Orbital shape can be quadruple-ellipsoidal four-leaf clover {d orbital}, with two crossing points and two rotation axes. d orbitals have four elongated lobes, two each along both orthogonal lines, with two crossings in middle. Four-leaf-clover quadruple ellipsoidal orbit can align with x-axis and y-axis; between xy-axis, xz-axis, or yz-axis; or with z-axis, as double ellipsoid and torus. If with x and y or between xy, added angular momentum is -2 or +2, because both axes are perpendicular to z-axis. If between xz or yz, added angular momentum is -1 or +1, because one axis is perpendicular to z-axis. If with z, added angular momentum is 0, because axis aligns with spin axis. There can only be five kinds of quadruple-ellipsoidal orbital, because axes can have only five independent spatial orientations, which fill space. For same shell and same orbital angular momentum, all orientations are equally probable and have equal energy. All orientations add to make spherical orbital with zero net angular momentum.
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Date Modified: 2022.0224