Quantum Information Patterns Between Atoms in a Molecule.

Quantum information theory provides a powerful toolbox of descriptors that characterize many-electron systems based on quantum information patterns between open quantum systems. Despite the wealth of insights gained in the con- densed matter community, the use of these descriptors to study interactions between atoms in a molecule remains limited. In this study, we develop a quantum information framework for molecules that characterizes the quantum in- formation patterns between quantum atoms as defined in the Quantum Theory of Atoms in Molecules. We show that quantum information analyses capture key properties of quantum atoms and how they interact with their molec- ular environment. Additionally, we show that the presence of bond critical points can remain invariant despite large changes in the quantum information patterns between the quantum atoms. Our findings indicate that quantum infor- mation theory can shed a new light on molecular electronic structure.

Solvent Effect on Dative and Ionic Bond Strengths: A Unified Theory from the Potential Analysis and Valence Bond (VB) Computation.

Solvent molecules interact with a solute through various intermolecular forces. Here we employed a potential energy surface (PES) analysis to interpret the solvent-induced variations in the strengths of dative (Me3NBH3) and ionic (LiCl) bonds, which possess both ionic and covalent (neutral) characteristics. The change of a bond is driven by the gradient (force) of the solvent-solute interaction energy with respect to the focused bond length. Positive force shortens the bond length and increases the bond force constant, leading to a blue-shift of the bond stretching vibrational frequency upon solvation. Conversely, negative force elongates the bond, resulting in a reduced bond force constant and red-shift of the stretching vibrational frequency. The different responses of Me3NBH3 and LiCl to solvation are studied with valence bond (VB) theory, as Me3NBH3 and LiCl are dominated by the neutral covalent VB structure and the ionic VB structure, respectively. The dipole moment of an ionic VB structure increases along the increasing bond distance, while the dipole moment of a neutral covalent VB structure increases with the decreasing bond distance. The roles of the dominating VB structures are further examined by the geometry optimizations and frequency calculations with the block-localized wavefunction (BLW) method.

C5 Pentacle Structures: A Localization-Delocalization Matrices Approach.

This article explores the possible presence of a pentacle valence bond structure in C 5 ${_5 }$ cyclic molecules. At this end, we have used quantum chemistry tools to elucidate the possible arrangement and the nature of chemical bonds within linear, cyclic, and three-dimensional structures only formed by five carbon atoms. While the linear structure is clearly the most stable one, local minima were obtained for both bi- and three-dimensional structures. Using the localization-delocalization matrices approach, we characterize both the minimum linear structure and the cyclic ones. Interestingly, the linear structure is a combination of ionic and covalent bonds, albeit the four distances are almost identical, when using Density Functional Theory. For cyclic C 5 ${_5 }$ , the pentacle bonding arrangement emerges as a significant Lewis structure, indicative of an unusual formal configuration characterized by five intersecting C-C bonds. Our calculations show that this pentacle arrangement in cyclic C 5 ${_5 }$ scheme is also present in the more known cyclo-pentadienyl molecule.

The Peptide Bond: Resonance Increases Bond Order and Complicates Fragmentation.

The enhancement of the peptide bond order by a resonance in the lone pair of N and the π-bond of CO is analyzed. A decomposition of the bond order in terms of localized molecular orbitals is developed and applied to the peptide bond. A combination of two rotations of hybrid orbitals is proposed to improve the boundary treatment in the fragment molecular orbital method. The developed approach is applied to peptide bonds, and it is found crucial to retain the π orbital in the variational space of both fragments across the boundary. The interaction energies between conventional amino acid residues in Trp-cage (1L2Y) are discussed.

3,4-Dimethylenecyclobutene: A Building Block for Design of Macrocycles with Excited State Aromatic Low-Lying High-Spin States.

3,4-Dimethylenecyclobutene (DMCB) is an unusual isomer of benzene. Motivated by recent synthetic progress to substituted derivatives of this scaffold, we carried out a theoretical and computational analysis with a particular focus on the extent of (anti)aromatic character in the lowest excited states of different multiplicities. We found that the parent DMCB is non-aromatic in its singlet ground state (S0), lowest triplet state (T1), and lowest singlet excited state (S1), while it is aromatic in its lowest quintet state (Q1) as this state is represented by a triplet multiplicity cyclobutadiene (CBD) ring and two uncoupled same-spin methylene radicals. Interestingly, the Q1 state, despite having four unpaired electrons, is placed merely 4.8 eV above S0, and there is a corresponding singlet tetraradical 0.16 eV above. The DMCB is potentially a highly useful structural motif for the design of larger molecular entities with interesting optoelectronic properties. Here, we designed macrocycles composed of fused DMCB units, and according to our computations, two of these have low-lying nonet states (i. e., octaradical states) at energies merely 2.40 and 0.37 eV above their S0 states as a result of local Hückel- and Baird-aromatic character of individual 6π- and 4π-electron monocycles.

