The VB-QMC method is presented in this chapter. It consists of using in quantum Monte Carlo (QMC) approaches with a wave function expressed as a usually short expansion of classical Valence-Bond (VB) structures supplemented by a Jastrow factor to account for dynamical correlation. Two variants exist: the VB-VMC (using variational Monte Carlo) and VB-DMC (using diffusion Monte Carlo) methods. QMC algorithms circumvent the notorious non-orthogonality issue of classical VB approaches, and allow highly efficient calculations on massively parallel machines. Calculation of VB weights and resonance energies are possible at the VB-VMC level, which makes VB-VMC a correlated method retaining all the interpretative capabilities of classical VB methods. Several recent applications are shown to illustrate the potential of this method as a modern alternative to classical VB methods to study ground and excited states of molecules.

Xiamen Valence Bond (XMVB) is a quantum electronic structure software focusing on ab initio nonorthogonal valence bond (VB) computation. Various ab initio VB methods are implemented in the XMVB package, including "classical" VB methods such as VBSCF, BOVB, VBCI and VBPT2, "modern" VB methods such as SCGVB, as well as molecular orbital-based BLW method. In this chapter, a tutorial on XMVB, explaining step-by-step how to run an ab initio VB calculation, will be provided. The chapter starts with information on how to install the XMVB package and how to configure the computing environment. This is followed by a brief description of the structure and content of the input and output files. Finally, seven illustrative examples are provided with more detailed practical guidelines. These examples involve the calculations of bonding energies, resonance energies, energy gaps and reaction barriers, all of which are important quantities of interest in theoretical/quantum chemistry.

We present an efficient criterion for probing the critical temperature of hydrogen based superconductors. We start by expanding the applicability of 3D descriptors of electron localization to superconducting states within the framework of superconducting DFT. We first apply this descriptor to a model system, the hydrogen chain, which allows to prove two main concepts: i) that the electron localization changes very little when the transition from the normal to the superconducting state takes place, i.e. that it can be described at the DFT level from the normal state; and ii) that the formation of molecules can be characterized within this theoretical framework, enabling to filter out systems with marked molecular character and hence with low potential to be good superconductors. These two ideas, are then exploited in real binary and ternary systems, showing i) that the bonding type can be characterized automatically; and ii) that this provides a new index which enables to feed machine learning algorithms for a better prediction of critical temperatures. Overall, this sets a grounded theoretical scenario for an automatic and efficient high-throughput of potential hydrogen based superconductors.

This article is devoted to the mathematical and numerical treatments of a shape optimization problem emanating from the desire to reconcile quantum theories of chemistry and classical heuristic models: we aim to identify Maximum Probability Domains (MPDs), that is, domains $$\Omega $$ of the 3d space where the probability $${\mathbb {P}}_\nu (\Omega )$$ to find exactly $$\nu $$ among the n constituent electrons of a given molecule is maximum. In the Hartree-Fock framework, the shape functional $${\mathbb {P}}_\nu (\Omega )$$ arises as the integral over $$\nu $$ copies of $$\Omega $$ and $$(n-\nu )$$ copies of the complement $${\mathbb {R}}^3 \setminus \Omega $$ of an analytic function defined over the space $${\mathbb {R}}^{3n}$$ of all the spatial configurations of the n electron system. Our first task is to explore the mathematical well-posedness of the shape optimization problem: under mild hypotheses, we prove that global maximizers of the probability functions $${\mathbb {P}}_\nu (\Omega )$$ do exist as open subsets of $${\mathbb {R}}^3$$ ; meanwhile, we identify the associated necessary first-order optimality condition. We then turn to the numerical calculation of MPDs, for which we resort to a level set based mesh evolution strategy: the latter allows for the robust tracking of complex evolutions of shapes, while leaving the room for accurate chemical computations, carried out on high-resolution meshes of the optimized shapes. The efficiency of this procedure is enhanced thanks to the addition of a fixed-point strategy inspired from the first-order optimality conditions resulting from our theoretical considerations. Several three-dimensional examples are presented and discussed to appraise the efficiency of our algorithms.

This article analyzes the nature of the chemical bond in coinage metal halides using high-level ab initio Valence Bond (VB) theory. It is shown that these bonds display a large Charge-Shift Bonding character, which is traced back to the large Pauli pressure arising from the interaction between the bond pair with the filled semicore d shell of the metal. The gold-halide bonds turn out to be pure Charge-Shift Bonds (CSBs), while the copper halides are polar-covalent bonds and silver halides borderline cases. Among the different halogens, the largest CSB character is found for fluorine, which experiences the largest Pauli pressure from its σ lone pair. Additionally, all these bonds display a secondary but non-negligible π bonding character, which is also quantified in the VB calculations.

