We present a new dimensional scaling transformation of the Schrodinger equation for the two electron bond. This yields, for the first time, a good description of the two electron bond via D-scaling. There also emerges, in the large-D limit, an intuitively appealing semiclassical picture, akin to a molecular model proposed by Niels Bohr in 1913. In this limit, the electrons are confined to specific orbits in the scaled space, yet the uncertainty principle is maintained because the scaling leaves invariant the position-momentum commutator. A first-order perturbation correction, proportional to 1/D, substantially improves the agreement with the exact ground state potential energy curve. The present treatment is very simple mathematically, yet provides a strikingly accurate description of the potential energy curves for the lowest singlet, triplet and excited states of H_2. We find the modified D-scaling method also gives good results for other molecules. It can be combined advantageously with Hartree-Fock and other conventional methods.
We introduce a vector-based interpretation of the chemical bond within the quantum theory of atoms in molecules (QTAIM), the bond-path framework set $\mathbb{B} = \{p, q, r\}$, to follow variations in the 3-D morphology of all bonds for the four infra-red (IR) active normal modes of benzene. The bond-path framework set comprises three unique paths $p$, $q$ and $r$ where $r$ is the familiar QTAIM bond concept of bond-path ($r$) while the two new paths $p$ and $q$ are formulated from the least and most preferred directions of electron density accumulation respectively. We find 3-D distortions in…
A model of localized electron wave packets (WPs) with variable position and width (floating and breathing) that are spin-coupled as per the valence-bond theory is presented. It produces accurate potential energy curves of LiH in the ground singlet and triplet states. Quantization in a mean-field approximation of the motion of a WP that corresponds to the Li 2s electron generates semi-quantitative potential energy curves of low energy excited states. Real-time semiquantal dynamics of the WP induced by an intense laser pulse gives high-harmonic generation spectra that capture qualitative feature…
Our curiosity-driven desire to "see" chemical bonds dates back at least one-hundred years, perhaps to antiquity. Sweeping improvements in the accuracy of measured and predicted electron charge densities, alongside our largely bondcentric understanding of molecules and materials, heighten this desire with means and significance. Here we present a method for analyzing chemical bonds and their energy distributions in a two-dimensional projected space called the condensed charge density. Bond "silhouettes" in the condensed charge density can be reverse-projected to reveal precise three-dimensional…
Crystal orbital overlap population based on all-electron ab initio simulation with numeric atom-centered orbitals and its application to chemical-bonding analysis in Li-intercalated layered materials
Chemical bonding is the stabilization of a composite molecular system caused by different interactions in and between the subsystems, among the strong kinds of bonding is covalent bonding especially important. Characteristic for covalent bonding are small atom groups with short distances between the involved atoms, indicating that covalent bonding is essentially a local effect, according to Lewis, this is caused by shared electron pairs. However, the energetic stabilization is an approximately additive one-electron effect, as was shown by Ruedenberg and coworkers. In systems composed of many-e…
The "chemical bond" is a central concept in molecular sciences, but there is no consensus as to what a bond actually is. Therefore, a variety of bonding models have been developed, each defining the structure of molecules in a different manner with the goal of explaining and predicting chemical properties. This thesis describes the initial development of gradient bundle analysis (GBA), a chemical bonding model that creates a high resolution picture of chemical interactions within the charge density framework. GBA is based on concepts from the quantum theory of atoms in molecules (QTAIM), but u…
We use a new interpretation of the chemical bond within QTAIM. The bond-path framework set $\mathbb{B} = \{p, q, r\}$ with associated linkages with lengths $\mathbb{H}^*,m\mathbb{H}$ and the familiar bond-path length is used to describe a torsion $θ$, $0.0^{\circ} \leq θ\lt 22.0^{\circ}$ of \emph{para}-substituted biphenyl, $\mathrm{C}_{12}\mathrm{H}_{9-x}$, $x = \mathrm{N}(\mathrm{CH}_3)_2$, $\mathrm{NH}_2$, $\mathrm{CH}_3$, CHO, CN, $\mathrm{NO}_{2}$. We include consideration of the H---H bonding interactions and find that the lengths $\mathbb{H} \gt \mathbb{H}^{*}$ that we explain in terms …
