Molecular Vibrations

Transcription

1 Molecular Vibrations K. Srihari Department of Chemistry IIT Kanpur 6th March 2007

2 Chemical Reactions Make/break chemical bonds Rates: How fast? Calculate? Mechanism: Why specific bond(s) break? Control?

3 Chemical Reactions Make/break chemical bonds Rates: How fast? Calculate? Mechanism: Why specific bond(s) break? Control?

4 Chemical Reactions Make/break chemical bonds Rates: How fast? Calculate? Mechanism: Why specific bond(s) break? Control?

5 Molecular vibrations network of nonlinear oscillators Low energy - uncoupled harmonic oscillators fingerprinting" High energy - coupled nonlinear oscillators Multidimensions: nontrivial dynamics. Frequency Ω = Ω(E), vibrational energy flow between modes.

6 Molecular vibrations network of nonlinear oscillators Low energy - uncoupled harmonic oscillators fingerprinting" High energy - coupled nonlinear oscillators Multidimensions: nontrivial dynamics. Frequency Ω = Ω(E), vibrational energy flow between modes.

7 Molecular vibrations network of nonlinear oscillators Low energy - uncoupled harmonic oscillators fingerprinting" High energy - coupled nonlinear oscillators Multidimensions: nontrivial dynamics. Frequency Ω = Ω(E), vibrational energy flow between modes.

8 Theory Transition State Theory: No recrossings, 1930s. RRKM Theory: Energy redistribution instantaneous", 1950s. Intramolecular Vibrational Energy Redistribution (IVR) is not intantaneous and can lead to barrier recrossings.

9 Theory Transition State Theory: No recrossings, 1930s. RRKM Theory: Energy redistribution instantaneous", 1950s. Intramolecular Vibrational Energy Redistribution (IVR) is not intantaneous and can lead to barrier recrossings.

10 Theory Transition State Theory: No recrossings, 1930s. RRKM Theory: Energy redistribution instantaneous", 1950s. Intramolecular Vibrational Energy Redistribution (IVR) is not intantaneous and can lead to barrier recrossings.

11 Nonlinear mode-mode resonances are crucial Energy flow diffusion. Nature of diffusion?

12 Molecular Vibrations IVR transport on resonance highway Expressways, bylanes, Dead-ends etc. = Mechanism of IVR.

13 Classical Quantum Correspondence? Bifurcations birth of new modes. Quantum fingerprints? Local control based on the Arnol d web. Will Quantum obey the traffic rules"? Classical Quantum. Finite. Acc. Chem. Res. (2007); Phys. Rev. E (2005); Nature (2001).

14 Classical Quantum Correspondence? Bifurcations birth of new modes. Quantum fingerprints? Local control based on the Arnol d web. Will Quantum obey the traffic rules"? Classical Quantum. Finite. Acc. Chem. Res. (2007); Phys. Rev. E (2005); Nature (2001).

15 Classical Quantum Correspondence? Bifurcations birth of new modes. Quantum fingerprints? Local control based on the Arnol d web. Will Quantum obey the traffic rules"? Classical Quantum. Finite. Acc. Chem. Res. (2007); Phys. Rev. E (2005); Nature (2001).

16 Contrasting viewpoints? Zewail: Let us do the thinking Rabitz: Let the molecule think for itself Rice: Just interfere!

17 Contrasting viewpoints? Zewail: Let us do the thinking Rabitz: Let the molecule think for itself Rice: Just interfere!

18 Contrasting viewpoints? Zewail: Let us do the thinking Rabitz: Let the molecule think for itself Rice: Just interfere!

19 The Fundamental Problem: Poincaré 1890 Perturbations of the conditionally periodic motions: H(I, θ) = H 0 (I) + m Φ m V m (I) exp(i(m + m ) θ) IVR today: Identical viewpoint! At a time when no physical theory can properly be termed fundamental - the known theories appear to be merely more or less fundamental in certain directions - it may be asserted with confidence that ordinary differential equations in the real domain, and particularly equations of dynamical origin, will continue to hold a position of highest importance." (Birkhoff 1927)

20 Poincaré versus Bohr? Burbanks, Waalkens, Wiggins (2004). Jaffe, Uzer, Wiggins (2003).

21 Bifurcations: Quantum imprints Low energy: Count nodes, Helmholtz Bifurcation: Quantum knows, Spectral perturbations! Monodromy: No unique assignment i.e., quantum numbers. Joyeux, Univ. Joseph-Fourier, Grenoble.

22 Bifurcations: Quantum imprints Low energy: Count nodes, Helmholtz Bifurcation: Quantum knows, Spectral perturbations! Monodromy: No unique assignment i.e., quantum numbers. Joyeux, Univ. Joseph-Fourier, Grenoble.

23 Bifurcations: Quantum imprints Joyeux, Univ. Joseph-Fourier, Grenoble. Low energy: Count nodes, Helmholtz Bifurcation: Quantum knows, Spectral perturbations! Monodromy: No unique assignment i.e., quantum numbers.

24 Hearing" the intramolecular music Time-frequency analysis L g z(a, b) = 1 + ( ) t b dt z(t)g a a 1 Ω(t = b) = max a L g z(a, b) 2 Stickiness = Dynamical correlation. 3 Visualizing the Arnol d web. Arevalo and Wiggins, 2001.

25 Nature of the diffusion? P return t d/2 Semparithi and KS, J. Chem. Phys. (comm) Anisotropic. Ergodicity? Dynamical traps anomalous? IVR manifold dimension d fractal. Alexander-Orbach conjecture?

26 Rotor-Vibration coupling High frequency excitations decay over long time scales. Chaotic diffusion of Rotor momenta Forced oscillator. Quantum: suppression of rotor momentum diffusion? Martens and Reinhardt, Manikandan and KS, 2007 (unpublished).

27 Quo Vadis 1 Local control: Influencing the web with weak fields (Astha and KS, unpublished 2007.). 2 Conformational IVR in large molecules. 3 Rotation-Torsion-Vibration : Putting it all together. 4 Hydrogen bonds as efficient conduits for IVR?

28 Thanks Aravindan Semparithi, Paranjyoti Manikandan and Astha Sethi. Arul Lakshminarayan (IITM). Steve Tomsovic (Pullman). Peter Schlagheck (Regensburg). Steve Wiggins and Holger Waalkens (Bristol). Martin Gruebele (Urbana Champaign). David Leitner (Reno). Marc Joyeux (Grenoble). Funding: IITK, DST, CSIR.