Scott Correction for Large Atoms and Molecules in a Self-Generated Magnetic Field

We consider a large neutral molecule with total nuclear charge Z in non-relativistic quantum mechanics with a self-generated classical electromagnetic field. To ensure stability, we assume that Z alpha (2) a parts per thousand currency sign kappa (0) for a sufficiently small kappa (0), where alpha denotes the fine structure constant. We show that, in the simultaneous limit Z -> a, alpha -> 0 such that kappa = Z alpha (2) is fixed, the ground state energy of the system is given by a two term expansion c (1) Z (7/3) + c (2)(kappa) Z (2) + o(Z (2)). The leading term is given by the non-magnetic Thomas-Fermi theory. Our result shows that the magnetic field affects only the second (so-called Scott) term in the expansion.