CODE | CHE3100 | ||||||||||||
TITLE | Statistical Mechanics and Molecular Modelling | ||||||||||||
UM LEVEL | 03 - Years 2, 3, 4 in Modular Undergraduate Course | ||||||||||||
MQF LEVEL | 6 | ||||||||||||
ECTS CREDITS | 5 | ||||||||||||
DEPARTMENT | Chemistry | ||||||||||||
DESCRIPTION | Pre-requisite study-unit CHE2370 - Chemical Thermodynamics and Kinetics Content 1. Potential energy surfaces: - Introduction - Energy minima and saddle points - Potential energy surfaces of simple processes 2. Introduction to molecular modelling: - Types and scales of modelling - Molecular modelling - the input / processing / output phases - Introduction to the three main types of molecular modelling methods: Ab initio simulations; Semi-empirical simulations; Empirical simulations 3. Force-field based molecular modelling: - Empirical fit to the energy surface The energy expression; Introduction to Valence (bond), valence cross-terms and non-bond terms in a force- field; Introduction to force-fields - A closer look at force-fields Types of force-fields; A review of a few widely used force-fields; Advantages of having several force-fields - A technical look force-field methods Atom typing; Charge assignment; Functional forms: valence (bond) terms; valence cross-terms; non-bond terms - Handling non-bonded interactions The problem: number of non-bond terms; the significance of nonbond interactions beyond the cutoff distance; Aside - Periodic systems; The solutions: the step function; the spline function; the minimum-image convention; explicit-image model; the cell multipole method (CMM); the Ewald model 4. Energy minimisations - The minimisation process - Minimisation algorithms Line searches; Steepest descent; Conjugate gradient; Newton- Raphson methods - Convergence criteria - Choosing the 'right' minimiser 5. Quantum mechanical calculations - Introduction - Semi-empirical calculations: a) Methods: Huckel methods, NDO semi-emprirical methods: (CNDO, INDO, MINDO/3, MNDO, AM1, PM3, ZINDO/1, ZINDO/S) b) Applications of semi-empirical calculations 6. Introduction to statistical thermodynamics - What is statistical thermodynamics? - The distribution of molecular states - Instantaneous configurations, weight of configurations: a) The dominating configuration b) The Boltzmann distribution and the molecular partition function c) Energy states & energy levels d) The molecular partition function: translational contribution; rotational contribution; vibrational contribution; electronic contribution; overall partition function Ensembles a) Introduction (The concept of an ensemble, the canonical ensembles, the canonical partition function, other types of ensembles) b) The relationships/differences between the canonical partition function and the molecular partition function 7. Calculation of the various thermodynamic properties from the partition functions - Internal energy - Statistical entropy a) S = k ln W b) Derivation of the statistical entropy in terms of the partition function c) Residual entropies - Helmholtz energy - Pressure - Enthalpy - Gibbs energy - Heat capacities 8. Applications of statistical thermodynamics to perfect gases - Derivation of the equation of state of gas of independent particles from statistical thermodynamics. - Derivation of the thermodynamic properties for monoatomic perfect gasses. 9. Applications of statistical thermodynamics to chemical processes - The equilibrium constant a) Derivation of the equilibrium constant in terms of the partition function b) The physical basis for equilibrium constants - Activated complex theory a) Introduction b) The Eyring equation c) The experimental observation of the activated complex d) A thermodynamic approach to the Activated Complex Theory e) The activated complex theory and reactions between ions. - Aside: An alternative approach to studying reactions: a) Reactive encounters in the Gas Phase (The kinetic theory of gases, The Collision Theory) b) Reactive encounters in the Liquid Phase (Diffusion-controlled reactions, Activation-controlled reactions) 10. Simulating chemical processes: Vibrational calculations - Application of 'energy minimisations' to vibrational theory - Calculation of the vibrational frequencies: a) Transition states b) Binding 11. Molecular Dynamics and Monte Carlo Simulations - Introduction to Molecular Dynamics (MD) simulations (Deterministic approach): Integrators in MD Simulations; Introduction; Verlet integrators; What should we look for in an integrator; Choosing the right time-step; Integration Errors. - Ensembles in MD: NVT ensemble ; NVE ensemble; NPT ensemble; NPH ensemble. - Calculation and control of Temperature: Calculation of Temperature ; How temperature is controlled; Direct velocity scaling; Berendsen method of temperature-bath coupling. - Calculation and control of Pressure and stress: Introduction; Calculation of pressure and stress; Methods of controlling pressure - Types of MD simulations: Quenched dynamics; Simulated annealing; Consensus dynamics; Impulse dynamics; Langevin dynamics; Stochastic boundary dynamics - General methodology for dynamics calculations: Prerequisites ; Stages and duration of dynamics simulations; Equilibration stage; Production (data-collection) stage; How to run a simulation - Monte-Carlo Methods (Stochastic approach) 12. Molecular modelling in action - Applications of molecular modelling techniques to life sciences and materials science - An evaluation of commercially available molecular modelling packages Recommended texts: - Atkins' Physical Chemistry, 7th edition, by P.W. Atkins & de Paula (OUP) - Thermodynamics and Statistical Mechanics by J. M. Seddon and J.D. Gale (RSC publications) - Molecular Modelling, Principles and Applications, 2nd Edition by Andrew R. Leach (Longman Ltd.) - Computational Chemistry (Oxford Chemistry Primers), Guy H. Grant and W. Graham Richards (OUP) |
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STUDY-UNIT TYPE | Lecture and Tutorial | ||||||||||||
METHOD OF ASSESSMENT |
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LECTURER/S | Daphne Attard Joseph Noel Grima |
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The availability of optional units may be subject to timetabling constraints. Units not attracting a sufficient number of registrations may be withdrawn without notice. It should be noted that all the information in the description above applies to study-units available during the academic year 2024/5. It may be subject to change in subsequent years. |