Abstract
A closed-form kinetic energy operator (KEO) for tetra-atomic planar molecules in Eckart frame has been expressed explicitly in terms of the internal coordinates with a parameter θ1e which labels a specific Eckart frame. This KEO has zero Coriolis coupling at equilibrium and an expression for the best θ1e has been given that makes zero centrifugal coupling. A method treating the singularities of this KEO has been shown and all matrix elements are finite in the basis presented in this paper.
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