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We quantify the thermodynamic equilibrium conditions that govern the formation of crystalline heptazine-based carbon nitride materials, currently of enormous interest for photocatalytic applications including solar hydrogen evolution. Key phases studied include the monomeric phase melem, the 1D polymer melon, and the hypothetical hydrogen-free 2D graphitic carbon nitride phase "g-C3N4". Our study is based on density functional theory including van der Waals dispersion terms with different experimental conditions represented by the chemical potential of NH3. Graphitic carbon nitride is the subject of a vast number of studies, but its existence is still controversial. We show that typical conditions found in experiments pertain to the polymer melon (2D planes of 1D hydrogen-bonded polymer strands). In contrast, equilibrium synthesis of heptazine (h)-based g-h-C3N4 below its experimentally known decomposition temperature requires much less likely conditions, equivalent to low NH3 partial pressures around 1 Pa at 500 °C and around 10³ Pa even at 700 °C. A recently reported synthesis of triazine (t)-based g-t-C3N4 in a salt melt is interpreted as a consequence of the altered local chemical environment of the C3N4 nanocrystallites. [ABSTRACT FROM AUTHOR]

We present an accurate computational approach to calculate absolute K -edge core electron excitation energies as measured by X-ray absorption spectroscopy. Our approach employs an all-electron Bethe-Salpeter equation (BSE) formalism based on GW quasiparticle energies (BSE@ GW ) using numeric atom-centered orbitals (NAOs). The BSE@ GW method has become an increasingly popular method for the computation of neutral valence excitation energies of molecules. However, it was so far not applied to molecular K -edge excitation energies. We discuss the influence of different numerical approximations on the BSE@ GW calculation and employ in our final setup (i) exact numeric algorithms for the frequency integration of the GW self-energy, (ii) G 0 W 0 and BSE starting points with ∼50% of exact exchange, (iii) the Tamm-Dancoff approximation and (iv) relativistic corrections. We study the basis set dependence and convergence with common Gaussian-type orbital and NAO basis sets. We identify the importance of additional spatially confined basis functions as well as of diffuse augmenting basis functions. The accuracy of our BSE@ GW method is assessed for a benchmark set of small organic molecules, previously used for benchmarking the equation-of-motion coupled cluster method [Peng et al., J. Chem. Theory Comput. , 2015 , 11 , 4146], as well as the medium-sized dibenzothiophene (DBT) molecule. Our BSE@ GW results for absolute excitation energies are in excellent agreement with the experiment, with a mean average error of only 0.63 eV for the benchmark set and with errors <1 eV for the DBT molecule.

Quaternary chalcogenide semiconductors are promising materials for energy conversion and nonlinear optical applications, with properties tunable primarily by varying the elemental composition and crystal structure. Here, we first analyze the connections among several cubic crystal structure types, as well as the orthorhombic Ag 2 PbGeS 4 -type structure, reported for select members within the Ag-B II -M IV -X (B II = Sr, Pb; M IV = Si, Ge, Sn; X = S, Se) compositional space. Focusing on the Ag-Pb-Si-S and Ag-Sr-Sn-S systems, we show that one structure type, with the formulas Ag 2 Pb 3 Si 2 S 8 and Ag 2 Sr 3 Sn 2 S 8 , is favored. We have prepared powder and single-crystal samples of Ag 2 Pb 3 Si 2 S 8 and Ag 2 Sr 3 Sn 2 S 8 , showing that each takes on the noncentrosymmetric cubic space group I 4̅3 d and is isostructural to the previously reported compound Ag 2 Sr 3 Ge 2 Se 8 . Through hybrid density functional theory calculations, these cubic compounds are demonstrated to be (quasi-)direct band gap semiconductors with high densities of states at the band maxima. The band-gap energies are measured by reflectance spectroscopy as 1.95(3) and 2.66(4) eV for Ag 2 Pb 3 Si 2 S 8 and Ag 2 Sr 3 Sn 2 S 8 , respectively. We further measure the optical properties and show the electronic band structures of three other isostructural A I -B II -M IV -X-type materials, i.e., Ag 2 Sr 3 Si 2 S 8 , Ag 2 Sr 3 Ge 2 S 8 , and Ag 2 Sr 3 Ge 2 Se 8 , showing that the band gaps can be predictably tuned by element substitution. Detailed visual analyses of the different structures and of their relationships with other members of the Ag-B II -M IV -X compositional family provide a basis for a broader understanding of the structure formation and optoelectronic properties within the quaternary chalcogenide semiconductor family.

