisza on His 75th Birthday, p. 111-149, edited by A. Shimony and H. Feshbach (MIT, Cambridge, MA , 1982); For a revised version see Int. J. Quantum Chem. 24, pp. 243-277 (1983).

[76] John P. Perdew, Robert G. Parr, Mel Levy, and Jose L. Balduz, Jr., “Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy”, Phys. Rev. Lett. 49, 1691 (1982).

[77] John P. Perdew and Mel Levy, “Physical Content of the Exact Kohn-Sham Orbital Energies: Band Gaps and Derivative Discontinuities”, Phys. Rev. Lett. 51, 1884-1887 (1983).

[78] L. J. Sham and M. Schlüter, “Density-Functional Theory of the Energy Gap”, Phys. Rev. Lett. 51, 1888-1891 (1983).

[79] ☎ Mel Levy, John P. Perdew, and Viraht Sahni, “Exact differential equation for the density and ionization energy of a many-particle system”, Phys. Rev. A 30, 2745-2748 (1984).

[80] John P. Perdew, “Density-functional approximation for the correlation energy of the inhomogeneous electron gas”, Phys. Rev. B 33, 8822 (1986).

[81] Weitao Yang, “Direct Calculation of Electron Density in Density-Functional Theory”, Phys. Rev. Lett. 66, 1438 (1991).

[82] B. Miehlich, A. Savin, H. Stoll, and H. Preuss. Results obtained with the correlation energy density functionals of Becke and Lee, Yang and Parr. , Chem. Phys. Lett. 157 (1989) 200-206.

[83] P.M.W. Gill, B.G. Johnson, J.A. Pople, and M.J. Frisch. An Investigation of the Performance of a Hybrid of Hartree-Fock and Density Functional Theory. , Int. J. Quantum Chem.: Quantum Chem. Symp. 26 (1992) 319-331.

[84] John A. Pople, Peter M.W. Gill, Benny G. Johnson “Kohn-Sham density-functional theory within a finite basis set”, Chem. Phys. Lett. 199, 557 (1992).

[85] P.M.W. Gill, B.G. Johnson, and J.A. Pople. A standard grid for density functional calculations . , Chem. Phys. Lett. 209 (1993) 506-512.

[86] B.G. Johnson, P.M.W. Gill, and J.A. Pople. The performance of a family of density functional methods. , J. Chem. Phys.98 (1993) 5612-5626;Erratum:The performance of a family of density functional methods. , J. Chem. Phys.101 (1994) 9202.

[87] Axel D.Becke, “Density-functional exchange-energy approximation with correct asymptotic behaviour”, Phys. Rev. A 38, 3098-3100 (1988).

[88] A.D. Becke. A multicenter numerical integration scheme for polyatomic molecules. Journal of Chemical Physics 88, (1988) 2547.

[89] A.D. Becke and R. M. Dickson, “Numerical solution of Schrödinger's equation in polyatomic molecules”, Journal of Chemical Physics 92, 3610-3612 (1990).

[90] Axel .D. Becke, “Density-functional thermochemistry. I. The effect of the exchange-only gradient correction”, Journal of Chemical Physics 96, 2155-2160 (1992).

[91] Axel .D. Becke, “Density-functional thermochemistry. II. The effect of the Perdew-Wang generalized-gradient correlation correction”, Journal of Chemical Physics 97, 9173-9177 (1992).

[92] Axel .D. Becke, “A new mixing of Hartree-Fock and local density-functional theories”, Journal of Chemical Physics 98, 1372-1377 (1993).

[93] A.D.Becke, “Density-functional thermochemistry. III. The role of exact exchange”, J. Chem. Phys. 98, 5648-5652 (1993).

[94] R. van Leeuwen and E. J. Baerends, “Exchange-correlation potential with correct asymptotic behavior”, Phys. Rev. A 49, 2421-2431 (1994).

[95] Axel D.Becke, “Density-functional thermochemistry. IV. A new dynamical correlation functional and implications for exact-exchange mixing”, J. Chem. Phys. 104, 1040-1046 (1996).

[96] C.Lee, W.Yang, and R.G.Parr, “Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density”, Phys. Rev. B 37, 785-789 (1988).

[97] J.P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple”, Phys. Rev. Lett. 77, 3865-3868 (1996).

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

[99] John P. Perdew and Yue Wang, “Accurate and simple analytic representation of the electron-gas correlation energy”, Phys. Rev. B 45, 13244-13249 (1992).

