Bond Picture Research Articles

Theoretical study on open-shell electronic structures of through-bond/through-space hybrid conjugated ladder graphs

In this study, we theoretically investigated open-shell electronic structures of face-to-face π-stacked n-mers of diradicaloids with through-bond/through-space (TB/TS) hybrid conjugation structure of n-ladder graphs. Based on the Hückel theory and the valence bond (VB) picture of diradical character (y), we considered y for the local TB and TS interactions, yTB and yTS, and derived sets of conditions between yTB and yTS when y of the entire system, y(n), takes the maximum for a given n. The approximate relations between yTB, yTS, and y(n) help predict the open-shell electronic structures of face-to-face π-stacked n-mers of realistic diradicaloids with different yTB.

Modular Cluster Circuits for the Variational Quantum Eigensolver.

The variational quantum eigensolver algorithm recently became a popular method to compute the quantum chemical properties of molecules on noisy intermediate scale quantum (NISQ) devices. In order to avoid noise accumulation from the NISQ device in the quantum circuit, it is important to keep the so-called quantum depth of the circuit at a minimum, defined as the minimum number of quantum gates that must be operated sequentially. In the present work, we introduce a modular 2-qubit cluster circuit that allows for the design of a shallow-depth quantum circuit compared to previously proposed architectures without loss of chemical accuracy. Moreover, by virtue of the simplicity of the cluster circuit, it is possible to assign a valence bond chemical interpretation to the cluster circuit. The design was tested on the H2, (H2)2, and LiH molecules, as well as the finite-size transverse-field Ising model, as the latter provides additional insights into the construction of the circuit in a resonating valence bond picture.

Insight into the Structural and Emissive Behavior of a Three-Dimensional Americium(III) Formate Coordination Polymer.

We report the structural, vibrational, and optical properties of americium formate (Am(CHO2 )3 ) crystals synthesized via the in situ hydrolysis of dimethylformamide (DMF). The coordination polymer features Am3+ ions linked by formate ligands into a three-dimensional network that is isomorphous to several lanthanide analogs, (e. g., Eu3+ , Nd3+ , Tb3+ ). Structure determination revealed a nine-coordinate Am3+ metal center that features a unique local C3v symmetry. The metal-ligand bonding interactions were investigated by vibrational spectroscopy, natural localized molecular orbital calculations, and the quantum theory of atoms in molecules. The results paint a predominantly ionic bond picture and suggest the metal-oxygen bonds increase in strength from Nd-O<Eu-O<Am-O. The optical properties were probed using diffuse reflectance and photoluminescence spectroscopies. Notably, the rarely reported 5 D1' →7 F0' emission band is observed and dominates the emission spectrum. This behavior is unusual and is attributed to the C3v coordination environment of the metal center.

Unifying Kitaev Magnets, Kagomé Dimer Models, and Ruby Rydberg Spin Liquids

The exploration of quantum spin liquids (QSLs) has been guided by different approaches including the resonating valence bond (RVB) picture, deconfined lattice gauge theories and the Kitaev model. More recently, a spin liquid ground state was numerically established on the ruby lattice, inspired by the Rydberg blockade mechanism. Here we unify these varied approaches in a single parent Hamiltonian, in which local fluctuations of anyons stabilize deconfinement. The parent Hamiltonian is defined on kagom\'e triangles -- each hosting four RVB-like states -- and includes only Ising interactions and single-site transverse fields. In the weak-field limit, the ruby spin liquid and exactly soluble kagom\'e dimer models are recovered, while the strong-field limit reduces to the Kitaev honeycomb model, thereby unifying three seemingly different approaches to QSLs. We similarly obtain the chiral Yao-Kivelson model, honeycomb toric code and a new spin-1 quadrupolar Kitaev model. The last is shown to be in a QSL phase by a non-local mapping to the kagom\'e Ising antiferromagnet. We demonstrate various applications of our framework, including (a) an adiabatic deformation of the ruby lattice model to the exactly soluble kagom\'e dimer model, conclusively establishing the QSL phase in the former; and (b) demystifying the dynamical protocol for measuring off-diagonal strings in the Rydberg implementation of the ruby lattice spin liquid. More generally, we find an intimate connection between Kitaev couplings and the repulsive interactions used for emergent dimer models. For instance, we show how a spin-1/2 XXZ model on the ruby lattice encodes a Kitaev honeycomb model, providing a new route toward realizing the latter in cold-atom or solid-state systems.

