CHEM20190 Intermediate Physical & Theoretical Chemistry

Unit catalogue DLM

Molecular Energies

Lecturers Professor Fred Manby and Professor Mike Ashfold
Format 9 lectures
Learning objectives Understand:
  • the origin of quantization of molecular energies and to demonstrate wavefunctions are solutions to the Schrödinger equation for any 1-D problem; for particle in the 2-D box and for the hydrogen atom.
  • the linearity of operators, and identify eigenvalues and eigenvalues.
  • the quantum mechanics of particle-in-a-box and its relationship to simple properties of ideal gases.
  • the quantum mechanics of the rigid rotor and its relationship to microwave spectroscopy, and be able to deduce structural parameters from microwave spectra.
  • the relationship between the quantum mechanics of the harmonic oscillator and its relationship to IR spectroscopy.
Be able to:
  • identify stable structures, transition states and reaction pathways on simple potential energy surfaces.
  • explain the phenomenon of quantum tunnelling.
  • use the Eyring equation to estimate rates of unimolecular processes, and be able to use this in the context of NMR spectroscopy.
  • explain the concepts of correlated and uncorrelated many-electron wavefunctions.
  • account for the role of spin and the Pauli principle in the quantum mechanics of many-electron systems.
  • demonstrate a quantum mechanical understanding of the phenomena of fluorescence, phosphorescence, internal conversion and intersystem crossing, and (pre)dissociation.
  • understand the kinetics of two competing processes, including quenching of fluorescence/phosphorescence.
Synopsis Molecules have discrete energy levels. Transitions between these energy levels can be explored using spectroscopy, revealing exquisitely detailed information about molecular structure, nuclear motions and reactivity.
When many molecules are present, thermal energy is distributed amongst the molecules leading to statistical contributions to the forces that drive chemical change.
In this course we will study the quantum mechanics of simple systems to explore the theoretical basis for our understanding of atomic line spectra, the behaviour of ideal gases, molecular vibrations and rotations and chemical reactivity.

Course outline:

  1. A brief account of how it all works
  2. Free particle and particle in a box
  3. The rigid rotor, rotations and microwave spectroscopy
  4. The hydrogen atom
  5. Nuclear motion, the harmonic oscillator and infra-red spectroscopy
  6. The potential energy surface
  7. Many-electron systems
  8. Approximations in quantum mechanics
  9. Photochemistry

Essential reading

  • Atkins' Physical Chemistry, 10th Edition, PW Atkins and J de Paula, Oxford, 2014 (although earlier editions will be useful)
Recommended reading
  • Molecular Driving Forces, 2nd Edition, KA Dill and S Bromberg, Garland, 2011
  • Quanta, Matter, and Change, P W Atkins, J de Paula and R Friedman, Oxford, 2009

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Molecular Thermodynamics

Lecturer Dr Jeroen van Duijneveldt
Format 9 lectures
Learning objectives
  • Reproduce derivation of Boltzmann distribution
  • Define partition function and calculate for single molecule
  • Calculate mean energy from partition function and derive barometric law
  • Apply the first law to characterise reversible changes.
  • Use enthalpy to characterise changes and reactions at constant pressure.
  • Explain the origin and usefulness of the Joule-Thomson effect.
  • Define entropy and Helmholtz and Gibbs free energies
  • Identify requirements for spontaneous changes.
  • Use chemical potential and osmotic pressure to describe ideal solutions.
Synopsis This course will introduce thermodynamics starting from molecules and their energy levels. The course focuses on pure compounds and non interacting molecules. Key topics are:
  • The Boltzmann distribution is the most probable one.
  • The molecular partition function.
  • Mean energy, equipartition and the canonical partition function.
  • The first law.
  • Heat capacity and enthalpy.
  • Thermochemistry , Hess’s law, Kirchoff’s law, and the Joule-Thomson effect.
  • The second law: entropy and spontaneous change. Carnot cycles.
  • Entropy, the third law, and Helmholtz and Gibbs free energies.
  • Spontaneous change and chemical potential.
Essential reading
  • Atkins’ Physical Chemistry, 10th Edition, PW Atkins and J de Paula, Oxford, 2014 (although earlier editions will be useful)
Recommended reading
  • Quanta, Matter, and Change, PW Atkins, J de Paula, and R Friedman, Oxford, 2009
  • Molecular Driving Forces, 2nd Edition, KA Dill and S Bromberg, Garland, 2011

