<p>The electronic structures and redox properties of the [Co(bpy)<InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(_{\varvec{3}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow> <mn mathvariant="bold">3</mn> </mrow> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>]<InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(^{{\varvec{2+/3+}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mrow> <mn mathvariant="bold">2</mn> <mo mathvariant="bold">+</mo> <mo mathvariant="bold" stretchy="false">/</mo> <mn mathvariant="bold">3</mn> <mo mathvariant="bold">+</mo> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation> and [Co(phen)<InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(_{\varvec{3}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow> <mn mathvariant="bold">3</mn> </mrow> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>]<InlineEquation ID="IEq12"> <EquationSource Format="TEX">\(^{{\varvec{2+/3+}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mrow> <mn mathvariant="bold">2</mn> <mo mathvariant="bold">+</mo> <mo mathvariant="bold" stretchy="false">/</mo> <mn mathvariant="bold">3</mn> <mo mathvariant="bold">+</mo> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation> redox couple were investigated using the two different exchange–correlation functional, namely CAM-B3LYP and TPSSh, with the def2-SVP and def2-TZVP basis sets. Our results indicate that [Co(bpy)<InlineEquation ID="IEq13"> <EquationSource Format="TEX">\(_{\varvec{3}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow> <mn mathvariant="bold">3</mn> </mrow> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>]<InlineEquation ID="IEq14"> <EquationSource Format="TEX">\(^{{\varvec{2+}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mrow> <mn mathvariant="bold">2</mn> <mo mathvariant="bold">+</mo> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation> and [Co(phen)<InlineEquation ID="IEq15"> <EquationSource Format="TEX">\(_{\varvec{3}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow> <mn mathvariant="bold">3</mn> </mrow> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>]<InlineEquation ID="IEq16"> <EquationSource Format="TEX">\(^{{\varvec{2+}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mrow> <mn mathvariant="bold">2</mn> <mo mathvariant="bold">+</mo> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation> complexes exhibit a high-spin ground state, whereas [Co(bpy)<InlineEquation ID="IEq17"> <EquationSource Format="TEX">\(_{\varvec{3}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow> <mn mathvariant="bold">3</mn> </mrow> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>]<InlineEquation ID="IEq18"> <EquationSource Format="TEX">\(^{{\varvec{3+}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mrow> <mn mathvariant="bold">3</mn> <mo mathvariant="bold">+</mo> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation> [Co(phen)<InlineEquation ID="IEq19"> <EquationSource Format="TEX">\(_{\varvec{3}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow> <mn mathvariant="bold">3</mn> </mrow> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>]<InlineEquation ID="IEq20"> <EquationSource Format="TEX">\(^{{\varvec{3+}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mrow> <mn mathvariant="bold">3</mn> <mo mathvariant="bold">+</mo> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation> complexes adopt a low-spin ground state. Both basis sets and exchange–correlation functionals consistently predict the same ground-state spin configurations for these complexes. For <InlineEquation ID="IEq21"> <EquationSource Format="TEX">\([ \text {Co(bpy)}_{\varvec{3}} ]^{{\varvec{2+}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mo stretchy="false">[</mo> <msub> <mtext>Co(bpy)</mtext> <mrow> <mn mathvariant="bold">3</mn> </mrow> </msub> <mo stretchy="false">]</mo> </mrow> <mrow> <mn mathvariant="bold">2</mn> <mo mathvariant="bold">+</mo> </mrow> </msup> </math></EquationSource> </InlineEquation>, the energy gap between the doublet and quartet spin states is relatively small when using the TPSSh functional, amounting to 2.21&#xa0;kcal/mol with the Def2-SVP basis set and 0.09&#xa0;kcal/mol with the Def2-TZVP basis set. In contrast, when the CAM-B3LYP functional is employed, the energy splitting becomes significantly larger, with values of 7.91&#xa0;kcal/mol and 