Effect of confinement on PH₃ and OH₃⁺ inversion

Encapsulating molecules in nanocages such as C₆₀ provides a unique opportunity to probe how spatial confinement alters structure and dynamics. We examine umbrella inversion in hydronium (OH₃⁺) and phosphine (PH₃) in the gas phase and inside C₆₀. Inversion profile computations for OH₃⁺ and PH₃ are based on high-level correlated methods [CCSD(T)/aug-cc-pVTZ and aug-cc-pVQZ]. Modelling confined systems requires dealing with the cage and the encapsulated molecules together, which is computationally complex. Therefore, results pertaining to encapsulated systems are based on dispersion-corrected DFT (B97-D/aug-cc-pVTZ). Barrier heights and tunnelling splittings for OH₃⁺ and PH₃ are benchmarked against CCSD(T)/aug-cc-pVQZ results. For free OH₃⁺, the CCSD(T) barrier is computed to be ∼706 cm^-1, while B97-D yields a slightly lower value (612 cm^-1). The predicted tunnelling doublets closely match the experimental findings. Encapsulation of hydronium in C₆₀ (denoted as OH₃⁺@C₆₀, where X@C₆₀ indicates the encapsulation of X within C₆₀) raises the barrier height from 612 to 871 cm^-1 and markedly suppresses the splittings. In contrast, PH₃ exhibits an extremely high inversion barrier (∼11 000 cm^-1), effectively quenching tunnelling. Upon confinement, the barrier is lowered marginally, and the vibrational eigenstate energies are shifted upward. The interaction energies obtained using the DLPNO-CCSD(T)/def2-TZVP method confirm the stability of the encapsulated systems: -30.8 kcal mol^-1 for OH₃⁺@C₆₀ and -13.4 kcal mol^-1 for PH₃@C₆₀. Energy decomposition analysis shows that OH₃⁺@C₆₀ stabilization is predominantly electrostatic in nature, whereas the dispersion term in PH₃@C₆₀ is considerably larger.