A double-index atomic partitioning of the molecular first-order density matrix is proposed. Contributions diagonal in the atomic indices correspond to atomic density matrices, whereas off-diagonal contributions carry information about the bonds. The resulting matrices have good localization properties, in contrast to single-index atomic partitioning schemes of the molecular density matrix. It is shown that the electron density assigned to individual atoms, when derived from the density matrix partitioning, can be made con- sistent with well-known partitions of the electron density over AIM basins, either with sharp or with fuzzy boundaries. The method is applied to a test set of about 50 molecules, representative for various types of chemical binding. A close correlation is observed between the trace of the bond matrices and the SEDI (shared electron density index) bond index.
For the Hirshfeld-I atom-in-molecule model, associated single-atom energies and interaction energies at the Hartree-Fock level are determined efficiently in one-electron Hilbert space. In contrast to most other approaches, the energy terms are fully consistent with the partitioning of the underlying one-electron density matrix. Starting from the Hirshfeld-I atom-in-molecule model for the electron density, the molecular one-electron density matrix is partitioned with a previously introduced double-atom scheme [Vanfleteren D. et al., J Chem Phys 2010, 132, 164111]. Single-atom density matrices a…
We present an intuitive and general analytical approximation estimating the energy of covalent single and double bonds between participating atoms in terms of their respective nuclear charges with just three parameters, $[{E_\text{AB} \approx a - b Z_\text{A} Z_\text{B} + c (Z_\text{A}^{7/3} + Z_\text{B}^{7/3})}]$. The functional form of our expression models an alchemical atomic energy decomposition between participating atoms A and B. After calibration, reasonably accurate bond energy estimates are obtained for hydrogen-saturated diatomics composed of $p$-block elements coming from the same …
A double-atom partitioning of the molecular one-electron density matrix is used to describe atoms and bonds. All calculations are performed in Hilbert space. The concept of atomic weight functions (familiar from Hirshfeld analysis of the electron density) is extended to atomic weight matrices. These are constructed to be orthogonal projection operators on atomic subspaces, which has significant advantages in the interpretation of the bond contributions. In close analogy to the iterative Hirshfeld procedure, self-consistency is built in at the level of atomic charges and occupancies. The method…
Chemical bonding concepts emerge naturally from maximally entangled atomic orbitals
Ludwig-Maximilians-Universität München（慕尼黑大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Donostia International Physics Center (DIPC)（圣塞巴斯蒂安国际物理中心）
We extend the localized operator partitioning method (LOPM) [J. Nagesh, A.F. Izmaylov, and P. Brumer, J. Chem. Phys. 142, 084114 (2015)] to the time-dependent density functional theory (TD-DFT) framework to partition molecular electronic energies of excited states in a rigorous manner. A molecular fragment is defined as a collection of atoms using Stratman-Scuseria-Frisch atomic partitioning. A numerically efficient scheme for evaluating the fragment excitation energy is derived employing a resolution of the identity to preserve standard one- and two-electron integrals in the final expressions…
The eigenvectors of the electronic stress tensor have been identified as useful for the prediction of chemical reactivity because they determine the most preferred directions to move the bonds that correspond to a qualitative change in the molecular electronic structure. A new 3-D vector based interpretation of the chemical bond that we refer to as the bond-path framework set $\mathbb{B} = \{p,q,r\}$ provides a version of the quantum theory of atoms in molecules (QTAIM) beyond the minimum definition for bonding that is particularly suitable for understanding changes in molecular electronic str…
