ID4105 : Density-based Quantum Mechanics of Many-electron Systems (Autumn 2012)

Details of ID4105 (Autumn 2012)

Level: 4

Type: Theory

Credits: 3.0

Course Code	Course Name	Instructor(s)
ID4105	Density-based Quantum Mechanics of Many-electron Systems	Bidyendu Mohan Deb

Syllabus
ID4105: Density-based Quantum Mechanics of Many-electron Systems (This course involves concepts and formalisms as well as their applications for understanding microscopic structure, properties and dynamics in chemistry, physics and biology) Introduction. Wavefunction vs. density. Wavefunctions to reduced density matrices to densities. Quantum mechanics in three-dimensional space; links to classical concepts. The N-representability problem. Need for equation(s) for the direct calculation of time-independent and time-dependent densities bypassing the wavefunction. Charge and current densities as fundamental variables. Local property densities. Spin densities; charge density and spin density waves. Asymptotic bahaviour; monotonic behaviour. Hellman-Feynman and virial theorems. Cusp condition. Electrostatic potential. Miscellaneous applications. The Thomas-Fermi-Dirac-Weizscker theory and its various implications. Kinetic energy in terms of density. Density-potential correspondence. Lagrange multiplier as chemical potential. Ground-state density-functional theory : Definition of a functional. Hohenberg-Kohn theorems. Kohn-Sham equations. Various interpretations and implications. The chemical potential; its significance and connection to the grand canonical ensemble. Global and local concepts in chemical reactivity. Exchange-correlation hole and exchange-correlation functional. The kinetic energy functional. Two major interlinked problems of ground-state density-functional theory : Excited states and time-dependence. Various applications to atoms, molecules and solids. Quantum fluid dynamics : Analogy between quantum systems and classical fluids. Transcription of non-relativistic quantum mechanics (both pure and mixed states) into fluid dynamical equations. Miscellaneous consequences and generalizations. Connection to stochastic mechanics. Concept of an internal stress tensor; stability of matter. Hydrodynamical trajectories. A statistical-mechanical and thermodynamic view of the electron fluid. Relativistic quantum fluid dynamics. Applications. Time-dependent density functional theory via quantum fluid dynamics. Excited-state density-functional theory. Hybrid wavefunction-density approach. Applications to atoms, molecules and solids. Algebraic and integro-differential single equations for the direct calculation of electron density. Applications to structure and properties, e.g., 2L-pole polarizability, collisions; universal criterion for atomic, ionic, Wigner-Seitz radii, etc. Correspondence to time-dependent Schrdinger equation. Diffusion quantum Monte Carlo approach to ground state energy and density; applications. Applications of time-dependent density approaches to femtosecond and attosecond interactions between intense laser fields and atoms/molecules. Interactions with strong magnetic fields. Linear as well as nonlinear polarizabilities (static / dynamic) and susceptibilities. Possible connections to Berry-Pancharatnam phase and solitons. Concept of quantum subspace. Atoms in molecules. Topological criterion for chemical bonds. Applications in quantum biochemistry. Possible applications in toxicity, drug design, catalyst design, etc. through the concept of molecular similarity.

Syllabus

ID4105: Density-based Quantum Mechanics of Many-electron Systems

(This course involves concepts and formalisms as well as their applications for understanding microscopic structure, properties and dynamics in chemistry, physics and biology)

Introduction. Wavefunction vs. density. Wavefunctions to reduced density matrices to densities. Quantum mechanics in three-dimensional space; links to classical concepts. The N-representability problem. Need for equation(s) for the direct calculation of time-independent and time-dependent densities bypassing the wavefunction. Charge and current densities as fundamental variables. Local property densities. Spin densities; charge density and spin density waves. Asymptotic bahaviour; monotonic behaviour. Hellman-Feynman and virial theorems. Cusp condition. Electrostatic potential. Miscellaneous applications.

The Thomas-Fermi-Dirac-Weizscker theory and its various implications. Kinetic energy in terms of density. Density-potential correspondence. Lagrange multiplier as chemical potential.

