CH4203 : Symmetry in Chemistry (Spring 2013) | Academic Portal of IISER Kolkata

Details of CH4203 (Spring 2013)

Level: 4

Type: Theory

Credits: 3.0

Course Code	Course Name	Instructor(s)
CH4203	Symmetry in Chemistry	Amlan Kusum Roy

Syllabus
Introduction and motivation. Symmetry as a mathematical concept ; a holistic approach in terms of geometry, profile, connectivity, fractals, cellular automata, etc. Symmetry in chemical sciences explored through group theory and topology. Significance of symmetry concepts in bringing about conceptual unification and universalization across microscopic, mesoscopic and macroscopic systems and phenomena. Linkages with quantum mechanics. Group theory in chemistry : Symmetry operations and their associated algebra. Dipole moment and optical activity. Group, subgroup, symmetric (permutation) group, simple group, semi-simple group, colour (magnetic/Shubnikov) group, point group, space group. Isomorphism and homomorphism. Properties of groups. Schoenflies and Hermann-Maugin notations for point groups / space groups. Generating elements of a group. Elementary theory of representations of groups; transformation operators, function spaces, invariant subspaces. Equivalent, reducible and irreducible representations. Character tables. Grand orthogonality thorem (without proof) and other theorems/relations involving irreducible representations and characters. The reduction of a representation; projection operators. Notations for character tables for point groups. Definition of an algebra. Direct product group; direct product representation. Representations and quantum mechanics. The vanishing of quantum mechanical integrals. Applications of group theory to bonding, structure, spectroscopy, reactivity and other properties: Symmetry-adapted LCAO-MOs of small and medium-size molecules (e.g., AH3, benzene, MX6, etc), using projection operators. Mulliken-Walsh angular correlation diagrams. Molecular vibrations (classification of normal modes ; normal coordinate analysis). Proof of Jahn-Teller theorem; first- and second-order Jahn-Teller effects and their influence on molecular geometry and spectra. Selection rules for single-photon and two-photon spectroscopy involving various types of transitions. Forbidden transitions; intensity borrowing. Magnetic dipole selection rules. Woodward-Hoffmann and FMO approaches to reactivity. Symmetry selection rules for transition states and reaction paths. Symmetry and other properties. Topology in chemistry : Topology of electron density, critical points, classification of bonds; atoms in molecules. Graph theory and molecular descriptors of various kinds; their correlations with various properties and applications to the design of different types of materials, e.g., pesticides, catalysts, drugs, etc. Fractals, deterministic chaos and their applications in chemistry, e.g., Brownian motion, electrolysis, heterogeneous catalysis, protein folding, reaction mechanisms. Applications of cellular automata in chemistry.

Syllabus

Introduction and motivation. Symmetry as a mathematical concept ; a holistic approach in terms of geometry, profile, connectivity, fractals, cellular automata, etc.

Symmetry in chemical sciences explored through group theory and topology.
Significance of symmetry concepts in bringing about conceptual unification and universalization across microscopic, mesoscopic and macroscopic systems and phenomena. Linkages with quantum mechanics.

Group theory in chemistry : Symmetry operations and their associated algebra. Dipole moment and optical activity. Group, subgroup, symmetric (permutation) group, simple group, semi-simple group, colour (magnetic/Shubnikov) group, point group, space group. Isomorphism and homomorphism. Properties of groups. Schoenflies and Hermann-Maugin notations for point groups / space groups. Generating elements of a group. Elementary theory of representations of groups; transformation operators, function spaces, invariant subspaces. Equivalent, reducible and irreducible representations. Character tables. Grand orthogonality thorem (without proof) and other theorems/relations involving irreducible representations and characters. The reduction of a representation; projection operators. Notations for character tables for point groups. Definition of an algebra. Direct product group; direct product representation. Representations and quantum mechanics. The vanishing of quantum mechanical integrals.

Applications of group theory to bonding, structure, spectroscopy, reactivity and other properties: Symmetry-adapted LCAO-MOs of small and medium-size molecules (e.g., AH3, benzene, MX6, etc), using projection operators. Mulliken-Walsh angular correlation diagrams. Molecular vibrations (classification of normal modes ; normal coordinate analysis). Proof of Jahn-Teller theorem; first- and second-order Jahn-Teller effects and their influence on molecular geometry and spectra. Selection rules for single-photon and two-photon spectroscopy involving various types of transitions. Forbidden transitions; intensity borrowing. Magnetic dipole selection rules. Woodward-Hoffmann and FMO approaches to reactivity. Symmetry selection rules for transition states and reaction paths. Symmetry and other properties.

