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The feasibilities and electronic structures of five ten- π -electron fused conjugated molecules involving cyclopropenyl rings are explored using second-order Moller-Plesset perturbation theory (MP2), spin-coupled (SC) and complete-active-space self-consistent-field (CASSCF) wavefunctions, in the cc-pVTZ basis. All five fused conjugated molecules are predicted to have rigid planar ground state geometries of C 2 v or D 2 h symmetry and large dipole moments (if not of D 2 h symmetry). The compact ground state SC(10) wavefunctions with ten active orbitals for these molecules are found to be of comparable quality to the respective CASSCF(10,10) constructions, but much easier to interpret. The analyses of the ground state SC(10) wavefunctions for all five fused conjugated molecules reveal resonance patterns which indicate that all of these molecules are aromatic in their electronic ground states; on the other hand, the SC(10) approximations to the first singlet electronic excited states are found to exhibit “antiresonance” which suggests that each of the five molecules switches from aromatic to antiaromatic upon vertical excitation from the ground state to its first singlet excited state. Ring strain prevents the formation of a fused structure involving three cyclopropenyl rings and a cycloheptatrienyl ring; the alternative stable dehydro compound which resembles m -benzyne is shown, using a SC(12) wavefunction, to involve a weak σ bond between the dehydro centres.

The nature of the chemical bond in the pentagonal-pyramidal benzene dication and related species was described by Modern Valence Bond calculations and the Generalized Product Function Energy Partitioning method. The results suggest that the π space of C 6 H 6 2+ is composed of a donor-acceptor bond from a cyclopentadienyl anion moiety, described as a 5c–6e π bonding, to a triply charged Lewis acid CH structure. Similar results were found for isoelectronic species, such as C 5 H 5 BH + , C 5 H 5 BeH, and C 5 H 5 LiH − , leading to different main-group hexa-coordinate atom-bearing structures. A pictorial mechanism for the bonding of the studied molecules was constructed, and different geometrical and electronic features could be explained by this straightforward model. Finally, the results suggest that several poly-coordinate atom-containing molecules, sandwich-type compounds, oligomers, and polymers could be formed by the interaction of a π system and Lewis acid moieties.

When orthogonal orbitals are used to construct configuration state functions (CSF) the latter are orthogonal to each other. Such CSFs are either neutral or ionic, they never change their character along a reaction path. This is in contrast to conventional Valence Bond CSFs based on non-orthogonal orbitals. When orthogonal, delocalized molecular orbitals from CASSCF (complete active space SCF) calculations are localized to defined fragments using orthogonal transformations, the localized fragment orbitals retain their orthogonality, and the CASSCF configuration state functions constructed are of Valence Bond type describing the same state but in terms of orthogonal fragment orbitals. This analysis of the CASSCF state function reveals local properties and processes that are hidden by the use of delocalized orbitals but that are responsible for symmetry forbiddenness or symmetry allowedness of chemical reactions.

Proton-coupled electron transfer (PCET) broadly exists in chemical and biological processes and can be intuitively described in terms of diabatic (resonance) states. The conventional molecular orbital (MO) based methods, however, have the difficulty in rationally defining diabatic states which are strictly electron-localized. Here we used the block-localized wavefunction (BLW) method, which is the simplest variant of valence bond (VB) theory, to define four major diabatic states and compare the concerted and the sequential transfers of electron and proton between formamide and its radical form. Our preliminary computations with partial breathing orbitals (BOs) show that the BLW method can locate the intermediate state in the stepwise mechanism, though the barriers are overestimated with references to high-level MO results, indicating the importance of dynamical electron correlation at transition states and the need for full BOs. But all computations at all levels concur that the concerted mechanism is preferred over the stepwise mechanism in the system studied in this work.

For {FeNO}7 nitrosyl heme and non-heme complexes, with 17 valence shell electrons, FeIINO, FeIINO* and FeIIINO- valence bond structures of the increased-valence type are generated primarily from Lewis valence bond structures by delocalizing non-bonding electrons into diatomic bonding molecular orbitals. Valence bond formulations for the reactions 2MbNO + 2H+ → 2metMb + N2O + H2O and cis MbNO + NO- + 2H+ → metMb + N2O + H2O are also presented.

A general approach to hybridization, without imposing orthogonality of the hybrids of the central atom, is formulated. It is shown that the overlapping hybrids follow the rules of electronegativity of the central atom, and they increase with the increase of electronegativity (e.g. NH 4 + > CH 4 > BH 4 − ). For a given electronegativity, the hybrid-hybrid overlap decreases as the number of equivalent bonds increases (e.g., CH 4 3 + , CH 2 2+ ). Having the hybrid-hybrid overlap enables us to deduce the promotion energy invested by the various atoms to form the molecule; the larger the overlap the smaller the degree of hybridization, and the lesser is the promotion energy needed from the central atom to achieve maximum bonding. The approach is applied to the dicarbon molecule, C 2 . It is shown that after taking into account the promotion energy (∼46 kcal mol −1 per C), C 2 exhibits a quadruple bond.

International audience; The multi-configurational ansatz of valence-bond theory may serve as basis for calculating in-termolecular interaction energies in a non-orthogonal basis. We look in the present contribution at the possibility to obtain the 1st-order electrostatic interactions from breathing-orbital valence-bond densities, and the 2nd-order dispersion energy from dipole-dipole interactions. The discussion is based on numerical results for the interaction of two N 2 O molecules.

