Here, the effective Hamiltonian operator is obtained by a similarity transformation of the ground state Hamiltonian operator. This nonlinear transformation tends to include the effects of higher excitations thereby recovering more of the correlation energy in the excited states and, as a result, gives more accurate excitation energies. These calculations generally have an error of less than 0.1-0.3 eV in the excitation energies (∼ 2.39 -7 kcal/mol) for the low-lying electronic states and the relative state ordering is usually better when compared to time-dependent density functional theory (TD-DFT).