The mechanics of charge-shift bonds: A perspective from the electronic stress tensor

Warning! The negative divergence of the stress-tensor does not always yield the Ehrenfest force

It has been assumed that the negative divergence of all stress tensors in common use yields the same force. This work finds that this is untrue, and, in fact, can vary wildly. We demonstrate this for the hydrogen atom, the one-particle isotropic harmonic oscillator, and a particle in an infinite spherical well where the exact density, pair-density, and the first order reduced density matrix are known for ground and excited states without any approximation. The Ehrenfest stress-tensor is introduced as any stress-tensor whose negative divergence will yield the corresponding Ehrenfest force for the same system when the exact wave-function is utilized. Stress-tensors within the literature are examined to show those that are Ehrenfest stress-tensors. Those that differ are demonstrated by how they differ within an exact formulation. The proof that the negative divergence of an Ehrenfest stress-tensor yields the Ehrenfest force is summarized.

Exploring the nature of electron-pair bonds: an energy decomposition analysis perspective

In this paper, the nature of electron-pair bonds is explored from an energy decomposition perspective. The recently developed valence bond energy decomposition analysis (VB-EDA) scheme is extended for the classification of electron-pair bonds, which divides the bond dissociation energy into frozen, reference state switch, quasi-resonance and polarization terms. VB-EDA investigations are devoted to a series of electron-pair bonds, including the covalent bonds (H-H, H₃C-CH₃, H₃C-H, and H₂N-NH₂), the ionic bonds (Na-Cl, Li-F), the charge-shift (CS) bonds (HO-OH, F-F, Cl-Cl, Br-Br, H-F, F-Cl, H₃Si-F and H₃Si-Cl), and the inverted central carbon-carbon bond in [1.1.1] propallene. It is shown that the VB-EDA approach at the VBSCF level is capable of predicting the characters of the electron-pair bonds. The perspective from VB-EDA illustrates that a relatively high value of quasi-resonance term indicates a CS bond while a large portion of polarization term suggests a classical covalent bond.

Quantum chemical study of reaction mechanism between plutonium and nitrogen

The study of the reaction between plutonium and nitrogen is helpful in further understanding the interaction between plutonium and air molecules. Currently, there is no research on the microscopic reaction mechanism of plutonium nitridation reactions. Therefore, the microscopic mechanism of the Pu with N₂ gas phase reaction is explored in this study, based on density functional theory (DFT) using different basis functions. In this paper, the geometry of stationary points on the potential energy surface is optimized. In addition, the transition states are verified by frequency analysis and intrinsic reaction coordination (IRC). Finally, we obtained the reaction potential energy curve and micro reaction pathways. Analysis of the reaction mechanism shows that the reaction of Pu with N₂ has two pathways. Pathway 1 (Pu + N₂ → R1 → TS1 → PuN₂) has a T-shaped transition state and pathway 2 (Pu + N₂ → R2 → TS2 → PuN + N) has an L-shaped transition state. Both transition states have only one imaginary frequency. According to the comparison of the energy at each stagnation point along the two pathways, and the heat energy emitted by the two reaction paths, we found that pathway 1 is the main reaction pathway. The nature of Pu-N bonding evolution along the pathways was studied by atoms in molecules (AIM) and electron localization function (ELF) topological approaches. In order to analyze the role of the plutonium atom 5f orbital in the reaction, the variation in density state along the pathways was measured. Results show that the 5f orbital mainly contributes to the formation of Pu-N bonds, and the influence of temperature on the reaction rate is revealed by calculating the rate constants of the two reaction pathways.

1-Aza-2,4-disilabicyclo[1.1.0]butanes with Superelongated C-N σ-Bonds

Two silylene molecules oxidatively react under formal [1 + 2 + 1]-cycloaddition to the C≡N bond of nitriles to yield 1-aza-2,4-disilabicyclo[1.1.0]butanes (L)(Cl)Si[μ-η^1,2-NC(p-RC₆H₄)]Si(Cl)(L) (L = PhC(NtBu)₂, R = CF₃ (2), F (3), Cl (4), Br (5)). The strongly folded bicyclic SiCNSi cores in 2-5 feature inverted bridgehead carbon atoms and superelongated C-N bonds [1.745(12) to 1.801(2) Å], exceeding the lengths of C-N single bonds in known silaaziridines by up to 23%. Detailed bonding analysis discloses C-N bonding interactions, sharing far-reaching similarities with the central C-C bond in [1.1.1]propellane.

Charge-Shift Bonding: A New and Unique Form of Bonding

Charge-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.

