Mercury correlation energy

Figure 4. Contributions of correlating functions, as well as s, p, and d functions (inset), to the CISD correlation energy of the 5 d state of mercury. The absolute values of the incremental correlation energy lowerings, AEcon are plotted in mEh against the number offunctions in the expansions for spdf... functions. The solid lines are exponential fits.

Figure 6, Basis set errors for the HF energy and CISD correlation energy with the final cc-pVnZ-PP basis sets for the ( , ) S and (O, ) P states of mercury. The open symbols correspond to the HF results (left axis), while the filled symbols refer to the CISD correlation energies (right axis). Note that the correlation energy results are plotted on a log scale.

The one-body terms of the correlation-energy expansion are repulsive for mercury and have nearly no dependence on the lattice parameter. The first term in the expansion to examine closely with respect to the effect of the lattice parameter is therefore the two-body increment. This is shown in Fig. 18 with respect to the Hg Hg distance. Here the potential is actually very flat, and thus the minimum can be shifted noticeably by the use of an... 

What factors determine whether an elemental substance adopts a metallic or a covalent structure From the simple model for metallic bonding, which views a metal as a lattice of cations embedded in a sea of delocalised electrons, it may be supposed that atoms having low ionisation potentials are most likely to become assembled as metallic substances. This correlation is far from perfect, however. Thus the first and second ionisation energies of mercury are comparable with those of sulphur, but the alchemists viewed elemental mercury and sulphur as the quintessential metal and nonmetal respectively. A closely-related correlation can be found with electronegativity. 

In summary, ionisation potentials, dissociation and cohesive energies for mercury clusters have been determined. The mass spectrum of negatively charged Hg clusters is reported. The influence of the transition from van der Waals (n < 13), to covalent (30 < n < 70) to metallic bonding (n > 100) is discussed. A cluster is defined to be metallic , if the ionisation potential behaves like that calculated for a metal sphere. The difference between the measured ionisation potential and that expected for a metallic cluster vanishes rather suddenly around n 100 Hg atoms per cluster. Two possible interpretations are discussed, a rapid decrease of the nearest-neighbour distance and/or the analogue of a Mott transition in a finite system. Electronic correlation effects are strong they make the experimentally observed transitions van der Waals/covalent and covalent/metallic more pronounced than calculated in an independent electron theory. 

This experiment allowed the direct exploration of the radial part of the excited-state electron-transfer surface, here at the transition-state level and also partially in the exit valley. It has also provided further evidence of the angular dependence of the electron transfer which is addressed in the following example. This example does not take into account the correlations with excited ionic surfaces accessed by 6s electron transfer because these surfaces lie at too high energy in the case of mercury. This type of electron transfer will be described in the following section. 

Deb and Yoffe [66] compared the photochemical decomposition of mercury(I) azide with that of triphenylmethyl azide. The first step in the decomposition is suggested to be the fission of the longer N-N bond of the azide group. Results were compared with data for reactions of inorganic azides and it was concluded that there is no clear distinction between the energy requirements of the two classes of azides, covalent and ionic. Deb [67] has determined the electron energy levels of several azides and correlated the band structures with observed stabilities. 

Figure 3.1 Size dependence of cohesive energies per atom (CE/n) of mercury clusters Hgn from calculations using a large-core EC-PP and CPP for Hg. Valence correlation is accounted for either within die hybrid model approach (HM) by a pair-potential adjusted for Hg2 or by pure-diffusion quantum Monte Carlo (PDMC) calculations (Wang etal 2000).

The density profiles obtained from atomic models (platinum [49] and rigid mercury surfaces [40]), where water-metal interactions are described by pairwise additive atomatom interaction potentials, are similar in shape. Height and width are correlated with the depth and force constant of the interaction potential. A similar correlation between peak height and interaction energy holds for water near a variety of different smooth model surfaces (see Ref. 139 and references therein). 

---