There are 3 p-orbitals per subshell, which are $p_x$, $p_y$ and $p_z$. As well as there are 5 d-orbitals, which are $d_{xy}$, $d_{yz}$, $d_{zx}$, $d_{x^2-y^2}$, and $d_{z^2}$.

My Question: What is the basis for choosing the axes as $x$, $y$, and $z$? Can we rearrange the axes, suppose lets replace $x$ with $y$, $y$ with $z$, and $z$ with $x$. Then we will have the d-orbitals to be $d_{yz}$, $d_{zx}$, $d_{xy}$, also you would get $d_{y^2-z^2}$, and $d_{x^2}$, orbitals. Why do we choose that particularly?

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    $\begingroup$ We prefer to not use MathJax in the title field, see here for details. $\endgroup$ – Martin - マーチン Apr 23 '17 at 15:13

The choice of axes is arbitrary in this case (isolated atom with no external influence).

You could choose about any set of co-ordinate axes, and that wouldn't really affect the behavior of any of the electrons there ;)

However, in the presence of external influences, such as a magnetic field, it's customary to take the positive axis in the direction of the field as the positive z axis. Though ultimately, the choice of notation is left to you.

EDIT: Since you seem to have an issue here, I'll mention this as well:

Quoting from chemguide.co.uk

A) $\mathrm{d_{xy}}$, $\mathrm{d_{yz}}$, $\mathrm{d_{zx}}$

The names tell you that these orbitals lie in the x-y plane, the x-z plane and the y-z plane respectively.

Each orbital has four lobes. Notice that each of the lobes is pointing between two of the axes - not along them.

enter image description here

B) $\mathrm{d_{x^2 - y^2}}$, $\mathrm{d_{z^2}}$

Although these two orbitals look totally different, what they have in common is that their lobes point along the various axes. That's different from the first three where the lobes pointed in between the axes

The $\mathrm{d_{x^2 - y^2}}$ orbital looks exactly like the first group - apart, of course, from the fact that the lobes are pointing along the x and y axes, not between them.

enter image description here

The $\mathrm{d_{z^2}}$ orbital looks like a p orbital wearing a collar! The main lobes point along the z axis.

enter image description here

  • $\begingroup$ So the reason why they call it $d_{z^2}$ is because of the magnetic field applied? $\endgroup$ – Pritt says Reinstate Monica Apr 23 '17 at 14:40
  • $\begingroup$ I'm sorry but I'm still not quite satisfied. I am asking why they call the particular orientation of the ${d_z^2}$ as ${z}$? Why not call it as ${x}$, with its name being ${d_x^2}$ instead? $\endgroup$ – Pritt says Reinstate Monica Apr 23 '17 at 15:36
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    $\begingroup$ yes it could be $d_{x^2}$ but its useful to use the same convention to distinguish the orbitals and so we use $d_{z^2}$ . $\endgroup$ – porphyrin Apr 23 '17 at 16:21

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