Efficient adiabatic connection approach for strongly correlated systems. Application to singlet-triplet gaps of biradicals

Strong correlation can be essentially captured with multireference wavefunction methods such as complete active space self-consistent field (CASSCF) or density matrix renormalization group (DMRG). Still, an accurate description of the electronic structure of strongly correlated systems requires accounting for the dynamic electron correlation, which CASSCF and DMRG largely miss. In this work a new approach for the correlation energy based on the adiabatic connection (AC) is proposed. The AC$_{\rm n}$ method accounts for terms up to the desired order n in the coupling constant, is rigorously size-consistent, free from instabilities and intruder states. It employs the particle-hole multireference random phase approximation and the Cholesky decomposition technique, which leads to a computational cost growing with the fifth power of the system size. Thanks to AC$_{\rm n}$ depending solely on one- and two-electron CAS reduced density matrix, the method is much more efficient than existing ab initio dynamic correlation methods for strong correlation. AC$_{\rm n}$ affords excellent results for singlet-triplet gaps of challenging organic biradicals. Development presented in this work opens new perspectives for accurate calculations of systems with dozens of strongly correlated electrons.