Anharmonic motionsversusdynamic disorder at the Mg ion from the charge densities in pyrope (Mg₃Al₂Si₃O₁₂) crystals at 30 K: six of one, half a dozen of the other

Abstract

The possible occurrence of static/dynamic disorder at the Mg site in pyrope (MgAlSiO), with or without anharmonic contribution to the thermal vibrations even at low temperatures, has been largely debated but conclusions were contrasting. Here a report is given on the experimental charge density distribution, ρ, of synthetic pyrope at T = 30 K, built through a Stewart multipolar expansion up to l = 5 and based on a very precise and accurate set of in-home measured single-crystal X-ray diffraction amplitudes with a maximum resolution of 0.44 Å. Local and integral topological properties of ρ are in substantial agreement with those of ρ, the corresponding DFT-grade quantum charge density of an ideal pyrope crystal, and those derived from synchrotron investigations of chemical bonding in olivines. Relevant thermal atomic displacements, probably anharmonic in nature, clearly affect the whole structure down to 30 K. No significant (> 2.5σ) residual Fourier peaks are detectable from the ρ distribution around Mg, after least-squares refinement of a multipole model with anharmonic thermal motion at the Mg site. Experimental findings were confirmed by a full analysis of normal vibration modes of the DFT-optimized structure of the perfect pyrope crystal. Mg undergoes wide displacements from its equilibrium position even at very low temperatures, as it is allocated in a ∼ 4.5 Å large dodecahedral cavity and involved in several soft phonon modes. Implications on the interplay among static/dynamic disorder of Mg and lattice vibrational degrees of freedom are discussed.

Anharmonic Thermal Motion Modelling in the Experimental XRD Charge Density Determination of 1-Methyluracil at T = 23 K

“…The introduction of 81 fourth-order GC coefficients in model C also causes modest variations: the most remarkable change is the increase, by 5–7 times, of the esds, due to the large correlation of all new anharmonic parameters with the U ij s, with correlation coefficients in the range of 0.824–0.957. This effect is not unexpected and has been described previously [ 20 , 55 ].…”

“…As for the anharmonicity of thermal motion, the relevance of its inclusion in ADP models when analyzing EDDs in crystals is still an open question, the uncertainty being partly related to the fact that very asphericity in atomic charge densities can be due to genuine anharmonic thermal motion and/or to chemical bonding [ 19 ], as well as to static or dynamic disorder [ 20 , 21 ]. Long ago, at an international symposium on the accuracy in structure factor measurement, Werner F. Kuhs presented [ 22 ] a review on the properties of the most widely used formalisms to describe anharmonicity in crystallographic structure analysis and later published a paper [ 23 ] on both the theoretical and experimental aspects of generalized ADPs.…”

Unravelling the Chemistry of the [Cu(4,7-Dichloroquinoline)2Br2]2 Dimeric Complex through Structural Analysis: A Borderline Ligand Field Case

“…As expected, the charge density Laplacian, ∇ 2 ρ(r), is invariably positive at the bond critical points (bcp's) of the Cu-N and Cu-Br bonds (Table S16), as these interactions fall in the valence shell charge depletion (VSCD) region of the metal [37,51]. No direct metal-metal bonds [52] are detected: the two copper centers are connected through an asymmetric µ-Br bridge that involves Br(1) ions on axial positions (Figure 3).…”

“…The complexity of the least-squares model was incremented progressively, until quadrupoles (l = 2) for H; octupoles (l = 3) for C and N; and hexadecapoles (l = 4) for heavier Cl, Br and Cu atoms were included. Third-order Gram-Charlier coefficients were used for chlorine and bromine atoms to account for residual anharmonicity at low temperature [36,37]. Radial scaling parameters κ and κ' for each atomic species were also refined.…”

Experimental Charge Density Analysis and Electrostatic Properties of Crystalline 1,3-Bis(Dimethylamino)Squaraine and Its Dihydrate from Low Temperature (T = 18 and 20 K) XRD Data

“…A previous paper on DMACB (the 1,2 substituted isomer of SQ) summarises the EDD topological analysis [34], originally devised for theoretical charge densities, but then widely applied to experimental electron distributions [37] (for very recent applications see refs. [38,39]). Selected values of ρ(r) and its Laplacian ∇ 2 ρ(r) at the (3, −1) bond critical points (bcps) of the squaraine molecules are listed in Table 6.…”