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Valence bond theory (VB) was used to determine the extent and driving forces for covalent vs. dative bonding in 10-valence-electron diatomic molecules N2, CO, NO+, CN−, P2, SiS, PS+, and SiP−. VBSCF calculations were performed at the CCSD(T)/cc-pVDZ optimized geometries. The full triply bonded system included 20 VB structures. A separation of the σ and π space allowed for a subdivision of the full 20 structure set into sets of 8 and 3 for the π and σ systems, respectively. The smaller structure sets allowed for a more focused look at each type of bond. In situ bond energies for σ bonds, individual π bonds, the π system, and triple bonds follow expected trends. Our data shows that N2 and P2 have three covalent bonds whereas CO and SiS contain two covalent and one dative bond, and charged species NO+, CN−, PS+, and SiP− are a mixture of N2 and CO type electronic arrangements, resulting in a nearly equal charge distribution. Dative bonds prefer to be in the π position due to enhanced σ covalency and π resonance. Both σ and π resonance energies depend on a balance of ionic strength, orbital compactness, σ constraints, and bond directionality. Resonance energy is a major contributor to bond strength, making up more than 50% of the π bonds in SiS and PS+ (charge-shift bonds), and is greater than charge transfer in dative bonds. [ABSTRACT FROM AUTHOR]

Solvent molecules interact with a solute through various intermolecular forces. Here we employed a potential energy surface (PES) analysis to interpret the solvent‐induced variations in the strengths of dative (Me3NBH3) and ionic (LiCl) bonds, which possess both ionic and covalent (neutral) characteristics. The change of a bond is driven by the gradient (force) of the solvent‐solute interaction energy with respect to the focused bond length. Positive force shortens the bond length and increases the bond force constant, leading to a blue‐shift of the bond stretching vibrational frequency upon solvation. Conversely, negative force elongates the bond, resulting in a reduced bond force constant and red‐shift of the stretching vibrational frequency. The different responses of Me3NBH3 and LiCl to solvation are studied with valence bond (VB) theory, as Me3NBH3 and LiCl are dominated by the neutral covalent VB structure and the ionic VB structure, respectively. The dipole moment of an ionic VB structure increases along the increasing bond distance, while the dipole moment of a neutral covalent VB structure increases with the decreasing bond distance. The roles of the dominating VB structures are further examined by the geometry optimizations and frequency calculations with the block‐localized wavefunction (BLW) method. [ABSTRACT FROM AUTHOR]

This article explores the possible presence of a pentacle valence bond structure in C5 ${_5 }$ cyclic molecules. At this end, we have used quantum chemistry tools to elucidate the possible arrangement and the nature of chemical bonds within linear, cyclic, and three‐dimensional structures only formed by five carbon atoms. While the linear structure is clearly the most stable one, local minima were obtained for both bi‐ and three‐dimensional structures. Using the localization‐delocalization matrices approach, we characterize both the minimum linear structure and the cyclic ones. Interestingly, the linear structure is a combination of ionic and covalent bonds, albeit the four distances are almost identical, when using Density Functional Theory. For cyclic C5 ${_5 }$ , the pentacle bonding arrangement emerges as a significant Lewis structure, indicative of an unusual formal configuration characterized by five intersecting C−C bonds. Our calculations show that this pentacle arrangement in cyclic C5 ${_5 }$ scheme is also present in the more known cyclo‐pentadienyl molecule. [ABSTRACT FROM AUTHOR]

3,4‐Dimethylenecyclobutene (DMCB) is an unusual isomer of benzene. Motivated by recent synthetic progress to substituted derivatives of this scaffold, we carried out a theoretical and computational analysis with a particular focus on the extent of (anti)aromatic character in the lowest excited states of different multiplicities. We found that the parent DMCB is non‐aromatic in its singlet ground state (S0), lowest triplet state (T1), and lowest singlet excited state (S1), while it is aromatic in its lowest quintet state (Q1) as this state is represented by a triplet multiplicity cyclobutadiene (CBD) ring and two uncoupled same‐spin methylene radicals. Interestingly, the Q1 state, despite having four unpaired electrons, is placed merely 4.8 eV above S0, and there is a corresponding singlet tetraradical 0.16 eV above. The DMCB is potentially a highly useful structural motif for the design of larger molecular entities with interesting optoelectronic properties. Here, we designed macrocycles composed of fused DMCB units, and according to our computations, two of these have low‐lying nonet states (i. e., octaradical states) at energies merely 2.40 and 0.37 eV above their S0 states as a result of local Hückel‐ and Baird‐aromatic character of individual 6π‐ and 4π‐electron monocycles. [ABSTRACT FROM AUTHOR]

