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The Rayleigh-Schrödinger perturbation theory is applied to energy levels calculation of excited vibrational states for different molecules. The calculations are carried out for the vibrational states that correspond to three- to seven-fold vibrational excitations. Perturbation series diverge in the case of strong resonance interactions. Nevertheless, considering vibrational energy of each excited state not as a real number, but as a complex function and applying corresponding analytical functions theory, we were able not only to get the exact value of energy, but to find the reason of divergence, and to choose the best summation technique. Our summation technique is based on high-order Pade-Hermite approximations. Further research shows that series behavior completely depends on the singularities of complex energy function inside unit circle. This analysis helped us to make the first exact definition of resonance interaction and to develop a unique technique for vibrational energy spectrum calculations avoiding resonances.