Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole method: Analytical gradients

Wannier Function Localization Using Bloch Intrinsic Atomic Orbitals

We extend the intrinsic atomic orbital (IAO) method for the localization of molecular orbitals to calculate well-localized generalized Wannier functions in crystals in the spirit of the Pipek-Mezey method. We furthermore present a one-shot diabatic Wannierization procedure that aligns the phases of the Bloch functions, providing immediate Wannier localization, which serves as an excellent initial guess for optimization. We test our Wannier localization implementation on a number of solid-state systems, highlighting the effectiveness of the diabatic preparation, especially for localizing core bands. Partial charges of Wannier functions generated using Bloch IAOs align well with chemical intuition, which we demonstrate through the example of the adsorption of CO on a MgO surface.

Host-Guest Interactions of Ruthenium(II) Arene Complexes with Cucurbit[7/8]uril

Cucurbit[n]urils (CB[n]s) have been recognized for their chemical and thermal stability, and their ability to bind many neutral and cationic guest molecules makes them excellent hosts in a range of supramolecular applications. In drug delivery, CB[n]s can enhance drug solubility, improve chemical and physical drug stability, and allow for triggered and controlled release. This study aimed to investigate the ability of CB[7] and CB[8] as molecular hosts to bind ruthenium(II) arene complexes that are current anticancer lead structures in the area of metallodrugs. Both, experimental and computational methods, led to insights into the binding preferences and geometries of [RuII(cym)Cl2]2 (1; cym = η6-p-cymene), [RuII(cym)(dmb)Cl2]) (2; cym = η6-p-cymene; dmb = 1,3-dimethylbenzimidazol-2-ylidene), and [RuII(cym)(pta)Cl2] (3, RAPTA-C; cym = η6-p-cymene; pta = 1,3,5-triaza-7-phospha-adamantane) with CB[7] and CB[8]. Competition experiments by mass spectrometry revealed clear preferences of 2 for CB[8] and 3 for CB[7]. Based on a comparison of the associated interaction energies from quantum chemical calculations as well as experimental data, 3@CB[7] clearly prefers a binding mode, where the pta ligand is located inside the cavity of the host, and the metal ion interacts with two of the carbonyl groups on the rim of CB[7]. In contrast, complex 2 binds in two different orientations with interaction energies similar to those of both CB[n]s, with the cym ligand being either inside or outside of the cavity. These findings suggest that ruthenium(II) arene complexes are able to form stable host-guest interactions with CB[n]s, which can be exploited as drug delivery vehicles in further metallodrug development to improve their chemical stability.

Spin-Symmetry Breaking and Hyperfine Couplings in Transition-Metal Complexes Revisited Using Density Functionals Based on the Exact-Exchange Energy Density

A small set of mononuclear manganese complexes evaluated previously for their Mn hyperfine couplings (HFCs) has been analyzed using density functionals based on the exact-exchange energy density─in particular, the spin symmetry breaking (SSB) found previously when using hybrid functionals. Employing various strong-correlation corrected local hybrids (scLHs) and strong-correlation corrected range-separated local hybrids (scRSLHs) with or without additional corrections to their local mixing functions (LMFs) to mitigate delocalization errors (DE), the SSB and the associated dipolar HFCs of [Mn(CN)4]2-, MnO3, [Mn(CN)4N]-, and [Mn(CN)5NO]2- (the latter with cluster embedding) have been examined. Both strong-correlation (sc)-correction and DE-correction terms help to diminish SSB and correct the dipolar HFCs. The DE corrections are more effective, and the effects of the sc corrections depend on their damping factors. Interestingly, the DE-corrections reduce valence-shell spin polarization (VSSP) and thus SSB by locally enhancing exact-exchange (EXX) admixture near the metal center and thereby diminishing spin-density delocalization onto the ligand atoms. In contrast, sc corrections diminish EXX admixture locally, mostly on specific ligand atoms. This then reduces VSSP and SSB as well. The performance of scLHs and scRSLHs for the isotropic Mn HFCs has also been analyzed, with particular attention to core-shell spin-polarization contributions. Further sc-corrected functionals, such as the KP16/B13 construction and the DM21 deep-neural-network functional, have been examined.