The finite-basis, pair formulation of the Spectral Theory of chemical bonding is briefly surveyed. Solutions of the Born-Oppenheimer polyatomic Hamiltonian totally antisymmetric in electron exchange are obtained from diagonalization of an aggregate matrix built up from conventional diatomic solutions to atom-localized problems. A succession of transformations of the bases of the underlying matrices and the unique character of symmetric orthogonalization in producing the archived matrices calculated "once-of-all" in the pairwise-antisymmetrized basis are described. Application is made to molecu…
This paper introduces a new representation method that is mainly based on chemical bonds among atoms in materials. Each chemical bond and its surrounded atoms are considered as a unified unit or a local structure that is expected to reflect a part of materials' nature. First, a material is separated into local structures; and then represented as matrices, each of which is computed by using information about the corresponding chemical bond as well as orbital-field matrices of two related atoms. After that, all local structures of the material are utilized by using the statistics point of view. …
Chemical bond analysis for the entire periodic table: Energy Decomposition and Natural Orbitals for Chemical Valence in the Four-Component Relativistic Framework
The chemistry (composition and bonding information) of metallic glasses (MGs) is at least as important as structural topology for understanding their properties and production/processing peculiarities. This article reports a machine learning (ML)-based approach that brings an unprecedented "big picture" view of chemical bond strengths in MGs of a prototypical alloy system. The connection between electronic structure and chemical bonding is given by crystal orbital Hamilton population (COHP) analysis; within the framework of density functional theory (DFT). The stated comprehensive overview is …
This is a critical review of MAX-phase carbides and nitrides from an electronic-structure and chemical bonding perspective. This large group of nanolaminated materials is of great scientific and technological interest and exhibit a combination of metallic and ceramic features. These properties are related to the special crystal structure and bonding characteristics with alternating strong M-C bonds in high-density MC slabs, and relatively weak M-A bonds between the slabs. Here, we review the trend and relationship between the chemical bonding, conductivity, elastic and magnetic properties of t…
A precise discussion of a single bond requires consideration of two-particle wave function for the particles involved. Here we define and determine rigorously the intrinsic covalency and connected characteristics on the canonical example of \ch{H2} molecule. This is achieved by starting from analytic form for the two--particle wave function for electrons forming the bond, in which we single out the atomic contribution (\textit{atomicity}) in an unequivocal manner. The presence the of atomicity and ionicity factors complements the existing attributes of the bond. In this way, a gradual evolutio…
We assess the predictive accuracy of perturbation theory based estimates of changes in covalent bonding due to linear alchemical interpolations among molecules. We have investigated $σ$ bonding to hydrogen, as well as $σ$ and $π$ bonding between main-group elements, occurring in small sets of iso-valence-electronic molecular species with elements drawn from second to fourth rows in the $p$-block of the periodic table. Numerical evidence suggests that first order estimates of covalent bonding potentials can achieve chemical accuracy if (i) the alchemical interpolation is vertical (fixed geometr…
The molecular dissociation energy has often been explained and discussed in terms of singlet bonds, formed by bounded pairs of valence electrons. In this work we use a highly correlated resonating valence bond ansatz, providing a consistent paradigm for the chemical bond, where spin fluctuations are shown to play a crucial role. Spin fluctuations are known to be important in magnetic systems and correspond to the zero point motion of the spin waves emerging from a magnetic broken symmetry state. Recently, in order to explain the excitation spectrum of the carbon dimer, an unusual quadruple bon…
According to the correspondence principle, classical mechanics and quantum mechanics agree in the semiclassical limit, although presently it has become more and more clear how intriguing would be to try to fix a boundary between them. Here we give a significant example in which the agreement concerns Newtonian trajectories of an electron with initial data corresponding to a quantum ground state. The example is the simplest case in which a chemical bond occurs, i.e. the $H_2^+$ ion. By molecular dynamics simulations for the full system (two protons and one electron) we show that there exist ini…
A dielectric material's response to light is macroscopically described by electric displacement fields due to polarization and susceptibility, but the atomistic origin is light-cycle-driven motion of electron densities in the restoring forces of the atomic environment. Here we report how the macroscopic nonlinear-optical response of a heteronuclear crystal relates to the alignment and orientation of its chemical bonds. Substantial nonlinear emission is only observed if the electric field of an optical single-cycle pulse points from the less electronegative to the more electronegative element a…
