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Category:Electrochemistry

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Electrochemistry studies chemical reactions in which electrons are transferred between an electrode and an electrolyte. Such reactions either generate an electrical potential difference, as in batteries and fuel cells, or are driven by an applied one, as in electrolysis. The overall reaction is split into half-reactions, each described by an electrochemical half-cell, such as the hydrogen half-cell:

[math]\displaystyle{ 2\mathrm{H}^+(\mathrm{aq}) + 2e^- \rightleftharpoons \mathrm{H}_2(\mathrm{g}) }[/math]

On a platinum electrode under standard conditions, i.e., unit activity of H+ (pH 0) and an H2 pressure of 1 bar, this half-cell is the standard hydrogen electrode (SHE). By convention, its potential is 0 V at all temperatures, and it serves as the reference for all other electrode potentials.

Modeling electrochemical half-cells from first principles generally means treating a charged interface. For an introduction to slabs, see Surfaces, thin films, and 2D materials. This page covers explicitly charged interfaces and redox potentials from thermodynamic integration. Many other approaches exist, most notably the computational hydrogen electrode (CHE), which references reaction free energies to the SHE without charging the cell[1][2].

Coulomb kernel truncation

Coulomb kernel truncation predicts the correct physical, linear behaviour of the electrostatic potential into the vacuum for a charged slab (2D truncated, +1), which is not seen without (3D periodic, +1).
Mind: Coulomb kernel truncation is only available as of VASP 6.5.0.

The electrode potential can be changed by applying excess charge (NELECT), adding or removing electrons and compensating with a homogeneous background charge. This background charge introduces spurious electrostatic interactions (magnitude dependent on the cell size and on the dimensionality of the system), which must be corrected for.

To solve this for charged molecules and surfaces, a Coulomb kernel truncation can be applied. This replaces the periodic Coulomb kernel by a truncated one along the non-periodic directions, i.e., along the surface normal for slabs and in all three directions for molecules. This removes the interaction between periodic images and therefore the need for a compensating background charge [3][4][5]. This is the recommended approach for treating charged molecules and slabs.

For further reading, see Charged systems with density functional theory, Electrostatic corrections, and the Electrostatics category page.

Redox potential using thermodynamic integration

Thermodynamic integration allows integration from a non-interacting system (λ = 0) to an interacting system (λ = 1). E.g., between Fe2+ and Fe3+ for an electrochemical half-cell.

The tendency of a species to gain or lose electrons is quantified by the redox potential of the couple formed by its oxidized and reduced states. Thermodynamic integration is used to compute the free energy differences between two systems, e.g., the Fe3+/Fe2+ electrochemical half-cell following Jinnouchi, Karsai, and Kresse [6]. A series of how-to pages covers this procedure, beginning with an overview page:

Absolute redox potential

Alignment of the periodic bulk-water calculation with the vacuum reference, cf. Vacuum reference theory for more details [6].

A computed potential is only meaningful relative to a reference. In a slab calculation, this can be taken relative to the local potential in the vacuum (cf. Computing the work function and WRT_POTENTIAL). For a liquid or bulk system, the local potential is in the system, not in the vacuum. Instead, reference can be taken to the vacuum of a slab, e.g., water, from a common reference: the energy levels of the [math]\displaystyle{ O_{1s} }[/math] orbitals of water [6][7]. This allows a calculated redox potential for a liquid or bulk system to be referenced to the vacuum.

References

  1. ↑ J. Nørskov, J. Rossmeisl, A. Logadottir, L. Lindqvist, J. Kitchin, T. Bligaard, H. Jónsson, Origin of the Overpotential for Oxygen Reduction at a Fuel-Cell Cathode, J. Phys. Chem. B 108 17886 (2004).
  2. ↑ J. Nørskov, T. Bligaard, A. Logadottir, J. Kitchin, J. Chen, S. Pandelov, U. Stimming, Trends in the Exchange Current for Hydrogen Evolution, J. Electrochem. Soc. 152 J23 (2005).
  3. ↑ C. A. Rozzi, D. Varsano, A. Marini, E. K. Gross, A. J. Rubio, Phys. Rev. B 73, 20511 (2006).
  4. ↑ T. Sohier, M. Calandra, and F. Mauri, Phys. Rev. B 96, 75448 (2017).
  5. ↑ S. Vijay, M. Schlipf, H. Miranda, F. Karsai, M. Kaltak, M. Marsman, and G. Kresse, Efficient periodic density functional theory calculations of charged molecules and surfaces using Coulomb kernel truncation, Phys. Rev. B 112, 045409 (2025).
  6. ↑ a b c R. Jinnouchi, F. Karsai, and G. Kresse, Machine learning-aided first-principles calculations of redox potentials, npj Comput. Mater. 10, 107 (2024).
  7. ↑ R. Jinnouchi, F. Karsai, and G. Kresse, Absolute standard hydrogen electrode potential and redox potentials of atoms and molecules: machine learning aided first principles calculations, Chem. Sci. 16, 2335 (2025).


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