Abstract
A theoretical interpretation and justification of the basic approaches proposed in parametrical methods is presented in this paper. The idea of providing a fundamental understanding of these methods can be considered as a guide for further development in this area. The application of functional analysis concepts to understanding the nature of parametric functionals in terms of the Riesz and Weiestrass's theorems is discussed. In addition, applications of virial and hypervirial theorems to constrain the type of functional and the parameters used in these methods is addressed. A justification of the use of a single determinantal wavefunction and the nature and conditions of optimized orbital basis in terms of different electronic environments involved in different interactions was also established.
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