Solving the electron-nuclear Schrödinger equation of helium atom and its isoelectronic ions with the free iterative-complement-interaction method

Abstract

Our previous paper [J. Chem. Phys. 127, 224104 (2007)] revealed that the Schrodinger equation in the fixed-nucleus approximation could be very accurately solved for helium atom and its isoelectronic ions (Z=1-10) with the free iterative-complement-interaction (ICI) method combined with the variation principle. In this report, the quantum effect of nuclear motion has further been variationally considered by the free ICI formalism for the Hamiltonian including mass-polarization operator. We obtained -2.903 304 557 729 580 294 733 816 943 892 697 752 659 273 965 a.u. for helium atom, which is over 40 digits in accuracy, similarly to the previous result for the fixed-nucleus level. Similar accuracy was also obtained for the helium isoelectronic ions. The present results may be regarded to be the nonrelativistic limits. We have further analyzed the physics of the free ICI wave function by applying it to an imaginary atom called "eneon," [e(-)e(10+)e(-)](8+), in which both of the quantum effect of nuclear motion and the three-particle collisions are differently important from the helium and its isoelectronic ions. This revealed the accurate physics automatically generated by the free ICI formalism.