Higher-order adiabatic separation of strongly coupled systems. II. Generalized Hénon–Heiles Hamiltonian

The phase corrected adiabatic approximation [Y. Maréchal, J. Chem. Phys. 83, 247 (1985); T. T. Nguyen-Dang and A. D. Bandrauk, J. Chem. Phys. 85, 7224 (1986)], is applied to obtain a second-order adiabatic representation for the generalized Hénon–Heiles system. This representation provides a formal link between nonintegrable Hénon–Heiles systems and the integrable anti-Hénon–Heiles system, for which the representation denotes exact separability in terms of normal coordinates q1=(1/√2)(x+y), q2=(1/√2)(x−y). In the nonintegrable cases, the representation denotes a higher-order adiabatic separability of the two coupled modes of the Hénon–Heiles systems, as its basis states are unitarily equivalent to Born–Oppenheimer-type product states, and are coupled only by residual couplings that are of second-order in the original coupling constant λ.