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In this contribution, we studied the OC-C bond in carbon suboxide and related allene compounds using the valence bond method. The nature of this bond has been the subject of debate, whether it is a regular, electron sharing bond or a dative bond. We compared the nature of this bond in carbon suboxide with the gold-CO bond in Au(CO)(2)(+), which is a typical dative bond, and we studied its charge-shift bond character. We found that the C-CO bond in carbon suboxide is unique in the sense that it cannot be assigned as either a dative or electron sharing bond, but it is an admixture of electron sharing and dative components, together with a high contribution of ionic character. These findings provide a clear basis for distinguishing the commonly found dative bonds between ligands and transition metals and the present case of what may be described as coordinative bonding to carbon.

The electronic structure of benzene is a battleground for competing viewpoints of electronic structure, with valence bond theory localising electrons within superimposed resonance structures, and molecular orbital theory describing delocalised electrons. But, the interpretation of electronic structure in terms of orbitals ignores that the wavefunction is anti-symmetric upon interchange of like-spins. Furthermore, molecular orbitals do not provide an intuitive description of electron correlation. Here we show that the 126-dimensional electronic wavefunction of benzene can be partitioned into tiles related by permutation of like-spins. Employing correlated wavefunctions, these tiles are projected onto the three dimensions of each electron to reveal the superposition of Kekulé structures. But, opposing spins favour the occupancy of alternate Kekulé structures. This result succinctly describes the principal effect of electron correlation in benzene and underlines that electrons will not be spatially paired when it is energetically advantageous to avoid one another., The electronic structure of benzene has been a test bed for competing theories along the years. Here the authors show via quantum chemistry calculations that the wavefunction of benzene can be partitioned into tiles which show that the two electron spins exhibit staggered Kekulé structures.

Tuning of the electronic spectra of carbon dots by means of inserting heteroatoms into the π-conjugated polycyclic aromatic hydrocarbon (PAH) system is a popular tool to achieve a broad range of absorption and emission frequencies. Especially nitrogen atoms have been used successfully for that purpose. Despite the significant progress achieved with these procedures, the prediction of specific shifts in the UV-vis spectra and the understanding of the electronic transitions is still a challenging task. In this work, high-level quantum chemical methods based on multireference (MR) and single-reference (SR) methods have been used to predict the effect of different nitrogen doping patterns inserted into the prototypical PAH pyrene on its absorption spectrum. Furthermore, a simple classification scheme based on valence bond (VB) theory and the Clar sextet rule in combination with the harmonic oscillator measure of aromaticity (HOMA) index was applied to arrange the different doping structures into groups and rationalize their electronic properties. The results show a wide variety of mostly redshifts in the spectra as compared to the pristine pyrene case. The most interesting doping structures with the largest red shifts leading to absorption energies below one eV could be readily explained by the occurrence of diradical VB structures in combination with Clar sextets. Moreover, analysis of the electronic transitions computed with MR methods showed that several of the low-lying excited states possess double-excitation character, which cannot be realized by the popular SR methods and, thus, are simply absent in the calculated spectra.

Classification of bonds is essential for understanding and predicting the reactivity of chemical compounds. This classification mainly manifests in the bond order and the contribution of different Lewis resonance structures. Here, we outline a first principles approach to obtain these orders and contributions for arbitrary wave functions in a manner that is both, related to the quantum theory of atoms in molecules and consistent with valence bond theory insight: the Lewis structures arise naturally as attractors of the all-electron probability density |Ψ|2. Doing so, we introduce a valence bond weight definition that does not collapse in the basis set limit.

Graphene is a two-dimensional crystal in which sp2-hybridized carbon atoms have valence bonds with three neighbors. Theoretically, other two-dimensional carbon structures were predicted, in which each carbon atom has valence bonds with three neighbors. In this paper, the molecular dynamics method is used to analyze the mechanical properties and structural transformations of such materials under uniaxial and biaxial stretching. The dependences of the tensile membrane forces on the applied tensile strain are constructed, the limiting values of the membrane forces and strains are determined. The three structures studied differ in their density, and it could be expected that the strength of the structures should decrease with decreasing density. However, it turned out that such a correlation did not manifest itself in all cases: a less dense structure may turn out to be stronger due to the fact that all interatomic bonds in it turn out to be loaded more uniformly. The results can be useful in analyzing the potentialities of application of sp2-carbon membranes in various technologies.

Approximate CASΠDFT scheme of the E c calculation is considered, in which its non-dynamic E c nd and dynamic E c d components are calculated with the complete active space (CAS) configuration interaction (CI) for valence bonds in a small basis and density functional theory (DFT) in the same basis, respectively. The DFT contribution is corrected for the suppression of dynamic correlation (SDC) with non-dynamic correlation. The present CASΠDFT closely reproduces both complete basis set (CBS) E c limits and their trends in the series of the prototype multiple-bonded molecules C 2 , HCN, N 2 , and CO.