[100] O. Treutler and R. R. Ahlrichs, “Efficient molecular numerical integration schemes”, J. Chem. Phys. 102, 346-354 (1995).

[101] Michael E. Mura and Peter J. Knowles, “Improved radial grids for quadrature in molecular density-functional calculations”, J. Chem. Phys. 104, 9848 (1996)

[102] P. Jemmer and P.J. Knowles. Generation of functional derivatives in Kohn-Sham density-functional theory. , Computer Physics Communications 100 (1997) 93-98 (The program can be obtained online at http://www.tc.bham.ac.uk/~peterk/papers/fderiv/).

[103] Roland H. Hertwig and Wolfram Koch, “On the parameterization of the local correlation functional. What is Becke-3-LYP?”, Chem. Phys. Lett. 268, 345-351 (1997)

[104] C. J. Umrigar and Xavier Gonze, “Accurate exchange-correlation potentials and total-energy components for the helium isoelectronic series”, Phys. Rev. A 50, 3827-3837 (1994).

Lebedev Quadratures

[105] V.I.Lebedev and D.N.Laikov, “A quadrature formula for the sphere of the 131st algebraic order of accuracy”, Doklady Mathematics 59, 477-481 (1999); The Fortran source code for the quadrature routines described in the article can be obtained over the Internet from the following URL address http://www.ccl.net/cca/software/SOURCES/FORTRAN/Lebedev-Laikov-Grids/.

[106] V.I.Lebedev, “A quadrature formula for the sphere of 59th algebraic order of accuracy”, Russian Acad. Sci. Dokl. Math. 50, 283-286 (1995).

[107] V.I.Lebedev and A.L. Skorokhodov, “Quadrature formulas of orders 41, 47, and 53 for the sphere”, Russian Acad. Sci. Dokl. Math. 45, 587-592 (1992).

[108] V.I.Lebedev, “Spherical quadrature formulas exact to orders 25-29”, Siberian Mathematical Journal (Sibirsk. Mat. Zh.) 18, 99-107 (1977).

[109] V.I.Lebedev, “Values of the nodes and weights of ninth to seventeenth order Gauss-Markov Quadrature Formulae invariant under the octahedron group with inversion”, Zh. Vyschisl. Mat. Mat. Fiz. (U.S.S.R. Comput. Math. and Math. Phys.) 15, 48-54 (1975).

[110] V.I.Lebedev, “Quadratures on a sphere”, Zh. Vyschisl. Mat. Mat. Fiz. (U.S.S.R. Comput. Math. and Math. Phys.) 16, 293-306 (1976).

[111] S. L.Sobolev, “On formulas of mechanical volume integrations on a spherical surface”, Sibirsk. Mat. Zh. (Sibirsk. Mat. Zh.) 3, 769 (1962).

[112] C.-O.Almbladh and A.C.Pedroza, “Density-functional exchange-correlation potentials and orbital eigenvalues for light atoms”, Phys. Rev. A 29, 2322-2330 (1984).

Gaussian Integrals

[113] E.Clementi and D.R.Davis, “Electronic Structure of Large Molecular Systems”, Journal of Computational Physics 2, 223-244 (1967).

[114] V.R. Saunders, “An Introduction to Molecular Integral Evaluation”, in Computational Techniques in Quantum Chemistry and Molecular Physics , p. 347-424, edited by Diercksen et al. (D. Reidel Publishing Company , 1975).

Finite-Difference and Finite-Element Methods

[115] Steven R. White and John W. Wilkins, “Finite-element method for electronic structure”, Phys. Rev. B 39, 5819-5833 (1989).

[116] François Gygi, “Electronic-structure calculations in adaptive coordinates”, Phys. Rev. B 48, 11692-11700 (1993).

[117] James R. Chelikowsky, N. Troullier, K. Wu, and Y. Saad, “Higher-order finite-difference pseudopotential method: An application to diatomic molecules”, Phys. Rev. B 50, 11355-11364 (1994).

[118] James R. Chelikowsky, N. Troullier, and Y. Saad, “Finite-difference-pseudopotential method: Electronic structure calculations without a basis”, Phys. Rev. Lett. 72, 1240-1243 (1994).

[119] Takeo Hoshi, Masao Arai, and Takeo Fujiwara, “Density-functional molecular dynamics with real-space finite difference”, Phys. Rev. B 52, R5459-R5462 (1995).