Quantum dimer model on fullerenes: Resonance, scarring, and confinement

The earliest known examples of quantum superposition were found in organic chemistry -- in molecules that `resonate' among multiple arrangements of $\pi$-bonds. Small molecules such as benzene resonate among a few bond arrangements. In contrast, a large system that stretches over a macroscopic lattice may resonate among an extensive number of configurations. This is analogous to a quantum spin liquid as described by Anderson's resonating valence bond (RVB) picture. In this article, we study the intermediate case of somewhat large molecules, the C$_{20}$ and C$_{60}$ fullerenes. We build a minimal description in terms of quantum dimer models, allowing for local resonance processes and repulsion between proximate $\pi$-bonds. This allows us to characterize ground-states, e.g., with C$_{60}$ forming a superposition of 5828 dimer covers. Despite the large number of contributing dimer covers, the ground state shows strong dimer-dimer correlations. Going beyond the ground state, the full spectrum of C$_{60}$ shows many interesting features. Its Hilbert space is bipartite, leading to spectral reflection symmetry. It has a large number of protected zero-energy states. In addition, the spectrum contains many scar-like states, corresponding to localized dimer-rearrangement-dynamics. Resonance dynamics in QDMs can manifest in the behaviour of defects, potentially binding defects via an effective attractive interaction. To test this notion, we introduce pairs of vacancies at all possible separations. Resonance energy reaches its lowest value when the vacancies are closest to one another. This suggests confinement of monomers, albeit within a finite cluster. We discuss qualitative pictures for understanding bonding in fullerenes and draw connections with results from quantum chemistry.

Bulk topological signatures of a quasicrystal

We show how measuring real space properties such as the charge density in a quasiperiodic system can be used to gain insight into their topological properties. In particular, for the Fibonacci chain, we show that the total onsite charge oscillates when plotted in the appropriate coordinates, and the number of oscillations is given by the Chern number of the gap in which the Fermi level lies. We show that these oscillations have two distinct interpretations, obtained by extrapolating results from the two extreme limits of the Fibonacci chain -- the valence bond picture in the strong modulation limit, and perturbation around the periodic chain in the weak modulation limit. This effect is found to remain robust at moderate interactions, as well as in the presence of disorder. We conclude that experimental measurement of the real space charge distribution can yield information on topological properties in a straightforward way.

Matrix product wave function of the ground state and elementary excitations in the spin- 12 chain

We present a variational matrix product state (vMPS) for the ground state of the spin-1/2 Heisenberg model. The MPS effectively organizes the various dimer configurations, in faithful reflection of the resonating valence bond picture of the spin liquid, with the energy only 0.024% higher than the exact value given by Bethe ansatz. Building on the ground-state vMPS, the one-spin wave function is constructed in a simple manner with the dispersion that matches well with the exact spectrum. The vMPS scheme is applied to the family of Hamiltonian extrapolating between the Heisenberg model and the Majumdar-Ghosh model.

Beyond the Classical Electron-Sharing and Dative Bond Picture: Case of the Spin-Polarized Bond.

Chemical bonds are traditionally assigned as electron‐sharing or donor‐acceptor/dative. External criteria such as the nature of the dissociation process, energy partitioning schemes, or quantum chemical topology are invoked to assess the bonding situation. However, for systems with marked multi‐reference character, this binary categorization might not be precise enough to render the bonding properties. A third scenario can be foreseen: spin polarized bonds. To illustrate this, the case of a NaBH3 − cluster is presented. According to the analysis NaBH3 − exhibits a strong diradical character and cannot be classified as either electron‐sharing or a dative bond. Elaborated upon are the common problems of popular bonding descriptions. Additionally, a simple model, based on the bond order and local spin indicators, which discriminates between all three bonding situations, is provided.

