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Adiabatic electron transfer
Canley: reword lede
'''Adiabatic electron-transfer''' is the basis of oxidation-reduction processes, which are ubiquitous in nature in both the inorganic and biological spheres. The mechanism of these reactions—the simplest of which proceed without making or breaking chemical bonds—remained unknown until the mid 1950s, when several independent theoretical studies showed that it was due to modulation of coupling between electronic and vibrational motions.
According to his Royal Society election citation,<ref></ref> [[Noel Hush]]'s research in the area of homogeneous and heterogeneous electron transfer<ref name="h61a">Liquid error: wrong number of arguments (given 1, expected 2)</ref> showed that electron transfer occurring during a collision between a molecule and either another molecule or else an electrode surface occurs adiabatically on a continuous potential-energy surface, and that electron transfer can occur by either optical or thermal mechanisms with the corresponding rates being closely connected.<ref name="h67_">Liquid error: wrong number of arguments (given 1, expected 2)</ref>
[[File:Hush wiki Fig 1.png|thumb|Fig. 1. Electron transfer occurs between donor (D) and acceptor (A) species separated by distance ''R'' that may be found in many forms in both condensed phases and the gas phase. Internal structure, external structure, or chance collisions provide interconnection between the species. Upon electron transfer, the structure of the local chemical environments involving D and A change, as does the polarization these species induce on any surrounding media.]]
Figure 1 sketches the basic elements of adiabatic electron-transfer theory. Two chemical species (ions, molecules, polymers, protein cofactors, etc.) labelled D (for "donor") and A (for "acceptor") become a distance ''R'' apart, either through collisions, covalent bonding, location in a material, protein or polymer structure, etc. These species have different chemical bonding environments and they polarize any surrounding condensed media. A key feature is that both species must be able to sustain different charge (valence) states. Electron-transfer theories specify equations describing the rate of charge transfer processes that utilize these different charged states. All [[Electrochemistry|electrochemical reactions]] occur by this mechanism. Adiabatic electron-transfer theory stresses that intricately coupled to such charge transfer is the ability of any D-A system to absorb or emit light. Hence fundamental understanding of any electrochemical process demands simultaneous understanding of the optical processes that the system can undergo.
[[File:Hush wiki Fig 2.png|thumb|Fig. 2. When the donor species absorbs light energy, it goes into a high-energy excited state, generating significant changes to its local chemical environment and the polarization of its external environment. These environments facilitate coupling <math> V_{DA} </math> between the donor and acceptor, which drives photochemical charge separation with a rate given by Eqn. (3) in the weak-coupling limit. This rate is also dependent on the energy <math> \lambda </math> required to rearrange the atoms to the preferred local geometry and environment polarization of the charge-separated state D<sup>+</sup>-A<sup>−</sup> and the energy change <math> \Delta G_0 </math> associated with charge separation.]]
Figure 2 sketches what happens if light is absorbed by just one of the chemical species, taken to be the charge donor. This produces an excited state of the donor. As the donor and acceptor are close to each other and surrounding matter, they experience a coupling <math> V_{DA} </math>. If the free energy change <math> \Delta G_0 </math> is favorable, this coupling facilitates primary charge separation to produce D<sup>+</sup>-A<sup>−</sup> ,[https://ift.tt/3aDOjYu] producing charged species. In this way, solar energy is captured and converted to electrical energy. This process is typical of [[photosynthesis|natural photosynthesis]] as well as modern [[Organic solar cell|organic photovoltaic]] and [[artificial photosynthesis]] solar-energy capture devices.<ref name="whpchov86">Liquid error: wrong number of arguments (given 1, expected 2)</ref> The inverse of this process is also used to make organic light-emitting diodes ([[OLED]]s).
[[File:Hush wiki Fig 3.png|thumb|Fig. 3. Light energy is absorbed by the donor and acceptor, initiating intervalence charge transfer to directly convert solar energy into electrical energy as D<sup>+</sup>-A<sup>−</sup>. In the weak-coupling limit, the coupling <math> V_{DA} </math>, reorganization energy <math> \lambda </math>, and the free energy change <math> \Delta G_0 </math> control the rate of light absorption (and hence charge separation) via Eqn. (1).]]
