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.

Structure Factors and Charge Density Description of Aluminum: A Quantum Crystallographic Study.

Static structure factors and charge density for metallic aluminum were investigated by periodic calculations using atom-centered Gaussian-type basis sets with the Perdew-Burke-Ernzerhof (PBE) functional implemented in the CRYSTAL14 package and X-ray constrained wave function (XCW) fitting. The effects of additional diffuse d and f basis functions on structure factors were compared with synchrotron powder X-ray diffraction and quantitative convergent electron beam diffraction data. Changes in structure factors from an independent atom model at 022, 113, and 222 reflections introduced d and f basis functions similar to those of the experimental data. The XCW fitting was applied to different sizes of aluminum clusters. The charge density features for a 50-atom cluster clearly demonstrated electron accumulation at tetrahedral sites and electron depletion at octahedral sites. The resolution dependence of the XCW study suggests that structure factors of the five lowest resolution reflections with 0.1% accuracy were indispensable for determining the detailed bonding description in the case of metallic aluminum.

The Relevance of Experimental Charge Density Analysis in Unraveling Noncovalent Interactions in Molecular Crystals.

The work carried out by our research group over the last couple of decades in the context of quantitative crystal engineering involves the analysis of intermolecular interactions such as carbon (tetrel) bonding, pnicogen bonding, chalcogen bonding, and halogen bonding using experimental charge density methodology is reviewed. The focus is to extract electron density distribution in the intermolecular space and to obtain guidelines to evaluate the strength and directionality of such interactions towards the design of molecular crystals with desired properties. Following the early studies on halogen bonding interactions, several "sigma-hole" interaction types with similar electrostatic origins have been explored in recent times for their strength, origin, and structural consequences. These include interactions such as carbon (tetrel) bonding, pnicogen bonding, chalcogen bonding, and halogen bonding. Experimental X-ray charge density analysis has proved to be a powerful tool in unraveling the strength and electronic origin of such interactions, providing insights beyond the theoretical estimates from gas-phase molecular dimer calculations. In this mini-review, we outline some selected contributions from the X-ray charge density studies to the field of non-covalent interactions (NCIs) involving elements of the groups 14-17 of the periodic table. Quantitative insights into the nature of these interactions obtained from the experimental electron density distribution and subsequent topological analysis by the quantum theory of atoms in molecules (QTAIM) have been discussed. A few notable examples of weak interactions have been presented in terms of their experimental charge density features. These examples reveal not only the strength and beauty of X-ray charge density multipole modeling as an advanced structural chemistry tool but also its utility in providing experimental benchmarks for the theoretical studies of weak interactions in crystals.

Revisiting a Historical Concept by Using Quantum Crystallography: Are Phosphate, Sulfate and Perchlorate Anions Hypervalent?

There are many examples of atoms in molecules that violate Lewis' octet rule, because they have more than four electron pairs assigned to their valence. These atoms are referred to as hypervalent. However, hypervalency may be regarded as an artifact arising from Lewis' description of molecules, which is based on the assumption that electrons are localized in two-center two-electron bonds and lone pairs. In the present paper, the isoelectronic phosphate (PO4 3- ), sulfate (SO4 2- ) and perchlorate (ClO4 - ) anions were examined with respect to the concept of hypervalency. Lewis formulas containing a hypervalent central atom exist for all three anions. Based on X-ray wavefunction refinements of high-resolution X-ray diffraction data of representative crystal structures (MgNH4 PO4 ⋅6 H2 O, Li2 SO4 ⋅H2 O, and KClO4 ), complementary bonding analyses were performed. In this way, experimental information from the new field of quantum crystallography validate long-known facts, or refute long-standing misunderstandings. It is shown that the P-O and S-O bonds are highly polarized covalent bonds and, thus, the increase in the valence population following three-center four-electron bonding is not sufficient to yield hypervalent phosphorus or sulfur atoms, respectively. However, for the highly covalent Cl-O bond, most bonding indicators imply a hypervalent chlorine atom.

Covalency and Ionicity Do Not Oppose Each Other-Relationship Between Si-O Bond Character and Basicity of Siloxanes.

