Efficient modeling of liquid phase photoemission spectra and reorganization energies: Difficult case of multiply charged anions

Abstract

An efficient approach for quantitative modeling of liquid phase photoelectron spectra, reorganization energies, and redox potentials with DFT-based molecular dynamics simulations is presented. The method is based on a large scale cluster-continuum approach combined with the so-called reflection principle (RP). Finite size clusters of solute molecules with solvating water molecules are at first generated using either classical molecular dynamics or molecular dynamics with a quantum thermostat which accounts for nuclear quantum effects. In the next step, the electron binding energies are calculated. Finite-size corrections for (i) positions of electron binding energies and (ii) width of the spectrum are evaluated via a dielectric continuum approach. The performance of such a reflection principle with additional broadening approach (RP-AB) for oxidation of multiply charged iron anions, [Fe(CN) ] and [Fe(CN) ] is demonstrated. The role of nuclear quantum effects is discussed as well as the relation between spectroscopic data and electrochemical quantities. Results are compared with recent liquid photoemission experiments, explaining the obstacles for applying liquid phase photoemission spectroscopy as a direct method for obtaining absolute redox potentials and suggesting a way to overcome them. © 2017 Wiley Periodicals, Inc.

Do water's electrons care about electrolytes?

“…Here, an important aspect is the proper treatment of the dielectric continuum. First, the non-equilibrium character of the ionization process has to be acknowledged 37,89. Second, we should adjust the dielectric continuum model to reflect the finite ionic strength of the studied solution.…”

“…, the distribution of binding energies along the classical MD trajectory:where ρ ( R[combining right harpoon above] ) is the nuclear density evaluated with the classical MD simulations, BE n is the binding energy of the ejected electron, KE is the kinetic energy of an ejected electron, E is the incident photon energy, and f Fr, n is the contribution from the n -th electron of the fragment of interest. In the modelled photoemission spectra we included solvent spectral broadening via the reflection principle with an additional broadening scheme (RP-AB),89 i.e. , each point is broadened with a Gaussian function with a variance reflecting the reorganization energy calculated by means of dielectric continuum methods.…”

Ionization energies in solution with the QM:QM approach

“…On the other hand, the ionization energies calculated within the polarizable continuum model are shifted to lower values and furthermore, the spectral width is not accessible. [77] We show that the fragmentation QM:QM approach represents a reliable approach for ionization in the condensed phase. We can observe a gradual transition of VIE from an isolated molecule to the bulk with the solvent shift below 0.5 eV (for largest studied clusters).…”

Solvation energies of ions with ensemble cluster-continuum approach

“…Here, we benefit from previous successful calculations of vertical quantities in the extended cluster-continuum model, such as vertical excitation energy or vertical ionization energy (VIE). [45][46][47]53,54 In our approach, we let the outer sphere described by a dielectric continuum to fully relax. For the inner sphere, we calculate vertical quantities (hVIEi DR , where the subscript DR denotes ''full dielectric relaxation'') for the ensemble of structures sampling (classical) thermal equilibrium.…”

“…Intuitively, the hybrid approach should connect the implicit dielectric model and full quantum calculations. Such hybrid approaches have been shown to largely improve the calculations of acidity constants or redox potentials [37][38][39][40][41][42][43][44] as well as the calculations of ionization energies [45][46][47] in solution.…”