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A molecular Mott insulator $\kappa$-(ET)$_2$B(CN)$_4$ [ET = bis(ethylenedithio)tetrathiafulvalene] with a distorted triangular lattice exhibits a quantum disordered state with gapped spin excitation in the ground state. $^{13}$C nuclear magnetic resonance, magnetization, and magnetic torque measurements reveal that magnetic field suppresses valence bond order and induces long-range magnetic order above a critical field $\sim 8$ T. The nuclear spin-lattice relaxation rate $1/T_1$ shows persistent evolution of antiferromagnetic correlation above the transition temperature, highlighting a quantum spin liquid state with fractional excitations. The field-induced transition as observed in the spin-Peierls phase suggests that the valence bond order transition is driven through renormalized one-dimensionality and spin-lattice coupling., Comment: 8 pages, 10 figures

Chemists explaining a molecule’s stability and reactivity often refer to the concepts of delocalization, resonance, and aromaticity. Resonance is commonly discussed within valence bond theory as the stabilizing effect of mixing different Lewis structures. Yet, most computational chemists work with delocalized molecular orbitals, which are also usually employed to explain the concept of aromaticity, a ring delocalization in cyclic planar systems which abide certain number rules. However, all three concepts lack a real space definition, that is not reliant on orbitals or specific wave function expansions. Here, we outline a redefinition from first principles: delocalization means that likely electron arrangements are connected via paths of high probability density in the many-electron real space. In this picture, resonance is the consideration of additional electron arrangements, which offer alternative paths. Most notably, the famous 4n + 2 Hückel rule is generalized and derived from nothing but the antisymmetry of fermionic wave functions., The concept of delocalization, resonance and aromaticity are commonly discussed within electronic structure frameworks relying on specific wave function expansions. Here the authors propose a redefinition of these concepts from first-principles by investigating saddle points of the all-electron probability density.

International audience; A full-dimensional quantum dynamical study for the bimolecular reactions of hydrogen molecules with amino radicals for different isotopologues is reported. The nonreactive amino radical is described by two Radau vectors that are very close to the valence bond coordinates. Potential-optimized discrete variable representation basis is used for the vibrational coordinates of the amino radical. Starting from the reaction H2 + NH2, we study the isotope effects for the two reagents separately, i.e., H2 + NH2/ND2/NHD and H2/D2/HD + NH2. The effects of different vibrational mode excitations of the reagents on the reactivities are studied. Physical explanations about the isotope effects are also provided thoroughly including the influence of vibrational energy differences between the different isotopologues and the impact of the tunneling effect

The enzyme-catalyzed degradation of the biogenic amine serotonin is an essential regulatory mechanism of its level in the human organism. In particular, monoamine oxidase A (MAO A) is an important flavoenzyme involved in the metabolism of monoamine neurotransmitters. Despite extensive research efforts, neither the catalytic nor the inhibition mechanisms of MAO enzymes are currently fully understood. In this article, we present the quantum mechanics/molecular mechanics simulation of the rate-limiting step for the serotonin decomposition, which consists of hydride transfer from the serotonin methylene group to the N5 atom of the flavin moiety. Free-energy profiles of the reaction were computed by the empirical valence bond method. Apart from the enzymatic environment, the reference reaction in the gas phase was also simulated, facilitating the estimation of the catalytic effect of the enzyme. The calculated barrier for the enzyme-catalyzed reaction of 14.82 +/- 0.81 kcal mol(-1) is in good agreement with the experimental value of 16.0 kcal mol(-1), which provides strong evidence for the validity of the proposed hydride-transfer mechanism. Together with additional experimental and computational work, the results presented herein contribute to a deeper understanding of the catalytic mechanism of MAO A and flavoenzymes in general, and in the long run, they should pave the way toward applications in neuropsychiatry.

Magnetic and magnetocaloric properties of a spin-1 Heisenberg diamond cluster with two different coupling constants are investigated with the help of an exact diagonalization based on the Kambe's method, which employs a local conservation of composite spins formed by spin-1 entities located in opposite corners of a diamond spin cluster. It is shown that the spin-1 Heisenberg diamond cluster exhibits several intriguing quantum ground states, which are manifested in low-temperature magnetization curves as intermediate plateaus at 1/4, 1/2 and 3/4 of the saturation magnetization. Besides, the spin-1 Heisenberg diamond cluster may also exhibit an enhanced magnetocaloric effect, which may be relevant for a low-temperature refrigeration achieved through the adiabatic demagnetization. It is evidenced that the spin-1 Heisenberg diamond cluster with the antiferromagnetic coupling constants J1/kB = 41.4 K and J2/kB = 9.2 K satisfactorily reproduces a low-temperature magnetization curve recorded for the tetranuclear nickel complex [Ni4(CO3)2(aetpy)8](ClO4)4 (aetpy = 2-aminoethyl-pyridine) including a size and position of intermediate plateaus detected at 1/2 and 3/4 of the saturation magnetization. A microscopic nature of fractional magnetization plateaus observed experimentally is clarified and interpreted in terms of valence-bond crystal with either a single or double valence bond. It is suggested that this frustrated magnetic molecule can provide a prospective cryogenic coolant with the maximal isothermal entropy change - Delta S = 10.6 J/(K.kg) in a temperature range below 2.3 K., Comment: 17 pages, 10 figures

The molecular dissociation energy has often been explained and discussed in terms of singlet bonds, formed by bounded pairs of valence electrons. In this work we use a highly correlated resonating valence bond ansatz, providing a consistent paradigm for the chemical bond, where spin fluctuations are shown to play a crucial role. Spin fluctuations are known to be important in magnetic systems and correspond to the zero point motion of the spin waves emerging from a magnetic broken symmetry state. Recently, in order to explain the excitation spectrum of the carbon dimer, an unusual quadruple bond has been proposed. Within our ansatz, a satisfactory description of the carbon dimer is determined by the magnetic interaction of two Carbon atoms with antiferromagnetically ordered S = 1 magnetic moments. This is a first step that, thanks to the highly scalable and efficient quantum Monte Carlo technique, may open the way for understanding challenging complex systems containing atoms with large spins (e.g. transition metals).

