Electronic Structures of Metal Complexes

We can use the d-orbital energy-level diagram in Figure 1.1 to predict electronic structures and some of the properties of transition-metal complexes.

Figure 1.1 : An Octahedral Arrangement of Six Negative Charges around a Metal Ion Causes the Five d Orbitals to Split into Two Sets with Different Energies.

We start with the Ti³⁺ ion, which contains a single d electron, and proceed across the first row of the transition metals by adding a single electron at a time. We place additional electrons in the lowest-energy orbital available, while keeping their spins parallel as required by Hund’s rule. As shown in Figure 24.6.2, for d¹–d³ systems—such as [Ti(H₂O)₆]³⁺, [V(H₂O)₆]³⁺, and [Cr(H₂O)₆]³⁺, respectively—the electrons successively occupy the three degenerate t_2g orbitals with their spins parallel, giving one, two, and three unpaired electrons, respectively. We can summarize this for the complex [Cr(H₂O)₆]³⁺, for example, by saying that the chromium ion has a d³ electron configuration or, more succinctly, Cr³⁺ is a d³ ion.

Figure 1.2 : The Possible Electron Configurations for Octahedral dⁿ Transition-Metal Complexes (n = 1–10). Two different configurations are possible for octahedral complexes of metals with d⁴, d⁵, d⁶, and d⁷ configurations; the magnitude of Δ_o determines which configuration is observed.

When we reach the d⁴ configuration, there are two possible choices for the fourth electron: it can occupy either one of the empty e_g orbitals or one of the singly occupied t_2g orbitals. Recall that placing an electron in an already occupied orbital results in electrostatic repulsions that increase the energy of the system; this increase in energy is called the spin-pairing energy (P). If Δ_o is less than P, then the lowest-energy arrangement has the fourth electron in one of the empty e_g orbitals. Because this arrangement results in four unpaired electrons, it is called a high-spin configuration, and a complex with this electron configuration, such as the [Cr(H₂O)₆]²⁺ ion, is called a high-spin complex. Conversely, if Δ_o is greater than P, then the lowest-energy arrangement has the fourth electron in one of the occupied t_2g orbitals. Because this arrangement results in only two unpaired electrons, it is called a low-spin configuration, and a complex with this electron configuration, such as the [Mn(CN)₆]³⁻ ion, is called a low-spin complex. Similarly, metal ions with the d⁵, d⁶, or d⁷ electron configurations can be either high spin or low spin, depending on the magnitude of Δ_o.

In contrast, only one arrangement of d electrons is possible for metal ions with d⁸–d¹⁰ electron configurations. For example, the [Ni(H₂O)₆]²⁺ ion is d⁸ with two unpaired electrons, the [Cu(H₂O)₆]²⁺ ion is d⁹ with one unpaired electron, and the [Zn(H₂O)₆]²⁺ ion is d¹⁰ with no unpaired electrons.

If Δ_o is less than the spin-pairing energy, a high-spin configuration results. Conversely, if Δ_o is greater, a low-spin configuration forms.