Ab initio classical valence bond theory in terms of localized orbitals has several advantages over electronic structure methods based on canonical delocalized Hartree-Fock molecular orbitals, with two key distinctions being greater applicability to inherently multiconfigurational systems (also called multireference systems or strongly correlated systems) and great interpretability in terms of covalent and ionic valence bond configurations (also called valence bond structures). This can be especially advantageous for applications to chemical reactions. However, until now only limited work tested the quantitative accuracy for the energetics of chemical reactions. The present study provides such tests and validations for a representative test set of six barrier heights corresponding to forward and reverse barriers of three hydrogen transfer reactions. In particular, we test the valence bond self-consistent-field theory (VBSCF) and three post-VBSCF methods that use VBSCF as a reference function for adding dynamic correlation, in particular valence bond configuration interaction (VBCI), breathing orbital valence bond (BOVB), and valence bond second-order perturbation theory (VBPT2). The VBSCF method itself is, as expected, not quantitatively accurate, with a mean unsigned error (MUE) for the six barrier heights of ∼17 kcal/mol. But the post-VBSCF methods are found to be quite successful. Depending on the basis set, and valence bond structure selection we obtain MUEs (in kcal/mol) as low as 3.7 for VBCI, 4.5 for BOVB, and (using a bigger basis-set) 1.3 for VBPT2. These compare well, on the same data set, with 1.6 for coupled clusters with singles and doubles (CCSD) and 1.5 for multireference second order perturbation theory based on a complete active space self-consistent field reference function (MRPT2). We discuss the results in terms of the pros and cons of each of these methods.

We introduce the atomic valence active space (AVAS), a simple and well-defined automated technique for constructing active orbital spaces for use in multi-configuration and multireference (MR) electronic structure calculations. Concretely, the technique constructs active molecular orbitals capable of describing all relevant electronic configurations emerging from a targeted set of atomic valence orbitals (e.g., the metal d orbitals in a coordination complex). This is achieved via a linear transformation of the occupied and unoccupied orbital spaces from an easily obtainable single-reference wavefunction (such as from a Hartree-Fock or Kohn-Sham calculations) based on projectors to targeted atomic valence orbitals. We discuss the premises, theory, and implementation of the idea, and several of its variations are tested. To investigate the performance and accuracy, we calculate the excitation energies for various transition metal complexes in typical application scenarios. Additionally, we follow the homolytic bond breaking process of a Fenton reaction along its reaction coordinate. While the described AVAS technique is not an universal solution to the active space problem, its premises are fulfilled in many application scenarios of transition metal chemistry and bond dissociation processes. In these cases the technique makes MR calculations easier to execute, easier to reproduce by any user, and simplifies the determination of the appropriate size of the active space required for accurate results., Comment: 51 pages

An inverse phase transfer catalyst typically enhances the rate of biphasic reaction by bringing the water-insoluble reactant from the organic to the aqueous phase. We use the empirical valence bond (EVB) approach to obtain reaction free energy profiles for a model SN2 reaction inside the β-cyclodextrin (β-CD) cavity at the water/1-bromooctane interface and in bulk water to show that a significant rate enhancement is taking place at the liquid/liquid interface rather than in the bulk. By examining several solvent–solute structural and energetic properties, we demonstrate that the rate enhancement when the reaction takes place inside the cavity at the interface is primarily due to limited accessibility of interfacial water molecules, which results in destabilization of the reactants. Greater accessibility of water molecules when the catalyst is in the bulk stabilizes the reactants and does not lead to rate enhancement despite the significant hydrophobicity of the cavity’s interior.

The nature of the chemical bond is perhaps the central subject in theoretical chemistry. Our understanding of the behavior of molecules developed amazingly in the last century, mostly with the rise of quantum mechanics (QM) and QM-based theories such as valence bond theory and molecular orbital theory. Such theories are very successful in describing molecular properties, but they are not able to explain the origin of the chemical bond. This problem was first analyzed in the 1960s by Ruedenberg, who showed that covalent bonds are the direct result of quantum interference between one-electron states. The generality of this result and its quantification were made possible through the recent development of the generalized product function energy partitioning (GPF-EP) method by our group, which allows the partitioning of the electronic density and energy into their interference and quasi-classical (noninterference) contributions. Furthermore, with GPF wave functions these effects can be analyzed separately for each bond of a molecule. This interference energy analysis has been applied to a large variety of molecules, including diatomics and polyatomics, molecules with single, double, and triple bonds, molecules with different degrees of polarity, linear or branched molecules, cyclic or acyclic molecules, conjugated molecules, and aromatics, in order to verify the role played by quantum interference. In all cases the conclusion is exactly the same: for each bond in each of the molecules considered, the main contribution to its stability comes from the interference term. Two-center one-electron (2c1e) bonds are the simplest kind of chemical bonds. Yet they are often viewed as odd or unconventional cases of bonding. Are they any different from conventional (2c2e) bonds? If so, what differences can we expect in the nature of (2c1e) bonds relative to electron-pair bonds? In this Account, we extend the GPF-EP method to describe bonds involving N electrons in M orbitals (NM) and show its application to (2c1e) bonds. As examples we chose the molecules H

