Ralf Peter Stoffel

Ab Initio Thermochemistry of Solid‐State Materials

In this contribution we introduce an electronic-structure-theory-based approach to a quantum-chemical thermochemistry of solids. We first deal with local and collective atomic displacements and explain how to calculate these. The fundamental importance of the phonons, their dispersion relations, their experimental determination as well as their calculation is elucidated, followed by the systematic construction of the thermodynamic potentials on this basis. Subsequently, we provide an introduction for practical computation as well as a critical analysis of the level of accuracy obtainable. We then show how different solid-state chemistry problems can be solved using this approach. Among these are the calculation of activation energies in perovskite-like oxides, but we also consider the use of theoretical vibrational frequencies for determining crystal structures. The pressure and temperature polymorphism of elemental tin which has often been classically described is also treated, and we energetically classify the metastable oxynitrides of tantalum. We also demonstrate, using the case of high-temperature superconductors, that such calculations may be used for an independent evaluation of thermochemical data of unsatisfactory accuracy. Finally, we show the present limits and the future challenges of the theory.

Ab initio study of the high‐temperature phase transition in crystalline GeO2

Germanium dioxide (GeO2) takes two forms at ambient pressure: a thermodynamically stable rutile‐type structure and a high‐temperature quartz‐type polymorph. Here, we investigate the phase stability at finite temperatures by ab initio phonon and thermochemical computations. We use gradient‐corrected density‐functional theory (PBE‐GGA) and pay particular attention to the modeling of the “semicore” germanium 3d orbitals (ascribing them either to the core or to the valence region). The phase transition is predicted correctly in both cases, and computed heat capacities and entropies are in excellent agreement with thermochemical database values. Nonetheless, the computed formation energies of α‐quartz‐type GeO2 (and, consequently, the predicted transition temperatures) differ significantly depending on theoretical method. Remarkably, the simpler and cheaper computational approach produces seemingly better results, not worse. In our opinion, GeO2 is a nice test case that illustrates both possibilities and limitations of modern ab initio thermochemistry.

Ab initio ORTEP drawings: a case study of N-based molecular crystals with different chemical nature

The thermal motion of atoms and functional groups is a key characteristic of any molecular crystal, and such motion derived from scattering experiments is conveniently visualised by means of thermal ellipsoids (the famous “ORTEP” drawings). Unfortunately, it is often impossible to obtain the underlying anisotropic displacement parameters (ADPs) for hydrogen atoms, due to their low X-ray scattering power, and sometimes no ADPs can be refined at all even for heavier atoms. In these cases, it would seem advantageous to estimate ADPs by first-principles techniques, and indeed such ab initio ORTEP plots have become available very recently. Here, we test this young method for a representative set of hydrogen-bonded molecular crystals: first, we study urea (CON2H4) as a well-known benchmark, then, its all-nitrogen analogue guanidine (CN3H5); finally, we move on to rubidium guanidinate (RbCN3H4) as a specimen with pronounced ionic interactions. For all three systems, ADPs have been obtained from density-functional theory (DFT) based phonon computations using the PHONOPY software. The results are compared with neutron-diffraction data as the experimental “benchmark” in this regard, and a critical discussion of experimental aspects is given. We observe excellent agreement between experiment and theory for the hydrogen-bonded systems urea and guanidine at low temperature, whereas high-temperature data for guanidine deviate visibly, and the more salt-like RbCN3H4 may suffer from a less-than-ideal description even at 12 K. Both are discussed in depth as there are possible solutions and directions for further research. Generally, the present results shine a favourable light on a future, more routine application of combined experimental/theoretical approaches in chemical crystallography.

Thermodynamic Properties of Molecular Crystals Calculated within the Quasi-Harmonic Approximation.

A computational study of the possibilities of contemporary theoretical chemistry as regards calculated thermodynamic properties for molecular crystals from first-principles is presented. The study is performed for a testing set of 22 low-temperature crystalline phases whose properties such as densities of phonon states, isobaric heat capacities, and densities are computed as functions of temperature within the quasi-harmonic approximation. Electronic structure and lattice dynamics are treated by plane-wave based calculations with optPBE-vdW functional. Comparison of calculated results with reliable critically assessed experimental data is especially emphasized.

