Stable highly excited vibrational eigenvalues without the variational principle

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Abstract
The energy spectrum in the stochastic region for a model Hamiltonian of two strongly coupled modes is calculated by diagonalizing small matrices which do not provide the Hylleraas–Undheim–MacDonald variational energy upper bounds. In addition, a method for selecting the most important basis functions by artificial intelligence algorithms is utilized. The energy convergence is determined by the Hazi–Taylor stabilization method and by the nearest‐neighbor‐spacing distribution function which measures the local fluctuations in the spectrum.