  We extend our density matrix embedding theory (DMET) [Phys. Rev. Lett. 109
186404 (2012)] from lattice models to the full chemical Hamiltonian. DMET
allows the many-body embedding of arbitrary fragments of a quantum system, even
when such fragments are open systems and strongly coupled to their environment
(e.g., by covalent bonds). In DMET, empirical approaches to strong coupling,
such as link atoms or boundary regions, are replaced by a small, rigorous
quantum bath designed to reproduce the entanglement between a fragment and its
environment. We describe the theory and demonstrate its feasibility in strongly
correlated hydrogen ring and grid models; these are not only beyond the scope
of traditional embeddings, but even challenge conventional quantum chemistry
methods themselves. We find that DMET correctly describes the notoriously
difficult symmetric dissociation of a 4x3 hydrogen atom grid, even when the
treated fragments are as small as single hydrogen atoms. We expect that DMET
will open up new ways of treating of complex strongly coupled, strongly
correlated systems in terms of their individual fragments.
