Thermodynamics and Molecular Modeling This course is for M.Sc. II (Sem-IV), Physical Chemistry students. It covers advanced level understanding of thermodynamics including statistical mechanics and molecular modeling. The course is intended to learn use of computation tools such molecular mechanics and molecular dynamics simulations to understand thermodynamic properties at molecular level. The detailed syllabus for the course is provided below.

PCH-XIII: Thermodynamics and Molecular Modeling

# 15 hrs

Exact and inexact differential expressions in two variables. Total differentials. Techniques of partial differentiations. Transformation of variables. Maxima and mimima. Integrating factors, Paff differential equations, Caratheodary’s theory. Legendre transformations. Derivation of thermodynamic identities. The second law of thermodynamics, classical formulations, mathematical consequences of second law. Entropy changes, Clausius inequality. Free energy concept. General condition of equilibrium. Thermodynamic potentials.

# 15 hrs

Ensembles, ensemble average and time average of the property, ergodic hypothesis, partition functions and thermodynamic properties, classical and quantum statistics, properties of photon gas, thermodynamic properties bosons, use of quantum statistics for evaluation of absolute entropies, condensation of helium, Fermi energy, electron gas in metals.

Heat capacity of solids, Einstein and Debye specific heat equations. Characteristic temperatures. Debye T3 law.

Molecular Mechanics: Introduction, the Morse potential model, harmonic oscillator model, force fields development, various energy terms and non-covalent interactions included in force fields, Lennrad-Jones type and truncated Lennard-Jones potentials, Kihara potential, commonly used force fields, parameterization, introduction to software packages used for performing molecular mechanics.

# 15 hrs

Introduction, microscopic and macroscopic properties, time scale of chemical/biological process, force field methods, bonded and non-bonded interactions, advantages and limitations of Force Field Methods, molecular dynamics methods, neighbour searching, Trotter decomposition, cut-offs, temperature and pressure coupling methods, integration algorithms: Verlet algorithm, Leap-frog algorithm, Velocity Verlet, Beeman’s algorithm, Constraint algorithms: shake, lincs, etc., Stochastic and Brownian dynamics, topology files, energy minimization: steepest descent method, conjugate gradient method, L-BFGS. Solvent models, Solvation, implicit and explicit solvation, heating dynamics, equilibration dynamics, production dynamics, trajectory analysis, particle mesh Edward dynamics, boundary conditions, Exclusions and 1-4 interactions, gradient based methods, steepest descent method, conjugate gradient method, replica exchange method, conformational analysis, normal mode analysis, free energy calculation: free energy perturbation method, thermodynamic integration method, thermodynamic cycles for free energy calculations, determination of hydration/solvation free energy, protein folding free energy, protein-ligand binding free energy etc. Software packages for performing Monte-Carlo and Molecular dynamic simulation as well as for visualization and analysis trajectories

# 15 hrs

Conversion of mass in closed and open systems, conservation of energy in closed and open systems. Law of increasing entropy. Non-adiabatic process and clausius inequality, steady state. Thermodynamic equations of motion. Chemical and electrochemical affinities. Coupling reactions. Rates and affinities. Generalized fluxes, forces and their transformation. Phenomenological equations and coefficients. Concepts of reciprocity relations and Onsager theorem of microscopic reversibility. Entropy production in closed and open systems. Entropy production due to heat flow. Chemical potentials. Diffusion, electromotive force, electro-osmosis, thermoelectric effect and other reactions involving cross relations. Saxens relations.

## Reference Books:

1.      S. N. Blinder, Advanced physical Chemistry, The Macmilan Company, 1967.

2.      L. K. Nash, Elements of statistical thermodynamics, 2nd Edition, Addison Wesley, 1974.

3.      T.L. Hill, An Introduction to Statistical Thermodynamics, Addison-Wesley, 1960.

4.      S. Glasstone, Theoretical Chemistry: An introduction to quantum mechanics, statistical mechanics, and molecular spectra for chemists, D. Van Nostrand Company, Inc., 1944.

5.      D. A. McQuarrie and J. D. Simon, Physical Chemistry: A molecular Approach, Viva Books, New Delhi, 1998.

6.      Allen, M. P., Tildesley, D. J. Computer Simulations of Liquids, Oxford: Oxford Science Publications. 1987.

7.      Frenkel, D.; Smit, B. Understanding Molecular Simulation: From Algorithms to Applications, 2nd Edition, Academic Press, San Diego, 2002.

8.      K.I. Ramachandran, G. Deepa and K. Nimboori, Computational Chemistry and Molecular Modelling: Principles and Applications, Springer-Verlag, Berlin, Germany, 2008.

9.      F. Jensen, Introduction to Computational Chemistry, 2nd Edition, John Wiley & Sons Ltd, West Sussex, England, 2007.

10.  Schlick, T. Molecular modeling and simulation: an interdisciplinary guide, Springer-Verlag New York, Inc., Secaucus, NJ, USA, 2002.

11.  D.B. Cook, Handbook of Computational Chemistry, Oxford University Press, New York, 1998.

12.  Online Manuals for simulation and visualization packages such as GROMACS, VMD, NAMD, AMBER, TINKER, etc.

13.  I. Prigogine, Introduction to Thermodynamics of Irreversible Processes, Wiley, New York, 1968.

14.  R.P. Rastogi, Introduction to Non-equilibrium Physical Chemistry: Towards Complexity and Non-linear Science, Elsevier, Oxford, 2008.