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.

The effects of experimentally obtained electron correlation and polarization on electron densities and exchange-correlation potentials.

In X-ray constrained wavefunction (XCW) fitting, external information, such as electron correlation and polarization, is included into a single-determinantal isolated-molecule wavefunction. In a first step, we show that the extraction of these two physical effects by XCW fitting is complete and accurate by comparing to theoretical reference calculations. In a second step, we show that fitting to data from single-crystal x-ray diffraction measurements provides the same results qualitatively and how the physical effects can be separated, although always inherently convolved in the experiment. We further demonstrate that exchange-correlation potentials are systematically affected by XCW fitting in a physically meaningful way, which could be exploited for method development in quantum chemistry, subject to some remaining challenges that we also outline.

The N,N,N-trimethylammonium moiety as tetrel bond donor site: crystallographic and computational studies.

Five structures bearing the N,N,N-trimethylammonium unit have been investigated to address the ability of the N+-CH3 unit to function as a tetrel bond donor site. Charged and neutral electron density donors display close contacts with different carbon atoms of methyl groups on the ammonium moiety. The Hirshfeld atom refinement (HAR) technique was used on selected structures to accurately and precisely determine the hydrogen atom positions and, consequently, to get better insights into the N+-C⋯Nu (Nu = nucleophile) interactions occurring in the crystals. In particular, the performed analyses highlighted specific geometrical features of the moieties involved in the interactions and allowed distinguishing between tetrel and hydrogen bonds.

Initial Maximum Overlap Method Embedded with Extremely Localized Molecular Orbitals for Core-Ionized States of Large Systems.

Despite great advances in X-ray absorption spectroscopy for the investigation of small molecule electronic structure, the application to biosystems of experimental techniques developed within this research field remains a challenge. To partially circumvent the problem, users resort to theoretical methods to interpret or predict the X-ray absorption spectra of large molecules. To accomplish this task, only low-cost computational strategies can be exploited. For this reason, some of them are single Slater determinant wavefunction approaches coupled with multiscale embedding techniques designed to treat large systems of biological interest. Therefore, in this work, we propose to apply the recently developed IMOM/ELMO embedding method to the determination of core-ionized states. The IMOM/ELMO technique resulted from the combination of the single Slater determinant Δself-consistent-field-initial maximum overlap approach (ΔSCF-IMOM) with the QM/ELMO (quantum mechanics/extremely localized molecular orbital) embedding strategy, a method where only the chemically relevant region of the examined system is treated at fully quantum chemical level, while the rest is described through transferred and frozen extremely localized molecular orbitals (ELMOs). The IMOM/ELMO technique was initially validated by computing core-ionization energies for small molecules, and it was afterwards exploited to study larger biosystems. The obtained results are in line with those reported in previous studies that applied alternative ΔSCF approaches. This makes us envisage a possible future application of the proposed method to the interpretation of X-ray absorption spectra of large molecules.

A Step toward the Quantification of Noncovalent Interactions in Large Biological Systems: The Independent Gradient Model-Extremely Localized Molecular Orbital Approach.

The independent gradient model (IGM) is a recent electron density-based computational method that enables to detect and quantify covalent and noncovalent interactions. When applied to large systems, the original version of the technique still relies on promolecular electron densities given by the sum of spherically averaged atomic electron distributions, which leads to approximate evaluations of the inter- and intramolecular interactions occurring in systems of biological interest. To overcome this drawback and perform IGM analyses based on quantum mechanically rigorous electron densities also for macromolecular systems, we coupled the IGM approach with the recently constructed libraries of extremely localized molecular orbitals (ELMOs) that allow fast and reliable reconstructions of polypeptide and protein electron densities. The validation tests performed on small polypeptides and peptide dimers have shown that the novel IGM-ELMO strategy provides results that are systematically closer to the fully quantum mechanical ones and outperforms the IGM method based on the crude promolecular approximation, but still keeping a quite low computational cost. The results of the test calculations carried out on proteins have also confirmed the trends observed for the IGM analyses conducted on small systems. This makes us envisage the future application of the novel IGM-ELMO approach to unravel complicated noncovalent interaction networks (e.g., in protein-protein contacts) or to rationally design new drugs through molecular docking calculations and virtual high-throughput screenings.

Three-Layer Multiscale Approach Based on Extremely Localized Molecular Orbitals to Investigate Enzyme Reactions.

