Self-Consistent Calculations on the Atomic Electron Affinity and Ionization Energy with Taking Effects of the Nonspherical Distribution of Electrons into Account

Mitiyasu Miyasita, Katsuhiko Higuchi, Masahiko Higuchi

.

DOI: 10.4236/jmp.2011.210144                

Abstract

We perform the self-consistent calculations on the atomic electron affinity and ionization energy for the first-row atoms by means of our scheme. A striking feature of the present work is the variational method with taking into account effects of the nonspherical distribution of electrons explicitly. Comparing the present results with those of the conventional spherical approximation, the systematical improvement can be found. This means that effects of the nonspherical distribution of electrons may play an essential role on the description of the atomic structures.

Keywords

Nonspherical Distribution of Electrons, Spherical Approximation, Atomic Structure, First-Row Atoms, Electron Affinity, Ionization Energy

Conflicts of Interest

The authors declare no conflicts of interest.

References

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[33]	J. F. Janak and A. R. Williams, “Method for Calculating Wave Functions in a Nonspherical Potential,” Physical Review B, Vol. 23, No. 12, 1981, pp. 6301-6306. doi:10.1103/PhysRevB.23.6301
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[43]	M. Miyasita, K. Higuchi and M. Higuchi, “A Scheme for Calculating Atomic Structures beyond the Spherical Approximation,” Journal of Modern Physics, Vol. 2 No. 5, 2011, pp. 421-430. doi:10.4236/jmp.2011.25052
[44]	A. Narita, “Nonspherical Potential due to Orbital Polarization and Its Effect in Atoms—Approach to Hund’s Second Rule in Terms of One-Electron Picture,” Journal of the Physical Society of Japan, Vol. 77, 2008, p. 124303. doi:10.1143/JPSJ.77.124303
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[46]	V. Fock and Z. Physik, “N?herungsmethode zur L?sung des Quantenmechanischen Mehrk?rperproblems,” Zeitsch- rift Für Physik, Vol. 61, No. 1-2, 1930, pp. 126-148.
[47]	J. C. Slater, “A Simplification of the Hartree-Fock Me- thod,” Physical Review, Vol. 81, No. 3, 1951, pp. 385- 390. doi:10.1103/PhysRev.81.385
[48]	F. Herman and S. Skillman, “Atomic Structure Calcula- tions,” Prentice-Hall Inc., New Jersey, 1963.
[49]	T. Andersen, H. K. Haugen and H. Hotop, “Binding Energies in Atomic Negative Ions: III,” Journal of Physical and Chemical Reference Data, Vol. 28, 1999, p. 1511. doi:10.1063/1.556047
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[53]	W. A. Harrison, “Electronic Structure and the Properties of Solids—The Physics of the Chemical Bonds,” W. H. Freeman and Co., San Francisco, 1980.
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[57]	J. C. Slater, “The Calculation of Molecular Orbitals,” John Wiley & Sons, New York, 1979.
[58]	J. F. Janak and A. R. Williams, “Method for Calculating Wave Functions in a Nonspherical Potential,” Physical Review B, Vol. 23, No. 12, 1981, pp. 6301-6306. doi:10.1103/PhysRevB.23.6301
[59]	F. W. Kutzler and G. S. Painter, “Energies of Atoms with Nonspherical Charge Densities Calculated with Nonlocal Density-Functional Theory,” Physical Review Letters, Vol. 59, No. 12, 1987, pp. 1285-1288. doi:10.1103/PhysRevLett.59.1285
[60]	A. D. Becke, “Local Exchange-Correlation Approximations and First-Row Molecular Dissociation Energies,” International Journal of Quantum Chemistry, Vol. 27, No. 5, 1985, pp. 585-594. doi:10.1002/qua.560270507
[61]	A. D. Becke, “Current Density in Exchange-Correlation Functionals: Application to Atomic States,” Journal of Chemical Physics, Vol. 117, No. 15, 2002, pp. 6935- 6938. doi:10.1063/1.1503772