Ab initio software packages

[120] M.W. Schmidt, K.K. Baldridge, J.A. Boatz, S.T. Elbert, M.S. Gordon, J.H. Jensen, S. Koseki, N. Matsunaga, K.A. Nguyen, S. Su, T.L. Windus, M. Dupuis, and J.A. Montgomery, “General Atomic and Molecular Electronic Structure System”, J. Comput. Chem. 14, 1347-63 (1993).

[121] X. Gonze, J.-M. Beuken, R. Caracas, F. Detraux, M. Fuchs, G.-M. Rignanese, L. Sindic, M. Verstraete, G. Zerah, F. Jollet, M. Torrent, A. Roy, M. Mikami, Ph. Ghosez, J.-Y. Raty, and D.C. Allan, “First-principles computation of material properties: the ABINIT software project”, Computational Materials Science 25, 478-492 (2002).

[122] M.A.L. Marques, A. Castro, G.F. Bertsch, and A. Rubio, “octopus: a first principles tool for excited states electron-ion dynamics”, Comp. Phys. Comm. 151, 60 (2003).

Pseudopotential methods

[123] M.C. Payne, M.P. Teter, D.C. Allan, and T.A. Arias, J.D. Joannopoulos, “Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients”, Rev. Mod. Phys. 64, 1045 (1992).

[124] G. Onida, L. Reining, and A. Rubio, “Electronic excitations: density-functional versus many-body Green's-function approaches”, Rev. Mod. Phys. 74, 601 (2002).

[125] V. Heine, “The pseudopotential concept”, in Solid State Physics , vol. 24, p. 1, edited by F.Seitz and D. Turnbull (Academic Press, New York , 1973).

[126] M.L. Cohen and V. Heine, “The Fitting of Pseudopotentials to Experimental Data and Their Subsequent Application”, in Solid State Physics , vol. 24, p. 37, edited by F.Seitz and D. Turnbull (Academic Press, New York , 1973).

[127] W.E. Pickett, “Pseudopotential methods in condensed matter applications”, Comp. Phys. Rep. 9, 115-197 (1989).

[128] Martin Fuchs and Matthias Scheffler, “Ab initio pseudopotentials for electronic structure calculations of poly-atomic systems using density-functional theory”, Comput. Phys. Commun. 119, 67-98 (1999); This article and the fhi98PP pseudopotential program can be obtained over the Internet from the following URL address http://www.fhi-berlin.mpg.de/th/fhi98md/fhi98PP/.

[129] M. Bockstedte, A. Kley, J. Neugebauer and Matthias Scheffler, “Density-functional theory calculations for polyatomic systems:Electronic structure, static and elastic properties and ab initio molecular dynamics”, Comput. Phys. Commun. 107, 187 (1997); This article can be obtained over the Internet from the following URL address http://www.fhi-berlin.mpg.de/th/fhi98md/references.html and the ab initio DFT program fhi98MD can be downloaded at http://www.fhi-berlin.mpg.de/th/fhi98md/index.html.

[130] James C. Phillips and Leonard Kleinman, “New method for calculating wave functions in crystals and molecules”, Phys. Rev. 116, 287 (1959).

[131] William C. Topp and John J. Hopfield, “Chemically Motivated Pseudopotential for Sodium”, Phys. Rev. B 7, 1295 (1973).

[132] D.R. Hamann, M. Schlüter, and C. Chiang, “Norm-conserving pseudopotentials”, Phys. Rev. Lett. 43, 1494 (1979).

[133] G. P. Kerker, “Non-singular atomic pseudopotentials for solid state applications”, J. Phys. C 13(9), L189 (1980).

[134] Leonard Kleinman and D. M. Bylander, “Efficacious form for model pseudopotentials”, Phys. Rev. Lett. 48, 1425 (1982).

[135] Leonard Kleinman, “Relativistic norm-conserving pseudopotential”, Phys. Rev. B 21, 2630-2631 (1980).

[136] Giovanni B. Bachelet and M. Schlüter, “Relativistic norm-conserving pseudopotentials”, Phys. Rev. B 25, 2103-2108 (1982).

[137] G. B. Bachelet, D. R. Hamann, and M. Schlüter, “Pseudopotentials that work: From H to Pu”, Phys. Rev. B 26, 4199 (1982).

[138] D. R. Hamann, “Generalized norm-conserving pseudopotentials”, Phys. Rev. B 40, 2980-2987 (1989).