Unifying standard electrochemical electron-transfer processes with this type of solar energy harvesting, adiabatic electron-transfer theory also depicts a third application in which the donor and acceptor are both involved in light absorption, as sketched in Figure 3. Here, light absorption directly leads to charge separation D<sup>+</sup>-A<sup>−</sup>. Hush's theory for this process<ref name="h67_"/> considers the donor-acceptor coupling <math> V_{DA} </math>, the energy <math> \lambda </math> required to rearrange the atoms from their initial geometry to the preferred local geometry and environment polarization of the charge-separated state, and the energy change <math> \Delta G_0 </math> associated with charge separation. In the weak-coupling limit ( <math> 4V_{DA}^2/\lambda^2 \ll 1 </math>), Hush showed<ref name="h67_"/> that the rate of light absorption (and hence charge separation) is given from the [[Einstein coefficients|Einstein equation]] by
:<math> k \propto \frac {V_{DA}^2 R^2}{\lambda + \Delta G_0}. </math> … (1)
This theory explained<ref name="h67_"/> how the worlds first modern synthetic dye, [[Prussian blue]] absorbes light, creating<ref name="nit97">Liquid error: wrong number of arguments (given 1, expected 2)</ref>
<ref name="g79">Liquid error: wrong number of arguments (given 1, expected 2)</ref><ref name="srlk03">Liquid error: wrong number of arguments (given 1, expected 2)</ref>
<ref name="nwllz06">Liquid error: wrong number of arguments (given 1, expected 2)</ref><ref name="rs08">Liquid error: wrong number of arguments (given 1, expected 2)</ref> the field of [[Intervalence charge transfer| intervalence charge transfer spectroscopy]].
Hush's theory also provides theoretical underpinning for the [[Inner sphere electron transfer|Robin-Day classification system]]<ref name="rd67">Liquid error: wrong number of arguments (given 1, expected 2)</ref> for mixed-valence systems. [[Inner sphere electron transfer|Mixed valence]] is widespread in chemistry, from superconductors to minerals, magnetic molecular clusters and enzymes. It occurs when the same chemical species is found in two formally different oxidation states in the same system.<ref name="dhc08">Liquid error: wrong number of arguments (given 1, expected 2)</ref>
The synthesis of the mixed-valence [[Creutz–Taube complex|Creutz-Taube ion]], an event leading significantly to the award of the [https://ift.tt/2Q1ahg3 1983 Nobel Prize in Chemistry] to [[Henry Taube]], demonstrated the successfulness of adiabatic electron-transfer theory. In this molecule, the coupling <math> V_{DA} </math> is not small, delivering unprecedented chemical phenomena in which charge is not localized on just one chemical species but is shared quantum mechanically between two, presenting classically forbidden half-integral valence states. Hush showed<ref name="h75">Liquid error: wrong number of arguments (given 1, expected 2)</ref> that the critical requirement for this phenomenon is
:<math> \frac {2|J_{DA}|} {\lambda} \ge 1. </math> … (2)
Adiabatic electron-transfer theory stems from [[Fritz London|London's]] approach to charge-transfer and indeed general chemical reactions<ref name="l32">Liquid error: wrong number of arguments (given 1, expected 2)</ref> applied by Hush using parabolic potential-energy surfaces.<ref name="h53">Liquid error: wrong number of arguments (given 1, expected 2)</ref><ref name="h58_">Liquid error: wrong number of arguments (given 1, expected 2)</ref> Hush himself has carried out many theoretical and experimental studies of mixed valence complexes and long range electron transfer in biological systems. Hush's quantum-electronic adiabatic approach to electron transfer was unique; directly connecting with the [[Quantum chemistry|Quantum Chemistry]] concepts of [[Robert S. Mulliken|Mulliken]], it forms the basis of all modern computational approaches to modeling electron transfer.<ref name="ktu97">Liquid error: wrong number of arguments (given 1, expected 2)</ref><ref name="ku98">Liquid error: wrong number of arguments (given 1, expected 2)</ref><ref name="d80">Liquid error: wrong number of arguments (given 1, expected 2)</ref><ref name="cn96">Liquid error: wrong number of arguments (given 1, expected 2)</ref> Its essential feature is that electron transfer can never be regarded as an "instantaneous transition"; instead, the electron is partially transferred at all molecular geometries, with the extent of the transfer being a critical quantum descriptor of all thermal, tunneling, and spectroscopic processes. It also leads seamlessly<ref name="rh17">Liquid error: wrong number of arguments (given 1, expected 2)</ref> to understanding electron-transfer transition-state spectroscopy pioneered by [[Ahmed Zewail|Zewail]].