Frustrated rare-earth pyrochlore titanates, Yb$_2$Ti$_2$O$_7$, and Tb$_2$Ti$_2$O$_7$ have been proposed as promising candidates to realize quantum spin ice (QSI). Multiple exotic quantum phases, including Coulombic ferromagnet, quantum valence-bond solid, and quadrupolar ordering, have been predicted to emerge in the QSI state upon application of a (111)-oriented external magnetic field. Here, we report on the primal successful layer-by-layer growth of ultra-thin films of frustrated quantum pyrochlores, R$_2$Ti$_2$O$_7$ (R = Er, Yb, and Tb), along the (111) direction. We confirm their high crystallinity and proper chemical composition by a combination of methods, including in-situ RHEED, x-ray diffraction, reciprocal space mapping, and x-ray photoelectron spectroscopy. The availability of large area (111)-oriented QSI structures with planar geometry offers a new complementary to the bulk platform to explore strain and magnetic field dependent properties in the quasi-2D limit.

The Empirical Valence Bond (EVB) method offers a suitable framework to obtain reactive potentials through the coupling of nonreactive force fields. In this formalism, most of the implemented coupling terms are built using functional forms that depend on spatial coordinates, while parameters are fitted against reference data to model the change of chemistry between the participating nonreactive states. In this work, we demonstrate that the use of such coupling terms precludes the computation of the stress tensor for condensed phase systems and prevents the possibility to carry out EVB molecular dynamics in the isothermal-isobaric (NPT) ensemble. Alternatively, we make use of coupling terms that depend on the energy gaps, defined as the energy differences between the participating nonreactive force fields, and derive a general expression for the EVB stress tensor suitable for computation. Implementation of this new methodology is tested for a model of a single reactive malonaldehyde solvated in nonreactive water. Mass densities and probability distributions for the values of the energy gaps computed in the NPT ensemble reveal a negligible role of the reactive potential in the limit of low concentrated solutions, thus corroborating for the first time the validity of approximations based on the canonical NVT ensemble, customarily adopted for EVB simulations. The presented formalism also aims to contribute to future implementations and extensions of the EVB method to research the limit of highly concentrated solutions.

Motivated by recent experiments on magnetically frustrated heavy fermion metals, we theoretically study the phase diagram of the Kondo lattice model with a nonmagnetic valence bond solid ground state on a ladder. A similar physical setting may be naturally occurring in YbAl$_3$C$_3$, CeAgBi$_2$, and TmB$_4$ compounds. In the insulating limit, the application of a magnetic field drives a quantum phase transition to an easy-plane antiferromagnet, which is described by a Bose-Einstein condensation of magnons. Using a combination of field theoretical techniques and density matrix renormalization group calculations we demonstrate that in one dimension this transition is stable in the presence of a metallic Fermi sea and its universality class in the local magnetic response is unaffected by the itinerant gapless fermions. Moreover, we find that fluctuations about the valence bond solid ground state can mediate an attractive interaction that drives unconventional superconducting correlations. We discuss the extensions of our findings to higher dimensions and argue that, depending on the filling of conduction electrons, the magnon Bose-Einstein condensation transition can remain stable in a metal also in dimensions two and three., 6 pages + Supplementary

Although it is well accepted that the spin-$1/2$ triangular lattice Heisenberg antiferromagnet (TLHAF) has a long-range ordered ground state, a thorough understanding of its spin dynamics is still missing. While the linear spin wave theory (LSWT) predicts three branches of magnon mode in the magnetic Brillouin zone (MBZ), the $1/S$ expansion at the next order is found to break down in a large portion of the MBZ centered around the $M$ point, leaving the fate of the magnon modes there undecided. Recent neutron scattering measurement on ${\mathrm{Ba}}_{3}{\mathrm{CoSb}}_{2}{\mathrm{O}}_{9}$, an ideal realization of the spin-$1/2$ TLHAF, provides a surprising answer to this issue. Two, rather than three branches, of magnon mode are observed around the $M$ point, whose dispersion is strongly renormalized with respect to the LSWT prediction and exhibit pronounced rotonlike minimum at the $M$ point. This is accompanied by a strong spin fluctuation continuum at higher energy, inside which two strong and broad spectral peaks of unknown origin are observed. In this work, we propose a simple picture for these spectral anomalies by invoking the resonating valence bond (RVB) physics in the description of the ground state of the system. We find that the rotonlike minimum in the magnon dispersion can be explained by the coupling between the collective spin fluctuation and the continuum of Dirac spinon excitation moving in a $\ensuremath{\pi}$-flux background. We also propose that the two broad peaks in the continuum can be understood respectively as the Landau damped third magnon mode and the Landau damped longitudinal mode. Such a picture can be verified by studying the polarization character of the various spectral features.

In this work the nature of the three-center two-electron (3c2e) chemical bonds in the diborane (6) molecule and the octahydrotriborate anion (B3H8−) is investigated by the Generalized Product Function Energy Partitioning (GPF-EP) method using modern valence bond wave functions. The Interference Energy Analysis shows that 3c2e bonds have the same features of a 2c2e bond: interference dominates the energetic balance for the formation of the bond and the kinetic energy drop is responsible for its stabilization. Also, 3c2e are generally way more energetic than a 2c2e analogous one, because interference can occur in three different ways (multiple interference effect), rather than just in one as for the two-center bonds. Furthermore, with the GPF-EP method one could establish a more rigorous way for discussing the idea of a “supported” bond in the diborane (6) molecule.

