Which effect distinguish a dxy orbital from dyz orbital?
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It’s just the naming scheme for the hydrogen atom l = 2 wavefunctions in real form.
When you solve the Schrodinger equation you do it in spherical coordinates and the solution you get out involve complex numbers. These are named the d−2d−2, d−1d−1, d0d0, d1d1, and d2d2 orbitals.
Thanks to the properties of the Schrodinger equation you can transform these 5 complex valued orbitals in spherical coordinates into 5 new real values orbitals, also in spherical coordinates (or into 6 real valued orbitals in Cartesian coordinates).
They are named because of their shapes.
First, the dz2dz2 orbital is actually short for d2z2−x2−y2,d2z2−x2−y2, which is sometimes written as d3z2−r2d3z2−r2, and represents a wavefunction which is proportional to 3z2−r2r23z2−r2r2.
The dxydxy orbital is proportional to xyr2xyr2, and so on.
We do this because our new real d orbitals are both real and orthogonal, which are not only properties we like but back when quantum mechanics was new these properties made the math a lot easier.
Also, from here you can convert the orbitals into their Cartesian form where you, unfortunately, end up with 6 orbitals instead of 5 (dzzdzz, dy
When you solve the Schrodinger equation you do it in spherical coordinates and the solution you get out involve complex numbers. These are named the d−2d−2, d−1d−1, d0d0, d1d1, and d2d2 orbitals.
Thanks to the properties of the Schrodinger equation you can transform these 5 complex valued orbitals in spherical coordinates into 5 new real values orbitals, also in spherical coordinates (or into 6 real valued orbitals in Cartesian coordinates).
They are named because of their shapes.
First, the dz2dz2 orbital is actually short for d2z2−x2−y2,d2z2−x2−y2, which is sometimes written as d3z2−r2d3z2−r2, and represents a wavefunction which is proportional to 3z2−r2r23z2−r2r2.
The dxydxy orbital is proportional to xyr2xyr2, and so on.
We do this because our new real d orbitals are both real and orthogonal, which are not only properties we like but back when quantum mechanics was new these properties made the math a lot easier.
Also, from here you can convert the orbitals into their Cartesian form where you, unfortunately, end up with 6 orbitals instead of 5 (dzzdzz, dy
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