Research highlights


Molecular electronic structure and theoretical spectroscopy


  • Fock Space Multireference coupled cluster (FS-MRCC) formalisms: Mukherjee was one of he earliest developers of the FS-MRCC. These suite of theories are versatile, capable of describing molecular electronic states of general complexity and spin multiplicity. They provide powerful and compact description of the energetics of molecules in ground, excited, or ionized states with quantitative accuracy. The attractive aspects of these formalisms are size-extensivity and high accuracy. Several suite of standard softwares were based on these theories, and are probably the most widely applied MRCC theories.

  • A Linear response theory based on coupled cluster formalism (CCLRT), which is similar in scope to the SAC-CI and done independently of it. It pioneered the use of a dressed hamiltonian for energy differences. Appropriate modifications to the formalism to include strong relaxation effects such as core ionization or core electron spectroscopy led to further theoretical developments, such as relaxation-inducing cluster expansions.

  • Development of size-extensive many-body theories involving incomplete model spaces (IMS): Mukherjee resolved a long-standing problem of guaranteeing size-extensive theories starting with arbitrary reference functions. Many comprehensive papers on these topics have elicited much interest. A whole suite of molecular codes have been developed in Tel Aviv University, Israel, and in the program system DIRAC, which relies on both the FS-MRCC and the method of Mukherjee involving IMS.


State-specific Multireference coupled cluster (SS-MRCC) formalisms and Cumulant based quantum chemistry


  • Mukherjee was the earliest developer of a suite of state-specific many-body formalisms like coupled cluster and perturbative theories which bypass the difficulty of the intruder problem for computing potential energy surfaces. These methods alleviate the shortcomings of the previously used Effective Hamiltonian formalisms applied to cases warranting a multireference description. This theory has been extensively implemented by the group of Henry F. Schaefer, III, who coined the name Mk-MRCC for this method. The Mk-MRCC is probably the most extensively used method for potential energy surface studies, and it has led to the evolution of a widely used software in Psi4.

  • 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. This required developing a Wick-like reduction formula using the concept of generalized normal ordering for arbitrary reference functions. This has led to very compact and efficient formulation of several internally contracted SS-MRCC (IC-SS-MRCC). This formed many other activities in the international arena and there are several groups who are taking forward these ideas further. An important spin-off from the Generalized Wick's theorem had been the methods of directly determining the various reduced density matrices via generalized Brillouin's theorem and the contracted Schrödinger equations. Mukherjee developed such methods starting from this generalized Wick's theorem. The later theoretical formalisms were done in collaboration with Werner Kutzelnigg.


Relativistic coupled cluster theory


  • 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. These are regarded as the state-of-the art contributions in this field. This theory is flexible enough to take care of strong orbital relaxations accompanying core ionization for studying core ionization and core excitation spectroscopy without changing the orbitals of the parent neutral molecule. This recent development is increasingly finding its use in the international community.

  • Formulated with Bhanu Pratap Das a highly correlated coupled cluster method for understanding the effect of weak interaction in atoms and molecules, generated by Parity and CP violating terms in the Standard Model and beyond, which is one of the first theoretical formulations of this phenomenon which promises to be of high spectroscopic accuracy.


Statistical field theory


  • Developed a rigorous finite – temperature field theory to study Statistical Mechanics of Many-Body systems. This method is now widely known as thermal coupled cluster or thermal cluster cumulant (TCC) theories. The most important advantage of the formulation is that the working equations of TCC show polynomial scaling with resepct to the number of cluster amplitudes and is thus computationally very convenient. Unlike in the traditional Thermofield Dynamics formulations, which maps a finite temperature theory to a zero-temperature one, TCC has the advantage of working directly with the physical variables in the finite temperature range and is thus both more natural and compact.

  • Applications on partition functions for strongly coupled correlated systems. A useful spin-off of the method is the combined use of time-dependent coupled cluster method and boson-mapping of stochastic variables to provide a rigorous and systematic cluster expansion method for monitoring quantum dynamics of systems strongly perturbed by colored noise.


Quantum many-body dynamics


  • Development of a general time – dependent perturbative theory which remains valid for arbitrarily large time range and is free from secular divergences.

  • Generalization to the many-body regime and formulation of the first general time-dependent coupled cluster theory for wave functions of arbitrary complexity, with first applications to photo-excitations and energy transfer. The method should prove to be useful to study photo-fragmentation and dissociation processes.