Optical trapping of molecules with long coherence times is crucial for many protocols in quantum information and metrology. However, the factors that limit the lifetimes of the trapped molecules remain elusive and require improved understanding of the underlying molecular structure. Here we show that measurements of vibronic line strengths in weakly and deeply bound ^{88}Sr_{2} molecules, combined with ab initio calculations, allow for unambiguous identification of vibrational quantum numbers. This, in turn, enables the construction of refined excited potential energy curves, informing the selection of magic wavelengths that facilitate long vibrational coherence. We demonstrate Rabi oscillations between far-separated vibrational states that persist for nearly 100 ms.
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