Where for generality a free constant, C, has been introduced rather than that
determined for the homogeneous electron gas. This functional form is much more
widely applicable than is implied from its derivation and can be established from
scaling arguments [1 ]. The functional form for the correlation energy density, e
c,
is
unknown and has been simulated for the homogeneous electron gas in numerical
quantum Monte Carlo calculations which yield essentially exact results [ 15]. The
resultant exchange correlation energy has been fitted by a number of analytic forms
[16,17,18] all of which yield similar results in practice and are collectively referred to
as LDA functionals.
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