Porphyrins are present in many metalloproteins, and they are also important components of a variety of nonbiological functional materials. Furthermore, they are representative of the kind of large, strongly correlated system that is especially difficult for accurate calculations. For example, predicting the order of their spin states has been challenging. Here we study the energetic order of four states (one singlet, two triplets, and one quintet) of iron porphyrin, FeP, by the multiconfiguration pair-density functional theory (MC-PDFT). Five active space prescriptions, namely, CAS(8, 6), CAS(8, 11), CAS(16, 15), RAS(34,2,2;13,6,16), and DMRG(34, 35), are used to obtain the kinetic energy, density, and on-top density. Although the prediction of which spin state of FeP is the ground state depends on the selection of the active space when one uses multireference second-order perturbation theory and such calculations lead incorrectly to a quintet ground state with the largest studied active space, all five active spaces correctly lead to a triplet ground state when one uses MC-PDFT. We conclude that the (34,35) active space is large enough to give a qualitatively correct description of the orbital space and configuration space such that one obtains the correct spin state prediction when the external correlation energy is added accurately in a post-SCF step. We also conclude that MC-PDFT can provide an efficient and accurate approach to treat the electron correlation in large, strongly correlated systems with the complexity of iron porphyrin.
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