[139] Peter E. Blöchl, “Generalized separable potentials for electronic-structure calculations”, Phys. Rev. B 41, 5414 (1990).

[140] David Vanderbilt, “Soft self-consistent pseudopotentials in a generalized eigenvalue formalism”, Phys. Rev. B 41, 7892 (1990).

[141] N. Troullier and José Luís Martins, “Efficient pseudopotentials for plane-wave calculations”, Phys. Rev. B 43, 1993 (1991).

[142] N. Troullier and José Luís Martins, “Efficient pseudopotentials for plane-wave calculations: II. operators for fast iterative diagonalization”, Phys. Rev. B 43, 8861 (1991).

[143] Xavier Gonze, Roland Stumpf, and Matthias Scheffler, “Analysis of separable potentials”, Phys. Rev. B 44, 8503-8513 (1991).

[144] K. Karch and F. Bechstedt, “Ab initio lattice dynamics of BN and AlN: Covalent versus ionic forces”, Phys. Rev. B 56, 7404 (1997).

[145] S. Goedecker, M. Teter, and J. Hutter, “Separable dual space Gaussian Pseudopotentials”, Phys. Rev. B 54, 1703 (1996).

[146] C. Hartwigsen, S. Goedecker, and J. Hutter, “Relativistic separable dual-space Pseudopotentials from H to Rn”, Phys. Rev. B 58, 3641 (1998).

[147] M. Krauss and W.J. Stevens, “Effective Potentials in Molecular Quantum Chemistry”, Ann. Rev. Phys. Chem. 35, 357 (1984).

[148] M.N. Ringnalda, M. Belhadj, and R.A. Friesner, “*”, J. Chem. Phys. 93, 3397 (1990).

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[150] Thomas R. Cundari, Michael T. Benson, M. Leigh Lutz, and Shaun O. Sommerer, “Effective Core Potential Approaches to the Chemistry of the Heavier Elements”, Rev. Comput. Chem. 8, 145 (1996).

[151] P.E. Blöchl, P. Margl, and K. Schwarz, “Ab Initio Molecular Dynamics with the Projector Augmented Wave Method”, in Chemical Applications of Density Functional Theory , edited by B.B.Laird, R.B. Ross, and T. Ziegler, (American Chemical Society, Washington DC , 1996).

Orbital-Dependent Functionals and Exact-Exchange Methods

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[153] James D. Talman and William F. Shadwick, “Optimized effective atomic central potential”, Phys. Rev. A 14, 36-40 (1976).

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[155] John P. Perdew and Michael R. Norman, “Electron removal energies in Kohn-Sham density-functional theory”, Phys. Rev. B 26, 5445-5450 (1982); S.B. Trickey, Comment on “Electron removal energies in Kohn-Sham density-functional theory”, Phys. Rev. B 30, 3523-3524 (1984); John P. Perdew and Michael R. Norman, Reply to “Comment on ‘Electron removal energies in Kohn-Sham density-functional theory’”, Phys. Rev. B 30, 3525-3526 (1984).

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[158] C.-O. Almbladh and U. von Barth, “Exact results for the charge and spin densities, exchange-correlation potentials, and density-functional eigenvalues”, Phys. Rev. B 31, 3231-3244 (1985).

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[160] J. B. Krieger, Yan Li, and G. J. Iafrate, “Exact relations in the optimized effective potential method employing an arbitrary E xc ⁡ [ { ψ iσ } ] ”, Phys. Lett. A 148, 470-474 (1990).

[161] J. B. Krieger, Yan Li, and G. J. Iafrate, “Construction and application of an accurate local spin-polarized Kohn-Sham potential with integer discontinuity: Exchange-only theory”, Phys. Rev. A 45, 101-126 (1992).

[162] J. B. Krieger, Yan Li, and G. J. Iafrate, “Systematic approximations to the optimized effective potential: Application to orbital-density-functional theory”, Phys. Rev. A 46, 5453-5458 (1992).

[163] Yan Li, J. B. Krieger, and G. J. Iafrate, “Self-consistent calculations of atomic properties using self-interaction-free exchange-only Kohn-Sham potentials”, Phys. Rev. A 47, 165-181 (1993).

[164] V. R. Shaginyan, “Construction of the exact exchange potential of density-functional theory”, Phys. Rev. A 47, 1507-1509 (1993).

