Zero-Point Method

Kinetic parameters can also be obtained by using the zero-point method as described earlier.40 The advantage of this method is that the values of a and k° can be deduced independent of the determination of values of the double-layer capacitance, electrode impedance, and potential difference across the electrode/solution 

In order to apply the zero-point method, it is necessary to know the value of the frequency at which the rectification voltage tends to zero. The experimental determination of the zero-point frequency has some practical difficulties, because over a small frequency range, the rectification signal is indistinguishable. Hence, the zero-point frequencies have been determined by extrapolating plots of EJ V versus w 1/2 for those redox concentration ratios which intercept the abscissa (i.e., when AE = 0). 

The kinetic parameters can also be obtained using the values of a) corresponding to zero-point frequencies (o , ol9 and o 2, i.e., the frequencies at the respective concentrations). On substituting these values in Eq. (12) and Eqs. (a) and (b) of Appendix A, the expressions reduce to39 

For simplification, the second term on the right-hand side in each of the above three equations may be taken as approximately equal. On subtracting Eq. (17) from Eq. (16) and Eq. (18) from Eq. (16), one obtains 

Let the values of cj 1/2 at the zero-point frequencies be (o 1/29 q)i1/29 and co21/2 at three oxidant/reductant ratios. Referring to Eqs. (f), (g), and (h) in Appendix A and substituting AEoo = 0, the expressions obtained are39 

---

The present chapter will cover detailed studies of kinetic parameters of several reversible, quasi-reversible, and irreversible reactions accompanied by either single-electron charge transfer or multiple-electrons charge transfer. To evaluate the kinetic parameters for each step of electron charge transfer in any multistep reaction, the suitably developed and modified theory of faradaic rectification will be discussed. The results reported relate to the reactions at redox couple/metal, metal ion/metal, and metal ion/mercury interfaces in the audio and higher frequency ranges. The zero-point method has also been applied to some multiple-electron charge transfer reactions and, wheresoever possible, these results have been incorporated. Other related methods and applications will also be treated. 

Redox couple Supporting electrolyte Concentration of redox couple (oxid red) D0 x 106 (cm2/s) a (meas.) k°a (cm/s) Zero-point method ... 

However, the rate constant determined by the zero-point method is 0.04 cm/s in HC1 and H2S04 media and in HN03 it is... 

The AEco/V2a versus a) 1/2 plots in 1.0 N NaCi04 are shown in Fig. 15 and the kinetic parameters obtained from extrapolation of these plots and using the zero-point method are given in Table 4. It may be pointed out that when C°R is kept constant and C0o is varied, the value of C°Rl is obtained from Eq. (e) of Appendix A, that of ki from Eq. (c) of Appendix A, and that of k from Eq. (12). For determining the value of the two rate constants by the zero-point method, the theoretical formulations for multiple-electron charge transfer have suitably been modified, and corresponding expressions for k2, k , and C°Rl have been deduced from Eqs. (16), (19), and (21). 

The rate constants k°x and k determined by the zero-point method are generally 10-1 to 10 2 times lower than those obtained by extrapolation techniques. The influence of different electrolytes... 

Historically, the first and most important capacitance method is the vibrating capacitor approach implemented by Lord Kelvin in 1897. In this technique (now called the Kelvin probe), the reference plate moves relative to the sample surface at some constant frequency and tlie capacitance changes as tlie interelectrode separation changes. An AC current thus flows in the external circuit. Upon reduction of the electric field to zero, the AC current is also reduced to zero. Originally, Kelvin detected the zero point manually using his quadrant electrometer. Nowadays, there are many elegant and sensitive versions of this technique. A piezoceramic foil can be used to vibrate the reference plate. To minimize noise and maximize sensitivity, a phase-locked... 

