Abstract: The free complement (FC) theory is an exact general theory for solving the Schrödinger equation of atoms and molecules. Since the Schrödinger equation is the governing principle of chemistry, we can develop an exactly predictive quantum chemistry on the basis of the FC theory. We will sow the high accuracy and the generality of the FC theory by some applications to real molecules. The elemental functions of the FC theory, called complement functions (cf’s), consist of the integratable function set and the non-integratable function set, which we refer to i-set and n-set, respectively. The i-set includes only one-electron functions and the n-set is characterized by the inclusion of the (inter electron) functions. Therefore, intuitively we can say that the important specific natures of chemistry are governed mostly by the i-set and the roles of the n-set are mainly to shift the total energies by some amounts. This implies that with the variational solutions using only i-set, we can study the general features of chemistry displayed by atoms and molecules. For example, the potential curves of the ground and excited states of small diatomic molecules are obtained from the variational study with i-set cf’s alone. By adding the effect of the n-set cf’s with the FC theory, we can always obtain the exact results as the extrapolations from the variational approximate solutions to the exact solutions of the system under study. The variational FC theory is a new general electronic structure theory that is different from the VB theory and the MO theory but belongs to the family of the FC theory that covers the exact solutions of the Schrödinger equation.
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