Molecular Vibrations - IIT Kanpur · Molecular Vibrations Molecular Vibrations K. Srihari...
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Molecular Vibrations Molecular Vibrations K. Srihari Department of Chemistry IIT Kanpur 6th March 2007
Transcript of Molecular Vibrations - IIT Kanpur · Molecular Vibrations Molecular Vibrations K. Srihari...
Molecular Vibrations
Molecular Vibrations
K. Srihari
Department of ChemistryIIT Kanpur
6th March 2007
Molecular Vibrations
Chemical Reactions≡Make/break chemical bonds
Rates: How fast? Calculate?
Mechanism: Why specific bond(s)break?
Control?
Molecular Vibrations
Chemical Reactions≡Make/break chemical bonds
Rates: How fast? Calculate?
Mechanism: Why specific bond(s)break?
Control?
Molecular Vibrations
Chemical Reactions≡Make/break chemical bonds
Rates: How fast? Calculate?
Mechanism: Why specific bond(s)break?
Control?
Molecular Vibrations
Molecular vibrations∼ network of nonlinear oscillators
Low energy - uncoupledharmonicoscillators“fingerprinting"
High energy - couplednonlinearoscillators
Multidimensions: nontrivialdynamics.
FrequencyΩ = Ω(E), vibrational energy flow between modes.
Molecular Vibrations
Molecular vibrations∼ network of nonlinear oscillators
Low energy - uncoupledharmonicoscillators“fingerprinting"
High energy - couplednonlinearoscillators
Multidimensions: nontrivialdynamics.
FrequencyΩ = Ω(E), vibrational energy flow between modes.
Molecular Vibrations
Molecular vibrations∼ network of nonlinear oscillators
Low energy - uncoupledharmonicoscillators“fingerprinting"
High energy - couplednonlinearoscillators
Multidimensions: nontrivialdynamics.
FrequencyΩ = Ω(E), vibrational energy flow between modes.
Molecular Vibrations
Theory
Transition State Theory: No recrossings, 1930s.
RRKM Theory: Energy redistribution “instantaneous", 1950s.
Intramolecular Vibrational Energy Redistribution (IVR) is notintantaneous and can lead to barrier recrossings.
Molecular Vibrations
Theory
Transition State Theory: No recrossings, 1930s.
RRKM Theory: Energy redistribution “instantaneous", 1950s.
Intramolecular Vibrational Energy Redistribution (IVR) is notintantaneous and can lead to barrier recrossings.
Molecular Vibrations
Theory
Transition State Theory: No recrossings, 1930s.
RRKM Theory: Energy redistribution “instantaneous", 1950s.
Intramolecular Vibrational Energy Redistribution (IVR) is notintantaneous and can lead to barrier recrossings.
Molecular Vibrations
Nonlinear mode-mode resonances are crucial
Energy flow∼ diffusion. Nature of diffusion?
Molecular Vibrations
IVR ∼ transport on resonance highway
Expressways, bylanes, Dead-ends etc.=⇒ Mechanism of IVR.
Molecular Vibrations
Classical↔ Quantum Correspondence?
Bifurcations→ birth of new modes. Quantum fingerprints?
Local controlbased on the Arnol’d web. Will Quantum obey the“traffic rules"?
Classical! Quantum. Finite ~.
Acc. Chem. Res. (2007); Phys. Rev. E (2005); Nature (2001).
Molecular Vibrations
Classical↔ Quantum Correspondence?
Bifurcations→ birth of new modes. Quantum fingerprints?
Local controlbased on the Arnol’d web. Will Quantum obey the“traffic rules"?
Classical! Quantum. Finite ~.
Acc. Chem. Res. (2007); Phys. Rev. E (2005); Nature (2001).
Molecular Vibrations
Classical↔ Quantum Correspondence?
Bifurcations→ birth of new modes. Quantum fingerprints?
Local controlbased on the Arnol’d web. Will Quantum obey the“traffic rules"?
Classical! Quantum. Finite ~.
Acc. Chem. Res. (2007); Phys. Rev. E (2005); Nature (2001).
Molecular Vibrations
Contrasting viewpoints?
Zewail: Let us do the thinking
Rabitz:Let the molecule think for itself
Rice: Just interfere!
Molecular Vibrations
Contrasting viewpoints?
Zewail: Let us do the thinking
Rabitz:Let the molecule think for itself
Rice: Just interfere!
Molecular Vibrations
Contrasting viewpoints?
Zewail: Let us do the thinking
Rabitz:Let the molecule think for itself
Rice: Just interfere!
Molecular Vibrations
The Fundamental Problem: Poincaré 1890
Perturbations of the conditionally periodic motions:
H(I ,θ) = H0(I) +∑
m
ΦmVm(I) exp(i(m+ −m−) · θ)
IVR today: Identical viewpoint!
“At a time when no physical theory can properly be termedfundamental - the known theories appear to be merely more or lessfundamental in certain directions - it may be asserted with confidencethat ordinary differential equations in the real domain, andparticularly equations of dynamical origin, will continue to hold aposition of highest importance." (Birkhoff 1927)
Molecular Vibrations
Poincaré versus Bohr?
Burbanks, Waalkens, Wiggins (2004).
Jaffe, Uzer, Wiggins (2003).
Molecular Vibrations
Bifurcations: Quantum imprints
Low energy: Count nodes, Helmholtz
Bifurcation: Quantum knows, Spectralperturbations!
Monodromy: No unique assignmenti.e.,quantum numbers.
Joyeux, Univ. Joseph-Fourier, Grenoble.
Molecular Vibrations
Bifurcations: Quantum imprints
Low energy: Count nodes, Helmholtz
Bifurcation: Quantum knows, Spectralperturbations!
Monodromy: No unique assignmenti.e.,quantum numbers.
Joyeux, Univ. Joseph-Fourier, Grenoble.
Molecular Vibrations
Bifurcations: Quantum imprints
Low energy: Count nodes, Helmholtz
Bifurcation: Quantum knows, Spectralperturbations!
Monodromy: No unique assignmenti.e.,quantum numbers.
Joyeux, Univ. Joseph-Fourier, Grenoble.
Molecular Vibrations
“Hearing" the intramolecular music
Time-frequency analysis
Lgz(a, b) =1√a
∫ +∞
−∞dt z(t)g∗
(t − b
a
)
1 Ω(t = b) = maxa|Lgz(a, b)|2 Stickiness=⇒ Dynamical
correlation.3 Visualizingthe Arnol’d web.
Arevalo and Wiggins, 2001.
Molecular Vibrations
Nature of the diffusion?Preturn∼ t−d/2
Anisotropic.Ergodicity?
Dynamical traps→ anomalous?
IVR manifold dimensiond∼ fractal.
Alexander-Orbach conjecture?Semparithi and KS, J. Chem. Phys. (comm) 2006.
Molecular Vibrations
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, 1991.
Manikandan and KS, 2007 (unpublished).
Molecular Vibrations
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?
Molecular Vibrations
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.