[165] J. B. Krieger, Yan Li, and G. J. Iafrate, “Recent Developments in Kohn-Sham Theory for Orbital-Dependent Exchange-Correlation Energy Functionals”, in Density Functional Theory , Edited by E.K.U. Gross and R.M. Dreizler, (Plenum Press, New York , 1995).

[166] E. Engel and S. H. Vosko, “Accurate optimized-potential-model solutions for spherical spin-polarized atoms: Evidence for limitations of the exchange-only local spin-density and generalized-gradient approximations”, Phys. Rev. A 47, 2800-2811 (1993).

[167] ☎ Andreas Görling and Mel Levy, “Requirements for correlation energy density functionals from coordinate transformations”, Phys. Rev. A 45, 1509-1517 (1992).

[168] ☎ Andreas Görling, “Symmetry in density-functional theory”, Phys. Rev. A 47, 2783-2799 (1993).

[169] ☎ Andreas Görling and Mel Levy, “Correlation-energy functional and its high-density limit obtained from a coupling-constant perturbation expansion”, Phys. Rev. B 47, 13105-13113 (1993).

[170] Andreas Görling and Mel Levy, “Exact Kohn-Sham scheme based on perturbation theory”, Phys. Rev. A 50, 196-204 (1994).

[171] Andreas Görling and Mel Levy, “DFT Ionization Formulas and a DFT Perturbation Theory for Exchange and Correlation, Through Adiabatic Connection”, Int. J. Quantum Chem: Quantum Chem. Symp. 29, 93-108 (1995).

[172] Mark E. Casida, “Generalization of the Optimized Effective Potential Model to Include Electron Correlation: A Variational Derivation of the Sham--Schluter Equation for the Exact Exchange-Correlation Potential”, Phys. Rev. A 51, 2505 (1995); http://zurbaran.ujf-grenoble.fr/PERSONNEL/LEDSS7/casida/research/complete.html

Generalization of the Optimized Effective Potential Model to Include Electron Correlation: A Variational Derivation of the Sham--Schluter Equation for the Exact Exchange-Correlation Potential

[173] ☎ Mel Levy and Andreas Görling, “Bounds for the exchange and correlation potentials”, Phys. Rev. A 51, 2851-2856 (1995).

[174] A. Savin, C. J. Umrigar, and Xavier Gonze, “Relationship of Kohn-Sham eigenvalues to excitation energies”, Chem. Phys. Lett. 288, 391-395 (1998).

[175] Claudia Filippi, C. J. Umrigar, and Xavier Gonze, “Excitation energies from density functional perturbation theory”, Journal of Chemical Physics 107, 9994-10002 (1997).

[176] Andreas Görling, “New KS Method for Molecules Based on an Exchange Charge Density Generating the Exact Local KS Exchange Potential”, Phys. Rev. Lett. 83, 5459-5462 (1999).

[177] Fabio Della Sala and Andreas Görling, “Efficient localized Hartree-Fock methods as effective exact-exchange Kohn-Sham methods for molecules”, Journal of Chemical Physics 115, 5718-5732 (2001).

[178] Yong-Hoon Kim, Martin Städele, and Richard M. Martin, “Density-functional study of small molecules within the Krieger-Li-Iafrate approximation”, Phys. Rev. A 60, 3633-3640 (1999).

[179] Tobias Grabo, T. Kreibich, and E.K.U. Gross, “ Optimized effective potential for atoms and molecules”, Molecular Engineering 7, 27 (1997).

[180] Tobias Grabo and E.K.U. Gross, “ The optimized effective potential method of density functional theory: Applications to atomic and molecular systems”, Int. J. Quantum Chem. 64, 95 (1997); A preprint can also be downloaded at http://arxiv.org/find/chem-ph/1/au:+Grabo_T/0/1/0/all/0/1

[181] E. Engel and R. M. Dreizler, “From explicit to implicit density functionals”, Journal of Computational Chemistry 20, 31-50 (1999).

[182] Tobias Grabo and T. Kreibich, S. Kurth, E.K.U. Gross, “ Orbital functionals in density functional theory: the optimized effective potential method”, in Strong Coulomb Correlations in Electronic Structure Calculations: Beyond the Local Density Approximation (Advances in Condensed Matter Science), pp. 203-311, edited by Vladimir I. Anisimov, (Taylor & Francis, London , 2000);

[183] Stanislav Ivanov, So Hirata, and Rodney J. Bartlett, “Exact Exchange Treatment for Molecules in Finite-Basis-Set Kohn-Sham Theory”, Phys. Rev. Lett. 83, 5455-5458 (1999).

