Clusters potentials

The orbitals of the d states in clusters of the 3d, 4d, and 5d transition elements (or in the bulk metals) are fairly localized on the atoms as compared with the sp valence states of comparable energy. Consequently, the d states are not much perturbed by the cluster potential, and the d orbitals of one atom do not strongly overlap with the d orbitals of other atoms. Intraatomic d-d correlations tend to give a fixed integral number of d electrons in each atomic d-shell. However, the small interatomic d-d overlap terms and s-d hybridization induce intraatomic charge fluctuations in each d shell. In fact, a d orbital contribution to the conductivity of the metals and to the low temperature electronic specific heat is obtained only by starting with an extended description of the d electrons.7... 

The lattice potential V (or the cluster potential) is written as a sum of atomic potentials V, centered on the lattice sites i. 

The value of the critical nuclearity allowing the transfer from the monitor depends on the redox potential of this selected donor S . The induction time and the donor decay rate both depend on the initial concentrations of metal atoms and of the donor [31,62]. The critical nuclearity corresponding to the potential threshold imposed by the donor and the transfer rate constant value, which is supposed to be independent of n, are derived from the fitting between the kinetics of the experimental donor decay rates under various conditions and numerical simulations through adjusted parameters (Fig. 5) [54]. By changing the reference potential in a series of redox monitors, the dependence of the silver cluster potential on the nuclearity was obtained (Fig. 6 and Table 5) [26,63]. 

One of the important applications of mono- and multimetallic clusters is to be used as catalysts [186]. Their catalytic properties depend on the nature of metal atoms accessible to the reactants at the surface. The possible control through the radiolytic synthesis of the alloying of various metals, all present at the surface, is therefore particularly important for the catalysis of multistep reactions. The role of the size is twofold. It governs the kinetics by the number of active sites, which increase with the specific area. However, the most crucial role is played by the cluster potential, which depends on the nuclearity and controls the thermodynamics, possibly with a threshold. For example, in the catalysis of electron transfer (Fig. 14), the cluster is able to efficiently relay electrons from a donor to an acceptor, provided the potential value is intermediate between those of the reactants [49]. Below or above these two thresholds, the transfer to or from the cluster, respectively, is thermodynamically inhibited and the cluster is unable to act as a relay. The optimum range is adjustable by the size [63]. 

In summary, the dynamics of the electronic decay of inner-shell vacancies in a charged environment, such as created by interaction of a cluster with a high intensity FEL radiation, can be qualitatively different from the one induced by a low-intensity source. If the emitted electrons are slow enough to be trapped by the neighboring charges, the familiar exponential decay will be suppressed by quantum beats between the initial state and the quasi-continuum of discrete final states. Physically, the predicted oscillations correspond to creation of the initial vacancy due to the reflections of the emitted electron by the charged cluster potential and the subsequent inverse Auger transition. 

Sinnokrot, M.O. and Sherrill C.D., Highly Accurate Coupled Cluster Potential Energy Curves for the Benzene Dimer Sandwich, T-Shaped, and Parallel-Displaced Configurations. J. Phys. Chem. 

Sinnokrot, M. O. Sherrill, C. D. Highly accurate coupled cluster potential energy curves for the benzene dimer sandwich, T-shaped, and parallel-displaced configurations, 7. Phys. Chem. A 2004,108, 10200-10207. 

For metal hydride clusters, much less is known about electronic and geometrical size effects, except for very small clusters that can be relatively easily traced with computational methods. Results on other ionic compounds, such as ZnS clusters, indicate less well defined size effects, and only for small cluster sizes [11]. As the size dependence will be clearly different than for metal clusters, potentially there is a large influence of size on the stability differences between small hydride and the corresponding metal clusters. However, the practical impact of these effects is probably limited, as in the bulk experimental preparation of light metal (hydride) clusters, generally, polydisperse samples are obtained, and hence pronounced effects of... 

By changing the reference potential in a series of redox monitors, it is then possible to determine the dependence of the cluster potential on the nuclearity. The general trend of increasing redox potential with nuclearity is the same for all metals in solution as it is illustrated in Fig. 2 in the case of E°(AgVAg,) q. However, in gas phase, the variation of the ionization potential IV(Ag ) exhibits the opposite trend versus the nuclearity n. Indeed, since the Fermi potential of the normal hydrogen electrode (NHE) in water is 4.5 eV, and since the solvation free energy of Ag decreases with size as deduced from the Born model, one can explain the two opposite variations with size of F°(Ag /AgJ q and IP (AgJ as illustrated in Fig. 2. 

K. B. Ghose, P. Piecuch, and L. Adamovicz,/. Chem. Phys., 103, 9331 (1995). Improved Computational Strategy for the State-Selective Coupled-Cluster Theory with Semi-Internal Triexcited Clusters Potential Energy Surface of the HF Molecule. 

The cluster potentials were obtained by superimposing the self-consistent Xa charge densities for the individual Pt... 

Physics and Applications of Semiconductor Electrodes Covered with Metal Clusters Potential-Modulated Reflectance Spectroscopy Studies of the Electronic Transitions of Chemisorbed Carbon Monoxide... 

Figure 1. Principle of the determination of short-lived cluster redox potential by kinetics methods. The reference electron donor, S of a given potential and the metal atoms are generated by a single puke. During cluster coalescence, the redox potential of the couple E°(M -Mn) progressively increases, so that an effective transfer is observed after a critical time when the cluster potential becomes higher than that of the reference, constituting a threshold. Repeatedly, a new adsorption of excess cations, M, onto the reduced cluster, (n xkch (dlows another electron transfer from S with incrementation of nuclearity. The subcritical clusters Mn(n

Few reports of the temperature dependence of 4Fe-4S cluster potentials have appeared in the literature. With the exception of a small number of c-type cytochromes, the enthalpic component is typically found to be negative for the available data on heme proteins and 4Fe-4S proteins, reflecting favorable bonding changes on reduction. For HiPIPs, the A// values typically lie within 4 to 5 kcal moP of each other (Table VII), which is consistent with their similar values and the importance of the enthalpy term in defining the free en-... 

On the basis of structural and electronic similarities, the clusters [Fe4S4(SR)4] serve as close representations of protein sites with the iso-electronic [4Fe-4S] core. Because the proteins function as electron carriers (where their function is known), the redox chemistry of synthetic clusters has been a matter of considerable interest. As seen in Fig. 3, the analogue electron-transfer series encompasses four core oxidation levels, three of which have been detected in proteins. Analogues corresponding to these three levels have been isolated and characterized in very considerable detail. The [4Fe-4S] + + or Fdox/red redox couple is one of the more pervasive in biology. Note that the native [4Fe-4S] state has been proven only in the HP proteins, which should be considered as a special class of ferredoxins. Synthetic cluster potentials, which are strongly dependent on the R substituent, have been found to be —0.2-0.6 V more negative than the E o values for Fd x,ed in aqueous solution (76, 77). 

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