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Important Research Activities :

Dr. P.K. Chattaraj has been actively engaged in the research activities comprising atomic and molecular electronic structure, reactivity and dynamics calculations within a broad density-based quantum mechanical framework occasionally supplemented by ab initio calculations. He has proposed new forms for kinetic and exchange-correlation energy functionals and solved the associated Euler-Lagrange equations for many atomic and ionic species to calculate various physico-chemical properties like energy, moments, electronegativity, hardness, covalent radii etc. and all these values compare very well with other existing theoretical/experimental results.

Formal proofs of the maximum hardness principle (MHP) and hard-soft acid-base (HSAB) principle have been provided and their validity has been tested through ab initio calculation of hardness associated with molecular vibrations, molecular internal rotations, acid-base reactions,dissociation reactions, proton transfer reactions, isomerization reactions etc.  Related profiles of energy, bond index, molecular valency and chemical potential along the reaction path have been calculated ab initio. They generally mimic the corresponding hardness behaviour.  In general chemical bond-making, bond-breaking and electron transfer processes in solution can be understood in the light of MHP.  State-of-the-art calculations on several acid-base reactions in both gas and solution phases reveal that HSAB principle is valid in most cases and the validity of MHP implies that of HSAB principle.

In order to understand the dynamical processes a quantum fluid density functional theory (QFDFT) which is an amalgamation of quantum fluid dynamics (QFD) and time dependent density functional theory (TDDFT) is made use of.  Various time dependent processes like atomic collisions, atom-field interaction, model chemical reactions etc. have been studied using QFDFT.  A molecular reaction dynamics has been envisaged in terms of the temporal evolution of quantities like electronegativity, hardness, entropy and polarizability.  It has been observed that in general, the natural direction of a process is that which leads to a state of maximum hardness, maximum entropy and minimum polarizability.  This study complements other conventional approaches involving potential energy profile or bond index profile.  Electronegativity equalization principle, maximum hardness principle, maximum entropy principle (MEP), minimum polarizability principle (MPP) etc. are now better understood for both ground and excited states, especially in a dynamical context.  These calculations are supplemented by ab initio SCF calculations wherever possible.

Global reactivity parameters like the softness and the polarizability and local reactivity parameters like the Fukui function and the local hardness have been calculated for the ground and several excited electronic states of various helium isoelectronic systems and the corresponding two � state equi - ensembles. Only the lowest energy state of a given symmetry is chosen because of the validity of excited state DFT for this type of states only. It has been demonstrated for the first time that: (a) The softness varies linearly with the cube root of polarizability also for the excited states, (b) the ground state of a system is harder and less polarizable than any of its excited states, as expected from MHP and MPP, (c) prominent atomic shell structures are exhibited by the radial distributions of the charge density, Fukui function and the local hardness in both the ground and the excited states. It has also been shown that a system is the hardest and the least polarizable in its ground state and becomes softer and more polarizable as the excited-state contribution in a two state ensemble increases, a fact in conformity with MHP and MPP. Validity of MHP and MPP for several molecules in different electronic states has also been analyzed through ab initio and DFT studies.Connections among chemical periodicity and MHP and MPP have been explored.

Both ab initio and DFT calculations have been performed in order to understand the implications of MHP and MPP in various physico-chemical processes like molecular vibrations, molecular internal rotations and chemical reactions. Woodward-Hoffmann rule has also been studied in the light of MHP and MPP. A local  thermodynamic method has been developed in understanding chemical bonding and reactivity. Atoms-in-a-molecule are defined in terms of a new density partitioning scheme. 

Since the QFD equations are nonlinear in charge and current densities it is hoped that they would constitute a better vehicle for understanding typical nonlinear phenomena like quantum solitons and quantum chaos.  QFD of classical nonlinear dynamical systems exhibiting soliton solutions or chaos have been studied.  As a complement to QFD, another quantum potential based approach, viz., quantum theory of motion (QTM) in the sense of classical interpretation of quantum mechanics as developed by de Broglie and Bohm has been applied in understanding quantum domain behaviour of classically chaotic systems.  Quantum Lyapunov exponent and Kolmogorov -  Sinai entropy are defined in terms of Bohmian trajectories. These quantum potential based approaches have been applied successfully in analyzing chaotic dynamics of several quantum anharmonic oscillators, field induced quantum barrier penetration, Rydberg atoms in external fields etc. A cantorus like structure has been shown to be the quantum equivalent of a classical Kolmogorov-Arnold-Moser (KAM) torus. Standard diagnostics of quantum chaos like autocorrelation function ,the associated power spectrum, nearest neighbour spacing distribution, spectral rigidity etc. support these results.

 

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