| Summary: | Over the past few decades, constrained minimization of the energy with respect to the two- electron reduced-density-matrix (2-RDM) has emerged as a tantalizing alternative to study electronic structure of strongly correlated molecular and atomic systems at favorable polyno- mial scaling. In this thesis, we extend this variational minimization procedure to conducting systems in presence of a non-zero charge flux to mimic situations in single-molecular de- vices. We replicate the exponential length scaling of zero-bias conductance in off-resonant tunnelling dominated transport in oligoacenes (with a reasonable estimate of the decay con- stant) and even the trend reversal due to orientation flipping, all from the intrinsic features of the systems. When the method is applied to benchmark cases like 1,4-benzenedithiol clipped with Au electrodes, we see that unlike current theoretical standards, the theory does not over-predict the conductance by orders of magnitude compared to experimental results. In fact it is even consistent with all trends seen with respect to changing electrodes, linkers and chemical substitution over the molecular backbone studied experimentally over the years. The technique was also applied to a binuclear vanadium complex and its positively charged state known to exhibit Kondo resonance. We see that both the partners offers multiple orbital degeneracies necessitating important multi-reference effects completely missed in the previ- ous interpretation of the experiment based on model Hamiltonians. Such strongly correlated cases are untreatable by transport methodologies based on DFT. We not only reproduce the conductance trend seen experimentally but highlight the importance of many-body analysis in enhancing the Kondo features. We also apply the method to study switching action in pH sensors identifying the role of energetics and zero-field polarizability in controlling the conductance of the 'on' and 'off' states of the switch. Lastly we study the effect of spatially homogeneous electric field in altering quantum correlations and entanglement in molecular systems and interpret the results using geometric arguments.
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