Stress Tensor of the Hydrogen Molecular Ion

The electronic stress tensor of the hydrogen molecule ion H_2^+ is investigated for the ground state (sigma_g 1s) and the first excited state (sigma_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.Comment: 9 pages, 4 figure

Theoretical study of lithium clusters by electronic stress tensor

We study the electronic structure of small lithium clusters Li_n (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.Comment: 28 pages, 9 figure

A Theoretical Study on a Reaction of Iron(III) Hydroxide with Boron Trichloride by Ab Initio Calculation

We investigate a reaction of boron trichloride (BCl3) with iron(III) hydroxide (Fe(OH)3) by ab initio quantum chemical calculation as a simple model for a reaction of iron impurities in BCl3 gas. We also examine a reaction with water. We find that compounds such as Fe(Cl)(OBCl2)2(OHBCl2) and Fe(Cl)2(OBCl2)(OHBCl2) are formed while producing HCl and reaction paths to them are revealed. We also analyze the stabilization mechanism of these paths using newly-developed interaction energy density derived from electronic stress tensor in the framework of the Regional DFT (Density Functional Theory) and Rigged QED (Quantum ElectroDynamics).Comment: 21 pages, 12 figure

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 bε 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 bε 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

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 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.Comment: 22 pages, 8 figure

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.Comment: 22 pages, 13 figures, published online, Theoretical Chemistry Account

Energy density concept: A stress tensor approach

Conceptual insights from the density functional theory have been enormously powerful in the fields of physics, chemistry and biology. A natural outcome is the concept of “energy density” as has been developed recently: drop region, spindle structure, interaction energy density. Under external source of electromagnetic fields, charged particles can be accelerated by Lorentz force. Dissipative force can make the state of the charged particles stationary. In quantum mechanics, the energy eigenstate is another rule of the stationary state. Tension density of quantum field theory has been formulated in such a way that it can compensate the Lorentz force density at any point of space–time. This formulation can give mechanical description of local equilibrium leading to the quantum mechanical stationary state. The tension density is given by the divergence of stress tensor density. Electronic spin can be accelerated by torque density derived from the stress tensor density. The spin torque density can be compensated by a force density, called zeta force density, which is the intrinsic mechanism describing the stationary state of the spinning motion of electron

General relativistic symmetry of electron spin torque

In our recent paper, the electron spin torque is found to be counter-balanced by the chiral electron density. In this paper, we shall show that the origin of the chiral nature is manifest in the principle of equivalence in general relativity