Ph.D. THESIS COLLOQUIUM
Name: Mr. Subhajit Acharya
Ph. D. Supervisor: Prof. Biman Bagchi
Title: From Multidimensional non-Markovian Rate Theory to diffusion-entropy Scaling and Investigations into the validity of Stokes Law
Date &Time: Friday, 19th January 2024 at 4.00 P.M.
Venue: Rajarshi Bhattacharya Memorial hall, Chemical Sciences Building
Abstract: Multidimensional rate theory provides a theoretical framework for understanding chemical reactions that occur in systems with more than one reaction coordinate, such as isomerization reactions, protein folding, or electron transfer reactions.[1]Although recent years have seen many computational studies employing advanced simulation techniques, like umbrella sampling and metadynamics,to construct the reaction-free energy surface in terms of several reaction coordinates, less effort has been directed to calculate the rate by quasi-analytical means.In this context, we formulate a non-Markovian multidimensional rate theory, explicitly considering coupling at the level of Hamiltonian and friction between reactive and non-reactive modes. The formulation is quite general, allowing recovery of other theoretical approaches, such as Langer’s theory, Pollak’s Hamiltonian formulation, and van der Zwan-Hynes theory, under appropriate conditions. We then use the non-Markovian theory to calculate the rate in several interesting systems, namely (i) the isomerization rate of stilbene molecule in hexane solvent, (ii) the escape rate of a particle moving on a two-dimensional periodic potential energy landscape, (iii) dissociation rate of insulin dimer in water and (iv)homogeneousgas-liquid nucleation rate in LJ system. The rate predicted by the non-Markovian theory is found to bein good agreement with experimental and theoretical findings. An intriguing interplay between dimensionality and memory effects was observed in rate calculations. In this context, we unveil the microscopic mechanism for the early stage of insulin dimer dissociation and the role of water molecules in explicitly facilitating the hydrophobic disentanglement. [2-8]
In the second part, we derivean intriguingscaling relation between diffusion and entropy, starting from the basic principles of statistical mechanics. We explore this relation in different deterministic model systems, like two-dimensional periodic potential energy surface, periodic Lorentz gas, and the box-hole model introduced by Zwanzig. Our study reveals a noteworthy crossover in the plot of diffusion against entropy due to the correlated random walk induced by the characteristic nature of the potential energy surface. This study motivated us to investigate the non-monotonic friction dependence of diffusion in a multidimensional potential energy landscape. [2,9]
In the third part, we examine the validity of Stokes’ Law (SL) of hydrodynamics at molecular length scales for LJ and soft sphere systems at two different thermodynamic state points. We explain the origin of the enhanced linear regime in the absence of the attractive part of the interaction potential between the particles.[10]We also investigate the build-up of density in front of the moving sphere and the velocity profile to understand the origin of the wide validity of Stokes Law and, thereby, of linear response theory. Finally, as reported in recent experimental studies, we discuss the analytical, simulation, and quantum mechanical calculations to elucidate the rate enhancement observed in various reactions within charged microdroplets.[11-13].
References:
[1] B. Bagchi, Non-equilibrium Statistical Mechanics: An Introduction with Applications (CRC Press, 2023).
[2] S. Acharya, B. Bagchi, J. Chem. Phys. 156, 134101 (2022)
[3] S. Acharya and B. Bagchi, Phys. Rev. E.107, 024127 (2023)
[4] S. Acharya, S. Mondal, S. Mukherjee, and B. Bagchi. J. Phys. Chem. B.125, (34), 9678–9691 (2021)
[5] S. Mukherjee, S. Acharya, S. Mondal, P. Banerjee, and B. Bagchi. J. Phys. Chem. B.125 (43), 11793–11811 (2021) (special issue “125 Years of The Journal of Physical Chemistry”).
[6] S. Mukherjee, S. Mondal, S. Acharya, and B. Bagchi, Phys. Rev. Lett. 128, 108101 (2022)
[7] S. Acharya and B. Bagchi, “Friction and Memory Effects in Homogeneous Gas-Liquid Nucleation: Quest for Quantitative Rate Calculation” (manuscript under preparation)
[8] S. Mondal, S. Mukherjee, S. Acharya, and B. Bagchi. J. Phys. Chem. B.125 (29), 7958–7966 (2021)
[9] S. Acharya and B Bagchi. J. Chem. Phys. 153 (18), 184701 (2020).
[10] S. Acharya and B. Bagchi, “Stokes Law at Molecular Length Scales: Effects of Intermolecular Interactions and Linear Response Theory” (manuscript under review), 2023
[11] S. Mondal, S. Acharya, R. Biswas, B. Bagchi and R. N. Zare, J. Chem. Phys. 148(24), 244704 (2018)
[12] S. Kumar, S. Acharya, B. Bagchi, Physical Review E.107, 024138, (2023)
[13] S. Mondal, S. Acharya, and B. Bagchi. Phys. Rev. Research. 1(3), 033145 (2019)