Quaternary chalcogenide materials have long been a source of semiconductors for optoelectronic applications. Recent studies on I 2 -II-IV-X 4 (I = Ag, Cu, Li; II = Ba, Sr, Eu, Pb; IV = Si, Ge, Sn; X = S, Se) materials have shown particular versatility and promise among these compounds. These semiconductors take advantage of a diverse bonding scheme and chemical differences among cations to target a degree of antisite defect resistance. Within this set of compounds, the materials containing both Ag and Sr have not been experimentally studied and leave a gap in the full understanding of the family. Here, we have synthesized powders and single crystals of two Ag- and Sr-containing compounds, Ag 2 SrSiS 4 and Ag 2 SrGeS 4 , each found to form in the tetragonal I 4̅2 m structure of Ag 2 BaGeS 4 . During the synthesis targeting the title compounds, two additional materials, Ag 2 Sr 3 Si 2 S 8 and Ag 2 Sr 3 Ge 2 S 8 , have also been identified. These cubic compounds represent impurity phases during the synthesis of Ag 2 SrSiS 4 and Ag 2 SrGeS 4 . We show through hybrid density functional theory calculations that Ag 2 SrSiS 4 and Ag 2 SrGeS 4 have highly dispersive band-edge states and indirect band gaps, experimentally measured as 2.08(1) and 1.73(2) eV, respectively. Second-harmonic generation measurements on Ag 2 SrSiS 4 and Ag 2 SrGeS 4 powders show frequency-doubling capabilities in the near-infrared range.

With the advent of efficient electronic structure methods, effective continuum solvation methods have emerged as a way to, at least partially, include solvent effects into simulations without the need for expensive sampling over solvent degrees of freedom. The multipole moment expansion (MPE) model, while based on ideas initially put forward almost 100 years ago, has recently been updated for the needs of modern electronic structure calculations. Indeed, for an all-electron code relying on localized basis sets and-more importantly-a multipole moment expansion of the electrostatic potential, the MPE method presents a particularly cheap way of solving the macroscopic Poisson equation to determine the electrostatic response of a medium surrounding a solute. In addition to our implementation of the MPE model in the FHI-aims electronic structure theory code [ Blum , V. ; Comput. Phys. Commun. 2009 , 180 , 2175 - 2196 , DOI: 10.1016/j.cpc.2009.06.022 ], we describe novel algorithms for determining equidistributed points on the solvation cavity-defined as a charge density isosurface-and the determination of cavity surface and volume from just this collection of points and their local density gradients. We demonstrate the efficacy of our model on an analytically solvable test case, against high-accuracy finite-element calculations for a set of ≈140000 2D test cases, and finally against experimental solvation free energies of a number of neutral and singly charged molecular test sets [ Andreussi , O. ; J. Chem. Phys. 2012 , 136 , 064102 , DOI: 10.1063/1.3676407 ; Marenich , A. V. ; Minnesota Solvation Database , Version 2012; University of Minnesota : Minneapolis, MN, USA , 2012 . ]. In all test cases we find that our MPE approach compares very well with given references at computational overheads < 20% and sometimes much smaller compared to a plain self-consistency cycle.