One dimensional $(1d)$ interacting systems with local Hamiltonians can be studied with various well-developed analytical methods. Recently novel $1d$ physics was found numerically in systems with either spatially nonlocal interactions, or at the $1d$ boundary of $2d$ quantum critical points, and the critical fluctuation in the bulk also yields effective nonlocal interactions at the boundary. This work studies the edge states at the $1d$ boundary of $2d$ strongly interacting symmetry protected topological (SPT) states, when the bulk is driven to a disorder-order phase transition. We will take the $2d$ Affleck-Kennedy-Lieb-Tasaki (AKLT) state as an example, which is a SPT state protected by the SO(3) spin symmetry and spatial translation. We found that the original $(1+1)d$ boundary conformal field theory of the AKLT state is unstable due to coupling to the boundary avatar of the bulk quantum critical fluctuations. When the bulk is fixed at the quantum critical point, within the accuracy of our expansion method, we find that by tuning one parameter at the boundary, there is a generic direct transition between the long range antiferromagnetic N\'{e}el order and the valence bond solid (VBS) order. This transition is very similar to the N\'{e}el-VBS transition recently found in numerical simulation of a spin-1/2 chain with nonlocal spatial interactions. Connections between our analytical studies and recent numerical results concerning the edge states of the $2d$ AKLT-like state at a bulk quantum phase transition will also be discussed., Comment: 7 pages, 3 figures

We use the half-filled zeroth Landau level in graphene as a regularization scheme to study the physics of the SO(5) nonlinear sigma model subject to a Wess-Zumino-Witten topological term in 2+1 dimensions. As shown by Ippoliti et al. [Phys. Rev. B 98, 235108 (2019)PRBMDO2469-995010.1103/PhysRevB.98.235108], this approach allows for negative sign free auxiliary field quantum Monte Carlo simulations. The model has a single free parameter U_{0} that monitors the stiffness. Within the parameter range accessible to negative sign free simulations, we observe an ordered phase in the large U_{0} or stiff limit. Remarkably, upon reducing U_{0} the magnetization drops substantially, and the correlation length exceeds our biggest system sizes, accommodating 100 flux quanta. The implications of our results for deconfined quantum phase transitions between valence bond solids and antiferromagnets are discussed.

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 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.

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 $S=1/2$ 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

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.

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

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

Reactive molecular dynamics simulations enable a detailed understanding of solvent effects on chemical reaction mechanisms and reaction rates. While classical molecular dynamics using reactive force fields allows significantly longer simulation time scales and larger system sizes compared with ab initio molecular dynamics, constructing reactive force fields is a difficult and complex task. In this work, we describe a general approach following the empirical valence bond framework for constructing ab initio reactive force fields for condensed phase simulations by combining physics-based methods with neural networks (PB/NNs). The physics-based terms ensure the correct asymptotic behavior of electrostatic, polarization, and dispersion interactions and are compatible with existing solvent force fields. NNs are utilized for a versatile description of short-range orbital interactions within the transition state region and accurate rendering of vibrational motion of the reacting complex. We demonstrate our methodology for a simple deprotonation reaction of the 1-ethyl-3-methylimidazolium cation with acetate to form 1-ethyl-3-methylimidazol-2-ylidene and acetic acid. Our PB/NN force field exhibits ∼1 kJ mol−1 mean absolute error accuracy within the transition state region for the gas-phase complex. To characterize the solvent modulation of the reaction profile, we compute potentials of mean force for the gas-phase reaction as well as the reaction within a four-ion cluster and benchmark against ab initio molecular dynamics simulations. We find that the surrounding ionic environment significantly destabilizes the formation of the carbene product, and we show that this effect is accurately captured by the reactive force field. By construction, the PB/NN potential may be directly employed for simulations of other solvents/chemical environments without additional parameterization.

I studied the non-equilibrium response of an initial N\'{e}el state under time evolution with the Kitaev honeycomb model. With isotropic interactions ($J_x = J_y = J_z$) the system quickly loses its antiferromagnetic order and crosses over into a steady state valence bond solid, which can be inferred from the long-range dimer correlations. There is no signature of a dynamical phase transition. Upon including anisotropy ($J_x = J_y \neq J_z$), an exponentially long prethermal regime appears with persistent magnetization oscillations whose period derives from an effective toric code., Comment: 17 pages, 7 figures. Resubmission to SciPost

A central idea in strongly correlated systems is that doping a Mott insulator leads to a superconductor by transforming the resonating valence bonds (RVBs) into spin-singlet Cooper pairs. Here, we argue that a spin-triplet RVB (tRVB) state, driven by spatially, or orbitally anisotropic ferromagnetic interactions can provide the parent state for triplet superconductivity. We apply this idea to the iron-based superconductors, arguing that strong on site Hund's interactions develop intra-atomic tRVBs between the ${t}_{2g}$ orbitals. On doping, the presence of two iron atoms per unit cell allows these interorbital triplets to coherently delocalize onto the Fermi surface, forming a fully gapped triplet superconductor. This mechanism gives rise to a unique staggered structure of on site pair correlations, detectable as an alternating $\ensuremath{\pi}$ phase shift in a scanning Josephson tunneling microscope.

