Structural and Temperature Behavior of Metallic Clusters

In this section the results obtained from AIMD-B-LYP simulations by energizing three isomers of Li9 clusters will be analyzed [39]. For this purpose three types of quantities will be used. One of them is the root-mean-square (RMS) bond-length fluctuation 8 [25], which is calculated at the end of trajectories. A sharp increase of the 8 value is known as the Lindemann criterion for bulk melting, while in the context of finite-size clusters it can be taken as an indication of transition from solid-like to liquid-like state. We find it particularly instructive to analyze the trajectories in terms of atomic equivalence indexes , 

Additional information about the dynamical behavior of a cluster associated with a local structure can be obtained from the power spectrum defined as 

is the number of time origins t j to be averaged over the trajectory. 

In contrast, small values of 8 are characteristic of the C2v and Cbv structures at low energies indicating solid-like behavior and the abrupt change for small increase in energy 

In the range of T 200-500 K the values of S for simulations initialized from configurations related to the isomers C2v and Csv lie above the (almost constant) S values obtained form trajectories initialized by distorting the D4d form. The details may change in longer simulations. 

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The first problem to address is that of the experimental and theoretical tools . Single-crystal X-ray crystallography has, of course, been the method of choice for the determination of the solid-state structures of transition metal clusters. Their structural variability, complexity, and even, at times, unpredictability preceded, in terms of experimental challenge, that of large biomolecules and proteins. New scientific challenges such as, on the one hand, the advent of area detector techniques and powerful X-ray radiation sources and, on the other hand, the use of variable temperature techniques, combined with spectroscopic solid-state methods enables in depth investigation of the temperature-dependence of solid-state molecular and crystal structures and the study of their phase transitional behavior. 

In Section 2.3 the structural and optical properties of neutral and cationic Na clusters at r = 0 K as functions of size are presented and compared with experimental data recorded at low temperature. The temperature-dependent line-broadening will be illustrated by the example of Na9, since in this case a comparison with experimental data at different temperatures is particularly instructive. In Section 2.4 the results of ab initio molecular dynamics (AIMD) studies on Li9 will serve to show different temperature behavior of distinct types of structures as well as their isomerization mechanisms. The study of possible metal-insulator transitions and segregation into metallic and ionic parts in finite systems carried out on prototypes of nonstoichiometric alkali halide and alkali hydride clusters with single and multiple excess electrons is presented in Section 2.5. A comparison of structural and optical characteristics of Na F and lAnUm (n > m) series allows us to illustrate the influence of different bonding properties. 

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