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39
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85038132137
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GAUSSIAN 92, Gaussian, Inc., Pittsburgh, PA
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(1992)
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Frisch, M.J.1
Trucks, G.W.2
Head-Gordon, M.3
Gill, P.M.W.4
Wong, M.W.5
Foresman, J.B.6
Johnson, B.G.7
Schlegel, H.B.8
Robb, M.A.9
Replogle, E.S.10
Gomperts, R.11
Andres, J.L.12
Raghavachari, K.13
Binkley, J.S.14
Gonzalez, C.15
Martin, R.L.16
Fox, D.J.17
Defrees, D.J.18
Baker, J.19
Stewart, J.J.P.20
Pople, J.A.21
more..
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40
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85038133294
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We have previously termed functionals only of [formula omitted] and [formula omitted] zeroth-order functionals because they contain no derivative-correction terms. Functionals which also incorporate some or all of the γ’s but no higher-order derivatives are called first-order functionals. In general, we refer to functionals which involve nontrivially the spin densities and their first n derivatives as nth-order functionals, though we currently know of no functional higher than first-order which is widely used. We note that the original formulation of the LYP functional (Ref. 19) contains the density Laplacian, apparently making LYP second order, but this second-derivative dependence is trivial and can be eliminated by partial integration (Ref. 37). Therefore, the LYP functional is actually first order
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54
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85038132195
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In the Appendix of Ref. 22, Delley briefly discusses the effect of the weight derivatives on equilibrium bond length geometry and states which, omitting the weight derivative term, leads to “a residual of [formula omitted] at the energy minimum” (the grid used is not stated). He accepts this error as tolerable and does not include the weight derivatives, but we feel it is too large to be ignored.
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62
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85038142111
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We note that the function t(μ)is singular when μ = 1, but in practice this does not arise because μ = 1 implies the particular cell function is equal to zero, and a cutoff scheme avoids the evaluation
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69
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84983920787
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(1981)
Int. J. Quantum Chem. Symp
, vol.15
, pp. 269
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Pople, J.A.1
Schlegel, H.B.2
Krishnan, R.3
Defrees, D.J.4
Binkley, J.S.5
Frisch, M.J.6
Whiteside, R.A.7
Hout, R.F.8
Hehre, W.J.9
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