Abstract This article explores the possible presence of a pentacle valence bond structure in C 5 cyclic molecules. At this end, we have used quantum chemistry tools to elucidate the possible arrangement and the nature of chemical bonds within linear, cyclic, and three‐dimensional structures only formed by five carbon atoms. While the linear structure is clearly the most stable one, local minima were obtained for both bi‐ and three‐dimensional structures. Using the localization‐delocalization matrices approach, we characterize both the minimum linear structure and the cyclic ones. Interestingly, the linear structure is a combination of ionic and covalent bonds, albeit the four distances are almost identical, when using Density Functional Theory. For cyclic C 5 , the pentacle bonding arrangement emerges as a significant Lewis structure, indicative of an unusual formal configuration characterized by five intersecting C−C bonds. Our calculations show that this pentacle arrangement in cyclic C 5 scheme is also present in the more known cyclo‐pentadienyl molecule.

Valence bond theory (VB) was used to determine the extent and driving forces for covalent vs. dative bonding in 10-valence-electron diatomic molecules N2, CO, NO+, CN−, P2, SiS, PS+, and SiP−. VBSCF calculations were performed at the CCSD(T)/cc-pVDZ optimized geometries. The full triply bonded system included 20 VB structures. A separation of the σ and π space allowed for a subdivision of the full 20 structure set into sets of 8 and 3 for the π and σ systems, respectively. The smaller structure sets allowed for a more focused look at each type of bond. In situ bond energies for σ bonds, individual π bonds, the π system, and triple bonds follow expected trends. Our data shows that N2 and P2 have three covalent bonds whereas CO and SiS contain two covalent and one dative bond, and charged species NO+, CN−, PS+, and SiP− are a mixture of N2 and CO type electronic arrangements, resulting in a nearly equal charge distribution. Dative bonds prefer to be in the π position due to enhanced σ covalency and π resonance. Both σ and π resonance energies depend on a balance of ionic strength, orbital compactness, σ constraints, and bond directionality. Resonance energy is a major contributor to bond strength, making up more than 50% of the π bonds in SiS and PS+ (charge-shift bonds), and is greater than charge transfer in dative bonds.

We conducted ab initio valence bond (VB) calculations employing the valence bond self-consistent field (VBSCF) and breathing orbital valence bond (BOVB) methods to investigate the nature of the coordination bonding between ferrous heme and carbon monoxide (CO) within cytochrome P450. These calculations revealed the significant influence exerted by both proximal and equatorial ligands on the π-backdonation effect from the heme to the CO. Moreover, our VB calculations unveiled a phenomenon of synergistic charge transfer (sCT). In the case of ferrous heme–CO bonding, the significant stabilization in this sCT arises from cooperative resonance between the VB structures associated with σ donation and π backdonation. Unlike many other ligands, CO possesses the unique ability to establish two mutually perpendicular π-backdonation orbital interaction pairs, leading to an intensified stabilization attributed to σ–π resonance. Furthermore, while of a smaller energy magnitude, sCT due to one π–π pair is also present, contributing to the differential stabilization of ferrous heme–CO bonding. [ABSTRACT FROM AUTHOR]

The chemical bonding of 3C2O and 3N2C is analyzed in this work through the topological quantum approach using the electronic localization function (ELF) at the CASSCF level and by energetic calculations at the CCSD(T) level using four different basis sets. The results show that the dissociation of the molecules occurs via cleavage of the C‐C bond in the case of 3C2O, while in the case of 3N2C, it occurs via cleavage of the N‐C bond. Furthermore, the results obtained with ELF show monosynaptic basins containing excess electrons and disynaptic basins with a low electron population. This leads us to indicate the existence of three‐center‐two‐electron bonds according to previous results. From the valence bond model, a series of resonance structures have been proposed that support our calculations. In addition, the proposed structures have an ionic nature, indicating a charge shift character. [ABSTRACT FROM AUTHOR]