Peculiar bond characters of fivefold coordinated octet compound crystals.

The present work exemplifies complementary perspectives offered by the band and bond pictures of solids, with an emphasis on the chemical intuition pertaining to the latter, especially in the presence of interfaces. The modern computational method of constructing a unique set of maximally localized Wannier functions from delocalized band states imparts new interpretations to the familiar concept of chemical bonds in the context of crystalline solids. By bridging the band and bond pictures using advanced computational tools, we reveal for the first time the unusual bond characters of a long-predicted fivefold coordinated structure of binary octet compounds ANB8−N consisting of AA′ stacked planar AB honeycombs. While the isolated monolayer retains the familiar pz–π bonding in a honeycomb framework as in graphene and hexagonal boron nitride, the bulk foregoes in-plane π bonding and embraces out-of-plane ⋯A–B–A–B⋯ chain bonding via overlapping pz orbitals. Not only does the chemical intuition gained by invoking the bond picture clarify the chemical nature of the fivefold coordination, but it also facilely explains a salient discrepancy in theoretical predictions in otherwise sound ample experimental evidence in the form of epitaxial thin films, paving the way towards rational synthesis of such thin films for optoelectronic applications. On the other hand, we show that the conduction band minimum, important in determining the electrical and optical properties, is a distinctly extended state that can only be properly described within the band picture.

Strong Odd Bond - Weak Even Bond Picture in the Half-Filled One-Dimensional Hubbard Model

We study the strong odd bond - weak even bond picture by measuring the bond energy and the half-chain entanglement entropy in the one-dimensional Hubbard model. By using the infinite density matrix renormalization group with matrix product operator, we obtain the ground state of the matrix product state. As a function of the bond dimension, the bond energy and the half-chain entanglement entropy support the strong odd bond - weak even bond picture. From the expectation values of the occupation number, we numerically observe that the odd - even effect appears only for the half-filling case with a finite bond dimension. Our results confirm that the matrix product operator method is successful in exploring itinerant fermionic systems.

Molecular interactions in electron-groups embedding generalized valence bond picture

Theoretical description of molecular interactions remains a challenge for computational chemistry. In particular, systems dominated by static correlation, in which bonds are stretched or twisted, are often beyond capabilities of methods based on a single-electron approximation, being usually a method of choice. For interacting multireference systems, it is necessary to apply either high-level coupled-cluster methods (which however include multireference effects only partially) or base the theoretical description on a multireference wavefunction. Popular multireference methods like CASPT2 (complete active space perturbation theory) do not provide satisfactory results since they may suffer from problems with size consistency and poor accuracy. Recently we have shown that combining a simple multireference wavefunction, perfect-pairing generalized valence bond (GVB) with extended random phase approximation in embedding framework (EERPA) leads to a method EERPA-GVB providing accurate results for challenging multireference systems. In this paper, good performance of EERPA-GVB is confirmed by its application to van der Waals and hydrogen-bonded complexes. In addition, we show that the decomposition of the EERPA-GVB correlation energy into contributions from pairs of geminals can provide useful insight into the investigated interactions.

‘Jumping on the Bondwagon’: The Spy Cycle in British Cinema in the 1960s

The article examines the significant cycle of spy thrillers in British cinema in the 1960s. It argues that the success of the early James Bond pictures, which commenced with Dr. No in 1962, initiated a popular cycle of spy films that lasted through the decade. The interest in fictional intrigue generated by the new-style espionage stories of Len Deighton and John le Carré further fuelled the cycle, and there appeared a number of adaptations of these authors’ novels. The article pays particular attention to the critical reception of the cycle and the two styles of Bond-inspired spy thriller and Deighton/le Carré-inspired espionage drama, carefully considering the mounting reviewer fatigue regarding the overworked spy picture and recounting the decline of the cycle.

