Generalized complete orthonormal sets of Exponential-Type functions

New generalized complete orthonormal sets of psi((alpha*,mu))-exponential type functions are described and applied to LCAO calculations for the total energies of atomic systems within the framework of the minimal basis sets approximation in combined Hartree-Fock-Roothaan method. A new variational parameter mu is proposed in the complete orthonormal sets of psi((alpha*,mu))-exponential type functions where alpha* parameter changes in the range -infinity < alpha* < 3. The combined Hartree-Fock-Roothaan calculations have been performed to determine the performance of new basis sets. The comparison has been made by the use of different generalized exponential type basis sets used in the literature. The optimal values of parameters are determined by minimizing the total energies. According to obtained total energy results, the psi((alpha*,mu)) basis sets are more effective than standard definition of psi(alpha*) basis sets and there is no restriction on alpha* values studied systems in this work.