[184] E. J. Baerends, “Exact Exchange-Correlation Treatment of Dissociated H2 in Density Functional Theory”, Phys. Rev. Lett. 87, 133004 (2001).

[185] So Hirata, Stanislav Ivanov, Ireneusz Grabowski, Rodney J. Bartlett, Kieron Burke, and James D. Talman, “Can optimized effective potentials be determined uniquely?”, Journal of Chemical Physics 115, 1635-1649 (2001).

[186] Sébastien Hamel, Mark E. Casida, and Dennis R. Salahub, “Exchange-only optimized effective potential for molecules from resolution-of-the-identity techniques: Comparison with the local density approximation, with and without asymptotic correction”, Journal of Chemical Physics 116, 8276-8291 (2002); http://zurbaran.ujf-grenoble.fr/PERSONNEL/LEDSS7/casida/research/complete.html

[187] Sébastien Hamel, Patrick Duffy, Mark E. Casida, and Dennis R. Salahub, “Kohn-Sham orbitals and orbital energies: fictitious constructs but good approximations all the same”, Journal of Electron Spectroscopy and Related Phenomena 123, 345-363 (2002).

[188] Fabio Della Sala and Andreas Görling, “The asymptotic behavior of the Kohn-Sham exchange potential”, Phys. Rev. Lett. 89, 033003 (2002).

[189] Stephan Kümmel and John P. Perdew, “Simple Iterative Construction of the Optimized EFFective Potential for Orbital Functionals, Including Exact Exchange”, Phys. Rev. Lett. 90, 043004 (2003).

[190] Stephan Kümmel and John P. Perdew, “Optimized effective potential made simple: Orbital functionals, orbital shifts, and the exact Kohn-Sham exchange potential”, Phys. Rev. B 68, 035103 (2003).

[191] ☎ Fabio Della Sala and Andreas Görling, “Excitation energies using an effective exact-exchange Kohn-Sham potential for molecules”, Int. J. Quantum Chem. 91, 131-138 (2003).

[192] ☎ Fabio Della Sala and Andreas Görling, “Open-shell Localized Hartree-Fock approach for an efficient effective exact-excahnge Kohn-Sham treatment of open-shell atoms and molecules”, Journal of Chemical Physics 118, 10439 (2003).

Density-Functional Theory of Excited States

[193] E.K.U. Gross, L. N. Oliveira, and W. Kohn, “Rayleigh-Ritz variational principle for ensembles of fractionally occupied states”, Phys. Rev. A 37, 2805-2808 (1988).

[194] E.K.U. Gross, L. N. Oliveira, and W. Kohn, “Density-functional theory for ensembles of fractionally occupied states. I. Basic formalism”, Phys. Rev. A 37, 2809 (1988).

[195] L. N. Oliveira, E.K.U. Gross, and W. Kohn, “Density-functional theory for ensembles of fractionally occupied states. II. Application to the He atom”, Phys. Rev. A 37, 2821-2833 (1988).

[196] Andreas Görling, “Density-functional theory for excited states”, Phys. Rev. A 54, 3912-3915 (1996).

[197] Frank De Proft and Paul Geerlings, “Calculation of ionization energies, electron affinities, electronegativities, and hardnesses using density functional methods”, Journal of Chemical Physics 106, 3270-3279 (1997).

[198] ☎ Andreas Görling, “Exact exchange-correlation kernel for dynamic response properties and excitation energies in density-functional theory”, Phys. Rev. A 57, 3433-3436 (1998).

[199] ☎ Andreas Görling, “Exact exchange kernel for time-dependent density-functional theory”, Int. J. Quantum Chem. 69, 265 (1998).

[200] Ranbir Singh and B. M. Deb, “Developments in excited-state density functional theory”, Physics Reports 311, 47-94 (1999).

[201] Mel Levy and Ágnes Nagy, “Variational Density-Functional Theory for an Individual Excited State”, Phys. Rev. Lett. 83, 4361-4364 (1999).

[202] Andreas Görling, “Proper Treatment of Symmetries and Excited States in a Computationally Tractable Kohn-Sham Method”, Phys. Rev. Lett. 85, 4229-4232 (2000).

[203] N.I. Gidopoulos, P.G. Papaconstantinou, and E.K.U. Gross, “Spurious Interactions, and Their Correction, in the Ensemble-Kohn-Sham Scheme for Excited States”, Phys. Rev. Lett. 88, 033003-1 (2002).