The second, third, and fourth corrections to [MPd/b-Jl lG(d,p)] are analogous to A (- -). The zero point energy has been discussed in detail (scale factor 0.8929 see Scott and Radom, 1996), leaving only HLC, called the higher level correction, a purely empirical correction added to make up for the practical necessity of basis set and Cl truncation. In effect, thermodynamic variables are calculated by methods described immediately below and HLC is adjusted to give the best fit to a selected group of experimental results presumed to be reliable. 

Many semiempirical methods compute energies as heats of formation. The researcher should not add zero-point corrections to these energies because the thermodynamic corrections are implicit in the parameterization. 

The worked out soi ption-photometric method of NIS determination calls preliminary sorption concentration of NIS microamounts from aqueous solutions on silica L5/40. The concentrate obtained is put in a solution with precise concentration of bromthymol-blue (BTB) anionic dye and BaCl, excess. As a result the ionic associate 1 1 is formed and is kept comparatively strongly on a surface. The BTB excess remains in an aqueous phase and it is easy to determinate it photometrically. The linear dependence of optical density of BTB solutions after soi ption on NIS concentration in an interval ITO - 2,5T0 M is observed. The indirect way of the given method is caused by the fact the calibration plot does not come from a zero point of coordinates, and NIS zero concentration corresponds to initial BTB concentration in a solution. 

Frequencies computed with methods other than Hartree-Fock are also scaled to similarly eliminate known systematic errors in calculated frequencies. The followng table lists the recommended scale factors for frequencies and for zero-point energies and for use in computing thermal energy corrections (the latter two items are discussed later in this chapter), for several important calculation types ... 

Predict the zero point or thermal energy by running a frequency job at the optimized geometry, using the same method and basis set. (Note that these two steps maybe run via a single Gaussian job via the Opt Freq keyword.)... 

Selecting Methods (or Zero-Point and Thermal Energies... 

CBS-4 is the less expensive of these two methods. It begins with a FlF/3-21G(d) geometry optimization the zero-point energy is computed at the same level. It then uses a large basis set SCF calculation as a base energy, and an MP2/6-31+Gt calculation with a CBS extrapolation to correct the energy through second order. A... 

Compute the frequencies at each optimized geometry using the same method to obtain the zero point energy corrections. 

Cs NMR results for Cs on the surfaces of illite, kaolinite, boehmite and silica gel (Figure 3) show that for this large, low charge cation the surface behavior is quite similar to the interlayer behavior. They also illustrate the capabilities of NMR methods to probe surface species and the effects of RH on the structural environments and dynamical behavior of the Cs. The samples were prepared by immersing 0.5 gm of powdered solid in 50 ml of O.IM CsCl solution at 2 5°C for 5 days. Final pHs were between 4.60 and 7.77, greater than the zero point of charge, except for boehmite, which has a ZPC... 

Conventional Partial Molal Entropy of (H30)+ and (OH)-. Let us now consider the partial molal entropy for the (1I30)+ ion and the (OH)- ion. If we wish to add an (HsO)+ ion to water, this may be done in two steps we first add an H2O molecule to the liquid, and then add a proton to this molecule. The entropy of liquid water at 25°C is 16.75 cal/deg/mole. This value may be obtained (1) from the low temperature calorimetric data of Giauque and Stout,1 combined with the zero point entropy predicted by Pauling, or (2) from the spectroscopic entropy of steam loss the entropy of vaporization. 2 Values obtained by the two methods agree within 0.01 cal/deg. 

The quantum chemical methods introduced in part 2.2 calculate only individual molecules at the temperature of 0 K. The energies obtained in these cases represent the energies of the molecules directly in the minimum of the potential energy, i.e. the zero point energy which is evident at 0 K and the thermic energy of an ensemble of... 

Table III displays VEDEs obtained with the Brueckner-reference methods discussed in Section 5.2 and augmented, correlation-consistent, triple- basis sets [41]. AEDEs include zero-point energy differences and relaxation energies pertaining to geometrical relaxation on the neutral s potential energy surface. The average absolute error with respect to experiment is 0.05 eV [26].

---