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We report the analytical nuclear gradient theory for complete active spacesecond-order perturbation theory (CASPT2) with imaginary shift, which iscommonly used to avoid divergence of the perturbation expression. Ourformulation is based on the Lagrangian approach and is an extension of thealgorithm for CASPT2 nuclear gradients with real shift. The working equationsare derived and implemented into an efficient parallel program. Numericalexamples are presented for the ground- and excited-state geometries and conicalintersections of a green fluorescent protein model chromophore, $p$-HBDI$^-$.We also report timing benchmarks with adenine, $p$-HBDI$^-$, and ironporphyrin. It is demonstrated that the energies and geometries obtained withthe imaginary shift improve accuracy at a minor additional cost which is mainlyassociated with evaluating the effective density matrix elements for theimaginary shift term.

Imaginary shift in CASPT2 nuclear gradient and derivative coupling theory