Variational Calculation of Lithium-Like Ions from B+2 to N+4 Using β-Type Roothaan–Hartree–Fock Wavefunction
DOI:
https://doi.org/10.15407/ujpe66.8.684Keywords:
Roothaan–Hartree–Fock, B-type orbitals, X-ray form factor, nuclear magnetic shielding constant, diamagnetic susceptibilityAbstract
Within the KaKB, KaLa, and KBLa shells in the position space, the properties of a series of three-electron systems, for instance, B+2, C+3, and N+4 ions, have been studied. This required the partitioning of the two-particle space-spin density and was explicit for the Hartree–Fock description which have been proposed by considering a basis set based on single-zeta B-type orbitals (BTOs). The one- and two-body radial electronic densities R(r1), R(r1, r2), moments ⟨rn1⟩, X-ray form factor F(s), nucleus density R(0), nuclear magnetic shielding constant qd, and the diamagnetic susceptibility бs in the position space are reported. Our results are realized via the Mathematica program and compared with previous theoretical values in the literature.
References
A. Cooksy. Physical Chemistry: Quantum Chemistry and Molecular Interactions (Prentice Hall, 2013).
C. H¨attig, W. Klopper, A. K¨ohn, D.P. Tew. Explicitly correlated electrons in molecules. Chem. Rev. 112, 4 (2012).
https://doi.org/10.1021/cr200168z
Jason K. Pearson, Peter M. W. Gill, Jesus M. Ugalde, and Russell J. Boyd. Can correlation bring electrons closer together? Mol. Phys. 107, 1089 (2009).
https://doi.org/10.1080/00268970902740563
G.A. Sekh, B.T.S. Chatterjee. Insights from intracules and Coulomb holes. Eur. J. Phys. 41 45403 (2020).
https://doi.org/10.1088/1361-6404/ab835f
E. Clementi, C. Roetti. Roothaan-Hartree-Fock atomic wavefunctions: Basis functions and their coefficients for ground and certain excited states of neutral and ionized atoms, Z ≤ 54. At. Data Nucl. Data Tables 14, 177 (1974).
https://doi.org/10.1016/S0092-640X(74)80016-1
C.F. Bunge, J.A. Barrientos, A.V. Bunge, J.A. Cogordan. Hartree-Fock and Roothaan-Hartree-Fock energies for the
ground states of He through Xe. Phys. Rev. A 46, 3691 (1992).
https://doi.org/10.1103/PhysRevA.46.3691
I.I. Guseinov, E. Sahin, M. Erturk. An improvement on ф(a*) exponential type orbitals for atoms in standard convention. Mol. Phys. 112, 35 (2014).
https://doi.org/10.1080/00268976.2013.795665
I. Ema, J.M. Garcia de la Vega, B. Miguel, J. Dotterweich, H. Meissner, E.O. Steinborn. Expotential-type basis functions: Single- and double-zeta B function basis sets for the ground states of neutral atoms from Z = 2 to Z = 36. At. Data Nucl. Data Tables. 72, 57 (1999).
https://doi.org/10.1006/adnd.1999.0809
E. Filter, E.O. Steinborn. Extremely compact formulas for molecular two-center one-electron integrals and Coulomb integrals over Slater-type atomic orbitals. Phys. Rev. A 18, 1 (1978).
https://doi.org/10.1103/PhysRevA.18.1
M. Ert¨urk, E. Ozturk. Modified B function basis sets with generalized hyperbolic cosine functions. Comput. Theor. Chem. 1127, 37 (2018).
https://doi.org/10.1016/j.comptc.2018.02.003
M. Ert¨urk, E. Sahin. Generalized B functions applied to atomic calculations Chem. Phys. 529, 110549 (2020).
https://doi.org/10.1016/j.chemphys.2019.110549
J. Weniger, E.O. Steinborn. The Fourier transforms of some exponential-type basis functions and their relevance to multicenter problems. J. Chem. Phys. 78, 6121 (1983).
https://doi.org/10.1063/1.444574
J. Weniger, E.O. Steinborn. Numerical properties of the convolution theorems of B functions. Phys. Rev. A 28, 2026 (1983).
https://doi.org/10.1103/PhysRevA.28.2026
F.W. King. Calculations on the 2S ground states of some members of the Li isoelectronic series. Phys. Rev. A 40, 1735 (1989).
https://doi.org/10.1103/PhysRevA.40.1735
F.W. King. Progress on high precision calculations for the ground state of atomic lithium J. Mol. Struct. (Theochem) 400, 7 (1997).
https://doi.org/10.1016/S0166-1280(97)90265-7
F.W. King, P.R. Dressel. Compact expressions for the radial electronic density functions for the 2S states of threeelectron systems J. Chem. Phys. 90, 6449 (1989).
