Systematic analysis of electronic barrier heights and widths for concerted proton transfer in cyclic hydrogen bonded clusters: (HF)n, (HCl)n and (H2O)n where n = 3, 4, 5

Abstract

The MP2 and CCSD(T) methods are paired with correlation consistent basis sets as large as aug-cc-pVQZ to optimize the structures of the cyclic minima for (HF)_n, (HCl)_n and (H₂O)_n where n = 3–5, as well as the corresponding transition states (TSs) for concerted proton transfer (CPT). MP2 and CCSD(T) harmonic vibrational frequencies confirm the nature of each minimum and TS. Both conventional and explicitly correlated CCSD(T) computations are employed to assess the electronic dissociation energies and barrier heights for CPT near the complete basis (CBS) limit for all 9 clusters. Results for (HF)_n are consistent with prior studies identifying C_nh and D_nh point group symmetry for the minima and TSs, respectively. Our computations also confirm that CPT proceeds through C_s TS structures for the C₁ minima of (H₂O)₃ and (H₂O)₅, whereas the process goes through a TS with D_2d symmetry for the S₄ global minimum of (H₂O)₄. This work corroborates earlier findings that the minima for (HCl)₃, (HCl)₄ and (HCl)₅ have C_3h, S₄ and C₁ point group symmetry, respectively, and that the C_nh structures are not minima for n = 4 and 5. Moreover, our computations show the TSs for CPT in (HCl)₃, (HCl)₄ and (HCl)₅ have D_3h, D_2d, and C₂ point group symmetry, respectively. At the CCSD(T) CBS limit, (HF)₄ and (HF)₅ have the smallest electronic barrier heights for CPT (≈15 kcal mol⁻¹ for both), followed by the HF trimer (≈21 kcal mol⁻¹). The barriers are appreciably higher for the other clusters (around 27 kcal mol⁻¹ for (H₂O)₄ and (HCl)₃; roughly 30 kcal mol⁻¹ for (H₂O)₃, (H₂O)₅ and (HCl)₄; up to 38 kcal mol⁻¹ for (HCl)₅). At the CBS limit, MP2 significantly underestimates the CCSD(T) barrier heights (e.g., by ca. 2, 4 and 7 kcal mol⁻¹ for the pentamers of HF, H₂O and HCl, respectively), whereas CCSD overestimates these barriers by roughly the same magnitude. Scaling the barrier heights and dissociation energies by the number of fragments in the cluster reveals strong linear relationships between the two quantities and with the magnitudes of the imaginary vibrational frequency for the TSs.