Synergistic Charge Transfer Effect in Ferrous Heme-CO Bonding within Cytochrome P450.

We conducted ab initio valence bond (VB) calculations employing the valence bond self-consistent field (VBSCF) and breathing orbital valence bond (BOVB) methods to investigate the nature of the coordination bonding between ferrous heme and carbon monoxide (CO) within cytochrome P450. These calculations revealed the significant influence exerted by both proximal and equatorial ligands on the π-backdonation effect from the heme to the CO. Moreover, our VB calculations unveiled a phenomenon of synergistic charge transfer (sCT). In the case of ferrous heme-CO bonding, the significant stabilization in this sCT arises from cooperative resonance between the VB structures associated with σ donation and π backdonation. Unlike many other ligands, CO possesses the unique ability to establish two mutually perpendicular π-backdonation orbital interaction pairs, leading to an intensified stabilization attributed to σ-π resonance. Furthermore, while of a smaller energy magnitude, sCT due to one π-π pair is also present, contributing to the differential stabilization of ferrous heme-CO bonding.

Stabilization of Diborynes versus Destabilization of Diborenes by Coordination of Lewis Bases: Unravelling the Dichotomy.

We have quantum chemically investigated the boron-boron bonds in B2 , diborynes B2 L2 , and diborenes B2 H2 L2 (L=none, OH2 , NH3 ) using dispersion-corrected relativistic density functional theory at ZORA-BLYP-D3(BJ)/TZ2P. B2 has effectively a single B-B bond provided by two half π bonds, whereas B2 H2 has effectively a double B=B bond provided by two half π bonds and one σ 2p-2p bond. This different electronic structure causes B2 and B2 H2 to react differently to the addition of ligands. Thus, in B2 L2 , electron-donating ligands shorten and strengthen the boron-boron bond whereas, in B2 H2 L2 , they lengthen and weaken the boron-boron bond. The aforementioned variations in boron-boron bond length and strength become more pronounced as the Lewis basicity of the ligands L increases.

Blueshift in Trifurcated Hydrogen Bonds: A Tradeoff between Tetrel Bonding and Steric Repulsion.

We have quantum chemically investigated the origin of the atypical blueshift of the H-C bond stretching frequency in the hydrogen-bonded complex X- •••H3 C-Y (X, Y=F, Cl, Br, I), as compared to the corresponding redshift occurring in Cl- •••H3 N and Cl- •••H3 C-H, using relativistic density functional theory (DFT) at ZORA-BLYP-D3(BJ)/QZ4P. Previously, this blueshift was attributed, among others, to the contraction of the H-C bonds as the H3 C moiety becomes less pyramidal. Herein, we provide quantitative evidence that, instead, the blueshift arises from a direct and strong X- •••C interaction of the HOMO of A- with the backside lobe on carbon of the low-lying C-Y antibonding σ* LUMO of the H3 C-Y fragment. This X- •••C bond, in essence a tetrel bond, pushes the H atoms towards a shorter H-C distance and makes the H3 C moiety more planar. The blueshift may, therefore, serve as a diagnostic for tetrel bonding.

δ-Bonding and Spin-Orbit Coupling Make SrAg4Sb2 a Topological Insulator.

Bonding interactions and spin-orbit coupling in the topological insulator SrAg4Sb2 are investigated using DFT with orbital projection analysis. Ag-Ag delta bonding is a key ingredient in the topological insulating state because the 4 d x y + 4 d x 2 - y 2 ${4d_{xy} + 4d_{x^2 - y^2 } }$ delta antibonding band forms a band inversion with the 5 s sigma bonding band. Spin-orbit coupling is required to lift d orbital degeneracies and lower the antibonding band enough to create the band inversion. These bonding effects are enabled by a longer-than-covalent Ag-Ag distance in the crystal lattice, which might be a structural characteristic of other transition metal based topological insulators. A simplified model of the topological bands is constructed to capture the essence of the topological insulating state in a way that may be engineered in other materials.

