Variational Two-electron Reduced Density Matrix Theory of Periodic Systems

The recovery of static correlation through electronic structure calculations has led to manynovel insights and more accurate prediction of chemical properties for many molecular systems which exhibit a high degree of degeneracy. However, such calculations are often prohibitively expensive for nontrivial systems when using wavefunction-based methods. The use of Reduced Density Matrix (RDM) theories can lessen the computational cost, leading to the possibility of computing electron structures for larger systems that include static correlation. Here, the Variational 2-electron Reduced Density Matrix (V2RDM) theory is applied to periodic systems both in the gamma-point representation and utilizing Brillouin Zone sampling, to analyze how static correlation is affected by periodic boundary conditions and to determine whether static correlation is affected by the momentum of the underlying periodic basis functions. Additionally, the amount of static correlation present in a system is quantified using an adapted form of the Von Neumann Entropy which incorporates 3-body correlation while remaining size-extensive. I show that static correlation is an important factor in the electronic structure of periodic materials, and that in some cases the static correlation in periodic materials is more significant than in their molecular counterparts.