Analysis of crystal field effects and interactions using X-ray restrained ELMOs

Critical assessment of the x-ray restrained wave function approach: Advantages, drawbacks, and perspectives for density functional theory and periodic ab initio calculations

The x-ray restrained wave function (XRW) method is a quantum crystallographic technique to extract wave functions compatible with experimental x-ray diffraction data. The approach looks for wave functions that minimize the energies of the investigated systems and also reproduce sets of x-ray structure factors. Given the strict relationship between x-ray structure factors and electron distributions, the strategy practically allows determining wave functions that correspond to given (usually experimental) electron densities. In this work, the capabilities of the XRW approach were further tested. The aim was to evaluate whether the XRW technique could serve as a tool for suggesting new exchange-correlation functionals for density functional theory or refining existing ones. Additionally, the ability of the method to address the influences of the crystalline environment was also assessed. The outcomes of XRW computations were thus compared to those of traditional gas-phase, embedding quantum mechanics/molecular mechanics, and fully periodic calculations. The results revealed that, irrespective of the initial conditions, the XRW computations practically yield a consensus electron density, in contrast to the currently employed density functional approximations (DFAs), which tend to give a too large range of electron distributions. This is encouraging in view of exploiting the XRW technique to develop improved functionals. Conversely, the calculations also emphasized that the XRW method is limited in its ability to effectively address the influences of the crystalline environment. This underscores the need for a periodic XRW technique, which would allow further untangling the shortcomings of DFAs from those inherent to the XRW approach.

Influence of N-protonation on electronic properties of acridine derivatives by quantum crystallography

Applications of 9-aminoacridine (9aa) and its derivatives span fields such as chemistry, biology, and medicine, including anticancer and antimicrobial activities. Protonation of such molecules can alter their bioavailability as weakly basic drugs like aminoacridines exhibit reduced solubility at high pH levels potentially limiting their effectiveness in patients with elevated gastric pH. In this study, we analyse the influence of protonation on the electronic characteristics of the molecular organic crystals of 9-aminoacridine. The application of quantum crystallography, including aspherical atom refinement, has enriched the depiction of electron density in the studied systems and non-covalent interactions, providing more details than previous studies. Our experimental results, combined with a topological analysis of the electron density and its Laplacian, provided detailed descriptions of how protonation changes the electron density distribution around the amine group and water molecule, concurrently decreasing the electron density at bond critical points of N/O-H bonds. Protonation also alters the molecular architecture of the systems under investigation. This is reflected in different proportions of the N⋯H and O⋯H intermolecular contacts for the neutral and protonated forms. Periodic DFT calculations of the cohesive energies of the crystal lattice, as well as computed interaction energies between molecules in the crystal, confirm that protonation stabilises the crystal structure due to a positive synergy between strong halogen and hydrogen bonds. Our findings highlight the potential of quantum crystallography in predicting crystal structure properties and point to its possible applications in developing new formulations for poorly soluble drugs.

Introduction of a weighting scheme for the X-ray restrained wavefunction approach: advantages and drawbacks

In a quite recent study [Genoni et al. (2017). IUCrJ, 4, 136-146], it was observed that the X-ray restrained wavefunction (XRW) approach allows a more efficient and larger capture of electron correlation effects on the electron density if high-angle reflections are not considered in the calculations. This is due to the occurrence of two concomitant effects when one uses theoretical X-ray diffraction data corresponding to a single-molecule electron density in a large unit cell: (i) the high-angle reflections are generally much more numerous than the low- and medium-angle ones, and (ii) they are already very well described at unrestrained level. Nevertheless, since high-angle data also contain important information that should not be disregarded, it is not advisable to neglect them completely. For this reason, based on the results of the previous investigation, this work introduces a weighting scheme for XRW calculations to up-weight the contribution of low- and medium-angle reflections, and, at the same time, to reasonably down-weight the importance of the high-angle data. The proposed strategy was tested through XRW computations with both theoretical and experimental structure-factor amplitudes. The tests have shown that the new weighting scheme works optimally if it is applied with theoretically generated X-ray diffraction data, while it is not advantageous when traditional experimental X-ray diffraction data (even of very high resolution) are employed. This also led to the conclusion that the use of a specific external parameter λ_J for each resolution range might not be a suitable strategy to adopt in XRW calculations exploiting experimental X-ray data as restraints.

On the termination of the X-ray constrained wavefunction procedure: reformulation of the method for an unequivocal determination of λ

The X-ray constrained/restrained wavefunction (XCW/XRW) approach of quantum crystallography is revisited by introducing the stationary condition of the Jayatilaka functional with respect to the Lagrange multiplier λ. The theoretical derivation has unequivocally shown that the right value of λ is a maximum stationary point of the functional to optimize, thus enabling the solution of the longstanding problem of establishing the point at which to halt the XCW/XRW procedure. Based on the new finding, a reformulation of the X-ray constrained wavefunction algorithm is proposed and its implementation is envisaged. In addition to relying on more solid mathematical grounds, the new variant of the method will be intrinsically more physically meaningful, allowing a straightforward evaluation of the highest level of confidence with which the experimental X-ray diffraction data can be possibly reproduced.