Applicability of transferable multipole pseudo-atoms for restoring inner-crystal electronic force density fields. Chemical bonding and binding features in the crystal and dimer of 1,3-bis(2-hydroxyethyl)-6-methyluracil.

We considered it timely to test the applicability of transferable multipole pseudo-atoms for restoring inner-crystal electronic force density fields. The procedure was carried out on the crystal of 1,3-bis(2-hydroxyethyl)-6-methyluracil, and some derived properties of the scalar potential and vector force fields were compared with those obtained from the experimental multipole model and from the aspherical pseudo-atom model with parameters fitted to the calculated structure factors. The procedure was shown to accurately replicate the general vector-field behavior, the peculiarities of the quantum potentials and the characteristics of the force-field pseudoatoms, such as charge, shape and volume, as well as to reproduce the relative arrangement of atomic and pseudoatomic zero-flux surfaces along internuclear regions. It was found that, in addition to the quantum-topological atoms, the force-field pseudoatoms are spatially reproduced within a single structural fragment and similar environment. In addition, the classical and nonclassical hydrogen bonds in the uracil derivative crystal, as well as the H...O, N...O and N...C interactions in the free π-stacked dimer of the uracil derivative molecules, were studied using the potential and force fields within the concepts of interatomic charge transfer and electron lone pair donation-acceptance. Remarkably, the nitrogen atoms in the N...O and N...C interactions behave rather like a Lewis base and an electron contributor. At the same time, the hydrogen atom in the H...O interaction, being a Lewis acid, also participates in the interatomic electron transfer by acting as a contributor. Thus, it has been argued that, when describing polar interatomic interactions within orbital-free considerations, it makes more physical sense to identify electronegative (electron occupier) and electropositive (electron contributor) atoms or subatomic fragments rather than nucleophilic and electrophilic sites.

From an Isolable Bismolyl Anion to an Yttrium-Bismolyl Complex with µ-Bridging Bismuth(I) Centers and Polar Covalent Y-Bi Bonds.

The synthesis and first structural characterization of the [K(18-crown-6)] bismolyl Bitet (C4 Me4 Bi) contact ion pair (1) is presented. Notably, according to Natural Resonance Theory calculations, the Bitet anion of 1 features two types of leading mesomeric structures with localized anionic charge and two lone pairs of electrons at the BiI center, as well as delocalized anionic charge in the π-conjugated C4 Bi ring. The lone pairs at Bi enable a unique bridging coordination mode of the bismolyl ligand, as shown for the first rare earth metal bismolyl complex (Cptet 2 Y)2 (µ-η1 -Bitet )2 (2). The latter results from the salt metathesis reaction of KBitet with Cptet 2 Y(BPh4 ) (Cptet =C5 Me4 H). The Y-Bi bonding interaction in 2 of 16.6 % covalency at yttrium is remarkably large.

The Challenging World of Simple Inorganic Rings: Revisiting Roesky's Ketone and Roesky's Sulfoxide.

The surprising differences between the experimental solid-state and calculated gas-phase structures of 5-oxo-1,3,2,4-dithiadiazole (Roesky's ketone, 1) and 1-oxo-1,2,4,3,5-trithiadiazole (Roesky's sulfoxide, 2), identified and studied in a series of papers published between 2004 and 2010 but then never satisfactorily explained, have been revisited, making use of the more advanced computational possibilities currently available. The previous calculations' considerable overestimations of the C-S and S-S bond lengths in 1 and 2, respectively, have been partly explained based on the results of periodic calculations and the application of Valence Bond (VB) Theory. In the case of 1, the crystal environment appears to stabilize a structure with a highly polarized C=O bond, which features a C-S bond with considerable double-bond character - an effect which does not exist for the isolated molecule - explaining the much shorter bond in the solid state. For 2, a similar conclusion can be drawn for the S-S distance. For both compounds, though, packing effects are not the sole source of the differences: the inability of Density Functional Theory (DFT) to properly deal with the electronic structures of these apparently simple main-group systems remains a contributing factor.

Phase Structure, Bond Features, and Microwave Dielectric Characteristics of Ruddlesden-Popper Type Sr2TiO4 Ceramics.

