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Study information

Principles and Applications of Molecular Statistics

Module titlePrinciples and Applications of Molecular Statistics
Module codeNSC3010
Academic year2023/4
Credits15
Module staff

Dr Stephen Green (Convenor)

Duration: Term123
Duration: Weeks

11

Number students taking module (anticipated)

45

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 ActivitiesGuided independent studyPlacement / study abroad
221280

Details of learning activities and teaching methods

CategoryHours of study timeDescription
Scheduled Learning and Teaching22Lectures (11 x 2 hours)
Guided Independent Study68Guided reading of scientific literature and textbook references, plus revision
Guided Independent Study20Preparation for problems in lectures
Guided Independent Study30Completion of continuous assessments
Guided Independent Study10Preparation of group essay and presentation

Formative assessment

Form of assessmentSize of the assessment (eg length / duration)ILOs assessedFeedback method
Problems and lecturer feedback during lecturesOngoing in lecturesAllOral
Feedback via ELE Forumad hocAllWritten

Summative assessment (% of credit)

CourseworkWritten examsPractical exams
40600

Details of summative assessment

Form of assessment% of creditSize of the assessment (eg length / duration)ILOs assessedFeedback method
Examination602 hours1-8Written via tutor
Problem set 1, comprising numerical and short answers202 sides of A43-8Written
Problem set 2, comprising computational, numerical and short answers202 sides of A41-2, 6-10Written

Details of re-assessment (where required by referral or deferral)

Original form of assessmentForm of re-assessmentILOs re-assessedTimescale for re-assessment
ExaminationSee note below1-8Referral/deferral period
Problem set 1See note below3-8Referral/deferral period
Problem set 2See note below1-2, 6-10Referral/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

Key words search

statistical thermodynamics, molecular simulation, computational chemistry

Credit value15
Module ECTS

7.5

Module pre-requisites
  • NSC2002 Physical Chemistry
Module co-requisites

None

NQF level (module)

6

Available as distance learning?

No

Origin date

07/06/2019

Last revision date

04/05/2023