We study the interplay between spin-orbit coupling (SOC) and Coulomb repulsion in a Hubbard model on a decorated honeycomb lattice which leads to a plethora of phases. While a quantum spin hall insulator is stable at weak Coulomb repulsion and moderate SOC, a semimetallic phase emerges at large SOC in a broad range of Coulomb repulsion. This semimetallic phase has topological properties not observed in conventional metals such as a finite, non-quantized spin Hall conductivity. At large Coulomb repulsion and negligible spin-orbit coupling, electronic correlations stabilize a resonance valence bond (RVB) spin liquid state in contrast to the classical antiferromagnetic state predicted by mean-field theory. Under sufficiently strong SOC, such RVB state is transformed into a magnetic insulator consisting on S~3/2 localized moments on a honeycomb lattice with antiferromagnetic order and topological features., 13 pages, 10 figures

We present numerical evidence for the emergence of an extended valence bond solid (VBS) phase at $T=0$ in the kagome $S=1/2$ Heisenberg antiferromagnet with ferromagnetic further-neighbor interactions. The VBS is located at the boundary between two magnetically ordered regions and extends close to the nearest-neighbor Heisenberg point. It exhibits a diamond-like singlet covering pattern with a $12$-site unit-cell. Our results suggest the possibility of a direct, possibly continuous, quantum phase transition from the neighboring $\mathbf{q}=0$ coplanar magnetically ordered phase into the VBS phase. Moreover, a second phase which breaks lattice symmetries, and is of likely spin-nematic type, is found close to the transition to the ferromagnetic phase. The results have been obtained using numerical Exact Diagonalization. We discuss implications of our results on the nature of nearest-neighbor Heisenberg antiferromagnet., 4 pages, 4 figures, supplementary material

Designing and characterizing the many-body behaviors of quantum materials represents a prominent challenge for understanding strongly correlated physics and quantum information processing. We constructed artificial quantum magnets on a surface by using spin-1/2 atoms in a scanning tunneling microscope (STM). These coupled spins feature strong quantum fluctuations due to antiferromagnetic exchange interactions between neighboring atoms. To characterize the resulting collective magnetic states and their energy levels, we performed electron spin resonance on individual atoms within each quantum magnet. This gives atomic-scale access to properties of the exotic quantum many-body states, such as a finite-size realization of a resonating valence bond state. The tunable atomic-scale magnetic field from the STM tip allows us to further characterize and engineer the quantum states. These results open a new avenue to designing and exploring quantum magnets at the atomic scale for applications in spintronics and quantum simulations., The resonating valence bond state is a spin-liquid state where spins continuously alter their singlet partners. Here Yang et al. use spin-1/2 atoms precision-placed by a scanning tunnelling microscope to create artificial quantum magnets exhibiting the resonating valence bond state.

The spin-$1/2$ ${J}_{1}$-${J}_{2}$ Heisenberg model on the square lattice represents one of the simplest examples in which the effects of magnetic interactions may suppress magnetic order, eventually leading to a pure quantum phase with no local order parameters. This model has been extensively studied in the last three decades, with conflicting results. Here, by using Gutzwiller-projected wave functions and recently developed methods to assess the low-energy spectrum, we show the existence of a level crossing between the lowest-energy triplet and singlet excitations for ${J}_{2}/{J}_{1}\ensuremath{\approx}0.54$. This fact supports the existence of a phase transition between a gapless spin liquid (which is stable for $0.48\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\lesssim}0.54$) and a valence-bond solid (for $0.54\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\lesssim}0.6$), even though no clear sign of dimer order is visible in the correlations functions. These results, which confirm recent density-matrix renormalization calculations on cylindrical clusters [L. Wang and A. W. Sandvik, Phys. Rev. Lett. 121, 107202 (2018)], reconcile the contradicting results obtained within different approaches over the years.

A novel valence-bond-based automatic diabatization method by compression, called valence-bond-based compression approach for dibatization (VBCAD), is presented in this Letter. It is a "black-box" type method that provides an automatic diabatization from a classical valence bond (VB) perspective. In VBCAD, a model space projection is performed by an eigenvalue decomposition algorithm followed by dimensional reduction based on a sequence of Householder transformations. Our diabaticity criterion is implemented in a way that maximizes the diversity of VB structure weights between different diabatic states. Owing to the rigorous Householder transformations employed in this entire procedure, the invariance of the target eigensubspace is preserved. This is illustrated on two prototypical examples.

We study the short-imaginary-time quantum critical dynamics (SITQCD) in the J-Q$_3$ spin chain, which hosts a quasi-long-range-order phase to a valence bond solid transition. By using the scaling form of the SITQCD with a saturated ordered phase, we are able to locate the critical point at $q_{\rm c}=0.170(14)$. We also obtain the critical initial slip exponent $\theta=-0.507(3)$ and the static exponent $\beta/\nu=0.498(2)$. More strikingly, we find that the scaling dimension of the initial order parameter $x_{0}$ is close to zero, which suggests that the initial order parameter is a marginal operator. As a result, there is no initial increase behavior of the order parameter in the short-imaginary-time relaxation process for this model, which is very different from the relaxation dynamics in the Ising-type phase transitions. Our numerical results are realized by the projector quantum Monte Carlo algorithm., Comment: 8 pages, 8 figures

Improving the fundamental understanding of the basic structures of ligand-protected gold nanoclusters is essential to their bottom-up synthesis as well as their further application explorations. The thiolate ligands that cover the central metal core in staple motifs are vital for the stability of the gold clusters. However, the knowledge about the geometrical and bonding characters of the thiolate ligands has not been fully uncovered yet. In this work, density functional theory calculations and molecular orbital analysis are applied to show that the Au atoms in the thiolate ligands are hypervalent. The chemical insights of the linear SAuS configuration as well as the lengthened AuS bond by combining the 3-center 4-electron (3c-4e) model and the well-recognized valence shell electron pair repulsion theory are revealed. Valence bond formulations of the motifs are given to provide more chemical insights, for example, the resonant structures, to show how the thiolate motif forms one covalent bond and one dative covalent bond with the Au core. This work provides a thorough understanding of the structure and bonding pattern of thiolate ligands of Au nanoclusters, which is important for the rational design of ligands-protected Au nanoclusters.

