We have examined the relative abilities of Hartree-Fock, density-functional theory (DFT), and coupled-cluster theory in describing second-order (pseudo) Jahn-Teller (SOJT) effects, perhaps the most commonly encountered form of symmetry breaking in polyatomic molecules. As test cases, we have considered two prototypical systems: the (2)Sigma(u)(+) states of D-infinityh BNB and C-3(+) for which interaction with a low-lying (2)Sigma(g)(+) excited state leads to symmetry breaking of the nuclear framework. We find that the Hartree-Fock and B3LYP methods correctly reproduce the pole structure of quadratic force constants expected from exact SOJT theory, but that both methods appear to underestimate the strength of the coupling between the electronic states. Although the Tamm-Dancoff (CIS) approximation gives excitation energies with no relationship to the SOJT interaction, the random-phase-approximation (RPA) approach to Hartree-Fock and time-dependent DFT excitation energies predicts state crossings coinciding nearly perfectly with the positions of the force constant poles. On the other hand, the RPA excited-state energies exhibit unphysical curvature near their crossings with the ground (reference) state, a problem arising directly from the mathematical structure of the RPA equations. Coupled-cluster methods appear to accurately predict the strength of the SOJT interactions between the (2)Sigma(u)(+) and (2)Sigma(g)(+) states, assuming that the inclusion of full triple excitations provides a suitable approximation to the exact wave function, and are the only methods examined here which predict symmetry breaking in BNB. However, coupled-cluster methods are plagued by artifactual force constant poles arising from the response of the underlying reference molecular orbitals to the geometric perturbation. Furthermore, the structure of the "true" SOJT force constant poles predicted by coupled-cluster methods, although correctly positioned, has the wrong structure. (C) 2004 American Institute of Physics.