The crystal structures, electro–optical properties, and charge carrier effective masses of Cs 2 TeW 3 O 12 and Cs 2 TeMo 3 O 12 with hexagonal, polar and non–centrosymmetric crystal structure were investigated based on density functional theory. Cs 2 TeW 3 O 12 and Cs 2 TeMo 3 O 12 are found to be indirect K (1/3, 1/3, 0) → G (0, 0, 0) band gap semiconductors ( E g > 3 eV) with small effective masses of photogenerated charge carriers. The mixing of octahedrally coordinated d ° transition metal cations (W 6+ and Mo 6+ ) with the filled p orbitals of the oxygen ligands leads to the formation of some W 5+ /Mo 5+ sites and splitting of d orbitals into the partially filled t 2g ( dxy , dyz , and dzx ) orbitals and empty e g ( dz 2 and dx 2 – y 2 ) orbitals. The top of the valence bond is mainly contributed by O 2 p orbital of the oxygen ligands mixed with the partially filled t 2g orbitals of W 5 d /Mo 4 d , while the conduction band mainly consists of empty e g orbitals of W 5 d /Mo 4 d with a little contribution of O 2 p orbitals. The dielectric function exhibits a slight anisotropic behavior and optical absorption peak for Cs 2 TeW 3 O 12 and Cs 2 TeMo 3 O 12 belonging to the strong electronic transition O 2 p → W 5 d /Mo 4 d within the octahedral units. According to the estimated valence band and conduction band edges, Cs 2 TeW 3 O 12 and Cs 2 TeMo 3 O 12 can be applied as visible−light−responsive photocatalysts for the decomposition of organic pollutants and dye molecules. Also, Cs 2 TeMo 3 O 12 can be used in water splitting for hydrogen generation but Cs 2 TeW 3 O 12 requires further experimental studies to confirm its ability for water splitting.

Proton transfer processes in water are of fundamental importance for, among others, electrochemical proton discharge. Empirical valence bond (EVB) approaches were shown in the past to be a versatile tool for modeling complex phenomena such as proton discharge at metal electrodes. By replacing empirical fitting procedures with on-the-fly quantum chemistry (QC) calculations, we arrive at a transferable and systematically tunable description of proton transfer in water with EVB.

Bond dissociation energies and resonance energies for HnA–BHm molecules (A, B = H, C, N, O, F, Cl, Li, and Na) have been determined in order to re-evaluate the concept of electronegativity in the context of modern valence bond theory. Following Pauling’s original scheme and using the rigorous definition of the covalent–ionic resonance energy provided by the breathing orbital valence bond method, we have derived a charge-shift corrected electronegativity scale for H, C, N, O, F, Cl, Li, and Na. Atomic charge shift character is defined using a similar approach resulting in values of 0.42, 1.06, 1.43, 1.62, 1.64, 1.44, 0.46, and 0.34 for H, C, N, O, F, Cl, Li, and Na, respectively. The charge-shift corrected electronegativity values presented herein follow the same general trends as Pauling’s original values with the exception of Li having a smaller value than Na (1.57 and 1.91 for Li and Na respectively). The resonance energy is then broken down into components derived from the atomic charge shift character...

The nature of the electronic-structure of polyenes, their delocalization features, and potential diradicaloid characters constitute a fundamental problem in chemistry. To address this problem, we used valence bond self-consistent field (VBSCF) calculations and modeling of polyenes, C2nH2n+2 (n = 2–10). The theoretical treatment shows that starting with n = 5, the polyene’s wave function is mainly a shifting 1,4-diradicaloid, a character that increases as the chain length increases, while the contribution of the fundamental Lewis structure with alternating double and single bonds (1) decays quite fast and becomes minor relative to the diradicaloid pack. We show how, nevertheless, it is this wave function that predicts that polyenes will still exhibit alternating short/long CC bonds like the fundamental structure 1. Furthermore, despite the decay of the VB contribution of 1, it remains the single structure with the largest weight among all the individual structures. The mixing of all the 1,4-diradicaloid st...

Polyhalogen monoanions [X2n+1 ]- (X=Cl and Br; n=1, 2, 3, 4, and 5) have been systematically studied using the block-localized wave function (BLW) method, which offers a valence bond (VB) analysis. For each species, the most stable isomer can be described as a central halide anion X- non-classically bonded to a number of dihalogen molecules X2 via "halogen bonds". VB analyses confirm the dominant role of the charge-transfer interaction between the lone pair on X- and the σ-anti-bonding orbital of X2 molecule (n→σ*) in X3- and higher analogues. Thus, our study demonstrates that these halogen bonds are essentially dative covalent interactions. Importantly, the charge-transfer interaction between [X2n-1 ]- and X2 decreases with the increasing n, in accord with the weakening of the Lewis basicity as characterized by the corresponding HOMO energy. The reduction of the charge transfer interaction underscores the reduction of covalence in halogen bonds in [X2n+1 ]- . This tendency highlights the anti-cooperative effect in polyhalogen monoanions. All in all, the halogen bond between X- and nX2 molecules exhibits the same trends as in X- with a single X2 molecule. In other words, halogen bonding in the larger clusters derives from the same bonding mechanism as the [X3 ]- anion. As such, the X- ⋅⋅⋅X2 halogen bond at different bond lengths forms a gauge of covalence for the entire [X2n+1 ]- family.

