Electronic States vs Molecular Levels - Revision history

Cmditradmin at 19:32, 29 December 2009

2009-12-29T19:32:07Z

← Older revision		Revision as of 12:32, 29 December 2009
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			[[category:electronic band structure]]
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Cmditradmin at 21:06, 7 December 2009

2009-12-07T21:06:10Z

← Older revision		Revision as of 14:06, 7 December 2009
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	The literature can be confusing in using the terminology of electronic states vs electrical levels.		The literature can be confusing in using the terminology of electronic states vs electrical levels.

	'''Molecular level''' is a '''one electron''' ~~wavefunction~~ which is by definition a molecular orbital. Molecular levels corresponds to molecular orbitals (HOMO, LUMO etc).		'''Molecular level''' is a '''one electron''' wave function which is by definition a molecular orbital. Molecular levels corresponds to molecular orbitals (HOMO, LUMO etc).

	'''Molecular states''' (which is what you can observe) is a ~~wavefunction~~ that results from '''all the electrons''' in the molecule.		'''Molecular states''' (which is what you can observe) is a wave function that results from '''all the electrons''' in the molecule.
	=== Point Groups and symmetry ===		=== Point Groups and symmetry ===
	[[Image:C2h_pointgroup.jpg\|thumb\|300px\|Hexatriene C<sub>2h</sub> point group]]		[[Image:C2h_pointgroup.jpg\|thumb\|300px\|Hexatriene C<sub>2h</sub> point group]]
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	The electronic configuration is shown with six molecular orbitals, three of which on the π level are fully occupied. Another configuration in which individual electrons move up to the π* level are called '''singly excited'''. If two electrons are elevated from occupied levels into unoccupied levels these are called '''doubly excited''' configurations. The way electrons fill into the orbitals corresponds to electronic configurations.		The electronic configuration is shown with six molecular orbitals, three of which on the π level are fully occupied. Another configuration in which individual electrons move up to the π* level are called '''singly excited'''. If two electrons are elevated from occupied levels into unoccupied levels these are called '''doubly excited''' configurations. The way electrons fill into the orbitals corresponds to electronic configurations.

	The ~~wavefunctions~~ can be classified according their symmetry. The lowest level is the fully bonding an is unsymmetrical; it is labeled '''ungerade''' (u- german for odd). The next level up has a node in the middle and it is symmetrical and is labeled '''gerade''' (g - german for even). In π conjugated systems molecular orbitals alternative between gerade and ungerade with each level.		The wave functions can be classified according their symmetry. The lowest level is the fully bonding an is unsymmetrical; it is labeled '''ungerade''' (u- german for odd). The next level up has a node in the middle and it is symmetrical and is labeled '''gerade''' (g - german for even). In π conjugated systems molecular orbitals alternative between gerade and ungerade with each level.

	=== The Ground State ===		=== The Ground State ===

Cmditradmin at 21:56, 15 September 2009

2009-09-15T21:56:27Z

← Older revision		Revision as of 14:56, 15 September 2009
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			The literature can be confusing in using the terminology of electronic states vs electrical levels.

	The literature can be confusing in using the terminology of electronic states vs electrical levels.		'''Molecular level''' is a '''one electron''' wavefunction which is by definition a molecular orbital. Molecular levels corresponds to molecular orbitals (HOMO, LUMO etc).

			'''Molecular states''' (which is what you can observe) is a wavefunction that results from '''all the electrons''' in the molecule.
	=== Point Groups and symmetry ===		=== Point Groups and symmetry ===
	[[Image:C2h_pointgroup.jpg\|thumb\|300px\|Hexatriene C<sub>2h</sub> point group]]		[[Image:C2h_pointgroup.jpg\|thumb\|300px\|Hexatriene C<sub>2h</sub> point group]]
	There is always an identity symmetry (E). The hexatriene molecule is symmetrical around the C<sub>2</sub> axis. The C<sub>2</sub> axis is perpendicular from the plane of the molecule. A rotation of 180 degrees brings the same structure. The σ<sub> h</sub> denotes symmetry above and below the plane, there must be the same electronic density above the plane as below. There is also an inversion symmetry (i) where the C<sub>2</sub> axis meets the plane. These together have a point group called C<sub>2h</sub>.		There is always an identity symmetry (E). The hexatriene molecule is symmetrical around the C<sub>2</sub> axis. The C<sub>2</sub> axis is perpendicular from the plane of the molecule. A rotation of 180 degrees brings the same structure. The σ<sub> h</sub> denotes symmetry above and below the plane, there must be the same electronic density above the plane as below. There is also an inversion symmetry (i) where the C<sub>2</sub> axis meets the plane. These together have a point group called C<sub>2h</sub>.

