Solvent Effect on Dative and Ionic Bond Strengths: A Unified Theory from Potential Analysis and Valence-Bond Computations.

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.

3,4-Dimethylenecyclobutene: A Building Block for Design of Macrocycles with Excited State Aromatic Low-Lying High-Spin States.

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.

Synergistic Charge Transfer Effect in Ferrous Heme-CO Bonding within Cytochrome P450.

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.

The Challenging World of Simple Inorganic Rings: Revisiting Roesky's Ketone and Roesky's Sulfoxide.

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.

Dichotomy of Delocalization/Localization and Charge-Shift Bonding in Germanazene and its Heavier Group 14 Analogues: a Valence Bond Study.

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).

Response to comment on "Superposition of waves or densities: Which is the nature of chemical resonance?"

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.

Superposition of waves or densities: Which is the nature of chemical resonance?

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.

A Valence-Bond-Based Multiconfigurational Density Functional Theory: The λ-DFVB Method Revisited.

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.

A Critical Look at Linus Pauling's Influence on the Understanding of Chemical Bonding.

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.

Na⋠⋠⋠B Bond in NaBH3 - : Solving the Conundrum.

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".

Attraction between electrophilic caps: A counterintuitive case of noncovalent interactions.

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.

Hydrogen- and Halogen-Bonds between Ions of like Charges: Are They Anti-Electrostatic in Nature?

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.

X-ray Constrained Spin-Coupled Wavefunction: a New Tool to Extract Chemical Information from X-ray Diffraction Data.

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.

Pleading for a Dual Molecular-Orbital/Valence-Bond Culture.

Electron pairs through the looking glass might well discover that they can show two faces, one delocalized or the other localized, and that both are perfectly correct. Going back and forth between these two representations, according to which one is the most relevant and insightful for the case at hand, is easy and essential to get a complete understanding of electronic structure.

Response to "Covalent Bonding and Charge Shift Bonds: Comment on 'The Carbon-Nitrogen Bonds in Ammonium Compounds Are Charge Shift Bonds'".

A response to the comment by Gernot Frenking, outlining common ground, as well as differences, with regard to a recent paper on charge-shift bonding in quaternary ammonium cations.

Covalent Bonding and Charge Shift Bonds: Comment on "The Carbon-Nitrogen Bonds in Ammonium Compounds Are Charge Shift Bonds".

The paper by Gershoni-Poranne and Chen (R. Gershoni-Poranne, P. Chen, Chem. Eur. J. 2017, 23, 4659) gives an incorrect definition of covalent bonding. Furthermore, the assignment of so-called charge shift bonds in ammonium compounds has no physical foundation and is conceptually redundant.

Bonding in Heavier Group 14 Zero-Valent Complexes-A Combined Maximum Probability Domain and Valence Bond Theory Approach.

The bonding in heavier Group 14 zero-valent complexes of a general formula L2 E (E=Si-Pb; L=phosphine, N-heterocyclic and acyclic carbene, cyclic tetrylene and carbon monoxide) is probed by combining valence bond (VB) theory and maximum probability domain (MPD) approaches. All studied complexes are initially evaluated on the basis of the structural parameters and the shape of frontier orbitals revealing a bent structural motif and the presence of two lone pairs at the central E atom. For the VB calculations three resonance structures are suggested, representing the "ylidone", "ylidene" and "bent allene" structures, respectively. The influence of both ligands and central atoms on the bonding situation is clearly expressed in different weights of the resonance structures for the particular complexes. In general, the bonding in the studied E0 compounds, the tetrylones, is best described as a resonating combination of "ylidone" and "ylidene" structures with a minor contribution of the "bent allene" structure. Moreover, the VB calculations allow for a straightforward assessment of the π-backbonding (E→L) stabilization energy. The validity of the suggested resonance model is further confirmed by the complementary MPD calculations focusing on the E lone pair region as well as the E-L bonding region. Likewise, the MPD method reveals a strong influence of the σ-donating and π-accepting properties of the ligand. In particular, either one single domain or two symmetrical domains are found in the lone pair region of the central atom, supporting the predominance of either the "ylidene" or "ylidone" structures having one or two lone pairs at the central atom, respectively. Furthermore, the calculated average populations in the lone pair MPDs correlate very well with the natural bond orbital (NBO) populations, and can be related to the average number of electrons that is backdonated to the ligands.

On the Nature of Bonding in Parallel Spins in Monovalent Metal Clusters.

As we approach the Lewis model centennial, it may be timely to discuss novel bonding motifs. Accordingly, this review discusses no-pair ferromagnetic (NPFM) bonds that hold together monovalent metallic atoms using exclusively parallel spins. Thus, without any traditional electron-pair bonds, the bonding energy per atom in these clusters can reach 20 kcal mol(-1). This review describes the origins of NPFM bonding using a valence bond (VB) analysis, which shows that this bonding motif arises from bound triplet electron pairs that are delocalized over all the close neighbors of a given atom in the cluster. The VB model accounts for the tendency of NPFM clusters to assume polyhedral shapes with rather high symmetry and for the very steep rise of the bonding energy per atom. The advent of NPFM clusters offers new horizons in chemistry of highly magnetic species sensitive to magnetic and electric fields.

The application of cholesky decomposition in valence bond calculation.

The Cholesky decomposition (CD) technique, used to approximate the two-electron repulsion integrals (ERIs), is applied to the valence bond self-consistent field (VBSCF) method. Test calculations on ethylene, C2 n H2 n +2 , and C2 n H4 n -2 molecules (n = 1-7) show that the performance of the VBSCF method is much improved using the CD technique, and thus, the integral transformation from basis functions to VB orbitals is no longer the bottleneck in VBSCF calculations. The errors of the CD-based ERIs and of the total energy are controlled by the CD threshold, for which a value of 10(-6) ensures to control the total energy error within 10(-6) Hartree. © 2016 Wiley Periodicals, Inc.

Adjacent Lone Pair (ALP) Effect: A Computational Approach for Its Origin.

The adjacent lone pair (ALP) effect is an experimental phenomenon in certain nitrogenous heterocyclic systems exhibiting the preference of the products with lone pairs separated over other isomers with lone pairs adjacent. A theoretical elucidation of the ALP effect requires the decomposition of intramolecular energy terms and the isolation of lone pair-lone pair interactions. Here we used the block-localized wavefunction (BLW) method within the ab initio valence bond (VB) theory to derive the strictly localized orbitals which are used to accommodate one-atom centered lone pairs and two-atom centered σ or π bonds. As such, interactions among electron pairs can be directly derived. Two-electron integrals between adjacent lone pairs do not support the view that the lone pair-lone pair repulsion is responsible for the ALP effect. Instead, the disabling of π conjugation greatly diminishes the ALP effect, indicating that the reduction of π conjugation in deprotonated forms with two σ lone pairs adjacent is one of the major causes for the ALP effect. Further electrostatic potential analysis and intramolecular energy decomposition confirm that the other key factor is the favorable electrostatic attraction within the isomers with lone pairs separated.