The shape invariance condition is the integrability condition in supersymmetric quantum mechanics (SUSYQM). It is a difference-differential equation connecting the superpotential W and its derivative at two different values of parameters. We show that this difference equation is equivalent to a non-linear partial differential equation whose solutions are translational shape invariant superpoten...

Among the various theoretical tools for investigating microscopic material properties, ab initio (first principles) methods based on density functional theory and pseudopotentials have had a very good track record over the last two decades in terms of accuracy, reliability, and efficiency. The application of these methods to nanostructures to investigate their structural, electronic, and optica...

We extend the application of ab initio Gibbs ensemble method to metallic system by including contribution excited electronic states.

NMR chemical shifts for an L-alanine molecular crystal are calculated using ab initio plane wave density functional theory. Dynamical effects including anharmonicity may be included by averaging chemical shifts over an ensemble of structural configurations generated using molecular dynamics (MD). The time scales required mean that ab initio MD is prohibitively expensive. Yet the sensitivity of ...

Low-energy nuclear theory has entered an era of ab initio nuclear structure and reaction calculations based on QCD. One of the most promising paths from QCD to nuclear observables employs Hamiltonians constructed within chiral effective field theory as starting point for precise ab initio studies. However, the full inclusion of chiral twoplus three-nucleon (NN+3N) interactions in exact and appr...

This article addresses a fundamental problem faced by the ab initio community: the lack of an effective formalism for the rapid exploration and exchange of new methods. To rectify this, we introduce a novel, basis-set independent, matrix-based formulation of generalized density functional theories which reduces the development, implementation, and dissemination of new ab initio techniques to th...

RNA molecules are essential cellular machines performing a wide variety of functions for which a specific three-dimensional structure is required. Over the last several years, the experimental determination of RNA structures through x-ray crystallography and NMR seems to have reached a plateau in the number of structures resolved each year, but as more and more RNA sequences are being discovere...

In this chapter, an introduction to ab initio molecular dynamics (AIMD) has been given. Many of the basic concepts, like the Hellman-Feynman forces, the difference between the Car-Parrinello molecular dynamics and AIMD, have been explained. Also a very versatile AIMD code, the CP2K, has been introduced. On the application, the emphasis was on the aqueous systems and chemical reactions. The bioc...

We report a highly correlated multireference configuration interaction calculation of the near-equilibrium potential energy surface of ozone using a large correlation consistent basis set. Three-dimensional analytical expressions are obtained for the potential energy and dipole moment functions using least-squares fits to ab initio points near the C2v equilibrium geometry. Low-lying vibrational...

This article addresses a fundamental problem faced by the ab initio community: the lack of an effective formalism for the rapid exploration and exchange of new methods. To rectify this, we introduce a novel, basis-set independent, matrix-based formulation of generalized density functional theories which reduces the development, implementation, and dissemination of new ab initio techniques to th...