Iterative and non-iterative triple excitation corrections in coupled-cluster methods for excited electronic states: the EOM-CCSDT-3 and EOM-CCSD(T̃) methods

New iterative and non-iterative triple excitation corrections to EOM-CCSD are presented based upon the CCSDT-3 method. This method is recommended formally, since it fully employs the EOM-CCSD Hamiltonian H̃ = exp[−(T1 + T2)]H exp(T1 + T2) in its development. This permits defining iterative EOM-CCSDT-3 and non-iterative EOM-CCSD(T̃) corrections correct through second-order in H̃. Results for some full CI examples demonstrate average errors of 0.09 eV and 0.08 eV, respectively. We also study trans-butadiene as a more demanding example. We also consider a computationally simpler but accurate approximation to EOM-CCSD(T̃), EOM-CCSD(T′).