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The Cx \ coefficient is weight dependent and it appears as a correction over Dirac\ \[CloseCurlyQuote]s Cx coefficient.", FontColor->RGBColor[1, 0, 0]]], "Text", CellChangeTimes->{{3.7826266896125298`*^9, 3.782626751796768*^9}, { 3.782627617737678*^9, 3.7826277263447857`*^9}, {3.782627817686021*^9, 3.78262782048987*^9}},ExpressionUUID->"b83db319-04e5-42b8-ae4c-\ 57f93abe09fd"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["eLDA correlation", "Section", CellChangeTimes->{{3.7826249982517223`*^9, 3.782625006542748*^9}, { 3.7826250653667927`*^9, 3.7826250672414913`*^9}, 3.782625112301036*^9},ExpressionUUID->"258ca12d-c8c5-4bc9-84ec-\ 1711f7860786"], Cell[CellGroupData[{ Cell["Ground state correlation functional for glomium", "Subsection", CellChangeTimes->{{3.782625187684318*^9, 3.782625205187807*^9}, { 3.7826253413716393`*^9, 3.7826253532482758`*^9}, {3.782625846786179*^9, 3.782625848068905*^9}, {3.7826293000392017`*^9, 3.7826293054927187`*^9}},ExpressionUUID->"ee1991f0-6627-4afa-871c-\ 73710071f6fd"], Cell["\<\ The ground-state correlation energy of glomium can be very accurately \ computed with Hylleraas-type calculations. We use a Pade-type fit to obtain the functional which reads\ \>", "Text", CellChangeTimes->{{3.782629312827221*^9, 3.782629358270515*^9}},ExpressionUUID->"a6c10556-4f53-4da2-8cf0-\ 79bbf3ec1242"], Cell[BoxData[ FrameBox[ RowBox[{ RowBox[{ SubsuperscriptBox["e", "c", RowBox[{"(", "0", ")"}]], "[", "\[Rho]", "]"}], "\[Equal]", RowBox[{ FractionBox[ SuperscriptBox["a", RowBox[{"(", "0", ")"}]], RowBox[{"1", "+", RowBox[{ SuperscriptBox["b", RowBox[{"(", "0", ")"}]], SuperscriptBox["\[Rho]", RowBox[{ RowBox[{"-", "1"}], "/", "6"}]]}], "+", RowBox[{ SuperscriptBox["c", RowBox[{"(", "0", ")"}]], SuperscriptBox["\[Rho]", RowBox[{ RowBox[{"-", "1"}], "/", "3"}]]}]}]], "\t", SuperscriptBox["a", RowBox[{"(", "0", ")"}]]}], "\[Equal]", RowBox[{ RowBox[{"-", "0.0238184"}], "\t", SuperscriptBox["b", RowBox[{"(", "0", ")"}]]}], "\[Equal]", RowBox[{"0.00575719", "\t", SuperscriptBox["c", RowBox[{"(", "0", ")"}]]}], "\[Equal]", "0.0830576"}]]], "Input", CellChangeTimes->{{3.782626098078829*^9, 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correlation functional is then\ \>", "Text", CellChangeTimes->{{3.782626772664956*^9, 3.7826268526294622`*^9}, { 3.782629595887004*^9, 3.782629603557575*^9}},ExpressionUUID->"f0dac186-7114-4a5e-b53c-\ f938d8c4fd37"], Cell[BoxData[ RowBox[{ RowBox[{ SubsuperscriptBox[ OverscriptBox["e", "_"], "c", "w"], "[", "\[Rho]", "]"}], "\[Equal]", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", "-", "w"}], ")"}], RowBox[{"(", RowBox[{ RowBox[{ SubsuperscriptBox["e", "c", RowBox[{"(", "0", ")"}]], "[", "\[Rho]", "]"}], "+", RowBox[{"(", RowBox[{ RowBox[{ SubsuperscriptBox["e", "c", "LDA"], "[", "\[Rho]", "]"}], "-", RowBox[{ SubsuperscriptBox["e", "c", RowBox[{"(", "0", ")"}]], "[", "\[Rho]", "]"}]}], ")"}]}], ")"}]}], "+", RowBox[{"w", " ", RowBox[{"(", RowBox[{ RowBox[{ SubsuperscriptBox["e", "c", RowBox[{"(", "1", ")"}]], "[", "\[Rho]", "]"}], "+", RowBox[{"(", RowBox[{ RowBox[{ SubsuperscriptBox["e", "c", "LDA"], "[", "\[Rho]", "]"}], "-", RowBox[{ SubsuperscriptBox["e", "c", RowBox[{"(", "0", 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