6.12&#xa0;kcal/mol for the Def2-SVP and Def2-TZVP basis sets, respectively. We also observed similar trends for <InlineEquation ID="IEq22"> <EquationSource Format="TEX">\([ \text {Co(phen)}_{\varvec{3}} ]^{{\varvec{2+}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mo stretchy="false">[</mo> <msub> <mtext>Co(phen)</mtext> <mrow> <mn mathvariant="bold">3</mn> </mrow> </msub> <mo stretchy="false">]</mo> </mrow> <mrow> <mn mathvariant="bold">2</mn> <mo mathvariant="bold">+</mo> </mrow> </msup> </math></EquationSource> </InlineEquation>. In contrast, <InlineEquation ID="IEq23"> <EquationSource Format="TEX">\([ \text {Co(bpy)}_{\varvec{3}} ]^{{\varvec{3+}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mo stretchy="false">[</mo> <msub> <mtext>Co(bpy)</mtext> <mrow> <mn mathvariant="bold">3</mn> </mrow> </msub> <mo stretchy="false">]</mo> </mrow> <mrow> <mn mathvariant="bold">3</mn> <mo mathvariant="bold">+</mo> </mrow> </msup> </math></EquationSource> </InlineEquation> exhibits a significantly larger energy separation between spin states. Using the CAM-B3LYP functional, the energy difference between the singlet ground state and the quintet excited state is calculated to be 41.42&#xa0;kcal/mol and 42.07&#xa0;kcal/mol with the Def2-SVP and Def2-TZVP basis sets, respectively. When the TPSSh functional is employed, this singlet-quintet energy gap becomes slightly larger, further reinforcing the strong preference for the low-spin singlet configuration in the oxidized complex. Additionally, we have observed that adiabatic ionization potentials are less affected by the choice of basis when the CAM-B3LYP functional is used. In contrast, vertical ionization potential exhibits a more pronounced basis set dependence. However, ionization potentials calculated with the TPSSh functional exhibit significantly reduced sensitivity to basis set choice. The calculated oxidation potentials (<InlineEquation ID="IEq24"> <EquationSource Format="TEX">\({\varvec{E}}^{\varvec{\circ }}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mrow> <mi mathvariant="bold-italic">E</mi> </mrow> </mrow> <mrow> <mo mathvariant="bold">∘</mo> </mrow> </msup> </math></EquationSource> </InlineEquation>) using CAM-B3LYP functional for the [Co(bpy)<InlineEquation ID="IEq25"> <EquationSource Format="TEX">\(_{\varvec{3}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow> <mn mathvariant="bold">3</mn> </mrow> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>]<InlineEquation ID="IEq26"> <EquationSource Format="TEX">\(^{{\varvec{2+/3+}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mrow> <mn mathvariant="bold">2</mn> <mo mathvariant="bold">+</mo> <mo mathvariant="bold" stretchy="false">/</mo> <mn mathvariant="bold">3</mn> <mo mathvariant="bold">+</mo> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation> couple are 5.32&#xa0;V and 5.26&#xa0;V employing the def2-SVP and def2-TZVP basis sets, respectively, whereas (<InlineEquation ID="IEq27"> <EquationSource Format="TEX">\({\varvec{E}}^{\varvec{\circ }}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mrow> <mi mathvariant="bold-italic">E</mi> </mrow> </mrow> <mrow> <mo mathvariant="bold">∘</mo> </mrow> </msup> </math></EquationSource> </InlineEquation>) calculated at the TPSSh functional is 4.62&#xa0;V and 4.55&#xa0;V. We also have observed that the standard oxidation potential of <InlineEquation ID="IEq28"> <EquationSource Format="TEX">\([ \text {Co(phen)}_{\varvec{3}} ]^{{\varvec{2+/3+}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mo stretchy="false">[</mo> <msub> <mtext>Co(phen)</mtext> <mrow> <mn mathvariant="bold">3</mn> </mrow> </msub> <mo stretchy="false">]</mo> </mrow> <mrow> <mn mathvariant="bold">2</mn> <mo mathvariant="bold">+</mo> <mo mathvariant="bold" stretchy="false">/</mo> <mn mathvariant="bold">3</mn> <mo mathvariant="bold">+</mo> </mrow> </msup> </math></EquationSource> </InlineEquation> is relatively higher than the values of [Co(bpy)<InlineEquation ID="IEq29"> <EquationSource Format="TEX">\(_{\varvec{3}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow> <mn mathvariant="bold">3</mn> </mrow> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>]<InlineEquation ID="IEq30"> <EquationSource Format="TEX">\(^{{\varvec{2+/3+}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mrow> <mn mathvariant="bold">2</mn> <mo mathvariant="bold">+</mo> <mo