Calculation of optical and $K$ pre-edge absorption spectra for ferrous iron of distorted sites in oxide crystals

Advanced semiempirical calculations have been performed to compute simultaneously optical absorption and $K$ pre-edge x-ray absorption spectra of ${\mathrm{Fe}}^{2+}$ in four distinct site symmetries found in minerals. The four symmetries, i.e., a distorted octahedron, a distorted tetrahedron, a square planar site, and a trigonal bipyramidal site, are representative of the ${\mathrm{Fe}}^{2+}$ sites found in crystals and glasses. A particular attention has been paid to the definition of the $p\text{−}d$ hybridization Hamiltonian which occurs for noncentrosymmetric symmetries in order to account for electric dipole transitions. For the different sites under study, an excellent agreement between calculations and experiments was found for both optical and x-ray absorption spectra, in particular in terms of relative intensities and energy positions of electronic transitions. To our knowledge, these are the first calculations of optical absorption spectra on ${\mathrm{Fe}}^{2+}$ placed in such diverse site symmetries, including centrosymmetric sites. The proposed theoretical model should help to interpret the features of both the optical absorption and the $K$ pre-edge absorption spectra of $3d$ transition metal ions and to go beyond the usual fingerprint interpretation.

Figure 1

Configuration interaction used to describe the on-site $4p$–$3d$ mixing in the XAS initial and final state configurations. T is the transition operator defined in Eq. (3).

Figure 2

Optical (left) and x-ray (right) spectra of siderite [(a) and (b)], staurolite [(c) and (d)], gillespite [(e) and (f)], and grandidierite [(g) and (h)]. The experimental and calculated OAS spectra are in black dashed line (– –) and in bold red line $\left(red---\right)$, respectively. The assignment of the transitions from the ground state is given for each symmetry. The experimental XAS data are in black lines: not corrected $(\cdots )$ and corrected (– –) from the main edge tail. The calculated XAS $K$ pre-edge spectra are in bold red line $\left(red---\right)$. Purple and green curves represent the respective contributions of the electric dipole and quadrupole transitions. The assignment of transitions is given using the $3d^7$ approximation. For grandidierite, simulated spectra for site A are in red, and spectra for site B are in blue, E1 and E2 XAS features are given for site A only (because they are very similar for site B).

Figure 3

Lifting of degeneracy of the ${}^{5}D$ spectroscopic term (free ${\mathrm{Fe}}^{2+}$ ion) caused by trigonal distortion in the case of siderite.

Figure 4

Lifting of degeneracy of the ${}^{5}D$ spectroscopic term (free ${\mathrm{Fe}}^{2+}$ ion) caused by tetragonal distortion in the case of gillespite.

Figure 5

Lifting of degeneracy of the ${}^{5}D$ spectroscopic term (free ${\mathrm{Fe}}^{2+}$ ion) caused by tetragonal distortion in the case of grandidierite.

Figure 6

Orientation of the tetrahedron.

Figure 7

Orientation of the trigonal bipyramid and the octahedron in $C_{3v}$.

Figure 8

Orientation for the $C_{4v}$ geometry.