<p>Attention is drawn to the structural topology of the electronic potential energy density gradient <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\nabla\!\left[-v(\mathbf{r})\right]\)</EquationSource> </InlineEquation> in transition states of chemical reactions in which bond formation and bond cleavage are coupled to pronounced, spatially localized charge redistribution. In the transition states of the bimolecular nucleophilic substitution reactions analyzed herein, for a representative polar partial bond <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\omega\)</EquationSource> </InlineEquation>···<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\alpha\)</EquationSource> </InlineEquation>—where <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\omega\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\alpha\)</EquationSource> </InlineEquation> denote the nuclei of the electron-donor and electron-acceptor atoms, respectively—the pseudoatomic basin <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\Omega_{W}^{\omega}\)</EquationSource> </InlineEquation>, defined in <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\nabla\!\left[-v(\mathbf{r})\right]\)</EquationSource> </InlineEquation> and associated with <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\omega\)</EquationSource> </InlineEquation>, extends into the neighboring atomic basin <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(\Omega_{S}^{\alpha}\)</EquationSource> </InlineEquation>, defined in the electron density gradient <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(\nabla\rho(\mathbf{r})\)</EquationSource> </InlineEquation> and associated with <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(\alpha\)</EquationSource> </InlineEquation>, thereby following the force-field pseudoatomic basin <InlineEquation ID="IEq12"> <EquationSource Format="TEX">\(\Omega_{P}^{\omega}\)</EquationSource> </InlineEquation>, defined in the total static force field <InlineEquation ID="IEq13"> <EquationSource Format="TEX">\(\mathcal{F}(\mathbf{r})\)</EquationSource> </InlineEquation> and associated with <InlineEquation ID="IEq14"> <EquationSource Format="TEX">\(\omega\)</EquationSource> </InlineEquation>. Across the partial bonds examined, the extension of <InlineEquation ID="IEq15"> <EquationSource Format="TEX">\(\Omega_{W}^{\omega}\)</EquationSource> </InlineEquation> trails behind that of <InlineEquation ID="IEq16"> <EquationSource Format="TEX">\(\Omega_{P}^{\omega}\)</EquationSource> </InlineEquation>, with a tendency toward a larger disparity for those with lower covalent character. Moreover, it has been demonstrated that, in these transition states, the topological pattern of <InlineEquation ID="IEq17"> <EquationSource Format="TEX">\(\nabla\!\left[-v(\mathbf{r})\right]\)</EquationSource> </InlineEquation> with respect to the reference vector fields is inherited from the energetically closest stationary state along the reaction pathway. Taken together, these considerations render <InlineEquation ID="IEq18"> <EquationSource Format="TEX">\(\nabla\!\left[-v(\mathbf{r})\right]\)</EquationSource> </InlineEquation>-based spatial partitioning a computationally tractable diagnostic tool for identifying and rationalizing the electron-transfer-induced responsive phenomenon within incipient and partially broken interatomic interactions. </p>

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Structural topology of the vector field of the electronic virial energy density gradient in relation to the electron-transfer-induced responsive phenomenon. Part 2: transition states and partial chemical bonds

  • Sergey V. Kartashov,
  • Robert R. Fayzullin

摘要

Attention is drawn to the structural topology of the electronic potential energy density gradient \(\nabla\!\left[-v(\mathbf{r})\right]\) in transition states of chemical reactions in which bond formation and bond cleavage are coupled to pronounced, spatially localized charge redistribution. In the transition states of the bimolecular nucleophilic substitution reactions analyzed herein, for a representative polar partial bond \(\omega\) ··· \(\alpha\) —where \(\omega\) and \(\alpha\) denote the nuclei of the electron-donor and electron-acceptor atoms, respectively—the pseudoatomic basin \(\Omega_{W}^{\omega}\) , defined in \(\nabla\!\left[-v(\mathbf{r})\right]\) and associated with \(\omega\) , extends into the neighboring atomic basin \(\Omega_{S}^{\alpha}\) , defined in the electron density gradient \(\nabla\rho(\mathbf{r})\) and associated with \(\alpha\) , thereby following the force-field pseudoatomic basin \(\Omega_{P}^{\omega}\) , defined in the total static force field \(\mathcal{F}(\mathbf{r})\) and associated with \(\omega\) . Across the partial bonds examined, the extension of \(\Omega_{W}^{\omega}\) trails behind that of \(\Omega_{P}^{\omega}\) , with a tendency toward a larger disparity for those with lower covalent character. Moreover, it has been demonstrated that, in these transition states, the topological pattern of \(\nabla\!\left[-v(\mathbf{r})\right]\) with respect to the reference vector fields is inherited from the energetically closest stationary state along the reaction pathway. Taken together, these considerations render \(\nabla\!\left[-v(\mathbf{r})\right]\) -based spatial partitioning a computationally tractable diagnostic tool for identifying and rationalizing the electron-transfer-induced responsive phenomenon within incipient and partially broken interatomic interactions.