Development of approximately spin projected energy derivatives for biradical systems

摘要

In this article, we summarize a recent progress in our spin-projected energy derivative method for broken-symmetry (BS) solutions of singlet biradical systems. Because, the spin projection procedure that is based on the approximate spin projection (AP) method does not involve a spin contamination error, it improves the accuracy of an optimized geometry and a calculated vibrational frequency for the singlet biradical molecule with the low cost of computation. To examine the spin contamination error in the BS energy derivatives and to demonstrate the efficiency of the AP method, we carry out the geometry optimization and the vibrational calculation of singlet CR_2 (R = H, F, and CH_3) molecules that are the typical singlet biradical systems. The results indicate that the error in the singlet CH_2 and C(CH_3)_2 molecules are serious, however, the error in the singlet CF_2 molecule, which has electron withdrawing fluorine atoms is negligible.