Atomic orbitals - Revision history

Apm: /* Real d orbitals */ added link to page Ligand field theory

2025-06-28T10:13:59Z

Real d orbitals: added link to page Ligand field theory

← Older revision		Revision as of 12:13, 28 June 2025
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	* https://physics.stackexchange.com/questions/613123/how-can-real-d-orbitals-be-computed-from-complex-orbitals		* https://physics.stackexchange.com/questions/613123/how-can-real-d-orbitals-be-computed-from-complex-orbitals
	* https://en.m.wikipedia.org/wiki/Table_of_spherical_harmonics#Real_spherical_harmonics		* https://en.m.wikipedia.org/wiki/Table_of_spherical_harmonics#Real_spherical_harmonics

			Related: [[Ligand field theory]]

	[[Category:Programming]]		[[Category:Programming]]

Apm: /* External links */ added section === Real d orbitals ===

2025-02-08T23:35:37Z

External links: added section === Real d orbitals ===

← Older revision		Revision as of 01:35, 9 February 2025
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	----		----
	* [https://de.wikipedia.org/wiki/Slater_Type_Orbitals Slater Type Orbitals]		* [https://de.wikipedia.org/wiki/Slater_Type_Orbitals Slater Type Orbitals]

			=== Real d orbitals ===

			* https://physics.stackexchange.com/questions/613123/how-can-real-d-orbitals-be-computed-from-complex-orbitals
			* https://en.m.wikipedia.org/wiki/Table_of_spherical_harmonics#Real_spherical_harmonics

	[[Category:Programming]]		[[Category:Programming]]

Apm: added link to List of programmatic 3D modelling tools

2025-02-08T23:24:09Z

added link to List of programmatic 3D modelling tools

← Older revision		Revision as of 01:24, 9 February 2025
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	[[File:Libfive p-orbital Screenshot 20201110 001820.png\|400px\|thumb\|right\|Positive lobe of a p-orbital (single electron solution for the Schrödinger equation) this was rendered using the software "libfive". Related: F-Rep in [[constructive solid geometry]].]]		[[File:Libfive p-orbital Screenshot 20201110 001820.png\|400px\|thumb\|right\|Positive lobe of a p-orbital (single electron solution for the Schrödinger equation) this was rendered using the software "libfive". Related: F-Rep in [[constructive solid geometry]] & [[List of programmatic 3D modelling tools]].]]

	= Math for constructing orbitals =		= Math for constructing orbitals =

Apm: a bit of a stretch but I added Category:Programming

2023-07-11T11:01:42Z

a bit of a stretch but I added Category:Programming

← Older revision		Revision as of 13:01, 11 July 2023
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	----		----
	* [https://de.wikipedia.org/wiki/Slater_Type_Orbitals Slater Type Orbitals]		* [https://de.wikipedia.org/wiki/Slater_Type_Orbitals Slater Type Orbitals]

			[[Category:Programming]]

Apm: /* External links */

2023-06-07T13:16:13Z

External links

← Older revision		Revision as of 15:16, 7 June 2023
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	* '''[https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation#Hydrogen_atom SG for the hydrogen atom]'''		* '''[https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation#Hydrogen_atom SG for the hydrogen atom]'''
	----		----
	* [[https://de.wikipedia.org/wiki/Slater_Type_Orbitals Slater Type Orbitals]]		* [https://de.wikipedia.org/wiki/Slater_Type_Orbitals Slater Type Orbitals]

Apm: /* External links */ Slater_Type_Orbitals

2023-06-07T13:16:04Z

External links: Slater_Type_Orbitals

← Older revision		Revision as of 15:16, 7 June 2023
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	----		----
	* [https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation Schrödinger equation (SG)]		* [https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation Schrödinger equation (SG)]
	* [https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation#Hydrogen_atom SG for the hydrogen atom]		* '''[https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation#Hydrogen_atom SG for the hydrogen atom]'''
			----
			* [[https://de.wikipedia.org/wiki/Slater_Type_Orbitals Slater Type Orbitals]]

Apm: /* Ignoring entanglement between electrons in first approximation */

2023-06-07T13:12:58Z

Ignoring entanglement between electrons in first approximation

← Older revision		Revision as of 15:12, 7 June 2023
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	In practice as first approximation it's assumed though that the electrons are mostly non-entangled.		In practice as first approximation it's assumed though that the electrons are mostly non-entangled.
	That is that the multi particle wave function can be written as a product of single particle wave functions. Product states.		That is that the multi particle wave function can be written as a product of single particle wave functions. Product states.
	~~Entangles~~ states are exactly the ones that cannot be written as product states.		Entangled states are exactly the ones that cannot be written as product states.
	Some modelling methods later on introduce ways to account for the error that originates from ignoring entanglement here.		Some modelling methods later on introduce ways to account for the error that originates from ignoring entanglement here.