TURBOMOLE: Today and Tomorrow

TURBOMOLE is a highly optimized software suite for large-scale quantum-chemical and materials science simulations of molecules, clusters, extended systems, and periodic solids. TURBOMOLE uses Gaussian basis sets and has been designed with robust and fast quantum-chemical applications in mind, ranging from homogeneous and heterogeneous catalysis to inorganic and organic chemistry and various types of spectroscopy, light-matter interactions, and biochemistry. This Perspective briefly surveys TURBOMOLE's functionality and highlights recent developments that have taken place between 2020 and 2023, comprising new electronic structure methods for molecules and solids, previously unavailable molecular properties, embedding, and molecular dynamics approaches. Select features under development are reviewed to illustrate the continuous growth of the program suite, including nuclear electronic orbital methods, Hartree-Fock-based adiabatic connection models, simplified time-dependent density functional theory, relativistic effects and magnetic properties, and multiscale modeling of optical properties.

Performance of Common Density Functionals for Excited States of Tetraphenyldibenzoperiflanthene

Time-dependent density functional theory is the method of choice to efficiently calculate excitation spectra with the functional and basis set choice allowing one to compromise between accuracy and computational cost. In this work, the performance of different functionals as well as the second-order approximate coupled cluster singles and doubles model CC2 is evaluated by comparing the results to experimental results of the example molecule tetraphenyldibenzoperiflanthene (DBP). The choice of the functional has a significant impact on the calculated spectrum of DBP. The performance of a number of different functionals was evaluated, quantified, and, where possible, discussed. The best functional, tuned-CAM-B3LYP, is used to investigate DBP on a surface of hexagonal boron nitride (h-BN). The resulting spectrum shows excellent agreement with experimental results for a monolayer of DBP on h-BN.

A benchmark for non-covalent interactions in organometallic crystals

Organometallic complexes are the basis for homogeneous catalysis, have applications in materials science and are also active pharmaceutical ingredients. The interaction between transition metal complexes in the solid state is determining their thermodynamics and bio-availability. Non-covalent interactions such as hydrogen bonding and van der Waals are stabilizing crystals of transition metal complexes. The variation of ligand field, central metal atoms and their oxidation and spin states are determinants of the magnitude of their inter-molecular interactions. A comparison of a set of 43 manually curated experimental heats of sublimation (the new XTMC43 set) and results from periodic DFT calculations shows that an agreement to within 9% can be achieved using GGA or mGGA functionals with atom-centred Gaussian-type basis functions. The need for careful assessments of consistency, calibration and reproducibility of experimental and computational data is discussed. Results regarding the new XTMC43 benchmark set are suggested to serve as a starting point for further method development, systematic screening and crystal engineering.

Cooperativity of silanol defect chemistry in zeolites

Deboronation treatment of zeolite B-SSZ-55 can generate vacancy defects consisting of four silanol groups (silanol nests). However, ¹H solid-state NMR spectroscopy indicates the prevalence of two silanol groups (silanol dyads) instead of four silanol groups. Such silanol dyads must be formed by the silanol condensation of two silanol groups at the silanol nests. Yet, the exact mechanism of this condensation and detailed structure of the silanol defect are not known. Here, the structure and formation mechanism of silanol dyads in the SSZ-55 zeolite have been investigated by both cluster and periodic density functional theory calculations. The calculated ¹H NMR chemical shifts agree with the experimental values, showing that the silanol dyads are indeed commonly present at the vacancies and the vacancy density plays a role in the relaxation of the zeolite framework. The nature (size) of the silanol clusters influences their acidity.

Efficient Evaluation of Two-Center Gaussian Integrals in Periodic Systems

By using Poisson's summation formula, we calculate periodic integrals over Gaussian basis functions by partitioning the lattice summations between the real and reciprocal space, where both sums converge exponentially fast with a large exponent. We demonstrate that the summation can be performed efficiently to calculate two-center Gaussian integrals over various kernels including overlap, kinetic, and Coulomb. The summation in real space is performed using an efficient flavor of the McMurchie-Davidson recurrence relation. The expressions for performing summation in the reciprocal space are also derived and implemented. The algorithm for reciprocal space summation allows us to reuse several terms and leads to a significant improvement in efficiency when highly contracted basis functions with large exponents are used. We find that the resulting algorithm is only between a factor of 5 and 15 slower than that for molecular integrals, indicating the very small number of terms needed in both the real and reciprocal space summations. An outline of the algorithm for calculating three-center Coulomb integrals is also provided.

