Electronic Stress Tensor Research Articles

Stress tensor eigenvector following with next‐generation quantum theory of atoms in molecules

AbstractThe 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. A new 3–D vector based interpretation of the chemical bond that we refer to as the bond‐path framework set B 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 structure that occur during reactions. We demonstrate that the most preferred direction for bond motion using the stress tensor corresponds to the most compressible direction and not to the least compressible direction as previously reported. We show the necessity for a directional approach constructed using the eigenvectors along the entire bond‐length and demonstrate the insufficiency of scalar measures for capturing the nature of the stress tensor within the QTAIM partitioning.

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.

Theoretical study of atoms by the electronic kinetic energy density and stress tensor density

The electronic structure of atoms in the first, second, and third periods were analyzed using the electronic kinetic energy density and stress tensor density, which are local quantities motivated by quantum field theoretic consideration, specifically the rigged quantum electrodynamics. The zero surfaces of the electronic kinetic energy density, which are called as the electronic interfaces, of the atoms were computed. It was found that their sizes exhibited clear periodicity and were comparable to the conventional atomic and ionic radii. The electronic stress tensor density and its divergence, tension density, of the atoms, were also computed and how their electronic structures were characterized by them was discussed. © 2016 Wiley Periodicals, Inc.

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.

Use of Electronic Stress Tensor Density and Energy Density in Chemistry

The concepts of electronic stress tensor density and energy density give new viewpoints for conventional ideas in chemistry. In this paper, we introduce the electronic stress tensor and energy density and other related quantities such as tension density and kinetic energy density, which are based on quantum field theory, and show their connection to the concepts in chemistry. The topics are: (i) zero surface of the electronic kinetic energy density and size of atoms, (ii) separatrix of the tension field as a boundary surface of atoms in a molecule, (iii) interpretation of energy density based bond order as directional derivative of a total energy of a molecule regarding the bond direction, and (iv) eigenvalues of the stress tensor as tools to classify types of chemical bond.

How does the ambiguity of the electronic stress tensor influence its ability to serve as bonding indicator

The electronic stress tensor is not uniquely defined. Possible bonding indicators originating from the quantum stress tensor may inherit this ambiguity. Based on a general formula of the stress tensor this ambiguity can be described by an external parameterλfor indicators derived from the scaled trace of the stress tensor (whereby the scaling function is proportional to the Thomas–Fermi kinetic energy density). The influence ofλis analyzed and the consequences for the representation of chemical bonding are discussed in detail. It is found that the scaled trace of the stress tensor may serve as suitable bonding indicator over a wide range ofλvalues, excluding the value range between −0.15 and −0.48. Focusing on the eigenvalues of the stress tensor, it is found that the sign of the eigenvalues heavily depends on the chosen representation of the stress tensor. Therefore, chemical bonding analyses which are based on the interpretation of the eigenvalue sign (e.g., the spindle structure) are strongly dependent on the chosen form of the stress tensor. © 2014 Wiley Periodicals, Inc.

How does the ambiguity of the electronic stress tensor influence its ability to reveal the atomic shell structure

The electronic stress tensor is not uniquely defined. Therefore, shell indicators stemming from the quantum stress tensor may inherit this ambiguity. Based on a general formula of the stress tensor this ambiguity can be described by an external parameter λ. Two functions derived from the quantum stress tensor have been evaluated according to their ability to serve as shell indicators. The influence of λ is analyzed and the consequences for the representation of the atomic shell structure are discussed in detail. It is found that the trace of the stress tensor does not fully reveal the atomic shell structure. In contrast, the scaled trace (whereby the scaling function is proportional to the Thomas-Fermi kinetic energy density) produces fairly good representation of the atomic shell structure over a wide range of λ values.