The surprising differences between the experimental solid‐state and calculated gas‐phase structures of 5‐oxo‐1,3,2,4‐dithiadiazole (Roesky's ketone, 1) and 1‐oxo‐1,2,4,3,5‐trithiadiazole (Roesky's sulfoxide, 2), identified and studied in a series of papers published between 2004 and 2010 but then never satisfactorily explained, have been revisited, making use of the more advanced computational possibilities currently available. The previous calculations' considerable overestimations of the C−S and S−S bond lengths in 1 and 2, respectively, have been partly explained based on the results of periodic calculations and the application of Valence Bond (VB) Theory. In the case of 1, the crystal environment appears to stabilize a structure with a highly polarized C=O bond, which features a C−S bond with considerable double‐bond character – an effect which does not exist for the isolated molecule – explaining the much shorter bond in the solid state. For 2, a similar conclusion can be drawn for the S−S distance. For both compounds, though, packing effects are not the sole source of the differences: the inability of Density Functional Theory (DFT) to properly deal with the electronic structures of these apparently simple main‐group systems remains a contributing factor. [ABSTRACT FROM AUTHOR]

We present here a valence bond analysis of structure and π‐delocalization in Ge3(NH)3, which models germanazene that was prepared by Power et al. To get a broader perspective, we explore the entire E3(NH)3 series (E=C, Si, Ge, Sn, Pb). Thus, while (4n+2)π systems of carbon rings are aromatic with cyclic π‐delocalization, the E3(NH)3 rings are dominated by a nonbonded structure, wherein π‐lone pairs are localized on the N atoms. Nevertheless, these molecules enjoy large covalent‐ionic resonance energies of 153.0, 86.6, 74.2, 61.2, and 58.9 kcal/mol, respectively, for E=C, Si, Ge, Sn, Pb. The covalent‐ionic mixing in E3(NH)3 creates π‐systems, which are stabilized by charge‐shift bonding. Thus, unlike in benzene, in Ge3(NH)3 delocalization of π‐electron pairs of the N atoms is primarily confined to the domains of their adjacent Ge atoms. These features carry over to the substituted germanazene, Ge3(NAr)3 (Ar=Ph). [ABSTRACT FROM AUTHOR]

We conducted ab initio valence bond (VB) calculations employing the valence bond self-consistent field (VBSCF) and breathing orbital valence bond (BOVB) methods to investigate the nature of the coordination bonding between ferrous heme and carbon monoxide (CO) within cytochrome P450. These calculations revealed the significant influence exerted by both proximal and equatorial ligands on the π-backdonation effect from the heme to the CO. Moreover, our VB calculations unveiled a phenomenon of synergistic charge transfer (sCT). In the case of ferrous heme–CO bonding, the significant stabilization in this sCT arises from cooperative resonance between the VB structures associated with σ donation and π backdonation. Unlike many other ligands, CO possesses the unique ability to establish two mutually perpendicular π-backdonation orbital interaction pairs, leading to an intensified stabilization attributed to σ–π resonance. Furthermore, while of a smaller energy magnitude, sCT due to one π–π pair is also present, contributing to the differential stabilization of ferrous heme–CO bonding.

A novel strategy for the construction of many‐electron symmetry‐adapted wave function is proposed for ab initio valence bond (VB) calculations and is implemented for valence bond self‐consistent filed (VBSCF) and breathing orbital valence bond (BOVB) methods with various orbital optimization algorithms. Symmetry‐adapted VB functions are constructed by the projection operator of symmetry group. The many‐electron symmetry‐adapted wave function is expressed in terms of symmetry‐adapted VB functions, and thus the VB calculations can be performed with the molecular symmetry restriction. Test results show that molecular symmetry reduces the computational cost of both the iteration numbers and CPU time. Furthermore, excited states with specific symmetry can be conveniently obtained in VB calculations by using symmetry‐adapted VB functions. [ABSTRACT FROM AUTHOR]

This Rosarium Philosophorum essay tells the story of the author's "conversion" to a theorist, and then the events which led him to stumble over valence bond (VB) theory, and his developments of "VB diagrams" as conceptual tools which enable one to describe all chemical reactions. The story continues to the adventure with the enzyme Cytochrome P450, and how this interest led eventually the author to treat the reactivity of this enzyme using VB diagrams. And finally, the essay describes the author's struggle with complexity through molecular dynamics of these enzymes. This is also a story of interactions between individuals who seek insight and wisdom and how they influence one another through friendships and teacher‐disciples relations. This is the key wisdom one garners through scientific life. [ABSTRACT FROM AUTHOR]

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

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". [ABSTRACT FROM AUTHOR]

