Marcus Theory and Reorganization Energy - Revision history

Cmditradmin: /* DFT-calculated reorganization energies */

2010-08-11T16:23:21Z

DFT-calculated reorganization energies

← Older revision		Revision as of 09:23, 11 August 2010
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	\| pentacene		\| pentacene
	\| 0.098 eV		\| 0.098 eV
	\| [<ref name="gruhn"></~~ref~~>]		\| [<ref name="gruhn"/>]
	\|-		\|-
	\| TPD		\| TPD

Cmditradmin: /* DFT-calculated reorganization energies */

2010-08-11T16:18:20Z

DFT-calculated reorganization energies

← Older revision		Revision as of 09:18, 11 August 2010
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	\| pentacene		\| pentacene
	\| 0.098 eV		\| 0.098 eV
	\| [<ref>~~JACS 124, 7918 (2002)~~</ref>]		\| [<ref name="gruhn"></ref>]
	\|-		\|-
	\| TPD		\| TPD

Cmditradmin: /* Gas UPS Measurements */

2010-08-11T16:17:51Z

Gas UPS Measurements

← Older revision		Revision as of 09:17, 11 August 2010
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	=== Gas UPS Measurements ===		=== Gas UPS Measurements ===

	[[Image:pentacene_GPUPS.png\|thumb\|400px\|UPS experimental vs simulated values for pentacene JACS 2002<ref> Nadine E. Gruhn,et al, "The Vibrational Reorganization Energy in Pentacene: Molecular Influences on Charge Transport" JACS 2002 124 (27), 7918-7919 {{Doi\|10.1021/ja0175892}}		[[Image:pentacene_GPUPS.png\|thumb\|400px\|UPS experimental vs simulated values for pentacene JACS 2002<ref name="gruhn"> Nadine E. Gruhn,et al, "The Vibrational Reorganization Energy in Pentacene: Molecular Influences on Charge Transport" JACS 2002 124 (27), 7918-7919 {{Doi\|10.1021/ja0175892}}
	</ref>]]		</ref>]]
	The [[gas phase UPS]] was used to measure pentacene. The experimental data shows good agreement with the simulation.		The [[gas phase UPS]] was used to measure pentacene. The experimental data shows good agreement with the simulation.

Cmditradmin: /* Gas UPS Measurements */

2010-08-11T16:14:42Z

Gas UPS Measurements

← Older revision		Revision as of 09:14, 11 August 2010
Line 54:		Line 54:
	=== Gas UPS Measurements ===		=== Gas UPS Measurements ===

	[[Image:pentacene_GPUPS.png\|thumb\|400px\|UPS experimental vs simulated values for pentacene JACS 2002<ref> Nadine E. Gruhn,et al, "The Vibrational Reorganization Energy in Pentacene: Molecular Influences on Charge Transport" ~~Journal of the American Chemical Society~~ 2002 124 (27), 7918-7919 {{Doi\|10.1021/ja0175892}}		[[Image:pentacene_GPUPS.png\|thumb\|400px\|UPS experimental vs simulated values for pentacene JACS 2002<ref> Nadine E. Gruhn,et al, "The Vibrational Reorganization Energy in Pentacene: Molecular Influences on Charge Transport" JACS 2002 124 (27), 7918-7919 {{Doi\|10.1021/ja0175892}}
	</ref>]]		</ref>]]
	The [[gas phase UPS]] was used to measure pentacene. The experimental data shows good agreement with the simulation.		The [[gas phase UPS]] was used to measure pentacene. The experimental data shows good agreement with the simulation.

Cmditradmin: /* Gas UPS Measurements */

2010-08-11T16:14:11Z

Gas UPS Measurements

← Older revision		Revision as of 09:14, 11 August 2010
Line 54:		Line 54:
	=== Gas UPS Measurements ===		=== Gas UPS Measurements ===

	[[Image:pentacene_GPUPS.png\|thumb\|400px\|UPS experimental vs simulated values for pentacene JACS 2002<ref> Nadine E. Gruhn,, ~~Demetrio A. da Silva Filho,, Tonja G. Bill,, Massimo Malagoli,, Veaceslav Coropceanu,, Antoine Kahn, and, Jean-Luc Brédas,~~ "The Vibrational Reorganization Energy in Pentacene: Molecular Influences on Charge Transport" Journal of the American Chemical Society 2002 124 (27), 7918-7919 {{Doi\|10.1021/ja0175892}}		[[Image:pentacene_GPUPS.png\|thumb\|400px\|UPS experimental vs simulated values for pentacene JACS 2002<ref> Nadine E. Gruhn,et al, "The Vibrational Reorganization Energy in Pentacene: Molecular Influences on Charge Transport" Journal of the American Chemical Society 2002 124 (27), 7918-7919 {{Doi\|10.1021/ja0175892}}
	</ref>]]		</ref>]]
	The [[gas phase UPS]] was used to measure pentacene. The experimental data shows good agreement with the simulation.		The [[gas phase UPS]] was used to measure pentacene. The experimental data shows good agreement with the simulation.