We consider a family of SU(2)-symmetric Projected Entangled Paired States (PEPS) on the square lattice, defining colored-Resonating Valence Bond (RVB) states, to describe the quantum disordered phase of the $J_1-J_2$ frustrated Heisenberg model.For $J_2/J_1\sim 0.55$ we show the emergence of critical (algebraic) dimer-dimer correlations -- typical of Rokhsar-Kivelson (RK) points of quantum dimer models on bipartite lattices -- while, simultaneously, the spin-spin correlation length remains short. Our findings are consistent with a spin liquid or a weak Valence Bond Crystal in the neighborhood of an RK point., 19 pages, 8 figures, v2 minor modifications, 1 ref added

The H-abstraction reaction between fluorine atom and deuterated acetonitrile (CD3CN) is highly exothermic and the resulting deuterium fluoride (DF) molecule is formed with a significant amount of energy that requires several picoseconds to relax into the solvent environment. Previous empirical valence bond (EVB) modelling work (D. R. Glowacki, et al., J. Chem. Phys., 2015, 143, 044120) showed that reproducing the experimental relaxation timescale is quite sensitive to the potential energy surface (PES) used, and the physical effects responsible for cooling were not fully clear. Here, we study the rate of cooling on two new carefully designed PESs, and by comparison to behaviour on other PESs, this provides additional insight into these effects. The first PES is a MMFF (Merck Molecular Force Field) based covalent-ionic two-state EVB model constructed utilizing the valence-bond resonance structures of DF, which is shown to give a good description of the PES for interaction of hydrogen fluoride through hydrogen bonding with one acetonitrile molecule, but performs relatively poorly in predicting the vibrational relaxation rate in bulk solvent. The second new PES uses the polarizable AMOEBA force field formalism, and describes both the DF-acetonitrile dimer PES and the rate of vibrational cooling very well, with good computational efficiency. Comparison of those PESs shows that as well as a good description of the non-bonded interactions in the DF-acetonitrile dimer, successful prediction of cooling dynamics requires a good description of many-body effects involving the supramolecular complex formed by DF, the H-bonded CD3CN and nearby solvent molecules.

In the quest for materials with unconventional quantum phases, the organic triangular-lattice antiferromagnet κ-(ET)2Cu2(CN)3 has been extensively discussed as a quantum spin liquid (QSL) candidate. The description of its low temperature properties has become, however, a particularly challenging task. Recently, an intriguing quantum critical behaviour was suggested from low-temperature magnetic torque experiments. Here we highlight significant deviations of the experimental observations from a quantum critical scenario by performing a microscopic analysis of all anisotropic contributions, including Dzyaloshinskii–Moriya and multi-spin scalar chiral interactions. Instead, we show that disorder-induced spin defects provide a comprehensive explanation of the low-temperature properties. These spins are attributed to valence bond defects that emerge spontaneously as the QSL enters a valence-bond glass phase at low temperature. This theoretical treatment is applicable to a general class of frustrated magnetic systems and has important implications for the interpretation of magnetic torque, nuclear magnetic resonance, thermal transport and thermodynamic experiments., The low temperature magnetic properties of organic Mott insulator κ-(ET)2-Cu2(CN)3 a quantum spin liquid candidate is notoriously difficult to understand. Here, a model based on defect spins is introduced that allows to describe results of complementary experiments on the same theoretical footing.