The quantum mechanical description of the chemical bond is generally given in terms of delocalized bonding orbitals, or, alternatively, in terms of correlations of occupations of localised orbitals. However, in the latter case, multiorbital correlations were treated only in terms of two-orbital correlations, although the structure of multiorbital correlations is far richer; and, in the case of bonds established by more than two electrons, multiorbital correlations represent a more natural point of view. Here, for the first time, we introduce the true multiorbital correlation theory, consisting…
Neural networks are being used to make new types of empirical chemical models as inexpensive as force fields, but with accuracy close to the ab-initio methods used to build them. Besides modeling potential energy surfaces, neural-nets can provide qualitative insights and make qualitative chemical trends quantitatively predictable. In this work we present a neural-network that predicts the energies of molecules as a sum of bond energies. The network learns the total energies of the popular GDB9 dataset to a competitive MAE of 0.94 kcal/mol. The method is naturally linearly scaling, and applicab…
The structure of Ge$_{20}$Sb$_{10}$S$_{70}$, Ge$_{23}$Sb$_{12}$S$_{65}$ and Ge$_{26}$Sb$_{13}$S$_{61}$ glasses was investigated by neutron diffraction (ND), X-ray diffraction (XRD), extended X-ray absorption fine structure (EXAFS) measurements at the Ge and Sb K-edges as well as Raman scattering. For each composition, large scale structural models were obtained by fitting simultaneously diffraction and EXAFS data sets in the framework of the reverse Monte Carlo (RMC) simulation technique. Ge and S atoms have 4 and 2 nearest neighbors, respectively. The structure of these glasses can be describ…
The advent of ultrashort soft x-ray pulse sources permits the use of established gas phase spectroscopy methods to investigate ultrafast photochemistry in isolated molecules with element and site specificity. In the present study, we simulate excited state wavepacket dynamics of a prototypical process, the ultrafast photodissociation of methyl iodide. Based on the simulation, we calculate time-dependent excited state carbon edge photoelectron and Auger electron spectra. We observe distinct signatures in both types of spectra and show their direct connection to C-I bond dissociation and charge …
We developed recently [A. Ferté, et al., J. Phys. Chem. Lett. 11, 4359 (2020)] a method to compute single site double core hole (ssDCH or K$^{-2}$) spectra. We refer to that method as NOTA+CIPSI. In the present paper this method is applied to the O K$^{-2}$ spectrum of the CO$_2$ molecule, and we use this as an example to discuss in detail its convergence properties. Using this approach, a theoretical spectra in excellent agreement with the experimental one is obtained. Thanks to a thorough interpretation of the shake-up states responsible for the main satellite peaks and with the help of a co…
Recently, the correlation theory of the chemical bond was developed, which applies concepts of quantum information theory for the characterization of chemical bonds, based on the multiorbital correlations within the molecule. Here for the first time, we extend the use of this mathematical toolbox for the description of electron-deficient bonds. We start by verifying the theory on the textbook example of a molecule with three-center two-electron bonds, namely the diborane(6). We then show that the correlation theory of the chemical bond is able to properly describe bonding situation in more exo…
SITH: A Quantum-Chemical Framework for Predicting Bond Destabilization in Stretched Molecules
Heidelberg Institute for Theoretical Studies（海德堡理论研究所）；Max Planck Institute for Polymer Research（马克斯·普朗克聚合物研究所）；Department of Physics and Astronomy, University of Heidelberg（海德堡大学物理与天文学系）；University of Notre Dame（圣母大学）；Interdisciplinary Center for Scientific Computing, Heidelberg University（海德堡大学跨学科科学计算中心）
Transferability of the chemical bond-based machine learning model for dipole moment: the GHz to THz dielectric properties of liquid propylene glycol and polypropylene glycol
The short range order in Ge$_{30}$Ga$_{5}$Sb$_{10}$Se$_{55}$ and Ge$_{21}$Ga$_{5}$Sb$_{10}$Se$_{64}$ glasses was investigated by X-ray (XRD) and neutron diffraction (ND) as well as extended X-ray absorption fine structure (EXAFS) measurements at the Ge, Ga, Sb and Se K-edges. Large scale structural models were obtained by fitting simultaneously the experimental data sets by reverse Monte Carlo (RMC) simulation technique. It was found that Ge, Sb and Se atoms follow the Mott-rule and have 4, 3 and 2 nearest neighbors, respectively. The average coordination number of the Ga atoms was around 4. T…
