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Atomic orbitals: 4dThe shape of the five 4d orbitals. From left to right: (top row) 4d_{x2y2} and 4d_{z2} (bottom row) 4d_{xy}, 4d_{xz}, and 4d_{yz}. For each, the blue zones are where the wave functions have negative values and the red zones denote positive values. For each atom, there are five 4d orbitals. These are labelled 4d_{xy}, 4d_{xz}, 4d_{yz}, 4d_{x2y2} and 4d_{z2}. Four of these functions have the same shape but are aligned differently in space. The fifth function (4d_{z2}) has a different shape. Each 4d_{xy}, 4d_{xz}, 4d_{yz}, and 4d_{x2y2} orbital has eight lobes. There are two planar node normal to the axis of the orbital (so the 4d_{xy} orbital has yz and xz nodal planes, for instance). The 4d_{z2} orbital is a little different and has two conical nodes. In addition, apart from the planar nodes, all five orbitals have a single spherical node that partitions off the small inner lobes. The higher dorbitals (5d and 6d) are more complex since they have further spherical nodes. The origin of the planar nodes becomes clear if we examine the wave equation which, for instance, includes an xy term in the case of the 4d_{xy} orbital. Clearly when either x = 0 or y = 0, then we must have a node, and this by definition is the case for the yz and a xz planes.  

The Orbitron is a gallery of orbitals on the WWW The Orbitron^{TM}, a gallery of orbitals on the WWW, URL: http://winter.group.shef.ac.uk/orbitron/Copyright 20022015 Prof Mark Winter [The University of Sheffield]. All rights reserved. Document served: Monday 6th April, 2020 