A Strategy to Determine Appropriate Active Orbitals and Accurate Magnetic Couplings in Organic Magnetic Systems

This work addresses the following paradox observed in diradicalar conjugated hydrocarbons: while the natural orbitals occupation numbers clearly indicate only two open-shell orbitals, i.e. two unpaired electrons, the minimal CAS zero-order description fails to reproduce accurately the electronic structures of the lowest states (spin density distribution and singlet-triplet energy gap, i.e., magnetic coupling). We will focus on the question of the optimization of both magnetic and nonmagnetic orbitals for the determination of accurate magnetic interactions in organic compounds. It is analytically demonstrated (in the Appendix) and numerically shown from multireference configuration interaction calculations performed on a series of original organic ferro- and antiferromagnetic compounds that, (i) some double excitations must be considered to obtain reliable magnetic orbitals for the calculation of magnetic couplings, (ii) the account of these excitations results in a larger spatial extent of the magnetic orbitals on the surrounding ligands and hence better drives the interaction between several magnetic centers, and (iii) the reliability of the orbitals is a crucial ingredient for the determination of accurate magnetic couplings. A strategy which optimizes the orbitals at a reasonable computational cost is proposed. It relies on a CAS(2,2) zero-order description and provides orbitals of the same quality as the CAS(full valence π)SCF orbitals. The values of the magnetic couplings computed using the difference dedicated configuration interaction on top of the CAS(2,2) references with the new orbital set are very close to those obtained at the much more computationally demanding CAS(full valence π)PT2 level of treatment.