Understanding charge transfer at electrochemical interfaces requires consistent treatment of electronic energy levels in solids and in water at the same level of the electronic structure theory. Using density-functional-theory-based molecular dynamics and thermodynamic integration, the free energy levels of six redox couples in water are calculated at the level of the random phase approximation and a double hybrid density functional. The redox levels, together with the water band positions, are aligned against a computational standard hydrogen electrode, allowing for critical analysis of errors compared to the experiment. It is encouraging that both methods offer a good description of the electronic structures of the solutes and water, showing promise for a full treatment of electrochemical interfaces.
We thank Professors Michiel Sprik and Xin Xu for helpful discussion. J. V. acknowledges financial support by the European Union FP7 in the form of an ERC Starting Grant under Contract No. 277910. This research was partly supported by NCCR MARVEL, funded by the Swiss National Science Foundation. Calculations were enabled by the Swiss National Supercomputer Centre (CSCS) under Project ID No. ch5. J. C. is grateful for funding support by the National Natural Science Foundation of China (Grant No. 21373166), and the Thousand Youth Talents Plan of China.