Our group focuses mainly on molecular many body theory, theoretical spectroscopy, finite temperature non-perturbative many body theories. We were the first to develop and implement a class of many-body methods for electronic structure, known as the Multireference Coupled Cluster methods, which are now standard works in the field. A long-standing problem of guaranteeing proper scaling of energy for many electron wave-functions of arbitrary complexity has also been first resolved by us.
Our research interests comprise of:
Molecular electronic structure and theoretical spectroscopy
- Back in 1975, we came up with the idea of Valence Universal Cluster expansion theories for difference energies. We also developed a linear response theory based on coupled cluster formalism (CCLRT).
Quantum many-body dynamics
- We have developed a general time – dependent perturbative theory which remains valid for arbitrarily large time range and is free from secular divergences. Later, it was generalized to the many – body regime and formulated the first general time-dependent coupled cluster theory for wave functions of arbitrary complexity.
Statistical field theory
- We have developed a rigorous finite – temperature field theory to study Statistical Mechanics of Many-Body systems. Unlike the traditional Thermofield Dynamics formulations, which maps a finite temperature theory to a zero-temperature one, the method has the advantage of working directly with the physical variables in the finite temperature range and is thus both more natural and compact
Cummulant based quantum chemistry
- We have also formulated an electron correlation theory for strongly correlated systems by starting from a combination of reference functions using a generalization of the usual Ursell-Meyer cluster expansion. In order to achieve this, he developed a Wick-like reduction formula using the concept of generalized normal ordering for arbitrary reference functions. An important spin-off from the Generalized Wick’s Theoremhad been the methods of directly determining the various reduced density matrices via generalized Brillouin’s theorem and the contracted Schrödinger equations
State-specific Multireference (Mk-MR) Methods
- Recently, we have developed a suite of state-specific many-body formalisms which bypass the difficulty of the notorious intruder problem for computing potential energy surfaces. These methods do not share the shortcomings of the previously used Effective Hamiltonian formalisms applied to cases warranting a multireference description.
Relativistic coupled cluster theory
- We have, very recently, developed one of the most versatile many-body methods which can predict with quantitative accuracy the energetics, hyperfine interactions and transition probabilities of heavy atoms and ions where relativistic effects are important.