TY - JOUR

T1 - Convergence of the partial wave expansion of the He ground state

AU - Bromley, Michael

AU - Mitroy, James

PY - 2007

Y1 - 2007

N2 - The configuration interaction (CI) method, using a very large Laguerre orbital basis, is applied to the calculation of the He ground state. The largest calculations included a minimum of 35 radial orbitals for each ? ranging from 0 to 12, resulting in basis sets in excess of 400 orbitals. The convergence of the energy and electron-electron ?-function with respect to J (the maximum angular momenta of the orbitals included in the CI expansion) were investigated in detail. Extrapolations to the limit of infinite angular momentum using expansions of the type ?XJ = AX[J + 1/2] -p + BX[J + 1/2]-p-1 + ..., gave an energy accurate to 10-7 Hartree and a value of ??? accurate to about 0.5%. Improved estimates of ?E? and ???, accurate to 10-8 Hartree and 0.01%, respectively, were obtained when extrapolations to an infinite radial basis were done prior to the determination of the J ? ? limit. Round-off errors were the main impediment to achieving even higher precision, since determination of the radial and angular limits required the manipulation of very small energy and ??? differences. � 2006 Wiley Periodicals, Inc.

AB - The configuration interaction (CI) method, using a very large Laguerre orbital basis, is applied to the calculation of the He ground state. The largest calculations included a minimum of 35 radial orbitals for each ? ranging from 0 to 12, resulting in basis sets in excess of 400 orbitals. The convergence of the energy and electron-electron ?-function with respect to J (the maximum angular momenta of the orbitals included in the CI expansion) were investigated in detail. Extrapolations to the limit of infinite angular momentum using expansions of the type ?XJ = AX[J + 1/2] -p + BX[J + 1/2]-p-1 + ..., gave an energy accurate to 10-7 Hartree and a value of ??? accurate to about 0.5%. Improved estimates of ?E? and ???, accurate to 10-8 Hartree and 0.01%, respectively, were obtained when extrapolations to an infinite radial basis were done prior to the determination of the J ? ? limit. Round-off errors were the main impediment to achieving even higher precision, since determination of the radial and angular limits required the manipulation of very small energy and ??? differences. � 2006 Wiley Periodicals, Inc.

KW - Convergence of numerical methods

KW - Error analysis

KW - Extrapolation

KW - Functions

KW - Helium

KW - Basis set convergence

KW - Configuration interactions

KW - Laguerre type orbitals

KW - Partial wave expansion

KW - Ground state

M3 - Article

VL - 107

SP - 1150

EP - 1161

JO - International Journal of Quantum Chemistry

JF - International Journal of Quantum Chemistry

SN - 0020-7608

IS - 5

ER -