Principles and Applications of Molecular Statistics
Module title | Principles and Applications of Molecular Statistics |
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Module code | NSC3010 |
Academic year | 2023/4 |
Credits | 15 |
Module staff | Dr Stephen Green (Convenor) |
Duration: Term | 1 | 2 | 3 |
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Duration: Weeks | 11 |
Number students taking module (anticipated) | 45 |
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Module description
Previously, in NSC1003 Foundations in Natural Sciences, you have taken a largely classical approach to the laws of thermodynamics and their applications in chemistry, noting that classical thermodynamics relies upon no microscopic model of matter. You have also in NSC1003 and then further in NSC2002 Physical Chemistry, studied the quantum mechanics of atoms and molecules, which is our microscopic model of matter.You looked at the quantum mechanics behind atomic structure, periodicity, bonding and spectroscopy. We now must provide the link between the quantum mechanics of individual atoms and molecules and the laws of classical thermodynamics that apply to large collections of these particles. This is the realm of statistical thermodynamics and provides you with our “principles” of molecular statistics. The explosion of computer power over the last half a century means that “in silico” experiments can be readily performed. This enables you to apply the principles of molecular statistics to real-world scenarios and calculate quantities that are beyond the reach of analytical solutions. You will look at the principles and applications of molecular statistics and provide a deep understanding of how these topics underpin the fundamental properties and behaviour of matter.
Module aims - intentions of the module
The aim of this module is to build on the chemistry covered in NSC1003 Foundations in Natural Sciences and NSC2002 Physical Chemistry. The specific aims are to reconcile classical thermodynamics to quantum mechanics through statistical thermodynamics and to use computational techniques to explore applications of molecular statistics to complex systems.
You will develop the following graduate attributes:
- People skills in communicating with peers and discussing scientific ideas
- Independent research skills related to further reading around the topic
- Applied thinking and problem-solving – applying the knowledge you have gained to solve problems related to aspects of physical chemistry
Intended Learning Outcomes (ILOs)
ILO: Module-specific skills
On successfully completing the module you will be able to...
- 1. Describe in detail the consequences of degeneracy in terms of quantum states and levels in statistical thermodynamics, including the dilute limit.
- 2. Provide a physical interpretation of the molecular partition function and, given spectroscopic and other data, employ the equations relating the molecular partition function to thermodynamic functions, including the equilibrium constant.
- 3. Explain the principles of the ensemble method in statistical thermodynamics.
- 4. Describe in detail how a Monte Carlo simulation is implemented including the derivation of the selection rules and how to sample different ensembles.
- 5. Explain how computational approaches can be used to calculate thermodynamic properties including changes in free energy.
ILO: Discipline-specific skills
On successfully completing the module you will be able to...
- 6. Demonstrate and apply a knowledge and understanding of molecular statistics and symmetry as part of the sub-discipline of chemistry.
- 7. Describe and begin to evaluate aspects of current research in chemistry and chemistry-related areas (e.g. aspects of computational chemistry and materials chemistry) with reference to textbooks and other literature sources.
ILO: Personal and key skills
On successfully completing the module you will be able to...
- 8. Communicate ideas effectively and professionally by written means.
- 9. Participate and interact effectively and professionally in discussion of scientific ideas.
- 10. With some guidance, begin to develop the skills for independent study.
Syllabus plan
Whilst the module’s precise content may vary from year to year, it is envisaged that the syllabus will cover some or all of the following topics:
- A summary of combinatorial statistics and the Legendre method of undetermined multipliers.
- Derivation of the Fermi-Dirac and Bose-Einstein distributions, followed by their conflation in the dilute limit, within which the molecular partition function is introduced.
- The formulation of the functions of thermodynamics, including the equilibrium constant, in terms of the molecular partition function.
- A reprise of the quantisation of translational, rotational, vibrational and electronic energies of atoms and molecules, leading to equations for the contribution of these energy modes to the molecular partition function.
- The calculation of thermodynamic parameters, including the equilibrium constant, using the equations of statistical thermodynamics.
- An introduction to the ensemble method in statistical thermodynamics.
- A summary of how computational approaches can be used as “in silico” experiments for statistical thermodynamic theory.
- Derivation of selection rules and move types for Monte Carlo simulations and detailed understanding of the practicalities of running a simulation.
- How to calculate thermodynamic properties from computer simulations, focusing on free energy calculations.
Learning activities and teaching methods (given in hours of study time)
Scheduled Learning and Teaching Activities | Guided independent study | Placement / study abroad |
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22 | 128 | 0 |
Details of learning activities and teaching methods
Category | Hours of study time | Description |
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Scheduled Learning and Teaching | 22 | Lectures (11 x 2 hours) |
Guided Independent Study | 68 | Guided reading of scientific literature and textbook references, plus revision |
Guided Independent Study | 20 | Preparation for problems in lectures |
Guided Independent Study | 30 | Completion of continuous assessments |
Guided Independent Study | 10 | Preparation of group essay and presentation |
Formative assessment
Form of assessment | Size of the assessment (eg length / duration) | ILOs assessed | Feedback method |
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Problems and lecturer feedback during lectures | Ongoing in lectures | All | Oral |
Feedback via ELE Forum | ad hoc | All | Written |
Summative assessment (% of credit)
Coursework | Written exams | Practical exams |
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40 | 60 | 0 |
Details of summative assessment
Form of assessment | % of credit | Size of the assessment (eg length / duration) | ILOs assessed | Feedback method |
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Examination | 60 | 2 hours | 1-8 | Written via tutor |
Problem set 1, comprising numerical and short answers | 20 | 2 sides of A4 | 3-8 | Written |
Problem set 2, comprising computational, numerical and short answers | 20 | 2 sides of A4 | 1-2, 6-10 | Written |
Details of re-assessment (where required by referral or deferral)
Original form of assessment | Form of re-assessment | ILOs re-assessed | Timescale for re-assessment |
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Examination | See note below | 1-8 | Referral/deferral period |
Problem set 1 | See note below | 3-8 | Referral/deferral period |
Problem set 2 | See note below | 1-2, 6-10 | Referral/deferral period |
Re-assessment notes
Deferral – if you have been deferred for any assessment you will be expected to submit the relevant assessment. The mark given for a re-assessment taken as a result of deferral will not be capped and will be treated as it would be if it were your first attempt at the assessment.
Referral – if you have failed the module overall (i.e. a final overall module mark of less than 40%) you will be required to sit a further examination. The mark given for a re-assessment taken as a result of referral will count for 100% of the final mark and will be capped at 40%.
Indicative learning resources - Basic reading
Indicative basic reading list:
- N.M. Laurendeau, “Statistical Thermodynamics: Fundamentals and Applications”, Cambridge University Press.
- D. Frenkel and B. Smit, “Understanding Molecular Simulation: From Algorithms to Applications”, Elsevier
- M. P. Allen and D. J. Tildesley, “Computer simulation of Liquids”, Oxford University Press
Credit value | 15 |
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Module ECTS | 7.5 |
Module pre-requisites |
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Module co-requisites | None |
NQF level (module) | 6 |
Available as distance learning? | No |
Origin date | 07/06/2019 |
Last revision date | 04/05/2023 |