[62]	E. Orestes, T. Marcasso and K. Capelle, “Density-Func- tional Calculation of Ionization Energies of Current- Carrying Atomic States,” Physical Review A, Vol. 68, No. 2, 2003, p. 022105. doi:10.1103/PhysRevA.68.022105
[63]	E. Orestes, A. B. F. da Silva and K. Capelle, “Energy Lowering of Current-Carrying Single-Particle States in Open-Shell atoms due to an Exchange-Correlation Vector Potential,” International Journal of Quantum Chemistry, Vol. 103, No. 5, 2005, pp. 516-522. doi:10.1002/qua.20575
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[65]	G. Vignale and M. Rasolt, “Current- and Spin-Density- Functional Theory for Inhomogeneous Electronic Systems in Strong Magnetic Fields,” Physical Review B, Vol. 37, No. 18, 1988, pp. 10685-10696. doi:10.1103/PhysRevB.37.10685
[66]	M. Higuchi and A. Hasegawa, “A Relativistic Current and Spin-Density Functional Theory and a Single-Particle Equation,” Journal of the Physical Society of Japan, Vol. 66, No. 1, 1997, p. 149. doi:10.1143/JPSJ.66.149
[67]	M. Higuchi and A. Hasegawa, “Single-Particle Equation of Relativistic Current- and Spin-Density Functional Theory and Its Application to the Atomic Structure of the Lanthanide Series,” Journal of the Physical Society of Japan, Vol. 67, No. 6, 1998, pp. 2037-2047. doi:10.1143/JPSJ.67.2037
[68]	M. Miyasita, K. Higuchi and M. Higuchi, “A Scheme for Calculating Atomic Structures beyond the Spherical Approximation,” Journal of Modern Physics, Vol. 2 No. 5, 2011, pp. 421-430. doi:10.4236/jmp.2011.25052
[69]	A. Narita, “Nonspherical Potential due to Orbital Polarization and Its Effect in Atoms—Approach to Hund’s Second Rule in Terms of One-Electron Picture,” Journal of the Physical Society of Japan, Vol. 77, 2008, p. 124303. doi:10.1143/JPSJ.77.124303
[70]	D. R. Hartree, “The Wave Mechanics of an Atom with a Noncoulomb Central Field. PartI: Theory and Method. Part II: Some Results and Discussions,” Proceedings of Cambridge Philosophical Society, Vol. 24, No. 1, 1928, pp. 111-132. doi:10.1017/S0305004100011920
[71]	V. Fock and Z. Physik, “N?herungsmethode zur L?sung des Quantenmechanischen Mehrk?rperproblems,” Zeitsch- rift Für Physik, Vol. 61, No. 1-2, 1930, pp. 126-148.
[72]	J. C. Slater, “A Simplification of the Hartree-Fock Me- thod,” Physical Review, Vol. 81, No. 3, 1951, pp. 385- 390. doi:10.1103/PhysRev.81.385
[73]	F. Herman and S. Skillman, “Atomic Structure Calcula- tions,” Prentice-Hall Inc., New Jersey, 1963.
[74]	T. Andersen, H. K. Haugen and H. Hotop, “Binding Energies in Atomic Negative Ions: III,” Journal of Physical and Chemical Reference Data, Vol. 28, 1999, p. 1511. doi:10.1063/1.556047
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[76]	N. F. Mott, “The Basis of the Electron Theory of Metals, with Special Reference to the Transition Metals,” Proceedings of the Physical Society, London, Section A, Vol. 62, No. 7, 1949, p. 416.
[77]	P. W. Anderson, “New Approach to the Theory of Super- Exchange Interactions,” Physical Review, Vol. 115, No. 1, 1959, pp. 2-13. doi:10.1103/PhysRev.115.2
[78]	W. A. Harrison, “Electronic Structure and the Properties of Solids—The Physics of the Chemical Bonds,” W. H. Freeman and Co., San Francisco, 1980.
[79]	V. I. Anisimov, J. Zaanen and O. K. Andersen, “Band Theory and Mott Insulators: Hubbard U instead of Stoner,” Physical Review B, Vol. 44, No. 3, 1991, pp. 943-954. doi:10.1103/PhysRevB.44.943
[80]	A. I. Liechtenstein, V. I. Anisimov and J. Zaanen, “Density-Functional Theory and Strong Interations: Orbital Ordering in Mott-Hubbard Insulators,” Physical Review B, Vol. 52, No. 8, 1995, pp. R5468-R5470. doi:10.1103/PhysRevB.52.R5467
[81]	A. Messiah, “Quantum Mechanics,” Dover Publications, New York, 1999.