Author(s): Liu, YY; Zheng, F; Jiang, X; Luo, JW; Li, SS; Wang, LW | Abstract: Accurate microscopic description of the charge-trapping process from semiconductor to defects in the dielectric-oxide layer is of paramount importance for understanding many microelectronic devices such as complementary metal-oxide-semiconductor (CMOS) transistors, as well as electrochemical reactions. Unfortunately, most current microscopic descriptions of such processes are based on empirical models with parameters fitted to experimental device performance results or simplified approximations like the Wentzel-Kramers-Brillouin (WKB) method. Some critical questions are still unanswered, including: What controls the charge-hopping rate, the coupling strength between the defect level to semiconductor level, or the energy difference? How does the hopping rate decay with defect-semiconductor distance? What is the fluctuation of the defect level, especially in amorphous dielectrics? Many of these questions can be answered by ab initio calculations. However, to date, there are few ab initio studies for this problem mainly due to technical challenges from atomic-structure construction to large-system calculations. Here, using the latest advances in calculation methods and codes, we study the carrier-trapping problem using density-functional theory (DFT) based on the Heyd-Scuseria-Ernzerhof (HSE) exchange correlation functional. The valence bond random-switching method is used to construct the crystalline-Si-amorphous-SiO2 (c-Si/a-SiO2) interfacial atomic structure, and the HSE yields a band offset that agrees well with experiments. The hopping rate is calculated with the Marcus theory, and the hopping-rate dependences on the gate potential and defect distances are revealed, as well as the range of fluctuation results from amorphous structural variation. We also analyze the result with the simple WKB model and find a major difference in the description of the coupling constant decay with the defect-semiconductor distance. Our results provide the ab initio simulation insights for this important carrier-trapping process for device operation.

The authors of the above entitled paper suggest that molecular orbital (MO) and valence bond (VB) theories may generate conflicting insights into bonding. Therefore, they derive a real-space (RS) quantum chemical topology (QCT) approach (QCT-RS), and use it to extract insight into the H2 and LiH bonds, and contrast this insight with the one generated by VB calculations. The authors’ conclusions strongly contradict the usual bonding paradigms that arise from classical VB theory. Our Comment critically examines these claims and shows that MO and VB theories do not differ in their interpretations of bonding when both are applied on equal footing. It is furthermore shown that the conclusions based on this QCT-RS approach originate from a redefinition of VB structures in a manner that departs from the commonly accepted ones. This disparity of definitions of VB structures creates confusion. Thus, (a) the claim that in QCT-RS all covalency emanates from the covalent-ionic resonance, is generally incorrect in classical VB theory; and (b) contrary to the description of LiH as fully ionic in the above entitled paper, classical VB theory shows that this bond is well described as a superposition of a major covalent structure (albeit polarized) and a less important ionic one. The s–p hybridization of Li in the covalent structure is the major contributor to the dipole moment of LiH.

DC-magnetization data measured down to 40 mK speak against conventional freezing and reinstate YbMgGaO$_4$ as a triangular spin-liquid candidate. Magnetic susceptibility measured parallel and perpendicular to the $c$-axis reaches constant values below 0.1 and 0.2 K, respectively, thus indicating the presence of gapless low-energy spin excitations. We elucidate their nature in the triple-axis inelastic neutron scattering experiment that pinpoints the low-energy ($E$ $\leq$ $J_0$ $\sim$ 0.2 meV) part of the excitation continuum present at low temperatures ($T$ $$ $J_0$ that is rooted in the breaking of nearest-neighbor valence bonds and persists to temperatures well above $J_0$/$k_B$, the low-energy one originates from the rearrangement of the valence bonds and thus from the propagation of unpaired spins. We further extend this picture to herbertsmithite, the spin-liquid candidate on the kagome lattice, and argue that such a hierarchy of magnetic excitations may be a universal feature of quantum spin liquids., Comment: accepted in Phys. Rev. Lett

An extended Hubbard model on a honeycomb lattice with two orbitals per site at charge neutrality is investigated with unbiased large-scale quantum Monte Carlo simulations. The Fermi velocity of the Dirac fermions is renormalized as the cluster charge interaction increases, until a mass term emerges and a quantum phase transition from Dirac semimetal to valence bond solid (VBS) insulator is established. The quantum critical point is discovered to belong to the 3D $N=4$ Gross-Neveu chiral $XY$ universality with the critical exponents obtained at high precision. Further enhancement of the interaction drives the system into two different VBS phases, the properties and transition between them are also revealed. Since the model is related to magic-angle twisted bilayer graphene, our results may have relevance towards the symmetry breaking order at the charge neutrality point of the material, and associate the wide range of universal strange metal behavior around it with quantum critical fluctuations.

To investigate the factors that may cause bond length alternation and π-bond localization in annelated benzenes, ab initio valence bond calculations were performed. The results reveal that the bond length alternation of annelated benzene is determined by the strain-induced hybridization change from the partially optimized geometries, in which the central benzene ring is constrained to a regular hexagon, to the equilibrium geometries rather than the previously recognized re-hybridization effect that the carbon atoms in the central ring are deviated from sp2 hybridization. Meanwhile, the π–π interaction also provides a sort of driving force, which facilitates bond length alternation, which in turn magnifies π-bond localization. A subsequent potential energy curve study shows that σ-strain and π–π interactions have different mechanisms for the effect.