Apm: /* Ignoring entanglement between electrons in first approximation */

2023-06-07T13:12:05Z

Ignoring entanglement between electrons in first approximation

← Older revision		Revision as of 15:12, 7 June 2023
Line 111:		Line 111:

	In practice as first approximation it's assumed though that the electrons are mostly non-entangled.		In practice as first approximation it's assumed though that the electrons are mostly non-entangled.
	That is that the multi particle wave function as be written as a product of single particle wave functions. Product states.		That is that the multi particle wave function can be written as a product of single particle wave functions. Product states.
	Entangles states are exactly the ones that cannot be written as product states.		Entangles states are exactly the ones that cannot be written as product states.
	Some modelling methods later on introduce ways to account for the error that originates from ignoring entanglement here.		Some modelling methods later on introduce ways to account for the error that originates from ignoring entanglement here.

Apm: /* Math - how to find these solutions */

2023-06-07T13:10:12Z

Math - how to find these solutions

← Older revision		Revision as of 15:10, 7 June 2023
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	* SG with the Hamiltonian containing the field of a nucleus as a point charge for the potential energy		* SG with the Hamiltonian containing the field of a nucleus as a point charge for the potential energy
	* separation of variables - to solve the radial and the two spherical parts as separate equations<br> (equations remaining linked only via eigenvalue constants which are the quantum numbers)		* separation of variables - to solve the radial and the two spherical parts as separate equations<br> (equations remaining linked only via eigenvalue constants which are the quantum numbers)
	* do some smart linear super-positioning get to standing waves <br>For an intuitive interpretation: A 90° phase shift between real and complex part indicates the direction of a moving/spinning wave. <br>You want't to get rid of that phase shift by superpositioning.<br> Note that nothing that indicates direction of motion is visible in the absolute square.		* do some smart linear super-positioning get to standing waves <br>For an intuitive interpretation: A 90° phase shift between real and complex part indicates the direction of a moving/spinning wave. <br>You want to get rid of that phase shift by superpositioning.<br> Note that nothing that indicates direction of motion is visible in the absolute square.
	----		----
	As a side-note: <br>		As a side-note: <br>

Apm: /* Math - how to find these solutions */ plenty of resources note & a reformulation

2023-06-07T13:09:53Z

Math - how to find these solutions: plenty of resources note & a reformulation

← Older revision		Revision as of 15:09, 7 June 2023
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	=== Math - how to find these solutions ===		=== Math - how to find these solutions ===

			There are plenty of resources describing this in excruciating detail. So just a rough outline here.
	* Schrödinger equation (SG) in 3D - the static version suffices HΨ = EΨ <br>where H is the Hamiltonian a differential operator extracting infromation about both potential and kinetic energy from the wave function.		* Schrödinger equation (SG) in 3D - the static version suffices HΨ = EΨ <br>where H is the Hamiltonian a differential operator extracting infromation about both potential and kinetic energy from the wave function.
	* SG with the Hamiltonian containing the field of a nucleus as a point charge for the potential energy		* SG with the Hamiltonian containing the field of a nucleus as a point charge for the potential energy
	* separation of variables - to solve the radial and the two spherical parts as separate equations<br> (equations remaining linked only via eigenvalue constants which are the quantum numbers)		* separation of variables - to solve the radial and the two spherical parts as separate equations<br> (equations remaining linked only via eigenvalue constants which are the quantum numbers)
	* linear ~~superposition~~ to standing waves <br>(For an intuitive interpretation: A 90° phase shift between real and complex part indicates the direction of a moving/spinning wave~~, but~~ nothing that indicates direction of motion is visible in the absolute square)		* do some smart linear super-positioning get to standing waves <br>For an intuitive interpretation: A 90° phase shift between real and complex part indicates the direction of a moving/spinning wave. <br>You want't to get rid of that phase shift by superpositioning.<br> Note that nothing that indicates direction of motion is visible in the absolute square.
	----		----
	As a side-note: <br>		As a side-note: <br>