https://doi.org/10.1063/1.456311
Guan Xiao-xu, Wang Zhi-wen. Radial electronic density for the ground state of the lithium isoelectronic sequence. Chin. Phys. Lett. 15, 489 (1998).
https://doi.org/10.1088/0256-307X/15/7/008
C. Chen, W. Zhi-Wen. Inequalities of the electron density at the nucleus and radial expectation values of the ground state for the lithium isoelectronic sequence. Chinese Phys. 12, 604 (2003).
https://doi.org/10.1088/1009-1963/12/6/306
C. Chen. Studies of the electron density at the nucleus and radial expectation values of the ground state for lithiumlike systems from Z = 11 to 18. Eur. Phys. J. D. 56, 303 (2010).
https://doi.org/10.1140/epjd/e2009-00293-3
C. Chen, W. Zhi-Wen. Quadrupole and octupole polarizabilities for the ground states of lithiumlike systems from Z = 3 to 20 J. Chem. Phys. 121, 4171 (2004).
https://doi.org/10.1063/1.1778132
H. Schmider, R.O. Esquivel, R.P. Sagar, V.H. Smith, Jr. Spin magnetic form factors for lithium and its isoelectronic series in position and momentum space. J. Phys. B 26, 2943 (1993).
https://doi.org/10.1088/0953-4075/26/17/025
C. Chen, W. Zhi-Wen. Total atomic scattering factors for the ground states of the lithium isoelectronic sequence from Na+8 to Ca+17. J. Chem. Phys. 122, 024305 (2005).
https://doi.org/10.1063/1.1830482
C. Chen, W. Zhi-Wen. Total atomic scattering factors of 1s23s2S states for lithium isoelectronic sequence. Commun. Theor. Phys. 50, 473 (2008).
https://doi.org/10.1088/0253-6102/50/2/38
R. Benesch. Algebraic determination of electron-nuclear and electron-electron distribution functions from Hhlleraas type wavefunctions. J. Phys. B: At. Mol. Phys. 4, 1403 (1971).
https://doi.org/10.1088/0022-3700/4/11/004
R.J. Boyd, C. Sarasola, J.M. Ugalde. Intracule densities and electron correlation in the hydrogen molecule J. Phys. B: At. Mol. Opt. Phys. 21, 2555 (1988).
https://doi.org/10.1088/0953-4075/21/14/008
P. Atkins, J. De Paula, R.S. Friedman, Quanta, Matter, and Change. A Molecular Approach to Physical Chemistry (Oxford University Press, 2009).
H. Al-Jibbouri. Ground state of radial-radial distribution function for C+4 and O+6 ions. J. Phys. Con. Ser. 1294,
https://doi.org/10.1088/1742-6596/1294/5/052052
(2019).
H. Al-Jibbouri, Ammar Alhasan. Study the inter-particle function for some electronic system. J. Phys. Con. Ser. 1294, 022014 (2019).
https://doi.org/10.1088/1742-6596/1294/2/022014
J.F. Rico, R. Lopez, G. Ramirez, I. Ema. Multiple onecenter expansions of charge distributions associated with Slater orbitals. J. Mol. Struct. (Theochem) 433, 7 (1998). https://doi.org/10.1016/S0166-1280(98)00005-0
K.E. Banyard, K.H. Al-Bayati. Intra- and inter-shell correlation effects in Li-like ions: Coulomb holes and their interpretation. J. Phys. B: At. Mol. Phys. 19, 2211 (1986). https://doi.org/10.1088/0022-3700/19/15/004
K.E. Banyard, K.H. Al-Bayati, P.K. Youngman. Coulomb correlation in a doubly occupied K shell: the influence of outer electrons. J. Phys. B: At. Mol. Opt. Phys. 22, 971 (1989).
V.A. Volotka, A.D. Glazov, I.I. Tupitsyn, S.N. Oreshkina, G. Plunien, M.V. Shabaev. Ground-state hyperfine structure of H-, Li-, and B-like ions in the intermediate-Z region. Phys. Rev. A 78, 062507 (2008). https://doi.org/10.1103/PhysRevA.78.062507
L.S. Bartell, R.M. Gavin Jr. Effects of electron correlation in X-ray and electron diffraction. II. Influence of nuclear charge in two-electron systems. J. Chem. Phys. 43, 856 (1965). https://doi.org/10.1063/1.1696858
J.H. Hubbell, Wm.J. Veigele t, E.A. Briggs, R.T. Brown, D.T. Cromer, R. J. Howenon. Atomic form factors, incoherent scattering functions, and photon scattering cross sections. J. Phys. Chern. Ref. Data 4, 471 (1975). https://doi.org/10.1063/1.555523
R.T. Brown. Coherent and incoherent X-ray scattering by bound electrons. II. Three- and four-electron atoms. Phys. Rev. A 2, 614 (1970). https://doi.org/10.1103/PhysRevA.2.614
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