Chemical Reactivity Dynamics and Quantum Chaos in Highly Excited Hydrogen Atoms in an External Field: A Quantum Potential Approach

Abstract

Dynamical behavior of chemical reactivity indices like electronegativity, hardness, polarizability, electrophilicity and nucleophilicity indices is studied within a quantum fluid density functional framework for the interactions of a hydrogen atom in its ground electronic state (n = 1) and an excited electronic state (n = 20) with monochromatic and bichromatic laser pulses. Time dependent analogues of various electronic structure principles like the principles of electronegativity equalization, maximum hardness, minimum polarizability and maximum entropy have been found to be operative. Insights into the variation of intensities of the generated higher order harmonics on the color of the external laser field are obtained. The quantum signature of chaos in hydrogen atom has been studied using a quantum theory of motion and quantum fluid dynamics. A hydrogen atom in the electronic ground state (n = 1) and in an excited electronic state ( n = 20) behaves differently when placed in external oscillating monochromatic and bichromatic electric fields. Temporal evolutions of Shannon entropy, quantum Lyapunov exponent and Kolmogorov -Sinai entropy defined in terms of the distance between two initially close Bohmian trajectories for these two cases show marked differences. It appears that a larger uncertainty product and a smaller hardness value signal a chaotic behavior.

Electrophilicity Index

“…At the very large field intensity, the difference in response of μ and η is manifested in these plots. A corresponding analysis on the Rydberg states of hydrogen and helium atoms provides important insights into their chaotic ionization. −

22 Time evolution of electrophlicity index (ω) of a helium atom in ground and excited states in the presence of external electric fields with different colors and intensities. Reprinted with permission from ref .

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Chemical Reactivity Profiles of Two Selected Polychlorinated Biphenyls

“…Development of appropriate descriptors for the quantitative structure−activity relationship is an important area of research. Popular qualitative chemical concepts such as electronegativity and hardness have been widely used in understanding various aspects of chemical reactivity. − Density functional theory (DFT) provides a rigorous theoretical basis for these concepts. These reactivity indices are better appreciated in terms of the associated electronic structure principles such as the electronegativity equalization principle, the hard−soft acid base (HSAB) principle, 20 the maximum hardness principle (MHP), , the minimum polarizability principle (MPP), etc.…”

Structural and thermodynamic factors on adsorptive interaction of certain flavonoids onto polymeric resins and activated carbon

“…The HOMO-LUMO energy gap of the FV-adsorbent can be related to the hardness (Á) and softness (S). Hardness can be interpreted as the resistance of changing the number of electrons and softness correlates linearly with the polarizability which is a measure of the change of the electronic density due to the presence of an electric field [38]. The hardness and softness evaluations are based on the commonly used finite difference approximation, leading to Á = (E LUMO − E HOMO )/2, S = 1/2Á, −E HOMO = IP and −E LUMO = EA [39], the calculated Á and S are given in Table 5.…”