Ground-state density-functional theory : Definition of a functional. Hohenberg-Kohn theorems. Kohn-Sham equations. Various interpretations and implications. The chemical potential; its significance and connection to the grand canonical ensemble. Global and local concepts in chemical reactivity. Exchange-correlation hole and exchange-correlation functional. The kinetic energy functional. Two major interlinked problems of ground-state density-functional theory : Excited states and time-dependence. Various applications to atoms, molecules and solids.

Quantum fluid dynamics : Analogy between quantum systems and classical fluids. Transcription of non-relativistic quantum mechanics (both pure and mixed states) into fluid dynamical equations. Miscellaneous consequences and generalizations. Connection to stochastic mechanics. Concept of an internal stress tensor; stability of matter. Hydrodynamical trajectories. A statistical-mechanical and thermodynamic view of the electron fluid. Relativistic quantum fluid dynamics. Applications.

Time-dependent density functional theory via quantum fluid dynamics.

Excited-state density-functional theory. Hybrid wavefunction-density approach. Applications to atoms, molecules and solids.

Algebraic and integro-differential single equations for the direct calculation of electron density. Applications to structure and properties, e.g., 2L-pole polarizability, collisions; universal criterion for atomic, ionic, Wigner-Seitz radii, etc. Correspondence to time-dependent Schrdinger equation. Diffusion quantum Monte Carlo approach to ground state energy and density; applications. Applications of time-dependent density approaches to femtosecond and attosecond interactions between intense laser fields and atoms/molecules. Interactions with strong magnetic fields. Linear as well as nonlinear polarizabilities (static / dynamic) and susceptibilities. Possible connections to Berry-Pancharatnam phase and solitons.

Concept of quantum subspace. Atoms in molecules. Topological criterion for chemical bonds.

Applications in quantum biochemistry. Possible applications in toxicity, drug design, catalyst design, etc. through the concept of molecular similarity.

References
Suggested Text/Reference Books: 1. N. H. March, Electron Density Theory of Atoms and Molecules, Academic Press, London (1992). 2. R. G. Parr and W. Yang, Density Functional Theory of Atoms and Molecules, Oxford University Press, Oxford (1989). 3. N. H. March and B. M. Deb (Eds.), The Single-Particle Density in Physics and Chemistry, Academic Press, London (1987). 4. P. K. Chattaraj (Ed.), Chemical Reactivity Theory : A Density Functional View, CRC Press, New York (2009). 5. J. K. Labanowski and J. W. Andzelm, Density Functional Methods in Chemistry, Springer, Berlin (1991). 6. E. S. Kryachko and E. V. Ludena, Energy Density Functional Theory of Many-electron Systems, Kluwer, Dordrecht (1990). 7. R. E. Wyatt, Quantum Dynamics With Trajectories : Introduction to Quantum Hydrodynamics, Springer, New York (2005). 8. J. S. Murray and K. Sen (Eds.), Molecular Electyrostatic Potentials : Concepts and Applications, Elsevier, Amsterdam (1996). 9. R. F. W. Bader, Atoms in Molecules, Clarendon Press, Oxford (2003). 10. J. Maruani, C. Minot, R. McWeeny, Y. G. Smeyers and S. Wilson, New Theories in Quantum Systems in Chemistry and Physics, Kluwer, Dordrecht (2001). 11. M. A. L. Marques, C. A. Ulrich, F. Nogueira, A. Rubio, K. Burke and E. K U. Gross, Time-dependent Density Functional Theory, Springer, Hydelberg (2006). 12. C. Fiolhais, F. Nogueira and M. A. L. Marques (Eds.), A Primer in Density Functional Theory, Springer, Berlin (2003). 13. G. W. F. Drake (Ed.), Handbook of Atomic, Molecular and Optical Physics, Springer, New York (2006). 14. S. Wilson, P. F. Bernath and R. McWeeny (Eds.), Handbook of Molecular Physics and Quantum Chemistry, Vols. 1-3, Wiley-VCH, Weinheim (2003). 15. G. D. Mahan and K. R. Subbaswamy, Local Density Theory of Polarizability, Springer, Berlin (1990). 16. W. G. Richards, Quantum Pharmacology, Butterworth, London (2004). 17. R. Carbo-Dorca, X. Girones and P. G. Mezey (Eds.), Fundamentals of Molecular Similarity, Plenum, New York (2001). 18. K. Yamanouchi, S. L. Chin, P. Agostini, and G. Ferrante (Eds.), Progress in Ultrafast Intense Laser Science, Vols. 1 4, Springer, New York (2007-2010). 19. H. Ruder, G. Wunner, H. Herold and F. Geyer, Atoms in Strong Magnetic Fields, Springer, Berlin (1994). Selected research papers and review articles.

