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Visualization of Atomic Orbitals

d Orbitals

As the value of the angular momentum quantum number increases, the number of values of m increases (there are 2 l + 1 values of m) and the complexity of the orbital geometry increases. The d orbitals all possess l = 2. For this value of l, the magnetic quantum number may have values of m = -2, -1, 0, +1, and +2. Only orbitals with m = 0 are real; all other values of m give rise to complex wave functions. As is the case with p orbitals, chemists combine the m = -1 and +1 wave functions (which are complex) to obtain two new functions that are both real. Similarly, the wave functions with m = -2 and +2 are also combined to yield two new real wave functions.

The d orbital with m = 0 is designated z². The two orbitals created from the m = -1 and +1 orbitals are designated xz and yz. The two orbitals created from the m = -2 and +2 orbitals are designated xy and x²-y². These designations arise from the mathematical formulas for the wave functions and indicate the orientation of the orbital.