Solving the Schrödinger equation for helium atom and its isoelectronic ions with the free iterative complement interaction „ICI… method

Hiroyuki Nakashima and Hiroshi Nakatsujia

Quantum Chemistry Research Institute, Kyodai Katsura Venture Plaza 106, Goryo Oohara 1-36,

Nishikyo-ku, Kyoto 615-8245, Japan and Department of Synthetic Chemistry and Biological Chemistry,

Graduate School of Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8510, Japan

Received 31 July 2007; accepted 2 October 2007; published online 11 December 2007


Abstract

The Schrödinger equation was solved very accurately for helium atom and its isoelectronic ions Z=1–10 with the free iterative complement interaction ICI method followed by the variational principle. We obtained highly accurate wave functions and energies of helium atom and its isoelectronic ions. For helium, the calculated energy was −2.903 724 377 034 119 598 311 159 245 194 404 446 696 905 37 a.u., correct over 40 digit accuracy, and for H−, it was −0.527 751 016 544 377 196 590 814 566 747 511 383 045 02 a.u. These results prove numerically that with the free ICI method, we can calculate the solutions of the Schrödinger equation as accurately as one desires. We examined several types of scaling function g and initial function 0 of the free ICI method. The performance was good when logarithm functions were used in the initial function because the logarithm function is physically essential for three-particle collision area. The best performance was obtained when we introduce a new logarithm function containing not only r1 and r2 but also r12 in the same logarithm function.


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