Quantum mechanics/molecular mechanics (QM/MM) calculations are widely used embedding techniques to computationally investigate enzyme reactions. In most QM/MM computations, the quantum mechanical region is treated through density functional theory (DFT), which offers the best compromise between chemical accuracy and computational cost. Nevertheless, to obtain more accurate results, one should resort to wave function-based methods, which however lead to a much larger computational cost already for relatively small QM subsystems. To overcome this drawback, we propose the coupling of our QM/ELMO (quantum mechanics/extremely localized molecular orbital) approach with molecular mechanics, thus introducing the three-layer QM/ELMO/MM technique. The QM/ELMO strategy is an embedding method in which the chemically relevant part of the system is treated at the quantum mechanical level, while the rest is described through frozen ELMOs. Since the QM/ELMO method reproduces results of fully QM computations within chemical accuracy and with a much lower computational effort, it can be considered a suitable strategy to extend the range of applicability and accuracy of the QM/MM scheme. In this paper, other than briefly presenting the theoretical bases of the QM/ELMO/MM technique, we will also discuss its validation on the well-tested deprotonation of acetyl coenzyme A by aspartate in citrate synthase.

QM/ELMO: A Multi-Purpose Fully Quantum Mechanical Embedding Scheme Based on Extremely Localized Molecular Orbitals.

The development of computationally advantageous methods for the study of large systems is a long-standing research topic in theoretical chemistry. Among these techniques, a prominent place is certainly occupied by the multiscale embedding strategies, from the well-known QM/MM (quantum mechanics/molecular mechanics) methods to the latest and promising fully quantum mechanical approaches. In this Feature Article, we will briefly review the recently proposed QM/ELMO (quantum mechanics/extremely localized molecular orbital) scheme, namely a new multiscale embedding strategy in which the most chemically relevant region of the investigated system is treated at fully quantum chemical level, while the remaining part (namely, the environment) is described by means of transferred extremely localized molecular orbitals that remain frozen throughout the computation. Other than highlighting the theoretical bases, here we will also review the main results obtained through all the currently available variants of the novel method. In particular, we will show how the QM/ELMO embedding scheme has been successfully exploited to perform both ground and excited state calculations, reproducing the results of corresponding fully quantum mechanical computations but with a much lower computational cost. A first application to crystallography will be also discussed, and we will describe how the QM/ELMO approach has been recently coupled with the Hirshfeld atom refinement technique to accurately determine the positions of hydrogen atoms from X-ray diffraction data. Given the reliability and quality of the obtained results, future applications of the current versions of the QM/ELMO embedding strategy to different types of chemical problems are to be expected in the near future. Moreover, further algorithmic improvements and methodological developments are also envisaged, such as the development of a polarizable QM/ELMO scheme accounting for the effects of the QM region on the ELMO subsystem or the use of the new embedding approach in the context of quantum crystallography to perform unprecedented accurate refinements of macromolecular crystal structures.

Quantification of the Magnetic Anisotropy of a Single-Molecule Magnet from the Experimental Electron Density.

Reported here is an entirely new application of experimental electron density (EED) in the study of magnetic anisotropy of single-molecule magnets (SMMs). Among those SMMs based on one single transition metal, tetrahedral CoII-complexes are prominent, and their large zero-field splitting arises exclusively from coupling between the d x 2 - y 2 and dxy orbitals. Using very low temperature single-crystal synchrotron X-ray diffraction data, an accurate electron density (ED) was obtained for a prototypical SMM, and the experimental d-orbital populations were used to quantify the dxy-d x 2 - y 2 coupling, which simultaneously provides the composition of the ground-state Kramers doublet wave function. Based on this experimentally determined wave function, an energy barrier for magnetic relaxation in the range 193-268 cm-1 was calculated, and is in full accordance with the previously published value of 230 cm-1 obtained from near-infrared spectroscopy. These results provide the first clear and direct link between ED and molecular magnetic properties.

Insights into Single-Molecule-Magnet Behavior from the Experimental Electron Density of Linear Two-Coordinate Iron Complexes.

A breakthrough in the study of single-molecule magnets occurred with the discovery of zero-field slow magnetic relaxation and hysteresis for the linear iron(I) complex [Fe(C(SiMe3)3)2]- (1), which has one of the largest spin-reversal barriers among mononuclear transition-metal single-molecule magnets. Theoretical studies have suggested that the magnetic anisotropy in 1 is made possible by pronounced stabilization of the iron d z2 orbital due to 3d z2-4s mixing, an effect which is predicted to be less pronounced in the neutral iron(II) complex Fe(C(SiMe3)3)2 (2). However, experimental support for this interpretation has remained lacking. Here, we use high-resolution single-crystal X-ray diffraction data to generate multipole models of the electron density in these two complexes, which clearly show that the iron d z2 orbital is more populated in 1 than in 2. This result can be interpreted as arising from greater stabilization of the d z2 orbital in 1, thus offering an unprecedented experimental rationale for the origin of magnetic anisotropy in 1.