Three (M06-2X/Def2-TZVP, B3PW91/Def2-TZVP and B3LYP/LANL2DZ+dp) levels of theory are used to study the effect of substituents on the potential energy surfaces of RB[triple bond, length as m-dash]SbR (R = F, OH, H, CH3, SiH3, SiMe(SitBu3)2, SiiPrDis2 and NHC). The theoretical results demonstrate that the triply bonded RB[triple bond, length as m-dash]SbR molecules favor a bent geometry: that is, ∠R-B-Sb ≈ 180° and ∠B-Sb-R ≈ 120°. Regardless of the type of substituents that are attached to the RB[triple bond, length as m-dash]SbR compounds, theoretical evidence strongly indicates that their B[triple bond, length as m-dash]Sb triple bonds have a donor-acceptor nature and are proven to be very weak. Two valence bond models clarify the bonding characters of the B[triple bond, length as m-dash]Sb triple bond. For RB[triple bond, length as m-dash]SbR molecules that feature small substituents, the triple bond is represented as . For RB[triple bond, length as m-dash]SbR molecules that feature large substituents, the triple bond is represented as . Most importantly, this theoretical study predicts that only bulkier substituents significantly stabilize the triply bonded RB[triple bond, length as m-dash]SbR molecules, from the kinetic viewpoint.

The dynamical process of electron attachment to a guanine–cytosine pair in the normal (h-GC) and deuterated (d-GC) forms has been studied theoretically by semiclassical ring-polymer molecular dynamics (RPMD) simulations using the empirical valence bond model. The initially formed dipole-bound anion is converted rapidly to the valence-bound anion within about 0.1 ps in both h-GC and d-GC. However, the subsequent proton transfer in h-GC occurs with a rate five times greater than the deuteron transfer in d-GC. The change of rates with isotopic substitution and temperature variation in the RPMD simulations are quantitatively and qualitatively different from those in the classical molecular dynamics (MD) simulations, demonstrating the importance of nuclear quantum effects on the dynamics of this system.

A theoretical model was proposed to investigate the mechanism of ferromagnetism in ZnO as well as to simulate the experimental result that the ferromagnetism can be enhanced by UV irradiation as UV photon energy is equivalent to the band gap. In the model, the spin moments arise from the trapped electrons in oxygen vacancy states and coexist with the itinerant electrons which reside in zinc vacancy states and fall into resonant valence bond states. Charge exchange between the conduction band of ZnO and both vacancy states makes electrons on both vacancy states delocalized and results in a decrease of the ferromagnetism as well.

The non-spherical lowest-lying Li n (n = 15–17) isomers were found with high symmetric compact structures, of which the stability was not rationalized in a previous report (J. Chem. Phys. 119 9444 (2003)). Based on the newly proposed super-valence bond model, the three prolate lithium clusters can be viewed as magnetic superatomic molecules, which are composed by sharing valence electron pairs and nuclei between two superatom units, namely, Li10 or Li11, and thus their stability can be given a good understanding. Molecular orbital and chemical bonding analysis clearly reveal that the Li n (n = 15–17) clusters with prolate shapes are magnetic superatomic molecules. Our work may aid in the developments of the cluster-assembled materials or superatom-bonds.

This Perspective presents a survey of several issues in ab initio valence bond (VB) theory with a primary focus on recent advances made by the Xiamen VB group, including a brief review of the earlier history of the ab initio VB methods, in-depth discussion of algorithms for nonorthogonal orbital optimization in the VB self-consistent field method and VB methods incorporating dynamic electron correlation, along with a concise overview of VB methods for complex systems and VB models for chemical bonding and reactivity, and an outlook of opportunities and challenges for the near future of the VB theory.

Layered materials composed of weakly bonded rigid layers are of interest in modern material science since they exhibit new mechanisms of deformation when compressed along the layers. High strain-rate dynamics of such materials remains mostly unexplored, while some of potential applications, such as ballistic protection or high frequency loading, dictate the need for such research. This work is devoted to molecular dynamics investigation of the in-plane shock waves propagating in hexagonal lattices of graphene and boron nitride. It is shown that in graphene the shock waves radiate energy and slow down faster than in boron nitride. Shock wave attenuation in both materials is faster for the waves moving along the armchair direction as compared to the zigzag direction. These results are explained considering energy dissipation mechanism based on the analysis of oscillations of valence angles and valence bond lengths initiated by the shock wave. Our study uncovers the mechanisms of energy transport and dissipation in layered materials subject to high-speed loading along the layers.

