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Newly developed NeoGRRM has produced new results for BCNOS below.
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SHS method (Sphere expansion method) : SCW method (Sphere contraction method)

Reaction Intermediate Analysis : Sphere contraction directly ties reactant and product!

Explore itermediates of multistep reactions SCW method picks up intermediates very quickly

Many reactions connects reactants and products via several steps. As steps increase, intermediates become more difficult to be disclosed.
GRRM program has an excellent tool for searching intermediates of multi-step reactions. That is the SCW method, which is a unique approach related to the SHS method.
The SHS method explores reaction routes starting from an equlibrium structure by expanding the sphere sizes (Left figure above). In the case of searching intermediates, exploration can be started from the target structure, since it is known before the search. Thus the sphere size can be chosen at the product structure just placed on the sphere surface. Then, the sphere sizes may be decreased to reeach the reactant structure (Right figure above).
Through this sphere contraction procedures, reaction routes from the product to the reactant can be traced to yield intermediate structures very quickly. This is the sphere contraction walk (SCW) method, which is very efficient, since SCW only traces just one pathway, while the sphere expansion mode of the normal SHS traces many routes to consume consderable computation time.
When a series of structures R(reactant) → M → N → P(product) are found, each step, R→M, M→N, N→P, is not necessarily be an elementary reaction. Some intermediates other than M and N may be disreagarded in a single SCW search, because a single SCW tends to connect the sphere surface with the sphere center almost directly along the redius. To avoid overlooking, SCW search should be applied to the each step, R→M, M→N, N→P, repeatedly, until no inermediates appear between the two end points of SCW.
Although SCW skips TSs, it is rather easy to find TS, since two point SHS (2pSHS) search can find the TS connecting the two points very quickly. 2PSHS is also a very excellent tool equipped in the GRRM program.

Example of Intermediate Analysis : Intermediate Analysis of C20 Cluster

Structures of Cyclic C20 and fullerene type C20 are quite different. Even in such cases, SCW works very efficently to disclose many intermediates systematically. The following figure below shows thirty five intermediate between Cyclic C20 and C20 fullerene.
A combination of SCW and 2PSHS loaded in GRRM reveals reaction networks connecting reactant and product via various intermediates, even if reactant and product are quite different.