Topology in chemistry : Topology of electron density, critical points, classification of bonds; atoms in molecules. Graph theory and molecular descriptors of various kinds; their correlations with various properties and applications to the design of different types of materials, e.g., pesticides, catalysts, drugs, etc.

Fractals, deterministic chaos and their applications in chemistry, e.g., Brownian motion, electrolysis, heterogeneous catalysis, protein folding, reaction mechanisms.

Applications of cellular automata in chemistry.

References
1. D. M. Bishop, Group Theory in Chemistry, Dover, New York (1993). 2. F. A. Cotton, Chemical Applications of Group Theory, John Wiley, New York (1990). 3. J. M. Hollas, Symmetry in Molecules, Chapman and Hall, London (1972). 4. I. Hargittai and M. Hargittai, Symmetry Through the Eyes of a Chemist, Springer, Berlin (2007). 5. M. Tinkham, Group Theory and Quantum Mechanics, Dover, New York (2003). 6. C. D. H. Chisholm, Group Theoretical Techniques in Quantum Chemistry, Academic Press, London (1975). 7. M. Hamermesh, Group Theory and Its Applications to Physical Problems, Dover, New York (1990).. 8. R. F. W. Bader, Atoms in Molecules, Clarendon, Oxford (1994) . 9. A. T. Balaban (Editor), Chemical Applications of Graph Theory, Academic Press, New York (1976). 10. N. Trinajstic, Chemical Graph Theory, Vols. I and II, CRC Press, New York (1992). 11. J. Devillers and A.T. Balaban(Eitors), Topological Indices and Related Descriptors in QSAR and QSPR, Gordon and Breach, Amsterdam (1999). 12. B. Mandelbrot, The Fractal Geometry of Nature, W.H. Freeman, New York (1983). 13. W. G. Rothschild, Fractals in Chemistry, John Wiley, New York (1998). 14. Willi-Hans Steeb, Nonlinear Workbook, World Scientific, Singapore (1999) (This book connects cellular automata, neural networks, chaos, fractals, etc.). 15. S. K. Scott, Chemical Chaos, Clarendon Press, Oxford (1994).

References

1. D. M. Bishop, Group Theory in Chemistry, Dover, New York (1993).
2. F. A. Cotton, Chemical Applications of Group Theory, John Wiley, New York (1990).
3. J. M. Hollas, Symmetry in Molecules, Chapman and Hall, London (1972).
4. I. Hargittai and M. Hargittai, Symmetry Through the Eyes of a Chemist, Springer, Berlin (2007).
5. M. Tinkham, Group Theory and Quantum Mechanics, Dover, New York (2003).
6. C. D. H. Chisholm, Group Theoretical Techniques in Quantum Chemistry, Academic Press, London (1975).
7. M. Hamermesh, Group Theory and Its Applications to Physical Problems,
Dover, New York (1990)..
8. R. F. W. Bader, Atoms in Molecules, Clarendon, Oxford (1994) .
9. A. T. Balaban (Editor), Chemical Applications of Graph Theory, Academic Press, New York (1976).
10. N. Trinajstic, Chemical Graph Theory, Vols. I and II, CRC Press, New York (1992).
11. J. Devillers and A.T. Balaban(Eitors), Topological Indices and Related Descriptors in QSAR and QSPR, Gordon and Breach, Amsterdam (1999).
12. B. Mandelbrot, The Fractal Geometry of Nature, W.H. Freeman, New York (1983).
13. W. G. Rothschild, Fractals in Chemistry, John Wiley, New York (1998).
14. Willi-Hans Steeb, Nonlinear Workbook, World Scientific, Singapore (1999)
(This book connects cellular automata, neural networks, chaos, fractals, etc.).
15. S. K. Scott, Chemical Chaos, Clarendon Press, Oxford (1994).

Course Credit Options

Sl. No.	Programme	Semester No	Course Choice
1	IP	2	Elective
2	IP	4	Elective
3	MS	8	Core
4	RS	1	Elective

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Details of CH4203 (Spring 2013)

Course Credit Options