References

Suggested Text/Reference Books:

1. N. H. March, Electron Density Theory of Atoms and Molecules, Academic Press, London (1992).

2. R. G. Parr and W. Yang, Density Functional Theory of Atoms and Molecules, Oxford University Press, Oxford (1989).

3. N. H. March and B. M. Deb (Eds.), The Single-Particle Density in Physics and Chemistry, Academic Press, London (1987).

4. P. K. Chattaraj (Ed.), Chemical Reactivity Theory : A Density Functional View, CRC Press, New York (2009).

5. J. K. Labanowski and J. W. Andzelm, Density Functional Methods in Chemistry, Springer, Berlin (1991).

6. E. S. Kryachko and E. V. Ludena, Energy Density Functional Theory of Many-electron Systems, Kluwer, Dordrecht (1990).

7. R. E. Wyatt, Quantum Dynamics With Trajectories : Introduction to Quantum Hydrodynamics, Springer, New York (2005).

8. J. S. Murray and K. Sen (Eds.), Molecular Electyrostatic Potentials : Concepts and Applications, Elsevier, Amsterdam (1996).

9. R. F. W. Bader, Atoms in Molecules, Clarendon Press, Oxford (2003).

10. J. Maruani, C. Minot, R. McWeeny, Y. G. Smeyers and S. Wilson, New Theories in Quantum Systems in Chemistry and Physics, Kluwer, Dordrecht (2001).

11. M. A. L. Marques, C. A. Ulrich, F. Nogueira, A. Rubio, K. Burke and E. K U. Gross, Time-dependent Density Functional Theory, Springer, Hydelberg (2006).

12. C. Fiolhais, F. Nogueira and M. A. L. Marques (Eds.), A Primer in Density Functional Theory, Springer, Berlin (2003).

13. G. W. F. Drake (Ed.), Handbook of Atomic, Molecular and Optical Physics, Springer, New York (2006).

14. S. Wilson, P. F. Bernath and R. McWeeny (Eds.), Handbook of Molecular Physics and Quantum Chemistry, Vols. 1-3, Wiley-VCH, Weinheim (2003).

15. G. D. Mahan and K. R. Subbaswamy, Local Density Theory of Polarizability, Springer, Berlin (1990).

16. W. G. Richards, Quantum Pharmacology, Butterworth, London (2004).

17. R. Carbo-Dorca, X. Girones and P. G. Mezey (Eds.), Fundamentals of Molecular Similarity, Plenum, New York (2001).

18. K. Yamanouchi, S. L. Chin, P. Agostini, and G. Ferrante (Eds.), Progress in Ultrafast Intense Laser Science, Vols. 1 4, Springer, New York (2007-2010).

19. H. Ruder, G. Wunner, H. Herold and F. Geyer, Atoms in Strong Magnetic Fields, Springer, Berlin (1994).

Selected research papers and review articles.

Course Credit Options

Sl. No.	Programme	Semester No	Course Choice
1	IP	1	Not Allowed
2	IP	3	Not Allowed
3	MS	7	Not Allowed
4	RS	1	Not Allowed

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Details of ID4105 (Autumn 2012)

Course Credit Options