Quantum Mechanics/Extremely Localized Molecular Orbital Method: A Fully Quantum Mechanical Embedding Approach for Macromolecules.

The development of methods for the quantum mechanical study of macromolecules has always been an important challenge in theoretical chemistry. Nowadays, the techniques proposed in this context can be used to investigate very large systems and can be subdivided into two main categories: fragmentation and embedding strategies. In this paper, by modifying and improving the local self-consistent field approach originally proposed for quantum mechanics/molecular mechanics techniques, we introduce the new multiscale embedding quantum mechanics/extremely localized molecular orbital (QM/ELMO) method. The new strategy enables treatment of chemically relevant regions of large biological molecules through usual methods of quantum chemistry while describing the remaining parts of the systems by means of frozen extremely localized molecular orbitals transferred from properly constructed libraries. Test calculations have shown the correct functioning and the high reliability of the new approach, thus anticipating its possible applications to different fields of physical chemistry, such as rational drug design and structural refinements of proteins.

X-ray Constrained Spin-Coupled Wavefunction: a New Tool to Extract Chemical Information from X-ray Diffraction Data.

The X-ray constrained wavefunction (XCW) approach is a reliable and widely used method of quantum crystallography that allows the determination of wavefunctions compatible with X-ray diffraction data. So far, all the existing XCW techniques have been developed in the framework of molecular orbital theory and, consequently, provide only pictures of the "experimental" electronic structures that are far from the traditional chemical perception. Here a new strategy is proposed that, by combining the XCW philosophy with the spin-coupled method of valence bond theory, enables direct extraction of traditional chemical information (e.g., weights of resonance structures) from X-ray diffraction measurements. Preliminary results have shown that the new technique is really able to efficiently capture the effects of the crystal environment on the electronic structure, and can be considered as a new useful tool to perform chemically sound analyses of the X-ray diffraction data.

Quantum Crystallography: Current Developments and Future Perspectives.

Crystallography and quantum mechanics have always been tightly connected because reliable quantum mechanical models are needed to determine crystal structures. Due to this natural synergy, nowadays accurate distributions of electrons in space can be obtained from diffraction and scattering experiments. In the original definition of quantum crystallography (QCr) given by Massa, Karle and Huang, direct extraction of wavefunctions or density matrices from measured intensities of reflections or, conversely, ad hoc quantum mechanical calculations to enhance the accuracy of the crystallographic refinement are implicated. Nevertheless, many other active and emerging research areas involving quantum mechanics and scattering experiments are not covered by the original definition although they enable to observe and explain quantum phenomena as accurately and successfully as the original strategies. Therefore, we give an overview over current research that is related to a broader notion of QCr, and discuss options how QCr can evolve to become a complete and independent domain of natural sciences. The goal of this paper is to initiate discussions around QCr, but not to find a final definition of the field.

Libraries of Extremely Localized Molecular Orbitals. 3. Construction and Preliminary Assessment of the New Databanks.

The fast and reliable determination of wave functions and electron densities of macromolecules has been one of the goals of theoretical chemistry for a long time, and in this context, several linear scaling techniques have been successfully devised over the years. Different approaches have been adopted to tackle this problem, and one of them exploits the fact that, according to the traditional chemical perception, molecules can be seen as constituted of recurring units (e.g., functional groups) with well-defined chemical features. This has led to the development of methods in which the global wave functions or electron densities of macromolecules are obtained by simply transferring density matrices or fuzzy electron densities associated with molecular fragments. In this context, we propose an alternative strategy that aims at quickly reconstructing wave functions and electron densities of proteins through the transfer of extremely localized molecular orbitals (ELMOs), which are orbitals strictly localized on small molecular units and, for this reason, easily transferable from molecule to molecule. To accomplish this task we have constructed original libraries of ELMOs that cover all the possible elementary fragments of the 20 natural amino acids in all their possible protonation states and forms. Our preliminary test calculations have shown that, compared to more traditional methods of quantum chemistry, the transfers from the novel ELMO databanks allow to obtain wave function and electron densities of large polypeptides and proteins at a significantly reduced computational cost. Furthermore, notwithstanding expected discrepancies, the obtained electron distributions and electrostatic potentials are in very good agreement with those obtained at Hartree-Fock and density functional theory (DFT) levels. Therefore, the results encourage to use the new libraries as alternatives to the popular pseudoatom-databases of crystallography in the refinement of crystallographic structures of macromolecules. In particular, in this context, we have already envisaged the coupling of the ELMO databanks with the promising Hirshfeld atom refinement technique to extend the applicability of the latter to very large systems.

