Quartic-Scaling Analytical Gradient of Quasidegenerate Scaled Opposite Spin Second-Order Perturbation Corrections to Single Excitation Configuration Interaction

Quasidegenerate scaled second-order perturbation correction to single excitation configuration interaction (SOS-CIS(D0)) is a viable method that can describe excited-state potential energy surfaces of various chemical systems both reliably and efficiently [J. Chem. Phys. 2008, 128, 164106]. In this work, its analytical gradient theory is developed and implemented into an efficient quartic-scaling algorithm. This low order scaling, as opposed to the traditional quintic scaling of various second-order perturbation methods, is attained by using the resolution-of-the-identity approximation and the Laplace transform. The efficiency of the method is demonstrated by calculating the excited-state gradients of molecules with varying sizes. The proposed gradient method will thus be useful in studying various chemical systems, ranging from finding the optimized stable geometry on the excited surface to elucidating interesting excited-state dynamics around the avoided crossing region.