<p>This work investigates the nature of the Si–Pt, M–Pt (M = Ga, In, and Sn), and other coordinate bonds within a family of cationic complexes, analyzed through the superposition of the electrostatic force field <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbf{F}_{\text{es}}(\mathbf{r})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="bold">F</mi> <mtext>es</mtext> </msub> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="bold">r</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, the total static force field <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal{F}(\mathbf{r})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">F</mi> <mo stretchy="false">(</mo> <mi mathvariant="bold">r</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, and the electron density gradient <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\nabla\rho(\mathbf{r})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">∇</mi> <mi>ρ</mi> <mo stretchy="false">(</mo> <mi mathvariant="bold">r</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. It has been demonstrated that the Si–Pt coordinate bond represents a polar interatomic interaction exhibiting a pronounced covalent contribution to the transferred electronic&#xa0;charge and a notable localization of the Fermi exchange hole density <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(h_{x}(\mathbf{r}, \mathbf{r}')\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>h</mi> <mi>x</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="bold">r</mi> <mo>,</mo> <msup> <mrow> <mi mathvariant="bold">r</mi> </mrow> <mo>′</mo> </msup> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. Within this interaction, the zero-flux surface in <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\nabla\rho(\mathbf{r})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">∇</mi> <mi>ρ</mi> <mo stretchy="false">(</mo> <mi mathvariant="bold">r</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> is located closer to the Si nucleus of the Lewis-basic atom that provides its electron pair to the internuclear binding region, whereas the zero-flux surface in <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\mathbf{F}_{\text{es}}(\mathbf{r})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="bold">F</mi> <mtext>es</mtext> </msub> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="bold">r</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> lies closer to the Pt nucleus of the Lewis-acidic atom that hosts the subatomic electrophilic site. Consequently, the Si–Pt bond fails both&#xa0;to meet the criterion for the categorization of Lewis-type interactions and to conform to the underlying concept of electrophilic influence zones—these two constructs being theoretically arbitrary, yet methodologically well-established within quantum chemical topology. Instead, an interpretation predicated upon interatomic charge transfer and articulated within the framework of force-field pseudoatoms in molecules has been advanced as a compelling alternative. The Lewis-type character of the Si–Pt bond has been elucidated through the analysis of the exchange charge density <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(q_x(\mathbf{r})= \nabla \cdot \mathbf{F}_{x}(\mathbf{r})/(4\pi)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="bold">r</mi> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mi mathvariant="normal">∇</mi> <mo>·</mo> <msub> <mi mathvariant="bold">F</mi> <mi>x</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="bold">r</mi> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">/</mo> <mrow> <mo stretchy="false">(</mo> <mn>4</mn> <mi>π</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, the fermionic force <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\mathbf{F}_{\text{f}}(\mathbf{r})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="bold">F</mi> <mtext>f</mtext> </msub> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="bold">r</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, and the component contribution of the exchange force <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(\mathbf{F}_{x}(\mathbf{r})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="bold">F</mi> <mi>x</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="bold">r</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(\mathcal{F}(\mathbf{r})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">F</mi> <mo stretchy="false">(</mo> <mi mathvariant="bold">r</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, expressed as <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(\left[\mathbf{F}_{x}(\mathbf{r})\cdot \mathcal{F}(\mathbf{r})\right]/|\mathcal{F}(\mathbf{r})|\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mfenced close="]" open="["> <msub> <mi mathvariant="bold">F</mi> <mi>x</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="bold">r</mi> <mo stretchy="false">)</mo> </mrow> <mo>·</mo> <mi mathvariant="script">F</mi> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="bold">r</mi> <mo stretchy="false">)</mo> </mrow> </mfenced> <mo stretchy="false">/</mo> <mrow> <mo stretchy="false">|</mo> <mi mathvariant="script">F</mi> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="bold">r</mi> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">|</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>.</p> Graphical Abstract <p></p>

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Challenging the established view of Lewis-type interactions as formulated within quantum chemical topology: an interpretation of Si–Pt and M–Pt (M = Ga, In, and Sn) bonding in terms of electronic force fields

  • Sergey V. Kartashov,
  • Anton P. Fedonin,
  • Julia R. Khusnutdinova,
  • Robert R. Fayzullin

摘要

This work investigates the nature of the Si–Pt, M–Pt (M = Ga, In, and Sn), and other coordinate bonds within a family of cationic complexes, analyzed through the superposition of the electrostatic force field \(\mathbf{F}_{\text{es}}(\mathbf{r})\) F es ( r ) , the total static force field \(\mathcal{F}(\mathbf{r})\) F ( r ) , and the electron density gradient \(\nabla\rho(\mathbf{r})\) ρ ( r ) . It has been demonstrated that the Si–Pt coordinate bond represents a polar interatomic interaction exhibiting a pronounced covalent contribution to the transferred electronic charge and a notable localization of the Fermi exchange hole density \(h_{x}(\mathbf{r}, \mathbf{r}')\) h x ( r , r ) . Within this interaction, the zero-flux surface in \(\nabla\rho(\mathbf{r})\) ρ ( r ) is located closer to the Si nucleus of the Lewis-basic atom that provides its electron pair to the internuclear binding region, whereas the zero-flux surface in \(\mathbf{F}_{\text{es}}(\mathbf{r})\) F es ( r ) lies closer to the Pt nucleus of the Lewis-acidic atom that hosts the subatomic electrophilic site. Consequently, the Si–Pt bond fails both to meet the criterion for the categorization of Lewis-type interactions and to conform to the underlying concept of electrophilic influence zones—these two constructs being theoretically arbitrary, yet methodologically well-established within quantum chemical topology. Instead, an interpretation predicated upon interatomic charge transfer and articulated within the framework of force-field pseudoatoms in molecules has been advanced as a compelling alternative. The Lewis-type character of the Si–Pt bond has been elucidated through the analysis of the exchange charge density \(q_x(\mathbf{r})= \nabla \cdot \mathbf{F}_{x}(\mathbf{r})/(4\pi)\) q x ( r ) = · F x ( r ) / ( 4 π ) , the fermionic force \(\mathbf{F}_{\text{f}}(\mathbf{r})\) F f ( r ) , and the component contribution of the exchange force \(\mathbf{F}_{x}(\mathbf{r})\) F x ( r ) to \(\mathcal{F}(\mathbf{r})\) F ( r ) , expressed as \(\left[\mathbf{F}_{x}(\mathbf{r})\cdot \mathcal{F}(\mathbf{r})\right]/|\mathcal{F}(\mathbf{r})|\) F x ( r ) · F ( r ) / | F ( r ) | .

Graphical Abstract