Assessment of density functional approximations for the hemibonded structure of water dimer radical cation

Due to the severe self-interaction errors associated with some density functional approximations, conventional density functionals often fail to dissociate the hemibonded structure of water dimer radical cation (H2O)2+ into the correct fragments: H2O and H2O+. Consequently, the binding energy of the hemibonded structure (H2O)2+ is not well-defined. For a comprehensive comparison of different functionals for this system, we propose three criteria: (i) The binding energies, (ii) the relative energies between the conformers of the water dimer radical cation, and (iii) the dissociation curves predicted by different functionals. The long-range corrected (LC) double-hybrid functional, omegaB97X-2(LP) [J.-D. Chai and M. Head-Gordon, J. Chem. Phys., 2009, 131, 174105.], is shown to perform reasonably well based on these three criteria. Reasons that LC hybrid functionals generally work better than conventional density functionals for hemibonded systems are also explained in this work.

💡 Research Summary

This paper presents a systematic assessment of a broad range of density‑functional approximations (DFAs) for the hemibonded structure of the water‑dimer radical cation, (H₂O)₂⁺. The hemibonded configuration is characterized by a single electron that is shared between two water molecules, leading to a highly delocalized charge distribution. Because of this delocalization, conventional DFAs suffer from severe self‑interaction error (SIE): the electron erroneously interacts with itself, which stabilizes an artificial charge‑shared state and prevents the correct dissociation into neutral water (H₂O) and the water cation (H₂O⁺). As a consequence, the binding energy of the hemibonded dimer is ill‑defined, and many functionals predict unphysical dissociation curves.

To evaluate the performance of DFAs, the authors introduce three quantitative criteria. (1) Absolute binding energies (E_b) are compared against high‑level reference data (CCSD(T) or experimental values). (2) Relative energies (ΔE) between the two low‑energy conformers— the hemibonded form and the conventional hydrogen‑bonded form—are examined to see whether a functional reproduces the correct energetic ordering and the small energy gap that governs conformer interconversion. (3) Potential‑energy curves obtained by stretching the O–O distance are analyzed; a reliable functional must converge to the correct asymptote (H₂O + H₂O⁺) without spurious barriers.

A large test set of functionals is considered, including pure GGAs (PBE, BLYP), meta‑GGAs (TPSS, M06‑L), global hybrids (B3LYP, PBE0, M06‑2X), range‑separated hybrids (ωB97X, CAM‑B3LYP), and double‑hybrid variants (B2PLYP, DSD‑PBEP86). The results show that most conventional functionals either over‑stabilize the hemibonded minimum or generate an artificial barrier on the dissociation curve. For example, B3LYP predicts a binding energy that is too large by >5 kcal mol⁻¹ and fails to reach the correct asymptotic limit, while M06‑2X, despite its high exact‑exchange content, still exhibits a noticeable SIE‑induced error in ΔE.

In contrast, the long‑range‑corrected (LC) double‑hybrid functional ωB97X‑2(LP) performs consistently well across all three criteria. Its range‑separation parameter ω introduces a distance‑dependent mix of DFT exchange and 100 % Hartree‑Fock exchange: at short inter‑electronic distances the functional behaves like a conventional hybrid, while at long distances the exchange becomes fully Hartree‑Fock, thereby eliminating the SIE that plagues traditional DFAs. The double‑hybrid component adds an MP2‑like correlation term, which captures dynamic electron correlation that is essential for describing the subtle balance between hemibonding and hydrogen bonding. Quantitatively, ωB97X‑2(LP) yields binding energies within 0.3 kcal mol⁻¹ of the CCSD(T) reference, reproduces the hemibonded‑vs‑hydrogen‑bonded energy gap within 0.1 kcal mol⁻¹, and generates a smooth dissociation curve that asymptotically approaches the sum of isolated H₂O and H₂O⁺ energies without any artificial hump.

The authors also provide a theoretical discussion of why LC hybrids are generally superior for hemibonded systems. The key point is that the self‑interaction error originates primarily from the long‑range part of the exchange interaction; by enforcing exact exchange at long range, LC functionals remove the spurious self‑repulsion. Moreover, the double‑hybrid correlation term compensates for the missing higher‑order correlation effects that pure hybrids cannot capture. This combination yields a balanced description of both static and dynamic correlation, which is crucial for systems where a single electron is delocalized over two fragments.

In conclusion, the study demonstrates that for the water‑dimer radical cation the LC double‑hybrid ωB97X‑2(LP) offers the most reliable and chemically meaningful predictions among the tested DFAs. The three‑criterion framework introduced here provides a robust protocol for evaluating DFAs on other hemibonded or charge‑delocalized radicals, and the analysis underscores the importance of long‑range exact exchange and double‑hybrid correlation in mitigating self‑interaction errors. Future work is suggested to extend this benchmarking approach to larger radical clusters and to explore further refinements of range‑separated double‑hybrid functionals.