Postsynthetic Transformation of Imine- into Nitrone-Linked Covalent Organic Frameworks for Atmospheric Water Harvesting at Decreased Humidity.

Herein, we report a facile postsynthetic linkage conversion method giving synthetic access to nitrone-linked covalent organic frameworks (COFs) from imine- and amine-linked COFs. The new two-dimensional (2D) nitrone-linked covalent organic frameworks, NO-PI-3-COF and NO-TTI-COF, are obtained with high crystallinity and large surface areas. Nitrone-modified pore channels induce condensation of water vapor at 20% lower humidity compared to their amine- or imine-linked precursor COFs. Thus, the topochemical transformation to nitrone linkages constitutes an attractive approach to postsynthetically fine-tune water adsorption properties in framework materials.

Highly accurate σ- and τ-functionals for beyond-RPA methods with approximate exchange kernels.

σ-Functionals are promising new developments for the Kohn-Sham correlation energy based upon the direct Random Phase Approximation (dRPA) within the adiabatic connection formalism, providing impressive improvements over dRPA for a broad range of benchmarks. However, σ-functionals exhibit a high amount of self-interaction inherited from the approximations made within dRPA. Inclusion of an exchange kernel in deriving the coupling-strength-dependent density-density response function leads to so-called τ-functionals, which - apart from a fourth-order Taylor series expansion - have only been realized in an approximate fashion so far to the best of our knowledge, most notably in the form of scaled σ-functionals. In this work, we derive, optimize, and benchmark three types of σ- and τ-functionals including approximate exchange effects in the form of an antisymmetrized Hartree kernel. These functionals, based on a second-order screened exchange type contribution in the adiabatic connection formalism, the electron-hole time-dependent Hartree-Fock kernel (eh-TDHF) otherwise known as RPA with exchange (RPAx), and an approximation thereof known as approximate exchange kernel (AXK), are optimized on the ASCDB database using two new parametrizations named A1 and A2. In addition, we report a first full evaluation of σ- and τ-functionals on the GMTKN55 database, revealing our exchange-including functionals to considerably outperform existing σ-functionals while being highly competitive with some of the best double-hybrid functionals of the original GMTKN55 publication. In particular, the σ-functionals based on AXK and τ-functionals based on RPAx with PBE0 reference stand out as highly accurate approaches for a wide variety of chemically relevant problems.

Exponential averaging versus umbrella sampling for computing the QM/MM free energy barrier of the initial step of the desuccinylation reaction catalyzed by sirtuin 5.

The computational characterization of enzymatic reactions poses a great challenge which arises from the high dimensional and often rough potential energy surfaces commonly explored by static QM/MM methods such as adiabatic mapping (AM). The present study highlights the difficulties in estimating free energy barriers via exponential averaging over AM pathways. Based on our previous study [von der Esch et al., J. Chem. Theory Comput., 2019, 15, 6660-6667], where we analyzed the first reaction step of the desuccinylation reaction catalyzed by human sirtuin 5 (SIRT5) by means of QM/MM adiabatic mapping and machine learning, we use, here, umbrella sampling to compute the free energy profile of the initial reaction step. The computational investigations show that the initial step of the desuccinylation reaction proceeds via an SN2-type reaction mechanism in SIRT5, suggesting that the first step of the deacylation reactions catalyzed by sirtuins is highly conserved. In addition, the direct comparison of the extrapolated free energy barrier from minimal energy paths and the computed free energy path from umbrella sampling further underlines the importance of extensive sampling.

Statistically optimal analysis of the extended-system adaptive biasing force (eABF) method.

The extended-system adaptive biasing force (eABF) method and its newer variants offer rapid exploration of the configuration space of chemical systems. Instead of directly applying the ABF bias to collective variables, they are harmonically coupled to fictitious particles, which separates the problem of enhanced sampling from that of free energy estimation. The prevalent analysis method to obtain the potential of mean force (PMF) from eABF is thermodynamic integration. However, besides the PMF, most information is lost as the unbiased probability of visited configurations is never recovered. In this contribution, we show how statistical weights of individual frames can be computed using the Multistate Bennett's Acceptance Ratio (MBAR), putting the post-processing of eABF on one level with other frequently used sampling methods. In addition, we apply this formalism to the prediction of nuclear magnetic resonance shieldings, which are very sensitive to molecular geometries and often require extensive sampling. The results show that the combination of enhanced sampling by means of extended-system dynamics with the MBAR estimator is a highly useful tool for the calculation of ensemble properties. Furthermore, the extension of the presented scheme to the recently published Gaussian-accelerated molecular dynamics eABF hybrid is straightforward and approximation free.