A molecular mechanical model has been proposed for nanoribbons of graphone (graphene with single-sided hydrogenation), which takes into account deformations of valence bonds, valence and torsion angles, as well as non-bonded van der Waals and Coulomb interactions of atoms in a graphone nanoribbon. The ground states of the nanoribbons have been found using the proposed model. It has been shown that a rectangular fragment of graphone on a substrate formed by an infinite planar graphene sheet forms a flat monolayer, whereas a fragment that does not interact with the substrate takes a convex shape, the outer side of which contains the attached hydrogen atoms. The simulation of the dynamics has demonstrated that the single-sided structure of a graphone sheet is resistant to thermal vibrations (at temperatures T < 900 K, hydrogen atoms do not migrate from one side of the sheet to the other). The difference between the sides leads to a rapid folding of long-length free-standing graphone nanoribbons into scrolled structures. Thermal vibrations do not prevent the formation of scrolls, and the scrolls themselves are resistant to these vibrations.

The low-energy structures of AlnCm (n = 4, 6; m = 1–4) are determined by using the genetic algorithm combined with density functional theory and the QCISD models. The electronic structures and bonding features are analyzed through the density of states (DOS), valence molecular orbitals (MOs), and electron localization function (ELF). The results show that the carbon atoms tend to aggregate and sit at the center of the clusters. The C–C bond lengths in most cases agree with the double C═C bond. Because of the large difference between the electronegativities of carbon and aluminum atoms, almost all of the 3p electrons of Al transfer to C atoms. The 3s orbitals of Al and the 2s2p orbitals of C form bonding and antibonding orbitals; the bonding orbitals correspond to the covalent C–Al bonds, and the antibonding orbitals form lone pair electrons on the outer side of Al atoms. The lone pair electrons form large local dipole moments and enhance the electrostatic interactions between C and Al atoms. Planar geomet...

Pol η belongs to the important Y family of DNA polymerases that can catalyze translesion synthesis across sites of damaged DNA. This activity involves the reduced fidelity of Pol η for 8-oxo-7,8-dhyedro-2′-deoxoguanosin(8-oxoG). The fundamental interest in Pol η has grown recently with the demonstration of the importance of a 3rd Mg2+ ion. The current work explores both the fidelity of Pol η and the role of the 3rd metal ion, by using empirical valence bond (EVB) simulations. The simulations reproduce the observed trend in fidelity and shed a new light on the role of the 3rd metal ion. It is found that this ion does not lead to a major catalytic effect, but most probably plays an important role in reducing the product release barrier. Furthermore, it is concluded, in contrast to some implications, that the effect of this metal does not violate transition state theory, and the evaluation of the catalytic effect must conserve the molecular composition upon moving from the reactant to the transition state. Proteins 2017; 85:1446–1453. © 2017 Wiley Periodicals, Inc.

Novel DNA triangular pyrimidine derivatives are designed by metal decoration through replacement of H by Cu in the Watson–Crick hydrogen bond region. The DFT method is used to examine the coordination of triangle-arranged Cu with three pyrimidines in nonplanar three-bladed turbine geometries. The Cu···Cu cuprophilic bonds are ascribed to the partially occupied d orbitals without direct molecular orbital (MO) interactions. Four-center bonds depend on Cu–N/O bonds, which are contributed by p orbitals of N/O atoms along or perpendicular to the bond axis. The activity of frontier MOs is modulated, leading to the decrease of gaps, ionization potentials (IPs), and electron affinities (EAs) desired for the improvement of conductivity. The hole trapping ability is assured by virtue of the spin density distributed on Cu. On average, the single electron density is located on π orbitals of three aromatic base rings. There is paramagnetic electron delocalization on the inner d orbitals of triangle region. The analysis of electron localization function ELF-π and electrostatic potential maps reveals that the outer strong π–π stacking interaction together with the inner d orbital channel enable effective transduction of electrical signals along the Cu–DNA nanowires. The 3Cu-induced triangular pyrimidines have important potential applications as structural motifs of molecular electronic devices.

The cytochromes P450 are versatile enzymes in human physiology that perform substrate hydroxylation reactions extremely efficient. In this work, we present results of a computational study on the reactivity patterns of Compound I, Compound II and protonated Compound II with model substrates and addresses the question, which of those is the most effective oxidant. All calculations, regardless of the substrate, implicate that Compound I is the superior oxidant of the three. However, Compound II and protonated Compound II are found to react with free energies of activation that are only a few kcal mol-1 higher in energy than those obtained with Compound I. Therefore, Compound II and protonated Compound II should be able to react with aliphatic groups with moderate C-H bond strengths. We have analyzed all results in detail and give electronic, thermochemical, valence bond and molecular orbital rationalizations on the reactivity differences and explain experimental product distributions. Overall, the work implies that alternative oxidants could operate alongside Compound I in complex reaction mechanisms of enzymatic and synthetic iron porphyrin complexes VP and MS thanks the support of the Ministerio de Economía y Competitividad of Spain (Projects CTQ2014-54306-P and grant No. BES-2012-052801 to VP), Generalitat de Catalunya (project number 2014SGR931, Xarxa de Referència en Química Teòrica i Computacional, and ICREA Academia prizes for MS), and European Fund for Regional Development (FEDER grant UNGI10-4E-801)