Resonance is a fundamental and widely used concept in chemistry, but there exist two distinct theories of chemical resonance, based on quite different and incompatible premises: the wave‐function‐based resonance theory (WFRT), assuming the superposition of wave functions, versus the density‐matrix‐based resonance theory (DMRT), which interprets the resonance phenomenon as the superposition of density matrices. The latter theory, best known to the chemistry community as the natural resonance theory (NRT), has received much more popularity than the WFRT. In this contribution, the DMRT is shown to be inherently inadequate: (i) the exact density matrix expansion is mathematically impossible unless unphysical negative weights are introduced; (ii) any approximate density matrix representing the resonance hybrid lacks the idempotent property. Therefore, the validity of the NRT ansatz should be seriously questioned. The WFRT seems the only reasonable explanation of resonance so far, and has been shown to provide valuable insights into diverse chemical problems. [ABSTRACT FROM AUTHOR]

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

The influence of Linus Pauling on the understanding of chemical bonding is critically examined. Pauling deserves credit for presenting a connection between the quantum theoretical description of chemical bonding and Gilbert Lewis’s classical bonding model of localized electron pair bonds for a wide range of chemistry. Using the concept of resonance that he introduced, he was able to present a consistent description of chemical bonding for molecules, metals, and ionic crystals which was used by many chemists and subsequently found its way into chemistry textbooks. However, his one-sided restriction to the valence bond method and his rejection of the molecular orbital approach hindered further development of chemical bonding theory for a while and his close association of the heuristic Lewis binding model with the quantum chemical VB approach led to misleading ideas until today.

One of the well‐established methods of modern quantum crystallography is undoubtedly the X‐ray constrained wavefunction (XCW) approach, a technique that enables the determination of wavefunctions which not only minimize the energy of the system under examination, but also reproduce experimental X‐ray diffraction data within the limit of the experimental errors. Initially proposed in the framework of the Hartree–Fock method, the strategy has been gradually extended to other techniques of quantum chemistry, but always remaining limited to a single‐determinant ansatz for the wavefunction to extract. This limitation has been recently overcome through the development of the novel X‐ray constrained spin‐coupled (XCSC) approach [Genoni et al. (2018). Chem. Eur. J.24, 15507–15511] which merges the XCW philosophy with the traditional spin‐coupled strategy of valence bond theory. The main advantage of this new technique is the possibility of extracting traditional chemical descriptors (e.g. resonance structure weights) compatible with the experimental diffraction measurements, without the need to introduce information a priori or perform analyses a posteriori. This paper provides a detailed theoretical derivation of the fundamental equations at the basis of the XCSC method and also introduces a further advancement of its original version, mainly consisting in the use of molecular orbitals resulting from XCW calculations at the Hartree–Fock level to describe the inactive electrons in the XCSC computations. Furthermore, extensive test calculations, which have been performed by exploiting high‐resolution X‐ray diffraction data for salicylic acid and by adopting different basis sets, are presented and discussed. The computational tests have shown that the new technique does not suffer from particular convergence problems. Moreover, all the XCSC calculations provided resonance structure weights, spin‐coupled orbitals and global electron densities slightly different from those resulting from the corresponding unconstrained computations. These discrepancies can be ascribed to the capability of the novel strategy to capture the information intrinsically contained in the experimental data used as external constraints. [ABSTRACT FROM AUTHOR]

Intermolecular attractive interaction between electrophilic sites is a counterintuitive phenomenon, as the electrostatic interaction therein is repulsive and destabilizing. Here, we confirm this phenomenon in four representative complexes, using state‐of‐the‐art quantum mechanical methods. By employing the block‐localized wavefunction (BLW) method, which can turn off intermolecular charge transfer interactions, we profoundly demonstrated the significance of charge transfer interactions in these seemingly counterintuitive complexes. Indeed, after being "turned off" the intermolecular charge transfer interaction in, for example, the FNSi···BrF complex, the originally attractive intermolecular interaction turns to be repulsive. The energy decomposition approach based on the BLW method (BLW‐ED) can partition the overall stability gained on the formation of intermolecular noncovalent interaction into several physically meaningful components. According to the BLW‐ED analysis, the electrostatic repulsion in these counterintuitive cases is overwhelmed by the stabilizing polarization, dispersion interaction, and most importantly, the charge transfer interaction, resulting in the eventual counterintuitive overall attraction. The present study suggests that, predicting bonding sites of noncovalent interactions using only the "hole" concept may be not universally sufficient, because other significant stabilizing factors will contribute to the stability and sometimes, play even bigger roles than the electrostatic interaction and consequently govern the complex structures. © 2018 Wiley Periodicals, Inc. Computations based on the block‐localized wavefunction (BLW) method show that the charge transfer interactions are largely responsible for the intermolecular attraction between electrophilic sites which otherwise seems counterintuitive. If the intermolecular charge transfer interaction in the FNSi···BrF complex is "turned off," the originally attractive intermolecular interaction turns to be repulsive. The subsequent BLW energy decomposition analyses indicate that the electrostatic repulsion in other similar counterintuitive cases is overwhelmed by the stabilizing polarization, dispersion interaction, and most importantly, the charge transfer interaction. [ABSTRACT FROM AUTHOR]

