Chemical Reactivity Description in Density-Functional and Information Theories

In Quantum Information Theory(QIT) the classical measures of information content in probability distributions are replaced by the corresponding resultant entropic descriptors containing the nonclassical terms generated by the state phase or its gradient(electronic current). The classical Shannon(S[p]) and Fisher(I[p]) information terms probe the entropic content of incoherent local events of the particle localization, embodied in the probability distribution p, while their nonclassical phase-companions, S[ Φ ] and I[ Φ ], provide relevant coherence information supplements.Thermodynamic-like couplings between the entropic and energetic descriptors of molecular states are shown to be precluded by the principles of quantum mechanics. The maximum of resultant entropy determines the phase-equilibrium state, defined by "thermodynamic" phase related to electronic density,which can be used to describe reactants in hypothetical stages of a bimolecular chemical reaction.Information channels of molecular systems and their entropic bond indices are summarized, the complete-bridge propagations are examined, and sequential cascades involving the complete sets of the atomic-orbital intermediates are interpreted as Markov chains. The QIT description is applied to reactive systems R = A―B, composed of the Acidic(A) and Basic(B) reactants. The electronegativity equalization processes are investigated and implications of the concerted patterns of electronic flows in equilibrium states of the complementarily arranged substrates are investigated. Quantum communications between reactants are explored and the QIT descriptors of the A―B bond multiplicity/composition are extracted.

Effect of Width-to-Thickness Ratio and Thickness Profile Changing on the Critical Instable Shape During Cold Strip Rolling

Based on the volume constancy with equal flow-per-second and elastic sheet stability theory, a coupling relationship among lateral thickness difference, width-to-thickness ratio of cold rolling strip steel under ideal and actual working conditions, and shape is concluded according to the comprehensive influence principle of various factors on the critical instable shape analyzed in-depth. Firstly, the influence model under actual working condition is developed by referring to the basic relationship between lateral thickness difference and shape under ideal condition. The test results prove that for thin strips with thickness below 0.3 mm, their lateral thickness differences have significant effect on the shape. After then, the combined influence of lateral thickness difference and width-to-thickness ratio on the critical instable shape is concluded according to the elastic sheet stability model, with the synthetic effect of these three factors analyzed. Test data indicate that for cold rolling strip steel with width-to-thickness ratio above 3 000, the critical instability stress difference decreases significantly. Actual measurements are conducted on the lateral thickness differences of two rolls of typical strip manufactured by a sixhigh cold mill, with the influence law of lateral thickness variation and width-to-thickness ratio comprehensively investigated. It is demonstrated that during the production of ultrathin strip steel with different width-to-thickness ratios, the loading roll shapes should be fine adjusted according to the lateral thickness difference of input strips.Therefore, the variation of lateral thickness difference of output strips can meet the requirement of shape stability,so as to obtain fine shape.