In atomic cluster chemistry,most of the s and p block clusters follows the rule of minimum spin.i.e. most clusters like Al,Na and noble metals has spin multiplicity (2S+1) either 1 or 2 (singlet and doublet) depending on total number of electrons either even or odd.However same rule does not hold for transition metal clusters.Most of the d block element shows high spin S=4,5,7 etc. Can anyone explain the reason. I've doubt that may be splitting of d orbital is the reason. However,I'm not finding and clear cut answer anywhere.Also if there is a crystal field splitting,is there any way to find out the d orbital splitting by any quantum mechanical calculation?
Transition metals generally will show high spin for two major reasons: Firstly the atomic radii and electron compartment cell distances allow free spin relative to the nucleus at ground state level and secondly, at excited state electron sharing/pairing suggests that there should be increased spin/spartia distance or electron dislocation. whenever there is electron shell exchange spin is always involved. This is explained by Pauli' theory and I think you should revisit that theory.
Turbasu, I subscribe to Julius’ explanation with additions; that you should also consider the valence bond theory (VBT). Apart from accounting for stereochemical and magnetic properties this theory adequately deals with spin characteristics.
The origin of this phenomenon is the same as the ferromagnetic nature of some metal. It is a pure quantum mechanical effect: Heisenberg exchange interaction (it has not classical counterpart). The origin of the exchange interaction is the indistinguishable nature of electrons. It is related to the Pauli exclusion principle --> high spin state of half occupied orbitals in atoms
The resultant spin state of a cluster/molecule/atom is originated from the competition of spin-paring (coulomb repulsion) and decoupling of spin-pairs (exchange interaction). Coulomb repulsion increases the energy of system, but exchange interaction lowers it --> atomic states prefer the high spin state (Pauli principle)
The splitting of d-orbitals (the role of the symmetry) makes this picture more exciting. If the splitting is small, the spin state is high --> more unpaired spin. In this case the exchange interaction dominates over spin-pairing (coulomb repulsion), despite of one part of electrons live on higher orbitals. If the splitting is high, the exchange interaction can not compensate the spin-pairing/coulomb repulsion --> low spin state
https://en.wikipedia.org/wiki/Exchange_interaction
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