Repozytorium publikacji - Politechnika Gdańska

The subject of this thesis is the development and implementation of a method for the analytical calculation of the electronic integrals of the explicitly correlated functions of the atomic systems, particularly in the Hylleraas method with one odd correlation factor. In the course of the work, new theoretical methods were developed to obtain all considered the integrals as the closed-form analytic expression with elementary functions and dilogarithms. For some of the integrals, the analytic formulas had never been published before. The correctness of the derived formulae was checked by comparing the form of the expressions and values of the selected integrals with the data available in the literature. The agreement between the values obtained using the derived expressions and the data from previous studies is to 40 significant digits. The derivation of these integrals in this form represents an important step towards the applications of the Hylleraas method in the accurate calculations of atomic and molecular systems with more than a few electrons.

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