Theoretical study of lithium clusters by electronic stress tensor

We study the electronic structure of small lithium clusters Lin (n = 2 ∼ 8) using the electronic stress tensor. We find that the three eigenvalues of the electronic stress tensor of the Li clusters are negative and degenerate, just like the stress tensor of liquid. This leads us to propose that we may characterize a metallic bond in terms of the electronic stress tensor. Our proposal is that in addition to the negativity of the three eigenvalues of the electronic stress tensor, their degeneracy characterizes some aspects of the metallic nature of chemical bonding. To quantify the degree of degeneracy, we use the differential eigenvalues of the electronic stress tensor. By comparing the Li clusters and hydrocarbon molecules, we show that the sign of the largest eigenvalue and the differential eigenvalues could be useful indices to evaluate the metallicity or covalency of a chemical bond.

The cis-effect using the topology of the electronic charge density

We provide a physics-inspired coupling mechanism explaining the cis-effect in terms of electronic and nuclear degrees of freedom and explore the implications for three families of molecules. The cis- or trans-effect is related to the tendency of electronic charge density to move away from the bond critical point (BCP) and towards the associated nuclear attractors. A quantitative measure of this effect is given by the λ 3 eigenvalue of the Hessian matrix of the electronic charge density. The physical origin of the cis-effect is tied to the observation that the central X=X, X=C or N bond-paths of the cis-isomers are more bent (they are up to 1.5% longer than the internuclear distance) than the bond-paths of the corresponding trans-isomers. Greater bond-path bending is associated with a stronger cis-effect; the direction of bond deformation can in all cases be predicted by the most facile (least compressible) mode of the electronic stress tensor. Further to this, the ellipticity ε of the X=X BCPs of a molecule displaying the cis-effect is lower in the cis-isomer than for the corresponding trans-isomer, suggesting that the cis-effect is less counterintuitive than previously thought. The molecules that exhibit the greatest cis-effect are those with fluorinated double bonds; this is because the most facile modes of the C–F bond couple with the highest-symmetry normal mode of vibration. Qualitative agreement is found with existing experimental data and predictions are made where experimental data is lacking.

Aluminum Hydride Clusters as Hydrogen Storage Materials and their Electronic Stress Tensor Analysis

We study the chemical bonds of small Al clusters (Aln, n=2-8) and hydrogenated Al clusters (AlnHm , n=1-8 and m=1,2) using electronic stress tensor. We calculate the bond order based on energy density for these clusters. We also study the electronic structure under the presence of electronic current by the electronic stress tensor for AlH3 molecule.

Electronic stress tensor analysis of hydrogenated palladium clusters

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 between two atoms where the largest eigenvalue of the electronic stress tensor is negative and corresponding eigenvectors forming a pattern which connects them.

Pointing the way to the products? Comparison of the stress tensor and the second-derivative tensor of the electron density

The eigenvectors of the electronic stress tensor can be used to identify where new bond paths form in a chemical reaction. In cases where the eigenvectors of the stress tensor are not available, the gradient-expansion-approximation suggests using the eigenvalues of the second derivative tensor of the electron density instead; this approximation can be made quantitatively accurate by scaling and shifting the second-derivative tensor, but it has a weaker physical basis and less predictive power for chemical reactivity than the stress tensor. These tools provide an extension of the quantum theory of atoms and molecules from the characterization of molecular electronic structure to the prediction of chemical reactivity.

Inverted-sandwich-type and open-lantern-type dinuclear transition metal complexes: theoretical study of chemical bonds by electronic stress tensor

We study the electronic structure of two types of transition metal complexes, the inverted-sandwich-type and open-lantern-type, by the electronic stress tensor. In particular, the bond order b_e measured by the energy density which is defined from the electronic stress tensor is studied and compared with the conventional MO based bond order. We also examine the patterns found in the largest eigenvalue of the stress tensor and corresponding eigenvector field, the "spindle structure" and "pseudo-spindle structure". As for the inverted-sandwich-type complex, our bond order b_e calculation shows that relative strength of the metal-benzene bond among V, Cr and Mn complexes is V > Cr > Mn which is consistent with the MO based bond order. As for the open-lantern-type complex, we find that our energy density based bond order can properly describe the relative strength of Cr--Cr and Mo--Mo bonds by the surface integration of the energy density over the "Lagrange surface" which can take into account the spatial extent of the orbitals.

