VARIATIONAL CALCULATIONS ON THE 2P1/2 GROUND STATE OF BORON ATOM USING HYDROGENLIKE ORBITALS*
Ruiz Maria Belén, Rojas Miguel
Chair for Theoretical Chemistry of the Friedrich-Alexander University Erlangen-Nürnberg,
Egerlandstraβe 3, D-91058 Erlangen, Germany
e-mail: Maria. Belen. Ruiz@chemie. uni-erlangen. de
Received:
Rec. 15 February 2004
DOI: 10.12921/cmst.2003.09.01.101-112
OAI: oai:lib.psnc.pl:542
Abstract:
Variational calculations of the 2P1 / 2 ground state of boron atom are performed using a singleterm reference wave function and a 150-term wave function expansion without interelectronic distances. The wave function is constructed with hydrogenlike orbitals. These orbitals are superior to Slater orbitals, because the orbital 2s contains nodes. The calculated energy -24.550233 a.u. is compared with -24.541246 a.u. using Slater orbitals and the same basis function expansion, and with -24.5689998 a.u. obtained from full-CI calculations using a 4-31G basis set. The single-term wave function constructed with hydrogenlike orbitals leads to an energy value of-24.501187 a.u., which is lower than the Hartree-Fock energy using a single-zeta basis set of Slater orbitals and it is also lower than with a single-term wave function with Slater orbitals, both lead to an energy of-24.498369 a.u. The behavior of the node of the 2s orbital and its radial distribution function of the wave function series are discussed.
References:
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[2] C. Eckart, Phys. Rev. 36, 878 (1930).
[3] J. C. Slater, Phys. Rev. 36, 57 (1930).
[4] J. C. Slater, Phys. Rev. 42, 33 (1932).
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(1991); F. W. King. Advances in Atomic, Molecular and Optical Physics (1999), Academic Press,
San Diego, 40, 57.
[15] J. S. Sims and S. A. Hagstrom, Int. J. Quantum Chem. 90, 1600 (2002).
[16] H. Kleindienst and A. Lüchow, Int. J. Quantum Chem. 45, 85 (1993).
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[18] G. Büsse, H. Kleindienst, and A. Lüchow, Int. J. Quantum Chem. 66, 241 (1998); H. Kleindienst, G. Busse, and A. Lüchow, Int. J. Quantum Chem. 53, 575 (1995).
[19] J. Komasa, J. Rychlewski, and K. Jankowski, Phys. Rev. A 65, 042507, (2002); J. Komasa and
J. Rychlewski, Chem. Phys. Lett. 342, 185 (2001).
[20] J. Komasa, private communication.
[21] M. B. Ruiz, Int. I. Quantum Chem., to be published.
[22] MAPLE 8 Release by Waterloo Maple Inc. Copyright 1981-1997.
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[26] Huzinaga S. J Chem Phys 67, 5973 (1977).
[27] M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A Robb, J. R Cheeseman, V. G. Zakrzewski, J. A.. Montgomery, Ir. R. E. Stratmann, J. C. Burant, S. Dapprich, J. M. Millam,
A. D. Daniels, K. N. Kudin, M. C. Strain, O. Falkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi,
B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G. A. Petersson, P. Y. Ayala,
Q. Cui, K. Morokuma, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman,
J. Cioslowski, I. V. Ortiz, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, L. Komaromi,
R. Gomperts, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, C.
Gonzalez, M. Challacombe, P. M. W. Gill, B. G. lohnson, W. Chen, M. W. Wong, J. L. Andres,
M. Head-Cordon, E. S. Replogle, J. A Pople, Gaussian 98W, revision A.7; Gaussian, Inc.:
Pittsburgh, PA, 1998.
[28] I. Mayer, private comunication. HONDO-8, from MOTECC-91, contributed and documented by M. Dupuis and A. Farazdel, IBM Corporation Center for Scientific & Engineering Computations, Kingston, NY, 1991. P. J. Knowles and N. C. Handy, Chem. Phys. Letters 111, 315 (1984); Computer Phys. Comrnun. 54, 75 (1989).
[29] E. R. Davidson, S. A. Hagstrom, S. J. Chakravorty, V. M. Umar, and C. Froesse Fisher, Phys. Rev. A 44, 7071 (1993).
[30] P. Jönsson and C. Froese Fischer, Phys. Rev. A 50, 3080 (1994).
[31] S. J. Chakravorty, S. R. Gwaltney, E. R. Davidson, F. A. Parpia and C. Froesse Fisher, Phys. Rev. A 47, 3649 (1993).
Variational calculations of the 2P1 / 2 ground state of boron atom are performed using a singleterm reference wave function and a 150-term wave function expansion without interelectronic distances. The wave function is constructed with hydrogenlike orbitals. These orbitals are superior to Slater orbitals, because the orbital 2s contains nodes. The calculated energy -24.550233 a.u. is compared with -24.541246 a.u. using Slater orbitals and the same basis function expansion, and with -24.5689998 a.u. obtained from full-CI calculations using a 4-31G basis set. The single-term wave function constructed with hydrogenlike orbitals leads to an energy value of-24.501187 a.u., which is lower than the Hartree-Fock energy using a single-zeta basis set of Slater orbitals and it is also lower than with a single-term wave function with Slater orbitals, both lead to an energy of-24.498369 a.u. The behavior of the node of the 2s orbital and its radial distribution function of the wave function series are discussed.
