Correlations Work function

A method that avoids making the HF mistakes in the first place is called quantum Monte Carlo (QMC). There are several types of QMC variational, dilfusion, and Greens function Monte Carlo calculations. These methods work with an explicitly correlated wave function. This is a wave function that has a function of the electron-electron distance (a generalization of the original work by Hylleraas). 

Mainly for considerations of space, it has seemed desirable to limit the framework of the present review to the standard methods for treating correlation effects, namely the method of superposition of configurations, the method with correlated wave functions containing rij and the method using different orbitals for different spins. Historically these methods were developed together as different branches of the same tree, and, as useful tools for actual applications, they can all be traced back to the pioneering work of Hylleraas carried out in 1928-30 in connection with his study of the ground state of the helium atom. 

The three basic methods introduced by Hylleraas in his work on the He series have in modern terminology obtained the following names (a) Superposition of configurations (b) Correlated wave functions (c) Different orbitals for different spins. The first two approaches are developed almost to the full extent, whereas the last method is at least sketched in the 1929 paper. 

Taking up the idea of "correlated wave functions containing r12, James and Coolidge (1933) made a careful study of the H2 problem and, after a great deal of numerical work, they obtained finally an energy value in complete agreement with experience. This was another successful test of the validity of the Schrodinger... 

Measurements [113,368] of interfacial (contact) potentials or calculated values of the relative work functions of reactant and of solid decomposition product under conditions expected to apply during pyrolysis have been correlated with rates of reaction by Zakharov et al. [369]. There are reservations about this approach, however, since the magnitudes of work functions of substances have been shown to vary with structure and particle size especially high values have been reported for amorphous compounds [370,371]. Kabanov [351] estimates that the electrical field in the interfacial zone of contact between reactant and decomposition product may be of the order of 104 106 V cm 1. This is sufficient to bring about decomposition. 

Figure 14. Plot of the potential of zero charge, Ea=0 (from Table 26), against the work function,

Thus far, Ft has never found a definite position in Ea vs. correlations, more for the uncertainty in the reliability of its pzc than for its work function. On the other hand, Pt is a highly heterogeneous metal and the fact that only polycrystalline surfaces have been used in double-layer studies has not helped remove suspicions. According to Frumkin s data,10,14 the pzc ofpc-Pt is around 0.2 V(SHE) (in acidic solution). If this value is introduced into Fig. 14 (the 0 of pc-Pt is around 5.5 eV),22,65 343,856 865,866 the point of Pt would fall far distant from the line of mercurylike metals and near the line of d-metals. 

Figure 11.11. Correlation between the equivalent potentials of the supports defined in Figure 11.10 and of the work function or absolute potential of the supports measured via the Kelvin probe technique in po2 =1 atm at 400°C.22...

The values of electron work function (see Section 9.2.1) have been adduced most often when correlating electrocatalytic activities of given metals. They are situated between 3 and 5 eV. Two points were considered when selecting the electron work function as the parameter of comparison (1) it characterizes the energy of the electrons as basic, independent components of aU electrochemical reactions, and (2) it is closely related to many other parameters of metals. 

It was demonstrated, however, in 1947 by John O M. Bockris that between the exchange current densities of the hydrogen reaction at different metals and the values of the electron work function (into vacuum), a definite correfation does exist. Many workers have confirmed this correlation. An example of this correlation is shown as a plot of log f vs. X° in Fig. 28.2. 

Alloys of Au with Ag, Sn, Ni, Pd, Pt, A1 Qiarge between host and Au atoms from trends of isomer shift and work function data (ESCA) correlated with electronegativity of host elements... 

In electrochemistry it has been shown that for electron emission into an electrolyte there is a correlation between electrode potential E and the work function of the interface according to [31]... 

More than a decade ago, Hamond and Winograd used XPS for the study of UPD Ag and Cu on polycrystalline platinum electrodes [11,12]. This study revealed a clear correlation between the amount of UPD metal on the electrode surface after emersion and in the electrolyte under controlled potential before emersion. Thereby, it was demonstrated that ex situ measurements on electrode surfaces provide relevant information about the electrochemical interface, (see Section 2.7). In view of the importance of UPD for electrocatalysis and metal deposition [132,133], knowledge of the oxidation state of the adatom in terms of chemical shifts, of the influence of the adatom on local work functions and knowledge of the distribution of electronic states in the valence band is highly desirable. The results of XPS and UPS studies on UPD metal layers will be discussed in the following chapter. Finally the poisoning effect of UPD on the H2 evolution reaction will be briefly mentioned. 

Underpotential deposition of heavy metals on H2 evolving electrodes is a well known problem [133], The existence of a direct correlation between H2 evolution activity and metal work function, makes UPD very likely on high work function electrodes like Pt or Ni. Cathode poisoning for H2 evolution is aggravated by UPD for two reasons. First, deposition potentials of UPD metals are shifted to more anodic values (by definition), and second, UPD favors a monolayer by monolayer growth causing a complete coverage of the cathode [100]. Thus H2 evolution may be poisoned by one monolayer of cadmium for example, the reversible bulk deposition potential of which is cathodic to the H2 evolution potential. 

An interesting correlation exists between the work function of a metal and its pzc in a particular solvent. Consider a metal M at the pzc in contact with a solution of an inert, nonadsorbing electrolyte containing a standard platinum/hydrogen reference electrode. We connect a platinum wire (label I) to the metal, and label the platinum reference electrode with II. This setup is very similar to that considered in Section 2.4, but this time the metal-solution interface is not in electronic equilibrium. The derivation is simplified if we assume that the two platinum wires have the same work function, so that their surface potentials are equal. The electrode potential is then ... 

The changes in the dipole potentials are typically small, of the order of a few tenths of a volt, while work functions are of the order of a few volts. If we keep the solvent, and hence 3>ref, fixed and vary the metal, the potential of zero charge will be roughly proportional to the work function of the metal. This is illustrated in Fig. 3.6. A more detailed consideration of the dipole potentials leads to a subdivision into separate correlations for sp, sd, and transition metals [3]. 

Figure 4.10 Correlation between the upd shift 4>Upd and the work function difference for polycrystalline metals A/B denotes the upd of A on B.

Kolb [4] observed an interesting correlation for adsorption on polycrystalline substrates A plot of = 4>sub — 4 ad (in electron volts) between the work functions of the substrate and the adsorbate yields a straight line with a slope of about 1/2 (see Fig. 4.10). Often there are several upd potentials, and in these cases the highest value corresponding to the strongest substrate-... 

Figure 4.11 Correlation between surface energies and work functions of polycristalline sp metals.

The work functions of metals correlate with their surface energies Fig. 4.11 shows this for sp metals. Hence the surface energy of a metal with a high work function is lowered when it is covered with a monolayer of a metal with a lower work function and lower surface energy. 

Macroscopic n-type materials in contact with metals normally develop a Schottky barrier (depletion layer) at the junction of the two materials, which reduces the kinetics of electron injection from semiconductor conduction band to the metal. However, when nanoparticles are significantly smaller than the depletion layer, there is no significant barrier layer within the semiconductor nanoparticle to obstruct electron transfer [62]. An accumulation layer may in fact be created, with a consequent increase in the electron transfer from the nanoparticle to the metal island [63], It is not clear if and what type of electronic barrier exists between semiconductor nanoparticles and metal islands, as well as the role played by the properties of the metal. A direct correlation between the work function of the metal and the photocatalytic activity for the generation of NH3 from azide ions has been made for metallized Ti02 systems [64]. 

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