Abstract
In the free complement (FC) - local Schrödinger equation (LSE) theory for solving the Schrödinger equation, we need an efficient sampling methodology in the LSE step. We propose here the direct or inverse transformation local sampling method for use in the FC-LSE calculations. This method is mathematically straightforward, deterministic, and fast as a sampling method for solving the Schrödinger equation of atoms and molecules, in comparison with the Metropolis or related method. We showed the capabilities of this method for obtaining the solutions of the Schrödinger equations of the beryllium, carbon (5So(sp3) state) and nitrogen atoms and the CH+ molecule.
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