Benchmarking Semiempirical Methods To Compute Electrochemical Formal Potentials

Abstract

Computational methods to predict and tune electrochemical redox potentials are important for the development of energy technologies. Here, we benchmark several semiempirical models to compute reduction potentials of organic molecules, comparing approaches based on (1) energy differences between the S and one-electron-reduced D states of the isolated molecules and (2) an orbital energy shift approach based on tuning the charge-transfer triplet energy of the Ag-molecule complex; the second model enables explicit modeling of electrode-molecule interactions. For molecules in solution, the two models yield nearly identical results. Both PM7 and PM6 predict formal potentials with only a slight loss of accuracy compared to standard density functional theory models, and the results are robust across several choices of geometries and implicit solvent models. PM6 and PM7 show dramatically improved accuracy over older semiempirical Hamiltonians (MNDO, AM1, PM3, and INDO/S). However, our recently developed INDO parameters model the electronic properties of our Ag model electrode much more accurately than does PM7. These results demonstrate the need for further development of semiempirical models to accurately model molecules on surfaces.

Linear correlation models for the redox potential of organic molecules in aqueous solutions

“…The set of molecules was originally compiled by Marenich et al [26], and we have used the same set for convenience and consistency. Furthermore, this is a suitable set because redox potential data in aqueous solution studies is much more sparse than typical benchmarking data sets [3,28,[49][50][51][52][53]. The experimental potentials of the set of 53 molecules range from -0.24 to 1.47 V vs the standard hydrogen electrode (SHE).…”

“…The calculation of the redox potential of organic molecules in solutions is crucial for the rational design of such technologies. Various methodologies are currently employed to calculate redox potential in solutions: i) the Born-Haber thermodynamic cycle (BHTC) [24][25][26][27], ii) the S0-D0 energy difference approximation (EDA) [28][29][30], and iii) the molecular orbital energy approximation (MOEA) [28,31,32]. In the BHTC method, the redox potential is calculated from the standard free energy of product and reactants in a redox half-reaction.…”

“…However, the EDA and MOEA methods have been shown to work for a diverse set of molecules in a given solvent [27][28][29][30][31][32][33]. For example, Gillmore et al [29,30] and Méndez-Hernández et al [31,32] have reported strong correlations for a set of 74 diverse molecules in acetonitrile using the EDA and MOEA methodologies, respectively.…”

A new release of MOPAC incorporating the INDO/S semiempirical model with CI excited states

“…The introduction of parameters fit to experimental and high-level computational results has enabled high enough accuracy to provide understanding of chemical properties including thermochemistry, 13,21,22 noncovalent interactions, 13,21,23 excited states, 24,25 pKa, 14,19 magnetism, 26 solvatochromism, 27 and electrochemical formal potentials. 28 We note that the Density Functional Tight Binding (DFTB) model is a semiempirical-like model based on a Hamiltonian simplified from Density Functional Theory (DFT) and has many capabilities similar to those of Hartree-Fock-based SEQMs; [29][30][31] here, we focus exclusively on SEQMs derived from Hartree-Fock.…”

Linear Correlation Models for the Redox Potential of Organic Molecules in Aqueous Solutions

“…The calculation of the redox potential of organic molecules in solutions is crucial for the rational design of such technologies. Various methodologies are currently employed to calculate redox potential in solutions: i) the Born-Haber thermodynamic cycle (BHTC) [24][25][26][27], ii) the S0-D0 energy difference approximation (EDA) [28][29][30], and iii) the molecular orbital energy approximation (MOEA) [28,31,32]. In the BHTC method, the redox potential is calculated from the standard free energy of product and reactants in a redox half-reaction.…”