This paper explores the cavity Born–Oppenheimer (CBO) approximation and its relation to simpler models used in polariton chemistry. The CBO approach is more rigorous but requires rewriting electronic-structure code, making it less practical. The authors demonstrate that for realistic coupling strengths, CBO energies and spectra can be accurately recovered using only out-of-cavity quantities from standard electronic-structure calculations. This method provides physical insight into the effects underlying CBO results and offers a practical alternative to full CBO calculations. The study focuses on hydrogen fluoride (HF) and shows that the CBO ground-state potential energy and harmonic frequencies can be reproduced with high accuracy using perturbative corrections. The results indicate that the leading perturbative correction corresponds to the refractive index of the molecules in the cavity, explaining the frequency shift observed in CBO spectra. This suggests that the red shift in recent CBO literature may have a more mundane origin than previously thought. The authors also discuss the effects of adding more molecules to the cavity, showing that the N-molecule Hessian can be block-diagonalized, allowing for efficient calculations. The results demonstrate that the cCBO approximation, combined with perturbative corrections, can reproduce CBO results with high accuracy. The study highlights the importance of the refractive index in cavity frequency shifts and shows that the cCBO approach can be used to simulate cavity effects without requiring full CBO calculations. The paper concludes that the cCBO approach provides a practical and efficient alternative to full CBO calculations, offering physical insight into the effects of cavity coupling on molecular properties. The results suggest that the cCBO method can be used to study cavity effects in microcavities, providing a valuable tool for future research in polariton chemistry.This paper explores the cavity Born–Oppenheimer (CBO) approximation and its relation to simpler models used in polariton chemistry. The CBO approach is more rigorous but requires rewriting electronic-structure code, making it less practical. The authors demonstrate that for realistic coupling strengths, CBO energies and spectra can be accurately recovered using only out-of-cavity quantities from standard electronic-structure calculations. This method provides physical insight into the effects underlying CBO results and offers a practical alternative to full CBO calculations. The study focuses on hydrogen fluoride (HF) and shows that the CBO ground-state potential energy and harmonic frequencies can be reproduced with high accuracy using perturbative corrections. The results indicate that the leading perturbative correction corresponds to the refractive index of the molecules in the cavity, explaining the frequency shift observed in CBO spectra. This suggests that the red shift in recent CBO literature may have a more mundane origin than previously thought. The authors also discuss the effects of adding more molecules to the cavity, showing that the N-molecule Hessian can be block-diagonalized, allowing for efficient calculations. The results demonstrate that the cCBO approximation, combined with perturbative corrections, can reproduce CBO results with high accuracy. The study highlights the importance of the refractive index in cavity frequency shifts and shows that the cCBO approach can be used to simulate cavity effects without requiring full CBO calculations. The paper concludes that the cCBO approach provides a practical and efficient alternative to full CBO calculations, offering physical insight into the effects of cavity coupling on molecular properties. The results suggest that the cCBO method can be used to study cavity effects in microcavities, providing a valuable tool for future research in polariton chemistry.