Analytic gradient and derivative couplings for the spin-flip extended configuration interaction singles method: Theory, implementation, and application to proton transfer.

We present the formalism of analytic gradients and derivative couplings for the spin-flip extended configuration interaction with single excitations (SF-XCIS) method. We report an efficient implementation of the SF-XCIS method in the framework of semiempirical quantum chemistry that allows fast excited-state calculations for large systems. The performance of the SF-XCIS method in combination with semiempirical orthogonalization-corrected models (OMx) is statistically evaluated for vertical singlet excitation energies. The SF-XCIS method treats the ground state and excited states in a fully balanced manner and properly describes conical intersections involving the ground state. It can thus be used in fewest switches surface hopping (FSSH) simulations of nonadiabatic dynamics processes. This is demonstrated in an OM2/SF-XCIS FSSH pilot study of excited-state proton transfer in 7-(2-pyridyl)indole.