A variational theory called free-complement (FC) ${s}_{ij}$ theory for solving the Schr\"odinger equation of atoms and molecules using only one- and two-electron integrals over Slater or Gaussian functions is proposed. It is derived from the scaled Schr\"odinger equation [Phys Rev. Lett. 93, 030403 (2004)] by replacing the two-electron part ${r}_{ij}$ of the scaling $g$ operator with ${s}_{ij}={r}_{ij}^{2}$, both of which solve the divergence difficulty inherent to the original Schr\"odinger equation by avoiding the interelectron collisions. The ${s}_{ij}$ function can be rewritten with only one-electron functions so that when the initial wave function of the FC theory is composed of only one-electron functions, the FC wave function including ${s}_{ij}$ can be rewritten with only one-electron functions. Therefore, the variational calculations of the FC ${s}_{ij}$ theory can be performed with only one- and two-electron integrals. However, in comparison with the ${r}_{ij}$ function, the ${s}_{ij}$ function behaves less efficiently when two electrons come close to each other: the electron-electron cusp condition is not satisfied with the FC ${s}_{ij}$ theory, though the wave function has explicit ${r}_{ij}$ dependence. On the other hand, the electron-nuclear cusp condition is satisfied, even with the Gaussian functions, for the presence of the electron-nuclear function ${r}_{iA}$ in the $g$ operator. Test applications of the FC ${s}_{ij}$ theory were done to He, Li, and the $^{5}S^{\mathrm{o}} {\mathit{sp}}^{3}$ state of carbon atom and to hydrogen molecule using the local-molecular orbital (MO)- and valence bond (VB)-type initial functions. We examined both Slater and Gaussian functions. As the order of the FC theory increased, the wave functions were improved and the energies approached from a few kcal/mol to less than 1 kcal/mol accuracies relative to the known exact values. Thus, with the FC ${s}_{ij}$ theory, the Schr\"odinger equation was solved to less than 1 kcal/mol accuracy for all the systems examined. The costs for the ${s}_{ij}$ calculations were much smaller than those of the ${r}_{ij}$ theory. However, for the $^{5}S^{\mathrm{o}} {\mathit{sp}}^{3}$ state of the carbon atom, we observed that the convergence rate became slow when the calculation came close to $\ensuremath{\sim}1$ kcal/mol accuracy. This suggests that for the FC ${s}_{ij}$ theory, the calculations would become easier if the required accuracy is within a few kcal/mol for the absolute energy. Actually, what we need in chemical studies are mostly related to the difference energy, whose accuracy could be better than that of the absolute energy with the robust variational method. Two lines of future studies were suggested.

We identify quantum many-body scars in the transverse field quantum Ising model on a ladder. We make explicit how the corresponding (mid spectrum, low entanglement) many-body eigenstates can be approximated by injecting quasiparticle excitations into an exact, zero-energy eigenstate, which is of valence bond solid type. Next, we present a systematic construction of product states characterized, in the limit of a weak transverse field, by a sharply peaked local density of states. We describe how the construction of these 'peak states' generalizes to arbitrary dimension and we show that on the ladder their number scales with system size as the square of the golden ratio.

The $S=1/2$ square-lattice $J$-$Q$ model hosts a deconfined quantum phase transition between antiferromagnetic and dimerized (valence-bond solid) ground states. We here study two deformations of this model -- a term projecting staggered singlets as well as a modulation of the $J$ terms forming alternating "staircases" of strong and weak couplings. The first deformation preserves all lattice symmetries. Using quantum Monte Carlo simulations, we show that it nevertheless introduces a second relevant field, likely by producing topological defects. The second deformation induces helical valence-bond order. Thus, we identify the deconfined quantum critical point as a multicritical Lifshitz point -- the end point of the helical phase and also the end point of a line of first-order transitions. The helical-antiferromagnetic transitions form a line of generic deconfined quantum-critical points. These findings extend the scope of deconfined quantum criticality and resolve a previously inconsistent critical-exponent bound from the conformal-bootstrap method., Comment: v2: Minor changes and some improved numerical data

Molecular dynamics simulations and free energy sampling are employed in this work to investigate the surface affinity of the hydrated excess proton with two definitions of the interface: The Gibbs dividing interface (GDI) and the Willard-Chandler interface (WCI). Both the multistate empirical valence bond (MS-EVB) reactive molecular dynamics method and the density functional theory-based ab initio molecular dynamics (AIMD) were used to describe the hydrated excess proton species, including "vehicular" (standard diffusion) transport and (Grotthuss) proton hopping transport and associated structures of the hydrated excess proton net positive charge defect. The excess proton is found to exhibit a similar trend and quantitative free energy behavior in terms of its surface affinity as a function of the GDI or WCI. Importantly, the definitions of the two interfaces in terms of the excess proton charge defect are highly correlated and far from independent of one another, thus undermining the argument that one interface is superior to the other when describing the proton interface affinity. Moreover, the hydrated excess proton and its solvation shell significantly influence the location and local curvature of the WCI, making it difficult to disentangle the interfacial thermodynamics of the excess proton from the influence of that species on the instantaneous surface curvature.