A bismuth bond, a type of pnictogen bonding interaction, occurs in chemical systems when there is evidence of a net attractive interaction between the electrophilic region of a covalently or coordinately bonded bismuth atom and the nucleophilic region in another, or the same, molecular entity. In this review, we report on the signatory details of bismuth bonding in several crystalline systems, along with other non-covalent interactions such as hydrogen and halogen bonds, which are important driving forces in the rational design of various types of materials. Illustrative crystal structures wer…
We introduce "bond-counting" potentials, which provide an elementary description of covalent bonding. These simplistic potentials are intended for studies of the mechanisms behind a variety of phase transitions in elemental melts, including the liquid-liquid phase transitions (LLPT) in phosphorus and bismuth. As a first study employing such potentials, an analytic solution of a one-dimensional model system is presented, including its thermodynamic properties and its structure factor. In the simplest case, the chemical valency of each atom is $1$, and either single atoms or diatomic molecules a…
First-principles calculations and analysis of the thermodynamic, structural, and electronic properties of liquid SiO$_2$ characterize the bonded-to-atomic transition at 0.1--1.6 TPa and 10$^4$--10$^5$ K (1--7 eV), the high-energy-density regime relevant to understanding planetary interiors. We find strong ionic bonds that become short-lived due to high kinetics during the transition, with sensitivity of the transition temperature to pressure, and our calculated Hugoniots agree with past experimental data. These results reconcile previous experimental and theoretical findings by clarifying the …
Charge transfer among individual atoms in a molecule is the key concept in the modern electronic theory of chemical bonding. In this work, we defined an atomic region between two atoms by Slater orbital exponents of valence electrons and suggested a method for analytical calculation of charge penetration between all atoms in a molecule. Computation of charge penetration amount is self-consistently performed until each orbital exponent converges to its certain values respectively. Charge penetration matrix was calculated for ethylene and MgO, and bonding charge and its distribution were analyze…
Understanding the performance of machine learning algorithms is essential for designing more accurate and efficient statistical models. It is not always possible to unravel the reasoning of neural networks. Here we propose a method for calculating machine learning kernels in closed and analytic form by combining atomic property weighted radial distribution function (AP-RDF) descriptor with a Gaussian kernel. This allowed us to analyse and improve the performance of the Bag-of-Bonds descriptor, when the bond type restriction is included in AP-RDF. The improvement is achieved for the prediction …
By leveraging the fundamental doctrine of The Quantum Theory of Atoms in Molecules---the partitioning of the electron charge density ($ρ$) into regions bounded by surfaces of zero flux---we map the gradient field of $ρ$ onto a 2D space called the gradient bundle condensed charge density ($\cal{P}$). The topology of $\cal{P}$ appears to correlate with regions of chemical significance in $ρ$. The bond wedge is defined as the image in $ρ$ of the basin of attraction in $\cal{P}$, analogous to the Bader atom, which is the basin of attraction in $ρ$. A bond bundle is defined as the union of bond wed…
APLIP is a method for using a STIRAP-like three-state configuration with two laser pulses for continuous extension of a molecular bond, introduced in 1998. It is based on time-dependent light-induced potential surfaces (LIP). In VibLIP one extends the idea into a method for tailoring the vibrational state while changing the electronic state, introduced in 2000. Here I discuss the extension of both methods to situations that involve more than three electronic states, and note the possibility of using the method on adiabatic transport of atoms between microtraps or equivalent structures.