Introductory chemistry textbooks often present valence bond (VB) theory as useful, but incorrect and inferior to molecular orbital (MO) theory, citing the electronic structure of O2 and electron delocalization as evidence. Even texts that initially present the two theories on equal footing use language that biases students toward the MO approach. However, these "failures" of VB are really just misconceptions and/or misapplications of the theory. At their theoretical limits, both VB and MO are equivalent; they simply approach that limit from different sides. Certain concepts may be easier to grasp with one theory or the other so that having a commanding knowledge of both is extremely beneficial. However, presenting one theory as superior to the other suppresses the ability to look at a problem from both sides and is therefore detrimental to students and the whole of chemistry. It is time for VB and MO to be taught on equal footing like the complementary theories they are.

Angewandte Chemie International EditionVolume 60, Issue 23 p. 12613-12630 Graphical AbstractFree Access Graphical Abstract: Angew. Chem. Int. Ed. 23/2021 First published: 26 May 2021 https://doi.org/10.1002/anie.202182311AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Volume60, Issue23June 1, 2021Pages 12613-12630 RelatedInformation

Bonding in the recently synthesized NaBH3 - cluster is investigated using the high level Valence Bond BOVB method. Contrary to earlier conclusions, the Na-B bond is found to be neither a genuine dative bond, nor a standard polar-covalent bond at equilibrium. It is rather revealed as a split and polarized weakly coupled electron-pair, which allows this cluster to be more effectively stabilized by a combination of (major) dipole-dipole electrostatic interaction and (secondary) resonant one-electron bonding mechanism. Our analysis of this unprecedented bonding situation extends to similar clusters, and the VB model unifies and articulates the previously published variegated views on this exotic "bond".

In this chapter, the application of computational quantum mechanical methods to the understanding of radical reactions is introduced. For radical reactions, access to electronic configurations through quantum chemical calculations allows rationalization of unusual reactivities. Using the valence bond approach, the nature of bonding in three-electron bonds can be characterized by large resonance interactions. Similarly, some simple reactions that are commonly believed to be radical-free, such as [3 + 2] cycloadditions, are in fact governed by a high-lying biradical intermediate that helps to stabilize the transition state. More complex radical and enzymatic reactions can also be modelled, as illustrated by the example of horseradish peroxidase. These case studies show that computational analysis can complement experimental investigations and fill in the blanks to enable a more complete understanding of radical reactions.

The first steps of the oxidation process of amino acid methionine (Met, CAS 63-68-3) by •OH radicals, leading to Met-OH• adduct and then to Met radical cation, were investigated theoretically over the last few years considering the aqueous environment as a continuum. In this work, following the same procedure that we used for the oxidation of dimethyl sulfide as reported by Domin et al. (J Phys Chem B, 121:9321), discrete water molecules, as well as relative positions, of the •OH radical to Met were taken from molecular dynamics calculations. The presence of water molecules strongly modifies the relative energies of Met-OH adducts and cations when water is properly modeled. Depending on the terminal functional groups and on the position of the •OH radical, several stable structures were found; however, the most stable radical is the N-centered or the S∴N radical cation. QTAIM analysis and valence bond (VB) treatment allowed for the characterization of the 2c∴3e nature of S∴N and S∴OH bonds. VB analysis estimated the probability of the heterolytic rupture of the •OH adduct that is modified by the presence of water molecules.

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

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.

A novel state-averaged version of ab initio nonorthogonal valence bond method is described, for the sake of accurate theoretical studies of excited states in the valence bond framework. With respect to standard calculations in the molecular orbital framework, the state-averaged breathing-orbital valence bond (BOVB) method has the advantage to be free from the penalizing constraint for the ground and excited state(s) to share the same unique set of orbitals. The ability of the BOVB method to faithfully describe excited states and to compute accurate transition energies from the ground state is tested on the five lowest-lying singlet electronic states of ozone and sulfur dioxide, among which 1(1)B(2) and 2(1)A(1) are the challenging ones. As the 1(1)A(2), 1(1)B(1), and 1(1)B(2) states are of different symmetries than the ground state, they can be calculated at the state-specific BOVB level. On the other hand, the 2(1)A(1) states and the 1(1)A(1) ground states, which are of like symmetry, are calculated with the state-averaged BOVB technique. In all cases, the calculated vertical energies are close to the experimental values when available, and at par with the most sophisticated calculations in the molecular framework, despite the extreme compactness of the BOVB wave functions, made of no more than 5-9 valence bond structures in all cases. The features that allow the combination of compactness and accuracy in challenging cases are analyzed. For the "ionic" 1(1)B(2) states, which are the site of important charge fluctuations, it is because of the built-in dynamic correlation inherent to the BOVB method. For the 2(1)A(1) ones, this is the fact that these states have the degree of freedom of having different orbitals than the ground states, even though they are of like symmetry and calculated simultaneously using the newly implemented state-average BOVB algorithm. Finally, the description of the excited states in terms of Lewis structures is insightful, rationalizing the fast ring closure for the 2(1)A(1) state of ozone and predicting some diradical character in the so-called "ionic" 1(1)B(2) states.

