Study-Unit Description

Study-Unit Description


TITLE Statistical Mechanics and Molecular Modelling

LEVEL 03 - Years 2, 3, 4 in Modular Undergraduate Course



DESCRIPTION Pre-requisite study-unit

CHE2370 - Chemical Thermodynamics and Kinetics


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
    -  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
       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)

STUDY-UNIT TYPE Lecture and Tutorial

Assessment Component/s Assessment Due Resit Availability Weighting
Assignment SEM2 Yes 40%
Examination (2 Hours) SEM2 Yes 60%

LECTURER/S Daphne Attard
Joseph Noel Grima

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