Recently it has been proposed that the positron, the anti-particle analog of the electron, is capable of forming an anti-matter bond in a composite system of two hydride anions and a positron [Angew. Chem. Int. Ed. 57, 8859 (2018)]. In order to dig into the nature of this novel bond the newly developed multi-component quantum theory of atoms in molecules is applied to this positronic system. The topological analysis reveals that this species is composed of two atoms in molecules, each containing a proton and half of the electronic and the positronic populations. Further analysis elucidates tha…
A unified theoretical framework for fluctuating-charge models in atom-space and in bond-space
我们先前介绍的QTPIE（电荷转移与极化电流平衡）模型（J.Chen和T. J. Martinez，Chem.Phys.Lett. 438，315（2007））是具有正确渐近行为的波动电荷模型。与大多数其他波动电荷模型不同，QTPIE是根据电荷转移变量和成对电负性而不是原子电荷变量和电负性来制定的。QTPIE中电负性的成对特征避免了键断裂时的假电荷转移。然而，增加的变量数量导致相当大的计算费用和秩亏的工作方程组，这是数值上的不便。在这里，我们表明，QTPIE可以完全重新制定的原子电荷变量，从而大大降低了计算复杂性。原子和键变量之间的转换通常适用于任意波动电荷模型，并揭示了一个潜在的拓扑框架，可用于理解波动电荷模型和经典电路理论之间的关系。
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
In a recent paper [J. Organomet. Chem. (2013) doi: 10.1016 /j.jorganchem. 2013.03.047] analyzing the bonding mode of Trimethylenemethane (TMM) with some metal carbonyls, Mousavi and Frenking have declared the absence of bond paths, the so-called missed bond paths, between metal atoms and terminal carbon atoms in several complexes. In this communication, it is first demonstrated that the presupposition of the equivalence of a bond path and a chemical bond within the context of the quantum theory of atoms in molecules (QTAIM) is superficial and basically flawed which is not only against with the…
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 …
Recently, Tao and Mo (TM) derived a meta-generalized gradient approximation functional based on a model exchange-correlation hole. In this work, the performance of this functional is assessed on standard test sets, using the 6-311++G(3df,3pd) basis set. These test sets include 223 G3/99 enthalpies of formation, 99 atomization energies, 76 barrier heights, 58 electron affinities, 8 proton affinities, 96 bond lengths, 82 harmonic vibrational frequencies, 10 hydrogen-bonded molecular complexes, and 22 atomic excitation energies. Our calculations show that the TM functional can achieve high accura…
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…
There are views prevalent in the noncovalent chemistry literature that i) the O atom in molecules cannot form a chalcogen bond, and ii) if formed, this bond is very weak. We have shown in this study that these views are not necessarily true since the attractive energy between the oxygen atom of some molecules and several electron rich anionic bases examined in a series of 34 ion-molecule complexes varied from the weak (ca -2.30 kcal/mol) to the ultrastrong (-90.10 kcal/mol). The [MP2/aug-cc-pVTZ] binding energies for several of these complexes were found to be comparable to or significantly la…
Hydrogen bond is often assumed to be a purely electrostatic interaction between a electron-deficient hydrogen atom and a region of high electron density. Here, for the first time, we directly image hydrogen bond in real space by room-temperature scanning tunneling microscopy (STM) with the assistance of resonant tunneling effect in double barrier mode. STM observations demonstrate that the C=O:HO hydrogen bonds lifted several angstrom meters above metal surfaces appear shuttle-like features with a significant contrast along the direction connected the oxygen and hydrogen atoms of a single hydr…
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. …
A vector-based representation of the chemical bond is introduced that we refer to as the bond-path frame-work set = $\mathbb{B} = \{p, q, r\}$, where $p$, $q$ and $r$ represent three paths with corresponding eigenvector-following path lengths $\mathbb{H}^{*},\mathbb{H}$ and the familiar quantum theory of atoms in molecules (QTAIM) bond-path length. The eigenvector-following path lengths $\mathbb{H}^{*}$ and $\mathbb{H}$ are constructed along the bond-path from the $\underline{\mathbf{\mathit{e}}}_{1}$ and $\underline{\mathbf{\mathit{e}}}_{2}$ Hessian eigenvectors respectively, which correspond…
A two-orbital two-electron diatomic model resembling LiH is used to investigate the differences between the exact Löwdin-Shull and approximate Hartree-Fock-Bogoliubov and Baerends-Buijse density matrix functionals in the medium- to long-distance dissociation region. In case of homolytic dissociation (one electron on each atom), the approximate functionals fail to generate the correct energy due to a compromise between the Hartree-Fock component (which favors partial charge transfer) and the strong correlation component (which hampers charge transfer). The exact functional is able to generate t…
