Three- versus four-coordinate phosphorus in the gas phase and in solution: Treacherous relative energies for phosphine oxide and phosphinous acid

Previous ab initio studies have consistently predicted phosphine oxide $({\mathrm{H}}_{\mathrm{3}}\mathrm{PO})$ to be less stable than its nearly isoenergetic cis- and trans-phosphinous acid isomers $({\mathrm{H}}_{\mathrm{2}}\mathrm{POH}\mathrm{).}$ However, complete basis set extrapolations employing the coupled-cluster series show that phosphine oxide is actually ca. 1.0 kcal/mol more stable than its acid forms in the gas phase. Incorporation of tight d functions via Dunning’s core-valence (cc-pCVXZ) or newly constructed “plus d” $[\mathrm{cc-pV(X+d)Z}]$ basis sets is essential for rapid convergence of core polarization effects which are evident even at the SCF level. The precision to which the phosphorus hybridization is described in the three- and four-coordinate environments ultimately determines the predicted gas-phase relative energy orderings. Focal-point analyses demonstrate that this system represents a disturbing case where use of a conventional valence quadruple-ζ quality basis set (cc-pVQZ)—even at the CCSD(T) level—fails to provide the correct relative energy ordering for simple closed-shell species which do not exhibit appreciable multireference character. Thus, we underscore the importance of using phosphorus basis sets which have the flexibility to describe core polarization adequately. In addition, Monte Carlo (MC) free-energy perturbation simulations in solution clearly demonstrate that the small energy gap significantly increases in favor of the oxide (10.0 kcal/mol) upon solvation due to stronger hydrogen bonding with the highly polar ${\mathrm{P}}^{\mathrm{\delta +}}\to {\mathrm{O}}^{\mathrm{\delta -}}$ bond.