How does geometry affects the energy content of an Orbital?
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Crystal field theory (CFT) describes the breaking of orbital degeneracy in transition metal complexes due to the presence of ligands. CFT qualitatively describes the strength of the metal-ligand bonds. Based on the strength of the metal-ligand bonds, the energy of the system is altered. This may lead to a change in magnetic properties as well as color. This theory was developed by Hans Bethe and John Hasbrouck van Vleck
According to the Aufbau principle, electrons are filled from lower to higher energy orbitals. For the octahedral case above, this corresponds to the dxy, dxz, and dyz orbitals. Following Hund's rule, electrons are filled in order to have the highest number of unpaired electrons. For example, if one had a d3 complex, there would be three unpaired electrons. If one were to add an electron, however, it has the ability to fill a higher energy orbital ( dz² or dx²-y²) or pair with an electron residing in the dxy, dxz, or dyz orbitals. This pairing of the electrons requires energy (spin pairing energy). If the pairing energy is less than the crystal field splitting energy, ∆₀, then the next electron will go into the dxy, dxz, or dyz orbitals due to stability. This situation allows for the least amount of unpaired electrons, and is known as low spin. If the pairing energy is greater than ∆₀, then the next electron will go into the dz² or dx²-y² orbitals as an unpaired electron. This situation allows for the most number of unpaired electrons, and is known as high spin. Ligands that cause a transition metal to have a small crystal field splitting, which leads to high spin, are called weak-field ligands. Ligands that produce a large crystal field splitting, which leads to low spin, are called strong field ligands.
In addition to octahedral complexes, two common geometries observed are that of tetrahedral and square planar. These complexes differ from the octahedral complexes in that the orbital levels are raised in energy due to the interference with electrons from ligands. For the tetrahedral complex, the dxy, dxz, and dyz orbitals are raised in energy while the dz², dx²-y² orbitals are lowered. For the square planar complexes, there is greatest interaction with the dx²-y² orbital and therefore it has higher energy. The next orbital with the greatest interaction is dxy, followed below by dz². The orbitals with the lowest energy are the dxz and dyz orbitals. There is a large energy separation between the dz² orbital and the dxz and dyz orbitals, meaning that the crystal field splitting energy is large. We find that the square planar complexes have the greatest crystal field splitting energy compared to all the other complexes. This means that most square planar complexes are low spin, strong field ligands.