Time-Dependent Density-Functional Theory

[204] ☎ A. Zangwill and Paul Soven, “Density-functional approach to local-field effects in finite systems: Photoabsorption in the rare gases”, Phys. Rev. A 21, 1561-1572 (1980).

[205] Erich Runge and E.K.U. Gross, “Density-Functional Theory for Time-Dependent Systems”, Phys. Rev. Lett. 52, 997-1000 (1984).

[206] E.K.U. Gross and Walter Kohn, “Local density-functional theory of frequency-dependent linear response”, Phys. Rev. Lett. 55, 2850-2852 (1985).

[207] E.K.U. Gross, C.A. Ullrich, and U.J. Gossmann, “Density Functional Theory of Time-Dependent Systems”, in Density Functional Theory , p. 149, edited by E.K.U. Gross and R.M. Dreizler (Plenum Press, New York , 1995).

[208] Mark E. Casida “Time-dependent density-functional response theory for molecules”, in Recent Advances in Density Functional Methods, Part I , p. 155, edited by D.P. Chong (World Scientific, Singapore , 1995); http://zurbaran.ujf-grenoble.fr/PERSONNEL/LEDSS7/casida/research/complete.html

[209] C. A. Ullrich, U. J. Gossmann, and E.K.U. Gross, “Time-Dependent Optimized Effective Potential”, Phys. Rev. Lett. 74, 872-875 (1995).

[210] Mark E. Casida “Time-Dependent Density Functional Response Theory of Molecular Systems: Theory, Computational Methods, and Functionals”, in Recent Developments and Applications of Modern Density Functional Theory , p. 391, edited by J.M. Seminario (Elsevier, Amsterdam , 1996); http://zurbaran.ujf-grenoble.fr/PERSONNEL/LEDSS7/casida/research/complete.html

[211] M. Petersilka, U. J. Gossmann, and E.K.U. Gross, “Excitation Energies from Time-Dependent Density-Functional Theory”, Phys. Rev. Lett. 76, 1212-1215 (1996).

[212] Angel Rubio, J. A. Alonso, X. Blase, L. C. Balbás, and Steven G. Louie, “Ab Initio Photoabsorption Spectra and Structures of Small Semiconductor and Metal Clusters”, Phys. Rev. Lett. 77, 247-250 (1996).

[213] K. Yabana and G. F. Bertsch, “Time-dependent local-density approximation in real time”, Phys. Rev. B 54, 4484-4487 (1996).

[214] Andreas Görling, “Time-dependent Kohn-Sham formalism”, Phys. Rev. A 55, 2630-2639 (1997).

[215] Robert van Leeuwen, “Causality and Symmetry in Time-Dependent Density-Functional Theory”, Phys. Rev. Lett. 80, 1280-1283 (1998).

[216] S. J. A. van Gisbergen, F. Kootstra, P. R. T. Schipper, O. V. Gritsenko, J. G. Snijders, and E. J. Baerends, “Density-functional-theory response-property calculations with accurate exchange-correlation potentials”, Phys. Rev. A 57, 2556-2571 (1998).

[217] Mark E. Casida, Christine Jamorski, Kim C. Casida, and Dennis R. Salahub, “Molecular excitation energies to high-lying bound states from time-dependent density-functional response theory: Characterization and correction of the time-dependent local density approximation ionization threshold”, Journal of Chemical Physics 108, 4439-4449 (1998); http://zurbaran.ujf-grenoble.fr/PERSONNEL/LEDSS7/casida/research/complete.html

[218] K. Burke and E.K.U. Gross, “A guided tour of time dependent density functional theory ”, in Density functionals: Theory and applications , edited by D. Joubert (Springer, Berlin , 1998); http://dft.rutgers.edu/pubs/publist.html#BG98

[219] X. Gonze and M. Scheffler, “Exchange and Correlation Kernels at the Resonance Frequency: Implications for Excitation Energies in Density-Functional Theory”, Phys. Rev. Lett. 82, 4416-4419 (1999).

[220] Igor Vasiliev, Serdar Öğüt, and James R. Chelikowsky, “Ab Initio Excitation Spectra and Collective Electronic Response in Atoms and Clusters”, Phys. Rev. Lett. 82, 1919-1921 (1999).