In adiabatic electron-transfer theory, the ratio <math> 2V_{DA}/\lambda </math> is of central importance. In the very strong coupling limit when Eqn. (2) is satisfied, intrinsically quantum molecules like the Crautz-Taube ion result. Most intervalence spectroscopy occurs in the weak-coupling limit described by Eqn. (1), however. In both natural photosynthesis and in artificial solar-energy capture devices, <math> 2V{_DA}/\lambda </math> is maximized by minimiming <math> \lambda </math> through use of large molecules like chlorophylls, pentacenes, and conjugated polymers. The coupling <math> V_{DA} </math> can be controlled by controlling the distance ''R'' at which charge transfer occurs- the coupling typically decreases exponentially with distance. When electron transfer occurs during collisions of the D and A species, the coupling is typically large and the "adiabatic" limit applies in which rate constants are given by [[transition state theory]].<ref name="h61a"/> However, in biological applications as well as modern organic conductors and other device materials, ''R'' is externally constrained and so the coupling set at low or high values. In these situations, weak-coupling scenarios often become critical.
In the weak-coupling ("non-adiabatic") limit, the activation energy for electron transfer is given by the expression derived independently by [[Ryogo Kubo|Kubo]] and Toyozawa<ref name="kt55">Liquid error: wrong number of arguments (given 1, expected 2)</ref> and by Hush.<ref name="h58_"/>
Using adiabatic electron-transfer theory,<ref name="ld60_english">Liquid error: wrong number of arguments (given 1, expected 2)</ref>
in this limit [[Veniamin Levich|Levich]] and [[Revaz Dogonadze|Dogonadze]] then determined the electron-tunneling probability to express the rate constant for thermal reactions as<ref name="ld59_english">Liquid error: wrong number of arguments (given 1, expected 2)</ref>
:<math> k= \frac{2 \pi V_{DA}^2} {\hbar (4\pi \lambda k_{\beta} T)^{1/2} } \exp \frac{-(\Delta G_0+\lambda)^2} {4\lambda k_{\beta}T} </math>. … (3)
This approach is widely applicable to long-range ground-state intramolecular electron transfer, electron transfer in biology, and electron transfer in conducting materials. It also typically controls the rate of charge separation in the excited-state photochemical application described in Figure 2 and related problems.
[[Rudolph A. Marcus|Marcus]] showed<ref name="m56a">Liquid error: wrong number of arguments (given 1, expected 2)</ref> that the activation energy in Eqn. (3) reduces to <math> \lambda/4 </math> in the case of symmetric reactions with <math> \Delta G_0 = 0 </math>. In that work,<ref name="m56a"/> he also derived what is the standard expression for the solvent contribution to the reorganization energy, making the theory readily applicable to practical problems. Use of this solvation description (instead<ref name="h61a"/> of the form that Hush originally proposed<ref name="h58_"/>) in approaches spanning the adiabatic and non-adiabatic limits is often termed "Marcus-Hush Theory".<ref name="ku98"/><ref name="d80"/><ref name="schmickler"></ref><ref name="eb76">Liquid error: wrong number of arguments (given 1, expected 2)</ref> These and other contributions, including the widespread demonstration of the usefulness of Eqn. (3),<ref name="ms85">Liquid error: wrong number of arguments (given 1, expected 2)</ref> led to the award of the [https://ift.tt/2Q5HOWz 1992 Nobel Prize in Chemistry] to Marcus.
