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A detailed theoretical framework for highly excited Rydberg molecules isdeveloped based on the generalized local frame transformation. Our approachavoids the use of pseudopotentials and yields analytical expressions for thebody-frame reaction matrix. The latter is used to obtain the molecularpotential energy curves, but equally it can be employed for photodissociation,photoionization, or other processes. To illustrate the reliability and accuracyof our treatment we consider the Rb$^*-$Rb Rydberg molecule and compare ourtreatment with state-of-the-art alternative approaches. As a secondapplication, the present formalism is used to re-analyze the vibrationalspectra of Sr$^*-$Sr molecules, providing additional physical insight intotheir properties and a comparison of our results with correspondingmeasurements.

Generalized local frame transformation theory for ultralong-range Rydberg molecules