Calculating electron paramagnetic resonance g-matrices for triplet state molecules from multireference spin-orbit configuration interaction wave functions

Abstract

We present a way to calculate electron paramagnetic resonance (EPR) g-matrices from variationally optimized spin-orbit coupled wave functions. Our method constructs a triangular g-matrix from the matrix representation of the total electron magnetic moment in the basis of the spin-orbit coupled wave functions by means of a projection technique. Principal g-values are obtained in the standard fashion by forming from the triangular matrix g the tensor G=gg(t) and diagonalizing it. In principle, the scheme allows to calculate the spin-orbit orbital Zeeman cross term which usually gives the dominating contribution to the EPR g-shifts for any multiplicity. We have implemented this approach into a multireference spin-orbit configuration interaction (MRSOCI) program [M. Kleinschmidt et al., J. Chem. Phys. 124, 124101 (2006)]. Test applications are carried out for various triplet state sytems. The g-shifts of several of main group diatomics with X (3)Sigma(g)(-) ground state are investigated at the level of ab initio MRSOCI. We obtain perpendicular g-shifts which underestimate experimental Delta g(perpendicular) values from literature by approximately 13% on the average. For a set of organic triplet state molecules we employ the combined density functional theory/multireference configuration interaction (DFT/MRCI) technique [S. Grimme and M. Waletzke, J. Chem. Phys. 111, 5645 (1999)] to reduce the computational costs of the spin-free correlation problem. This approach yields principal g-values that match experiment well in many cases. Due to the small absolute g-shifts, a rigorous comparison will require the inclusion of first-order contributions such as the relativistic mass correction and gauge correction terms which have not been included here. For the triplet state dication trans-(CNSSS)(2)(2+) the principal g-shifts Delta g(a)=-0.3 ppt, Delta g(b)=17.5 ppt, and Delta g(c)=26.6 ppt are significantly larger and compare rather well to the experimental values Delta g(1)=-0.1+/-0.2 ppt, Delta g(2)=14.8+/-0.2 ppt, and Delta g(3)=24.8+/-0.1 ppt [A. Berces et al., Magn. Reson. Chem. 37, 353 (1999)]. In comparison to conventional truncated sum-over state techniques based on Rayleigh-Schrodinger perturbation theory, our new variational approach shows, in practice, robust and advantageous convergence characteristics with respect to the size of the many-particle basis set. We demonstrate that the DFT/MRSOCI technology is a very feasible means to compute reliable g-shifts for large organic triplet systems at low computational cost.