We report the failure of coupled-cluster valence-bond (CCVB) theory with two-pair configurations [D. W. Small and M. Head-Gordon, J. Chem. Phys. 130, 084103 (2009)] for open-shell (OS) spin-frustrated systems where including three-pair configurations is necessary to properly describe strong spin-correlations. We extend OS-CCVB by augmenting the model with three-pair configurations within the independent amplitude approximation. The resulting new electronic structure model, OS-CCVB+i3, involves only a quadratic number of independent wavefunction parameters. It includes the recently reported closed-shell CCVB+i3 as a special case. Its cost is dominated by integral transformations, and it is capable of breaking multiple bonds exactly for all systems examined so far. The strength of OS-CCVB+i3 is highlighted in realistic systems including the [CaMn3O4] cubane subunit of the oxygen-evolving complex and a molecular magnet with the [Cr9] core unit as well as model systems such as N3, V3O3, and P5. We show that OS-CCVB+i3 is only slightly dependent on the underlying perfect-pairing reference, while OS-CCVB shows a stronger dependence. We also emphasize the compactness of the OS-CCVB+i3 wavefunction compared to the heat-bath configuration interaction wavefunction, a recently introduced soft exponential-scaling approach.

A recent comment by Hiberty, Danovich and Shaik to our previous communication on interpreting valence bond (VB) concepts in real space raises concerns about the map between quantum chemical topology (QCT) concepts and those of other conceptual frameworks, such as VB theory. We clarify here why some of these discrepancies appear, particularly as resonance structures (RSs) are regarded. As originally shown in our communication, we do not redefine VB structures, but we compare them with their real space equivalent instead.

We present a thorough analysis of symmetry breaking observed in Hartree-Fock (HF) solutions of fullerenes C$_{60}$, C$_{36}$, and C$_{20}$ in order to characterize the nature of electron correlation in them. Our analysis is based on (1) the critical regularization strength to restore symmetry breaking in the recently developed regularized orbital optimized second-order M{\o}ller-Plesset perturbation theory ($\kappa$-OOMP2), (2) singlet-triplet gaps from various MP2 methods, and (3) natural orbital occupation numbers from restricted coupled-cluster with singles and doubles (RCCSD) and coupled-cluster valence bond with singles and doubles (CCVB-SD). Based on these three independent probes, we conclude that C$_{36}$ (D$_\text{6h}$) exhibits genuine strong correlation and symmetry breaking whereas C$_{60}$ exhibits {\it artificial} HF symmetry breaking and is not strongly correlated. Investigating the critical regularization strength, we discuss strong correlation in C$_{20}$ at the Jahn-Teller distorted geometries (C$_\text{2h}$, D$_\text{2h}$, C$_\text{i}$, and D$_\text{3h}$) and the I$_\text{h}$ geometry. Only C$_{20}$ (I$_\text{h}$) was found to be strongly correlated while others exhibit {\it artificial} HF symmetry breaking. This analysis highlights a useful feature of the recommended $\kappa$-OOMP2 method. It is an electronic structure method that describes dynamic correlation, and attenuates strong correlation in MP2 towards zero by regularization. Therefore, $\kappa$-OOMP2 will exhibit symmetry breaking in its reference determinant only when correlation is strong (i.e., essential symmetry breaking). Artificial symmetry breaking (arising in HF due to neglect of dynamic correlation) is thus removed in $\kappa$-OOMP2.

Recently measurements on various spin-1/2 quantum magnets such as H$_3$LiIr$_2$O$_6$, LiZn$_2$Mo$_3$O$_8$, ZnCu$_3$(OH)$_6$Cl$_2$ and 1T-TaS$_2$ -- all described by magnetic frustration and quenched disorder but with no other common relation -- nevertheless showed apparently universal scaling features at low temperature. In particular the heat capacity C[H,T] in temperature T and magnetic field H exhibits T/H data collapse reminiscent of scaling near a critical point. Here we propose a theory for this scaling collapse based on an emergent random-singlet regime extended to include spin-orbit coupling and antisymmetric Dzyaloshinskii-Moriya (DM) interactions. We derive the scaling $C[H,T]/T \sim H^{-\gamma} F_q[T/H]$ with $F_q[x] = x^{q}$ at small $x$, with $q \in$ (0,1,2) an integer exponent whose value depends on spatial symmetries. The agreement with experiments indicates that a fraction of spins form random valence bonds and that these are surrounded by a quantum paramagnetic phase. We also discuss distinct scaling for magnetization with a $q$-dependent subdominant term enforced by Maxwell's relations., Comment: v2. Expanded argument in Appendix 2 and revised for clarity. v3. Fixed typo in Fig 3 caption. Main text 4 pages 4 figures, Appendix 6 pages 1 figure