Covalency and ionicity are orthogonal rather than antipodal concepts. We demonstrate for the case of siloxane systems [R3 Si-(O-SiR2 )n -O-SiR3 ] that both covalency and ionicity of the Si-O bonds impact on the basicity of the Si-O-Si linkage. The relationship between the siloxane basicity and the Si-O bond character has been under debate since previous studies have presented conflicting explanations. It has been shown with natural bond orbital methods that increased hyperconjugative interactions of LP(O)→σ*(Si-R) type, that is, increased orbital overlap and hence covalency, are responsible for the low siloxane basicity at large Si-O-Si angles. On the other hand, increased ionicity towards larger Si-O-Si angles has been revealed with real-space bonding indicators. To resolve this ostensible contradiction, we perform a complementary bonding analysis, which combines orbital-space, real-space, and bond-index considerations. We analyze the isolated disiloxane molecule H3 SiOSiH3 with varying Si-O-Si angles, and n-membered cyclic siloxane systems Si2 H4 O(CH2 )n-3 . All methods from quite different realms show that both covalent and ionic interactions increase simultaneously towards larger Si-O-Si angles. In addition, we present highly accurate absolute hydrogen-bond interaction energies of the investigated siloxane molecules with water and silanol as donors. It is found that intermolecular hydrogen bonding is significant at small Si-O-Si angles and weakens as the Si-O-Si angle increases until no stable hydrogen-bond complexes are obtained beyond φSiOSi =168°, angles typically displayed by minerals or polymers. The maximum hydrogen-bond interaction energy, which is obtained at an angle of 105°, is 11.05 kJ mol-1 for the siloxane-water complex and 18.40 kJ mol-1 for the siloxane-silanol complex.

Linear MgCp*2 vs Bent CaCp*2: London Dispersion, Ligand-Induced Charge Localizations, and Pseudo-Pregostic C-H···Ca Interactions.

In the family of metallocenes, MgCp*2 (Cp* = pentamethylcyclopentadienyl) exhibits a regular linear sandwich structure, whereas CaCp*2 is bent in both the gas phase and solid state. Bending is typically observed for metal ions which possess a lone pair. Here, we investigate which electronic differences cause the bending in complexes lacking lone pairs at the metal atoms. The bent gas-phase geometry of CaCp*2 suggests that the bending must have an intramolecular origin. Geometry optimizations with and without dispersion effects/d-type polarization functions on MCp2 and MCp*2 gas-phase complexes (M = Ca, Mg) establish that attractive methyl···methyl London dispersion interactions play a decisive role in the bending in CaCp*2. A sufficient polarizability of the metal to produce a shallow bending potential energy curve is a prerequisite but is not the reason for the bending. Concomitant ligand-induced charge concentrations and localizations at the metal atoms are studied in further detail, for which real-space bonding and orbital-based descriptors are used. Low-temperature crystal structures of MgCp*2 and CaCp*2 were determined which facilitated the identification and characterization of intermolecular pseudo-pregostic interactions, C-H···Ca, in the CaCp*2 crystal structure.

Syn vs Anti Carboxylic Acids in Hybrid Peptides: Experimental and Theoretical Charge Density and Chemical Bonding Analysis.

A comparative study of syn vs anti carboxylic acids in hybrid peptides based on experimental electron density studies and theoretical calculations shows that, in the anti form, all three bond angles surrounding Ccarboxyl of the -COOH group are close to ∼120°, as expected for a C-sp2 atom, whereas in the syn form, the ∠Cα-C(O)-Ohydroxyl angle is significantly smaller by 5-10°. The oxygen atom in the carboxyl group is more electronegative in the anti form, so the polarity of the acidic O-H bond is higher in the anti form compared to the syn form, as observed within the limitations of H atom treatment in X-ray diffraction. Consequently, the investigated anti carboxylic acid forms the strongest O-H···O hydrogen bond among all model compounds. Furthermore, according to natural bond orbital analysis, the oxygen lone pairs are clearly nonequivalent, as opposed to the general notion of hybridization of equivalent sp2 and sp3 lone pairs on carbonyl or hydroxyl oxygen atoms. The hybridization of the lone pairs is directly related to the directionality and strength of hydrogen bonds.

SF5-Enolates in Ti(IV)-Mediated Aldol Reactions.

