doi:10.1016/S0022-0728(97)00622-0 
Copyright © 1998 Elsevier Science S.A. All rights reserved
Nonlocal nonlinear static dielectric response of polar liquids
Alexei A. Kornyshev1 and Godehard Sutmann*
Institut für Energieverfahrenstechnik, Forschungszentrum Jülich, D-52425 Jülich, Germany
Received 5 August 1997;
revised 6 October 1997.
Available online 2 December 1998.
References and further reading may be available for this article. To view references and further reading you must
purchase this article.
Abstract
A linear, phenomenological theory of the nonlocal dielectric response is extended to the non-linear case. For small external electric fields, we give solutions within a perturbation approach. Results, obtained by molecular dynamics computer simulations for the non-linear response of water are in very good agreement with the theory predictions. The results are applied to the calculation of the electrostatic potential of ions in solution. For the electric field strengths, for which the perturbation theory is still applicable, there are only minor differences with respect to the linear case. A fitting procedure to the simulation data, which covers a wider range of electric fields shows, however, that at larger fields the non-linear effects may change the results considerably, relative to those obtained on the basis of the linear response approximation. We discuss a generalization of the nonlocal electrostatic approach to the calculation of solvation energies, which takes into account non-linear effects.
Author Keywords: Nonlocal dielectric response; Polar liquids; Solvation energies
Index Terms: Water; Dielectric properties of liquids; Electric field effects; Electrostatics; Molecular dynamics; Approximation theory; Perturbation techniques; Computer simulation; Nonlocal dielectric response; Polar liquids; Solvation energy
Fig. 1. Comparison of the calculated values ci with the harmonic series (ci(1)), the logarithmic type (ci(2) with ã=1, =20) and the exponential type (ci(3) with ã=14.3, =0.47) approximation. From this graphical representation, convergence of the calculated ci, and, consequently, convergence of the expansion of P, Eq. 12, is evident.
Fig. 2. Comparison of the mean-field theory result for χ(k, E0) and the computer simulation results for a parameter σ=5×10−4 Å3/eV.
Fig. 3. Comparison between the computer simulation results for the ground wave response function, χ(k, E0) and predictions of the closed form expression for the field dependent response function, Eq. 24. The reduction of the maximum in χ(k, E0) with increasing field strength is parametrized via the field dependent coupling parameter L(E0) (shown in the inset) in Eq. 24.
Fig. 4. The charge density form factors of the BS and the SBS models, compared for radii a =1 Å and a=1.5 Å. The magnitude of ρ(k) at the maximum position of the response function, χ(k) varies with radius. This gives rise to different overlaps between ρ(k) and χ(k) in the corresponding integrals.
Fig. 5. Screening functions calculated with the help of the linear response approximation and with the non-linear response function based on the analytical expression of the perturbation approach, applied for a field of E0≈0.1 V/Å and a parameter σ=5×10−4 Å3/eV. Compared are results for BS and SBS models of radii a=1.5 Å and a=1.5 Å. For clarity, the results for the different radii are shifted with respect to each other. Left axis refers to the 1.5 Å ion, right axis corresponds to the 1 Å ion.
Fig. 6. Screening functions for the BS and SBS models calculated on the basis of the linear response approximation and on the quasi-linear approximation, Eq. 28, which takes into account the distance dependence of the ionic field strength. We also show the effect of a smearing of the ionic charge-distribution.
Fig. 7. The effective response function , Eq. 34, which takes into account a variation of the field strength with distance from the ion. reaches the linear response function at a distance r≈15 Å from the ion.
Fig. 8. Electrostatic parts of the hydration Gibbs energy for singly charged ions. The results from the non-linear calculation (solid line), based on Eq. 24, are compared to (i) experimental data (▪ anions, • cations) [36], (ii) linear response approximation (L=const in Eq. 24) (dashed line), and (iii) linear response calculation using a Lorentzian type response function with λ=3 Å(dotted line) and the dispersionless limit, i.e. Born equation [37] (dash-dotted line). In the inset we show the effect of smearing the external charge distribution (SBS model) on the nonlinear result.
Fig. 9. Modified from factors of the SBS model due to the cut-out-approximation. The modified form factor is compared to the native ρ(k) of the SBS and BS models. The inset shows the real space analogue of the cut-out modified form factor.
Table 1. The parameters ci as a function of the iteration step i of the perturbation series
Abstract
Purchase PDF (338 K)
E-mail Article
Add to my Quick Links
Cited By in Scopus (9)
0.09–0.10 eV. The second reason for deviation of solvation energy from the simple picture of continuum electrostatics lies in the preferable orientation of water molecules with H atoms towards the neutral solute creating a positive intraphase potential. The determination of this potential based on experimental data has been done. Its value for ferrocene in water is estimated as 
Purchase PDF (206 K)
