Free complement theory (FC) is a general theory for solving the Schrödinger equations (SE) of atoms and molecules. It is a potentially exact theory since the basic wave function has an exact structure. It does not have a divergence difficulty because it was overcome in 2004. We formulate here a variational FC theory and a non-variational FC theory as a general methodology for solving the SE. In the former, the electron-electron (e-e) scaling function of the scaled SE (SSE) is chosen to be an integrable one; then, we can fully utilize the robust nature of the variational method in solving the SE. In the latter, we use highly accurate e-e scaling functions in contrast to the conventional one; thus, the FC wave function becomes highly accurate, the local energy becomes stable, and the local SE (LSE) method gives highly accurate solutions of the SE’s efficiently and stably. Since chemistry is local, the inter-exchange theory simplifies anti-symmetrization tasks in calculations of large systems.

Free-complement theory for solving the Schrödinger equation of atoms and molecules

ACS Fall 2021

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