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We describe the LDA bandstructure of YBa2Cu3O7 in the F 2 eV range using orbital projections and compare with YBa2Cu4O8: Then, the high-energy and chain-related degrees of freedom are integrated out and we arrive at two, nearest-neighbor, orthogonal, two-center, 8-band Hamiltonians, H + 8 and H 8 ; for respectively the even and odd bands of the bi-layer. Of the 8 orbitals, Cu x 2 y 2 ; O2x; O3y; and Cus have character and Cuxz; Cuyz; O2z; and O3z have character. The roles of the Cus orbital, which has some Cu 3z 2 1 character, and the four orbitals are as follows: Cus provides 2nd-and 3rd-nearest-neighbor (t 0 and t 00 ) intra-plane hopping, as well as hopping between planes (t?): The -orbitals are responsible for bifurcation of the saddle-points for dimpled planes. The 4--band Hamiltonian is generic for at CuO2 planes and we use it for analytical studies. The k k -dependence is expressed as one on u (cos bky + cos akx) =2 and one on v (cos bky cos akx) =2: The latter arises solely through the in uence of Cus: The reduction of the -Hamiltonian to 3-and 1-band Hamiltonians is explicitly discussed and we point out that, in addition to the hoppings commonly included in many-body calculations, the 3-band Hamiltonian should include hopping between all 2nd-nearest-neighbor oxygens and that the 1-band Hamiltonian should include 3rd-nearest-neighbor hoppings. We calculate the single-particle hopping between the planes of a bi-layer and show that it is generically: t? k k 0:25 eV v 2 (1 2ut 0 =t) 2 : The hopping through insulating spacers such as (BaO)Hg(BaO) is an order of magnitude smaller, but seems to have the same k k -dependence. We show that the inclusion of t 0 is crucial for understanding ARPES for the anti-ferromagnetic insulator Sr2CuO2Cl2. Finally, we estimate the value of the inter-plane exchange constant J? for an un-doped bi-layer in mean-eld theory using di erent single-particle Hamiltonians, the LDA for YBa2Cu3O6, the eight-and four-band Hamiltonians, as well as an analytical calculation for the latter. We conclude that J? 20 meV.

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We provide a straightforward and efficient procedure to combine LDA+U total energy functional with the full potential linearized augmented plane wave method. A detailed derivation of the LDA+U Kohn-Sham type equations is presented for the augmented plane wave basis set, and a simple "second-variation" based procedure for self-consistent LDA+U calculations is given. The method is applied to calculate electronic structure and magnetic properties of NiO and Gd. The magnetic moments and band eigenvalues obtained are in very good quantitative agreement with previous full potential LMTO calculations. We point out that LDA+U reduces the total d charge on Ni by 0.1 in NiO.