The Principle of Minimum Chemical Distance and the Principle of Minimum Structure Change

Abstract

<jats:title>Abstract</jats:title><jats:p>The principle of minimum chemical distance (PMCD) is derived from the general theory of the BE- and R-matrices, and makes precise the vague classical “principle of minimum structure change”. In fact, the PMCD may be seen as the principle of minimum structure change in mathematical terms. It provides a quantitative measure of chemical similarity of isomeric molecular systems. Its applications lie in the fields of correlations of substructures, elucidation of reaction mechanisms, and evaluation of synthetic pathways as is illustrated by examples. The mathematical foundations of the computer assisted application of the PMCD are presented.</jats:p>

Chemistry, Computers, and the Mind

“…It can be shown that a minimal chemical distance, that is the shortest v reaction can be found. [17] This is coherent with the general principle of minimal action A (Equation 1) and the Hamilton variational principle (Equation 2) that is, the action A along the path p1→ p2 inside a segment Θ of space-time must be minimal, the variation around that path required to reach zero (Figure 8). The reaction matrices were categorized as, for example, breaking two bonds and forming two new bonds or breaking three bonds and forming three new bonds.…”

Efficient prediction of reaction paths through molecular graph and reaction network analysis

“…We invoke the so-called principle of minimum structure change, which states that most chemical reactions proceed along a pathway with minimum dissociation and formation of bonds. 68 , 69 This heuristic rule, often regarded as a principle, has been applied to various chemical problems including the elucidation of reaction mechanism. 68 , 69 To implement this idea in our method, we devised a novel way of discarding intermediates that are placed too far from reactants and products in a reaction network.…”

“… 68 , 69 This heuristic rule, often regarded as a principle, has been applied to various chemical problems including the elucidation of reaction mechanism. 68 , 69 To implement this idea in our method, we devised a novel way of discarding intermediates that are placed too far from reactants and products in a reaction network. The concept of chemical distance (CD) 68 , 69 is used to perform such geometric analysis, which is defined as where A and B denote the AC matrices of two intermediates, respectively.…”

Efficient Construction of a Chemical Reaction Network Guided By a Monte Carlo Tree Search

“…ACE-Reaction makes use of the graph-theoretic method to construct a reaction network for given reactants and products. It is based on the idea of the principle of minimal structure change (PMSC) [41,42] , which states that reaction paths to products are likely to have a minimal number of bond dissociation and formation, to collect only plausible paths. Here, we briefly discuss three major steps in ACE-Reaction.…”

“…After screening by energy, it further screens intermediates that are not a part of plausible paths with respect to the PMSC. To measure the extent of structure change, we use chemical distance (CD) [35,41,42] , which is defined as the sum of the number of minimal bond dissociation and formation to interconvert between the two intermediates. By using this CD, it removes intermediates that are far from both reactants and products by applying elliptic inequality given as [Eq.…”