Energy and information analysis of confined quantum systems by means of density functional theory

Majumdar, Sangita (2020) Energy and information analysis of confined quantum systems by means of density functional theory. PhD thesis, Indian Institute of Science Education and Research Kolkata.

Text (PhD thesis of Sangita Majumdar (15RS054)) 15RS054.pdf - Submitted Version Restricted to Repository staff only Download (1MB)

Abstract

This thesis deals with the energy spectrum as well as information theoretical analysis in some model and real quantum mechanical problems having chemical relevance. At first, we consider a model system represented by a generalized Kratzer potential. This is an exactly solvable potential having major significance in ro-vibrational spectroscopy in diatomic molecules. The objective is to quantify the probability distribution through Fisher information (I), Shannon entropy (S) and a complexity measure in conjugate r, p spaces. An exact analytical expression for Ir is derived for any given n, l, m state, while for Ip it is achievable only when m = 0. A simplified analytical formula is also obtained for Sr, but closed-form analytical solution remains elusive. They are expressed in terms of certain entropy integrals involving a class of orthogonal polynomials. Then we proceed for the atomic confinement studies. At first the simplest and celebrated confined H atom problem is addressed (in terms of information entropy), as the exact wave function is known in this case. Then we develop a suitable time-independent KS approach to pursue ground and excited states of a multi-electron atom enclosed inside a spherical cavity. Initially, it is applied to an impenetrable barrier and then to penetrable potential. This is accomplished by invoking a simple, physically motivated work-function-based exchange potential. The correlation effects are included by adopting (i) a simple, local, parametrized Wigner-type and (ii) a slightly involved nonlinear Lee-Yang-Parr functional. The eigenfunctions and eigenvalues are accurately obtained by means of a generalized pseudo-spectral method, satisfying appropriate boundary conditions. The energy spectrum, density moments as well as other properties are explored in a detailed, systematic manner. In order to probe the influence of confinement on these systems, several information measures like S, I, Onicescu energy, as well as the statistical complexity, are studied. Quite competitive results are obtained for Heisoelectronic series, as well as Li and Be atom, in both hard and soft confinement cases. In addition, the same scheme is also put to test for the prototypical so-called harmonium atoms; in free and confined environments. In recent years, this has played an important role in the construction of exchange-correlation functionals in density functional theory (DFT). These studies have opened up several avenues for further research, which are summarized in Chapter 8. In essence, we have presented a simple accurate and reliable scheme for atomic confinement within DFT.

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