Ab Initio Energy Landscape of GeF₂: A System Featuring Lone Pair Structure Candidates

Abstract

Dedicated to Professor Hansgeorg Schnöckel on the occasion of his 70th birthdayEach already known chemical configuration, as well as those that are stable but are still waiting to be experimentally discovered, corresponds to a minimum on the hyperspace of potential energy associated with the (chemical) configuration space. At finite temperatures, the configurations around such minimum structures are populated, constituting a "locally ergodic" region, corresponding to a macroscopic thermodynamic state, which can be addressed by the thermodynamic state functions G, H, and S. Since the structure of the potential energy landscape, and the locally ergodic regions present, are determined by natural laws, all chemical compounds and their structures are also predetermined. It follows that neither the composition, nor the structure, nor the properties of a specific chemical configuration is subject to external intervention, for example, by the synthetic chemist. [1] Projecting the whole wealth of existing and not yet realized chemical configurations onto the related landscape of potential energy at 0 K, and the ergodic states of matter evolving at finite temperatures, is the foundation of our concept for targeted materials and solid-state syntheses.[2] In this picture, the first step of synthesis planning, namely predicting stable configurations that can serve as targets for synthesis, imposes the task of analyzing the energy landscape for local minima. Since even subsections of such a landscape cannot be computed by solving the Schrödinger equation for the ensembles of atoms to be realistically involved, one has to resort to the tools developed for the exploration of multiminima landscapes, for example, by scanning it using random walks. We have employed simulated annealing, in combination with steps according to the Monte Carlo method, using the total energy as the only cost function, and number and type of atoms, their positional vectors, and, most importantly, the lattice basis as parameters to be varied (move classes). [2] Meanwhile, several related approaches for the prediction of structures by global optimization have been introduced, among them molecular dynamics in various variants (e.g. metadynamics, [3] or a combination of molecular dynamics and path sampling [4] ), genetic (evolutionary) algorithms, [5][6][7][8] or simply performing a local optimization, starting from random structures.[9] For overviews on structure prediction and energy landscapes, see, for example, references [2,[10][11][12].The shape of the energy landscape, as imaged by such a computational process, depends crucially on the quality and kind of the total energy calculations and to a lesser extent on the move classes applied, and will more or less deviate from the "true" landscape. Since the computational efforts to be made at exploring configuration spaces of significant size are huge, in the beginning, we based the total energy calculations on computationally "cheap" empirical two-body potentials. [2a-d] In spite of this approximation, th...

Compounds based on Group 14 elements: building blocks for advanced insulator dielectrics design

“…Ge is strongly bonded to 3 Y atoms, but has one other Y atom as its neighbor that it weakly bonds to, which means that although we see stacking of chains, there is stronger bonding between them than seen in PE. As previously explained by Doll et al [22], the 3 F atoms around Ge along with the lone pair of electrons on it result in a pseudo-tetrahedral geometry (a CN of 4). It should be noted that structure Type-B is a metastable state for SiF 2 and SiCl 2 , and Si(II) may indeed be the preferred state at higher temperatures.…”

“…Both GeF 2 and GeCl 2 crystallize in orthorhombic structure Type-B [21,22], where GeY 2 units (Y = F, Cl) are successively linked to each other via a bridge Y atom. Ge is strongly bonded to 3 Y atoms, but has one other Y atom as its neighbor that it weakly bonds to, which means that although we see stacking of chains, there is stronger bonding between them than seen in PE.…”

Conceptual Inorganic Materials Discovery – A Road Map

“…Thus, such systems might serve as meaningful touchstones to examine whether global optimizations on the ab initio level are suited to (re)produce reasonable structures expressing lone pair dependent topologies without recourse to any advance information. Such kind of investigation has been performed for germanium(II) fluoride . Its crystal structure under standard conditions was known .…”

“…This limitation undoubtedly challenges the ultimate objective of undertaking synthesis planning, which would imply the ability to identify stable configurations of any combination of the chemical elements. That is why, at least when it comes to analyzing combinations of elements where homo‐atomic bonds are expected to occur, it is indispensable to move on to carrying out the total energy calculations on the ab initio level …”

The energy landscape concept and its implications for synthesis planning

“…We have regarded it a meaningful touchstone and challenge to investigate whether our approach of global searches on the ab initio level is able to (re)produce correct and reasonable structures showing lone pair effects without recourse to any pre-information. For such a case study, we chose GeF 2 [73]. Addressing the germanium(II) fluoride system computationally has posed particular challenges, like treating the electron lone pair and the highly mutable bonding schemes involved, as there are strong covalent bonds between germanium and terminal fluorine atoms, significantly weaker ones to bridging F, and finally the van der Waals interactions effecting the bonding between the (GeF 2 ) n chains present.…”