The geometric--arithmetic indices are widely considered in the chemical graph theory in the last decade. The reason of introducing new indices is to gain prediction of target properties of considered molecules that is better than the prediction obtained by already known indices. In the case of the fifth geometric--arithmetic index hitherto no ability of prediction of some molecule property has been considered. In this paper we investigate correlations between the fifth geometric--arithmetic index and some other degree--based topological indices on the family of octane isomers and polyaromatic …
Potential energy surfaces of electron dynamics (ePES) are constructed from a model of localized electron wave packets (eWP) with non-orthogonal valence-bond (VB) spin coupling and applied to quantum dynamics simulations of high harmonic generation (HHG) spectra of hydrogen and helium atoms induced by intense laser pulses. The dynamics of the single electron on the ePES is calculated by numerically solving the time-dependent Schrodinger equation. The results reasonably reproduce previous studies. The dynamics of the electron wave function, dipole moment and dipole acceleration were analyzed by …
Verstraelen et al. (J. Chem. Theory Comput. 12 (2016) 3894-3912) recently introduced a new method for partitioning the electron density of a material into constituent atoms. Their approach falls within the class of atomic population analysis methods called stockholder charge partitioning methods in which a material electron distribution is divided into overlapping atoms. The Minimal Basis Iterative Stockholder (MBIS) method proposed by Verstraelen et al. composes the pro-atom density as a sum of exponential functions, where the number of exponential functions equals that element's row in the P…
An effective Hamiltonian is considered for hydrogen bonding between two molecules due to the quantum mechanical interaction between the orbitals of the H-atom and the donor and acceptor atoms in the molecules. The Hamiltonian acts on two diabatic states and has a simple chemically motivated form for its matrix elements. The model gives insight into the "H-bond puzzle", describes different classes of bonds, and empirical correlations between the donor-acceptor distance R and binding energies, bond lengths, and the softening of vibrational frequencies. A key prediction is the UV photo-dissociati…
'Oriented external electric fields (OEEFs)' have been shown to have great potential in being able to provide unprecedented control of chemical reactions, catalysis and selectivity with applications ranging from H2 storage to molecular machines. We report a theoretical study of the atomic origins of molecular changes due to OEEFs; understanding the characteristics of OEEF-induced couplings between atomic and molecular properties is an important step toward comprehensive understanding of the effects of strong external fields on molecular structure, stability, and reactivity. We focus on the atom…
This paper presents a proposal of a rather new type of effective interatomic interaction for molecular dynamics and similar applications. The model consists of atoms with prescribed geometric arrangement of active orbitals, represented by arms of the length of half of the relevant bond lengths. The interactions have a repulsive part between the atomic centers and an attraction between the arm ends of different atoms. For each atom pair only the closest pair of arms interacts attempting to form the bond. This is a picture of sigma bonds, the pi bonds are modeled by alignment of additional inter…
We study the chemical bonds of small palladium clusters Pd_n (n=2-9) saturated by hydrogen atoms using electronic stress tensor. Our calculation includes bond orders which are recently proposed based on the stress tensor. It is shown that our bond orders can classify the different types of chemical bonds in those clusters. In particular, we discuss Pd-H bonds associated with the H atoms with high coordination numbers and the difference of H-H bonds in the different Pd clusters from viewpoint of the electronic stress tensor. The notion of "pseudo-spindle structure" is proposed as the region bet…
Many atomic liquids can form transient covalent bonds reminiscent of those in the corresponding solid states. These directional interactions dictate many important properties of the liquid state, necessitating a quantitative, atomic-scale understanding of bonding in these complex systems. A prototypical example is liquid silicon, wherein transient covalent bonds give rise to local tetrahedral order and consequent non-trivial effects on liquid state thermodynamics and dynamics. To further understand covalent bonding in liquid silicon, and similar liquids, we present an ab initio simulation-base…
