2004
DOI: 10.1021/ja036479n
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Minimal Distortion Pathways in Polyhedral Rearrangements

Abstract: A definition of minimum distortion paths between two polyhedra in terms of continuous shape measures (CShM) is presented. A general analytical expression deduced for such pathways makes use of one parameter, the minimum distortion constant, that can be easily obtained through the CShM methodology and is herein tabulated for pairs of polyhedra having four to eight vertexes. The work presented here also allows us to obtain representative model molecular structures along the interconversion pathways. Several comm… Show more

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Cited by 390 publications
(366 citation statements)
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“…Also, the axial solvent molecule contributes to this effect in terms of different energy barrier heights [29]. In order to compare the coordination geometries of the Dy ions, these were analysed using the Shape program [30][31][32]. The results are shown in Table 2, and indicate that the coordination geometries of the Dy ions in 1, 2, 4 and Dy 1 in 3 are close to triangular dodecahedral (TDD) with D 2d symmetry.…”
Section: Structure-property Relationshipmentioning
confidence: 99%
“…Also, the axial solvent molecule contributes to this effect in terms of different energy barrier heights [29]. In order to compare the coordination geometries of the Dy ions, these were analysed using the Shape program [30][31][32]. The results are shown in Table 2, and indicate that the coordination geometries of the Dy ions in 1, 2, 4 and Dy 1 in 3 are close to triangular dodecahedral (TDD) with D 2d symmetry.…”
Section: Structure-property Relationshipmentioning
confidence: 99%
“…This technique is often useful for analyzing a particular structure by calculating its shape measures relative to two different reference polyhedra, conveniently plotted in a "shape map" [33,34]. This visualizes whether that structure lies along the minimal distortion path for the interconversion of the two polyhedra.…”
Section: Introduction To Shape Measuresmentioning
confidence: 99%
“…For six-coordinate metal ions, the minimal distortion pathway between the octahedron and the trigonal prism is usually considered [34], which corresponds to the Bailar trigonal twist [35]. A quantitative evaluation of how close (or how far) the structure is from the minimal distortion path is provided by the path deviation function, quoted as a percentage of the deviation relative to the total length of the path [33,36].…”
Section: Introduction To Shape Measuresmentioning
confidence: 99%
“…Not only are the shape measures correlated to the Co···H distance along the reaction path, but it is also seen that all the points in our linear transit pathway have shape measures for the {Co(CO) 4 } fragment that correspond to the minimaldistortion interconversion path between the tetrahedron and the vTBP according to the very small values of the pathdeviation function. [10] For that reason, we can describe the proton-transfer reaction by means of the generalized reaction coordinate [4] that corresponds to the conversion of a {Co(CO) 4 } tetrahedron into a vTBP (Figure 3). Using such a coordinate, the independent reactants are represented by 0 % of the polyhedral path, as the isolated [Co(CO) 4 ] À ion is perfectly tetrahedral.…”
Section: Polyhedral Interconversion Coupled With Protonmentioning
confidence: 99%