How to obtain reaction free energies from free-energy profiles.

For chemical reactions that occur via the rearrangement of atoms from a configuration about one minimum (reactant, R) of the potential energy surface (PES) to a configuration about another minimum (product, P), an exact relation between the Helmholtz reaction free energy (ΔFRP) and the free-energy profile (FEP) can be derived. Since the FEP assumes a form similar to that of the PES along the minimum energy path between R and P, there is an unfortunate tendency to regard the FEP as the "free-energy" analog of the minimum energy path and consequently to equate ΔFRP to the difference between the values of the FEP at the minima corresponding to R and P. Analytic treatments of one- and two-dimensional models are presented that show how this mistaken idea leads to errors. In effect, treating the FEP by analogy with the minimum energy path neglects the role of entropy. The FEP is a function of a collective variable (CV), which must be chosen to describe the course of the rearrangement consistently with the exact relation between ΔFRP and the FEP. For large systems of common interest, the PES is often so complex that a straightforward way of choosing a CV is lacking. Consequently, one is forced to make an educated guess. A criterion for judging the quality of the guess is proposed and applied to a two-dimensional model.

From free-energy profiles to activation free energies.

Given a chemical reaction going from reactant (R) to the product (P) on a potential energy surface (PES) and a collective variable (CV) discriminating between R and P, we define the free-energy profile (FEP) as the logarithm of the marginal Boltzmann distribution of the CV. This FEP is not a true free energy. Nevertheless, it is common to treat the FEP as the "free-energy" analog of the minimum potential energy path and to take the activation free energy, ΔFRP ‡, as the difference between the maximum at the transition state and the minimum at R. We show that this approximation can result in large errors. The FEP depends on the CV and is, therefore, not unique. For the same reaction, different discriminating CVs can yield different ΔFRP ‡. We derive an exact expression for the activation free energy that avoids this ambiguity. We find ΔFRP ‡ to be a combination of the probability of the system being in the reactant state, the probability density on the dividing surface, and the thermal de Broglie wavelength associated with the transition. We apply our formalism to simple analytic models and realistic chemical systems and show that the FEP-based approximation applies only at low temperatures for CVs with a small effective mass. Most chemical reactions occur on complex, high-dimensional PES that cannot be treated analytically and pose the added challenge of choosing a good CV. We study the influence of that choice and find that, while the reaction free energy is largely unaffected, ΔFRP ‡ is quite sensitive.

Amine-Linked Covalent Organic Frameworks as a Platform for Postsynthetic Structure Interconversion and Pore-Wall Modification.

Covalent organic frameworks have emerged as a powerful synthetic platform for installing and interconverting dedicated molecular functions on a crystalline polymeric backbone with atomic precision. Here, we present a novel strategy to directly access amine-linked covalent organic frameworks, which serve as a scaffold enabling pore-wall modification and linkage-interconversion by new synthetic methods based on Leuckart-Wallach reduction with formic acid and ammonium formate. Frameworks connected entirely by secondary amine linkages, mixed amine/imine bonds, and partially formylated amine linkages are obtained in a single step from imine-linked frameworks or directly from corresponding linkers in a one-pot crystallization-reduction approach. The new, 2D amine-linked covalent organic frameworks, rPI-3-COF, rTTI-COF, and rPy1P-COF, are obtained with high crystallinity and large surface areas. Secondary amines, installed as reactive sites on the pore wall, enable further postsynthetic functionalization to access tailored covalent organic frameworks, with increased hydrolytic stability, as potential heterogeneous catalysts.

Modular Assembly of Vibrationally and Electronically Coupled Rhenium Bipyridine Carbonyl Complexes on Silicon.

