INTERNATIONAL E-CONFERENCE ON FRONTIERS OF ENERGY EFFICIENT MATERIALS AND DEVICES (ICEEMD-2021)

Thin Film Technology, Crystal Growth, Non-Linear Optics,Conducting Polymers, Nano Technology, Solar Cells, Molecular Quantum Mechanics and Ultrasonics are being carried out. So far, more than 300 M.Phil and 35 Ph.D degrees were awarded. The department has published more than 500 research papers in SCI indexed international journals.

Continuity Relations, Probability Acceleration Current Sources and Internal Communications in Interacting Fragments

Classical issues of local continuities and density partition in molecular quantum mechanics are reexamined. An effective velocity of the probability current is identified as the current-per-particle and its properties are explored. The local probability acceleration and the associated force concept are introduced. They are shown to identically vanish in the stationary electronic states. This acceleration measure also determines the associated productions of physical currents, e.g., the local source of the resultant content of electronic gradient information. The probability partitioning between reactants is revisited and illustrated using the stockholder division rule of Hirshfeld. A simple orbital model is used to describe the polarized (disentangled) and equilibrium (entangled) molecular fragments containing the distinguishable and indistinguishable groups of electrons, respectively, and their mixed quantum character is emphasized. The fragment density matrix is shown to determine the subsystem internal electron communications.

Big picture of relativistic molecular quantum mechanics

Any quantum mechanical calculation on electronic structure ought to choose first an appropriate Hamiltonian H and then an Ansatz for parameterizing the wave function Ψ, from which the desired energy/property E(λ) can finally be calculated. Therefore, the very first question is: what is the most accurate many-electron Hamiltonian H? It is shown that such a Hamiltonian i.e. effective quantum electrodynamics (eQED) Hamiltonian, can be obtained naturally by incorporating properly the charge conjugation symmetry when normal ordering the second quantized fermion operators. Taking this eQED Hamiltonian as the basis, various approximate relativistic many-electron Hamiltonians can be obtained based entirely on physical arguments. All these Hamiltonians together form a complete and continuous ‘Hamiltonian ladder’, from which one can pick up the right one according to the target physics and accuracy. As for the many-electron wave function Ψ, the most intriguing questions are as follows. (i) How to do relativistic explicit correlation? (ii) How to handle strong correlation? Both general principles and practical strategies are outlined here to handle these issues. Among the electronic properties E(λ) that sample the electronic wave function nearby the nuclear region, nuclear magnetic resonance (NMR) shielding and nuclear spin-rotation (NSR) coupling constant are especially challenging: they require body-fixed molecular Hamiltonians that treat both the electrons and nuclei as relativistic quantum particles. Nevertheless, they have been formulated rigorously. In particular, a very robust ‘relativistic mapping’ between the two properties has been established, which can translate experimentally measured NSR coupling constants to very accurate absolute NMR shielding scales that otherwise cannot be obtained experimentally. Since the most general and fundamental issues pertinent to all the three components of the quantum mechanical equation HΨ = EΨ (i.e. Hamiltonian H, wave function Ψ, and energy/property E(λ)) have fully been understood, the big picture of relativistic molecular quantum mechanics can now be regarded as established.