We present results of the combined study of the magnetic properties of Li2RuO3 by means of nuclear magnetic resonance (NMR) spectroscopy and theoretical dynamical mean-field theory (LDA + DMFT) calculations. The NMR data clearly show the onset of a thermal activation process in the high temperature region, T > 560K, which is tentatively ascribed to the formation of the valence bond liquid. The LDA + DMFT calculations demonstrate that the magnetic response at these temperatures is mostly due to the xz/yz orbitals, while the xy orbitals of Ru still form molecular orbitals. Thus, Ru ions are in the orbital-selective state in the high temperature phase of Li2RuO3.

Background Many important geochemical and biogeochemical reactions occur in the mineral/formation water interface of the highly abundant mineral, goethite [α-Fe(OOH)]. Ab initio molecular dynamics (AIMD) simulations of the goethite α-FeOOH (100) surface and the structure, water bond formation and dynamics of water molecules in the mineral/aqueous interface are presented. Several exchange correlation functionals were employed (PBE96, PBE96 + Grimme, and PBE0) in the simulations of a (3 × 2) goethite surface with 65 absorbed water molecules in a 3D-periodic supercell (a = 30 Å, FeOOH slab ~12 Å thick, solvation layer ~18 Å thick). Results The lowest energy goethite (100) surface termination model was determined to have an exposed surface Fe3+ that was loosely capped by a water molecule and a shared hydroxide with a neighboring surface Fe3+. The water molecules capping surface Fe3+ ions were found to be loosely bound at all DFT levels with and without Grimme corrections, indicative that each surface Fe3+ was coordinated with only five neighbors. These long bonds were supported by bond valence theory calculations, which showed that the bond valence of the surface Fe3+ was saturated and surface has a neutral charge. The polarization of the water layer adjacent to the surface was found to be small and affected only the nearest water. Analysis by density difference plots and localized Boys orbitals identified three types of water molecules: those loosely bound to the surface Fe3+, those hydrogen bonded to the surface hydroxyl, and bulk water with tetrahedral coordination. Boys orbital analysis showed that the spin down lone pair orbital of the weakly absorbed water interact more strongly with the spin up Fe3+ ion. These weakly bound surface water molecules were found to rapidly exchange with the second water layer (~0.025 exchanges/ps) using a dissociative mechanism. Conclusions Water molecules adjacent to the surface were found to only weakly interact with the surface and as a result were readily able to exchange with the bulk water. To account for the large surface Fe–OH2 distances in the DFT calculations it was proposed that the surface Fe3+ atoms, which already have their bond valence fully satisfied with only five neighbors, are under-coordinated with respect to the bulk coordination. Graphical abstract All first principle calculations, at all practically achievable levels, for the goethite 100 aqueous interface support a long bond and weak interaction between the exposed surface Fe3+ and water molecules capping the surface. This result is supported by bond valence theory calculations and is indicative that each surface Fe3+ is coordinated with only 5 neighbors.

We describe a diabatic-at-construction (DAC) strategy for defining diabatic states to determine the adiabatic ground and excited electronic states and their potential energy surfaces using the multistate density functional theory (MSDFT). The DAC approach differs in two fundamental ways from the adiabatic-to-diabatic (ATD) procedures that transform a set of preselected adiabatic electronic states to a new representation. (1) The DAC states are defined in the first computation step to form an active space, whose configuration interaction produces the adiabatic ground and excited states in the second step of MSDFT. Thus, they do not result from a similarity transformation of the adiabatic states as in the ATD procedure; they are the basis for producing the adiabatic states. The appropriateness and completeness of the DAC active space can be validated by comparison with experimental observables of the ground and excited states. (2) The DAC diabatic states are defined using the valence bond characters of the asymptotic dissociation limits of the adiabatic states of interest, and they are strictly maintained at all molecular geometries. Consequently, DAC diabatic states have specific and well-defined physical and chemical meanings that can be used for understanding the nature of the adiabatic states and their energetic components. Here we present results for the four lowest singlet states of LiH and compare them to a well-tested ATD diabatization method, namely the 3-fold way; the comparison reveals both similarities and differences between the ATD diabatic states and the orthogonalized DAC diabatic states. Furthermore, MSDFT can provide a quantitative description of the ground and excited states for LiH with multiple strongly and weakly avoided curve crossings spanning over 10 Å of interatomic separation.

This paper reports the effect of randomness on a quantum spin liquid state of 1T-TaS${}_{2}$ with a two-dimensional perfect triangular lattice. Systematic measurements of heat capacity and thermal conductivity in pure, Se-substituted, and electron-irradiated crystals reveal the microscopic coexistence of localized orphan spins that form random valence bonds and itinerant spinons that appear to form a Fermi surface.

The present work is another contribution to a better understanding of the chemical bond in C2. A density functional approach is employed, and the obtained results (bond distance and bond dissociation energy) agrees very well with the previously [2-4] valence bond results. The obtained results also points to a bond order of four, reinforcing previously obtained data [3]. Furthermore, based on the calculated IR and Raman spectra, is proposed that C2 exhibits, at an electronic level, an asymmetry, and that such molecule has not, in fact, a centre of inversion.

