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.