Single atom chemistry, validity

In the literature, there sometimes occur inaccurate statements about the validity of Stirling s approximation in connection with the validity of single atom chemistry. 

Since the SHE chemistry is correlated with one-atom-at-a-time chemistry, one may ask if it is meaningful to carry out experiments with a single atom. From a theoretical point of view, as it was demonstrated above, for a 1 1 stoichiometry reaction the mass action law and the kinetics laws are valid. However, as there is no macrocomponent consumption, such reaction appears as of pseudo first order. Note that reactions with a 1 1 stoichiometry include all reactions between the microcomponent and a single macrocomponent. This concept can also be extended to stepwise reactions such as successive formation of metal complexes (hydrolysis, halide complexation) for example ... 

Not only must we consider whether the concepts of thermodynamics and kinetics used in classical chemistry are still valid at such low concentrations, but we must consider whether the chemical information deduced from experiments with a single atom make sense. And how many atoms must be identified to be statistically significant for discovery for confirmation or conversely, even for nonconfirmation of a discovery In many previously reported experiments, positive identification of the element being studied was not established. Without such identification the experiments are meaningless. This is especially difficult (if not impossible) in case of the detection of only spontaneous fission (SF), which effectively destroys information about the fissioning nuclide except for its half-Ufe. 

The use of CO as a chemical probe of the nature of the molecular interactions with the surface sites of metallic catalysts [6] was the first clear experimental example of the transposition to surface science and in particular to chemisorption of the concepts of coordination chemistry [1, 2, 5], In fact the Chatt-Duncanson model [7] of coordination of CO, olefins, etc. to transition metals appeared to be valid also for the interactions of such probes on metal surfaces. It could not fit with the physical approach to the surface states based on solid state band gap theory [8], which was popular at the end of 1950, but at least it was a simple model for the evidence of a localized process of chemical adsorption of molecules such as olefins, CO, H, olefins, dienes, aromatics, and so on to single metal atoms on the surfaces of metals or metal oxides [5]. 

Theoretical probability identifies the possible outcomes of a statistical experiment, and uses theoretical arguments to predict the probability of each. Many applications in chemistry take this form. In atomic and molecular structure problems, the general principles of quantum mechanics predict the probability functions. In other cases the theoretical predictions are based on assumptions about the chemical or physical behavior of a system. In all cases, the validity of these predictions must be tested by comparison with laboratory measurements of the behavior of the same random variable. A full determination of experimental probability, and the mean values that come from it, must be obtained and compared with the theoretical predictions. A theoretical prediction of probability can never be tested or interpreted with a single measurement. A large number of repeated measurements is necessary to reveal the true statistical behavior. 

The fact that an electronic state must be antisymmetric under interchange of any two electrons is an expression of the Pauli Principle. It implies also that no two electrons are allowed to be in exactly the same 1-electron state for if we replace V b by a second ipA the antisymmetric combination disappears In a many-electron atom, say, the state of lowest energy (the ground state ) must have electrons spread over different 1-electron states Vu, b> , not more than one in each, even if the energy of the A state is lower than all the others. Were it not for the antisymmetry restriction, the ground state would be the one in which all electrons crowded into i a- atoms would show no shell structure and would collapse into dense and compact clouds of electrons, in the immediate vicinity of their nuclei. It can be argued that the Pauli Principle is perhaps the most important single principle in the whole of physics were it not valid there would be no atoms, no chemistry, no life, no universe as we know it. 

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