Electronic stress tensor

The study of the density functional theory by Hohenberg-Kohn has invoked the new idea of energy in terms of electron density. A natural outcome is the concept of energy density, which has been published in a recent paper of stress tensor and the references cited therein. Electronic stress tensor plays a very significant role as has been originally formulated and reviewed by PauU in his textbook of quantum mechanics. 

It has been shown in the preceding paper that the QED electronic stress tensor plays a fundamentally important role in order to understand the electron spin dynamics the spin torque and zeta force originated from the chiral nature of electron that is intrinsic to the spin-1/2 Fermion. The dynamics of electron spin with the realization of spin-orbit coupling has recently been of keen interest, particularly in the field of spin torque transfer in spintronics see recent review and the references cited therein. ... 

Because in Equation 12.17 is symmetric, the antisymmetric component of the geometrical tensor and the antisymmetric component of the electronic stress tensor t >" ( ) should cancel each other out ... 

Antisymmetric electronic stress tensor drives the electron spin through vorticity."... 

This is called the quantum electron spin vorticity principle the time evolution of the electron spin s is driven by the antisymmetric component of the electronic stress tensor x through the vorticity rot . The quantum electron spin vorticity principle is schematically shown in Figure 12.1. 

It should be noted that the vorticity rot appears as a component of the electronic momentum as found in Equation 12.36. This proves the important role of the antisymmetric component of the electronic stress tensor X. It may be further proved that the symmetric component of the electronic stress tensor x plays an important role as tension x = divx compensating the Lorentz force L as... 

Abstract Several potentially useful scalar and vector fields that have been scarcely or even never used to date in Quantum Chemical Topology are defined, computed, and analyzed for a few small molecules. The fields include the Ehrenfest force derived from the second order density matrix, which does not show many of the spurious features encountered when it is computed from the electronic stress tensor, the exchange-correlation (xc) potential, the potential acting on one electron in a molecule, and the additive and effective energy densities. The basic features of the topology of some of these fields are also explored and discussed, paying attention to their possible future interest. 

The Ehrenfest force owes its popularity to a deep theoretical link with one-body quantities through the electronic stress tensor [1], Fe(r) = —V (r(r). The stress... 

Keywords Chemical reaction prediction. Conceptual density functional theory, Ehrenfest force, Electronic stress tensor, Reaction force partitioning. Quantum theory of atoms in molecules... 

We claim that the eigenvectors of the electronic stress tensor can be used to represent the normal modes of electronic rearrangement. Here we review previous work on this topic and pursue the key ideas further, focusing on the application of the electronic stress tensor to organic reactivity. 

We were motivated to study the electronic stress tensor because it is an electronic quantity that is closely analogous to the vibrational Hessian used in the electronfollowing picture. The elements of the Hessian represent the change in a component of the force (i = 1,2,3 corresponding to the three Cartesian directions) on the ath nucleus in response to a change in the position of the jSth nucleus in the j direction ... 

Although the electronic stress tensor can be computed directly from the W-electron wavefunction, , it is most convenient to write the equation for the stress tensor in terms of the one-electron density matrix ... 

Table 1 The eigenvalues of the electronic stress tensor (A1, A2, -I3) and the tensile to compressive ratio defined in (21), computed at the bcp of the indicated bond...

The eigenvectors of the electronic stress tensor, evaluated at critical points of the electron density and important structures along the reaction pathway for acetaldehyde tautomerization, are shown in Fig. 3. 

Jenkins S et al. (2011) The mechanics of charge-shift bonds A perspective from the electronic stress tensor. Chem Phys Lett 510 18-20... 

Ichikawa K, Wagatsuma A, Kusumoto M, Tachibana A (2010) Electronic stress tensor of the hydrogen molecular ion comparison between the exact wave fimctimi and approximate wave functions using Gaussian basis sets. J Mol Struct Theochem 951 49-59 Tachibana A (2010) Energy density concept a stress tensor approach. J Mol Struct Theochem 943 138-151... 

Ichikawa K et al (2009) A theoretical study on a reaction of iron(III) hydroxide with boron trichloride by ab initio calculation. J Mol Struct Theochem 915 1-10 Szarek P et al. (2009) Regional DFT electronic stress tensor study of aluminum nanostructures for hydrogen storage. In Wei DQ, Wang XJ (eds) Theory and applications of computational chemistry - 2008, AIP conference proceedings, vol 1102, pp 299-305 Tao JM, Vignale G, Tokatly IV (2008) Quantum stress focusing in descriptive chemistry. Phys Rev Lett 100 206405... 

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