Temperature-dependent analysis of thermal motion, disorder and structures of tris(ethylenediamine)zinc(II) sulfate and tris(ethylenediamine)copper(II) sulfate

Abstract

The crystal structures of the title compounds have been determined in the temperature range 140-290 K for the zinc complex, and 190-270 K for the copper complex. The two structures are isostructural in the trigonal space group P " 3 31c with the sulfate anion severely disordered on a site with 32 (D 3 ) symmetry. This sulfate disorder leads to a disordered three-dimensional hydrogen-bond network, with the N-H atoms acting as donors and the sulfate O atoms as acceptors. The displacement parameters of the N and C atoms in both compounds contain disorder contributions in the out-of-ligand plane direction owing to ring puckering and/or disorder in hydrogen bonding. In the Zn compound the vibrational amplitudes in the bond directions are closely similar. Their differences show no significant deviations from rigid-bond behaviour. In the Cu compound, a (presumably) dynamic Jahn-Teller effect is identified from a temperature-independent contribution to the displacement ellipsoids of the N atom along the N-Cu bond. These conclusions derive from analyses of the atomic displacement parameters with the Hirshfeld test, with rigid-body models at different temperatures, and with a normal coordinate analysis. This analysis considers the atomic displacement parameters (ADPs) from all different temperatures simultaneously and provides a detailed description of both the thermal motion and the disorder in the cation. The Jahn-Teller radii of the Cu compound derived on the basis of the ADP analysis and from the bond distances in the statically distorted low-temperature phase [Lutz (2010). Acta Cryst. C66, m330-m335] are found to be the same.

Distinction of disorder, classical and quantum vibrational contributions to atomic mean-square amplitudes in dielectric pentachloronitrobenzene

“…However, a normal coordinate analysis (NCA) approach, developed by Bürgi and co-workers 13 can overcome both problems for simple molecules such as benzene, urea, 14 hydroquinone, 15 hexamethylenetetramine, 16 naphthalene, 17 and tris-ethylenediamine zinc sulfate [(H 2 NCH 2 CH 2 NH 2 ) 3 Zn] SO 4 . 18 Key to this approach is the exploitation of a temperature parametric. ADPs from multiple-temperature crystallographic Bragg data sets provide a trend, U ii (T), that can be compared with that expected for a collection of simple harmonic oscillators.…”

Linear transformations of variance/covariance matrices

“…As the " tensor is symmetric and expressed in a Cartesian coordinate system, the matrix of the eigenvectors Q is orthogonal (Q À1 = Q t ) and the metric tensor is the identity matrix. From equation (13) we find Table 5 shows the " tensors of atoms Cu, N and C in tris-(ethylenediamine)copper(II) sulfate (Smeets et al, 2011).…”

Linear transformations of variance/covariance matrices

“…ð15Þ Table 5 shows the " tensors of atoms Cu, N and C in tris-(ethylenediamine)copper(II) sulfate (Smeets et al, 2011).…”

“…The input for this software must be in 1 (C 1 ) symmetry. If a molecule is on a special position, the coordinates, the ADPs and their standard uncertainties have to be expanded to 1 (C 1 ) symmetry (Smeets et al, 2011). The correct symmetry is then introduced later by the choice of appropriate local coordinate systems for the atoms.…”

“…Let T Ã be a doubly contravariant tensor representing a quadratic equation defined with respect to a reciprocal basis. The basis is not necessarily orthogonal: Table 5 " tensor components and eigenvalues (Å 2 ) in tris(ethylenediamine)copper(II) sulfate (Smeets et al, 2011 (5) respect to the corresponding direct basis ða 1 ; . .…”