Adiabatic electron-transfer theory is often also widely applied [https://ift.tt/2v9CAlm] in [[Molecular Electronics]]. In recent years it has been generalized to arbitrary chemical reactions, providing a single conceptual basis covering many different aspects of chemical research.<ref name="rmmh15a">Liquid error: wrong number of arguments (given 1, expected 2)</ref> In particular, this reconnects adiabatic electron-transfer theory with its roots in proton-transfer theory<ref name="hp35"></ref>
and hydrogen-atom transfer,<ref name="h53"/> leading back to [[Fritz London|London's]] theory of general chemical reactions.<ref name="l32"/> In this approach, most chemical processes can be depicted in terms of the three critical parameters <math> V_{DA} </math>, <math> \lambda </math> and <math> \Delta G_0 </math>, with for example the ''resonance energy'' that makes benzene and all aromatic compounds unique being nothing other than <math> V_{DA} </math>.<ref name="rmmh15a"/>
This approach also leads to a simple explanation in terms of the orbital Rydbergization processes discovered by [[Robert S. Mulliken|Mulliken]] as to why first-row elements like nitrogen have bond angles around the tetrahedral angles while later-row elements have very much larger angles.<ref name="rmmh15b">Liquid error: wrong number of arguments (given 1, expected 2)</ref> Adiabatic electron-transfer theory applied in a simple one-dimensional form also provides analytical or numerically exact solutions for chemical processes not involving conical intersections, providing critical testbeds for examining failure of the [[Born–Oppenheimer approximation|Born-Oppenheimer]] approximation that is fundamental to chemical understanding.<ref name="rmmh15c">Liquid error: wrong number of arguments (given 1, expected 2)</ref> Similarly, it provides a basis for classifying the usefulness of general chemical reactions for applications as qubits in [[Quantum information science|quantum information]] processors.<ref name="mmhr11">Liquid error: wrong number of arguments (given 1, expected 2)</ref>
==References==
[[Category:Physical chemistry]]
[[Category:Reaction mechanisms]]
According to his Royal Society election citation,<ref></ref> [[Noel Hush]]'s research in the area of homogeneous and heterogeneous electron transfer<ref name="h61a">Liquid error: wrong number of arguments (given 1, expected 2)</ref> showed that electron transfer occurring during a collision between a molecule and either another molecule or else an electrode surface occurs adiabatically on a continuous potential-energy surface, and that electron transfer can occur by either optical or thermal mechanisms with the corresponding rates being closely connected.<ref name="h67_">Liquid error: wrong number of arguments (given 1, expected 2)</ref>
[[File:Hush wiki Fig 1.png|thumb|Fig. 1. Electron transfer occurs between donor (D) and acceptor (A) species separated by distance ''R'' that may be found in many forms in both condensed phases and the gas phase. Internal structure, external structure, or chance collisions provide interconnection between the species. Upon electron transfer, the structure of the local chemical environments involving D and A change, as does the polarization these species induce on any surrounding media.]]
Figure 1 sketches the basic elements of adiabatic electron-transfer theory. Two chemical species (ions, molecules, polymers, protein cofactors, etc.) labelled D (for "donor") and A (for "acceptor") become a distance ''R'' apart, either through collisions, covalent bonding, location in a material, protein or polymer structure, etc. These species have different chemical bonding environments and they polarize any surrounding condensed media. A key feature is that both species must be able to sustain different charge (valence) states. Electron-transfer theories specify equations describing the rate of charge transfer processes that utilize these different charged states. All [[Electrochemistry|electrochemical reactions]] occur by this mechanism. Adiabatic electron-transfer theory stresses that intricately coupled to such charge transfer is the ability of any D-A system to absorb or emit light. Hence fundamental understanding of any electrochemical process demands simultaneous understanding of the optical processes that the system can undergo.