The F···Ti bonding in the transition structures determines high trans- and syn-diastereoselectivities for aldol reactions of SF5-acetates with aldehydes in the presence of TiCl4 in the non-nucleophilic solvent CH2Cl2. Such bonding is canceled in nucleophilic solvents where opposite cis-stereochemistry is observed. The potential of thus obtained stereoisomeric SF5-aryl acrylates as dipolarophiles in the preparation of SF5-containing heterocycles is demonstrated.

Exploring cyclopentadienone antiaromaticity: charge density studies of various tetracyclones.

A systematic study of six tetracyclones has been carried out using experimental and theoretical charge density analysis. A three pronged approach based on quantum theory of atoms in molecules (QTAIM), nucleus independent chemical shifts (NICS) criterion, and source function (SF) contributions has been performed to establish the degree of antiaromaticity of the central five-membered ring in all the derivatives. Electrostatic potentials mapped on the isodensity surface show that electron withdrawing substituents turn both C and O atoms of the carbonyl group more electropositive while retaining the direction of polarity.

Temperature-induced reversible first-order single crystal to single crystal phase transition in Boc-γ(4)(R)Val-Val-OH: interplay of enthalpy and entropy.

Crystals of Boc-γ(4)(R)Val-Val-OH undergo a reversible first-order single crystal to single crystal phase transition at Tc ≈ 205 K from the orthorhombic space group P22121 (Z' = 1) to the monoclinic space group P21 (Z' = 2) with a hysteresis of ∼2.1 K. The low-temperature monoclinic form is best described as a nonmerohedral twin with ∼50% contributions from its two components. The thermal behavior of the dipeptide crystals was characterized by differential scanning calorimetry experiments. Visual changes in birefringence of the sample during heating and cooling cycles on a hot-stage microscope with polarized light supported the phase transition. Variable-temperature unit cell check measurements from 300 to 100 K showed discontinuity in the volume and cell parameters near the transition temperature, supporting the first-order behavior. A detailed comparison of the room-temperature orthorhombic form with the low-temperature (100 K) monoclinic form revealed that the strong hydrogen-bonding motif is retained in both crystal systems, whereas the non-covalent interactions involving side chains of the dipeptide differ significantly, leading to a small change in molecular conformation in the monoclinic form as well as a small reorientation of the molecules along the ac plane. A rigid-body thermal motion analysis (translation, libration, screw; correlation of translation and libration) was performed to study the crystal entropy. The reversible nature of the phase transition is probably the result of an interplay between enthalpy and entropy: the low-temperature monoclinic form is enthalpically favored, whereas the room-temperature orthorhombic form is entropically favored.

π-Hole bonding in a new co-crystal hydrate of gallic acid and pyrazine: static and dynamic charge density analysis.

A new cocrystal hydrate of gallic acid with pyrazine (4GA, Py, 4H2O; GA4PyW4) was obtained and characterized by single crystal X-ray diffraction. In addition to structure determination, experimental charge density analysis was carried out in terms of Multipole Modelling (MP), X-ray wavefunction refinement (XWR) and maximum entropy method (MEM). As a part of XWR, the structural refinement via Hirshfeld atom refinement was carried out and resulted in O-H bond lengths close to values from neutron diffraction. A systematic comparison of molecular conformations and aromatic interactions in this new cocrystal hydrate was performed with other existing polymorphs of gallic acid. In GA4PyW4, the two symmetry-independent gallic acid molecules have a syn COOH orientation and form the common (COOH)2 dimeric synthon. The carboxyl C atom displays the characteristics of π-holes with electropositive regions above and below the molecular plane and engages in acceptor-donor interactions with oxygen atoms of acidic O-H groups and phenol groups of neighbouring gallic acid molecules. The signature of the π-hole was identified from experimental charge density analysis, both in static density maps in MP and XWR as well as dynamic density in MEM, but it cannot be pinned down to a specific atom-atom interaction. This study presents the first comparison between an XWR and a MEM experimental electron-density determination.

BN-Substitution in Dithienylpyrenes Prevents Excimer Formation in Solution and in the Solid State.