	~~'''Molecular level''' is a '''one electron''' wavefunction which is by definition a molecular orbital. Molecular levels corresponds to molecular orbitals (HOMO, LUMO etc).~~

	~~'''Molecular states''' (which is what you can observe) is a wavefunction that results from '''all the electrons''' in the molecule.~~
	<br clear='all'>		<br clear='all'>
	[[Image:sixMO_config.JPG\|thumb\|300px\|Electronic configuration and molecular orbitals for hexatriene]]		[[Image:sixMO_config.JPG\|thumb\|300px\|Electronic configuration and molecular orbitals for hexatriene]]

Cmditradmin: /* 2Ag excited state */

2009-08-31T20:55:52Z

2Ag excited state

← Older revision		Revision as of 13:55, 31 August 2009
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	As long as they have the same symmetries they can mix. These three configurations have approximately the same energies so they can mix strongly. They are one photon forbidden (but two photon allowed). This results in a 2A<sub>g</sub> state that is energetically lower than the 1B<sub>u</sub> state, thus it should be considered the S<sub>1</sub> state.		As long as they have the same symmetries they can mix. These three configurations have approximately the same energies so they can mix strongly. They are one photon forbidden (but two photon allowed). This results in a 2A<sub>g</sub> state that is energetically lower than the 1B<sub>u</sub> state, thus it should be considered the S<sub>1</sub> state.
	:<math>E 2 A_g < E 1B_u \,\!</math>		:<math>E 2 A_g < E 1B_u \,\!</math>
	:<math>S_1 \quad S_2\,\!</math>		:<math>S_1 \quad \quad \quad S_2\,\!</math>

Cmditradmin: /* 2Ag excited state */

2009-08-31T20:55:37Z

2Ag excited state

← Older revision		Revision as of 13:55, 31 August 2009
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	As long as they have the same symmetries they can mix. These three configurations have approximately the same energies so they can mix strongly. They are one photon forbidden (but two photon allowed). This results in a 2A<sub>g</sub> state that is energetically lower than the 1B<sub>u</sub> state, thus it should be considered the S<sub>1</sub> state.		As long as they have the same symmetries they can mix. These three configurations have approximately the same energies so they can mix strongly. They are one photon forbidden (but two photon allowed). This results in a 2A<sub>g</sub> state that is energetically lower than the 1B<sub>u</sub> state, thus it should be considered the S<sub>1</sub> state.
	:<math>~~\begin {gather}~~		:<math>E 2 A_g < E 1B_u \,\!</math>
	E 2 A_g < E 1B_u \\		:<math>S_1 \quad S_2\,\!</math>
	S_1 \quad S_2
	~~\end{gather}~~
	\,\!</math>
	<br clear='all'>		<br clear='all'>

Cmditradmin: /* 2Ag excited state */

2009-08-31T20:55:00Z

2Ag excited state

← Older revision		Revision as of 13:55, 31 August 2009
Line 51:		Line 51:

	As long as they have the same symmetries they can mix. These three configurations have approximately the same energies so they can mix strongly. They are one photon forbidden (but two photon allowed). This results in a 2A<sub>g</sub> state that is energetically lower than the 1B<sub>u</sub> state, thus it should be considered the S<sub>1</sub> state.		As long as they have the same symmetries they can mix. These three configurations have approximately the same energies so they can mix strongly. They are one photon forbidden (but two photon allowed). This results in a 2A<sub>g</sub> state that is energetically lower than the 1B<sub>u</sub> state, thus it should be considered the S<sub>1</sub> state.
	:<math>\begin {~~multline~~}		:<math>\begin {gather}
	E 2 A_g < E 1B_u \\		E 2 A_g < E 1B_u \\
	S_1 \quad S_2		S_1 \quad S_2
	\end{~~multline~~}		\end{gather}
	\,\!</math>		\,\!</math>
	<br clear='all'>		<br clear='all'>

Cmditradmin: /* 2Ag excited state */

2009-08-31T20:54:07Z

2Ag excited state

← Older revision		Revision as of 13:54, 31 August 2009
Line 51:		Line 51:

	As long as they have the same symmetries they can mix. These three configurations have approximately the same energies so they can mix strongly. They are one photon forbidden (but two photon allowed). This results in a 2A<sub>g</sub> state that is energetically lower than the 1B<sub>u</sub> state, thus it should be considered the S<sub>1</sub> state.		As long as they have the same symmetries they can mix. These three configurations have approximately the same energies so they can mix strongly. They are one photon forbidden (but two photon allowed). This results in a 2A<sub>g</sub> state that is energetically lower than the 1B<sub>u</sub> state, thus it should be considered the S<sub>1</sub> state.
	:<math>\begin {~~multiline~~}		:<math>\begin {multline}
	E 2 A_g < E 1B_u \\		E 2 A_g < E 1B_u \\
	S_1 \quad S_2		S_1 \quad S_2
	\end{~~multiline~~}		\end{multline}
	\,\!</math>		\,\!</math>
	<br clear='all'>		<br clear='all'>

Cmditradmin: /* 2Ag excited state */

2009-08-31T20:53:48Z

2Ag excited state

← Older revision		Revision as of 13:53, 31 August 2009
Line 51:		Line 51:

	As long as they have the same symmetries they can mix. These three configurations have approximately the same energies so they can mix strongly. They are one photon forbidden (but two photon allowed). This results in a 2A<sub>g</sub> state that is energetically lower than the 1B<sub>u</sub> state, thus it should be considered the S<sub>1</sub> state.		As long as they have the same symmetries they can mix. These three configurations have approximately the same energies so they can mix strongly. They are one photon forbidden (but two photon allowed). This results in a 2A<sub>g</sub> state that is energetically lower than the 1B<sub>u</sub> state, thus it should be considered the S<sub>1</sub> state.
			:<math>\begin {multiline}
			E 2 A_g < E 1B_u \\
			S_1 \quad S_2
			\end{multiline}
			\,\!</math>
	<br clear='all'>		<br clear='all'>

Cmditradmin: /* Point Groups and symmetry */

2009-08-31T18:42:15Z

Point Groups and symmetry

← Older revision		Revision as of 11:42, 31 August 2009
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	'''Molecular states''' (which is what you can observe) is a wavefunction that results from '''all the electrons''' in the molecule.		'''Molecular states''' (which is what you can observe) is a wavefunction that results from '''all the electrons''' in the molecule.
	<br clear='all'>		<br clear='all'>
	[[Image:sixMO_config.JPG\|thumb\|300px\|Electronic configuration and molecular orbitals]]		[[Image:sixMO_config.JPG\|thumb\|300px\|Electronic configuration and molecular orbitals for hexatriene]]
	The electronic configuration is shown with six molecular orbitals, three of which on the π level are fully occupied. Another configuration in which individual electrons move up to the π* level are called '''singly excited'''. If two electrons are elevated from occupied levels into unoccupied levels these are called '''doubly excited''' configurations. The way electrons fill into the orbitals corresponds to electronic configurations.		The electronic configuration is shown with six molecular orbitals, three of which on the π level are fully occupied. Another configuration in which individual electrons move up to the π* level are called '''singly excited'''. If two electrons are elevated from occupied levels into unoccupied levels these are called '''doubly excited''' configurations. The way electrons fill into the orbitals corresponds to electronic configurations.

Cmditradmin: /* Point Groups and symmetry */

2009-08-31T18:29:56Z

Point Groups and symmetry

← Older revision		Revision as of 11:29, 31 August 2009
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	'''Molecular states''' (which is what you can observe) is a wavefunction that results from '''all the electrons''' in the molecule.		'''Molecular states''' (which is what you can observe) is a wavefunction that results from '''all the electrons''' in the molecule.
			<br clear='all'>
	[[Image:sixMO_config.JPG\|thumb\|300px\|Electronic configuration and molecular orbitals]]		[[Image:sixMO_config.JPG\|thumb\|300px\|Electronic configuration and molecular orbitals]]
	The electronic configuration is shown with six molecular orbitals, three of which on the π level are fully occupied. Another configuration in which individual electrons move up to the π* level are called '''singly excited'''. If two electrons are elevated from occupied levels into unoccupied levels these are called '''doubly excited''' configurations. The way electrons fill into the orbitals corresponds to electronic configurations.		The electronic configuration is shown with six molecular orbitals, three of which on the π level are fully occupied. Another configuration in which individual electrons move up to the π* level are called '''singly excited'''. If two electrons are elevated from occupied levels into unoccupied levels these are called '''doubly excited''' configurations. The way electrons fill into the orbitals corresponds to electronic configurations.