Abstract: 
We consider a large neutral molecule with total nuclear charge Z in a model with selfgenerated classical magnetic field and where the kinetic energy of the electrons is treated relativistically. To ensure stability, we assume that Zα < 2/π, where α denotes the fine structure constant. We are interested in the ground state energy in the simultaneous limit Z → ∞, α → 0 such that κ = Zα is fixed. The leading term in the energy asymptotics is independent of κ, it is given by the ThomasFermi energy of order Z7/3 and it is unchanged by including the selfgenerated magnetic field. We prove the first correction term to this energy, the socalled Scott correction of the form S(αZ)Z2. The current paper extends the result of Solovej et al. [Commun. Pure Appl. Math.LXIII, 39118 (2010)] on the Scott correction for relativistic molecules to include a selfgenerated magnetic field. Furthermore, we show that the corresponding Scott correction function S, first identified by Solovej et al. [Commun. Pure Appl. Math.LXIII, 39118 (2010)], is unchanged by including a magnetic field. We also prove new LiebThirring inequalities for the relativistic kinetic energy with magnetic fields.