Comment on "The Nature of Chalcogen-Bonding-Type Tellurium-Nitrogen Interactions": Fixing the Description of Finite-Temperature Effects Restores the Agreement Between Experiment and Theory

Mitzel and co-workers recently presented an intriguing molecule displaying a tellurium-nitrogen interaction. Structural data obtained in the solid and in gas phase indicated a large increase of the Te-N equilibrium distance re from 2.64 to 2.92 Å, respectively. Although some DFT calculations appear to support the large re in gas phase, we argue that the lions share of the increase is due to an incomplete description of finite-temperature effects in the back-corrected experimental data. This hypothesis is based on high-level coupled-cluster (CC) and periodic DFT calculations, which consistently point towards a much smaller re in the isolated molecule. Further support comes through MD simulations with a tuned GFN2-xTB Hamiltonian: Calibrated against a CC reference, these show a six-times larger influence of temperature than with the originally used GFN1-xTB. Taking this into account, the back-corrected re in gas phase becomes 2.67±0.08 Å, in good agreement with high-level CC theory and most DFT methods.

Fast periodic Gaussian density fitting by range separation

We present an efficient implementation of periodic Gaussian density fitting (GDF) using the Coulomb metric. The three-center integrals are divided into two parts by range-separating the Coulomb kernel, with the short-range part evaluated in real space and the long-range part in reciprocal space. With a few algorithmic optimizations, we show that this new method-which we call range-separated GDF (RSGDF)-scales sublinearly to linearly with the number of k-points for small to medium-sized k-point meshes that are commonly used in periodic calculations with electron correlation. Numerical results on a few three-dimensional solids show about ten-fold speedups over the previously developed GDF with little precision loss. The error introduced by RSGDF is about 10^-5E_h in the converged Hartree-Fock energy with default auxiliary basis sets and can be systematically reduced by increasing the size of the auxiliary basis with little extra work.

Combining wavefunction frozen-density embedding with one-dimensional periodicity

We present the combination of wavefunction frozen-density embedding (FDE) with a periodic repetition in one dimension (1D) for molecular systems in the KOALA program. In this periodic orbital-uncoupled FDE ansatz, no wavefunction overlap is taken into account, and only the electron density of the active subsystem is computed explicitly. This density is relaxed in the presence of the environment potential, which is obtained by translating the updated active subsystem density, yielding a fully self-consistent solution at convergence. Treating only one subsystem explicitly, the method allows for the calculation of local properties in condensed molecular systems, while no orbital band structure is obtained preventing the application, e.g., to systems with metallic bonding. In order to illustrate possible applications of the new implementation, selected case studies are presented, ranging from ground-state dipole moments using configuration interaction methods via excitation energies using time-dependent density-functional theory to ionization potentials obtained from equation-of-motion correlation methods. Different levels of approximations are assessed, revealing that an active subsystem consisting of two or three molecules leads to results that are converged with respect to the environment contributions.

r2SCAN-3c: A "Swiss army knife" composite electronic-structure method

The recently proposed r²SCAN meta-generalized-gradient approximation (mGGA) of Furness and co-workers is used to construct an efficient composite electronic-structure method termed r²SCAN-3c. To this end, the unaltered r²SCAN functional is combined with a tailor-made triple-ζ Gaussian atomic orbital basis set as well as with refitted D4 and geometrical counter-poise corrections for London-dispersion and basis set superposition error. The performance of the new method is evaluated for the GMTKN55 database covering large parts of chemical space with about 1500 data points, as well as additional benchmarks for non-covalent interactions, organometallic reactions, and lattice energies of organic molecules and ices, as well as for the adsorption on polar salt and non-polar coinage-metal surfaces. These comprehensive tests reveal a spectacular performance and robustness of r²SCAN-3c: It by far surpasses its predecessor B97-3c at only twice the cost and provides one of the best results of all semi-local density-functional theory (DFT)/QZ methods ever tested for the GMTKN55 database at one-tenth of the cost. Specifically, for reaction and conformational energies as well as non-covalent interactions, it outperforms prominent hybrid-DFT/QZ approaches at two to three orders of magnitude lower cost. Perhaps, the most relevant remaining issue of r²SCAN-3c is self-interaction error (SIE), owing to its mGGA nature. However, SIE is slightly reduced compared to other (m)GGAs, as is demonstrated in two examples. After all, this remarkably efficient and robust method is chosen as our new group default, replacing previous composite DFT and partially even expensive high-level methods in most standard applications for systems with up to several hundreds of atoms.