Crystal Structure of the DFNKF Segment of Human Calcitonin Unveils Aromatic Interactions between Phenylalanines.

Although intensively studied, the high-resolution crystal structure of the peptide DFNKF, the core-segment of human calcitonin, has never been described. Here we report how the use of iodination as a strategy to promote crystallisation and facilitate phase determination, allowed us to solve, for the first time, the single-crystal X-ray structure of a DFNKF derivative. Computational studies suggest that both the iodinated and the wild-type peptides populate very similar conformations. Furthermore, the conformer found in the solid-state structure is one of the most populated in solution, making the crystal structure a reliable model for the peptide in solution. The crystal structure of DFNKF(I) confirms the overall features of the amyloid cross-ß spine and highlights how aromatic-aromatic interactions are important structural factors in the self-assembly of this peptide. A detailed analysis of such interactions is reported.

In vivo and in silico evaluation of a new nitric oxide donor, S,S'-dinitrosobucillamine.

PURPOSE: In a previous work, we have synthetized a new dinitrosothiol, i.e. S,S'-dinitrosobucillamine BUC(NO)2 combining S-nitroso-N-acetylpenicillamine (SNAP) and S-nitroso-N-acetylcysteine (NACNO) in its structure. When exposed to isolated aorta, we observed a 1.5-fold increase of •NO content and a more potent vasorelaxation (1 log higher pD2) compared to NACNO and SNAP alone or combined (Dahboul et al., 2014). In the present study, we analyzed the thermodynamics and kinetics for the release of •NO through computational modeling techniques and correlated it to plasma assays. Then BUC(NO)2 was administered in vivo to rats, assuming it will induce higher and/or longer hypotensive effects than its two constitutive S-mononitrosothiols. METHODS: Free energies for the release of •NO entities have been computed at the density functional theory level assuming an implicit model for the aqueous environment. Degradation products of BUC(NO)2 were evaluated in vitro under heating and oxidizing conditions using HPLC coupled with tandem mass spectrometry (MS/MS). Plasma from rats were spiked with RSNO and kinetics of RSNO degradation was measured using the classical Griess-Saville method. Blood pressure was measured in awake male Wistar rats using telemetry (n = 5, each as its own control, 48 h wash-out periods between subcutaneous injections under transient isoflurane anesthesia, random order: 7 mL/kg vehicle, 3.5, 7, 14 µmol/kg SNAP, NACNO, BUC(NO)2 and an equimolar mixture of SNAP + NACNO in order to mimic the number of •NO contained in BUC(NO)2). Variations of mean (ΔMAP, reflecting arterial dilation) and pulse arterial pressures (ΔPAP, indirectly reflecting venodilation, used to determine effect duration) vs. baseline were recorded for 4 h. RESULTS: Computational modeling highlights the fact that the release of the first •NO radical in BUC(NO)2 requires a free energy which is intermediate between the values obtained for SNAP and NACNO. However, the release of the second •NO radical is significantly favored by the concerted formation of an intramolecular disulfide bond. The corresponding oxidized compound was also characterized as related substance obtained under degradation conditions. The in vitro degradation rate of BUC(NO)2 was significantly greater than for the other RSNO. For equivalent low and medium •NO-load, BUC(NO)2 produced a hypotension identical to NACNO, SNAP and the equimolar mixture of SNAP + NACNO, but its effect was greater at higher doses (-62 ± 8 and -47 ± 14 mmHg, maximum ΔMAP for BUC(NO)2 and SNAP + NACNO, respectively). Its duration of effect on PAP (-50%) lasted from 35 to 95 min, i.e. shorter than for the other RSNO (from 90 to 135 min for the mixture SNAP + NACNO). CONCLUSION: A faster metabolism explains the abilities of BUC(NO)2 to release higher amounts of •NO and to induce larger hypotension but shorter-lasting effects than those induced by the SNAP + NACNO mixture, despite an equivalent •NO-load.

Structure and Stability Studies of Pharmacologically Relevant S-Nitrosothiols: A Theoretical Approach.