mathvariant="bold" stretchy="false">/</mo> <mn mathvariant="bold">3</mn> <mo mathvariant="bold">+</mo> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation>. Computational analyses of [Co(bpy)<InlineEquation ID="IEq31"> <EquationSource Format="TEX">\(_{\varvec{3}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow> <mn mathvariant="bold">3</mn> </mrow> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>]<InlineEquation ID="IEq32"> <EquationSource Format="TEX">\(^{{\varvec{3+/2+}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mrow> <mn mathvariant="bold">3</mn> <mo mathvariant="bold">+</mo> <mo mathvariant="bold" stretchy="false">/</mo> <mn mathvariant="bold">2</mn> <mo mathvariant="bold">+</mo> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation> and [Co(phen)<InlineEquation ID="IEq33"> <EquationSource Format="TEX">\(_{\varvec{3}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow> <mn mathvariant="bold">3</mn> </mrow> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>]<InlineEquation ID="IEq34"> <EquationSource Format="TEX">\(^{{\varvec{3+/2+}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mrow> <mn mathvariant="bold">3</mn> <mo mathvariant="bold">+</mo> <mo mathvariant="bold" stretchy="false">/</mo> <mn mathvariant="bold">2</mn> <mo mathvariant="bold">+</mo> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation> establish a unified redox picture grounded in Gaussian MO compositions and NBO donor–acceptor metrics. In both families, Co(III) displays ligand–<InlineEquation ID="IEq35"> <EquationSource Format="TEX">\({\varvec{\pi }}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="bold-italic">π</mi> </mrow> </math></EquationSource> </InlineEquation> HOMOs with a Co(3d) block immediately below, while Co-centered <InlineEquation ID="IEq36"> <EquationSource Format="TEX">\({\varvec{d}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="bold-italic">d</mi> </mrow> </math></EquationSource> </InlineEquation> acceptors comprise the LUMO/LUMO+1. One-electron reduction populates a metal-centered acceptor, yielding Co(II) doublets with a two-long/four-short Co–N pattern and quartets with uniformly longer Co–N bonds. NBO <InlineEquation ID="IEq37"> <EquationSource Format="TEX">\({\varvec{E}}^{{\varvec{(2)}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mrow> <mi mathvariant="bold-italic">E</mi> </mrow> </mrow> <mrow> <mo mathvariant="bold" stretchy="false">(</mo> <mn mathvariant="bold">2</mn> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msup> </math></EquationSource> </InlineEquation> values for LP(N)<InlineEquation ID="IEq38"> <EquationSource Format="TEX">\({\varvec{\rightarrow }}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo mathvariant="bold">→</mo> </mrow> </math></EquationSource> </InlineEquation>LV(Co) <InlineEquation ID="IEq39"> <EquationSource Format="TEX">\({\varvec{\sigma }}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="bold-italic">σ</mi> </mrow> </math></EquationSource> </InlineEquation> donation decrease systematically from Co(III) to Co(II), rationalizing bond elongation and modest increases in Co natural charges. Phenanthroline narrows the <InlineEquation ID="IEq40"> <EquationSource Format="TEX">\({\varvec{d/\pi }}^{\varvec{*}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mrow> <mi mathvariant="bold-italic">d</mi> <mo mathvariant="bold" stretchy="false">/</mo> <mi mathvariant="bold-italic">π</mi> </mrow> </mrow> <mrow> <mrow /> <mo mathvariant="bold">∗</mo> </mrow> </msup> </math></EquationSource> </InlineEquation> gap relative to bipyridine, making ligand-centered pathways slightly more competitive; nevertheless, the primary Co(III)<InlineEquation ID="IEq41"> <EquationSource Format="TEX">\({\varvec{\rightarrow }}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo mathvariant="bold">→</mo> </mrow> </math></EquationSource> </InlineEquation>Co(II) event remains metal-centered across spin states examined. These findings contribute to a deeper understanding of redox property calculations via DFT and may support the potential application of cobalt-containing redox couples in thermoelectric materials.</p>

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Standard redox potential of [Co(bpy)\(_3\)]\(^{2+/3+}\) and [Co(phen)\(_3\)]\(^{2+/3+}\) redox couples using a density functional theory protocol

  • Sapajan Ibragimov,
  • Leonard Komando