Density functional theory and ab initio calculations indicate that nucleophiles can significantly reduce enthalpic barriers to methane C-H bond activation. Valence bond analysis suggests the formation of a two-center three-electron bond as the origin for the catalytic nucleophile effect. A predictive model for methane activation catalysis follows, which suggests that strongly electron-attracting and electron-rich radicals, together with both a negatively charged and strongly electron-donating outer sphere nucleophile, result in the lowest reaction barriers. It is corroborated by the sensitivity of the calculated C-H activation barriers to the external nucleophile and to continuum solvent polarity. More generally, from the present studies, one may propose proteins with hydrophobic active sites, available strong nucleophiles, and hydrogen bond donors as attractive targets for engineering novel methane functionalizing enzymes.

We study the N\'eel to fourfold columnar valence bond solid (cVBS) quantum phase transition in a sign-free $S=1$ square-lattice model. This is the same kind of transition that for $S=1/2$ has been argued to realize the prototypical deconfined critical point. Extensive numerical simulations of the square-lattice $S=1/2$ N\'eel-VBS transition have found consistency with the deconfined critical point scenario with no direct evidence for first-order behavior. In contrast to the $S=1/2$ case, in our quantum Monte Carlo simulations for the $S=1$ model, we present unambiguous evidence for a direct conventional first-order quantum phase transition. Classic signs of a first-order transition demonstrating coexistence including double-peaked histograms and switching behavior are observed. The sharp contrast from the $S=1/2$ case is remarkable; we hypothesize that this is a striking demonstration of the role of the size of the quantum spin in the phase diagram of two-dimensional lattice models.

In recent years, with the development of molecular imprinting technology, the imprinting sites, nature of imprinting, selection of functional monomers, cross-linking agents, solvents, and the optimization of the imprinting ratio are all the hot spots of researchers. In this work, the theoretical prediction of the self-assembly system of formaldehyde (HCHO) molecularly imprinted polymer was carried out by the B3LYP/6-31 G(d,p) method. The geometric configuration and active sites of the stable complex of HCHO and methacrylic acid (MAA) were analyzed. The selection of the imprinting ratios, cross-linking agents, and solvents was discussed. The topological properties of electron density of HCHO-MAA complex were considered by using the topological analysis method of chemical bond electron density based on valence bond theory. This study cannot only reveal the relationship between the imprinting mechanism of molecularly imprinted polymers and the molecular structure and properties of molecularly imprinted polymers but also provide valuable reference for the design and preparation of molecularly imprinted polymers.

According to the Copenhagen interpretation of quantum mechanics a measurement leads to the collapse of a quantum system. A unified description of a quantum system before and after measurement of the position r1a and the spin s1a of one of its electrons is proposed based on the conditional amplitude and its density. Quantum collapse is described as reduction from continuum of the conditional amplitudes {φ(x2,⋯,xN|r1h,s1h)} in an initial quantum state to the single actualized amplitude φ(x2, ⋯,xN|r1a,s1a) in a collapsed state. The latter state contains the information about quantum entanglement, the extraction of which with fragment entanglement measure is demonstrated for the realistic valence bond models of the dissociating dihydrogen and ethylene molecules.

Based on the Valence Bond theory, an attempt is proposed to the complex network. The principle of chemical bonding of the basic particles that make up the substance creates a metaphor between the formation of social networks. By analyzing the integration of atoms by relying on the chemical bonds between particles, then the social basis for the connection between social network nodes should depend on the tangible or intangible attribute resources that characterize social capital around the main node. Based on the above analysis, the social node is divided into active nodes and passive nodes, and a dynamic model of social network formation is proposed, the Valence Bond model of social network. Through this model, the actual athlete group nodes are depicted, and the representation of the model and the evolution of network structure are given with the actual data.

Akin to the shell structures of atoms, shell-filling concepts from traditional valence bond theory can be applied to the description of cluster stability. In view of this, the result of a chemical interaction could be explained through the energy minimization attained when a cluster closes an incomplete electronic shell, either by direct ionization or through the formation of a covalent/ionic bond. Also, it has been widely recognized that cluster stability and reactivity are associated with a comprehensive picture involving geometric structure, electronic configuration and the resulted energetics, allowing for one atom to make a difference and active-sites cooperation as introduced in this chapter.

The {\em rainbow state} denotes a set of valence bond states organized concentrically around the center of a spin 1/2 chain. It is the ground state of an inhomogeneous XX Hamiltonian and presents maximal violation of the area law of entanglement entropy. Here, we add a tunable exchange coupling constant at the center, $\gamma$, and show that it induces entanglement transitions of the ground state. At very strong inhomogeneity, the rainbow state survives for $0 \leq \gamma \leq 1$, while outside that region the ground state is a product of dimers. In the weak inhomogeneity regime the entanglement entropy satisfies a volume law, derived from CFT in curved spacetime, with an effective central charge that depends on the inhomogeneity parameter and $\gamma$. In all regimes we have found that the entanglement properties are invariant under the transformation $\gamma \longleftrightarrow 1 - \gamma$, whose fixed point $\gamma = \frac{1}{2}$ corresponds to the usual rainbow model. Finally, we study the robustness of non trivial topological phases in the presence of the defect.

