next up previous contents index
Next: LHF Up: Implementation Previous: Implementation   Contents   Index

OEP-EXX

In the present implementation the OEP-EXX local potential is expanded as[160]:

vxEXX($\displaystyle \bf r$) = $\displaystyle \sum_{p}^{}$cp$\displaystyle \int$$\displaystyle {\frac{{g_p({\bf r}')}}{{\vert{\bf r-r'}\vert}}}$d$\displaystyle \bf r{^\prime}$  , (16.6)

where gp 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 cp . Actually, not all the coefficients cp are independent each other as there are other two conditions to be satisfied: the HOMO condition, see Eq. (16.4), and the charge condition

$\displaystyle \int$$\displaystyle \sum_{p}^{}$cpgp($\displaystyle \bf r$)d$\displaystyle \bf r$ = - 1  , (16.7)

which ensures that vxEXX($ \bf r$) 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.


next up previous contents index
Next: LHF Up: Implementation Previous: Implementation   Contents   Index
TURBOMOLE M