# Density functionals for non-relativistic Coulomb systems by Perdew J.P., Kurth S.

By Perdew J.P., Kurth S.

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Finally, expand δG in powers of q 2 , observing that |∇n|2 ∼ q 2 |δn(q)|2 , and extract the gradient coeﬃcient. 066725 . 191) The weak density dependence of β(n) is also known [74], as is its spindependence [75]. Neglecting small ∇ζ contributions, the gradient coeﬃcients (coeﬃcients of |∇n|2 /n4/3 ) for both exchange and correlation at arbitrary relative spin polarization ζ are found from those for ζ = 0 through multiplication by [76] 1 φ(ζ) = (1 + ζ)2/3 + (1 − ζ)2/3 . 183). There is another interesting similarity between the gradient coeﬃcients for exchange and correlation.

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