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To demonstrate its applicability, we present calculations of equilibrium structures and harmonic vibrational frequencies for the electronic ground and excited states of the radium mono-amide molecule (RaNH2) and the radium mono-methoxide molecule (RaOCH3). Spin\u2013orbit coupling is shown to quench Jahn\u2013Teller effects in the first excited state of RaOCH3, resulting in a C3v equilibrium structure. 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