A novel compound Cu3(CH3COO)4(OH)2·5H2O was obtained by a hydrothermal method with a special synthesis process. The crystal structure is found to exhibit a unique one-dimensional diamond chain along the c-axis. Magnetic measurements confirmed that this compound exhibits unusual magnetic behaviors of a possible valence-bond condensation state at low temperature, where the two-thirds of all spins are condensed into spin singlets and one-third of the spins still remain in the paramagnetic state.

The shared electron-pair bonding model was suggested by Gilbert Lewis more than 100 years ago. Emerging from the chemical experience of the time, Lewis structures described contemporary aspects of chemical reality in terms of empirically adapted models without any (then unknown) quantum physical underpinnings. This Perspective details the origins and historical development of the Lewis model, which we contrast with the physical understanding of chemical bonding in terms of contemporary quantum chemistry. Some intuitively plausible classical explanations of the past, not least of which are the sharing of electrons by two atoms and the subtypes of shared electron-pair bonding and dative bonding, turned out to be well founded. Some other chemical dogmata, including the concept that bonding occurs only between two nuclei and is caused by spin coupling or that bond energy is of purely electrostatic origin, are less well founded. We now know that covalent bonding is not driven by the formation of an electron pair but rather by the lowering of the kinetic energy density of the shared electrons in the bonding region, which is provided by the interference of the atomic wavefunctions. Lewis structures remain highly useful models for describing chemical bonding in molecular structures and chemical reactions, particularly when supported by quantum chemistry. The concepts behind the three most common quantum chemical approximations — the valence bond, molecular orbital and density functional theories — are described. These methods allow us to learn that bonding is an energetic phenomenon, from which descriptors such as bond length, bond dissociation energies and force constants are derivable. The energetic origins of bonding point to bond energy decomposition analysis as a natural tool for elucidating the actions of bonding electrons. Lewis’ shared electron-pair model was a stroke of genius, describing the structure and reactivity of molecules purely on the basis of his tremendous knowledge of empirical chemistry without any quantum chemistry. Unprecedented in simplicity, its success unfortunately concealed some misleading interpretations of the physical origin of chemical bonding.

Planar and quasi-planar boron clusters with a disk-like shape are investigated in search of common bonding characteristics. Methods used involve molecular orbital calculations based on Density Functional Theory (DFT), and valence bond partitioning using Adaptive Natural Density Partitioning (AdNDP) analysis. For high-symmetry cases the proposed bonding schemes are confirmed using the group-theoretical induction method. The focus is on the electron occupation of delocalized in-plane 3-center and 4-center bonds. For disks consisting of concentric rings this inner electron count is found to be equal to a multiple of the vertex count of the inner polygon. For two concentric rings the multiplying factor is four, for three concentric rings it is eight. The appropriate bonding schemes are presented which explain these results. Some giant clusters with two hexagonal holes are also discussed. ispartof: PHYSICAL CHEMISTRY CHEMICAL PHYSICS vol:21 issue:2 pages:729-735 ispartof: location:England status: published

Using as input data high-level structure electronic calculations, a new full-dimensional analytical potential energy surface (PES), named PES-2018, was developed for the title reaction, which is a valence bond/molecular mechanics based surface that depends on a set of adjustable parameters. The title reaction is practically thermoneutral, −0.18 kcal mol−1, with a high barrier, 11.62 kcal mol−1, and it presents features that make it very interesting for kinetics and dynamics studies. The PES simulates the high-level ab initio calculations used in the fitting process, with differences of less than 0.5 kcal mol−1. The quality of the fitting and the analytical expression was tested by comparing the results from this PES to different ab initio data. In the light of these results we believe that the new PES-2018 surface presents great versatility and satisfactory behaviour for the description of the nine-body reactive system. Based on this PES, in a forthcoming paper (Part II) an exhaustive kinetics and dynamics study of the title reaction will be presented.

The role of boron–ligand cooperation in activating molecular hydrogen by a set of six frustrated Lewis pair (FLP) systems is explored using density functional theory. The results obtained from thermochemical calculations show that all the studied FLP systems are capable of activating molecular hydrogen as the activation free energies are not too high (17.6–25.6 kcal mol−1). Sulphur based FLP 6 is the most promising one as it results in the smallest activation barrier among the studied sets. For a given FLP, the introduction of an electron donating –NMe2 group at the para position of the pyridine ring somewhat lowers the barrier and enhances the B–X (X = O, N, S) interaction. The B–X bond present within the FLPs plays a crucial role in facilitating the H2 activation process where it gets changed from the B+–X− type of interaction in the FLP to the B ← X dative bond upon H2 activation as understood from the energy decomposition analysis in combination with the natural orbital for chemical valence theory (EDA-NOCV). This mode of operation is termed as boron–ligand cooperation in analogy with the metal–ligand cooperation in transition metal complexes. The EDA-NOCV results obtained at the TS also support an electron transfer model where simultaneous electron transfer takes place from the Lewis basic center (N) of the FLP to σ*(H2) and from σ(H2) to the Lewis acidic center (B) of the FLP, resulting in a weakened H–H bond. The change in the aromaticity of the pyridine rings during the course of H2 activation is also monitored by nucleus independent chemical shift calculations. Finally, the ability of the studied FLP systems to act as hydrogenation catalysts is elucidated by studying the hydrogenation of CO2 to yield formic acid.