Valence bonds in elongated boron clusters

AbstractA well‐defined class of planar or quasi‐planar elongated boron clusters, of type , serves as a basis to identify the valence bond picture of delocalized boron networks. The origin of the series is the cluster, which exhibits σ‐aromaticity. The cluster generating step is the repetitive expansion by three boron atoms in the direction of elongation. Specific electron counting rules are obtained for π‐bonding, peripheral σ‐bonding and multicenter inner σ‐bonding. A valence bond structure is introduced which explains the remarkable regularity in the bonding pattern. The analysis supports 4c‐2e bonds as an alternative to the common 3c‐2e bonds. The results are validated by symmetry induction and ab initio calculations.

Imaging the Bonds of Dehalogenated Benzene Radicals on Cu(111) and Au(111).

Dissociative adsorption of doubly substituted benzene molecules leads to formation of benzyne radicals. In this study, co-adsorbed hydrogen molecules are used in scanning tunneling hydrogen microscopy to enhance the contrast of the meta- and the para-isomers of these radicals on Cu(111) and Au(111). Up to three hydrogen molecules are attached to one radical. One hydrogen molecule reveals the orientation of the carbon ring and its adsorption site, allowing discrimination between the two radicals. Two hydrogen molecules reflect the bond picture of the carbon skeleton and reveals that adsorption on Cu(111) distorts the meta- isomer differently from its gas-phase distortion. Three hydrogen molecules allow us to determine the bond picture of a minor species.

Several stories from theoretical chemistry with some Russian flavor and implications for theorems of chemistry, vagueness of its concepts, fuzziness of its definitions, iconicity of its language, and peculiarities of its nomenclature

We present an informal discussion of the problems related to emergence and development of theoretical chemistry concepts and their relation to those of quantum mechanics and general mathematical thinking. This also brings us to a discussion of axiomatization of chemical knowledge, relation between iconic language of (organic) chemistry and symbolic language of physics, relations between molecular orbital and valence bond pictures of molecular electronic structure and other similar problems. Because of the thematic orientation of the present issue of the Int. J. Quantum Chem. Russian contributions to setting and solving the above problems are highlighted. © 2015 Wiley Periodicals, Inc.

Stability and Electronic Properties of Hydrogenated Zigzag Carbon Nanotube Focused on Stone-Wales Defect**Supported by the Education Department of Henan Province under Grant No 14B140018.

We present a first-principles study of the chemisorption of hydrogen on a Stone-Wales (SW) defective carbon nanotube (10,0). The investigated configurations include four configurations covering single defects and double defects. One hydrogen dimer adsorption is energetically favored on bonds shared by carbon heptagon-heptagon for configurations with the defect parallel to the tube axis compared with the carbon pentagon-hexagon sites for ones with a slanted defect. This different behavior is also demonstrated for hydrogen dimer chain adsorption, the favored site for the former ones is through the defect, which is the nearest neighbor site to defect for the latter ones. It is found that the energy band gaps of hydrogenated configurations may be enlarged or decreased by altering the adsorption site or defect position. The semiconductor-to-metal transition may occur for configurations with the defect or defects parallel to the tube axis due to low electronic localization. Our results highlight the interest of the interaction of multi-factor system by providing a detailed bond and position picture of a hydrogenated defective carbon nanotube (10,0).

Charge transfer in strongly correlated systems: An exact diagonalization approach to model Hamiltonians

We study charge transfer in bridged di- and triruthenium complexes from a theoretical and computational point of view. Ab initio computations are interpreted from the perspective of a simple empirical Hamiltonian, a chemically specific Mott-Hubbard model of the complexes' π electron systems. This Hamiltonian is coupled to classical harmonic oscillators mimicking a polarizable dielectric environment. The model can be solved without further approximations in a valence bond picture using the method of exact diagonalization and permits the computation of charge transfer reaction rates in the framework of Marcus' theory. In comparison to the exact solution, the Hartree-Fock mean field theory overestimates both the activation barrier and the magnitude of charge-transfer excitations significantly. For triruthenium complexes, we are able to directly access the interruthenium antiferromagnetic coupling strengths.