Ionothermal Synthesis of Imide-Linked Covalent Organic Frameworks

Covalent organic frameworks (COFs) are an extensively studied class of porous materials, which distinguish themselves from other porous polymers in their crystallinity and high degree of modularity, enabling a wide range of applications. COFs are most commonly synthesized solvothermally, which is often a time-consuming process and restricted to well-soluble precursor molecules. Synthesis of polyimide-linked COFs (PI-COFs) is further complicated by the poor reversibility of the ring-closing reaction under solvothermal conditions. Herein, we report the ionothermal synthesis of crystalline and porous PI-COFs in zinc chloride and eutectic salt mixtures. This synthesis does not require soluble precursors and the reaction time is significantly reduced as compared to standard solvothermal synthesis methods. In addition to applying the synthesis to previously reported imide COFs, a new perylene-based COF was also synthesized, which could not be obtained by the classical solvothermal route. In situ high-temperature XRPD analysis hints to the formation of precursor-salt adducts as crystalline intermediates, which then react with each other to form the COF.

Rational Design of Covalent Cobaloxime-Covalent Organic Framework Hybrids for Enhanced Photocatalytic Hydrogen Evolution

Covalent organic frameworks (COFs) display a unique combination of chemical tunability, structural diversity, high porosity, nanoscale regularity, and thermal stability. Recent efforts are directed at using such frameworks as tunable scaffolds for chemical reactions. In particular, COFs have emerged as viable platforms for mimicking natural photosynthesis. However, there is an indisputable need for efficient, stable, and economical alternatives for the traditional platinum-based cocatalysts for light-driven hydrogen evolution. Here, we present azide-functionalized chloro(pyridine)cobaloxime hydrogen-evolution cocatalysts immobilized on a hydrazone-based COF-42 backbone that show improved and prolonged photocatalytic activity with respect to equivalent physisorbed systems. Advanced solid-state NMR and quantum-chemical methods allow us to elucidate details of the improved photoreactivity and the structural composition of the involved active site. We found that a genuine interaction between the COF backbone and the cobaloxime facilitates recoordination of the cocatalyst during the photoreaction, thereby improving the reactivity and hindering degradation of the catalyst. The excellent stability and prolonged reactivity make the herein reported cobaloxime-tethered COF materials promising hydrogen evolution catalysts for future solar fuel technologies.

TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations

TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy-cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe-Salpeter methods, second-order Møller-Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE's functionality, including excited-state methods, RPA and Green's function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE's current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE's development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted.

Intermolecular Interactions in Molecular Organic Crystals upon Relaxation of Lattice Parameters

Crystal structure prediction is based on the assumption that the most thermodynamically stable structure will crystallize first. The existence of other structures such as polymorphs or from counterenantiomers requires an accurate calculation of the electronic energy. Using atom-centered Gaussian basis functions in periodic Density Functional Theory (DFT) calculations in Turbomole, the performance of two dispersion-corrected functionals, PBE-D3 and B97-D, is assessed for molecular organic crystals of the X23 benchmark set. B97-D shows a MAE (mean absolute error) of 4 kJ/mol, compared to 9 kJ/mol for PBE-D3. A strategy for the convergence of lattice energies towards the basis set limit is outlined. A simultaneous minimization of molecular structures and lattice parameters shows that both methods are able to reproduce experimental unit cell parameters to within 4–5%. Calculated lattice energies, however, deviate slightly more from the experiment, i.e., by 0.4 kJ/mol after unit cell optimization for PBE-D3 and 0.5 kJ/mol for B97-D. The accuracy of the calculated lattice energies compared to the experimental values demonstrates the ability of current DFT methods to assist in the quest for possible polymorphs and enantioselective crystallization processes.

Structure of Diferrocenyl Thioketone: From Molecule to Crystal

Ferrocenyl-functionalized thioketones have recently been recognized as useful building blocks for sulfur-containing compounds with potential applications in materials chemistry. This work is devoted to a single representative of such thioketones, namely diferrocenyl thioketone (Fc₂CS), whose structure has been determined here for the first time. Both X-ray crystallography and a wide variety of quantum-chemical methods were used to explore the structure of Fc₂CS. In addition to the X-ray structure determination, intermolecular interactions occurring in the crystal structure of Fc₂CS were examined in detail by quantum-chemical methods. These methods were also an invaluable tool in studying the molecular structure of Fc₂CS, from the gas phase to solutions and to its crystal. Intramolecular interactions governing the conformational behavior of an isolated Fc₂CS molecule were deduced from quantum-chemical analyses carried out in orbital space and real space. Our experimental and theoretical results indicate that the main structural features of an isolated Fc₂CS molecule in its lowest-energy geometry are retained both upon solvation and in the crystal. The tilt of ferrocenyl groups is only slightly affected by crystal packing forces that are dominated by dispersion. Nonetheless, a network of intermolecular interactions, such as H···H, C···H and S···H, was detected in the Fc₂CS crystal but each of them is fairly weak.

