The Eckart-frame hamiltonian of a triatomic molecule in terms of the bond lengths and the intrabond angle

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Abstract
The work develops the general formalism to switch from a geometrically defined body-fixed frame, like the bisector frame, to the Eckart frame. The derived analytical formula for the axis-switching angle between the bisector and Eckart frames of an arbitrary ABC nonlinear molecule is used to parametrize the set of standard configurations, satisfying the Eckart conditions, by means of the bond lengths R 1, R 2 and the intrabond angle θ. This makes it possible to write the explicit expression for the Eckart-frame hamiltonian in terms of these geometrical variables. The hamiltonian of a linear molecule is obtained by making the equilibrium angle θe tend to π.