Hybrid inorganic/organic heterointerfaces are promising systems for next-generation photocatalytic, photovoltaic, and chemical-sensing applications. Their performance relies strongly on the development of robust and reliable surface passivation and functionalization protocols with (sub)molecular control. The structure, stability, and chemistry of the semiconductor surface determine the functionality of the hybrid assembly. Generally, these modification schemes have to be laboriously developed to satisfy the specific chemical demands of the semiconductor surface. The implementation of a chemically independent, yet highly selective, standardized surface functionalization scheme, compatible with nanoelectronic device fabrication, is of utmost technological relevance. Here, we introduce a modular surface assembly (MSA) approach that allows the covalent anchoring of molecular transition-metal complexes with sub-nanometer precision on any solid material by combining atomic layer deposition (ALD) and selectively self-assembled monolayers of phosphonic acids. ALD, as an essential tool in semiconductor device fabrication, is used to grow conformal aluminum oxide activation coatings, down to sub-nanometer thicknesses, on silicon surfaces to enable a selective step-by-step layer assembly of rhenium(I) bipyridine tricarbonyl molecular complexes. The modular surface assembly of molecular complexes generates precisely structured spatial ensembles with strong intermolecular vibrational and electronic coupling, as demonstrated by infrared spectroscopy, photoluminescence, and X-ray photoelectron spectroscopy analysis. The structure of the MSA can be chosen to avoid electronic interactions with the semiconductor substrate to exclusively investigate the electronic interactions between the surface-immobilized molecular complexes.

Accelerating seminumerical Fock-exchange calculations using mixed single- and double-precision arithmethic.

We investigate the applicability of single-precision (fp32) floating point operations within our linear-scaling, seminumerical exchange method sn-LinK [Laqua et al., J. Chem. Theory Comput. 16, 1456 (2020)] and find that the vast majority of the three-center-one-electron (3c1e) integrals can be computed with reduced numerical precision with virtually no loss in overall accuracy. This leads to a near doubling in performance on central processing units (CPUs) compared to pure fp64 evaluation. Since the cost of evaluating the 3c1e integrals is less significant on graphic processing units (GPUs) compared to CPU, the performance gains from accelerating 3c1e integrals alone is less impressive on GPUs. Therefore, we also investigate the possibility of employing only fp32 operations to evaluate the exchange matrix within the self-consistent-field (SCF) followed by an accurate one-shot evaluation of the exchange energy using mixed fp32/fp64 precision. This still provides very accurate (1.8 µEh maximal error) results while providing a sevenfold speedup on a typical "gaming" GPU (GTX 1080Ti). We also propose the use of incremental exchange-builds to further reduce these errors. The proposed SCF scheme (i-sn-LinK) requires only one mixed-precision exchange matrix calculation, while all other exchange-matrix builds are performed with only fp32 operations. Compared to pure fp64 evaluation, this leads to 4-7× speedups for the whole SCF procedure without any significant deterioration of the results or the convergence behavior.

Efficient low-scaling computation of NMR shieldings at the second-order Møller-Plesset perturbation theory level with Cholesky-decomposed densities and an attenuated Coulomb metric.

A method for the computation of nuclear magnetic resonance (NMR) shieldings with second-order Møller-Plesset perturbation theory (MP2) is presented which allows to efficiently compute the entire set of shieldings for a given molecular structure. The equations are derived using Laplace-transformed atomic orbital second-order Møller-Plesset perturbation theory as a starting point. The Z-vector approach is employed for minimizing the number of coupled-perturbed self-consistent-field equations that need to be solved. In addition, the method uses the resolution-of-the-identity approximation with an attenuated Coulomb metric and Cholesky decomposition of pseudo-density matrices. The sparsity in the three-center integrals is exploited with sparse linear algebra approaches, leading to reduced computational cost and memory demands. Test calculations show that the deviations from NMR shifts obtained with canonical MP2 are small if appropriate thresholds are used. The performance of the method is illustrated in calculations on DNA strands and on glycine chains with up to 283 atoms and 2864 basis functions.

Computational Design and Synthesis of a Deeply Red-Shifted and Bistable Azobenzene.