Cmditradmin: /* Gas UPS Measurements */

2010-08-11T16:12:31Z

Gas UPS Measurements

← Older revision		Revision as of 09:12, 11 August 2010
Line 54:		Line 54:
	=== Gas UPS Measurements ===		=== Gas UPS Measurements ===

	[[Image:pentacene_GPUPS.png\|thumb\|400px\|UPS experimental vs simulated values for pentacene JACS 2002<ref>~~JACS~~ 124, 7918 ~~(2002)~~</ref>]]		[[Image:pentacene_GPUPS.png\|thumb\|400px\|UPS experimental vs simulated values for pentacene JACS 2002<ref> Nadine E. Gruhn,, Demetrio A. da Silva Filho,, Tonja G. Bill,, Massimo Malagoli,, Veaceslav Coropceanu,, Antoine Kahn, and, Jean-Luc Brédas, "The Vibrational Reorganization Energy in Pentacene: Molecular Influences on Charge Transport" Journal of the American Chemical Society 2002 124 (27), 7918-7919 {{Doi\|10.1021/ja0175892}}
			</ref>]]
	The [[gas phase UPS]] was used to measure pentacene. The experimental data shows good agreement with the simulation.		The [[gas phase UPS]] was used to measure pentacene. The experimental data shows good agreement with the simulation.
	The resolution for gas phase UPS is smaller than .01 eV. The high resolution UPS view shows that the first ionization peak (taking an electron from the HOMO) has vibrations.		The resolution for gas phase UPS is smaller than .01 eV. The high resolution UPS view shows that the first ionization peak (taking an electron from the HOMO) has vibrations.

Cmditradmin: /* Limitations of Marcus theory */

2010-07-07T18:33:50Z

Limitations of Marcus theory

← Older revision		Revision as of 11:33, 7 July 2010
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	and		and

	:<math>S=\frac \lambda_1 \hbar\langle \omega_\upsilon\rangle\,\!</math> Marcus-Levich-Jortner electron transfer theory		:<math>S=\frac {\lambda_1} {\hbar\langle \omega_\upsilon\rangle}\,\!</math> Marcus-Levich-Jortner electron transfer theory

	When Marcus developed the theory 50 years ago he was looking at electron transfer reactions in solution in which case the “surrounding” was defined by the way the solvents arranged around the sites where electron transfer occurred. For example in organo-metallic systems with ruthenium 2 and ruthenium 3 there will be electron transfer in aqueous solution. There is an orientation of the water molecules surrounding the 2<sup>+</sup> ion that is different from the arrangement around the 3<sup>+</sup> ions. Rearrangement of the solvent involves rotations and translations that are very slow and involve smaller energies. Because these processes are slow its ok to treat them in a classical (simple) way. But intermolecular reorganization energy needs to be taken into account at the quantum level.		When Marcus developed the theory 50 years ago he was looking at electron transfer reactions in solution in which case the “surrounding” was defined by the way the solvents arranged around the sites where electron transfer occurred. For example in organo-metallic systems with ruthenium 2 and ruthenium 3 there will be electron transfer in aqueous solution. There is an orientation of the water molecules surrounding the 2<sup>+</sup> ion that is different from the arrangement around the 3<sup>+</sup> ions. Rearrangement of the solvent involves rotations and translations that are very slow and involve smaller energies. Because these processes are slow its ok to treat them in a classical (simple) way. But intermolecular reorganization energy needs to be taken into account at the quantum level.

