A balanced treatment of static and dynamic correlation in free- and Mg-porphyrin

Abstract: We present an ab-initio dynamical configuration interaction (DCI) study of free- and Mg-porphyrin. DCI is a recently developed active space theory based on the L\"owdin downfolding technique. In the active space, static correlation is described exactly with full configuration interaction. In the high energy, dynamically correlated subspace, we treat correlation at the quasiparticle level in the $GW$ approximation of Green's function theory. The final theory combines wave function and Green's function methods to give a balanced description of static and dynamic correlation. The theory and algorithm give a multireference treatment of ground and excited states for low computational cost. The four orbital Gouterman model of porphyrin offers an ideal active space in a large, correlated system to test the cost and accuracy of the embedding for large systems. Our parameter free, fully ab-initio DCI calculations in the minimal four-level active space agree well with both experiment and more expensive benchmark theories for the $Q_x$ and $Q_y$ transitions of free- and Mg-porphyrin. Studying the convergence of the excitation energies suggests that DCI correctly captures size extensive correlation effects, making it a promising active space theory for large, strongly-correlated systems.