Dipole corrections

The effect of the Axilrod-Teller term (also known as the triple-dipole correction) is to make the interaction energy more negative when three molecules are linear but to weaken it when the molecules form an equilateral triangle. This is because the linear arrangement enhances the correlations of the motions of the electrons, whereas the equilateral arrangement reduces it. 

Dipole corrections to DFT calculations for surface calculations are discussed in J. Neugebauer and M. Scheffler, Phys. Rev. B 46 (1992), 16067. 

Linear dynamic relationship between an ion peak intensity (or ion counts) of a polar lipid species and the concentration of the compound is very broad, depending on the instrument sensitivity at the low end and the aggregation concentration at the high end (see Chapter 15). It should be emphasized that for the lipids without large dipoles, correction factors or calibration curves for each individual molecular species have to be pre-determined. Alternatively, derivati-zation can be employed to modify the charge properties of these less ionizable lipid classes to enhance ionization (Figure 2.4). 

The dipole strength of an induced electric dipole transition is proportional to the square of the matrix element in the dipole operator and therefore also to the square of the electric field at the lanthanide site. However, in intensity studies, the lanthanide ions are not in a vacuum, but embedded in a dielectric medium. The lanthanide ion in a dielectric medium not only feels the radiation field of the incident light, but also the field from the dipoles in the medium outside a spherical surface. The total field consisting of the electric field E of the incident light (electric field in the vacuum), plus the electric field of the dipoles is called the effective field eff> i e. the field effective in inducing the electric dipole transition. The square of the matrix element in the electric dipole operator has to be multiplied by a factor E fflEf. In a first approximation, ( efr/ = ( + 2) /9. The factor (n + 2fl9 is the Lorentz local field correction and accounts for dipole-dipole corrections. 

Without a local electric field considered, the adsorption energy is 0.34 eV at a potential of 0.75 Vshe [eqn (3.15)]. The applied electric field causes a 0.10 eV energy difference at 0.75 Vshe, which is very close to the estimation (+0.11 eV) using a dipole-field interaction only. Clearly, the first order dipole correction was sufficient, with higher order corrections slightly lessening the field effect by... 

Figure 3.8 The adsorption energy of sulfate anion over Pt(lll) at (a) vacuum and (b) partially solvated interfaces. The diamond ( ) with solid line represents results from the linear free energy model (Model 2a. 1), the square with dotted line represents ( ) the linear free energy model with dipole correction (Model 2a.2), and the triangle (a) with dashed line represents the electric field model (Model 2a.3).

The fully solvated model cannot easily be used with the dipole-correction or applied field methods discussed above. The absence of a vacuum layer in the fully solvated model makes dipole moment evaluation and field application impossible within the periodic model. Hybrid approaches, in which the dipole is measured in an unsolvated model and solvation approximated in the fully solvated model, might be considered. However, the advantage of the fully solvated model is its integration within the direct charging of the electrochemical interface. 

This method may be improved upon by including similar advances in the model system as those presented above for reaction energy calculations. The inclusion of explicit water molecules can better approximate both the e2 and Go values in eqn (3.51). Dipole corrections and applied electric fields will provide corrections to the value of fi. Testing of the sensitivity and convergence of activation barriers calculated with this method, along with the application of this method to a variety of reactions, is a current research area in our group. 

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