We computationally dissected the electronic and geometrical influences of ortho-chlorinated azobenzenes on their photophysical properties. X-ray analysis provided the insight that trans-tetra-ortho-chloro azobenzene is conformationally flexible and thus subject to molecular motions. This allows the photoswitch to adopt a range of red-shifted geometries, which account for the extended n → π* band tails. On the basis of our results, we designed the di-ortho-fluoro di-ortho-chloro (dfdc) azobenzene and provided computational evidence for the superiority of this substitution pattern to tetra-ortho-chloro azobenzene. Thereafter, we synthesized dfdc azobenzene by ortho-chlorination via 2-fold C-H activation and experimentally confirmed its structural and photophysical properties through UV-vis, NMR, and X-ray analyses. The advantages include near-bistable isomers and an increased separation of the n → π* bands between the trans- and cis-conformations, which allows for the generation of unusually high levels of the cis-isomer by irradiation with green/yellow light as well as red light within the biooptical window.

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.

A range-separated generalized Kohn-Sham method including a long-range nonlocal random phase approximation correlation potential.

Based on our recently published range-separated random phase approximation (RPA) functional [Kreppel et al., "Range-separated density-functional theory in combination with the random phase approximation: An accuracy benchmark," J. Chem. Theory Comput. 16, 2985-2994 (2020)], we introduce self-consistent minimization with respect to the one-particle density matrix. In contrast to the range-separated RPA methods presented so far, the new method includes a long-range nonlocal RPA correlation potential in the orbital optimization process, making it a full-featured variational generalized Kohn-Sham (GKS) method. The new method not only improves upon all other tested RPA schemes including the standard post-GKS range-separated RPA for the investigated test cases covering general main group thermochemistry, kinetics, and noncovalent interactions but also significantly outperforms the popular G0W0 method in estimating the ionization potentials and fundamental gaps considered in this work using the eigenvalue spectra obtained from the GKS Hamiltonian.

A Fermi smearing variant of the Tamm-Dancoff approximation for nonadiabatic dynamics involving S1-S0 transitions: Validation and application to azobenzene.

The main shortcoming of time-dependent density functional theory (TDDFT) regarding its use for nonadiabatic molecular dynamics (NAMD) is its incapability to describe conical intersections involving the ground state. To overcome this problem, we combine Fermi smearing (FS) DFT with a fractional-occupation variant of the Tamm-Dancoff approximation (TDA) of TDDFT in the generalized gradient approximation. The resulting method (which we denote as FS-TDA) gives access to ground- and excited-state energies, gradients, and nonadiabatic coupling vectors, which are physically correct even in the vicinity of S1-S0 conical intersections. This is shown for azobenzene, a widely used photoswitch, via single point calculations and NAMD simulations of its cis-trans photoisomerization. We conclude that FS-TDA may be used as an efficient alternative to investigate these processes.

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.

Predicting 19 F†NMR Chemical Shifts: A Combined Computational and Experimental Study of a Trypanosomal Oxidoreductase-Inhibitor Complex.

The absence of fluorine from most biomolecules renders it an excellent probe for NMR spectroscopy to monitor inhibitor-protein interactions. However, predicting the binding mode of a fluorinated ligand from a chemical shift (or vice versa) has been challenging due to the high electron density of the fluorine atom. Nonetheless, reliable 19 F chemical-shift predictions to deduce ligand-binding modes hold great potential for in silico drug design. Herein, we present a systematic QM/MM study to predict the 19 F NMR chemical shifts of a covalently bound fluorinated inhibitor to the essential oxidoreductase tryparedoxin (Tpx) from African trypanosomes, the causative agent of African sleeping sickness. We include many protein-inhibitor conformations as well as monomeric and dimeric inhibitor-protein complexes, thus rendering it the largest computational study on chemical shifts of 19 F nuclei in a biological context to date. Our predicted shifts agree well with those obtained experimentally and pave the way for future work in this area.

Sustained Solar H2 Evolution from a Thiazolo[5,4-d]thiazole-Bridged Covalent Organic Framework and Nickel-Thiolate Cluster in Water.

