What is the significance of d (x^2-y^2) in the d subshell?

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The d (x^2-y^2) orbital is a specific orbital within the d subshell, characterized by its angular dependence on the coordinates x and y. The calculations for this orbital can be derived using the equations x = r sin θ cos φ and y = r sin θ sin φ. Resources such as the Fordham University document on spherical harmonics provide detailed explanations and visualizations of these concepts. The wave function for this orbital is obtained by solving the Schrödinger wave equation, revealing its mathematical relationship with trigonometric functions.

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americast
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Hi all,
One of the orbitals of the d subshell is called d (x^2-y^2). What is the reason behind that? It would be helpful if someone could give the calculations.

Thanx in advance...
 

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It is simply the angular part of x^2-y^2. Use ##x=r \sin \theta \cos \phi## and ##y=r\sin \theta \sin \phi##.
 
While any decent quantum chemistry or quantum mechanics book should have the calculation for you, I did find http://www.fordham.edu/images/undergraduate/chemistry/pchem1/spherical_harmonics.pdf online that should do the trick. There's plenty online on (visualization of) the spherical harmonics, so if you need more information on them in particular, shouldn't be too hard to find.
 
This is actually the wave function obtained after solving Schrödinger wave equation and by comparing linear part of the function with mathematical trigonometric functions it looks like the squad of rectangular coordinate x minus square of rectangular coordinate y
 

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