Brass (Cu-Zn) is one of the typical Hume-Rothery alloys, which is extensively used in material science and industry. Earlier studies revealed that the structures of Cu-Zn alloys correlate with the average number of valence electrons or the electron-per-atom (e/a) ratio, but structural evolution rule still remains unclear. In this work, the Cu-Zn nanoalloy clusters (elementary cells of bulk brass) are studied to reveal the evolutional rule of their structures with sizes. Systematic unbiased global search is performed for structural prediction of CuxZny nanoalloys in a size range (x + y = 3–10) by using genetic algorithm with density functional theory. The global minimum and low-lying isomers of the series of nanoalloy clusters are obtained, and the structural phase diagrams are plotted depending on the relative energy. The results show that geometric structures of Cu-Zn nanoalloys are also determined by the total number of valence electrons (n*), just as in bulk brass. Cu-Zn nanoalloys with same n* have similar geometric motifs. When n* = 6, the clusters adopt planar motif, which have σ-aromaticity following the (4n+2) rule. When n* = 8, 18 and 20, the clusters keep spherical motifs, which satisfy the magic numbers of Jellium model and could be viewed as stable superatoms. In most of cases for n* = 10, 12 and 14, the clusters adopt prolate motifs, which have similar electronic structures to N2, O2, and F2 molecules, respectively, based on the super valence bond model. Moreover, in some cases for n* = 10 and 12, the clusters can be seen as an 8e-superatom combined with one (8e+2e) or two (8e+2e+2e) separate Zn atoms.

Gold clusters, which display a variety of unusual geometric structures due to their strong relativistic effects, have attracted much attention. Among them, Au26 has a high-symmetry tubular structure (D6d) with a large HOMO–LUMO energy gap, but its electronic stability still remains unclear. In this paper, the electronic nature of the Au26 cluster is investigated using the density functional theory method. Depending on the super valence bond model, the tubular Au26 cluster with 26 valence electrons could be viewed as a superatomic molecule composed of two open cages based on spherical aromaticity, and its molecule-like electronic shell closure is achieved via a super triple bond (σ, 2π) between the two cages. Based on this new cage–cage superatomic structural model, a series of similar tubular clusters are predicted from the Au26 skeleton. The two capped Au atoms are replaced by Cu, Ag and In atoms, respectively, to form tubular D6d Au24Cu2 and Au24Ag2 (26e) and Au24In2 (30e) clusters, where the super triple bonds also exist. Moreover, tubular D5d Au20In2 (26e) is obtained by replacing hexatomic Au6 rings in the bulk of Au24In2 with pentagonal Au5 rings. Chemical bonding analysis reveals that there is a super quintuple bond (σ, 2π, 2δ) between two open (Au10In) cages, in accordance with the 26e Li20Mg3 superatomic molecule composed of two icosahedral superatoms. Our study proposes the new cage–cage structural model of superatomic molecules based on spherical aromaticity, which extends the range of the super valence bonding pattern and gives inferences for further study of superatomic clusters.

Imidazole has gained attention as an alternative to anhydrous proton conductor in high-temperature proton exchange membrane fuel cells. A detailed investigation of proton propensity and the orientation of the imidazolium cation at the liquid-vacuum interface is important for understanding the interfacial properties of imidazole-based proton-conductive materials. Here, we perform all-atom molecular dynamics simulation on a slab model of the liquid imidazole-vacuum interface. Proton transportation process between the imidazolium cation and neutral imidazole molecules is described by the multistate empirical valence bond model of imidazole developed previously. The imidazolium cation shows a tendency to stay in the bulk region rather than at the outermost surface, and the NN vectors and norm vectors of both the imidazolium cation and imidazole molecules are more probable to be perpendicular to the surface normal vector at the interface than in the bulk. The orientation of the hydrogen bond cluster shows the same tendency as the NN vectors, which indicates that proton transportation along the direction of the surface normal vector is hindered. The instantaneous surface analyses show that the fluctuation is depressed when the imidazolium cation is near the outermost surface, which makes it less favorable for the cation appearing at the interface.

Carbon nanotubes (CNTs) have very high mechanical properties and that is why they are used for making super strong and light yarns, ropes, fillers for composites, solid lubricants, etc. Mechanical properties of CNT bundles have been addressed in a number of experimental and theoretical studies. Development of efficient computational methods for solving this problem is an important step in design of new CNT based materials. In the present study, an atomistic chain model is used to analyse mechanical response of CNT crystal under plane strain conditions. The model takes into account tension and bending of CNT wall and the van der Waals interactions. Discrete character of the model allows description of large curvature of CNT wall and CNT fracture at very high pressure. Equilibrium structures of CNT crystal under biaxial, strain controlled loading are obtained and the potential energy of the structure is decomposed into the energy of valence bonds, valence angles and van der Waals interactions. It is shown that the main contribution to the potential energy comes from the energy of valence angles related to bending of CNT walls. The reported simulation results are in a good agreement with the existing literature. The chain model offered here can be efficiently applied to the analysis of mechanical properties of single-walled or multi-walled CNT bundles under plane strain conditions or, under straightforward modifications, to similar structures made of other 2D nanomaterials.

In a recent comments [arXiv:1909.12788 (2019)], Zhao et al. argue that the definition of dimer orders used in our paper [Phys. Rev. B 98, 241109 (2018)] may not rule out valence bond solid (VBS) orders of $J_1$-$J_2$ model on the open boundary conditions (OBC). In this reply, we show that their argument does not apply to our case.

A detailed Valence Bond‐Spin Coupled analysis of a series of halogenated molecules is here reported, allowing to get a rigorous ab initio demonstration of the qualitative models previously proposed to explain the origin of halogen bonding. The concepts of σ‐hole and negative belt observed around the halogen atoms in the electrostatic potential maps are here interpreted by analysis of the relevant Spin Coupled orbitals., Shedding light on halogens: A detailed Valence Bond‐Spin Coupled analysis of a series of halogenated molecules is here reported, allowing to get a rigorous ab initio demonstration of the formation of the σ‐hole responsible for the formation of halogen bonding.