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

The mechanism of charge-shift bonding is discussed from the perspective of the electronic stress tensor. In charge-shift bonds, the tensile mode of the stress tensor (attraction of electrons to the nuclei) is stronger, relative to the compressive modes (attraction of electrons toward the bond axis) than in conventional covalent bonds. Similar bonding indicators based on the eigenvalues of the tensor of second derivatives of the electron density and bond metallicity measures also correlate with charge-shift binding. These indicators seem preferable to the electron-density Laplacian and the local energy density because they can distinguish between weak covalent bonds and charge-shift bonds.

Reactivity and Regioselectivity of Aluminum Nanoclusters: Insights from Regional Density Functional Theory

The structure and bonding in charged and doped aluminum clusters have been investigated using Regional Density Functional Theory (RDFT). The RDFT method provides a measure of the electronic stress tensor from which it is possible to determine bond indices and electronic chemical potential. We find that the distribution of bond indices on the surface of Al12X clusters provides not only an understanding of the internal bonding and stability but also some insight into the regioselectivity observed in reactions of the clusters.

Theoretical study of hydrogenated tetrahedral aluminum clusters

We report on the structures of aluminum hydrides derived from a tetrahedral aluminum (Al4) cluster using ab initio quantum chemical calculation. Our calculation of binding energies of the aluminum hydrides reveals that stability of these hydrides increases as more hydrogen atoms are adsorbed, while stability of Al – H bonds decreases. We also analyze and discuss the chemical bonds of those clusters by using recently developed method based on the electronic stress tensor. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

How Ambiguous Is the Local Kinetic Energy?†

The local kinetic energy and the closely related local electronic stress tensor are commonly used to elucidate chemical bonding patterns, especially for covalent bonds. We use three different approaches-transformation properties of the stress tensor, quasiprobability distributions, and the virial theorem from density-functional theory-to clarify the inherent ambiguity in these quantities, discussing the implications for analyses based on the local kinetic energy and stress tensor. An expansive-but not universal-family of local kinetic energy forms that includes the most common choices and is suitable for both chemical-bonding and atoms-in-molecule analysis is derived. A family of local electronic stress tensors is also derived. Several local kinetic energy functions that are mathematically justified, but unlikely to be conceptually useful, are derived. The implications of these forms for atoms-in-molecule analysis are discussed.

Electronic stress tensor of the hydrogen molecular ion: Comparison between the exact wave function and approximate wave functions using Gaussian basis sets

We investigate the electronic stress tensor of the hydrogen molecular ion H 2 + for the ground state using the exact wave function and wave functions approximated by Gaussian function basis set expansion. The spatial distribution of the largest eigenvalue, corresponding eigenvectors, tension and kinetic energy density are compared. We find that the cc-pV6Z basis set gives the spindle structure very close to the one calculated from the exact wave function. Similarly, energy density at the Lagrange point is very well approximated by the cc-pV5Z or cc-pV6Z basis sets.

Electronic Stress Tensor Study of Aluminum Nanostructures for Hydrogen Storage

We report the new structures of aluminum hydrides derived from the Al4 tetrahedral cages. We perform ab initio quantum chemical calculation for these new aluminum hydrides. Our calculation of binding energies of the new aluminum hydrides reveal that stability of these hydrides increases as more hydrogen atoms are adsorbed, while stability of Al-H bonds decreases. We also calculate electronic stress tensor to evaluate the chemical bonds of these hydrides. As a result, we find that the bonds of the Al4 tetrahedral cage are strengthened as more hydrogen atoms are adsorbed on the aluminum hydrides. Our calculation of the potential energy surfaces and the regional chemical potential show that hydrogen atoms are likely to adsorb on bridge site at first.

Stress tensor of the hydrogen molecular ion

The electronic stress tensor of the hydrogen molecule ion H{sup +}{sub 2} is investigated for the ground state (sigma{sub g}1s) and the first excited state (sigma{sub u}*1s) using their exact wave functions. A map of its largest eigenvalue and corresponding eigenvector is shown to be closely related to the nature of chemical bonding. For the ground state, we also show the spatial distribution of interaction energy density to describe in which part of the molecule stabilization and destabilization take place.