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This study proposes an approach toward the first principles electronicstructure calculation with the aid of symbolic-numeric solving. The symboliccomputation enables us to express the Hartree-Fock-Roothaan equation and themolecular integrals in analytic forms and approximate them as a set ofpolynomial equations. By use of the Grobner bases technique, the polynomialequations are transformed into other ones which have identical roots. Theconverted equations take more convenient forms which will simplify numericalprocedures, from which we can derive necessary physical properties in order, inan a la carte way. This method enables us to solve the electronic structurecalculation, the optimization of any kind, or the inverse problem as a forwardproblem in a unified way, in which there is no need for iterativeself-consistent procedures with trials and errors.

A proposal to first principles electronic structure calculation: Symbolic-Numeric method