orbital subscript

Each orbital in a subshell (e.g. $2\mathrm{p}$) is identified by a subscript. The subscript depends on the azimuthal quantum number and the axis the orbital lies on.

• simple subscript ($l=0$): $x$, $y$, $z$
  • the two leafs grow in the direction of the specified axis (positive and negative directions)
  • wave function is positive in the positive direction and vice versa
• product ($l=1$): $xy$, $yz$, $xz$, etc
  • the four leafs grow in between each axis/quadrants
  • the leaf in both positive axes will carry a positive sign for wave function. the one on the opposite direction will also have positive sign; negative otherwise
  • e.g. for xz, the leaf in +x +z quadrant will be positive, the one in -x -z quadrant is also positive
• difference of squares ($l=2$): $x^2-y^2$
  • the four leafs grow the axes’s directions (positive and negative directions)
  • the axis with a positive sign (e.g. $x$) with have positive signs on both leafs, vice versa
• squares ($l=2$): $z^2$
  • two leafs grow in the positive and negative directions of the axis
  • one negative donut-shaped leaf grow in the plane that is normal to the axis, e.g. for z, there will be a negative donut on xy plane