[1] C. Zener. Phys. Rev. 36, 51 (1930).
[2] C. Eckart, Phys. Rev. 36, 878 (1930).
[3] J. C. Slater, Phys. Rev. 36, 57 (1930).
[4] J. C. Slater, Phys. Rev. 42, 33 (1932).
[5] P. M. Morse, L. A. Young and E. S. Haurwitz, Phys. Rev. 48, 948 (1935).
[6] A. Tubis, Phys. Rev. 102, 1049 (1956).
[7] E. A. Hylleraas, Z. Phys. 54, 347 (1929).
[8] C. Schwartz, J. Comp. Methods in S&E 2004, to be published. e-Print arXiv: physics/0208004.
[9] H. M. James and A. S. Coolidge, Phys. Rev. 49, 688 (1936).
[10] S. Larsson, Phys. Rev. 169, 49 (1968).
[11] Z.-C. Yan and G. W. F. Drake, Phys. Rev. A 66, 042504 (2002).
[12] R. F. Gentner and E. A. Burke, Phys. Rev. 176, 63 (1968).
[13] J. F. Perkins, Phys. Rev. A 8, 700 (1973).
[14] F. W. King and V. Shoup, Phys. Rev. A 33, 2940 (1986); F. W. King, Phys. Rev. A 43, 3285
(1991); F. W. King. Advances in Atomic, Molecular and Optical Physics (1999), Academic Press,
San Diego, 40, 57.
[15] J. S. Sims and S. A. Hagstrom, Int. J. Quantum Chem. 90, 1600 (2002).
[16] H. Kleindienst and A. Lüchow, Int. J. Quantum Chem. 45, 85 (1993).
[17] J. S. Sims and S. A. Hagstrom, Phys. Rev. A 4, 908 (1971); J. S. Sims and S. A. Hagstrom, Int.
J. Quantum Chem. 9, 149 (1975).
[18] G. Büsse, H. Kleindienst, and A. Lüchow, Int. J. Quantum Chem. 66, 241 (1998); H. Kleindienst, G. Busse, and A. Lüchow, Int. J. Quantum Chem. 53, 575 (1995).
[19] J. Komasa, J. Rychlewski, and K. Jankowski, Phys. Rev. A 65, 042507, (2002); J. Komasa and
J. Rychlewski, Chem. Phys. Lett. 342, 185 (2001).
[20] J. Komasa, private communication.
[21] M. B. Ruiz, Int. I. Quantum Chem., to be published.
[22] MAPLE 8 Release by Waterloo Maple Inc. Copyright 1981-1997.
[23] E. Clementi, MOTECC-89, ESCOM, The Netherlands, 1989.
[24] E. Clementi and C. Roetti, At. Data and Nucl. Data Tables, 14, 177 (1974).
[25] E. Clementi and D. L. Raimondi. J. Chem. Phys. 38, 2696 (1963).
[26] Huzinaga S. J Chem Phys 67, 5973 (1977).
[27] M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A Robb, J. R Cheeseman, V. G. Zakrzewski, J. A.. Montgomery, Ir. R. E. Stratmann, J. C. Burant, S. Dapprich, J. M. Millam,
A. D. Daniels, K. N. Kudin, M. C. Strain, O. Falkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi,
B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G. A. Petersson, P. Y. Ayala,
Q. Cui, K. Morokuma, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman,
J. Cioslowski, I. V. Ortiz, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, L. Komaromi,
R. Gomperts, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, C.
Gonzalez, M. Challacombe, P. M. W. Gill, B. G. lohnson, W. Chen, M. W. Wong, J. L. Andres,
M. Head-Cordon, E. S. Replogle, J. A Pople, Gaussian 98W, revision A.7; Gaussian, Inc.:
Pittsburgh, PA, 1998.
[28] I. Mayer, private comunication. HONDO-8, from MOTECC-91, contributed and documented by M. Dupuis and A. Farazdel, IBM Corporation Center for Scientific & Engineering Computations, Kingston, NY, 1991. P. J. Knowles and N. C. Handy, Chem. Phys. Letters 111, 315 (1984); Computer Phys. Comrnun. 54, 75 (1989).
[29] E. R. Davidson, S. A. Hagstrom, S. J. Chakravorty, V. M. Umar, and C. Froesse Fisher, Phys. Rev. A 44, 7071 (1993).
[30] P. Jönsson and C. Froese Fischer, Phys. Rev. A 50, 3080 (1994).
[31] S. J. Chakravorty, S. R. Gwaltney, E. R. Davidson, F. A. Parpia and C. Froesse Fisher, Phys. Rev. A 47, 3649 (1993).
