Based on the symmetry of the valence bond wavefunction and the correspondence between bonding patterns and bonded tableaus for chemical bonds in the ground and excited states, the conservation of orbital symmetry and ...Based on the symmetry of the valence bond wavefunction and the correspondence between bonding patterns and bonded tableaus for chemical bonds in the ground and excited states, the conservation of orbital symmetry and the bond symmetry rule can be expressed as "symmetry-adaptation of the valence bond (VB) structure". The symmetry-adaptation of the valence bond structure can directly predict the chemical reactivity by a symmetry analysis of the VB structures of reactants and products without carrying out explicitly theoretical calculations. Curve-crossing diagrams for atom exchange reactions H+HLi→H-2+Li and H+LiH→HLiH (cyclic)→HLi+H have been constructed with the multistructure VB approach and the valence bond structure symmetry rule. The formation mechanism of the barrier and the transition state was discussed. The calculated results show that the H exchange reaction H+LiH HLi+H is a two-step reaction.展开更多
Proposed here is a new framework for the analysis of complex systems as a non-explicitly programmed mathematical hierarchy of subsystems using only the fundamental principle of causality, the mathematics of groupoid s...Proposed here is a new framework for the analysis of complex systems as a non-explicitly programmed mathematical hierarchy of subsystems using only the fundamental principle of causality, the mathematics of groupoid symmetries, and a basic causal metric needed to support measurement in Physics. The complex system is described as a discrete set S of state variables. Causality is described by an acyclic partial order w on S, and is considered as a constraint on the set of allowed state transitions. Causal set (S, w) is the mathematical model of the system. The dynamics it describes is uncertain. Consequently, we focus on invariants, particularly group-theoretical block systems. The symmetry of S by itself is characterized by its symmetric group, which generates a trivial block system over S. The constraint of causality breaks this symmetry and degrades it to that of a groupoid, which may yield a non-trivial block system on S. In addition, partial order w determines a partial order for the blocks, and the set of blocks becomes a causal set with its own, smaller block system. Recursion yields a multilevel hierarchy of invariant blocks over S with the properties of a scale-free mathematical fractal. This is the invariant being sought. The finding hints at a deep connection between the principle of causality and a class of poorly understood phenomena characterized by the formation of hierarchies of patterns, such as emergence, selforganization, adaptation, intelligence, and semantics. The theory and a thought experiment are discussed and previous evidence is referenced. Several predictions in the human brain are confirmed with wide experimental bases. Applications are anticipated in many disciplines, including Biology, Neuroscience, Computation, Artificial Intelligence, and areas of Engineering such as system autonomy, robotics, systems integration, and image and voice recognition.展开更多
文摘Based on the symmetry of the valence bond wavefunction and the correspondence between bonding patterns and bonded tableaus for chemical bonds in the ground and excited states, the conservation of orbital symmetry and the bond symmetry rule can be expressed as "symmetry-adaptation of the valence bond (VB) structure". The symmetry-adaptation of the valence bond structure can directly predict the chemical reactivity by a symmetry analysis of the VB structures of reactants and products without carrying out explicitly theoretical calculations. Curve-crossing diagrams for atom exchange reactions H+HLi→H-2+Li and H+LiH→HLiH (cyclic)→HLi+H have been constructed with the multistructure VB approach and the valence bond structure symmetry rule. The formation mechanism of the barrier and the transition state was discussed. The calculated results show that the H exchange reaction H+LiH HLi+H is a two-step reaction.
文摘Proposed here is a new framework for the analysis of complex systems as a non-explicitly programmed mathematical hierarchy of subsystems using only the fundamental principle of causality, the mathematics of groupoid symmetries, and a basic causal metric needed to support measurement in Physics. The complex system is described as a discrete set S of state variables. Causality is described by an acyclic partial order w on S, and is considered as a constraint on the set of allowed state transitions. Causal set (S, w) is the mathematical model of the system. The dynamics it describes is uncertain. Consequently, we focus on invariants, particularly group-theoretical block systems. The symmetry of S by itself is characterized by its symmetric group, which generates a trivial block system over S. The constraint of causality breaks this symmetry and degrades it to that of a groupoid, which may yield a non-trivial block system on S. In addition, partial order w determines a partial order for the blocks, and the set of blocks becomes a causal set with its own, smaller block system. Recursion yields a multilevel hierarchy of invariant blocks over S with the properties of a scale-free mathematical fractal. This is the invariant being sought. The finding hints at a deep connection between the principle of causality and a class of poorly understood phenomena characterized by the formation of hierarchies of patterns, such as emergence, selforganization, adaptation, intelligence, and semantics. The theory and a thought experiment are discussed and previous evidence is referenced. Several predictions in the human brain are confirmed with wide experimental bases. Applications are anticipated in many disciplines, including Biology, Neuroscience, Computation, Artificial Intelligence, and areas of Engineering such as system autonomy, robotics, systems integration, and image and voice recognition.