Theoretical study of lithium ionic conductors by electronic stress tensor density and electronic kinetic energy density

We analyze the electronic structure of lithium ionic conductors, Li3PO4 and Li3PS4, using the electronic stress tensor density and kinetic energy density with special focus on the ionic bonds among them. We find that, as long as we examine the pattern of the eigenvalues of the electronic stress tensor density, we cannot distinguish between the ionic bonds and bonds among metalloid atoms. We then show that they can be distinguished by looking at the morphology of the electronic interface, the zero surface of the electronic kinetic energy density. © 2016 Wiley Periodicals, Inc.

Charge-Shift Bonding Emerges as a Distinct Electron-Pair Bonding Family from Both Valence Bond and Molecular Orbital Theories

The charge-shift bonding (CSB) concept was originally discovered through valence bond (VB) calculations. Later, CSB was found to have signatures in atoms-in-molecules and electron-localization-function and in experimental electron density measurements. However, the CSB concept has never been derived from a molecular orbital (MO)-based theory. We now provide a proof of principle that an MO-based approach enables one to derive the CSB family alongside the distinctly different classical family of covalent bonds. In this bridging energy decomposition analysis, the covalent-ionic resonance energy, RECS, of a bond is extracted by cloning an MO-based purely covalent reference state, which is a constrained two-configuration wave function. The energy gap between this reference state and the variational TCSCF ground state yields numerical values for RECS, which correlate with the values obtained at the VBSCF level. This simple MO-based method, which only takes care of static electron correlation, is already sufficient for distinguishing the classical covalent or polar-covalent bonds from charge-shift bonds. The equivalence of the VB and MO-based methods is further demonstrated when both methods are augmented by dynamic correlation. Thus, it is shown from both MO and VB perspectives that the bonding in the CSB family does not arise from electron correlation. Considering that the existence of the CSB family is associated also with quite a few experimental observations that we already reviewed ( Shaik , S. , Danovich , D. , Wu , W. , and Hiberty , P. C. Nat. Chem. , 2009 , 1 , 443 - 449 ), the new bonding concept has passed by now two stringent tests. This derivation, on the one hand, supports the new concept and on the other, it creates bridges between the two main theories of electronic structure.

Electronic stress tensor analysis of molecules in gas phase of CVD process for GeSbTe alloy

We analyze the electronic structure of molecules which may exist in gas phase of chemical vapor deposition process for GeSbTe alloy using the electronic stress tensor, with special focus on the chemical bonds between Ge, Sb, and Te atoms. We find that, from the viewpoint of the electronic stress tensor, they have intermediate properties between alkali metals and hydrocarbon molecules. We also study the correlation between the bond order which is defined based on the electronic stress tensor, and energy-related quantities. We find that the correlation with the bond dissociation energy is not so strong while one with the force constant is very strong. We interpret these results in terms of the energy density on the "Lagrange surface," which is considered to define the boundary surface of atoms in a molecule in the framework of the electronic stress tensor analysis.

Simultaneous Visualization of Covalent and Noncovalent Interactions Using Regions of Density Overlap

We introduce a density-dependent bonding descriptor that enables simultaneous visualization of both covalent and noncovalent interactions. The proposed quantity is tailored to reveal the regions of space, where the total electron density results from a strong overlap of shell, atomic, or molecular densities. We show that this approach is successful in describing a variety of bonding patterns as well as nonbonding contacts. The Density Overlap Regions Indicator (DORI) analysis is also exploited to visualize and quantify the concept of electronic compactness in supramolecular chemistry. In particular, the scalar field is used to compare the compactness in molecular crystals, with a special emphasis on quaterthiophene derivatives with enhanced charge mobilities.

Electronic stress as a guiding force for chemical bonding

In the electron-preceding picture of chemical change, the paramount problem is identifying favorable changes in electronic structure. The electronic stress tensor provides this information; its eigenvectors represent electronic normal modes, pointing the way towards energetically favorable (or unfavorable) chemical rearrangements. The resulting method is well founded in both density functional theory and the quantum theory of atoms in molecules (QTAIM). Stress tensor analysis is a natural way to extend the QTAIM to address chemical reactivity. The definition and basic properties of the electronic stress tensor are reviewed and the inherent ambiguity of the stress tensor is discussed. Extending previous work in which the stress tensor was used to analyze hydrogen-bonding patterns, this work focuses on chemical bonding patterns in organic reactions. Other related material (charge-shift bonding, links to the second-density-derivative tensor) is summarized and reviewed. The stress tensor provides a multifaceted characterization of bonding and can be used to predict and describe bond formation and migration.