Application of density functional theory and the random phase approximation under periodic boundary conditions employing Gaussian-type basis functions

This work presents a robust Random-Phase-Approximation (RPA) method to compute ground state energies not only for molecules but also for solids. A translation symmetry adapted Hartree kernel under periodic boundary conditions is derived using Bloch functions of local, atom-centered Gaussian-type basis functions and resolution of the identity (RI) factorization. Long-range Coulomb sums are evaluated in direct space using an adapted fast continuous multipole method (CFMM), which works for defined points in reciprocal space apart from Γ. The computational cost of this method scales as O(N hoch 4 log(N)) with system size N and as O(N hoch 2 _k) with the number of sampled points k in reciprocal space N_k . Explicit treatment of 1D and 2D periodic materials avoids the need of full 3D calculations for chains or films. This method is implemented in the quantum chemistry package TURBOMOLE and adapts sparse density matrix storage and pre-screening of shell pairs to achieve further speedup. As an addendum to these results a parallel implementation of the periodic electrostatic potential (ESP) is provided. This ESP implementation adopts the evaluation of the Coulomb lattice sums from density fitting (DF) accelerated CFMM present in the RIPER Code in TURBOMOLE. CPU parallelisation of the code yields a speedup of about 13 times for 16 cores compared to single core calculations. This main part is accompanied by studies on the triphenyl triazin thiazole covalent organic framework (TTT-COF). COFs distinguish themselves from other polymers by their covalent connectivity, porosity, and crystallinity. The challenge of COF synthesis is to both yield a stable and a highly crystalline product with a minimum amount of structural defects. Therefore, a two step process is established for the synthesis of the TTT-COF. First, the trihphenyl triazine imine COF (TTI-COF) is formed via a thermodynamically reversible order inducing step. Second, a post-synthetic topochemical conversion with elemental sulfur forms the aromatic sulfur rings of the TTT-COF. The TTT-COF exhibits enhanced chemical and electron stability compared to its precursor, allowing for an in-depth structural study via transmission electron microscopy (TEM). In particular, the TTT-COF displays one-dimensional defects, such as edge dislocations and grain dislocations introduced during the TTT-COF formation

Heterostructures of skutterudites and germanium antimony tellurides – structure analysis and thermoelectric properties of bulk samples

Heterostructures of germanium antimony tellurides with skutterudite-type precipitates are promising thermoelectric materials due to low thermal conductivity and multiple ways of tuning their electronic transport properties. Materials with the nominal composition [CoSb2(GeTe)_(0.5)]_x(GeTe)_(10.5)Sb_2Te_3 (x = 0–2) contain nano- to microscale precipitates of skutterudite-type phases which are homogeneously distributed. Powder X-ray diffraction reveals that phase transitions of the germanium antimony telluride matrix depend on its GeTe content. These are typical for this class of materials; however, the phase transition temperatures are influenced by heterostructuring in a beneficial way, yielding a larger existence range of the intrinsically nanostructured pseudocubic structure of the matrix. Using microfocused synchrotron radiation in combination with crystallite pre-selection by means of electron microscopy, single crystals of the matrix as well as of the precipitates were examined. They show nano-domain twinning of the telluride matrix and a pronounced structure distortion in the precipitates caused by GeTe substitution. Thermoelectric figures of merit of 1.4 ± 0.3 at 450 °C are observed. In certain temperature ranges, heterostructuring involves an improvement of up to 30% compared to the homogeneous material

Topochemical conversion of an imine-into a thiazole-linked covalent organic framework enabling real structure analysis

Stabilization of covalent organic frameworks (COFs) by post-synthetic locking strategies is a powerful tool to push the limits of COF utilization, which are imposed by the reversible COF linkage. Here we introduce a sulfur-assisted chemical conversion of a two-dimensional imine-linked COF into a thiazole-linked COF, with full retention of crystallinity and porosity. This post-synthetic modification entails significantly enhanced chemical and electron beam stability, enabling investigation of the real framework structure at a high level of detail. An in-depth study by electron diffraction and transmission electron microscopy reveals a myriad of previously unknown or unverified structural features such as grain boundaries and edge dislocations, which are likely generic to the in-plane structure of 2D COFs. The visualization of such real structural features is key to understand, design and control structure-property relationships in COFs, which can have major implications for adsorption, catalytic, and transport properties of such crystalline porous polymers

Random Phase Approximation for Periodic Systems Employing Direct Coulomb Lattice Summation

A method to compute ground state correlation energies from the random phase approximation (RPA) is presented for molecular and periodic systems on an equal footing. The supermatrix representation of the Hartree kernel in canonical orbitals is translation-symmetry adapted and factorized by the resolution of the identity (RI) approximation. Orbital expansion and RI factorization employ atom-centered Gaussian-type basis functions. Long ranging Coulomb lattice sums are evaluated in direct space with a revised recursive multipole method that works also for irreducible representations different from Γ. The computational cost of this RI-RPA method scales as O­(<i>N</i>⁴) with the system size in direct space, <i>N</i>, and as O­(<i>N_k</i>²) with the number of sampled <i>k</i>-points in reciprocal space, <i>N</i>_<i>k</i>. For chain and film models, the exploration of translation symmetry with 10 <i>k</i>-points along each periodic direction reduces the computational cost by a factor of around 10–100 compared to equivalent Γ-point supercell calculations