[221] J. Guan, Mark E. Casida, and Dennis R. Salahub, “Time-dependent density-functional theory investigation of excitation spectra of open-shell molecules”, J. Molec. Structure (Theochem) 527, 229 (2000); http://zurbaran.ujf-grenoble.fr/PERSONNEL/LEDSS7/casida/research/complete.html

[222] M. Petersilka, E.K.U. Gross, and K. Burke, “Excitation energies from time-dependent density functional theory using exact and approximate functionals”, Int. J. Quantum Chem. 80, 534 (2000); http://dft.rutgers.edu/pubs/publist.html

[223] T. Grabo, M. Petersilka, and E.K.U. Gross, “Molecular excitation energies from time-dependent density-functional theory”, J. Molec. Structure (Theochem) 501, 353 (2000); http://www.physik.fu-berlin.de/~ag-gross/articles.html

[224] K. Burke, M. Petersilka, and E.K.U. Gross, “A hybrid functional for the exchange-correlation kernel in time-dependent density functional theory ”, in Recent Advances in Density Functional Methods , vol. III, pp. 67-79, edited by V. Barone, P. Fantucci, and A. Bencini, (World Scientific Press , 2000); http://dft.rutgers.edu/pubs/BPG00.ps

[225] ♪ H. Heinze, Andreas Görling, and N. Rösch, “An efficient method for calculating molecular excitation energies by time-dependent density-functional theory”, Journal of Chemical Physics 113, 2088 (2000).

[226] M. Stener, P. Decleva, and Andreas Görling, “The role of exchange and correlation in time-dependent density-functional theory for photoionization”, Journal of Chemical Physics 114, 7816-7829 (2001).

[227] ☎ Mel Levy, “Basic time-independent density-functional theorems for ground states and excited states”, in Density Functional Theory and Its Application to Materials: Antwerp, Belgium, 8-10 June 2000 (Aip Conference Proceedings, 577), pp. 38-47, edited by V. Van Doren, C. Van Alsenoy, and P. Geerlings, (American Institute of Physics, New York , 2001); http://proceedings.aip.org/dbt/dbt.jsp?KEY=APCPCS&Volume=577&Issue=1

[228] Igor Vasiliev, Serdar Öğüt, and James R. Chelikowsky, “First-principles density-functional calculations for optical spectra of clusters and nanocrystals”, Phys. Rev. B 65, 115416 (2002).

[229] Mark E. Casida, “Jacob's ladder for time-dependent density-functional theory: Some rungs on the way to photchemical heaven ”, in Accurate Description of Low-Lying Molecular States and Potential Energy Surfaces, ACS Symposium Series 828 (Proceedings of ACS Symposium, San Diego, Calif., 2001), pp. 199-220, edited by Mark R. Hoffmann and Kenneth G. Dyall (ACS Press, Washington, D.C. , 2002); http://zurbaran.ujf-grenoble.fr/PERSONNEL/LEDSS7/casida/research/complete.html

[230] H. Appel, E.K.U. Gross, and K. Burke, “Excitations in Time-Dependent Density-Functional Theory”, Phys. Rev. Lett. 90, 043005-1 (2003).

[231] M.A.L. Marques and E.K.U. Gross, “Time-Dependent Density Functional Theory ”, in A Primer in Density-Functional Theory , edited by C. Fiolhais, F. Nogueira, and M.A.L. Marques, Lecture Notes in Physics , vol. 620, p. 144, (Springer, Berlin , 2003); http://cfc.fis.uc.pt/public.php?ano=2003

[232] M.A.L. Marques and E.K.U. Gross, “Time-dependent density functional theory ”, To appear in Annu. Rev. Phys. Chem. (2004); http://cfc.fis.uc.pt/public.php?ano=2004.

*Mixed-space formalism for the dielectric response in periodic systems X. Blase, Angel Rubio, Steven G. Louie, and Marvin L. Cohen Phys. Rev. B 52, R2225?R2228 (1995)

Ab initio Calculations for the Polarizabilities of Small Semiconductor Clusters Igor Vasiliev, Serdar Öğüt, and James R. Chelikowsky Phys. Rev. Lett. 78, 4805?4808 (1997)

Kohn-Sham calculations with self-interaction-corrected local-spin-density exchange-correlation energy functional for atomic systems Jiqiang Chen, J. B. Krieger, and Yan Li,G. J. Iafrate Phys. Rev. A 54, 3939?3947 (1996)


Appendix B. More information about the equations presented in Chapter 3.