We introduce a quantum spin-1/2 model with many-body correlated Heisenberg-type interactions on the 2D square lattice, designed to host a plaquette valence-bond solid (PVBS) ground state breaking $\mathbb{Z}_4$ symmetry. We carry out a detailed quantum Monte Carlo study of the quantum phase transition between the antiferromagnetic (AFM) and PVBS states. We find a first-order transition, in contrast to previously studied continuous 'deconfined' transitions between the AFM and columnar valence-bond solids. We show that the coexistence state at the AFM--PVBS transition is unexpectedly associated with SO(5) symmetry, which may indicate that the transition is connected to a deconfined critical point. We also discuss the first-order transition in the context of a recent proposal of spinons with fracton properties in the PVBS state, concluding that the fracton scenario is unlikely. Further, we discover a novel type of eight-fold degenerate VBS phase that breaks the remaining $\mathbb{Z}_2$ symmetry of the PVBS phase. The PVBS phase can then be regarded as an intermediate 'vestigial' phase, and we develop a general graph-theoretic approach to describe the two-stage discrete symmetry breaking. At finite temperature, we observe fluctuation-induced first-order transitions, which are hallmarks of vestigial phase transitions. We also mention possible connections to the SO(5) theory of high-T$_{\rm c}$ superconductivity., Comment: 30 pages, 22 figures

Using the molecular dynamics method, dynamics of hydrogen bond (HB) networks emerging on the surface of a graphene sheet during its functionalization with hydroxyl groups OH are simulated. It is demonstrated that two OH groups form an energetically more advantageous structure when they are covalently attached on one side of the sheet to carbon atoms forming opposite vertices of one hexagon of valence bonds of the sheet. Attaching of OH groups to carbon atoms located at the opposite vertices of hexagons of valence bonds leads to the emergence of hydroxygraphene C$_4$(OH). In such sheet lying on a flat substrate, attached oxygen atoms on its outer surface form a hexagonal lattice, and hydroxyl groups due to their turns can in various ways form chains of hydrogen bonds. The modification of the sheet from two sides results in forming of hydroxygraphene C$_2$(OH) with HB networks on both sides of the graphene sheet. Simulation of the dynamics of these sheets shows that their heat capacity at low temperatures $TT_0$ is explained by the "melting" of the lattice. For one chain of OH groups connected to the outer side of a nanoribbon the melting temperature is $T_0=500$K, while for a graphene sheet C4(OH) modified on one side $T_0=260$K, and for a graphene sheet C$_2$(OH) modified on both sides $T_0=485$K., Comment: 11 pages, 10 figures

By using first-principles calculations we put forward the Cu-dicyanoanthracene lattice as a platform to investigate strong electronic correlations in the family of Kagome metal-organic frameworks. We show that the low-energy model is composed by molecular orbitals which arrange themselves in a typical Kagome lattice at n = 2/3 filling, where the Fermi level lies at the Dirac point. The Coulomb interaction matrix expressed in this molecular orbitals basis, as obtained by large-scale constrained random-phase approximation calculations, is characterized by local U and non-local U ′ parameters exceeding more than ten times the Kagome bandwidth. For such Kagome systems, our findings suggest the possible emergence of peculiar electron–electron collective phenomena, such as an exotic valence bond solid order characterized by modulated bond strengths.

This study is focused on describing the molecular mechanism beyond the molecular picture provided by the evolution of molecular orbitals, valence bond structures along the reaction progress, or conceptual density functional theory. Using bonding evolution theory (BET) analysis, we have deciphered the mechanism of the 1,3-dipolar rearrangement between acetonitrile oxide and (1S,2R,4S)-2-cyano-7-oxabicyclo[2.2.1]hept-5-en-2-yl acetate derivatives. The BET study revealed that the formation of the C−C bond takes place via a usual sharing model before the O−C one that is also formed in the halogenated species through a not very usual sharing model. The mechanism includes depopulation of the electron density at the N−C triple bond and creation of the V(N) and V(C) monosynaptic basins, depopulation of the former C−C double bond with the creation of V(C,C) basins, and final formation of the V(O,C) basin associated with the O−C bond. The topological changes along the reaction pathway take place in a highly synchronous way. BET provides a convenient quantitative method for deriving curly arrows and electron flow representation to unravel molecular mechanisms.

We obtain a quantum dimer model (QDM) containing a Rokhsar-Kivelson (RK) point expressed by spin-1/2 Heisenberg antiferromagnets on a diamond-like decorated square lattice. This lattice has macroscopically degenerated nonmagnetic ground states, which are equivalent to the Hilbert space of a square-lattice QDM. Then, a square-lattice QDM containing the RK point as a second-order effective Hamiltonian is obtained by introducing further neighbor couplings as perturbation. Our model can provide a new method for the experimental realization of a resonating valence bond state in the QDM., Comment: 13 pages, 11 figures