Electronic structure of N-doped graphene with native point defects

Nitrogen doping in graphene has important implications in graphene-based devices and catalysts. We have performed the density functional theory calculations to study the electronic structures of N-doped graphene with vacancies and Stone-Wales defect. Our results show that monovacancies in graphene act as hole dopants and that two substitutional N dopants are needed to compensate for the hole introduced by a monovacancy. On the other hand, divacancy does not produce any free carriers. Interestingly, a single N dopant at divacancy acts as an acceptor rather than a donor. The interference between native point defect and N dopant strongly modifies the role of N doping regarding the free carrier production in the bulk $\ensuremath{\pi}$ bands. For some of the defects and N dopant-defect complexes, localized defect $\ensuremath{\pi}$ states are partially occupied. Discussion on the possibility of spin polarization in such cases is given. We also present qualitative arguments on the electronic structures based on the local bond picture. We have analyzed the 1$s$-related x-ray photoemission and adsorption spectroscopy spectra of N dopants at vacancies and Stone-Wales defect in connection with the experimental ones. We also discuss characteristic scanning tunneling microscope (STM) images originating from the electronic and structural modifications by the N dopant-defect complexes. STM imaging for small negative bias voltage will provide important information about possible active sites for oxygen reduction reaction.

Incommensurability effects in odd lengthJ1-J2quantum spin chains: On-site magnetization and entanglement

For the antiferromagnetic ${J}_{1}$-${J}_{2}$ quantum spin chain with an even number of sites, the point ${J}_{2}^{d}={J}_{1}/2$ is a disorder point. It marks the onset of incommensurate real space correlations for ${J}_{2}&gt;{J}_{2}^{d}$. At a distinct larger value of ${J}_{2}^{L}=0.520\phantom{\rule{0.16em}{0ex}}36(6){J}_{1}$, the Lifshitz point, the peak in the static structure factor begins to move away from $k=\ensuremath{\pi}$. Here, we focus on chains with an odd number of sites. In this case, the disorder point is also at ${J}_{2}^{d}={J}_{1}/2$ but the behavior close to the Lifshitz point, ${J}_{2}^{L}\ensuremath{\simeq}0.538{J}_{1}$, is quite different: starting at ${J}_{2}^{L}$, the ground state goes through a sequence of level crossings as its momentum changes away from $k=\ensuremath{\pi}/2$. An even length chain, on the other hand, is gapped for any ${J}_{2}&gt;0.24{J}_{1}$ and has the ground-state momentum $k=0$. This gradual change in the ground-state wave function for chains with an odd number of sites is reflected in a dramatic manner directly in the ground-state on-site magnetization as well as in the bipartite von Neumann entanglement entropy. Our results are based on DMRG calculations and variational calculations performed in a restricted Hilbert space defined in the valence bond picture. In the vicinity of the point ${J}_{2}={J}_{1}/2$, we expect the variational results to be very precise.

Chemical Reasoning Based on an Invariance Property: Bond and Lone Pair Pictures in Quantum Structural Formulas

Chemists use one set of orbitals when comparing to a structural formula, hybridized AOs or NBOs for example, and another for reasoning in terms of frontier orbitals, MOs usually. Chemical arguments can frequently be made in terms of energy and/or electron density without the consideration of orbitals at all. All orbital representations, orthogonal or not, within a given function space are related by linear transformation. Chemical arguments based on orbitals are really energy or electron density arguments; orbitals are linked to these observables through the use of operators. The Valency Interaction Formula, VIF, offers a system of chemical reasoning based on the invariance of observables from one orbital representation to another. VIF pictures have been defined as one-electron density and Hamiltonian operators. These pictures are classified in a chemically meaningful way by use of linear transformations applied to them in the form of two pictorial rules and the invariance of the number of doubly, singly, and unoccupied orbitals or bonding, nonbonding, and antibonding orbitals under these transformations. The compatibility of the VIF method with the bond pair – lone pair language of Lewis is demonstrated. Different electron lone pair representations are related by the pictorial rules and have stability understood in terms of Walsh’s rules. Symmetries of conjugated ring systems are related to their electronic state by simple mathematical formulas. Description of lone pairs in conjugated systems is based on the strength and sign of orbital interactions around the ring. Simple models for bonding in copper clusters are tested, and the bonding of O2 to Fe(II) in hemoglobin is described. Arguments made are supported by HF, B3LYP, and MP2 computations.