Parahydrogen is an inexpensive and readily available source of hyperpolarization used to enhance magnetic resonance signals by up to four orders of magnitude above thermal signals obtained at ∼10 T. A significant challenge for applications is fast signal decay after hyperpolarization. Here we use parahydrogen-based polarization transfer catalysis at microtesla fields (first introduced as SABRE-SHEATH) to hyperpolarize 13 C 2 spin pairs and find decay time constants of 12 s for magnetization at 0.3 mT, which are extended to 2 min at that same field, when long-lived singlet states are hyperpolarized instead. Enhancements over thermal at 8.5 T are between 30 and 170 fold (0.02 to 0.12% polarization). We control the spin dynamics of polarization transfer by choice of microtesla field, allowing for deliberate hyperpolarization of either magnetization or long-lived singlet states. Density functional theory calculations and experimental evidence identify two energetically close mechanisms for polarization transfer: First, a model that involves direct binding of the 13 C 2 pair to the polarization transfer catalyst and, second, a model transferring polarization through auxiliary protons in substrates.

Using multiwavelets, we have obtained total energies and corresponding atomization energies for the GGA-PBE and hybrid-PBE0 density functionals for a test set of 211 molecules with an unprecedented and guaranteed μHartree accuracy. These quasi-exact references allow us to quantify the accuracy of standard all-electron basis sets that are believed to be highly accurate for molecules, such as Gaussian-type orbitals (GTOs), all-electron numeric atom-centered orbitals (NAOs), and full-potential augmented plane wave (APW) methods. We show that NAOs are able to achieve the so-called chemical accuracy (1 kcal/mol) for the typical basis set sizes used in applications, for both total and atomization energies. For GTOs, a triple-ζ quality basis has mean errors of ∼10 kcal/mol in total energies, while chemical accuracy is almost reached for a quintuple-ζ basis. Due to systematic error cancellations, atomization energy errors are reduced by almost an order of magnitude, placing chemical accuracy within reach also for medium to large GTO bases, albeit with significant outliers. In order to check the accuracy of the computed densities, we have also investigated the dipole moments, where in general only the largest NAO and GTO bases are able to yield errors below 0.01 D. The observed errors are similar across the different functionals considered here.

Interfaces and subsurface layers are critical for the performance of devices made of 2D materials and heterostructures. Facile, nondestructive, and quantitative ways to characterize the structure of atomically thin, layered materials are thus essential to ensure control of the resultant properties. Here, we show that contact-resonance atomic force microscopy-which is exquisitely sensitive to stiffness changes that arise from even a single atomic layer of a van der Waals-adhered material-is a powerful experimental tool to address this challenge. A combined density functional theory and continuum modeling approach is introduced that yields sub-surface-sensitive, nanomechanical fingerprints associated with specific, well-defined structure models of individual surface domains. Where such models are known, this information can be correlated with experimentally obtained contact-resonance frequency maps to reveal the (sub)surface structure of different domains on the sample.

This work focuses on the control of the polymerization process for melon ("graphitic carbon nitride"), with the aim of improving its photocatalytic activity intrinsically. We demonstrate here that reduction of the synthesis temperature leads to a mixture of the monomer melem and its higher condensates. We show that this mixture can be separated and provide evidence that the higher condensates are isolated oligomers of melem. On evaluating their photocatalytic activity for hydrogen evolution, the oligomers were found to be the most active species, having up to twice the activity of the monomer/oligomer mixture of the as-synthesized material, which in turn has 3 times the activity of the polymer melon, the literature benchmark. These results highlight the role of "defects", i.e., chain terminations, in increasing the catalytic activity of carbon nitrides and at the same time point to the ample potential of intrinsically improving the photocatalytic activity of "carbon nitride", especially through the selective synthesis of the active phase.

We assess the performance of a group of exchange-correlation functionals for predicting the secondary structure of peptide chains, up to a new many-body dispersion corrected hybrid density functional, dubbed PBE0+MBD* by its original authors. For the purpose of validation, we first compare to published, high-level benchmark conformational energy hierarchies (coupled cluster at the singles, doubles, and perturbative triples level, CCSD(T)) for 73 conformers of small three-residue peptides, establishing that the van der Waals corrected PBE0 functional yields an average error of only ∼20 meV (∼0.5 kcal/mol). This compares to ∼40-50 meV for nondispersion corrected PBE0 and 40-100 meV for different empirical force fields (estimated for the alanine tetrapeptide). For longer peptide chains that form a secondary structure, CCSD(T) level benchmark data are currently unaffordable. We thus turn to the experimentally well studied Ac-Phe-Ala5-LysH(+) peptide, for which four closely competing conformers were established by infrared spectroscopy. For comparison, an exhaustive theoretical conformational space exploration yields at least 11 competing low energy minima. We show that (i) the many-body dispersion correction, (ii) the hybrid functional nature of PBE0+MBD*, and (iii) zero-point corrections are needed to reveal the four experimentally observed structures as the minima that would be populated at low temperature.

