Dr. Aniruddha Chakraborty

School of Basic Sciences

Indian Institute of Technology Mandi

Mandi, Himachal Pradesh 175001

India

ph: +(91)1905-237930

achakrab

**PROJECTS**

- Seed Grant (2012-15): "Dynamical Analysis of Highly Excited Molecular Spectra", IIT Mandi, India, INR. 4,70,000 (P.I.).

* Summary: Understanding dynamics of highly excited vibrational motion of small molecules is an interesting contemporary research area. The aim of *

* this research is to extract new dynamical** informations encoded in experimental frequency domain spectra. Effective spectroscopic Hamiltonians *

* are very useful to analyze and extract informations from experimental and simulated spectra. The standard approach for building an *

* effective spectroscopic Hamiltonian is well understood for systems far below the dissociation energy of any bond. This project is aimed to *

* extend our method to energies above the dissociation energy of any bond.*

- Research Grant (2012-17): "Supramolecular High Energy Compounds: synthesis, Characterization & theoretical Studies", Defence Research & Developement Organization, India, INR. 3600000 (Co-P.I.).

* Summary: High energy materials are widely used for several interesting applications. This project is aimed to synthesize a number of new high *

* energetic materials guided by advanced molecular modelling studies. Along with the synthesis, in the theoretical aspect of this project, heat *

* of formation of possible new materials will be estimated using standard density functional theory. *

- Research Grant (proposal - to be submitted): "Understanding complexity of internal dynamics of biological molecules", Department of BioTechnology, India (P.I.).

* Summary: T**he internal dynamics of biological macro-molecules are very complex. One of the major classes of these are proteins. An interesting problem, *

* still far from complete understanding is the connection between sequence of amino acid residues and the very specific native structure. So the *

* first question here is what dictates whether a given sequence has a reliable native structure or not, if it has what that structure would be? or what *

* it is about the sequence that makes it a good folder. Understanding sequence-structure connection is important because it would make it possible*

* to design sequences in the laboratory to fold to a definite structure, which then could be tailored to biological activity. The aim of this project is *

* to know **sequence-structure connection and then use that for predicting the kinetic mechanism by which a protein folds to its native structure.*

- Research Grant (submitted): "Dynamical Analysis of Highly Excited Molecular Spectra", EMR - Science & Engineering Research Board, India. INR. 27,60,000 (P.I.).

* Summary: The classical phase space structure and dynamics of vibrational Hamiltonian with mixed chaotic and regular motions are of great interest.*

* Standard method of studying this system is to use approximate effective Hamiltonians (although it is not correct), which possess a special *

* constant of the motion. This ``total action” with its corresponding quantum number is a very interesting feature of the actual dynamic. *

* The total action is in general called a ``polyad quantum number”. However, useful as an analytical tool, there are limitations in applying the *

* effective Hamiltonian for molecules at higher energies. The limitations are due to the fact that the exact dynamics actually contains in principle,*

* an infinite number of resonance couplings,hence breakdown of the total polyad action. The vibrational energy levels of systems with more than *

* two degrees of freedom that break the polyad action, time-dependent transport, and the representation of them by the use oeffective Hamiltonian *

* are entirely unexplored area of research. This project is aimed to constrcution of an effective polyad-breaking for a system with more than *

* three degrees of freedom & analyze the phase space structure to extruct dynamical information.*

- Research Grant (submitted): "Reaction-Diffusion Systems: Exact Solution Beyond Dirac Delta Function Sink Models", Mathematical Research Impact Centric Support,- Science & Engineering Research Board, India. INR. 6,00,000 (P.I.).

* Summary: Understanding the dynamics of diffusion controlled reactions in solution is an interesting problem. A reasonably good model for understanding *

* such reaction would be a particle executing one dimensional random walk on an appropriate potential in presence of a sink. This process can be*

* mathematically represented by the following modified Smoluchowski equation. Until now the exact analytical solutions of that Smoluchowski *

* equation is possible only in those cases where sink function is related to Dirac delta function of position coordinate. In this project we are planning *

* to find an exact analytical solution of the same equation** using a new localized sink function.*

- Research Grant (proposal - in preparation): "Electron solvation by a layer of polar adsorbates - realistic model", (P.I.).

* Summary: An electron near a metal surface feels the charge of its image in the metal and therefore it moves under the influence of this attractive *

* potential. Harris et. al., reported an experimental study of the dynamics of electron in image states of a metalsurface having polar adsorbates on *

* it - they find two kinds of states, viz., one localized and the other delocalized. There have been attemps to model the process, but the problem is *

* the nature of the image potential state is not known owing to the lack of detailed knowledge of the geometry of the metal surface. All the *

* theoretical calculations done so far have used flat metal surface. In this project we will consider a model in which we account for non-flateness *

* of the surface. *

- Research Grant (submitted): "Curve Crossing Problems with Arbitrary Coupling", Council of Scientific & Industrial Research, India, INR. 13,20,000 (P.I.).

* Summary: Nonadiabatic transition due to potential eenergy curve crossing is an interesting mechanism to induce electronic transitions in collision process. *

* There are examples where the transition is in between two states and also there are cases of involvement of more than two states in the process. *

* Thre are only few cases where exact analytical solution of two state problem is available but those involve specific shape of potentials and *

* coupling term. The aim of this project is to solve multi-state problems involving both potentials and coupling terms as arbitrary functions *

* of position and time. *

- Research Grant (proposal - in preparation): "Thermal Diffusivity in Realistic Solid", (P.I.).