We study a system of interacting triplons (the elementary excitations of a valence-bond solid) described by an effective interacting boson model derived within the bond-operator formalism. In particular, we consider the square lattice spin-1/2 $J_1$-$J_2$ antiferromagnetic Heisenberg model, focus on the intermediate parameter region, where a quantum paramagnetic phase sets in, and consider the columnar valence-bond solid phase. Within the bond-operator theory, the Heisenberg model is mapped into an effective boson model in terms of triplet operators $t$. The effective boson model is studied at the harmonic approximation and the energy of the triplons and the expansion of the triplon operators $b$ in terms of the triplet operators $t$ are determined. Such an expansion allows us to performed a second mapping, and therefore, determine an effective interacting boson model in terms of the triplon operators $b$. We then consider systems with a fixed number of triplons and determined the ground-state energy and the spectrum of elementary excitations within a mean-field approximation. We show that many-triplon states are stable, the lowest-energy ones are constituted by a small number of triplons, and the excitation gaps are finite. For $J_2=0.48 J_1$ and $J_2=0.52 J_1$, we also calculate spin-spin and dimer-dimer correlation functions, dimer order parameters, and the bipartite von Neumann entanglement entropy within our mean-field formalism in order to determine the properties of the many-triplon state as a function of the triplon number. We find that the spin and the dimer correlations decay exponentially and that the entanglement entropy obeys an area law, regardless the triplon number. Moreover, only for $J_2=0.48 J_1$, the spin correlations indicate that the many-triplon states with large triplon number might display a more homogeneous singlet pattern than the columnar valence-bond solid., 21 pages, 11 figures, final version

We use quantum Monte Carlo simulations to study a quantum $S=1/2$ spin model with competing multi-spin interactions. We find a quantum phase transition between a columnar valence-bond solid (cVBS) and a N\'eel antiferromagnet (AFM), as in the scenario of deconfined quantum-critical points, as well as a transition between the AFM and a staggered valence-bond solid (sVBS). By continuously varying a parameter, the sVBS--AFM and AFM--cVBS boundaries merge into a direct sVBS--cVBS transition. Unlike previous models with putative deconfined AFM--cVBS transitions, e.g., the standard $J$-$Q$ model, in our extended $J$-$Q$ model with competing cVBS and sVBS inducing terms the transition can be tuned from continuous to first-order. We find the expected emergent U(1) symmetry of the microscopically $Z_4$ symmetric cVBS order parameter when the transition is continuous. In contrast, when the transition changes to first-order the clock-like $Z_4$ fluctuations are absent and there is no emergent higher symmetry. We argue that the confined spinons in the sVBS phase are fracton-like. We also present results for an SU(3) symmetric model with a similar phase diagram. The new family of models can serve as a useful tool for further investigating open questions related to deconfined quantum criticality and its associated emergent symmetries., Comment: 14 pages, 14 figures

We study an asymmetric $J_1$-$J_2$ zigzag ladder consisting of two different spin-$\frac{1}{2}$ antiferromagnetic (AFM; $J_2$, $\gamma J_2>0$) Heisenberg legs coupled by zigzag-shaped ferromagnetic (FM; $J_1

High-harmonic generation (HHG) spectrum from a LiH molecule induced by an intense laser pulse is computed and analyzed with potential energy surfaces for electron motion (ePES) constructed from a model of localized electron wave packets (EWP) with valence-bond spin-coupling. The molecule has two valence ePES with binding energies of 0.39 hartree and 1.1 hartree. The HHG spectrum from an electron dynamics on the weaker bound valence ePES, virtually assigned to Li 2s, exhibits a dominant peak at the first harmonic without plateau and cut-off. This compares with the free electron spectrum under oscillating laser field and is comprehensive with the shape and depth of the ePES. The other valence ePES, assingned to H 1s, is deeper bound such that the overall profile of the wave function is well approximated by a Gaussian of the width comparable to the Li-H bond length. However, a small fraction, less than $10^{-3}$, of the probability density amplitude tunnels out from the bound potential with high wave number, and spreads over tens of nm's with parts recombining to the molecule due to the laser field oscillation. This minor portion of the electronic wave function is the major origin of the HHG extending up to 50 harmonic orders. Nonlinear dynamics within the potential well induced by the laser field oscillation also contributes to the HHG up to 30 harmonic orders., Comment: 6 pages, 9 figures

Molecular dynamics (MD) simulations based on the multistate empirical valence bond model have been performed to study the proton transfer (PT) process in aqueous solution. This study focuses on the details of the hydrogen bond (HB) dynamics in the solvation shells of an excess proton accompanied by PT events. The HB dynamics analyses show that the three water molecules in the first solvation shell of hydronium (H

The torsional dependence of the ground state magnetic exchange coupling (J) and the corresponding electronic coupling matrix element (HDA) for eight transition metal complexes possessing donor-acceptor (D-A) biradical ligands is presented. These biradical ligands are composed of an S = 1/2 metal semiquinone (SQ) donor and an S = 1/2 nitronylnitroxide (NN) acceptor, which are coupled to each other via para-phenylene, methyl-substituted para-phenylenes, or a bicyclo[2.2.2]octane ring. The observed trends in electronic absorption and resonance Raman spectral features are in accord with a reduction in electronic and magnetic coupling between D and A units within the framework of our valence bond configuration interaction model. Moreover, our spectroscopic results highlight different orbital mechanisms that modulate coupling in these complexes, which is not manifest in the ferromagnetic JSQ-B-NN values. The work provides new detailed insight into the effects of torsional rotations which contribute to inhomogeneities in experimentally determined exchange couplings, electron transfer rates, and electron transport conductance measurements.

