In this paper we study nine neutral copper clusters through the theoretical characterization of their molecular structures, binding energy, electronic properties, and reactivity descriptors. Geometry optimization and vibrational analysis were performed using density functional theory calculations with a hybrid functional combined with effective core potentials. It is shown that reactivity descriptors combined with reactivity principles like the minimum polarizability and maximum hardness are operative for characterizing and rationalizing the electronic properties of copper clusters.

We present results of density functional calculations for the standard reduction potential of the −10.56 eV to −10.99 eV for n = 6 and from -6.83 eV to -7.45 eV for n = 18, depending on the density functional and basis set quality. The aqueous standard reduction potential is overestimated when only the first solvation shell is treated explicitly and it is underestimated when the first and second solvation shells are treated explicitly.

The concept of the reaction force is presented and discussed in detail. For typical processes with energy barriers, it has a universal form which defines three key points along an intrinsic reaction coordinate: the force minimum, zero and maximum. We suggest that the resulting four zones be interpreted as involving preparation of reactants in the first, transition to products in the second and third, and relaxation in the fourth. This general picture is supported by the distinctive patterns of the variations in relevant electronic properties. Two important points that are brought out by the reaction force are that (a) the traditional activation energy comprises two separate contributions, and (b) the transition state corresponds to a balance between the driving and the retarding forces.

A theoretical study of double-proton-transfer processes in bimolecular complexes formed by combinations of molecules of the type CHX−XH (X = O, S) is reported. The reactions are rationalized in terms of the energy, chemical potential, and hardness of hydrogen-bonded and isolated species. Sanderson's rule to determine molecular chemical potential and hardness from the values of the constituent fragments is used to characterize the relaxation effects due to hydrogen bonding. In ten formation and seven double-proton transfer processes studied here, the principles of maximum hardness and minimum polarizability are verified. The mechanism for double proton transfer has been analyzed through the force acting on the system to bring reactants into products and the corresponding energy barriers have been qualitatively classified according to its through bond or through space nature.

Molecular vibrations in ammonia (NH3) and hydrogen sulfide (H2S), and internal rotations in hydrogen peroxide (HOOH), hydrogen thioperoxide (HSOH), hydrogen persulfide (HSSH), and ethylene (C2H4) are studied using ab initio SCF methods at the Hartree−Fock level using a standard Pople 6-311G** basis set. Polarizability values are calculated using both Pople's and Sadlej's basis sets. Any nontotally symmetric distortion in bond length or bond angle along the vibrational symmetry coordinates of a molecule around its equilibrium geometry decreases the equilibrium hardness value and increases the equilibrium polarizability value. During rotational isomerization the minimum energy conformation corresponds to the maximum hardness and minimum polarizability values and the maximum energy conformation corresponds to the minimum hardness and maximum polarizability values. Density functional calculations confirm these observed trends. In general we have found that the conditions of maximum hardness and minimum polarizability complement the minimum energy criterion for molecular stability.