Iterative and non-iterative triple excitation corrections in coupled-cluster methods for excited electronic states: The EOM-CCSDT-3 and EOM-CCSD((T)over-tilde) 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 (H) over tilde = exp[-(T-1 + T-2)]Hexp(T-1 + T-2) in its development. This permits defining iterative EOM-CCSDT-3 and non-iterative (<EOM-CCSD (T)over tilde>) corrections correct through second-order in (H) over tilde. 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 (T)over tilde>), EOM-CCSD(T').