Frequently Asked Question

## V^3+ Ground State Term Symbols and Energy Levels
Electronic Configuration:
V^3+ has the electron configuration [Ar] 3d^2.
Ground State Term Symbol:
Free Ion: To determine the ground state term symbol, we use Hund's rules:
1. Maximum Multiplicity: The maximum spin multiplicity (2S+1) is achieved when the electrons are unpaired and have parallel spins. In this case, we have two unpaired electrons (S = 1), so 2S+1 = 3 (triplet state).
2. Maximum L: The maximum total orbital angular momentum (L) is obtained by adding the individual orbital angular momenta of the electrons. Each d electron has l = 2, so the maximum L = 2 + 2 = 4. This corresponds to the 'G' term symbol.
3. Lowest J: For a more than half-filled d shell, the lowest J value is obtained by subtracting the spin and orbital angular momenta (J = L - S). In this case, J = 4 - 1 = 3.
Therefore, the free ion ground state term symbol is ^3G3.
Octahedral Field:
Splitting: In an octahedral field, the d orbitals split into two sets: the lower energy t2g orbitals (dxy, dyz, dxz) and the higher energy eg orbitals (dx^2-y^2, dz^2). Two electrons will occupy the t2g orbitals.
Term Symbol: The term symbol in the octahedral field is determined by the number of electrons in the t2g and eg orbitals. Since we have two electrons in the t2g orbitals, and their spins are parallel, the term symbol remains the same: ^3T2g.
Tetrahedral Field:
Splitting: In a tetrahedral field, the splitting pattern is reversed. The eg orbitals are lower in energy than the t2g orbitals. The two electrons will occupy the eg orbitals.
Term Symbol: Similar to the octahedral field, the term symbol is determined by the occupancy of the split orbitals. Since we have two electrons in the eg orbitals, and their spins are parallel, the term symbol remains the same: ^3E.
Note: The energy levels in both octahedral and tetrahedral fields are dependent on the ligand field strength and can be further determined using Tanabe-Sugano diagrams.