  A microscopic theory for the NMR anomalies of the planar Cu and O sites in
superconducting La_1.85Sr_0.15CuO_4 is presented that quantitatively explains
the observations without the need to invoke anit-ferromagnetic spin
fluctuations on the planar Cu sites and its significant discrepancy with the
observed incommensurate neutron spin fluctuations. The theory is derived from
the recently published ab-initio band structure calculations that correct LDA
computations tendency to overestimate the self-coulomb repulsion for the
half-filled Cu d_x2-y2 orbital for these ionic systems. The new band structure
leads to two bands at the Fermi level with holes in the Cu d_z2 and apical O
p_z orbitals in addition to the standard Cu d_x2-y2 and planar O p_sigma
orbitals. This band structure is part of a new theory for the cuprates that
explains a broad range of experiments and is based upon the formation of Cooper
pairs comprised of a k up spin electron from one band and a -k down spin
electron from another band (Interband Pairing Model).