[[File:Hush wiki Fig 2.png|thumb|Fig. 2. When the donor species absorbs light energy, it goes into a high-energy excited state, generating significant changes to its local chemical environment and the polarization of its external environment. These environments facilitate coupling <math> V_{DA} </math> between the donor and acceptor, which drives photochemical charge separation with a rate given by Eqn. (3) in the weak-coupling limit. This rate is also dependent on the energy <math> \lambda </math> required to rearrange the atoms to the preferred local geometry and environment polarization of the charge-separated state D<sup>+</sup>-A<sup>−</sup> and the energy change <math> \Delta G_0 </math> associated with charge separation.]]
Figure 2 sketches what happens if light is absorbed by just one of the chemical species, taken to be the charge donor. This produces an excited state of the donor. As the donor and acceptor are close to each other and surrounding matter, they experience a coupling <math> V_{DA} </math>. If the free energy change <math> \Delta G_0 </math> is favorable, this coupling facilitates primary charge separation to produce D<sup>+</sup>-A<sup>−</sup> ,[https://ift.tt/3aDOjYu] producing charged species. In this way, solar energy is captured and converted to electrical energy. This process is typical of [[photosynthesis|natural photosynthesis]] as well as modern [[Organic solar cell|organic photovoltaic]] and [[artificial photosynthesis]] solar-energy capture devices.<ref name="whpchov86">Liquid error: wrong number of arguments (given 1, expected 2)</ref> The inverse of this process is also used to make organic light-emitting diodes ([[OLED]]s).
[[File:Hush wiki Fig 3.png|thumb|Fig. 3. Light energy is absorbed by the donor and acceptor, initiating intervalence charge transfer to directly convert solar energy into electrical energy as D<sup>+</sup>-A<sup>−</sup>. In the weak-coupling limit, the coupling <math> V_{DA} </math>, reorganization energy <math> \lambda </math>, and the free energy change <math> \Delta G_0 </math> control the rate of light absorption (and hence charge separation) via Eqn. (1).]]
Unifying standard electrochemical electron-transfer processes with this type of solar energy harvesting, adiabatic electron-transfer theory also depicts a third application in which the donor and acceptor are both involved in light absorption, as sketched in Figure 3. Here, light absorption directly leads to charge separation D<sup>+</sup>-A<sup>−</sup>. Hush's theory for this process<ref name="h67_"/> considers the donor-acceptor coupling <math> V_{DA} </math>, the energy <math> \lambda </math> required to rearrange the atoms from their initial geometry to the preferred local geometry and environment polarization of the charge-separated state, and the energy change <math> \Delta G_0 </math> associated with charge separation. In the weak-coupling limit ( <math> 4V_{DA}^2/\lambda^2 \ll 1 </math>), Hush showed<ref name="h67_"/> that the rate of light absorption (and hence charge separation) is given from the [[Einstein coefficients|Einstein equation]] by
:<math> k \propto \frac {V_{DA}^2 R^2}{\lambda + \Delta G_0}. </math> … (1)
This theory explained<ref name="h67_"/> how the worlds first modern synthetic dye, [[Prussian blue]] absorbes light, creating<ref name="nit97">Liquid error: wrong number of arguments (given 1, expected 2)</ref>
<ref name="g79">Liquid error: wrong number of arguments (given 1, expected 2)</ref><ref name="srlk03">Liquid error: wrong number of arguments (given 1, expected 2)</ref>
<ref name="nwllz06">Liquid error: wrong number of arguments (given 1, expected 2)</ref><ref name="rs08">Liquid error: wrong number of arguments (given 1, expected 2)</ref> the field of [[Intervalence charge transfer| intervalence charge transfer spectroscopy]].
