Focus issue on Charge, Spin and Momentum Densities: SAGAMORE XVIII

The Sagamore series of triennial conferences, with their unique focus on electron charge, spin and momentum densities, has been in existence for over 50 years. Named after the location of the first two meetings, which were in the Adirondack hills of Upper New York state, the conferences are still held by and large in remote places with forests, lakes and mountains not far away and competing distractions not too near. They strive to maintain an accent on informal discussions sparked off by the keynote addresses. This article charts the history of the Sagamore series and the organisation behind them.

A new and powerful molecular descriptor termed the LDM (localization–delocalization matrix) has recently been proposed as a molecular fingerprinting tool and has been shown to yield robust quantitative-structure-to-activity/property-relationships (QSAR/QSPR). An LDM lists the average number of electrons localized within an atom in a molecule along its diagonal while the off-diagonal elements are the pair-wise average number of electrons shared between every pair of atoms in the molecule, bonded or not. Hence, the LDM is a representation of a fuzzy molecular graph that accounts for the whereabouts of all electron(s) in the molecule and can be expected to encode for several facets of its chemistry at once. We show that the LDM captures the aromatic character of a ring-in-a-molecule by comparing the aromaticity ranking based on the LDMs and their eigenvalues of 6-membered carbon rings within (polycyclic) benzenoid hydrocarbons with the ranking based on four well-established local aromaticity measures (harmonic oscillator model of aromaticity, acromatic fluctuation index, para delocalization index, and nucleus independent chemical shift(0)).

4-aminoquinoline antiplasmodials interfere with the biocrystallization of the malaria pigment, a key step of the malaria parasite metabolism. It is commonly believed that these drugs set stacking π···π interactions with the Fe-protoporphyrin scaffold of the free heme, even though the details of the heme:drug recognition process remain elusive. In this work, the local coordination of Fe(III) ions in acidic solutions of hematin at room temperature was investigated by extended x-ray absorption fine structure (EXAFS) spectroscopy in the 4.0–5.5 pH range, both in the presence and in the absence of the antimalarial drug chloroquine. EXAFS results were complemented by DFT simulations in polarizable continuum media to model solvent effects. We found evidence that a complex where the drug quinoline nitrogen is coordinated with the iron center might coexist with formerly proposed adduct geometries, based on stacking interactions. Charge-assisted hydrogen bonds among lateral chains of the two molecules play a crucial role in stabilizing this complex, whose formation is favored by the presence of lipid micelles. The direct Fe–N bond could reversibly block the axial position in the Fe 1st coordination shell in free heme, acting as an inhibitor for the crystallization of the malaria pigment without permanently hampering the catalytic activity of the redox center. These findings are discussed in the light of possible implications on the engineering of drugs able to thwart the adaptability of the malaria parasite against classical aminoquinoline-based therapies.

Recent studies have produced experimental triplet excited state structures with lifetimes of nanoseconds to microseconds. Photodifference maps, showing the total change on excitation, in principle include both the effect of the atomic shifts on excitation and that of the orbital transitions. The latter can be calculated theoretically thus achieving a formal deconvolution of the atomic and electronic shifts. In the three examples presented electronic shifts on excitation are orders of magnitude smaller than the effect of the atomic shifts and their electron shells and therefore not experimentally accessible at this time.

New and more robust models of chemical bonding are necessary to further our understanding of chemical phenomena. Among these are bond bundle and gradient bundle methods, which analyze bonding interactions in terms of property distributions over geometrically defined volumes. These methods have been shown to provide a systematic framework from which to search for structure–property relationships. In addition to providing a brief review of some of the relationships found using this framework, we present new findings that relate the lowering of kinetic energy in bonding regions to bond dissociation energy.

We are at the dawn of molecular simulations being carried out, literally, by atoms endowed by knowledge of how to behave quantum mechanically in the vicinity of other atoms. The 'next–next-generation' force field that aims to achieve this is called QCTFF, for now, although a more pronounceable name will be suggested in the conclusion. Classical force fields such as AMBER mimic the interatomic energy experienced by atoms during a molecular simulation, with simple expressions capturing a relationship between energy and nuclear position. Such force fields neither see the electron density nor exchange-delocalization itself, or exact electrostatic interaction; they only contain simple equations and elementary parameters such as point charges to imitate the energies between atoms. Next-generation force fields, such as AMOEBA, go further and make the electrostatics more accurate by introducing multipole moments and dipolar polarization. However, QCTFF goes even further and abolishes all traditional force field expressions (e.g. Hooke's law and extensions, Lennard-Jones) in favor of atomistic kriging models. These machine learning models learn how fundamental energy quantities, as well as high-rank multipole moments, all associated with an atom of interest, vary with the precise positions of atomic neighbors. As a result, all structural phenomena can be rapidly calculated as an interplay of intra-atomic energy, exchange-delocalization energy, electrostatic energy and dynamic correlation energy. The final QCTFF force field will generate a wealth of localized quantum information while being faster than a Car–Parrinello simulation (which does not generate local information).

Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too? (Douglas Adams).