Cmditradmin: /* Limitations of Marcus theory */

2010-07-07T18:33:12Z

Limitations of Marcus theory

← Older revision		Revision as of 11:33, 7 July 2010
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	:<math>k_{ET} = ( \frac {4 \pi^2} { h}) t^2 \left(\frac {1} {4\pi \lambda_s kT}\right)^{1/2} \sum_{\upsilon^\prime} exp(-S) \frac {S^{\upsilon^\prime}} {\upsilon^\prime !} exp \left(-\frac {(\Delta G^0 + \lambda_s + \upsilon^\prime \hbar \langle \omega_v \rangle)^2} {4\lambda_s kT} \right)\,\!</math>		:<math>k_{ET} = ( \frac {4 \pi^2} { h}) t^2 \left(\frac {1} {4\pi \lambda_s kT}\right)^{1/2} \sum_{\upsilon^\prime} exp(-S) \frac {S^{\upsilon^\prime}} {\upsilon^\prime !} exp \left(-\frac {(\Delta G^0 + \lambda_s + \upsilon^\prime \hbar \langle \omega_v \rangle)^2} {4\lambda_s kT} \right)\,\!</math>

	When Marcus developed the theory 50 years ago he was looking at electron transfer reactions in solution in which case the “surrounding” was defined by the way the solvents arranged around the sites where electron transfer occurred. For example in organo-metallic systems with ruthenium 2 and ruthenium 3 there will be electron transfer in aqueous solution. There is an orientation of the water molecules surrounding the 2<sup>+</sup> ion that is different from the arrangement around the 3<sup>+</sup> ions. Rearrangement of the solvent involves rotations and translations that are very slow and involve smaller energies. Because these processes are slow its ok to treat them in a classical (simple) way. But intermolecular reorganization energy needs to be taken into account at the quantum level.		and

			:<math>S=\frac \lambda_1 \hbar\langle \omega_\upsilon\rangle\,\!</math> Marcus-Levich-Jortner electron transfer theory

			When Marcus developed the theory 50 years ago he was looking at electron transfer reactions in solution in which case the “surrounding” was defined by the way the solvents arranged around the sites where electron transfer occurred. For example in organo-metallic systems with ruthenium 2 and ruthenium 3 there will be electron transfer in aqueous solution. There is an orientation of the water molecules surrounding the 2<sup>+</sup> ion that is different from the arrangement around the 3<sup>+</sup> ions. Rearrangement of the solvent involves rotations and translations that are very slow and involve smaller energies. Because these processes are slow its ok to treat them in a classical (simple) way. But intermolecular reorganization energy needs to be taken into account at the quantum level.

	== References ==		== References ==

Cmditradmin: /* Limitations of Marcus theory */

2010-07-07T18:30:58Z

Limitations of Marcus theory

← Older revision		Revision as of 11:30, 7 July 2010
Line 136:		Line 136:
	In order to determine if a molecule will have favorable transport properties in a device you would like to know how mobility changes going from low to high temperature when the material in a thin film or crystalline form. Marcus theory does allow you to do that. The electronic couple is derived for a single crystal structure but the Marcus equation doesn’t consider modifications in electronic coupling that occur with increasing temperature. The intermolecular component of reorganization energy (λ <sub>s</sub>)(s stands for surrounding) is treated in a purely classical way in Marcus theory.		In order to determine if a molecule will have favorable transport properties in a device you would like to know how mobility changes going from low to high temperature when the material in a thin film or crystalline form. Marcus theory does allow you to do that. The electronic couple is derived for a single crystal structure but the Marcus equation doesn’t consider modifications in electronic coupling that occur with increasing temperature. The intermolecular component of reorganization energy (λ <sub>s</sub>)(s stands for surrounding) is treated in a purely classical way in Marcus theory.

	:<math>k_{ET} = ( \frac {4 \pi^2} { h}) t^2 \left(\frac {1} {4\pi \lambda_s kT}\right)^{1/2} \sum_\upsilon \prime exp(-S) \frac {S^{\upsilon\prime}} {\upsilon \prime !} exp \left(-\frac {(\Delta G^0 + \lambda_s + \upsilon\prime \hbar \langle \omega_v \rangle)^2} {4\lambda_s kT} \right)\,\!</math>		:<math>k_{ET} = ( \frac {4 \pi^2} { h}) t^2 \left(\frac {1} {4\pi \lambda_s kT}\right)^{1/2} \sum_{\upsilon^\prime} exp(-S) \frac {S^{\upsilon^\prime}} {\upsilon^\prime !} exp \left(-\frac {(\Delta G^0 + \lambda_s + \upsilon^\prime \hbar \langle \omega_v \rangle)^2} {4\lambda_s kT} \right)\,\!</math>

