Question

How to find electronic state of ground state configuration in group theory?

Answer 1

Answer:

To find the ground state term symbol, you should be using symmetry and group theory arguments, you shouldn't have to resort to searching Tanabe-Sugano diagrams to get the answer.

We'll start with octahedral complexes (the general idea can be extended quite easily to tetrahedral or square planar complexes). As requested in the question, I will only cover ground-state term symbols, but this procedure can also be extended easily to excited configurations.

In an octahedral complex, the d orbitals are split into a t2g set and an eg set. You will need the direct product table for the Oh point group, which you can find here (I will reproduce it here for convenience). You simply need to tack on the g subscripts on everything (since g⊗g=g, there will never be any ungerade states involved).

A1A2ET1T2A1A1A2A2A1EEEA1+[A2]+ET1T1T2T1+T2A1+E+[T1]+T2T2T2T1T1+T2A2+E+T1+T2A1+E+[T1]+T2

I also want to make the disclaimer that there is not necessarily a one-to-one correspondence between electronic configurations and term symbols. Therefore, the configuration (dxy)2(dz2)1 does not necessarily lead to one specific term symbol. A term symbol may often be a linear combination of multiple electronic configurations, and vice versa. Nevertheless, I will use the traditional "orbital diagrams" to illustrate points as necessary.

Answer 2

To find the ground state term symbol, you should be using symmetry and group theory arguments, you shouldn't have to resort to searching Tanabe-Sugano diagrams to get the answer.

To find the ground state term symbol, you should be using symmetry and group theory arguments, you shouldn't have to resort to searching Tanabe-Sugano diagrams to get the answer.We'll start with octahedral complexes (the general idea can be extended quite easily to tetrahedral or square planar complexes). As requested in the question, I will only cover ground-state term symbols, but this procedure can also be extended easily to excited configurations.

To find the ground state term symbol, you should be using symmetry and group theory arguments, you shouldn't have to resort to searching Tanabe-Sugano diagrams to get the answer.We'll start with octahedral complexes (the general idea can be extended quite easily to tetrahedral or square planar complexes). As requested in the question, I will only cover ground-state term symbols, but this procedure can also be extended easily to excited configurations.In an octahedral complex, the d orbitals are split into a t2g set and an eg set. You will need the direct product table for the Oh point group, which you can find here (I will reproduce it here for convenience). You simply need to tack on the g subscripts on everything (since g⊗g=g, there will never be any ungerade states involved).

To find the ground state term symbol, you should be using symmetry and group theory arguments, you shouldn't have to resort to searching Tanabe-Sugano diagrams to get the answer.We'll start with octahedral complexes (the general idea can be extended quite easily to tetrahedral or square planar complexes). As requested in the question, I will only cover ground-state term symbols, but this procedure can also be extended easily to excited configurations.In an octahedral complex, the d orbitals are split into a t2g set and an eg set. You will need the direct product table for the Oh point group, which you can find here (I will reproduce it here for convenience). You simply need to tack on the g subscripts on everything (since g⊗g=g, there will never be any ungerade states involved).A1A2ET1T2A1A1A2A2A1EEEA1+[A2]+ET1T1T2T1+T2A1+E+[T1]+T2T2T2T1T1+T2A2+E+T1+T2A1+E+[T1]+T2

To find the ground state term symbol, you should be using symmetry and group theory arguments, you shouldn't have to resort to searching Tanabe-Sugano diagrams to get the answer.We'll start with octahedral complexes (the general idea can be extended quite easily to tetrahedral or square planar complexes). As requested in the question, I will only cover ground-state term symbols, but this procedure can also be extended easily to excited configurations.In an octahedral complex, the d orbitals are split into a t2g set and an eg set. You will need the direct product table for the Oh point group, which you can find here (I will reproduce it here for convenience). You simply need to tack on the g subscripts on everything (since g⊗g=g, there will never be any ungerade states involved).A1A2ET1T2A1A1A2A2A1EEEA1+[A2]+ET1T1T2T1+T2A1+E+[T1]+T2T2T2T1T1+T2A2+E+T1+T2A1+E+[T1]+T2I also want to make the disclaimer that there is not necessarily a one-to-one correspondence between electronic configurations and term symbols. Therefore, the configuration (dxy)2(dz2)1 does not necessarily lead to one specific term symbol. A term symbol may often be a linear combination of multiple electronic configurations, and vice versa. Nevertheless, I will use the traditional "orbital diagrams" to illustrate points as necessary.