Three-valued derived logics for classical phase spaces

Reichenbach proposed a three-valued logic to describe quantum mechanics. In his development, Reichenbach presented three different negation operators without providing any criteria for choosing among them. In this paper we develop two three-valuedderived logics for classical systems. These logics are derived in that they are based on a theory of physical measurement. In this regard they have some of the characteristics of the quantum logic developed by Birkhoff and von Neumann. The theory of measurement used in the present development is the one used previously in developingbivalent derived logics for classical systems. As these systems are derived logics, many of the ambiguities possessed by systems such as Reichenbach's are avoided.     

Strain Energies in Homoatomic Nitrogen Clusters N(4), N(6), and N(8)

Strain energies and resonance energies can be obtained as the energy changes for appropriate homodesmotic reactions using ab initio calculated total energies as the energies of the reactants and products involved. Homodesmotic reactions conserve bond types and preserve valence environments at all atoms, requirements that favor the cancellation of basis set and electron correlation errors in the ab initio energies. In this paper we calculate strain energies and resonance energies for N(4), N(6), and N(8) clusters in a number of chemically significant but, for nitrogen, hypothetical structural forms. The nitrogen cluster strain energies are generally of the same order of magnitude as those of isostructural hydrocarbon clusters, and individual differences can be explained by using the ring strain additivity rule and recognizing the effect of the presence of lone pairs of electrons on nitrogen clusters but not on the hydrocarbons. Resonance energies of the nitrogen clusters are much smaller than those of the comparable aromatic hydrocarbons. The differences can be rationalized by considering the relative strengths of CC and NN single and double bonds. Strain and resonance energies of nitrogen clusters are compared with those previously reported for homoatomic clusters of phosphorus and arsenic. Trends through the series are remarkably similar, but strain energies for clusters from lower periods are progressively smaller. Strain and resonance have been important organizing concepts in organic chemistry for many years. Estimates of corresponding parameters for inorganic analogs are only now becoming available.