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The exchange-correlation energy can thus be obtained by integrating the electron-electron interaction over the 1 variable and subtracting the Coulomb part. The right-hand side of eq. (B.18) can be written in terms of the second-order reduced density matrix eq. (6.14), and the definition of the exchange-correlation hole in eq. (6.21) allows the Coulomb energy to be separated out.

J p1(r1 )p1(r2)dr1dr2 +1 J pHr1>^1,r1,^ dr1dr2 (B.19)

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