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Molecular Driving Forces

Lecturer Professor Paul May
Format 6 lectures
Learning objectives
  • To appreciate how how the behaviour of atoms, molecules and energy levels gives rise to useful thermodynamic principles, such as Gibbs energy and equilibrium constants.
  • To understand that ΔG is a useful indicator of the direction of change, and to be able to calculate ΔG for a variety of different chemical systems and conditions.
  • To understand the differences between ideal and non-ideal mixing, and to show that ideal mixing is driven only by entropy.
  • To understand the concept of chemical potential and its predictive ability for chemical change.
  • To understand how equilibria arise, and the response of equilibria to changes in process conditions.
  • To realise that equilibria can also be calculated from first principles, by considering the partition functions of the reactants and products.
Synopsis This course of 6 lectures follows on directly from the course on Molecular Thermodynamics. The aim is to build on the concepts in this previous course, and to develop the concepts of chemical thermodynamics for interacting systems. The course will be taught using an approach which considers how the behaviour of atoms, molecules and energy levels gives rise to useful thermodynamic principles, such as Gibbs energy and equilibrium constants.
Course outline:
  1. Reversible systems, Trouton’s law & exceptions, Irreversible changes, ΔG as the indicator of direction of change, Lattice model example, ΔG as a function of temperature (Gibbs-Helmholtz Eqn).
  2. ΔG as a function of pressure for liquids/solids and gases, chemical potential, using ΔG to predict phase changes, phase boundaries, Clapeyron Eqn, Clausius-Clapeyron Eqn, simple phase diagrams.
  3. Mixtures – variation of ΔG with composition, partial molar quantities & chemical potential, the Fundamental Equation, equations for ΔG, ΔH and ΔS of mixing ideal gases derived from a (a) statistical method, (b) standard method, and (c) molecular interpretation.
  4. Ideal liquid mixtures and solutions, brief look at real solutions, chemical potentials in a mixture, Raoult’s Law, Henry’s Law, how concentration affects melting/boiling points of solutions, dissociation of salts in solution, degree of dissociation.
  5. Relationship between ΔG and equilibria, perfect gas equilibria, general reaction equilibria, response of equilibria to temperature & pressure, Le Chatelier’s principle, the van’t Hoff Eqn.
  6. Statistical description of equilibria, relating K to the partition functions of reactants & products for (a) exothermic, (b) endothermic reactions, (c) endothermic reactions where product has high d.o.s., a worked example of how to calculate K from q.
1 workshop (1 hour) accompanies the course. There will also be a linking workshop which covers some of the material common to this course and the previous one on Molecular Thermodynamics. Online questions will be available to give you examples of possible exam questions.
Essential reading
  • Atkins’ Physical Chemistry, 10th Edition, PW Atkins and J de Paula, Oxford, 2014 (although earlier editions will be useful)
Recommended reading
  • Molecular Driving Forces, 2nd Edition, KA Dill and S Bromberg, Garland, 2011
  • Quanta, Matter, and Change, P W Atkins, J de Paula and R Friedman, Oxford, 2009

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Chemical Reactivity

Lecturer Professor Dudley Shallcross
Format 6 lectures
Learning objectives At the end of the course students should be able to
  • Construct a rate of change equation for any species within a multi-step reaction sequence
  • Apply the steady-state approximation (SSA) to reactive intermediates
  • Simplify overall reaction rate equations using the SSA
  • Apply these ideas to unimolecular reactions, termolecular reactions, enzyme kinetics and reactions in solution.
  • Understand the inadequacies of simple collision theory and the advantages of transition state theory.
  • Understand some basic ideas about the different potential energy surfaces arising from the reaction systems studied.
Synopsis Chemical reactivity is at the heart of a chemical investigation. How fast a reaction proceeds and how it can be slowed down or speeded up are important pieces of information. In this course we will move on from single step reactions and consider multi-step processes involving free radicals. Examples are drawn from all areas of chemistry but showing a common theme and approach to analysis. It is assumed that students will know how to integrate zero, first and second order reactions from year 1 and that basic ideas such as order of reaction, molecularity and the Arrhenius Equation (A and Ea) are known.

Recap and Multi-step reactions

  • Importance of concentration, temperature, catalysts in determining the rate of a reaction.
  • Writing a rate equation.
  • Multi-step reactions
  • Consecutive reactions and the steady state approximation

Examples of the use of the steady state approximation

  • Unimolecular and termolecular reaction (Lindemann mechanism, Limitations of Lindemann, association reactions with an apparent negative activation energy)
  • Photochemical reactions (cf MNRA course)
(application of the steady state approximation to photochemical intermediates)
  • Pathways, quenching, reaction, etc.
  • Stern-Volmer analysis

Reactions in Solution

  • Diffusion controlled
  • Activation controlled
  • Enzyme kinetics (Michaelis-Menten etc.)

Theory of bimolecular rates

  • Collision Theory
  • Collision Theory and its limitations
  • Transition Theory
    kobs = {kBT}/{hCÓ©} exp(ΔS / R) exp(-ΔH / RT)

    Potential energy surfaces

    Following on from ideas introduced in Molecular Energies (FRM/MNRA) we will discuss qualitatively, different types of PES with reference to examples drawn from the course.
Essential reading
  • Atkins’ Physical Chemistry, 10th Edition, PW Atkins and J de Paula, Oxford, 2014 (although earlier editions will be useful)
Recommended reading
  • Reaction Kinetics, M.J. Pilling and P.W. Seakins, Oxford, 1995

