``Excited States Theory for Optimized Orbitals and Valence Optimized Orbitals Coupled-Cluster Doubles Models,'' A. I. Krylov, C. D. Sherrill, and M. Head-Gordon, J. Chem. Phys. 113, 6509-6527 (2000).

We introduce an excited state theory for the optimized orbital coupled cluster doubles (OO-CCD) and valence optimized orbital coupled cluster doubles (VOO-CCD) models. The equations for transition energies are derived using a similarity transformed Hamiltonian. The effects of orbital relaxation are discussed. We present results for several single-reference molecules (H2O, CH2O, C2H4O, C2H4, BeO), as well as for molecules with significant non-dynamical correlation in the ground state (CH+, BH, A 1A1 CH2), and for rectangular O4+. We find that: (i) OO-CCD excitation energies are very close to CCSD excitation energies; (ii) similarly to the complete active space SCF (CASSCF) model, the effects of orbital relaxation are very important for VOO-CCD excited states such that the excitation energies calculated by VOO-CCD and CASSCF with orbitals optimized for the ground state are very close to each other and unsatisfactory; (iii) the VOO-CCD model with an approximate treatment of orbital relaxation describes singly (valence and Rydberg) and doubly (valence) excited states within errors of 0.2-1.0 eV at equilibrium geometries and along bond-breaking coordinates; (iv) the above accuracy of VOO-CCD model does not degrade as molecules or basis sets grow in size; (v) the shapes of potential energy surfaces around excited states minima are reproduced well by VOO-CCD model suggesting the use of this method for excited states geometry optimization.