Faculty Information

Broad Area

Theoretical & Computational Chemical Physics

Specific Areas

• Dynamics of Barrierless Reactions.

The standard model for irreversible chemical reactions in solution would be a particle executing one-dimensional random walk on a harmonic potential, in presence of a point sink, located at an arbitrary position. An exact analytical time domain solution to this model was proposed by us. This has been an unsolved problem for long time and is of considerable importance as a model for chemical reaction in solution. We are able to solve problems beyond point sink model as well.

The standard model for reversible chemical reactions in solution would be a particle executing one dimensional random walk on two potential wells in presence of coupling between them. Exact Laplace domain solution of this model for point-like coupling between two potentials was proposed by us. This is an interesting & very important work in this field. Very recently we have proposed an exact analytical time domain solution of this same model, which was so far considered to be analytically intractable.

• Multi-state Problems in Quantum Mechanics.

Non-adiabatic transition due to potential curve crossing is one of the most important mechanisms to effectively induce electronic transitions in collisions. We consider two curves crossing each other & there is a point-like coupling between two curves, which causes transition from one curve to another. Exact solution of this model was proposed by us! This is an interesting & important work in this field. Our method of solution is used extensively to solve few related problems.

• Effective Spectroscopic Hamiltonian.

A reliable potential energy surface is required for studying the dynamics of a molecule in a particular electronic state. For polyatomic molecules, a global potential energy surface is out of reach of current computational capabilities. So one possible way to make progress is to use analytical functions with several parameters to fit the experimental data for constructing an effective Hamiltonian. One can use these effective Hamiltonians to extract new information about dynamics from information encoded in experimental spectra and to use these information to understand internal molecular energy flow and reaction dynamics. Even when the potential energy surface is available, effective Hamiltonians are constructed from the exact Hamiltonian in order to simplify the subsequent analysis. We have recently developed the first generalized polyad-breaking effective spectroscopic Hamiltonian for understanding bond dissociation process.

• Buckled Nano-Rod: A Two State System.

Two-state nano-mechanical systems (mechanical equivalent of 'bit') are very interesting examples for the possibility of observing quantum effects in them. The compression of a nano-rod would cause it to buckle. There are now two possible states, and the system is interesting, as a potential nano-sized device. We have developed quantum mechanical methods for the calculation of the rate of transitions between the two states, due to thermal fluctuations and tunnelling. Our method goes beyond the standard method (Transition State Theory). In future our plan is to analyze the same problem in detail using dynamical transition state theory.

• Proton Tunneling through aromatic/anti-aromatic ring - Two State Problem.

Proton tunnelling through ring compound with pi electrons is an interesting problem to study. It may be helpful in understanding electrophilic substitution reaction in solution as well as proton tunnelling in bio-systems. Here we will consider two types of planer ring compounds, one is aromatic and the other is anti-aromatic. Our aim is to study the effect of electron transfer from the ring compound to proton. So we will assume one dimensional model for motion of proton along a line perpendicular to the plane of benzene ring as well as through the middle of the benzene ring and construct a potential energy curve for the corresponding motion. We will repeat the same procedure for motion of neutral H-atom through positively charges benzene ring. We will use computational chemistry software for computation.

• Understanding Mechanism of Opening and Closing of Loop of a Long Polymer Chain.

Understanding the kinetics of loop formation of long chain polymer molecules has been an interesting research field both, to experimentalists and theoreticians. Loop formation is believed to be an initial step in understanding several protein events. The theories of loop formation dynamics are in general approximate. The looping dynamics of a single polymer chain having reactive end-groups have been modelled by simplest possible option. In our model, dynamics of end-to end distance is mathematically represented by an equation for a random walking under harmonic potential. Looping process is ensured by adding a sink of arbitrary strength in that equation. We have also incorporated the effect of all other chemical reactions involving either one or both of the end-group on rate of end-to-end loop formation - to the best of our knowledge this is the first time this has been done in any analytical model. An important future direction of this research is to understand the dynamics of contact formation between different parts of a long chain molecule. We will perform Brownian dynamics simulation studies of looping of a single polymer chains to see how ' shape of the sink function' decides the looping dynamics.