Solar hydrogen (H2) evolution from water utilizing covalent organic frameworks (COFs) as heterogeneous photosensitizers has gathered significant momentum by virtue of the COFs' predictive structural design, long-range ordering, tunable porosity, and excellent light-harvesting ability. However, most photocatalytic systems involve rare and expensive platinum as the co-catalyst for water reduction, which appears to be the bottleneck in the development of economical and environmentally benign solar H2 production systems. Herein, we report a simple, efficient, and low-cost all-in-one photocatalytic H2 evolution system composed of a thiazolo[5,4-d]thiazole-linked COF (TpDTz) as the photoabsorber and an earth-abundant, noble-metal-free nickel-thiolate hexameric cluster co-catalyst assembled in situ in water, together with triethanolamine (TEoA) as the sacrificial electron donor. The high crystallinity, porosity, photochemical stability, and light absorption ability of the TpDTz COF enables excellent long-term H2 production over 70 h with a maximum rate of 941 µmol h-1 g-1, turnover number TONNi > 103, and total projected TONNi > 443 until complete catalyst depletion. The high H2 evolution rate and TON, coupled with long-term photocatalytic operation of this hybrid system in water, surpass those of many previously known organic dyes, carbon nitride, and COF-sensitized photocatalytic H2O reduction systems. Furthermore, we gather unique insights into the reaction mechanism, enabled by a specifically designed continuous-flow system for non-invasive, direct H2 production rate monitoring, providing higher accuracy in quantification compared to the existing batch measurement methods. Overall, the results presented here open the door toward the rational design of robust and efficient earth-abundant COF-molecular co-catalyst hybrid systems for sustainable solar H2 production in water.

Structure Elucidation of a Melam-Melem Adduct by a Combined Approach of Synchrotron X-ray Diffraction and DFT Calculations.

Melam-melem (1:1), an adduct compound that can be obtained from dicyandiamide in autoclave reactions at 450 °C and elevated ammonia pressure, had previously been described based on mass spectrometry and NMR spectroscopy, but only incompletely characterized. The crystal structure of this compound has now been elucidated by means of synchrotron microfocus diffraction and subsequent quantum-chemical structure optimization applying DFT methods. The structure was refined in triclinic space group P 1 ‾ based on X-ray data. Cell parameters of a=4.56(2), b=19.34(8), c=21.58(11) Å, α=73.34(11)°, ß=89.1(2)°, and γ=88.4(2)° were experimentally obtained. The resulting cell volumes agree with the DFT optimized value to within 7 %. Molecular units in the structure form stacks that are interconnected by a vast array of hydrogen bridge interactions. Remarkably large melam dihedral angles of 48.4° were found that allow melam to interact with melem molecules from different stack layers, thus forming a 3D network. π-stacking interactions appear to play no major role in this structure.

Identifying Free Energy Hot-Spots in Molecular Transformations.

The free energy is one of the central quantities in material and natural sciences. While being well-established, e.g., in drug design or catalyst optimization, computational methods lack a straightforward way to gain deeper insights into the calculated free energy, and thus the underlying chemical or physical processes. Here, we present a generally applicable, spectrum-based ansatz that tackles this shortcoming by identifying contributions from specific atoms or groups to the vibrational free energy. We illustrate this in studies of the bromodomain-inhibitor binding and the anomeric effect in glucose providing quantitative evidence in line with chemical intuition in both cases. For the latter example we also report an experimental infrared spectrum and find excellent agreement with our simulated spectra.

Integral partition bounds for fast and effective screening of general one-, two-, and many-electron integrals.

We introduce tight upper bounds for a variety of integrals appearing in electronic structure theories. These include electronic interaction integrals involving any number of electrons and various integral kernels such as the ubiquitous electron repulsion integrals and the three- and four-electron integrals found in explicitly correlated methods. Our bounds are also applicable to the one-electron potential integrals that appear in great number in quantum mechanical (QM), mixed quantum and molecular mechanical (QM/MM), and semi-numerical methods. The bounds are based on a partitioning of the integration space into balls centered around electronic distributions and their complements. Such a partitioning leads directly to equations for rigorous extents, which we solve for shell pair distributions containing shells of Gaussian basis functions of arbitrary angular momentum. The extents are the first general rigorous formulation we are aware of, as previous definitions are based on the inverse distance operator 1/r12 and typically only rigorous for simple spherical Gaussians. We test our bounds for six different integral kernels found throughout quantum chemistry, including exponential, Gaussian, and complementary error function based forms. We compare to previously developed estimates on the basis of significant integral counts and their usage in both explicitly correlated second-order Møller-Plesset theory (MP2-F12) and density functional theory calculations employing screened Hartree-Fock exchange.