Nowadays, S-nitrosothiols (RSNOs) represent a promising class of nitric oxide (NO) donors that could be successfully used as drugs to compensate the decrease of NO production that usually arises in conjunction with cardiovascular diseases. Nevertheless, notwithstanding their pharmacological interest, the structure-stability relationship in RSNOs is still unclear, and this issue, together with the mechanism of NO donation in the physiological medium, deserves further investigation. As a first step forward in this direction, in this paper, the overall stability and structural preference of two pharmacologically relevant S-nitrosothiol molecules were studied in detail by means of computational strategies. In particular, performing calculations in implicit solvent (water) on the S-nitroso-N-acetylpenicillamine and the S-nitroso-N-acetylcysteine and analyzing the noncovalent interactions networks of their most stable conformers, we observed that the structure and the stability of these molecules can be directly related to the formation of stabilizing hydrogen-bond and chalcogen-chalcogen intramolecular interactions. The obtained results represent the starting point for further investigations to be conducted also on larger RSNOs to shed further light on the role played by intra- and intermolecular interactions and by solvation effects in stabilizing this class of molecules. The obtained insights will be hopefully helpful to design new RSNO-based drugs characterized by an enhanced pharmacological potency.

Current developments and trends in quantum crystallography.

Quantum crystallography is an emerging research field of science that has its origin in the early days of quantum physics and modern crystallography when it was almost immediately envisaged that X-ray radiation could be somehow exploited to determine the electron distribution of atoms and molecules. Today it can be seen as a composite research area at the intersection of crystallography, quantum chemistry, solid-state physics, applied mathematics and computer science, with the goal of investigating quantum problems, phenomena and features of the crystalline state. In this article, the state-of-the-art of quantum crystallography will be described by presenting developments and applications of novel techniques that have been introduced in the last 15 years. The focus will be on advances in the framework of multipole model strategies, wavefunction-/density matrix-based approaches and quantum chemical topological techniques. Finally, possible future improvements and expansions in the field will be discussed, also considering new emerging experimental and computational technologies.

Elucidating the nature of chemical bonds in a coordination compound through quantum crystallographic techniques.

Investigations simultaneously involving multiple techniques of quantum crystallography could be very useful to prove the consistency of obtained results or to highlight different facets of the same scientific phenomenon or problem. Pinto et al. [Acta Cryst. (2023), B79, 282-296] exploit three different quantum crystallographic techniques (Hansen & Coppens multipole model refinement, QTAIM analysis of the electron density, and Hirshfeld atom refinement) to characterize the nature of chemical bonds and of intra/intermolecular interactions in an organometallic compound.

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 λJ for each resolution range might not be a suitable strategy to adopt in XRW calculations exploiting experimental X-ray data as restraints.

Extracting Quantitative Information at Quantum Mechanical Level from Noncovalent Interaction Index Analyses.

The noncovalent interaction (NCI) index is nowadays a well-known strategy to detect NCIs in molecular systems. Even though it initially provided only qualitative descriptions, the technique has been recently extended to also extract quantitative information. To accomplish this task, integrals of powers of the electron distribution were considered, with the requirement that the overall electron density can be clearly decomposed as sum of distinct fragment contributions to enable the definition of the (noncovalent) integration region. So far, this was done by only exploiting approximate promolecular electron densities, which are given by the sum of spherically averaged atomic electron distributions and thus represent too crude approximations. Therefore, to obtain more quantum mechanically (QM) rigorous results from NCI index analyses, in this work, we propose to use electron densities obtained through the transfer of extremely localized molecular orbitals (ELMOs) or through the recently developed QM/ELMO embedding technique. Although still approximate, the electron distributions resulting from the abovementioned methods are fully QM and, above all, are again partitionable into subunit contributions, which makes them completely suitable for the NCI integral approach. Therefore, we benchmarked the integrals resulting from NCI index analyses (both those based on the promolecular densities and those based on ELMO electron distributions) against interaction energies computed at a high quantum chemical level (in particular, at the coupled cluster level). The performed test calculations have indicated that the NCI integrals based on ELMO electron densities outperform the promolecular ones. Furthermore, it was observed that the novel quantitative NCI-(QM/)ELMO approach can be also profitably exploited both to characterize and evaluate the strength of specific interactions between ligand subunits and protein residues in protein-ligand complexes and to follow the evolution of NCIs along trajectories of molecular dynamics simulations. Although further methodological improvements are still possible, the new quantitative ELMO-based technique could be already exploited in situations in which fast and reliable assessments of NCIs are crucial, such as in computational high-throughput screenings for drug discovery.