Free energy of a charge distribution in a spheroidal cavity surrounded by concentric dielectric continua

Abstract

sumably, mercaptoethanol selectively blocks Pd surface sites for activating bicarbonate, thus favoring the transfer of conductionband electrons to H2-evolving sites.A comparison of the selectivity factor can be made between the Pd-Ti02 systems and the previously examined p h o t~s y s t e m~~ consisting of the photosensitizer deazariboflavin, dRFI, the electron mediator MV2+, the electron donor oxalate, and the catalyst Pd(@-CD,60 "C) colloids. The best selectivity factor of the PdTi02 systems (SF = 2.3; see Table I) is larger than that of dRFI/MV2+/oxalate/Pd(P-CD,60 "C) (SF = 0.013), indicating that the former exhibits lower selectivity for HC0,-reduction with respect to H 2 evolution than the latter. The basis for this difference in selectivity remains to be established, however.In conclusion, electron transfer from Ti02 to properly prepared catalytic Pd surface sites promotes the reduction of C02/HC0,-to formate. The selectivity exhibited by the Pd-Ti02 particle systems is quite noteworthy in relation to other semiconductorbased systems, which generate a broad distribution of products. Specific sites on the Pd surface favor C02/HCO< reduction over H2 evolution. The experimental results reported here as well as those of others2" suggest that other metals might exhibit selectivity in catalyzing the reduction of CO, to other desirable organic photoproducts.We present a theoretical treatment for the Helmholtz free energy of an arbitrary discrete charge distribution in a central prolate or oblate spheroidal cavity surrounded by two and three concentric dielectric continua of the same symmetry. The electrostatic interaction is accounted for by a multipolar expansion. This model permits us to consider in a simple way nonlinear dielectric effects and the nonsphericity of solute molecules. The results are presented in a suitable form to discuss them in terms of a virtual polarization charge distribution. Also, we give an explicit expression for the contributions coming from the zeroth-order multipole moments for any number of shells.

Origin of Asymmetric Solvation Effects for Ions in Water and Organic Solvents Investigated Using Molecular Dynamics Simulations: The Swain Acity–Basity Scale Revisited

“…Since then, a wealth of modified Born equations have been proposed that involve diverse theoretical justifications (see further below) but often result in expressions involving such asymmetric radius increments − (see also refs − for other types of modified Born equations). In a similar way, numerical continuum-electrostatics calculations − involving solutes of arbitrary geometries and charge distributions, as well as corresponding generalized Born model approximations, − have relied on empirically optimized radii taking asymmetric hydration effects into account either implicitly (i.e., during the radius optimization) or explicitly ,,,− (e.g., by modifying the boundary conditions or making the radii depend on the atom or surface charges).…”

Dielectric continuum methods for quantum chemistry

“…Kirkwood's original result is actually more general, in that it allows a value ε in ≠ 1 inside the cavity, 86 whereas Equation () holds for ε in = 1 and ε out = ε . In the many decades since Kirkwood's original result, analytic formulas have also been derived for multipoles centered in ellipsoidal cavities, 95,101 for off‐center point charges 102 and higher‐order off‐center multipoles, 99 for multipoles in a layered dielectric material, 103,104 and for interactions between multipoles contained in disjoint spheres with a dielectric medium in between 105 . The point‐multipole model has also been generalized to include frequency dependence ε ( ω ), within the Debye relaxation model 106 …”