Partition bond degrees

Definition (Partition of valences, partition of bond degrees) Reorderingthe sequences of valences and of bond degrees, respectively, in a decreasing order, we obtain partitions of the numbers... 

Our main example is the following partial order on the set of number partitions of n. It occurs in several applications in this book, since it allows to rank partitions of bond degrees. For example, we shall derive results on the chirality of permutational isomers using the partial order to be introduced next. 

An important result of Ruch and Gutman [261] characterizes the partitions that occur as partitions of bond degrees, the graphical partitions. In order to formulate this result, we represent a partition ah 2- B(y) by its Young diagram [a] that consists of 2 B(y) ... 

Three of these graphical partitions give connected graphs, and therefore they occur as bond degree partitions of molecular graphs ... 

Summarizing, we obtain that a nmnber partition a h 2m is the sequence of bond degrees of a molecule with n atoms if and only if o 4 and m> acg - 1. 

One degree of freedom of the adsorbed molecule serves as the reaction coordinate. For desorption, the reaction coordinate is the vibration of the molecule with respect to the substrate. In the transition state this vibration is highly excited and the chance that the adsorption bond breaks is given by the factor kT/h. All other degrees of freedom of the excited molecule are in equilibrium with those of the molecule in the ground state and are accounted for by their partition functions. 

Phase space theory (PST) has been widely used for estimation of rates and energy partitioning for ion dissociations. It can be considered within the framework of transition-state theory as the limiting case of a loose transition state, in which all product degrees of freedom are statistically fully accessible at the transition state. As such, it is expected to give an upper limit for dissociation rates and to be best suited to barrierless dissociations involving reaction coordinates with simple bond cleavage character. 

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