I reply to the comment by Weinhold and Glendening on the article (J. Comput. Chem. 2021, 42, 412). I provide further explanation and an additional numerical example to support my previous assertion that the present form of natural resonance theory is fundamentally flawed, at least within the DFT framework. [ABSTRACT FROM AUTHOR]

A recently developed valence-bond-based multireference density functional theory, named λ-DFVB, is revisited in this paper. λ-DFVB remedies the double-counting error of electron correlation by decomposing the electron–electron interactions into the wave function term and density functional term with a variable parameter λ. The λ value is defined as a function of the free valence index in our previous scheme, denoted as λ-DFVB(K) in this paper. Here we revisit the λ-DFVB method and present a new scheme based on natural orbital occupation numbers (NOONs) for parameter λ, named λ-DFVB(IS), to simplify the process of λ-DFVB calculation. In λ-DFVB(IS), the parameter λ is defined as a function of NOONs, which are straightforwardly determined from the many-electron wave function of the molecule. Furthermore, λ-DFVB(IS) does not involve further self-consistent field calculation after performing the valence bond self-consistent field (VBSCF) calculation, and thus, the computational effort in λ-DFVB(IS) is approximately the same as the VBSCF method, greatly reduced from λ-DFVB(K). The performance of λ-DFVB(IS) was investigated on a broader range of molecular properties, including equilibrium bond lengths and dissociation energies, atomization energies, atomic excitation energies, and chemical reaction barriers. The computational results show that λ-DFVB(IS) is more robust without losing accuracy and comparable in accuracy to high-level multireference wave function methods, such as CASPT2.

The X‐ray constrained wavefunction (XCW) approach is a reliable and widely used method of quantum crystallography that allows the determination of wavefunctions compatible with X‐ray diffraction data. So far, all the existing XCW techniques have been developed in the framework of molecular orbital theory and, consequently, provide only pictures of the "experimental" electronic structures that are far from the traditional chemical perception. Here a new strategy is proposed that, by combining the XCW philosophy with the spin‐coupled method of valence bond theory, enables direct extraction of traditional chemical information (e.g. weights of resonance structures) from X‐ray diffraction measurements. Preliminary results have shown that the new technique is really able to efficiently capture the effects of the crystal environment on the electronic structure, and can be considered as a new useful tool to perform chemically sound analyses of the X‐ray diffraction data. From X‐ray diffraction to resonance structures weights. A new quantum crystallographic method that enables taking into account the X‐ray diffraction data in full Valence Bond calculations is proposed. Exploiting the new technique, insights into the electron distributions around each atomic center and, particularly, into the weights of resonance structures can be directly obtained from usual X‐ray diffraction measurements. [ABSTRACT FROM AUTHOR]

Recent theoretical studies suggested that hydrogen bonds between ions of like charges are of a covalent nature due to the dominating nD→σ*H‐A charge‐transfer (CT) interaction. In this work, energy profiles of typical hydrogen (H) and halogen (X) bonding systems formed from ions of like charges are explored using the block‐localized wavefunction (BLW) method, which can derive optimal geometries and wave functions with the CT interaction “turned off.” The results demonstrate that the kinetic stability, albeit reduced, is maintained for most investigated systems even after the intermolecular CT interaction is quenched. Further energy decomposition analyses based on the BLW method reveal that, despite a net repulsive Coulomb repulsion, a stabilizing component exists due to the polarization effect that plays significant role in the kinetic stability of all systems. Moreover, the fingerprints of the augmented electrostatic interaction due to polarization are apparent in the variation patterns of the electron density. All in all, much like in standard H‐ and X‐bonds, the stability of such bonds between ions of like charges is governed by the competition between the stabilizing electrostatic and charge transfer interactions and the destabilizing deformation energy and Pauli exchange repulsion. While in most cases of “anti‐electrostatic” bonds the CT interaction is of a secondary importance, we also find cases where CT is decisive. As such, this work validates the existence of anti‐electrostatic H‐ and X‐bonds. © 2017 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]