	When Marcus developed the theory 50 years ago he was looking at electron transfer reactions in solution in which case the “surrounding” was defined by the way the solvents arranged around the sites where electron transfer occurred. For example in organo-metallic systems with ruthenium 2 and ruthenium 3 there will be electron transfer in aqueous solution. There is an orientation of the water molecules surrounding the 2<sup>+</sup> ion that is different from the arrangement around the 3<sup>+</sup> ions. Rearrangement of the solvent involves rotations and translations that are very slow and involve smaller energies. Because these processes are slow its ok to treat them in a classical (simple) way. But intermolecular reorganization energy needs to be taken into account at the quantum level.		When Marcus developed the theory 50 years ago he was looking at electron transfer reactions in solution in which case the “surrounding” was defined by the way the solvents arranged around the sites where electron transfer occurred. For example in organo-metallic systems with ruthenium 2 and ruthenium 3 there will be electron transfer in aqueous solution. There is an orientation of the water molecules surrounding the 2<sup>+</sup> ion that is different from the arrangement around the 3<sup>+</sup> ions. Rearrangement of the solvent involves rotations and translations that are very slow and involve smaller energies. Because these processes are slow its ok to treat them in a classical (simple) way. But intermolecular reorganization energy needs to be taken into account at the quantum level.

Cmditradmin: /* Limitations of Marcus theory */

2010-07-07T18:30:14Z

Limitations of Marcus theory

← Older revision		Revision as of 11:30, 7 July 2010
Line 136:		Line 136:
	In order to determine if a molecule will have favorable transport properties in a device you would like to know how mobility changes going from low to high temperature when the material in a thin film or crystalline form. Marcus theory does allow you to do that. The electronic couple is derived for a single crystal structure but the Marcus equation doesn’t consider modifications in electronic coupling that occur with increasing temperature. The intermolecular component of reorganization energy (λ <sub>s</sub>)(s stands for surrounding) is treated in a purely classical way in Marcus theory.		In order to determine if a molecule will have favorable transport properties in a device you would like to know how mobility changes going from low to high temperature when the material in a thin film or crystalline form. Marcus theory does allow you to do that. The electronic couple is derived for a single crystal structure but the Marcus equation doesn’t consider modifications in electronic coupling that occur with increasing temperature. The intermolecular component of reorganization energy (λ <sub>s</sub>)(s stands for surrounding) is treated in a purely classical way in Marcus theory.

	:<math>k_{ET} = ( \frac {4 \pi^2} { h}) t^2 \left(\frac {1} {4\pi \lambda_s kT}\right)^1/2 \sum_\upsilon \prime exp(-S) \frac {S^\upsilon\prime} {\upsilon \prime !} exp \left(-\frac {(\Delta G^0 + \lambda_s + \upsilon\prime \hbar \langle \omega_v \rangle)^2} {4\lambda_s kT} \right)\,\!</math>		:<math>k_{ET} = ( \frac {4 \pi^2} { h}) t^2 \left(\frac {1} {4\pi \lambda_s kT}\right)^{1/2} \sum_\upsilon \prime exp(-S) \frac {S^{\upsilon\prime}} {\upsilon \prime !} exp \left(-\frac {(\Delta G^0 + \lambda_s + \upsilon\prime \hbar \langle \omega_v \rangle)^2} {4\lambda_s kT} \right)\,\!</math>

	When Marcus developed the theory 50 years ago he was looking at electron transfer reactions in solution in which case the “surrounding” was defined by the way the solvents arranged around the sites where electron transfer occurred. For example in organo-metallic systems with ruthenium 2 and ruthenium 3 there will be electron transfer in aqueous solution. There is an orientation of the water molecules surrounding the 2<sup>+</sup> ion that is different from the arrangement around the 3<sup>+</sup> ions. Rearrangement of the solvent involves rotations and translations that are very slow and involve smaller energies. Because these processes are slow its ok to treat them in a classical (simple) way. But intermolecular reorganization energy needs to be taken into account at the quantum level.		When Marcus developed the theory 50 years ago he was looking at electron transfer reactions in solution in which case the “surrounding” was defined by the way the solvents arranged around the sites where electron transfer occurred. For example in organo-metallic systems with ruthenium 2 and ruthenium 3 there will be electron transfer in aqueous solution. There is an orientation of the water molecules surrounding the 2<sup>+</sup> ion that is different from the arrangement around the 3<sup>+</sup> ions. Rearrangement of the solvent involves rotations and translations that are very slow and involve smaller energies. Because these processes are slow its ok to treat them in a classical (simple) way. But intermolecular reorganization energy needs to be taken into account at the quantum level.