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

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Discussion Overview

The discussion revolves around the significance of the d orbital labeled d (x^2-y^2) within the context of quantum chemistry and quantum mechanics. Participants explore the mathematical and conceptual underpinnings of this orbital, including its derivation and representation.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant inquires about the calculations related to the d (x^2-y^2) orbital and its significance.
  • Another participant suggests that the d (x^2-y^2) orbital can be understood as the angular part of the expression x^2 - y^2, referencing spherical coordinates.
  • A different participant points out that resources such as quantum chemistry textbooks and online materials on spherical harmonics can provide the necessary calculations and visualizations.
  • One participant describes the d (x^2-y^2) wave function as derived from the Schrödinger wave equation, relating it to trigonometric functions and rectangular coordinates.

Areas of Agreement / Disagreement

Participants present various perspectives on the significance and derivation of the d (x^2-y^2) orbital, with no clear consensus on the best approach or explanation. Multiple viewpoints and resources are shared, indicating an ongoing exploration of the topic.

Contextual Notes

Some assumptions about the mathematical background of participants may be present, and the discussion references external resources for further information, which may not be universally accessible or agreed upon.

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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