* Summary: Temperature and heat flow are the two important quantities in understanding heat conduction. When temperature distribution is not uniform *

* at all points of a solid, then heat energy flows in the direction of less temperature. The Fourier equation is in general used in understanding *

* heat conduction, which is valid only for a stationary homogeneous isotropic solid without any heat source. But in reality we have solids of *

* different shapes, e.g., we can have a cylinder with non-unifrom cylindricity, also there may be real life examples where cylindricity changes *

* with time. The aim of this project is to understand the effect of such types of non-uniformity in shape on thermal diffusivity. *

- Research Grant (proposal - in preparation): "Buckled Nano Rod A Two state System and its Quantum Dynamics using exact Hamiltonian model", (P.I.).

* Summary: This research project is on theoretical investigation of the dynamics of a mechanical two level system (mechanical equivalent of** the 'bit'). *

* The compression of a nano-rod would cause it to buckle. There are now two possible buckled state & the system is interesting as a nano *

* sized memory device. We have very recently developed a theoretical approach for the calculation of classical rate of transition between *

* two buckled state using an exact model Hamiltonian. Now the plan is to develope a method to calculate quantum rate using the same *

* model Hamiltonian. Then we will apply our method to the case of carbon nanotube. A calculation using system plus reserviour model will\*

* also be done.*

- Research Grant (PES accepted - Full proposal to be submitted): "Understanding the Dynamics of Vibrational excitation in C60 single molecule transistor - An effective Hamiltonian Approach", Nano Mission, Department of Science & Technology, India, INR. 15,73,000 (P.I.).

* Summary: In an interesting experiment, Park et. al., reported a three electrode transistor made using a single C60 molecule. Like standard field *

* effect transistors, the voltage on the "gate" electrode controls the current flowing from the source electrode through the C60 molecule to *

* the drain electrode. The experiment shows that the oscillatory motion of C60 trapped between the two electrodes can be excited by passage *

* electrons through the system. There are attemps to model the process. But this process involve several unknowns, which does not allow to *

* model it appropriately. The nature of potential for centre of mass motion of C60 is not known due to the lack of detailed knowledge of the *

* electrode geometry. The experimental and theoretical work jointly lead to the conclusion that the formation of negatively charged C60 *

* results in a shift of the equilibrium geometry by about 3-4 pm. It was suggested that this shift arises due to the image interaction, though the *

* details of the geometry that would lead to such a shift was never discussed. We plan to consider the simplest possible model, which describe \*

* the physics of the problem. The C60 molecule sits under the potential of both electrodes. Adding an extra electron to C60can change the *

* C60 - metal equilibrium distance due to the image image interaction. When this negatively charged C60 gives that extra electron to the *

* drain electrode, the former equilibrium position is regained and the molecule may be left in an excited state of "center of mass" oscillation. *

* This is reminiscent of two photon processes encountered in resonance Raman scattering. Here we will derive a formula for current, similar *

* to Kramers-Heisenberg-Dirac formula. Using this formula we will estimate the unknown parameters (non-linear experimental fit of the *

* experimental data) which will give us a relatively** good understanding of the relative contribution of differnt possible mechanisms for the process. *

- Research Grant (submitted): "Effective Hamiltonian for bond dissociation process", HRHR - Science & Engineering Research Board, India. INR. 36,00,000 (P.I.).

* Summary: A reliable potential energy surface is necessary for analysing the dynamics of a molecule in a particular electronic state. For large *

* polyatomic molecules, a global potential energy surface is out of reach of even the best current computational capabilities. So the only *

* way to make progress is to use analytical functions for potential with several parameters to ﬁt the experimental data. But this method requires *

* one to guess the possible analytical form that defines the potential energy surface. For unknown potential energy surface the effective *

* spectroscopic Hamiltonians are the only method for extracting information from experimental data. This type of Hamiltonian is very useful even *

* when it is too difﬁcult to calculate the spectra starting from the potential energy surface. So far it was not possible to construct an *

* effective Hamiltonian for energies above bond dissociation energy, because of lack of knowledge of how states above dissociation *

* energy (continuum of energy) interact with the states below dissociation energy (discrete of energy). The aim of this project is to propose a *

* method for constructing such effective Hamiltonian and use it for creating new knowledge of bond dissociation process. *

- Research Grant (to be submitted): "Electron-electron correlation in quantum dot", (P.I.).

* Summary: **Understanding the effect of electron correlation in Quantum dot is an interesting and important area of research both theoretically *

* and experimentally. One of the most interesting features of quantum dot is that it is possible to add extra electrons one at a *

* time, step by step. Electrons in a quantum dot feel a central potential due to the semiconductor nanostructure. This is equivalent to *

* an attractive oscillator potential. So the motion of these electrons in these systems is expected to be more like vibrating atoms in *

* real molecules. So one should expect all the effects of an-harmonicity, such as bifurcations, local and normal modes, Fermi resonances, *

* and approximate polyad numbers for electrons in a quantum dot. If these molecule-like effects turn out to have some interesting use *

* in electronic devices, this would become another important area of fundamental research. In this project we will try to explore this *

* option theoretically.*

For IIT Mandi Students (B.Tech./M.Tech./M.S./M.Sc./Ph.D.) - You are always welcome to inquire about working on a project (irrespective of your discipline). For more details - visit my office!

Dr. Aniruddha Chakraborty

School of Basic Sciences

Indian Institute of Technology Mandi

Mandi, Himachal Pradesh 175001

India

ph: +(91)1905-237930

achakrab