  We consider asymptotics of the ground state energy of heavy atoms and
molecules in the self-generatedl magnetic field. Namely, we consider $$
H=((D-A)\cdot\boldsymbol{\sigma})^2-V $$ with $$V=\sum_{1\le m\le M}
\frac{Z_m}{|x-y_m|}$$ and a corresponding Multiparticle Quantum Hamiltonian $$
\mathsf{H}=\sum_{1\le n\le N} H_{x_n} +\sum_{1\le n < n'\le N}|x_n-x_{n'}|^{-1}
$$ on the Fock space $\wedge _{1\le n\le N} L^2(\mathbb{R}^3, \mathbb{C}^2)$.
Here $A$ is a self-generated magnetic fiels. Then the ground state energy is
given by $$ \mathsf{E}(A)=\inf
\operatorname{Spec}(\mathsf{H})+\frac{1}{\alpha}\int |\nabla \times A|^2\,dx $$
where the last term is the energy of magnetic field. Under assumption $\alpha
Z\le \kappa^*$ (with a small constant $\kappa^*$) we study the ground State
Energy $$ \mathsf{E}^*=\inf _{A}\mathsf{E}(A). $$ We derive its asymptotics
including Scott, and Schwinger and Dirac corrections.
  We also consider related topics: an excessive negative charge, ionization
energy and excessive positive charge when atoms can still bind into molecules.