Using the minima hopping global optimization method at the density functional level, we found low-energy nanostructures for neutral Au26 and its anion. The local-density and a generalized gradient approximation of the exchange–correlation functional predict different nanoscale motifs. We found a vast number of isomers within a small energy range above the respective putative global minima with each method. Photoelectron spectroscopy of Au26(-) under different experimental conditions revealed definitive evidence of the presence of multiple isomers, consistent with the theoretical predictions. Comparison between the experimental and simulated photoelectron spectra suggests that the photoelectron spectra of Au26(-) contain a mixture of three isomers, all of which are low-symmetry core–shell-type nanoclusters with a single internal Au atom. We present a disconnectivity graph for Au26(-) that has been computed completely at the density functional level. The transition states used to build this disconnectivity graph are complete enough to predict Au26(-) to have a possible fluxional shell, which facilitates the understanding of its catalytic activity.

Helices are a key folding motif in protein structure. The question of which factors determine helix stability for a given polypeptide or protein is an ongoing challenge. Here we use van-der-Waals-corrected density functional theory to address a part of this question in a bottom-up approach. We show how intrinsic helical structure is stabilized with length and temperature for a series of experimentally well-studied unsolvated alanine-based polypeptides, Ac-Alan-LysH(+). By exhaustively exploring the conformational space of these molecules, we find that helices emerge as the preferred structure in the length range n = 4-8 not just due to enthalpic factors (hydrogen bonds and their cooperativity, van der Waals dispersion interactions, electrostatics) but importantly also by a vibrational entropic stabilization over competing conformers at room temperature. The stabilization is shown to be due to softer low-frequency vibrational modes in helical conformers than in more compact ones. This observation is corroborated by including anharmonic effects explicitly through ab initio molecular dynamics and generalized by testing different terminations and considering larger helical peptide models.

We study the initial steps of the interaction of water molecules with two unsolvated peptides: Ac-Ala(5)-LysH(+) and Ac-Ala(8)-LysH(+). Each peptide has two primary candidate sites for water adsorption near the C-terminus: a protonated carboxyl group and the protonated ammonium group of LysH(+), which is fully hydrogen-bonded (self-solvated) in the absence of water. Earlier experimental studies have shown that H(2)O adsorbs readily at Ac-Ala(5)-LysH(+) (a non-helical peptide) but with a much lower propensity at Ac-Ala(8)-LysH(+) (a helix) under the same conditions. The helical conformation of Ac-Ala(8)-LysH(+) has been suggested as the origin of the different behavior. We here use first-principles conformational searches (all-electron density functional theory based on a van der Waals corrected version of the PBE functional, PBE+vdW) to study the microsolvation of Ac-Ala(5)-LysH(+) with one to five water molecules and the monohydration of Ac-Ala(8)-LysH(+). In both cases, the most favorable water adsorption sites break intramolecular hydrogen bonds associated with the ammonium group, in contrast to earlier suggestions in the literature. A simple thermodynamic model yields Gibbs free energies ΔG(0)(T) and equilibrium constants in agreement with experiments. A qualitative change of the first adsorption site does not occur. For few water molecules, we do not consider carboxyl deprotonation or finite-temperature dynamics, but in a liquid solvent, both effects would be important. Exploratory ab initio molecular dynamics simulations illustrate the short-time effects of a droplet of 152 water molecules on the initial unsolvated conformation, including the deprotonation of the carboxyl group. The self-solvation of the ammonium group by intramolecular hydrogen bonds is lifted in favor of a solvation by water.