Quantum Chemical Topology as a Theory of Open Quantum Systems

Although real space regions have been widely used in theoretical chemistry, not much effort has been devoted to treat them as open quantum systems. We embrace this task here, finding closed expressions for the density operator of a quantum subsystem in real space by tracing out the degrees of freedom in its complementary region. Our results are then linked to previous knowledge. For single-determinant descriptions it is shown that the entanglement orbitals coincide with Ponec's domain natural orbitals. In general, the subsystem density operator is written as a direct sum of a fixed number of electron sectors, with weights that turn out to be equal to those found within the theory of electron distribution functions. As a computational application we show how to obtain the global first order density matrix of a subsystem and its eigensolution in a couple of toy systems. In the multideterminant wave function case, the domain natural orbitals defined through this open system approach do not coincide with those of Ponec and, contrary to the latter, have always strictly positive occupations.