摘要

The electronic structures and redox properties of the [Co(bpy) \(_{\varvec{3}}\) 3 ] \(^{{\varvec{2+/3+}}}\) 2 + / 3 + and [Co(phen) \(_{\varvec{3}}\) 3 ] \(^{{\varvec{2+/3+}}}\) 2 + / 3 + redox couple were investigated using the two different exchange–correlation functional, namely CAM-B3LYP and TPSSh, with the def2-SVP and def2-TZVP basis sets. Our results indicate that [Co(bpy) \(_{\varvec{3}}\) 3 ] \(^{{\varvec{2+}}}\) 2 + and [Co(phen) \(_{\varvec{3}}\) 3 ] \(^{{\varvec{2+}}}\) 2 + complexes exhibit a high-spin ground state, whereas [Co(bpy) \(_{\varvec{3}}\) 3 ] \(^{{\varvec{3+}}}\) 3 + [Co(phen) \(_{\varvec{3}}\) 3 ] \(^{{\varvec{3+}}}\) 3 + complexes adopt a low-spin ground state. Both basis sets and exchange–correlation functionals consistently predict the same ground-state spin configurations for these complexes. For \([ \text {Co(bpy)}_{\varvec{3}} ]^{{\varvec{2+}}}\) [ Co(bpy) 3 ] 2 + , the energy gap between the doublet and quartet spin states is relatively small when using the TPSSh functional, amounting to 2.21 kcal/mol with the Def2-SVP basis set and 0.09 kcal/mol with the Def2-TZVP basis set. In contrast, when the CAM-B3LYP functional is employed, the energy splitting becomes significantly larger, with values of 7.91 kcal/mol and 6.12 kcal/mol for the Def2-SVP and Def2-TZVP basis sets, respectively. We also observed similar trends for \([ \text {Co(phen)}_{\varvec{3}} ]^{{\varvec{2+}}}\) [ Co(phen) 3 ] 2 + . In contrast, \([ \text {Co(bpy)}_{\varvec{3}} ]^{{\varvec{3+}}}\) [ Co(bpy) 3 ] 3 + exhibits a significantly larger energy separation between spin states. Using the CAM-B3LYP functional, the energy difference between the singlet ground state and the quintet excited state is calculated to be 41.42 kcal/mol and 42.07 kcal/mol with the Def2-SVP and Def2-TZVP basis sets, respectively. When the TPSSh functional is employed, this singlet-quintet energy gap becomes slightly larger, further reinforcing the strong preference for the low-spin singlet configuration in the oxidized complex. Additionally, we have observed that adiabatic ionization potentials are less affected by the choice of basis when the CAM-B3LYP functional is used. In contrast, vertical ionization potential exhibits a more pronounced basis set dependence. However, ionization potentials calculated with the TPSSh functional exhibit significantly reduced sensitivity to basis set choice. The calculated oxidation potentials ( \({\varvec{E}}^{\varvec{\circ }}\) E ) using CAM-B3LYP functional for the [Co(bpy) \(_{\varvec{3}}\) 3 ] \(^{{\varvec{2+/3+}}}\) 2 + / 3 + couple are 5.32 V and 5.26 V employing the def2-SVP and def2-TZVP basis sets, respectively, whereas ( \({\varvec{E}}^{\varvec{\circ }}\) E ) calculated at the TPSSh functional is 4.62 V and 4.55 V. We also have observed that the standard oxidation potential of \([ \text {Co(phen)}_{\varvec{3}} ]^{{\varvec{2+/3+}}}\) [ Co(phen) 3 ] 2 + / 3 + is relatively higher than the values of [Co(bpy) \(_{\varvec{3}}\) 3 ] \(^{{\varvec{2+/3+}}}\) 2 + / 3 + . Computational analyses of [Co(bpy) \(_{\varvec{3}}\) 3 ] \(^{{\varvec{3+/2+}}}\) 3 + / 2 + and [Co(phen) \(_{\varvec{3}}\) 3 ] \(^{{\varvec{3+/2+}}}\) 3 + / 2 + establish a unified redox picture grounded in Gaussian MO compositions and NBO donor–acceptor metrics. In both families, Co(III) displays ligand– \({\varvec{\pi }}\) π HOMOs with a Co(3d) block immediately below, while Co-centered \({\varvec{d}}\) d acceptors comprise the LUMO/LUMO+1. One-electron reduction populates a metal-centered acceptor, yielding Co(II) doublets with a two-long/four-short Co–N pattern and quartets with uniformly longer Co–N bonds. NBO \({\varvec{E}}^{{\varvec{(2)}}}\) E ( 2 ) values for LP(N) \({\varvec{\rightarrow }}\) LV(Co) \({\varvec{\sigma }}\) σ donation decrease systematically from Co(III) to Co(II), rationalizing bond elongation and modest increases in Co natural charges. Phenanthroline narrows the \({\varvec{d/\pi }}^{\varvec{*}}\) d / π gap relative to bipyridine, making ligand-centered pathways slightly more competitive; nevertheless, the primary Co(III) \({\varvec{\rightarrow }}\) Co(II) event remains metal-centered across spin states examined. These findings contribute to a deeper understanding of redox property calculations via DFT and may support the potential application of cobalt-containing redox couples in thermoelectric materials.