This work studied the phase constitution, bond characteristics, and microwave dielectric performances of Sr2TiO4 ceramics. Based on XRD and Rietveld refinement analysis, pure tetragonal Ruddlesden-Popper type Sr2TiO4 ceramic is synthesized at 1425~1525 °C. Meanwhile, the microstructure is dense and without porosity, indicating its high sinterability and densification. Great microwave dielectric performances can be obtained, namely an εr value of 39.41, and a Q × f value of 93,120 GHz, when sintered at 1475 °C. Under ideal sintering conditions, the extrinsic factors are minimized and can be ignored. Thus, the intrinsic factors are considered crucial in determining microwave dielectric performances. Based on the P-V-L complex chemical bond theory calculation, the largest bond ionicity, and proportions to the bond susceptibility from Sr-O bonds suggest that Sr-O bonds mainly determine the dielectric polarizability. However, the Ti-O bonds show lattice energy about three times larger than Sr-O bonds, emphasizing that the structural stability of Sr2TiO4 ceramics is dominated by Ti-O bonds, and the Ti-O bonds are vital in determining the intrinsic dielectric loss. The thermal expansion coefficient value of the Sr2TiO4 structure is also mainly decided by Ti-O bonds.

A unified superatomic-molecule theory for local aromaticity in π-conjugated systems.

Aromaticity is one of the most important concepts in chemistry. However, there is still no unified chemical insight for various systems with conjugated sp2 carbon. Herein, we proposed a superatomic-molecule theory to build a generalized electron rule for polycyclic conjugated hydrocarbons, fullerenes and 2D periodic materials. Taking benzenoid units as 2D superatoms, polycyclic conjugated hydrocarbons and C60 can be seen as superatomic molecules consisting of bonded superatoms, resulting in local aromaticity. In superatomic molecules, π electrons are not totally delocalized, but localized in a single superatom forming superatomic lone pairs or shared by two atoms forming a superatomic bond, mimicking rules in classical valence bond theory. Moreover, two 2D superatomic crystals (C18H6 and C54H18) are predicted to have fairly large band gaps (∼1.8 eV), although the π electrons are conjugated and delocalized. The proposed superatomic-molecule theory provides generalized chemical insights into the nature of local aromaticity, which can be qualitatively evaluated by the chemical intuition given by superatomic Lewis structures.

Dichotomy of Delocalization/Localization and Charge-Shift Bonding in Germanazene and its Heavier Group 14 Analogues: a Valence Bond Study.

We present here a valence bond analysis of structure and π-delocalization in Ge3 (NH)3 , which models germanazene that was prepared by Power et al. To get a broader perspective, we explore the entire E3 (NH)3 series (E=C, Si, Ge, Sn, Pb). Thus, while (4n+2)π systems of carbon rings are aromatic with cyclic π-delocalization, the E3 (NH)3 rings are dominated by a nonbonded structure, wherein π-lone pairs are localized on the N atoms. Nevertheless, these molecules enjoy large covalent-ionic resonance energies of 153.0, 86.6, 74.2, 61.2, and 58.9 kcal/mol, respectively, for E=C, Si, Ge, Sn, Pb. The covalent-ionic mixing in E3 (NH)3 creates π-systems, which are stabilized by charge-shift bonding. Thus, unlike in benzene, in Ge3 (NH)3 delocalization of π-electron pairs of the N atoms is primarily confined to the domains of their adjacent Ge atoms. These features carry over to the substituted germanazene, Ge3 (NAr)3 (Ar=Ph).

Intermolecular Covalent Interactions: Nature and Directionality.

Quantum chemical methods were employed to analyze the nature and the origin of the directionality of pnictogen (PnB), chalcogen (ChB), and halogen bonds (XB) in archetypal Fm Z⋅⋅⋅F- complexes (Z=Pn, Ch, X), using relativistic density functional theory (DFT) at ZORA-M06/QZ4P. Quantitative Kohn-Sham MO and energy decomposition analyses (EDA) show that all these intermolecular interactions have in common that covalence, that is, HOMO-LUMO interactions, provide a crucial contribution to the bond energy, besides electrostatic attraction. Strikingly, all these bonds are directional (i.e., F-Z⋅⋅⋅F- is approximately linear) despite, and not because of, the electrostatic interactions which, in fact, favor bending. This constitutes a breakdown of the σ-hole model. It was shown how the σ-hole model fails by neglecting both, the essential physics behind the electrostatic interaction and that behind the directionality of electron-rich intermolecular interactions. Our findings are general and extend to the neutral, weaker ClI⋅⋅⋅NH3 , HClTe⋅⋅⋅NH3 , and H2 ClSb⋅⋅⋅NH3 complexes.