AbstractCharge‐shift bonds (CSBs) constitute a new class of bonds different than covalent/polar‐covalent and ionic bonds. Bonding in CSBs does not arise from either the covalent or the ionic structures of the bond, but rather from the resonance interaction between the structures. This Essay describes the reasons why the CSB family was overlooked by valence‐bond pioneers and then demonstrates that the unique status of CSBs is not theory‐dependent. Thus, valence bond (VB), molecular orbital (MO), and energy decomposition analysis (EDA), as well as a variety of electron density theories all show the distinction of CSBs vis‐à‐vis covalent and ionic bonds. Furthermore, the covalent–ionic resonance energy can be quantified from experiment, and hence has the same essential status as resonance energies of organic molecules, e.g., benzene. The Essay ends by arguing that CSBs are a distinct family of bonding, with a potential to bring about a Renaissance in the mental map of the chemical bond, and to contribute to productive chemical diversity.

Gleichsam sich durch den Spiegel betrachtende Elektronenpaare werden zwei Gesichter finden, ein delokalisiertes und ein lokalisiertes. Beide sind vollkommen korrekt. Je nach Relevanz und Aussagekraft für den jeweils vorliegenden Fall kann man problemlos zwischen beiden Darstellungen hin- und herschalten — und muss es sogar, um ein vollständiges Verständnis der elektronischen Struktur gewinnen zu können. Die Autoren erklären, dass keine Interessenkonflikte vorliegen.

Oxidative stress of sulfur-containing biological molecules in aqueous environments may lead to the formation of adduct intermediates that are too short-lived to be experimentally detectable. In this study we have modeled the simplest of such oxidative reactions: the attack of dimethyl sulfide (DMS) by a hydroxyl radical (·OH) to form a radical adduct, whose subsequent heterolytic dissociation leads to a radical cation (DMS+) that is important for further reactions. We have modeled the aqueous environment with a limited number of discrete water molecules, selected after an original multistep procedure, and further embedded in a polarizable continuum model, to observe the impact of the water configuration on the heterolytic dissociation of the radical adduct. Molecular dynamics and quantum chemical methods (DFT, MP2, and CCSD) were used to elucidate the lowest energy structures resulting from the ·OH attack on DMS. Subsequent high level ab initio valence bond (BOVB) calculations revealed the possibility for the occurrence of subsequent heterolytic dissociation.

In 2004 Randic and Balaban employed Kekule structures to assess the pi-electron content (EC) of rings in benzenoid hydrocarbons. In this paper we showed how ab initio Valence Bond (VB) calculations based on the set of Kekule structures of a given polycyclic conjugated molecule can be used to obtain more accurate pi-electron contents of rings (VB-EC) as the true computed weights of the Kekule structures are used, instead of postulating that all Kekule structures have equal weights as in the EC formula. In the case of benzenoid hydrocarbons, the values of VB-EC and EC are very close. The main difference is found for linear polyacenes, for which, contrary to the EC, the VB-EC values predict that the inner rings are more aromatic than the terminal rings. The original EC method has also the disadvantage that it cannot be applied to heterocyclic conjugated molecules. It was shown that the VB-EC method can be used to assess the local aromaticity in aza derivatives of naphthalene. The calculated VB-EC values were compared with several other aromaticity indices, namely: energy effect (ef), harmonic oscillator model of aromaticity (HOMA) index, six center delocalization index (SCI) and nucleus independent chemical shifts (NICS). The best correlation was found between the VB-EC and SCI, implying that these two indices carry similar information on the local aromaticity. (C) 2017 Elsevier B.V. All rights reserved.

The nature of the single bond in the three isoelectronic coinage metal dimers Cu-2, Ag-2 and Aug is investigated by means of the ab initio Breathing Orbital Valence Bond (BOVB) method, which allows one to calculate the respective contributions of the covalent and ionic structures to the total wave function, as well as the resonance energy arising from their mixing, It is shown that the BOVB method at its highest level provides bond dissociation energies in very good agreement with reference CCSD(T) values for the three dimers. It is also found that the covalent/ionic resonance energy is important in all three cases, contributing to 40-50% to the total bonding energy, thus qualifying the bonds in Cu-2 and Aug as quasi-charge-shift bonds, and that of Ag-2 as a borderline case in-between classical covalent bond and charge-shift one. These results are further confirmed by analyses of the wave functions in terms of the Atoms-in-Molecule theory, which show that the Laplacian of the density at the bond critical point is large and positive in all three cases, which classifies the three bonds as charge-shift bonds within this theory. (C) 2017 Elsevier B.V. All rights reserved.