# Variational Two-Electron Reduced-Density-Matrix (v2RDM) Methods

- Directly using reduced density matrices (RDM) instead of wavefunctions in quantum chemistry calculations is appealing since the ground state electronic energy is a exact functional of the 2-elelctron RDM.
- Enforcing full N-representability in 2-RDM, the variational 2-RDM (v2RDM) approach is equivalent to full CI. Such computations are in general computationally infeasible. So the v2RDM optimization is typically carried out under a subset of two- or three-particle N -representability conditions.
- v2RDM can be combined with CASSCF, in which the active spaces can be much larger than those in the conventional CI-driven CASSCF, and the computational cost could be polynomial.
- v2RDM-driven CASSCF should be competitive with the DMRG-based CASSCF to consider static correlation, and v2RDM methods are less sensitive to the dimensionality of the system than DMRG methods.
- Dynamic correlation can be obtained through pair-DFT and the adiabatic connection.

**Potential energy curves for the symmetric dissociation of water within the cc-pVTZ basis set**

**S-T energy gaps in linear polycyclic aromatic hydrocarbons calculated with v2RDM-CASSCF/cc-pvDZ**