Substituent Effect and Its Halogen-Atom Dependence of Halogen Bonding Viewed through Electron Density Changes.

Elucidating how the halogen-bonding ability and strength are controlled by the substituent effect and how this control depends on halogen atom will be essential for finely-tuned design of functionally important molecules. Here, this problem is tackled by analyzing the electron density differences/changes for variously substituted halobenzenes. It is shown that the anisotropy of the electron distribution around the halogen atom, which is an important factor for halogen-bonding ability, is not much affected by the substituent effect and rather simply depends on the halogen atom, while the partial charge on the halogen atom, which is related to the bond dipole of the C-X bond, is significantly modulated by the substituent effect and gives rise to enhancement of the electrostatic potential on the line extended from the C-X bond. The properties related to the polarization effect are also discussed.

Structure and bonding of proximity-enforced main-group dimers stabilized by a rigid naphthyridine diimine ligand.

The development of ligands capable of effectively stabilizing highly reactive main-group species has led to the experimental realization of a variety of systems with fascinating properties. In this work, we computationally investigate the electronic, structural, energetic, and bonding features of proximity-enforced group 13-15 homodimers stabilized by a rigid expanded pincer ligand based on the 1,8-naphthyridine (napy) core. We show that the redox-active naphthyridine diimine (NDI) ligand enables a wide variety of structural motifs and element-element interaction modes, the latter ranging from isolated, element-centered lone pairs (e.g., E = Si, Ge) to cases where through-space π bonds (E = Pb), element-element multiple bonds (E = P, As) and biradical ground states (E = N) are observed. Our results hint at the feasibility of NDI-E2 species as viable synthetic targets, highlighting the versatility and potential applications of napy-based ligands in main-group chemistry.

Low-Valent Mx Al3 Cluster Salts with Tetrahedral [SiAl3 ]+ and Trigonal-Bipyramidal [M2 Al3 ]2+ Cores (M=Si/Ge).

Schnöckel's [(AlCp*)4 ] and Jutzi's [SiCp*][B(C6 F5 )4 ] (Cp*=C5 Me5 ) are landmarks in modern main-group chemistry with diverse applications in synthesis and catalysis. Despite the isoelectronic relationship between the AlCp* and the [SiCp*]+ fragments, their mutual reactivity is hitherto unknown. Here, we report on their reaction giving the complex salts [Cp*Si(AlCp*)3 ][WCA] ([WCA]- =[Al(ORF )4 ]- and [F{Al(ORF )3 }2 ]- ; RF =C(CF3 )3 ). The tetrahedral [SiAl3 ]+ core not only represents a rare example of a low-valent silicon-doped aluminium-cluster, but also-due to its facile accessibility and high stability-provides a convenient preparative entry towards low-valent Si-Al clusters in general. For example, an elusive binuclear [Si2 (AlCp*)5 ]2+ with extremely short Al-Si bonds and a high negative partial charge at the Si atoms was structurally characterised and its bonding situation analysed by DFT. Crystals of the isostructural [Ge2 (AlCp*)5 ]2+ dication were also obtained and represent the first mixed Al-Ge cluster.

Birds of a Feather Get High Together: A Reconceptualization of the Social Bond with Latent Class Analysis and a Test with Different Forms of Drug Use.

Social bond theory has received significant empirical support in examinations of drug use for decades. However, research utilizing the theory has often been fragmented and has not incorporated all four dimensions of the social bond. Additionally, much of this research has collapsed drug use into categories rather than examining specific forms of drug use. These concerns confuse the theoretical and practical insights that may be derived from such analyses. I utilize Monitoring the Future (2019) data to examine social bonding wholistically as latent classes in line with the concept of the social bond described by Hirschi (1969) and estimate the effect of the classes on specific forms of drug use. I find there are four distinct classes of social bonding among U.S. seniors most clearly differentiated by levels of attachment and commitment. Logistic regression results indicated different classes of social bonding were associated with different forms of drug use. I discuss the theoretical implications of the results and how they can be applied for criminal justice practitioners.