Fourth Order for Semiclassical Electronegativity and Chemical Hardness

1 FOURTH ORDER FOR SEMICLASSICAL ELECTRONEGATIVITY AND CHEMICAL HARDNESS 

The present picture is based on speciahzation of the density matrix amplitude (x, Tj x, such as to become uniformly in the valence shell properties, such as the space-time Bohr-Slater quantification on orbits (in atomic units m = h = e l4ns = 1), see (Bohr, 1921 White, 1934) 

Note that for the semiclassical chemical hardness (3.136) the basic definition (3.3) was employed taking account that for neutral atoms we have N=Z, and where the minus sign was as well reconsidered according with the potential (3.135), while the Vz prefactor was formally abolished since at present semiclassical level an integer quantum leap LUMO-HOMO is considered to be in agreement with the integer fluctuation domain of quantum propagation, see below Eqs. (3.38)-(7.43), see Eq. (4.158) of Section 4.2.3.3 as well as the discussion of Eq. (4.252) in Section 4.5 of the present volume. 

Quantum Nanochemistry—Volume II Quantum Atoms and Periodicity 

we are faced with expressing the averaged values of the fluctuation paths in single or multiple time connection, i.e., (///t)), /.(t)//. (t) , r fx)rjp )), etc. For that, it can be readily shown that the first order of the averaged fluctuation path resembles the classical (observed) path, see also Eq. (3.117) 

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