Practical electronic ground-and excited-state calculation method for lanthanide complexes based on frozen core potential approximation to 4f electrons

A practical electronic ground- and excited-state calculation method for lanthanide complexes is proposed by introducing frozen core potential (FCP) approximation to 4f electrons of a lanthanide atom ion (Ln(3+)). Based on the fact that the FCP method is formally equivalent to the elongation method, the 4f-frozen FCP calculations of Ln(3+) complexes were successfully performed using the elongation method implemented in GAMESS quantum chemistry program. By comparing the 4f-frozen FCP calculation results of several lanthanide complexes with the results of the standard calculations, it was confirmed that the excitation energies by these calculations are comparable. Also, the SCF convergence and stability were significantly improved by the FCP approximation. We further propose a method to relax the rotational degrees of freedom for the frozen 4f orbitals. This relaxation slightly improves the accuracy of the excitation energies for f-f transitions.