Constant chemical potential approach for quantum chemical calculations in electrocatalysis

Abstract

In order to simulate electrochemical reactions in the framework of quantum chemical methods, density functional theory, methods can be devised that explicitly include the electrochemical potential. In this work we discuss a Grand Canonical approach in the framework of density functional theory in which fractional numbers of electrons are used to represent an open system in contact with an electrode at a given electrochemical potential. The computational shortcomings and the additional effort in such calculations are discussed. An ansatz for a SCF procedure is presented, which can be applied routinely and only marginally increases the computational effort of standard constant electron number approaches. In combination with the common implicit solvent models this scheme can become a powerful tool, especially for the investigation of omnipresent non-faradaic effects in electrochemistry.

Keywords: density functional theory; electrocatalysis; electrochemistry; electronic strutcture theory; nanoparticles; quantum chemistry.

Figure 1

Evolution of the number of electrons with the number of iterations for O₂ if the potential dependent energy is computed by inserting the aspired μ into Equation 2.

Figure 2

Change of the absolute potential for O₂ depending on the number of electrons, calculated numerically and approximated by Equation 3, respectively.

Figure 3

Chemical potential of the O₂ molecule, plotted against the number of electrons, calculated numerically and approximated by recalculation of the Fock matrix, respectively.

Figure 4

Scheme for a potential dependent calculation of the free energy.

Figure 5

Convergence of the number of electrons with the SCF iterations for different systems. Note that the calculation for the charge neutral molecules with fixed number of electrons for O₂ converges within 7, for C₆H₆ within 13, for Pt₄ within 73 and for Pt₁₀ within 177 SCF iterations, respectively.