**PHY ****523: Non-adiabatic Interactions in Physics,**** Chemistry and Biology**** (4)**

The Born-Oppenheimer Approach – The Time Independent Framework: (a) The Adiabatic Representation; (b) The Diabatic Representation

Mathematical Introduction: (a) The Hilbert Space and the Curl-Div Equations; (b) First Order Differential Equations along contours; (c) Abelian and non-Abelian Systems.

The Adiabatic-Diabatic Transformation (ADT). On the Single-valuedness of the newly formed Diabatic Potentials and the Quantization of the Born-Oppenheimer (BO) non-adiabatic coupling (NAC) matrix. Singularities, Poles and Seams characterizing the BO-NAC terms.

Molecular Fields as formed by Lorentz Wave-Equations.

The Jahn-Teller Model, The Renner-Teller model, the mixed Jahn-Teller/Renner-Teller model. The Privileged ADT phase and the corresponding Topological (Berry/Longuet-Higgins) phase.

The Extended Born-Oppenheimer Equation including Symmetry

The Born-Oppenheimer Approach – The Time Dependent Framework (emphasizing Field-dependent non-Adiabatic Coupling terms).

The interaction between molecular systems and electromagnetic fields: (a) The Classical treatment of the field (b) The Quantum treatment of the Field (based on Fock states).

If time allows various subjects related to Quantum Reactive Scattering Theory will be introduced. Among other things the concept of arrangement channels and decoupling of arrangement channels employing Absorbing Boundary conditions will be discussed.

*Suggested Books*:

- M. Baer and C-Y. Ng, (eds), State-Selected and State-to-State Ion-Molecule Reaction Dynamics. Ser. Advances of Chemical Physics, Vol. 82, Part 2, John Wiley, Hoboken, N.J. (1992)
- M. Baer and G.D. Billing (eds), The Role of Degenerate States in Chemistry, Ser. Advances of Chemical Physics, Vol. 124; John Wiley, Hoboken, N.J. (2002)
- W. Domcke, D.R. Yarkony and H. Koeppel, Conical Intersections, Advances Series In Physical Chemistry Vol. 15 (World Scientific, Hong-Kong (2004).
- Farad. Discussions, Non-Adiabatic Effects in Chemical Dynamics, Vol. 127 (R.S.C.), University Oxford, (2004)
- M. Baer, Beyond Born-Oppenheimer: Electronic Nonadiabatic Coupling Terms and Conical Intersections, Wiley Interscience, Hoboken, N.J., (2006).
- G.C. Schatz and M. A. Ratner, Quantum Mechanics in Chemistry, Prentice-Hall, Englwood Cliffs (1993)
- J.D. Jackson, Classical Electrodynamics, 2nd Edition, John Wiley, New York (1975)
- J. Z. H. Zhang, Theory and Application of Quantum Molecular Dynamics, World Scientific, Hong-Kong (1999)

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