Solving the Schrödinger equation for helium atom and its isoelectronic ions with the free iterative complementinteraction (ICI) method
Hiroyuki Nakashima and Hiroshi Nakatsuji
Received 31 July 2007; accepted 2 October 2007; published online 11 December 2007
The Schrödinger equation was solved very accurately for helium atom and its isoelectronic ionsZ=1–10with the free iterative complement interactionICImethod followed by the variationalprinciple. We obtained highly accurate wave functions and energies of helium atom anditsisoelectronicions.Forhelium,thecalculatedenergywas−2.903 724 377 034 119 598 311 159 245 194 404 446 696 905 37 a.u.,correctover40digitaccuracy, and for H−,itwas−0.527 751 016 544 377 196 590 814 566 747 511383 045 02 a.u.These results prove numerically that with the free ICI method, we can calculate the solutions of theSchrödinger equation as accurately as one desires. We examined several types of scaling functiongand initial function0of the free ICI method. The performance was good when logarithm functionswere used in the initial function because the logarithm function is physically essential forthree-particle collision area. The best performance was obtained when we introduce a new logarithmfunction containing not onlyr1andr2but alsor12in the same logarithm function.
https://repository.kulib.kyoto-u.ac.jp/dspace/bitstream/2433/84614/1/1210.pdf
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