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This work addresses the calculation of electronic coupling parameters Had from Kohn-Sham Density Functional Theory (DFT). Although ubiquitous in theoretical descriptions, electronic coupling matrix elements are challenging to calculate in practice due to their non-observable nature and formally non-unique definition. As a result, Had are often approximated and used qualitatively. Extracting electronic couplings from DFT requires a projection of the adiabatic electronic structure onto localized diabatic fragments. In the context of charge transfer, this localization procedure is known as diabatization. While numerous diabatization schemes have been developed for the study of e.g. charge hopping between pairs of molecules, electronic coupling on surfaces has been less well explored.
In this work, we concern ourselves with a method called Projection-Operator Diabatization (POD). Similar to other local projections of DFT, such as Mulliken partial charge analysis, the original POD method suffers from instability with respect to the atomic orbital basis set. By first modifying this with a Gram-Schmidt (GS) orthogonalization procedure, we provide an improved method (POD2GS) which is demonstrated with the Hab11 benchmark of molecular dimers. Next, we develop similar diabatization methods for adsorbates on surfaces. We validate these methods by calculating ultrafast electron transfer lifetimes for core-excited Argon adsorbates on transition metal surfaces. For this, we use the couplings to construct a first-principles Newns-Anderson chemisorption function, a coupling-weighted density of states (WDOS) which gives the line broadening of an adsorbate frontier orbital on a surface. This line broadening is interpreted as an ultrafast electron transfer lifetime with Fermi’s Golden Rule, yielding results in excellent agreement with experiment.
The use of first-principles electronic couplings within a Newns-Anderson chemisorption function is found to be highly advantageous. The chemisorption function is highly interpretable, containing rich information on the phase and symmetry of interacting orbitals and their role in the electron transfer. Furthermore, we find that a proper Brillouin-zone integration of the couplings yields a chemisorption function which is convergent with respect to the finite size of the periodic slab model. The couplings are also found to be reasonably stable with respect to the atomic basis set and with respect to the (non-unique) choice of diabatization scheme. Such convergence aspects are widely known to be nontrivial in the local representation of DFT, with the result that many insightful schemes, such as the projected density of states, are used mainly in a qualitative sense. In contrast, this work presents the chemisorption function and electronic couplings as viable quantitative tools with high interpretive power.
Considering the prevalence of electronic couplings in theoretical models, the diabatization methods developed in this work have potential application in a broad array of phenomena. The present schemes are demonstrated in weakly interacting or physisorbed systems. Challenges in the treatment of e.g. fully chemisorped systems are discussed.
