  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 $A=A^0+A'$ where $A^0=\frac{1}{2}(-B x_2, B x_1,0)$ is an external
magnetic field and $A'$ is self-generated magnetic field. 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 assumptions $\alpha Z\le \kappa^*$ (with a small constant $\kappa^*$)
and $M=1$ (atomic case) we study the ground State Energy
$$\mathsf{E}^*=\inf_{A'}\mathsf{E}(A).$$ We derive its asymptotics including
Scott, and Schwinger and Dirac corrections (depending on $B\ll Z^3$).
  In the next versions we will consider also molecules and related topics: an
excessive negative charge, ionization energy and excessive positive charge when
atoms can still bind into molecules.
