md2011-06-note_Part_12

md2011-06-note_Part_12 - F , LDA I Local density spin...

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Unformatted text preview: F , LDA I Local density spin approximation (LDSA) is based on the assumption that the exchange-correlation energy density at each point is the same as in a homogenous electron gas with that density E LDSA xc [ n , n ] = Z d 3 rn ( r ) hom xc ( n ( r ) , n ( r )) (49) where hom xc can be separated hom xc = hom x + hom c . I LD(S)A is the most general local approximation and can be given explicitly for exchange and by approximate or fitted expressions for correlation. Hence as long as there are no further approximations in the calculations, LD(S)A can be considered as a test of the local approximation itself; the results must match experiments. Notes I The reasoning behind LD(S)A is that for densities typical for solids, the range of the effects of exchange and correlation is rather short. I However, one must test whether it works for the actual application. I It can be expected to work best for metals with nearly-free electrons and worst for very inhomogeneous cases....
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This note was uploaded on 02/14/2012 for the course CSE 6590 taught by Professor Kotakoski during the Winter '12 term at York University.

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md2011-06-note_Part_12 - F , LDA I Local density spin...

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