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Molecular Interactions

Lecturer Professor Adrian Mulholland
Format 6 lectures
Learning objectives
  • To learn how molecules interact with one another, through electrostatic interactions and through polarization.
  • To understand how these interactions determine the structure of solids and liquids.
  • To understand how the complex nature of intermolecular interactions make it useful to use computer simulations to predict the structure of liquids (and also related systems such as biomolecules).
Synopsis
  • Electrostatic properties of molecules
  • Charges, Dipole moments, higher-order multipoles
  • Intermolecular interactions and Coulomb’s Law
  • Polarizability, electric fields, and induced dipoles
  • Dipole-dipole interactions, dispersion interactions
  • Hydrogen bonding
  • Interactions and the structure of solids and liquids
  • The structure of liquids: the radial distribution function
  • Computational modelling of liquids: empirical forcefields and molecular dynamics
  • The lattice model of liquids
  • Hydrophobic interactions
  • Interactions and structure of biomolecules
Essential reading
  • Atkins’ Physical Chemistry, 10thEdition, PW Atkins and J de Paula, Oxford, 2014 (although earlier editions will be useful)

Recommended reading
  • Molecular Driving Forces: Statistical Thermodynamics in Biology, Chemistry, Physics, and Nanoscience, Ken Dill and Sarina Bromberg, 2nd edition, Garland Science, 2010.

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Organized Molecules

Lecturer Dr Paul Bartlett
Format 6 lectures
Learning objectives
  • Rationalise the properties of materials from a knowledge of molecular interactions
  • Explain the energetics of surfaces and give examples of the effects of surface energy
  • Explain the reasons for the different molecular assembly found in liquid crystalline phases
  • Rationalize the stability of nanoparticle suspensions.
  • Describe the orientational order of liquid crystalline phases
Synopsis The purpose of this course is to provide an introduction to nanosystems where the specific molecular arrangement of molecules is the key to an understanding of their physical properties. In the course we will discuss how the nanoarchitecture at interfaces, in micelles, in liquid crystals, in polymers, and nanoparticles leads to novel and distinctive properties. Theoretical concepts will be illustrated by real-life, practical examples.
  • Why interfaces are important
  • Surface tension
  • Capillarity
  • Stable nano-sized systems
  • Molecular self-assembly
  • Liquid crystals
Essential reading
  • Atkins’ Physical Chemistry, 10th Edition, PW Atkins and J de Paula, Oxford, 2014 (although earlier editions will be useful)
Recommended reading
  • An Introduction to Soft Matter – synthetic and biological self-assembling materials, 2nd Edition, IW Hamley, Wiley, 2007
  • An introduction to Interfaces and Colloids, John Berg, World Scientific, 2010.
  • Soft Matter -The Stuff that Dreams are Made Of, R Piazza, Springer, 2011

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Interfaces, Energy Conversion and New Materials

Lecturer Professor David Smith and Dr Wuge Briscoe
Format 6 lectures
Learning objectives
  • Understand the concept of electrochemical potential of ions in condensed phase
  • Familiarize with the concept of ion activity and how it manifests itself in real solutions
  • Building from electrochemical potentials, to develop the notion of redox reactions
  • Rationalize the concept of electrode potential and its relationship with thermodynamic functions
  • Understand the basic thermodynamic relations in electrochemical cells – Nernst potentials
  • Examine the redox process underpinning batteries and fuel cell technology
  • Understand the potential distribution across metal/electrolyte interfaces – electrical double layer
  • Design strategies for constructing functional materials using electrostatic interactions in condensed phase
  • Integrate the basic thermodynamic concepts mentioned above in designing interfacial systems capable of converting chemical into electrical energy and vice versa.
Synopsis Electron transfer reactions not only lie at the centre of life-sustaining processes such as photosynthesis and cellular respiration, but also play an ever increasing role in powering our energy intensive society. This course will provide the thermodynamic concepts underpinning electrochemical reactions and the behaviour of ions in solution. These concepts will lead to a basic understanding of energy storage devices, from disposable batteries to sophisticated fuel cells and supercapacitors. This course will also give a brief description of the structure of electrochemical double layer and how ionic interactions can be used to make a wide range of functional materials. The course will cover the following topics:

The electrochemical potential of ions in solution and ion activity

  • The Galvani potential in condensed phases
  • Debye-Huckel theory

Redox equilibrium and the Galvani potential difference:

  • Potential difference between a metal electrode and redox species in solution
  • Liquid potentials
  • Electrochemical cells
  • The Nernst equation

Electrochemical energy conversion:

  • The cell potential and the electromotive force
  • Leclanche, alkaline, lead acid, Li insertion and Ni-Cd batteries
  • Hydrogen, methanol and formic acid fuel cells

The electrochemical double layer:

  • Potential distribution across the metal/electrolyte interface
  • The Stern model
  • Supercapacitors

From molecules to nanostructures to materials to systems:

  • Surface modification via self-assembly
  • Electrostatic stabilisation of nanostructures
  • Electrostatic adsorption
  • Constructing composite materials
  • Electrostatic layer-by-layer adsorption
Essential reading
  • Atkins’ Physical Chemistry, 10th Edition, PW Atkins and J de Paula, Oxford, 2014 (although earlier editions will be useful)
Recommended reading
  • Molecular Driving Forces, 2nd Edition, KA Dill and S Bromberg, Garland, 2011

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