Atomistic Simulations of Plasma-Enhanced Atomic Layer Deposition

Plasma-enhanced atomic layer deposition (PEALD) is a widely used, powerful layer-by-layer coating technology. Here, we present an atomistic simulation scheme for PEALD processes, combining the Monte Carlo deposition algorithm and structure relaxation using molecular dynamics. In contrast to previous implementations, our approach employs a real, atomistic model of the precursor. This allows us to account for steric hindrance and overlap restrictions at the surface corresponding to the real precursor deposition step. In addition, our scheme takes various process parameters into account, employing predefined probabilities for precursor products at each Monte Carlo deposition step. The new simulation protocol was applied to investigate PEALD synthesis of SiO₂ thin films using the bis-diethylaminosilane precursor. It revealed that increasing the probability for precursor binding to one surface oxygen atom favors amorphous layer growth, a large number of –OH impurities, and the formation of voids. In contrast, a higher probability for precursor binding to two surface oxygen atoms leads to dense SiO₂ film growth and a reduction of –OH impurities. Increasing the probability for the formation of doubly bonded precursor sites is therefore the key factor for the formation of dense SiO₂ PEALD thin films with reduced amounts of voids and –OH impurities.

Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole method: Stress tensor

A full implementation of the analytical stress tensor for periodic systems is reported in the TURBOMOLE program package within the framework of Kohn-Sham density functional theory using Gaussian-type orbitals as basis functions. It is the extension of the implementation of analytical energy gradients (Lazarski et al., Journal of Computational Chemistry 2016, 37, 2518-2526) to the stress tensor for the purpose of optimization of lattice vectors. Its key component is the efficient calculation of the Coulomb contribution by combining density fitting approximation and continuous fast multipole method. For the exchange-correlation (XC) part the hierarchical numerical integration scheme (Burow and Sierka, Journal of Chemical Theory and Computation 2011, 7, 3097-3104) is extended to XC weight derivatives and stress tensor. The computational efficiency and favorable scaling behavior of the stress tensor implementation are demonstrated for various model systems. The overall computational effort for energy gradient and stress tensor for the largest systems investigated is shown to be at most two and a half times the computational effort for the Kohn-Sham matrix formation. © 2019 Wiley Periodicals, Inc.

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.

Simplified DFT methods for consistent structures and energies of large systems

Kohn-Sham density functional theory (DFT) is routinely used for the fast electronic structure computation of large systems and will most likely continue to be the method of choice for the generation of reliable geometries in the foreseeable future. Here, we present a hierarchy of simplified DFT methods designed for consistent structures and non-covalent interactions of large systems with particular focus on molecular crystals. The covered methods are a minimal basis set Hartree-Fock (HF-3c), a small basis set screened exchange hybrid functional (HSE-3c), and a generalized gradient approximated functional evaluated in a medium-sized basis set (B97-3c), all augmented with semi-classical correction potentials. We give an overview on the methods design, a comprehensive evaluation on established benchmark sets for geometries and lattice energies of molecular crystals, and highlight some realistic applications on large organic crystals with several hundreds of atoms in the primitive unit cell.

A program for automatically predicting supramolecular aggregates and its application to urea and porphin

Not only the molecular structure but also the presence or absence of aggregates determines many properties of organic materials. Theoretical investigation of such aggregates requires the prediction of a suitable set of diverse structures. Here, we present the open-source program EnergyScan for the unbiased prediction of geometrically diverse sets of small aggregates. Its bottom-up approach is complementary to existing ones by performing a detailed scan of an aggregate's potential energy surface, from which diverse local energy minima are selected. We crossvalidate this approach by predicting both literature-known and heretofore unreported geometries of the urea dimer. We also predict a diverse set of dimers of the less intensely studied case of porphin, which we investigate further using quantum chemistry. For several dimers, we find strong deviations from a reference absorption spectrum, which we explain using computed transition densities. This proof of principle clearly shows that EnergyScan successfully predicts aggregates exhibiting large structural and spectral diversity. © 2018 Wiley Periodicals, Inc.