Boron-nitrogen substitutions in polycyclic aromatic hydrocarbons (PAHs) have a strong impact on the optical properties of the molecules due to a significantly more heterogeneous electron distribution. However, besides these single-molecule properties, the observed optical properties of PAHs critically depend on the degree of intermolecular interactions such as π-π-stacking, dipolar interactions, or the formation of dimers in the excited state. Pyrene is the most prominent example showing the latter as it exhibits a broadened and strongly bathochromically shifted emission band at high concentrations in solution compared to the respective monomers. In the solid state, the impact of intermolecular interactions is even higher as it determines the crystal packing crucially. In this work, a thiophene-flanked BN-pyrene (BNP) was synthesized and compared with its all-carbon analogue (CCP) in solution and in the solid state by means of crystallography, NMR spectroscopy, UV-vis spectroscopy, and photoluminescence (PL) spectroscopy. In solution, PL spectroscopy revealed the solvent-dependent presence of excimers of CCP at high concentrations. In contrast, no excimers were found in BNP. Clear differences were also observed in the single-crystal packing motifs. While CCP revealed overlapped pyrene planes with centroid distances in the range of classical π-stacking interactions, the BNP scaffolds were displaced and significantly more spatially separated.

Conformation-changing aggregation in hydroxyacetone: a combined low-temperature FTIR, jet, and crystallographic study.

Aggregation in hydroxyacetone (HA) is studied using low-temperature FTIR, supersonic jet expansion, and X-ray crystallographic (in situ cryocrystallization) techniques. Along with quantum chemical methods (MP2 and DFT), the experiments unravel the conformational preferences of HA upon aggregation to dimers and oligomers. The O-H···O═C intramolecular hydrogen bond present in the gas-phase monomer partially opens upon aggregation in supersonic expansions, giving rise to intermolecular cooperatively enhanced O-H···O-H hydrogen bonds in competition with isolated O-H···O═C hydrogen bonds. On the other hand, low-temperature IR studies on the neat solid and X-ray crystallographic data reveal that HA undergoes profound conformational changes upon crystallization, with the HOCC dihedral angle changing from ~0° in the gas phase to ~180° in the crystalline phase, hence giving rise to a completely new conformation. These conclusions are supported by theoretical calculations performed on the geometry derived from the crystalline phase.

Towards crystal structure prediction of complex organic compounds--a report on the fifth blind test.

Following on from the success of the previous crystal structure prediction blind tests (CSP1999, CSP2001, CSP2004 and CSP2007), a fifth such collaborative project (CSP2010) was organized at the Cambridge Crystallographic Data Centre. A range of methodologies was used by the participating groups in order to evaluate the ability of the current computational methods to predict the crystal structures of the six organic molecules chosen as targets for this blind test. The first four targets, two rigid molecules, one semi-flexible molecule and a 1:1 salt, matched the criteria for the targets from CSP2007, while the last two targets belonged to two new challenging categories - a larger, much more flexible molecule and a hydrate with more than one polymorph. Each group submitted three predictions for each target it attempted. There was at least one successful prediction for each target, and two groups were able to successfully predict the structure of the large flexible molecule as their first place submission. The results show that while not as many groups successfully predicted the structures of the three smallest molecules as in CSP2007, there is now evidence that methodologies such as dispersion-corrected density functional theory (DFT-D) are able to reliably do so. The results also highlight the many challenges posed by more complex systems and show that there are still issues to be overcome.

Fast and Accurate Quantum Crystallography: From Small to Large, from Light to Heavy.

The coupling of the crystallographic refinement technique Hirshfeld atom refinement (HAR) with the recently constructed libraries of extremely localized molecular orbitals (ELMOs) gives rise to the new quantum-crystallographic method HAR-ELMO. This method is significantly faster than HAR but as accurate and precise, especially concerning the free refinement of hydrogen atoms from X-ray diffraction data, so that the first fully quantum-crystallographic refinement of a protein is presented here. However, the promise of HAR-ELMO exceeds large molecules and protein crystallography. In fact, it also renders possible electron-density investigations of heavy elements in small molecules and facilitates the detection and isolation of systematic errors from physical effects.

Observation of a reversible isomorphous phase transition and an interplay of "σ-holes" and "π-holes" in Fmoc-Leu-ψ[CH2-NCS].

Fmoc-Leu-ψ[CH2NCS] undergoes a reversible isomorphous phase transition upon cooling. The crystal structure at 100 K displays a short N=C=S···N=C=S intermolecular interaction, which has been characterized based on experimental charge density analysis, as a stabilizing interaction with both σ-holes and π-holes acting cooperatively.