A long-standing problem of guaranteeing proper scaling of energy for many electron wave-functions of arbitrary complexity has also been first resolved by him.

He has also been the first to develop a rigorously size-extensive state-specific multi-reference coupled cluster formalism, and its perturbative counterpart which is getting increasingly recognized as a very promising methodological advance.

Mukherjee has been the earliest developer of a class of many-body methods for electronic structure which are now standard and highly acclaimed works in the field.

He also developed a linear response theory based on coupled cluster formalism (CCLRT),[2] which is similar in scope to the SAC-CI and done independently of it.

A long-standing problem of guaranteeing size-extensive theories starting with arbitrary reference functions has also been first resolved by him which has attracted wide international attention.

Mukherjee has developed a rigorous finite – temperature field theory to study Statistical Mechanics of Many-Body systems.

Recently Mukherjee has developed a suite of state-specific many-body formalisms[4] like coupled cluster and perturbative theories 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.

This theory has been extensively implemented by the group of Henry F. Schaefer, III, who coined the name Mk-MRCC for this method.

Mukherjee has 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.

Then, in 1978, he returned to Calcutta as Reader in the Department of Physical Chemistry at the Indian Association for the Cultivation of Science (IACS) where he has stayed to this day.