Alignment of electronic energy levels at electrochemical interfaces

Abstract

The position of electronic energy levels in a phase depends on the surface potentials at its boundaries. Bringing two phases in contact at an interface will alter the surface potentials shifting the energy levels relative to each other. Calculating such shifts for electrochemical interfaces requires a combination of methods from computational surface science and physical chemistry. The problem is closely related to the computation of potentials of electrochemically inactive electrodes. These so-called ideally polarizable interfaces are impossible to cross for electrons. In this perspective we review two density functional theory based methods that have been developed for this purpose, the workfunction method and the hydrogen insertion method. The key expressions of the two methods are derived from the formal theory of absolute electrode potentials. As an illustration of the workfunction method we review the computation of the potential of zero charge of the Pt(111)-water interface as recently published by a number of groups. The example of the hydrogen insertion method is from our own work on the rutile TiO(2)(110)-water interface at the point of zero proton charge. The calculations are summarized in level diagrams aligning the electronic energy levels of the solid electrode (Fermi level of the metal, valence band maximum and conduction band minimum of the semiconductor) to the band edges of liquid water and the standard potential for the reduction of the hydroxyl radical. All potentials are calculated at the same level of density functional theory using the standard hydrogen electrode as common energy reference. Comparison to experiment identifies the treatment of the valence band of water as a potentially dangerous source of error for application to electrocatalysis and photocatalysis.

Ab Initio Electrochemistry: Exploring the Hydrogen Evolution Reaction on Carbon Nanotubes

“…23 or Table 2 in ref. 22), the PZC is highly sensitive to the orientation of water molecules near the electrode and it is questionable whether reliable estimates can be obtained based on static calculations alone. Here, we calculate the PZC by averaging the electrode potential from a 6.5 ps molecular dynamics simulation following an initial 1 ps equilibration period.…”

“…For an in-depth review of electrochemical concepts in quantum chemical calculations, we refer the reader to ref. 22.…”

“…A potentially more serious issue is related to the use GGA functionals for the Kohn-Sham XC interaction, which, among other issues, leads to an incorrect description of energy levels and band gaps. 3 While most GGA functionals typically reproduce accurate vacuum work functions, 22 the incorrect alignment of solvent energy levels and the electrode Fermi level might result in unphysical charge transfer between the two combined components. 29 For the present system, this matter is addressed in full detail in Sec.…”

“…54 Thus, we find that the relative position of the Fermi level is less sensitive to GGA functional errors than the absolute alignment of electronic levels, in agreement with earlier studies. 22 After a substitutional nitrogen dopant is added to the nanotube, the extra electron from nitrogen is injected to the nanotube conduction band shifting the vacuum PBE work function to 4.15 eV, which is equivalent to a shift of 240 mV in the absolute electrode potential when compared to pristine CNT. This value also quantifies the minimum expected potential shift during an electrochemical reaction, e.g., when a proton is reduced on the nanotube during HER.…”

“…The absolute electrode potential, U abs. 0 , of an uncharged electrode can be calculated from 22 U abs.…”