Development of the pair density functional theory and its validity check

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The pair density (PD) functional theory is the theory that can reproduce the ground-state PD that contains more information on the electron-electron interaction than the electron density. In order to develop the PD functional theory, there exist two kinds of problems. One is how the kinetic energy (KE) is expressed as a functional of the PD. Another problem is how to set the search region of PDs.In this study, we have tackled with both two problems. Concerning the first problem, we have developed approximate forms of the KE functional both by utilizing relations and bounds as the restrictive conditions on the approximate functional and by utilizing the coupling-constant expression for the KE functional. Concerning the second problem, we have developed the PD functional theory utilizing the electron coordinates scaling (scaling method). We have successfully show the validities of both proposed approximate KE functionals and the scaling method through the actual calculations.