A general method is suggested which allows one to separate the quadratic, cubic, and pseudo Jahn-Teller contributions to the warping of the adiabatic potential energy surface ͑APES͒ of the E e problem employing ab initio calculations. Numerical results were obtained for NaCl: Rh 2+ in a cluster approximation and triangular molecules ͑Na 3 ,K 3 ,Cu 3 ,Ag 3 ͒ using density functional theory ͑DFT͒ and multireference second-order perturbation theory ͑CASPT2͒ methods. A largely unexpected result is that the contribution of cubic anharmonicity to the energy barrier between the minima of the lower and upper branches of the APES is dominant in all the systems and amounts for not less than 60% of the total. Another feature is that the three different contributions mentioned above may have different signs, thus either enhancing or diminishing each other, affecting in different ways the lower and upper branches of the APES. Other details of the numerical results are also analyzed.