The distribution of money is analysed in connection with the Boltzmann distribution of energy in the degenerate states of molecules. Plots of the population density of income distribution for various countries are well reproduced by a Gamma function, confirming the validity of the statistical distribution at equilibrium. The equilibrium state is reached through pair wise money transference processes, independently of the shape of the initial distribution and also of the detailed nature of the money transactions between the economic agents.Comment: 15 pages plus 1 table plus 3 figure

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The structure and reactivity of p-CrOH(NH(3))(2) and p-CrOH(H(2)O)(NH(3)) complexes were studied using mass-resolved one-colour resonance-enhanced multi-photon ionization and laser-induced fluorescence (LIF) spectroscopy together with DFT calculations. At the excitation energy of this work, the S(1) state of p-CrOH(NH(3))(2) shows a sub-nanosecond lifetime, as determined by time-resolved LIF spectra, as a consequence of a hydrogen transfer process that results in NH(4)(NH(3)) as a reaction product. Substitution of NH(3) by H(2)O closes the reaction channel as evidenced by the absence of excited-state hydrogen transfer (ESHT) reaction products, (H(3)O(NH(3)) or NH(4)(H(2)O)) and results in a dramatic effect on the S(1) lifetime of the p-CrOH(H(2)O)(NH(3)) complex which rises to (12 +/- 2) ns. According to density functional theory calculations, the most stable isomer of the p-CrOH(H(2)O)(NH(3)) complex is a cyclic structure, in which H(2)O acts as the H acceptor of the phenolic OH group (c-OH-H(2)O-NH(3)). However, the ESHT process is energetically disallowed upon electronic excitation.

An experimental and theoretical study of the photoionization energies (IE's) of Ba(H(2)O)(n) clusters containing up to n = 4 water molecules has been performed. The clusters were generated by a pick-up source combining laser vaporization with pulsed supersonic expansion, and then photoionized by radiation of 272.5-340 nm. The experimentally determined IE(e)'s for n = 1 to 4 are 4.56 ± 0.05, 4.26 ± 0.05, 3.90 ± 0.05 and 3.71 ± 0.05 eV. This cluster size dependence of IE is reproduced within ±0.06 eV employing the mPW1PW91 density-functional and CCSD(T, Full) quantum-chemical methods combined with the 6-311++G(d,p) basis set for the H and O atoms and three different relativistic effective core potentials for Ba atoms. The calculations indicate that the lowest energy hydration structures represent the most relevant contributions to both the vertical and adiabatic ionization energies. Experimental and theoretical evidence correlates with the progressive surface-delocalization of the electron from the hydration cavity around the Ba atom and suggests that the intra-cluster electron transfer is possible even for small aggregates.

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