Ab initio lattice dynamics and thermochemistry of layered bismuth telluride (Bi2Te3).

We present density-functional theory calculations of the lattice dynamics of bismuth telluride, yielding force constants, mean-square displacements and partial densities of phonon states which corroborate and complement previous nuclear inelastic scattering experiments. From these data, we derive an element- and energy-resolved view of the vibrational anharmonicity, quantified by the macroscopic Grüneisen parameter γ which results in 1.56. Finally, we calculate thermochemical properties in the quasiharmonic approximation, especially the heat capacity at constant pressure and the enthalpy of formation for bismuth telluride; the latter arrives at ΔHf (Bi2Te3)  =  -102 kJ mol(-1) at 298 K.

A density-functional study on the electronic and vibrational properties of layered antimony telluride

We present a comprehensive survey of electronic and lattice-dynamical properties of crystalline antimony telluride (Sb2Te3). In a first step, the electronic structure and chemical bonding have been investigated, followed by calculations of the atomic force constants, phonon dispersion relationships and densities of states. Then, (macroscopic) physical properties of Sb2Te3 have been computed, namely, the atomic thermal displacement parameters, the Grüneisen parameter γ, the volume expansion of the lattice, and finally the bulk modulus B. We compare theoretical results from three popular and economic density-functional theory (DFT) approaches: the local density approximation (LDA), the generalized gradient approximation (GGA), and a posteriori dispersion corrections to the latter. Despite its simplicity, the LDA shows excellent performance for all properties investigated-including the Grüneisen parameter, which only the LDA is able to recover with confidence. In the absence of computationally more demanding hybrid DFT methods, the LDA seems to be a good choice for further lattice dynamical studies of Sb2Te3 and related layered telluride materials.

Atomic motions in the layered copper pseudochalcogenide CuNCN indicative of a quantum spin-liquid scenario

We explore the thermodynamic properties of the layered copper(II) carbodiimide CuNCN by heat-capacity measurements and investigate the corresponding thermal atomic motions by means of neutron powder diffraction as well as inelastic neutron scattering. The experiments are complemented by a combination of density-functional calculations, phonon analysis and analytic theory. The existence of a soft flexural mode-bending of the layers, characteristic for the material structure-is established in the phonon spectrum of CuNCN by giving characteristic temperature-dependent contributions to the heat capacity and atomic displacement parameters. The agreement with the neutron data allows us to extract a residual-on top of the lattice-presumably spinon contribution to the heat capacity [Formula: see text], speaking in favor of the spin-liquid picture of the electronic phases of CuNCN.

Experimental and Theoretical Investigation of the Elastic Moduli of Silicate Glasses and Crystals

A combined quantum-mechanical and thermodynamic approach to the mechanical properties of multicomponent silicate glasses is presented. Quantum chemical calculations based on density-functional theory (DFT) on various silicate systems were performed to explore the crystalline polymorphs existing for a given chemical composition. These calculations reproduced the properties of known polymorphs even in systems with extensive polymorphism, like MgSiO3. Properties resting on the atomic and electronic structure, i.e., molar volumes (densities) and bulk moduli were predicted correctly. The theoretical data (molar equilibrium volumes, bulk moduli) were then used to complement the available experimental data. In a phenomenological evaluation, experimental data of bulk moduli, a macroscopic property resting on phononic structure, were found to linearly scale with the ratios of atomic space demand to actual molar volume in a universal way. Silicates ranging from high-pressure polymorphs to glasses were represented by a single master line. This suggests that above the Debye limit (in practice: above room temperature), the elastic waves probe the short range order coordination polyhedra and their next-neighbor linkage only, while the presence or absence of an extended translational symmetry is irrelevant. As a result, glasses can be treated – with respect to the properties investigated – as commensurable members of polymorphic series. Binary glasses fit the very same line as their one-component end-members, again both in the crystalline and glassy state. Finally, it is shown that the macroscopic properties of multicomponent glasses also are linear superpositions of the properties of their constitutional phases (as determined from phase diagrams or by thermochemical calculations) taken in their respective glassy states. This is verified experimentally for heat capacities and Young’s moduli of industrial glass compositions. It can be concluded, that the combined quantum mechanical and thermochemical approach is a truly quantitative approach for the design of glasses with desired mechanical properties, e.g., for the development of high-modulus glasses.