The paper explores the connection between the cavity Born–Oppenheimer (CBO) approximation and standard electronic-structure calculations, aiming to understand how vibrational strong coupling between molecular vibrations and light modes can alter molecular properties. The CBO approach, which treats photons on the same footing as nuclei, is more rigorous but requires significant computational effort. The authors propose a perturbative method to approximate the CBO ground state using only out-of-cavity quantities from standard electronic-structure calculations. They demonstrate this method on hydrogen fluoride (HF) molecules, showing that it can accurately reproduce CBO results for realistic coupling strengths. The perturbative corrections are physically meaningful, such as the refractive index of the molecules, and provide insights into the underlying effects of the cavity on the molecule. This approach offers a practical and efficient alternative to full CBO calculations, aiding in the interpretation of CBO results and the incorporation of more complex features in models.The paper explores the connection between the cavity Born–Oppenheimer (CBO) approximation and standard electronic-structure calculations, aiming to understand how vibrational strong coupling between molecular vibrations and light modes can alter molecular properties. The CBO approach, which treats photons on the same footing as nuclei, is more rigorous but requires significant computational effort. The authors propose a perturbative method to approximate the CBO ground state using only out-of-cavity quantities from standard electronic-structure calculations. They demonstrate this method on hydrogen fluoride (HF) molecules, showing that it can accurately reproduce CBO results for realistic coupling strengths. The perturbative corrections are physically meaningful, such as the refractive index of the molecules, and provide insights into the underlying effects of the cavity on the molecule. This approach offers a practical and efficient alternative to full CBO calculations, aiding in the interpretation of CBO results and the incorporation of more complex features in models.