Nonextensive Statistical Mechanics

7.2 Chemistry 265Fig. 7.58 Log–log plot of the time evolution of ξ ≡ N(t)/N(0) associated with MbCO inglycerol–water. The dots are the experimental data (Figs. 2a and 14 of [283]). The dashed linesindicate the fittings with Eq. (7.23) with the same n(T ) ≡ 1/[q(T ) − 1] used in [283]. The fulllines correspond to our best present fittings, with the same n(T ) used in [283], and r(T ), a q (T ),and a r (T ) as shown in Fig. 7.59 (from [282]).7.2.4 Ground State Energy of the Chemical Elements (Mendeleev’sTable) and of Doped FullerenesThere is nothing more basic in modern chemistry than Mendeleev’s Table of elements.However, its standard implementation makes no reference at all to a verybasic quantity, namely the energy of the ground state of each specific element. Thishas been recently addressed in [581]. The outcome is quite astonishing. The groundstateenergy of the free atom (as calculated by a performant ab-initio Hartree-Fockmethod) has been heuristically found to be given, from the hydrogen to the lawrencium,by2.4333 (Z−1)E = E H e0.58145 , (7.25)where E H = −13.60534 ev, and Z is the atomic number of the element. SeeFigs. 7.60 and 7.61.The ground-state energy of doped fullerenes (as calculated now through a densityfunctional theory method) has also been addressed in [581]. The doping atoms thathave been studied are the covalent atoms 6 C, 7 N, 8 O, 9 F, 14 Si, 615P, 16 S, 17 Cl, and35 Br, and the transition metals 21 Sc, 22 Ti, 23 V , 24 Cr, 25 Mn, 26 Fe, 27 Co, 28 Ni, and29 Cu. Discounting the energy of pure fullerene C 60 (i.e., without doping), which is62.21 K ev, the energies are given by precisely (!) the same Eq. (7.25) by substitutingE H by E FUL =−14.98 ev: see Fig. 7.62.