Extending the random phase approximation with renormalized ...

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Spin There is not a unique way to generalize to spin-polarized systems For a spinpaired system it is straightforward to show that =[ ALDA f Hx f Hxc = 1 4 ∑σ σ ' f σ σ ' Hxc The ALDA Hartree-exchange kernel is V +2f ALDA x [2n↑ ] V V V +2f x ALDA [2n↓]] It is clear that we cannot simply introduce cutoff on <strong>the</strong> diagonal
Instead we take =[ rALDA f Hx Spin V r rALDA [n↑+n ↓]+2f x [n↑+n ↓] V r [n ↑+n↓] V r [n↑+n ↓] V r [n ↑+n↓]+2f x rALDA [n↑+n ↓]] This breaks spin-scaling for <strong>the</strong> kernel and it cannot be regarded as pure exchange The choice is not unique!
Page 1 and 2: Beyond the Random Phase Approximati
Page 3 and 4: Correlation energy from ACDFT The e
Page 5 and 6: Correlation energy from ACDFT The e
Page 7 and 8: RPA Correlation energy RPA gives an
Page 9 and 10: Cohesive energies of solids PBE: ME
Page 11 and 12: Pros and cons in RPA The RPA correl
Page 13 and 14: Beyond RPA It should be possible to
Page 15 and 16: Homogeneous Electron Gas If we make
Page 17: ALDA The procedure can be generaliz
Page 21 and 22: ALDA The rALDA kernel has been impl
Page 23 and 24: Numbers are in kcal/mol = 43 meV rA
Page 25 and 26: ALDA - solids The two-point density
Page 27 and 28: ALDA - Static Correlation Dissociat
Page 29: Summary and Outlook Compared to RPA

Extending the random phase approximation with renormalized ...

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