Crystal field calculations for transition metal ions by application of an opposing potential

We propose a fully ab initio method, the opposing crystal potential (OCP), to calculate the crystal field parameters of transition metal impurities in insulator hosts. Through constrained density functional calculations, OCP obtains the constraining Lagrange multipliers, which act as cancellation potential against the crystal field and lead to spherical $d$-electron distribution. The method is applied to several insulators doped with Mn$^{4+}$ and Mn$^{2+}$ ions and shown to be in good agreement with experiment.