Research

Density functional theory (DFT)-based studies of confined many-electron systems, focusing on how spatial confinement modifies electron density and related structural properties. Atoms under soft/hard model confining potentials are examined using the generalized pseudospectral (GPS) method, examining changes in energy, electron density, and information-theoretic measures (such as Shannon entropy) as confinement parameters (e.g., box radius, potential strength) are tuned to control the degree of confinement. These studies are further extended to confined quantum systems under plasma environments and high-pressure conditions, examining the virial theorem, degeneracy, and metallization behavior induced by confinement, offering a broader picture of how confinement affects the structure and behavior of quantum systems.

Development and application of Cartesian-grid density functional theory (DFT) methods for electronic structure calculations of atoms and molecules. This includes efficient numerical schemes, such as Fourier convolution for Hartree-Fock exchange evaluation in orbital-dependent functionals, and a real-time TDDFT scheme for strong-field interactions. The framework is extended to compute static and dynamic electric response properties — polarizability and hyperpolarizability — along with excitation energies via Becke's exciton model and charge-transfer excitations within a hybrid Kohn-Sham approach. Related contributions include a self-consistent optimization of range-separated hybrid functionals and a simple ΔSCF method for optical gaps in organic chromophores. Together, these studies establish Cartesian-grid DFT as a versatile platform for ground- and excited-state properties, optical response, and strong-field electron dynamics.

Analytically solvable quantum systems and information-theoretic analysis of molecular and atomic potentials. A key contribution is a new, improved approximation to the centrifugal term in the D-dimensional Schrödinger equation, applied to the Eckart, Manning-Rosen, Pöschl-Teller, Deng-Fan, and Hulthén potentials, yielding accurate ro-vibrational energy levels and thermodynamic properties for molecular systems. This is complemented by information-theoretic characterization — using Shannon entropy and related measures — extended to other solvable potentials such as the Makarov potential and the one-dimensional Dunkl oscillator. A separate direction addresses time-dependent confinement, studying average energy, time-correlation functions, and entropy in harmonic and pseudo-harmonic oscillators confined within a moving boundary, capturing how these quantities evolve under dynamically changing confinement, with relevance to time-modulated traps and quantum dots.