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In the present implementation the OEP-EXX local potential is expanded as[160]:
*vxEXX*() = *c*_{p}*d* , |
(16.6) |

where *g*_{p}
are gaussian functions, representing a new type of auxiliary basis-set (see directory `xbasen`

).
Inserting Eq. (16.6) into Eq. (16.2) a matrix equation is easily obtained for the coefficient *c*_{p}
.
Actually, not all the coefficients *c*_{p}
are independent each other as there are other two conditions to be satisfied:
the HOMO condition, see Eq. (16.4), and the charge condition
*c*_{p}*g*_{p}()*d* = - 1 , |
(16.7) |

which ensures that
*vxEXX*()
approaches **-1/***r*
in the asymptotic region.
Actually Eq. (16.6) violates the condition (16.5) on the HOMO nodal surfaces
(such condition cannot be achieve in any simple basis-set expansion).
Note that for the computation of the final KS Hamiltonian, only orbital basis-set matrix elements
of
*vxEXX*
are required, which can be easily computes
as three-index Coulomb integrals. Thus the present OEP-EXX implementation is *grid-free*,
like Hartree-Fock, but in contrast to all other XC-functionals.

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