The performance of the valence bond self-consistent field (VBSCF) method was investigated in this paper by predicting the activation barriers and reaction energies in pericyclic and π bond shift reactions for hydrocarbons. The benchmarking set includes 3 electrocyclic reactions, 3 sigmatropic shifts, 3 cycloadditions, 2 cycloreversions, and 7 π bond shift reactions, where the first 11 reactions are taken from Houk's standard set (J. Phys. Chem. A 2003, 107, 11445). Computational results reveal that the VB(CI) method, which performs VBSCF calculations first with full covalent structures and then includes all mono- and di-ionic structures to compute the total energy without further orbital optimization, matches the accuracy of the complete active space SCF (CASSCF) method very well. The mean absolute error values (the deviations from the CASSCF data) are 0.01 kcal/mol for the reaction energy, and 0.26 and 0.32 kcal/mol for the activation energy with the 6-31G and 6-31G(d) basis sets, respectively. © 2018 Wiley Periodicals, Inc.

We investigate the phenomenon of high-temperature superconductivity within a strong coupling perspective. The occurence is traced to a quantum critical point that is in the phase diagram of the plaquette's t; t0-Hubbard model. We develop a bottom-up approach combining several methods, i.e. exact diagonalization of an isolated plaquette, the Lanczos-method for a plaquette within a bath and cluster dynamical Mean-Field theory with continuous time quantum Monte-Carlo solver to embedd the plaquette in a lattice environment. The quantum critical point is located where the N = 2; 3; 4-sectors of the plaquette cross. This point is also found to show optimal doping. The wave order turns out to be largest at the localized-itinerant transition of the electrons. Furthermore, we present an explenation for the pseudo-gap phenomenon, that is explained by a soft mode related to local singlets of the plaquette. The theory presented here is similar to the resonating valence bond theory, but stresses the importance of local singlets.

The VSEPR model has well-established limitations in its ability to represent accurate molecular and electronic geometries of simple molecules, which can create a significant need for students to relearn structure and bonding concepts in organic chemistry. We present an alternate method for describing molecular geometries and electronic structures to students that is far more consistent with experimental observations than VSEPR. Our alternate method of teaching structures extends VSEPR to account for conjugation to adjacent π-systems and the experimentally observed nature of lone pairs, which is supported by computational chemistry via WebMO’s HTML-export feature. If implemented, it allows students to reconcile hybridization, valence bond theory, molecular orbital theory, and resonance structures into a single coherent picture of electronic structure and bonding for organic molecules.

Aromaticity is one of the most fundamental and fascinating chemical topics, attracting both experimental and theoretical chemists owing to its many manifestations. Both σ- and π-aromaticity can be classified depending on the character of the cyclic electron delocalization. In general, σ-aromaticity stabilizes fully saturated rings with σ-electron delocalization whereas the traditional π-aromaticity describes the π-conjugation in fully unsaturated rings. Here, we demonstrate a strong correlation between nucleus-independent chemical shift (NICS) values and extra cyclic resonance energies (ECREs), which are used to evaluate the σ-aromaticity in an unsaturated three-membered ring (3MR) of cyclopropene, which were computed by molecular orbital (MO) theory and valence bond (VB) theory, respectively. Further study shows that the fully unsaturated ring in methylenecyclopropene and its metallic analogy is σ-aromatic. Our findings revolutionize the fundamental knowledge of the concept of σ-aromaticity, thus opening an avenue to design σ-aromaticity in other fully unsaturated systems, which are traditionally reserved as the domain of π-aromaticity.

Most recently, Wiberg and Rablen examined a few substituted methanes and identified the polar effect, which is associated with the atomic charge at the central carbon, as a possible factor for bond energy changes while the exact role of the hyperconjugation effect is unsettled. In this work, we revisited a series of substituted methanes CH4-nXn (n = 0–4, X= F, Cl, CN, OCH3) by explicitly computing the intramolecular electron delocalization energies using the simplest variant of ab initio valence bond (VB) theory, namely the block-localized wave function (BLW) method. This BLW method is designated to derive electron-localized states where intramolecular electron delocalization is “turned off”. Computations show that the deactivation of the intramolecular electron delocalization in these molecules only slightly increases the charge (i.e., reduces the atomic population) at the central carbon in all systems. This seems consistent with the polar effect therein as proposed by Wiberg and Rablen. But apart from t...

The tautomerism of protonated imidazoles concerns one aromatic (1H-Imi+) and one nonaromatic (4H-Imi+) tautomers. Both experiments and computations have shown that substituents to the imidazole ring can change the relative stability of tautomers. A detailed theoretical study of the inherent mechanism would benefit the rational design of experimental syntheses related to imidazoles. In this work, we used the block-localized wavefunction (BLW) method to explore the factors governing the tautomerism between 1H-Imi+ and 4H-Imi+. While π resonance always favors the aromatic tautomer 1H-Imi+, the aromaticity noticeably reduces with electron donating groups (EDGs) as substituents due to the increased π-π repulsion, leading to the stability of 4H-Imi+ over 1H-Imi+ with EDGs such as NH2 and OH. For electron withdrawing groups (EWGs), the reduced π-π repulsion promotes the aromatic stability and favors 1H-Imi+. DFT computations were also performed to study the tautomerism mechanisms. Results show that tautomerism can hardly occur in gaseous phase, but in aqueous solution, water molecules can build hydrogen bonding network with 1H-Imi+ and facilitate the hydrogen transfers.