Metal L-edge

Metal L-edge involves the excitation of a metal 2p electron to unfilled metal d orbitals (eg. 3d for first-row transition metals). The transition is formally electric-dipole allowed which not only makes it more intense than an electric-dipole forbidden metal K pre-edge (1s → 3d transition), but also makes it more feature rich as the lower required energy (~400-1000 eV scandium to copper) results in a higher-resolution experiment. In the simplest case, that of a cupric (Cu^II) complex, the 2p → 3d transition produces a 2p⁵3d¹⁰ final state. The 2p⁵ core hole created in the transition has an orbital angular momentum L=1 which will then couple to the spin angular momentum S=1/2 to produce J = 3/2 and J=1/2 final states. These states are directly observable in the L-edge spectrum as the two main peaks. The peak at lower energy has the greatest intensity and is called the L₃-edge while the peak at higher energy has less intensity and is called the L₂-edge.

As we move left across the periodic table (eg. from copper to iron), we create additional holes in the metal 3d orbitals. For example, a low-spin ferric (Fe^III) system in an octahedral environment has a ground state of (t_2g)⁵(e_g)⁰ resulting in transitions to the t_2g (dπ) and e_g (dσ) sets. Therefore, there are two possible final states: t_2g⁶e_g⁰ or t_2g⁵e_g¹. Since the ground-state metal configuration has one hole in the e_g orbital set and four holes in the t_2g orbital set, an intensity ratio of 1:4 might be expected. However, this model does not take into account covalent bonding and, indeed, a intensity ratio of 1:4 is not observed in the spectrum. In the case of iron, the d⁶ excited state will further split in energy due to d-d electron repulsion. This splitting is given by the right-hand (high-field) side of the d⁶ Tanabe-Sugano diagram and can be mapped onto a theoretical simulation of a L-edge spectrum. Other factors such as p-d electron repulsion and spin-orbit coupling of the 2p and 3d electrons must also be considered in order to fully simulate the data. For a ferric system, all of these effects result in 252 initial states and 1260 possible final states that together will comprise the final L-edge spectrum. Despite all of these possible states, it has been established that in a low-spin ferric system, the lowest energy peak is due to a transition to the t_2g hole and the more intense and higher energy (~3.5 eV) peak is to that of the unoccupied e_g orbitals.

In most systems, bonding between a ligand and a metal atom can be thought of in terms of metal-ligand covalent bonds where the occupied ligand orbitals donates some electron density to the metal. This is commonly known as ligand to metal charge transfer or LMCT. In some cases, there are low-lying unoccupied ligand orbitals (π*) which can receive back-donation (or backbonding) from the occupied metal orbitals. This has the opposite effect on the system, resulting in metal to ligand charge transfer, MLCT, and commonly appears as an additional L-edge spectral feature. An example of this feature occurs in low-spin ferric [Fe(CN)₆]^3- since CN^- is a ligand that can have back-bonding. While back-bonding is important in the initial state, it would only warrant a small feature in the L-edge spectrum. In fact, it is in the final state where the back bonding π* orbitals are allowed to mix with the very intense e_g transition, thus borrowing intensity and resulting in the final dramatic three peak spectrum.

XAS, as well as other spectroscopies, look at the excited state to infer information about the ground state. Thus, spectra of this nature contain many features that have to be accounted for and understood. In order to make a quantitative assignment, L-edge data is fit using a valence bond configuration interaction (VBCI) model where LMCT and MLCT are applied as needed in order to successfully simulate the observed spectral features. These simulations are then further compared to density functional theory (DFT) calculations in order to arrive at a final interpretation of the data and an accurate description of the electronic structure of the complex.

In the case of iron L-edge, the excited state mixing of the metal e_g orbitals into the ligand π* make this method a direct and very sensitive probe of backbonding.