Hush's theory also provides theoretical underpinning for the [[Inner sphere electron transfer|Robin-Day classification system]]<ref name="rd67">Liquid error: wrong number of arguments (given 1, expected 2)</ref> for mixed-valence systems. [[Inner sphere electron transfer|Mixed valence]] is widespread in chemistry, from superconductors to minerals, magnetic molecular clusters and enzymes. It occurs when the same chemical species is found in two formally different oxidation states in the same system.<ref name="dhc08">Liquid error: wrong number of arguments (given 1, expected 2)</ref>
The synthesis of the mixed-valence [[Creutz–Taube complex|Creutz-Taube ion]], an event leading significantly to the award of the [https://ift.tt/2Q1ahg3 1983 Nobel Prize in Chemistry] to [[Henry Taube]], demonstrated the successfulness of adiabatic electron-transfer theory. In this molecule, the coupling <math> V_{DA} </math> is not small, delivering unprecedented chemical phenomena in which charge is not localized on just one chemical species but is shared quantum mechanically between two, presenting classically forbidden half-integral valence states. Hush showed<ref name="h75">Liquid error: wrong number of arguments (given 1, expected 2)</ref> that the critical requirement for this phenomenon is
:<math> \frac {2|J_{DA}|} {\lambda} \ge 1. </math> … (2)
Adiabatic electron-transfer theory stems from [[Fritz London|London's]] approach to charge-transfer and indeed general chemical reactions<ref name="l32">Liquid error: wrong number of arguments (given 1, expected 2)</ref> applied by Hush using parabolic potential-energy surfaces.<ref name="h53">Liquid error: wrong number of arguments (given 1, expected 2)</ref><ref name="h58_">Liquid error: wrong number of arguments (given 1, expected 2)</ref> Hush himself has carried out many theoretical and experimental studies of mixed valence complexes and long range electron transfer in biological systems. Hush's quantum-electronic adiabatic approach to electron transfer was unique; directly connecting with the [[Quantum chemistry|Quantum Chemistry]] concepts of [[Robert S. Mulliken|Mulliken]], it forms the basis of all modern computational approaches to modeling electron transfer.<ref name="ktu97">Liquid error: wrong number of arguments (given 1, expected 2)</ref><ref name="ku98">Liquid error: wrong number of arguments (given 1, expected 2)</ref><ref name="d80">Liquid error: wrong number of arguments (given 1, expected 2)</ref><ref name="cn96">Liquid error: wrong number of arguments (given 1, expected 2)</ref> Its essential feature is that electron transfer can never be regarded as an "instantaneous transition"; instead, the electron is partially transferred at all molecular geometries, with the extent of the transfer being a critical quantum descriptor of all thermal, tunneling, and spectroscopic processes. It also leads seamlessly<ref name="rh17">Liquid error: wrong number of arguments (given 1, expected 2)</ref> to understanding electron-transfer transition-state spectroscopy pioneered by [[Ahmed Zewail|Zewail]].
In adiabatic electron-transfer theory, the ratio <math> 2V_{DA}/\lambda </math> is of central importance. In the very strong coupling limit when Eqn. (2) is satisfied, intrinsically quantum molecules like the Crautz-Taube ion result. Most intervalence spectroscopy occurs in the weak-coupling limit described by Eqn. (1), however. In both natural photosynthesis and in artificial solar-energy capture devices, <math> 2V{_DA}/\lambda </math> is maximized by minimiming <math> \lambda </math> through use of large molecules like chlorophylls, pentacenes, and conjugated polymers. The coupling <math> V_{DA} </math> can be controlled by controlling the distance ''R'' at which charge transfer occurs- the coupling typically decreases exponentially with distance. When electron transfer occurs during collisions of the D and A species, the coupling is typically large and the "adiabatic" limit applies in which rate constants are given by [[transition state theory]].<ref name="h61a"/> However, in biological applications as well as modern organic conductors and other device materials, ''R'' is externally constrained and so the coupling set at low or high values. In these situations, weak-coupling scenarios often become critical.