The activation of CO2 by chloride-tagged first-row transition metal anions [ClM]− (M = Sc–Zn), was examined by mass spectrometry, quantum chemical calculations, and statistical analysis. The direct formation of [ClM(CO2)]− complexes was demonstrated in the reaction between [ClM]− and neutral CO2. In addition, the reverse reaction was investigated by energy-variable collisionally induced dissociation (CID) of the corresponding [ClM(CO2)]− anions generated in-source. Five different mono- and bi-dentate binding motifs present in the ion/CO2 complexes were identified by quantum chemical calculations and the relative stability of each of these isomers was established and analyzed for all first-row transition metals based on the experimental and theoretical ion/molecule binding energies. It was found that the early first row transition metals form strong covalent bonds with the neutral CO2 molecule, while the late ones and in particular copper and zinc are weakly bonded. Using simple valence bond Lewis diagrams, the different binding motifs and their relative stabilities across the first row were described using multi-configurational self consistent field (MSCSCF) wavefunctions in a quantitative manner based on the electronic structure of the individual metals. This analysis provides an explanation for the change of the most favorite bonding motif of the transition metals with CO2 along the 1st transition metal row. The nature of the activated CO2 complex and the relationship between its stability and other structural and spectral properties was also analyzed by Principal Component Analysis (PCA) and artificial neural networks.

A valence bond (VB) block-diagonalization approach, named VBBDA, is proposed to construct the charge-localized diabatic state explicitly within the framework of ab initio VB theory. Since the VB structure built upon the localized orbitals represents the charge localized character of the diabatic state faithfully, we are able to obtain accurate electronic coupling between diabatic states by using a very compact VB wave function. Moreover, the potential energy curves of the diabatic states and hence the crossing points of them can be accurately evaluated. The pilot applications showed that the electronic couplings computed by the VB method are consistent with the complete active space self-consistent field method and may even be close to the results of other high-level ab initio methods such as full configuration interaction and multireference configuration interaction. In addition, the computed electronic couplings show the expected exponential attenuation for the donor-acceptor systems as the distance increases. Moreover, VBBDA has the capability for handling complicated systems based on either two-state or multi-state treatment. Finally, because of the outstanding performance of the Xiamen Valence Bond software package, which is an ab initio VB program, VBBDA is capable for systems consisting more than 1000 basis functions.

A valence bond theory based method has been developed to decompose hydrogen bond energies into contributions from geometry, electrostatics, polarization and charge transfer. This decomposition method has been carried out for F–H⋯FH, F–H⋯OH2, F–H⋯NH3, HO–H⋯OH2, HO–H⋯NH3, and H2N–H⋯NH3. Localized valence bond self-consistent field (L-VBSCF) and localized breathing orbital valence bond (L-BOVB) calculations were performed at the PBEPBE/aug-cc-pVDZ optimized geometries. It is shown that inclusion of valence bond structures that explicitly include charge transfer account for at least 32% (likely over half) of the hydrogen bond energy of all systems studied, indicating the dominant role of covalency. This is in agreement with calculated bond lengths, geometry deformation energies, and polarization energies. Electrostatic effects were found to play only a minor role in contrast to some widely held ideas regarding the nature of hydrogen bonding.

The effective atomic orbitals have been realized in the framework of Bader's atoms in molecules theory for a general wavefunction. This formalism can be used to retrieve from any type of calculation a proper set of orthonormalized numerical atomic orbitals, with occupation numbers that sum up to the respective Quantum Theory of Atoms in Molecules (QTAIM) atomic populations. Experience shows that only a limited number of effective atomic orbitals exhibit significant occupation numbers. These correspond to atomic hybrids that closely resemble the core and valence shells of the atom. The occupation numbers of the remaining effective orbitals are almost negligible, except for atoms with hypervalent character. In addition, the molecular orbitals of a calculation can be exactly expressed as a linear combination of this orthonormalized set of numerical atomic orbitals, and the Mulliken population analysis carried out on this basis set exactly reproduces the original QTAIM atomic populations of the atoms. Approximate expansion of the molecular orbitals over a much reduced set of orthogonal atomic basis functions can also be accomplished to a very good accuracy with a singular value decomposition procedure Financial help has been furnished by the Spanish MICINN Project No. CTQ2011-23441/BQU and Accion Complementaria del MCI (PCI2006-A7-0631). Financial support from MICINN and the FEDER fund (European Fund for Regional Development) was also provided by grant UNGI08-4E-003. Financial support from the Generalitat de Catalunya (SGR528 and Xarxa de Referncia en Qumica Terica i Computacional) is also acknowledged. E.R-C. acknowledges support from the Spanish FPU program (Grant No. AP2008-01231)

Real space bonding descriptors are orbital invariant indices that can be obtained independently of the theoretical framework used to compute a given wavefunction. Here we show how to use them to read in real space some widely used concepts in Valence Bond (VB) theory, such as ionic/covalent characters or covalent-ionic resonance energies. All of these are essential ingredients used when building VB chemical insight. Electron number distribution functions are employed to directly map ionic and covalent weights with real space delocalization indices. We show that covalency, understood as delocalization, emerges in position space from the fluctuation of electron populations. This is mapped in VB to covalent-ionic resonance. The reasons why this is not so in the standard language of non-orthogonal VB are examined. A simple real space ionic character index that maintains the essence of its VB equivalent is defined and examined in simple model systems. The conclusions of this work ease travelling among the sometimes conflicting molecular orbital, real space, and valence bond interpretations in chemical bonding theory.