[82]	J. C. Slater, “The Calculation of Molecular Orbitals,” John Wiley & Sons, New York, 1979.
[83]	J. F. Janak and A. R. Williams, “Method for Calculating Wave Functions in a Nonspherical Potential,” Physical Review B, Vol. 23, No. 12, 1981, pp. 6301-6306. doi:10.1103/PhysRevB.23.6301
[84]	F. W. Kutzler and G. S. Painter, “Energies of Atoms with Nonspherical Charge Densities Calculated with Nonlocal Density-Functional Theory,” Physical Review Letters, Vol. 59, No. 12, 1987, pp. 1285-1288. doi:10.1103/PhysRevLett.59.1285
[85]	A. D. Becke, “Local Exchange-Correlation Approximations and First-Row Molecular Dissociation Energies,” International Journal of Quantum Chemistry, Vol. 27, No. 5, 1985, pp. 585-594. doi:10.1002/qua.560270507
[86]	A. D. Becke, “Current Density in Exchange-Correlation Functionals: Application to Atomic States,” Journal of Chemical Physics, Vol. 117, No. 15, 2002, pp. 6935- 6938. doi:10.1063/1.1503772
[87]	E. Orestes, T. Marcasso and K. Capelle, “Density-Func- tional Calculation of Ionization Energies of Current- Carrying Atomic States,” Physical Review A, Vol. 68, No. 2, 2003, p. 022105. doi:10.1103/PhysRevA.68.022105
[88]	E. Orestes, A. B. F. da Silva and K. Capelle, “Energy Lowering of Current-Carrying Single-Particle States in Open-Shell atoms due to an Exchange-Correlation Vector Potential,” International Journal of Quantum Chemistry, Vol. 103, No. 5, 2005, pp. 516-522. doi:10.1002/qua.20575
[89]	G. Vignale and M. Rasolt, “Density-Functional Theory in Strong Magnetic Fields,” Physical Review Letters, Vol. 59, No. 20, 1987, pp. 2360-2363. doi:10.1103/PhysRevLett.59.2360
[90]	G. Vignale and M. Rasolt, “Current- and Spin-Density- Functional Theory for Inhomogeneous Electronic Systems in Strong Magnetic Fields,” Physical Review B, Vol. 37, No. 18, 1988, pp. 10685-10696. doi:10.1103/PhysRevB.37.10685
[91]	M. Higuchi and A. Hasegawa, “A Relativistic Current and Spin-Density Functional Theory and a Single-Particle Equation,” Journal of the Physical Society of Japan, Vol. 66, No. 1, 1997, p. 149. doi:10.1143/JPSJ.66.149
[92]	M. Higuchi and A. Hasegawa, “Single-Particle Equation of Relativistic Current- and Spin-Density Functional Theory and Its Application to the Atomic Structure of the Lanthanide Series,” Journal of the Physical Society of Japan, Vol. 67, No. 6, 1998, pp. 2037-2047. doi:10.1143/JPSJ.67.2037
[93]	M. Miyasita, K. Higuchi and M. Higuchi, “A Scheme for Calculating Atomic Structures beyond the Spherical Approximation,” Journal of Modern Physics, Vol. 2 No. 5, 2011, pp. 421-430. doi:10.4236/jmp.2011.25052
[94]	A. Narita, “Nonspherical Potential due to Orbital Polarization and Its Effect in Atoms—Approach to Hund’s Second Rule in Terms of One-Electron Picture,” Journal of the Physical Society of Japan, Vol. 77, 2008, p. 124303. doi:10.1143/JPSJ.77.124303
[95]	D. R. Hartree, “The Wave Mechanics of an Atom with a Noncoulomb Central Field. PartI: Theory and Method. Part II: Some Results and Discussions,” Proceedings of Cambridge Philosophical Society, Vol. 24, No. 1, 1928, pp. 111-132. doi:10.1017/S0305004100011920
[96]	V. Fock and Z. Physik, “N?herungsmethode zur L?sung des Quantenmechanischen Mehrk?rperproblems,” Zeitsch- rift Für Physik, Vol. 61, No. 1-2, 1930, pp. 126-148.
[97]	J. C. Slater, “A Simplification of the Hartree-Fock Me- thod,” Physical Review, Vol. 81, No. 3, 1951, pp. 385- 390. doi:10.1103/PhysRev.81.385
[98]	F. Herman and S. Skillman, “Atomic Structure Calcula- tions,” Prentice-Hall Inc., New Jersey, 1963.
[99]	T. Andersen, H. K. Haugen and H. Hotop, “Binding Energies in Atomic Negative Ions: III,” Journal of Physical and Chemical Reference Data, Vol. 28, 1999, p. 1511. doi:10.1063/1.556047