In the weak-coupling ("non-adiabatic") limit, the activation energy for electron transfer is given by the expression derived independently by [[Ryogo Kubo|Kubo]] and Toyozawa<ref name="kt55">Liquid error: wrong number of arguments (given 1, expected 2)</ref> and by Hush.<ref name="h58_"/>
Using adiabatic electron-transfer theory,<ref name="ld60_english">Liquid error: wrong number of arguments (given 1, expected 2)</ref>
in this limit [[Veniamin Levich|Levich]] and [[Revaz Dogonadze|Dogonadze]] then determined the electron-tunneling probability to express the rate constant for thermal reactions as<ref name="ld59_english">Liquid error: wrong number of arguments (given 1, expected 2)</ref>
:<math> k= \frac{2 \pi V_{DA}^2} {\hbar (4\pi \lambda k_{\beta} T)^{1/2} } \exp \frac{-(\Delta G_0+\lambda)^2} {4\lambda k_{\beta}T} </math>. … (3)
This approach is widely applicable to long-range ground-state intramolecular electron transfer, electron transfer in biology, and electron transfer in conducting materials. It also typically controls the rate of charge separation in the excited-state photochemical application described in Figure 2 and related problems.
[[Rudolph A. Marcus|Marcus]] showed<ref name="m56a">Liquid error: wrong number of arguments (given 1, expected 2)</ref> that the activation energy in Eqn. (3) reduces to <math> \lambda/4 </math> in the case of symmetric reactions with <math> \Delta G_0 = 0 </math>. In that work,<ref name="m56a"/> he also derived what is the standard expression for the solvent contribution to the reorganization energy, making the theory readily applicable to practical problems. Use of this solvation description (instead<ref name="h61a"/> of the form that Hush originally proposed<ref name="h58_"/>) in approaches spanning the adiabatic and non-adiabatic limits is often termed "Marcus-Hush Theory".<ref name="ku98"/><ref name="d80"/><ref name="schmickler"></ref><ref name="eb76">Liquid error: wrong number of arguments (given 1, expected 2)</ref> These and other contributions, including the widespread demonstration of the usefulness of Eqn. (3),<ref name="ms85">Liquid error: wrong number of arguments (given 1, expected 2)</ref> led to the award of the [https://ift.tt/2Q5HOWz 1992 Nobel Prize in Chemistry] to Marcus.
Adiabatic electron-transfer theory is often also widely applied [https://ift.tt/2v9CAlm] in [[Molecular Electronics]]. In recent years it has been generalized to arbitrary chemical reactions, providing a single conceptual basis covering many different aspects of chemical research.<ref name="rmmh15a">Liquid error: wrong number of arguments (given 1, expected 2)</ref> In particular, this reconnects adiabatic electron-transfer theory with its roots in proton-transfer theory<ref name="hp35"></ref>
and hydrogen-atom transfer,<ref name="h53"/> leading back to [[Fritz London|London's]] theory of general chemical reactions.<ref name="l32"/> In this approach, most chemical processes can be depicted in terms of the three critical parameters <math> V_{DA} </math>, <math> \lambda </math> and <math> \Delta G_0 </math>, with for example the ''resonance energy'' that makes benzene and all aromatic compounds unique being nothing other than <math> V_{DA} </math>.<ref name="rmmh15a"/>
This approach also leads to a simple explanation in terms of the orbital Rydbergization processes discovered by [[Robert S. Mulliken|Mulliken]] as to why first-row elements like nitrogen have bond angles around the tetrahedral angles while later-row elements have very much larger angles.<ref name="rmmh15b">Liquid error: wrong number of arguments (given 1, expected 2)</ref> Adiabatic electron-transfer theory applied in a simple one-dimensional form also provides analytical or numerically exact solutions for chemical processes not involving conical intersections, providing critical testbeds for examining failure of the [[Born–Oppenheimer approximation|Born-Oppenheimer]] approximation that is fundamental to chemical understanding.<ref name="rmmh15c">Liquid error: wrong number of arguments (given 1, expected 2)</ref> Similarly, it provides a basis for classifying the usefulness of general chemical reactions for applications as qubits in [[Quantum information science|quantum information]] processors.<ref name="mmhr11">Liquid error: wrong number of arguments (given 1, expected 2)</ref>
==References==
[[Category:Physical chemistry]]
[[Category:Reaction mechanisms]]
March 11, 2020 at 06:00AM