A novel concept for a high resolution Compton spectrometer is introduced. 88 keV radiation from an Inverse Compton Compact Source is focused using crossed cylindrically bent Laue-type Si perfect crystals, and dispersed on the sample with a constant energy gradient. Dispersion is compensated exactly at a Ge crystal analyzer, so that the same wavelength shift is observed for all wavelengths of the incident beam. The ThomX source is used as a concrete example. Detailed dimensions and flux estimates at successive locations of the spectrometer are given, and the performance is compared with the dispersion compensating spectrometer at ID15 of the ESRF. The momentum resolution is better than 0.1 atomic units in both cases. The intensity of scattering with the compact source is an order of magnitude smaller, but still adequate for high resolution Compton profile measurements.

In recent years multiple synchrotron radiation (SR) powder x-ray diffraction profiles have been successfully applied to advanced structural studies such as an accurate charge density study and a structure determination from powder diffraction. The results have been presented with several examples. Abilities and future prospects have been discussed using state of the art powder diffraction data.

Today, combined experimental and theoretical charge density studies based on quantum chemical calculations and x-ray diffraction experiments allow for the investigation of the topology of the electron density at subatomic resolution. When studying compounds containing transition metal elements, relativistic effects need to be adequately taken into account not only in quantum chemical calculations of the total electron density $\rho ({\bf{r}})$, but also for the atomic scattering factors employed to extract $\rho ({\bf{r}})$ from experimental x-ray diffraction data. In the present study, we investigate the magnitude of relativistic effects on x-ray structure factors and for this purpose ${\bf{F}}({{\bf{r}}}^{*})$ have been calculated for the model systems M(C₂H₂) (M = Ni, Pd, Pt) from four-component molecular wave functions. Relativistic effects are then discussed by a comparison to structure factors obtained from a non-relativistic reference and different quasi-relativistic approximations. We show, that the overall effects of relativity on the structure factors on average amount to 0.81%, 1.51% and 2.78% for the three model systems under investigation, but that for individual reflections or reflection series the effects can be orders of magnitude larger. Employing the quasi-relativistic Douglas–Kroll–Hess second order or the zeroth order regular approximation Hamiltonian takes these effects into account to a large extend, reducing the differences between the (quasi-)relativistic and the non-relativistic result by one order of magnitude. In order to further determine the experimental significance of the results, the magnitude of the relativistic effects is compared to the changes of the model structure factor data when charge transfer and chemical bonding is taken into account by a multipolar expansion of ${\bf{F}}({{\bf{r}}}^{*})$.

Boron atomic clusters show several interesting and unusual size-dependent features due to the small covalent radius, electron deficiency, and higher coordination number of boron as compared to carbon. These include aromaticity and a diverse array of structures such as quasi-planar, ring or tubular shaped, and fullerene-like. In the present work, we have analyzed features of the computed electron density distributions of small boron clusters having up to 11 boron atoms, and investigated the effect of doping with C, P, Al, Si, and Zn atoms on their structural and physical properties, in order to understand the bonding characteristics and discern trends in bonding and stability. We find that in general there are covalent bonds as well as delocalized charge distribution in these clusters. We associate the strong stability of some of these planar/quasiplanar disc-type clusters with the electronic shell closing with effectively twelve delocalized valence electrons using a disc-shaped jellium model. ${{{\rm{B}}}_{9}}^{-},$ B₁₀, B₇P, and B₈Si, in particular, are found to be exceptional with very large gaps between the highest occupied molecular orbital and the lowest unoccupied molecular orbital, and these are suggested to be magic clusters.

The electronic properties of transition metal atoms adsorbed on a graphene sheet are analyzed in the framework of the quantum theory of atoms in molecules (QTAIM). Particular attention is devoted to the spin dependence of the charge rearrangement upon the adsorption of magnetic adatoms. A comparison between the band structures and the charges in the atomic basins makes it possible to shed light on the different roles that the spin components play in the bond formation. This aspect is likely to be crucial in determining the spin-dependent properties required in spintronics applications and could help in tailoring them. We found that for early (Sc, Ti, and V) and late (Fe, Co) transition metals the two spin populations behave very differently, being involved in the bonding only the majority or the minority spin component for the lighter and heavier adsorbates, respectively. We expect that the response properties, in particular those related to the states at the Fermi level, will be very different for the two spin components. As a by-product of our study it becomes apparent that the QTAIM analysis is not the most suitable tool for catching the charge transfer phenomenon in the case of weakly interacting electronic populations.

The concept of the Fermi surface is at the very heart of our understanding of the metallic state. Displaying intricate and often complicated shapes, the Fermi surfaces of real metals are both aesthetically beautiful and subtly powerful. A range of examples is presented of the startling array of physical phenomena whose origin can be traced to the shape of the Fermi surface, together with experimental observations of the particular Fermi surface features.

We compare, from a crystallographic point of view, the data quality obtained using laboratory x-ray diffractometers equipped with a Molybdenum micro-source using different detector types: CCD, CMOS and XPAD hybrid pixel. First we give an overview of the working principle of these different detector types with a focus on their principal differences and their impact on the data quality. Then, using the example of an organic crystal, a comparison between the detector systems concerning the raw data statistics, the refinement agreement factors, the deformation electron density maps, and the residual density after multipolar refinement is presented. It is found that the data quality obtained with the XPAD detector is the best, even though the detection efficiency at the Mo energy (17.5 keV) is only 37% due to the Si-sensor layer thickness of 300 μm. Finally, we discuss the latest x-ray detector developments with an emphasis on the sensor material, where replacing Si by another material such as GaAs would yield detection efficiencies close to 100%, up to energies of 40 keV for hybrid pixel detectors.