We introduce valence bond fluctuations, or bipartite fluctuations associated to bond-bond correlation functions, to characterize quantum spin liquids and their entanglement properties. Using analytical and numerical approaches, we find an identical scaling law between valence bond fluctuations and entanglement entropy in the two-dimensional Kitaev spin model and in one-dimensional chain analogues. We also show how these valence bond fluctuations can locate quantum phase transitions between the three gapped and the gapless Majorana semi-metal phases in the honeycomb model. We then study the effect of a uniform magnetic field along the 111 direction opening a gap in the intermediate phase which becomes topological. We still obtain a robust signal to characterize the transitions towards the three gapped phases. The linear scaling behavior of such bipartite fluctuations in two dimensions is also distinguishable from the one in the Neel magnetic state., Comment: 21 pages, Version as Accepted for Physical Review Research

ECS journal of solid state science and technology 9(6), 061005 - (2020). doi:10.1149/2162-8777/ab9e18, The influence of the contracted corrole macrocycle, in comparison to the larger porphyrin macrocycle, on the electronic structure of nickel was studied with X-ray and ultraviolet photoelectron spectroscopy (XPS, UPS) and near-edge X-ray absorption fine structure (NEXAFS) spectroscopy. Synthesis and in situ characterization of the Ni complexes of octaethylporphyrin (NiOEP) and hexaethyldimethylcorrole (NiHEDMC) were performed in ultra-high vacuum. XPS and NEXAFS spectra reveal a +2 oxidation state and a low-spin d8 electron configuration of Ni in both complexes, despite the formal trianionic nature of the corrole ligand. UPS, in combination with density functional theory (DFT) calculations, support the electronic structure of a Ni(II) corrole with a π-radical character of the ligand. The NEXAFS spectra also reveal differences in the valence electronic structure, which are attributed to the size mismatch between the small Ni(II) center and the larger central cavity of NiOEP. Analysis of the gas-phase structures shows that the Ni−N bonds in NiOEP are 4%–6% longer than those in NiHEDMC, even when NiOEP adopts a ruffled conformation. The individual interactions that constitute the Ni−ligand bond are altogether stronger in the corrole complex, according to bonding analysis within the energy decomposition analysis and the natural orbitals for chemical valence theory (EDA-NOCV)., Published by ECS, Pennington, NJ

We find exponentially many exact quantum many-body scar states in a two-dimensional PXP model -- an effective model for a two-dimensional Rydberg atom array in the nearest-neighbor blockade regime. Such scar states are remarkably simple valence bond solids despite being at effectively infinite temperature, and thus strongly violate the eigenstate thermalization hypothesis. Given a particular boundary condition, such eigenstates have integer-valued energies. Moreover, certain charge-density-wave initial states give rise to strong oscillations in the Rydberg excitation density after a quantum quench and tower-like structures in their overlaps with eigenstates., Comment: 10 pages, 5 figures

A higher-order (HO) symmetry-protected topological (SPT) state can be realized in a plaquette-modulated square lattice antiferromagnet, which hosts a spin-$1/2$ degenerate mode on each corner of the lattice with open boundaries. In this work, we show with the field-theoretic analysis and quantum Monte Carlo simulations that the plaquette modulation can drive a direct topological quantum phase transition from the HOSPT to a trivial disordered phase across the deconfined quantum critical point (DQCP) between the antiferromagnetic (AF) order and the valence bond solid (VBS) order, thus the DQCP is a multicritical point bridging both the AF-VBS transition and the topological transition of the HOSPT phase. Our work thus reveals the ubiquitous duality between topological transitions of SPT phases and DQCPs., Comment: 5 pages, 5 figures

Elliot Quincy Adams was an American scientist born on September 13, 1888. He was the son of Edward Perkins and Etta Medora (Elliot) Adams from Cambridge, Massachusetts. He married Jane J. Pidgeon, and they had a daughter, Dora. According to Gilbert N. Lewis (1875–1946), known for the discovery of the covalent bond and his concept of electron pairs, Lewis dot structures and other contributions to valence bond theory, “the two most profound scientific minds, among the people he had known, were those of E[lliot] Q Adams and Albert Einstein. He also mentioned he would not think Adams would do much publishing.” [1] Adams passed away in Cleveland on March 11, 1971, at the age of 82.

We introduce a variational state for one-dimensional two-orbital Hubbard models that intuitively explains the recent computational discovery of pairing in these systems when hole doped. Our ansatz is an optimized linear superposition of Affleck–Kennedy–Lieb–Tasaki valence-bond states, rendering the combination a valence-bond liquid dubbed orbital resonant valence bond. We show that the undoped (one-electron/orbital) quantum state of two sites coupled into a global spin singlet is exactly written employing only spin-1/2 singlets linking orbitals at nearest-neighbor sites. Generalizing to longer chains defines our variational state visualized geometrically expressing our chain as a two-leg ladder, with one orbital per leg. As in Anderson’s resonating valence-bond state, our undoped variational state contains preformed singlet pairs that via doping become mobile, leading to superconductivity. Doped real materials with one-dimensional substructures, two near-degenerate orbitals, and intermediate Hubbard U/W strengths—W the carrier’s bandwidth—could realize spin-singlet pairing if on-site anisotropies are small. If these anisotropies are robust, spin-triplet pairing emerges.

Using the model of delocalized atoms, an explanation is offered for the linear dependence of the microhardness of inorganic glasses on their glass transition temperatures. In these systems, the elementary volume required for the delocalization of atoms is determined by the nature of the bridging atoms and bridging valence bonds. An estimate of the volume of atom delocalization is given, based on data for the glass transition temperature and microhardness.