[100]	See Instance, http://physics.nist.gov/PhysRefData/IonEnergy/tblNew.html.
[101]	N. F. Mott, “The Basis of the Electron Theory of Metals, with Special Reference to the Transition Metals,” Proceedings of the Physical Society, London, Section A, Vol. 62, No. 7, 1949, p. 416.
[102]	P. W. Anderson, “New Approach to the Theory of Super- Exchange Interactions,” Physical Review, Vol. 115, No. 1, 1959, pp. 2-13. doi:10.1103/PhysRev.115.2
[103]	W. A. Harrison, “Electronic Structure and the Properties of Solids—The Physics of the Chemical Bonds,” W. H. Freeman and Co., San Francisco, 1980.
[104]	V. I. Anisimov, J. Zaanen and O. K. Andersen, “Band Theory and Mott Insulators: Hubbard U instead of Stoner,” Physical Review B, Vol. 44, No. 3, 1991, pp. 943-954. doi:10.1103/PhysRevB.44.943
[105]	A. I. Liechtenstein, V. I. Anisimov and J. Zaanen, “Density-Functional Theory and Strong Interations: Orbital Ordering in Mott-Hubbard Insulators,” Physical Review B, Vol. 52, No. 8, 1995, pp. R5468-R5470. doi:10.1103/PhysRevB.52.R5467
[106]	A. Messiah, “Quantum Mechanics,” Dover Publications, New York, 1999.
[107]	J. C. Slater, “The Calculation of Molecular Orbitals,” John Wiley & Sons, New York, 1979.
[108]	J. F. Janak and A. R. Williams, “Method for Calculating Wave Functions in a Nonspherical Potential,” Physical Review B, Vol. 23, No. 12, 1981, pp. 6301-6306. doi:10.1103/PhysRevB.23.6301
[109]	F. W. Kutzler and G. S. Painter, “Energies of Atoms with Nonspherical Charge Densities Calculated with Nonlocal Density-Functional Theory,” Physical Review Letters, Vol. 59, No. 12, 1987, pp. 1285-1288. doi:10.1103/PhysRevLett.59.1285
[110]	A. D. Becke, “Local Exchange-Correlation Approximations and First-Row Molecular Dissociation Energies,” International Journal of Quantum Chemistry, Vol. 27, No. 5, 1985, pp. 585-594. doi:10.1002/qua.560270507
[111]	A. D. Becke, “Current Density in Exchange-Correlation Functionals: Application to Atomic States,” Journal of Chemical Physics, Vol. 117, No. 15, 2002, pp. 6935- 6938. doi:10.1063/1.1503772
[112]	E. Orestes, T. Marcasso and K. Capelle, “Density-Func- tional Calculation of Ionization Energies of Current- Carrying Atomic States,” Physical Review A, Vol. 68, No. 2, 2003, p. 022105. doi:10.1103/PhysRevA.68.022105
[113]	E. Orestes, A. B. F. da Silva and K. Capelle, “Energy Lowering of Current-Carrying Single-Particle States in Open-Shell atoms due to an Exchange-Correlation Vector Potential,” International Journal of Quantum Chemistry, Vol. 103, No. 5, 2005, pp. 516-522. doi:10.1002/qua.20575
[114]	G. Vignale and M. Rasolt, “Density-Functional Theory in Strong Magnetic Fields,” Physical Review Letters, Vol. 59, No. 20, 1987, pp. 2360-2363. doi:10.1103/PhysRevLett.59.2360
[115]	G. Vignale and M. Rasolt, “Current- and Spin-Density- Functional Theory for Inhomogeneous Electronic Systems in Strong Magnetic Fields,” Physical Review B, Vol. 37, No. 18, 1988, pp. 10685-10696. doi:10.1103/PhysRevB.37.10685
[116]	M. Higuchi and A. Hasegawa, “A Relativistic Current and Spin-Density Functional Theory and a Single-Particle Equation,” Journal of the Physical Society of Japan, Vol. 66, No. 1, 1997, p. 149. doi:10.1143/JPSJ.66.149
[117]	M. Higuchi and A. Hasegawa, “Single-Particle Equation of Relativistic Current- and Spin-Density Functional Theory and Its Application to the Atomic Structure of the Lanthanide Series,” Journal of the Physical Society of Japan, Vol. 67, No. 6, 1998, pp. 2037-2047. doi:10.1143/JPSJ.67.2037
[118]	M. Miyasita, K. Higuchi and M. Higuchi, “A Scheme for Calculating Atomic Structures beyond the Spherical Approximation,” Journal of Modern Physics, Vol. 2 No. 5, 2011, pp. 421-430. doi:10.4236/jmp.2011.25052
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