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The exchange coupling of the spins of two electrons in double well potentialsin a semiconductor background is calculated within the Heitler-London (HL)approximation. Atomic and quantum dot types of confining potentials areconsidered, and a systematic analysis for the source of inaccuracies in the HLapproach is presented. For the strongly confining coulombic atomic potentialsin the H2 molecule, the most dramatic failure occurs at very large interatomicdistances, where HL predicts a triplet ground state, both in 3D and in 2D,coming from the absence of electron-electron correlation effects in thisapproach. For a 2D double well potential, failures are identified at relativelysmaller interdot distances, and may be attributed to the less confining natureof the potential, leading to larger overlap and consequently an inadequaterepresentation of the two-particle states written, within HL, in terms of theground state orbital at each isolated well. We find that in the double dotcase, the range of validity of HL is improved (restricted) in a related 3D (1D)model, and that results always tend to become more reliable as the interdotdistance increases. Our calculated exchange coupling is of relevance to theexchange gate quantum computer architectures in semiconductors.Comment: 6 pages, 3 figures. As accepted in Physical Review

Exchange coupling in semiconductor nanostructures: Validity and limitations of the Heitler-London approach