Hydrogen waves

Figure 5.6 shows a typical CV of a thin Pt film electrode in a 0.1 M HCIO4 solution. The hydrogen waves in the potential range between —200 and about 50 mV were observed and surface oxidation and reduction peaks were observed in the positive potential region (>600 mV). This result confirmed that the conductivity of the Pt thin film was good enough to be used as an electrode. 

The complex catalytic polarographic hydrogen wave of the Irlv cystine complex (31) has been investigated in 1.2 M HC1.26,27... 

Analysis of total zinc by anodic stripping voltammetry is problematic because of interference by the hydrogen wave in acidified samples, and due to the inability to detect organically complexed zinc at natural pH values near 8 [ 185]. An improved understanding of zinc in marine systems now requires rapid, sensitive analytical methods that are less prone to contamination, and that can be performed at sea [624],... 

The Self-Consistent-Field (SCF) procedure can be initiated with hydrogenic wave functions and Thomas-Fermi potentials. It leads to a set of solutions w(fj), each with k nodes between 0 and oo, with zero nodes for the lowest energy and increasing by one for each higher energy level. The quantum number n can now be defined asn = / + l + A to give rise to Is, 2s, 2p, etc. orbitals. 

As required by (36), the variational parameter k is calculated to vary between k = 2 at R = 0 and k = 1 at R > 5ao- The parameter k is routinely interpreted as either a screening constant or an effective nuclear charge, as if it had real physical meaning. In fact, it is no more than a mathematical artefact, deliberately introduced to remedy the inadequacy of hydrogenic wave functions as descriptors of electrons in molecular environments. No such parameter occurs within the Burrau [84] scheme. 

The Hamiltonian for two electrons in the field of two fixed protons is given by (39). For large values of rab the system reasonably corresponds to two H atoms. The wave functions of the degenerate system are ipi = ui5a(l)ui 6(2) and ip2 = UiSt(l)u1Sa(2), where ul5o(l) is the hydrogenic wave function for electron 1 about nucleus A, etc. For smaller values of rab a linear combination of the two product functions is a reasonable variational trial function, i.e. 1p = 1pl +... 

Fig. 5. Stopping cross section for hydrogen in argon. Calculated from binary theory with shell correction based on Clementi [58] and hydrogenic wave functions. Experimental data from numerous laboratories compiled in Ref. [6].

The polarographic behavior of all the bipyridines with the exception of the 3,4 -isomer has been investigated in aqueous solution. The difficulty of reduction increases in the order 4,4 -, 2,4 -, 2,3 -, 2,2 -, and 3,3 -bipyr-idine. Most of the work has been concerned with 2,2 - and 4,4 -bipyridines. Both isomers are reduced in aqueous solution by a two-electron process, sometimes observed as two separate one-electron steps, which is pH dependent because of the formation of a dihydro derivative. Complications in interpretation of the waves due to prewaves, catalytic hydrogen waves, wave maxima, and adsorption phenomena have frequently been observed. ° Polarography and cyclic voltammetry investigations have been extended to the study of 2,2 - and 4,4 -bipyridines... 

The polarographic behavior of 1,10-phenanthroline,150-152 1,7-phenanthroline,153 and 4,7-phenanthroline154 has been studied in aqueous solution, but the interpretation of the reduction waves is not always certain because of complications due to adsorption and catalytic hydrogen waves. Some substituted 1,10-phenanthrolines have also been investigated in this way.151,155 Two clear reduction waves were obtained with 1,10-phenanthroline in dimethylformamide,156 however, and an attempt was made to correlate the reduction potentials with the energy levels of the molecule. Other studies in nonaqueous solvents with 1,10-, 1,7-, and 4,7-phenanthrolines also gave distinct waves.151,157... 

The classical dc polarography of vitamins A, B, B2, B6, BI2, and C, nicotinamide, tocopherols, and naphthoquinones has been reviewed [55]. Other studies have examined in detail the cyclic voltammetry of vitamin B12 employing rapid-scan voltammetry at the DME [90] and the HMDE [91]. Vitamin B12 is complexed with trivalent cobalt ion at the heterocyclic nitrogen atoms. As a result of the complexation, a catalytic hydrogen wave is formed for the compound. In addition to the catalytic wave, a wave corresponding to the reduction of the trivalent cobalt to the monovalent state is observed. 

Although the properties of the/and g functions are outlined in chapter 2, it is worth summarizing their properties here.8 The / and g coulomb functions are termed regular and irregular since asr— 0,/< rt+ and g oc r (. Due to the r = 0 behavior of the g function, in H only the/wave exists. As r — for Wt > 0 the/ and g waves are sine and cosine functions, and if Wt > 0, jiv simply specifies the phase of the wavefunction relative to the hydrogenic/wave. If Wt < 0 the/and g waves both have exponentially increasing and decreasing parts, and, as we have seen in Chapter 2, only if... 

Interestingly, a catalytic hydrogen wave is obtained from bis(dithiocarbamato)zinc(II) at a carbon (paste or graphite) electrode although not at mercury.396 This is probably because the zero valent complex is unstable with respect to loss of zinc metal to form an amalgam, whilst it is sufficiently stable on carbon to promote catalysis.396... 

Further evidence that cobalt metal is not responsible for the catalytic hydrogen waves comes from the observation that the higher the stability of the complex formed between the sulfur-containing ligand and Co2+, the more pronounced is the catalytic wave.378 This is confirmed since... 

A common alternative is to synthesize approximate state functions by linear combination of algebraic forms that resemble hydrogenic wave functions. Another strategy is to solve one-particle problems on assuming model potentials parametrically related to molecular size. This approach, known as free-electron simulation, is widely used in solid-state and semiconductor physics. It is the quantum-mechanical extension of the classic (1900) Drude model that pictures a metal as a regular array of cations, immersed in a sea of electrons. Another way to deal with problems of chemical interaction is to describe them as quantum effects, presumably too subtle for the ininitiated to ponder. Two prime examples are, the so-called dispersion interaction that explains van der Waals attraction, and Born repulsion, assumed to occur in ionic crystals. Most chemists are in fact sufficiently intimidated by such claims to consider the problem solved, although not understood. 

---