Room temperature ionic liquids (ILs), especially protic ionic liquids (PILs), are used in many areas of the chemical sciences. Ionicity, the extent of proton transfer, is a key parameter which determines many physicochemical properties and in turn the suitability of PILs for various applications. The spectrum of computational chemistry techniques applied to investigate ionic liquids includes classical molecular dynamics, Monte Carlo simulations, ab initio molecular dynamics, Density Functional Theory (DFT), CCSD(t) etc. At the other end of the spectrum is another computational approach: modern ab initio Valence Bond Theory (VBT). VBT differs from molecular orbital theory based methods in the expression of the molecular wave function. The molecular wave function in the valence bond ansatz is expressed as a linear combination of valence bond structures. These structures include covalent and ionic structures explicitly. Modern ab initio valence bond theory calculations of representative primary and tertiary ammonium protic ionic liquids indicate that modern ab initio valence bond theory can be employed to assess the acidity and ionicity of protic ionic liquids a priori.

The I335Y point mutation effect on the kinetics of phenylethylamine decomposition catalyzed by monoamine oxidase A was elucidated by means of molecular simulation. The established empirical valence bond methodology was used in conjunction with the free energy perturbation sampling technique and a classical force field representing the state of reactants and products. The methodology allows for the simulation of chemical reactions, in the present case the breaking of the α-C-H bond in a phenylethylamine substrate and the subsequent hydrogen transfer to the flavin cofactor, resulting in the formation of the N-H bond on flavin. The empirical parameters were calibrated against the experimental data for the simulated reaction in a wild type protein and then used for the calculation of the reaction free energy profile in the I335Y mutant. In very good agreement with the measured kinetic data, mutation increases the free energy barrier for the rate limiting step by slightly more than 1 kcal mol(-1) and consequently decreases the rate constant by about an order of magnitude. The magnitude of the computed effect slightly varies with simulation settings, but always remains in reasonable agreement with the experiment. Analysis of trajectories reveals a major change in the interaction between phenyl rings of the substrate and the neighboring Phe352 residue upon the I335Y mutation due to the increased local polarity, leading to an attenuated quadrupole interaction between the rings and destabilization of the transition state. Additionally, the increased local polarity in the mutant allows for a larger number of water molecules to be present near the active site, effectively shielding the catalytic effect of the enzyme and contributing to the increased barrier.

Linear response density matrix functional theory has been shown to solve the main problems of time-dependent density functional theory (deficient in case of double, charge transfer and bond breaking excitations). However, the natural orbitals preclude the description of excitations as (approximately) simple orbital-to-orbital transitions: many weakly occupied ‘virtual’ natural orbitals are required to describe the excitations. Kohn–Sham orbitals on the other hand afford for many excitations such a simple orbital description. In this communication we show that a transformation of the set of weakly occupied NOs can be defined such that the resulting natural excitation orbitals (NEOs) restore the single orbital transition structure for excitations generated by the linear response DMFT formalism.

In common with other iron-based high temperature superconductors, FeSe exhibits a transition to a ``nematic'' phase below 90Kelvin in which the crystal rotation symmetry is spontaneously broken. However, the absence of strong low-frequency magnetic fluctuations near or above the transition has been interpreted as implying the primacy of orbital ordering. In contrast, we establish that quantum fluctuations of spin-1 local moments with strongly frustrated exchange interactions can lead to a nematic quantum paramagnetic phase consistent with the observations in FeSe. We show that this phase is a fundamental expression of the existence of a Berry's phase associated with the topological defects of a N\'eel antiferromagnet, in a manner analogous to that which gives rise to valence bond crystal order for spin 1/2 systems. We present an exactly solvable model realizing the nematic quantum paramagnetic phase, discuss its relation with the spin-1 $J_1-J_2$ model, and construct a field theory of the Landau-forbidden transition between the N\'eel state and this nematic quantum paramagnet., Comment: updated preprint, 25 pages, 14 figures

A series of density functional theory and G4 calculations are performed to quantify the extent to which proton-coupled electron transfer (PCET) lowers the barrier for H-abstraction in the reaction between 1,1-dimethylhydrazine (UDMH) and the compound I intermediate of a cytochrome P450 enzyme. The homolytic bond dissociation energy of UDMH is larger than that of 1,4-cyclohexadiene; nevertheless, the H-abstraction barrier is significantly lower for the former substrate. The barrier lowering in the UDMH reaction caused by PCET is roughly estimated to be 9 kcal/mol. Valence bond structures are analyzed in detail to figure out how PCET lowers the barrier height.