X-ray constrained wavefunctions based on Hirshfeld atoms. II. Reproducibility of electron densities in crystals of α-oxalic acid dihydrate

The Hirshfeld atom-based X-ray constrained wavefunction fitting (HA-XCW) procedure is tested for its reproducibility, and the information content of the fitted wavefunction is critically assessed. Fourteen different α-oxalic acid dihydrate data sets are used for this purpose, and the first joint fitting to 12 of these data sets is reported. There are systematic features in the electron density obtained from all data sets which agree with higher level benchmark calculations, but there are also many other strong systematic features which disagree with the reference calculations, most notably those associated with the electron density near the nuclei. To enhance reproducibility, three new protocols are described and tested to address the halting problem of XCW fitting, namely: an empirical power-function method, which is useful for estimating the accuracy of the structure factor uncertainties; an asymptotic extrapolation method based on ideas from density functional theory; and a `conservative method' whereby the smallest value of the regularization parameter is chosen from a series of data sets, or subsets.

Remarks on X-ray constrained/restrained wavefunction fitting

X-ray constrained/restrained wavefunctions (XCWs/XRWs) result from a combination of theory and experiment and are therefore affected by experimental errors and model uncertainties. The present XCW/XRW procedure does not take this into account, thus limiting the meaning and significance of the obtained wavefunctions.

X-ray constrained wavefunctions based on Hirshfeld atoms. I. Method and review

The X-ray constrained wavefunction (XCW) procedure for obtaining an experimentally reconstructed wavefunction from X-ray diffraction data is reviewed. The two-center probability distribution model used to perform nuclear-position averaging in the original paper [Grimwood & Jayatilaka (2001). Acta Cryst. A57, 87-100] is carefully distinguished from the newer one-center probability distribution model. In the one-center model, Hirshfeld atoms are used, and the Hirshfeld atom based X-ray constrained wavefunction (HA-XCW) procedure is described for the first time, as well as its efficient implementation. In this context, the definition of the related X-ray wavefunction refinement (XWR) method is refined. The key halting problem for the XCW method - the procedure by which one determines when overfitting has occurred - is named and work on it reviewed.

lamaGOET: an interface for quantum crystallography

In quantum crystallography, theoretical calculations and crystallographic refinements are closely intertwined. This means that the employed software must be able to perform both quantum-mechanical calculations and crystallographic least-squares refinements. So far, the program Tonto is the only one able to do that. The lamaGOET interface described herein deals with this issue since it interfaces dedicated quantum-chemical software (the widely used Gaussian package and the specialized ELMOdb program) with the refinement capabilities of Tonto. Three different flavours of quantum-crystallographic refinements of the dipetide glycyl-l-threonine dihydrate are presented to showcase the capabilities of lamaGOET: Hirshfeld atom refinement (HAR), HAR-ELMO, namely HAR coupled with extremely localized molecular orbitals, and X-ray constrained wavefunction fitting.

The advanced treatment of hydrogen bonding in quantum crystallography

Although hydrogen bonding is one of the most important motifs in chemistry and biology, H-atom parameters are especially problematic to refine against X-ray diffraction data. New developments in quantum crystallography offer a remedy. This article reports how hydrogen bonds are treated in three different quantum-crystallographic methods: Hirshfeld atom refinement (HAR), HAR coupled to extremely localized molecular orbitals and X-ray wavefunction refinement. Three different compound classes that form strong intra- or intermolecular hydrogen bonds are used as test cases: hydrogen maleates, the tripeptide l-alanyl-glycyl-l-alanine co-crystallized with water, and xylitol. The differences in the quantum-mechanical electron densities underlying all the used methods are analysed, as well as how these differences impact on the refinement results.

Similarities and Differences between Crystal and Enzyme Environmental Effects on the Electron Density of Drug Molecules

The crystal interaction density is generally assumed to be a suitable measure of the polarization of a low-molecular weight ligand inside an enzyme, but this approximation has seldomly been tested and has never been quantified before. In this study, we compare the crystal interaction density and the interaction electrostatic potential for a model compound of loxistatin acid (E64c) with those inside cathepsin B, in solution, and in vacuum. We apply QM/MM calculations and experimental quantum crystallography to show that the crystal interaction density is indeed very similar to the enzyme interaction density. Less than 0.1 e are shifted between these two environments in total. However, this difference has non-negligible consequences for derived properties.

HgH2 meets relativistic quantum crystallography. How to teach relativity to a non-relativistic wavefunction

The capability of X-ray constrained wavefunction (XCW) fitting to introduce relativistic effects into a non-relativistic wavefunction is tested. It is quantified how much of the reference relativistic effects can be absorbed in the non-relativistic XCW calculation when fitted against relativistic structure factors of a model HgH₂ molecule. Scaling of the structure-factor sets to improve the agreement statistics is found to introduce a significant systematic error into the XCW fitting of relativistic effects.

Quantum Crystallography in the Last Decade: Developments and Outlooks

In this review article, we report on the recent progresses in the field of quantum crystallography that has witnessed a massive increase of production coupled with a broadening of the scope in the last decade. It is shown that the early thoughts about extracting quantum mechanical information from crystallographic experiments are becoming reality, although a century after prediction. While in the past the focus was mainly on electron density and related quantities, the attention is now shifting toward determination of wavefunction from experiments, which enables an exhaustive determination of the quantum mechanical functions and properties of a system. Nonetheless, methods based on electron density modelling have evolved and are nowadays able to reconstruct tiny polarizations of core electrons, coupling charge and spin models, or determining the quantum behaviour at extreme conditions. Far from being routine, these experimental and computational results should be regarded with special attention by scientists for the wealth of information on a system that they actually contain.

Hydrogen atoms in bridging positions from quantum crystallographic refinements: influence of hydrogen atom displacement parameters on geometry and electron density

Hydrogen atom positions can be obtained accurately from X-ray diffraction data of hydrogen maleate salts via Hirshfeld atom refinement.