Gradients of ground and excited states for CC2 and ADC(2) in polarizable continuum and atomistic embeddings within a generalized PTED coupling scheme

We present a state-specific implementation of ground- and excitation energies and analytic gradients thereof for the approximate coupled-cluster singles-and-doubles model CC2 in polarizable environments that is suitable for the description of long-living charge-transfer excited states. It employs a reaction field potential equilibrated self- consistently with the target state density and includes linear response constributions to account for the excitonic coupling to the optical polarizability of the environment. The implementation is available in combination with the conductor-like screening model COSMO as polarizable continuum model and the atomistic polarizable em- bedding in point multipoles and polarizabilities. For COSMO smooth potential en- ergy surfaces and convergence of structure optimizations are obtained with a Gaus- sian charge model. For the algebraic-diagrammatic construction through second-order, ADC(2), with COSMO it is identical with an earlier implementation [Lunkenheimer and Köhn, J. Chem. Theory Comput. 2013, 9, 977-994] but extends the latter to analytic gradients. Examplary applications are presented for structures, dipole mo- ments, and emission energies of the charge-transfer and locally excited states of 4-(N,N- Dimethylamino)benzonitrile and N-(9-anthryl)carbazole in different solvents. The re- sults demonstrate that not only solvent shifts but also physically correct structures are obtained for strongly polar states in polarizable environments.