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## Classical and Semiclassical Mechanics of Molecular Rotors in Tilted Fields

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**Author**

Arango, Carlos Alberto

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**Abstract**

We investigate the classical mechanics of diatomic and symmetric top molecules in tilted fields. These molecules exhibit regular, chaotic or mixed phase space depending on the tilt angle $\beta$, the energy $E$, and the relative intensity of the fields $\omega/\Delta\omega$. In the integrable collinear problem the projection of the angular momentum into the spatial $z$ axis is a constant of motion, $m$, which allows us to explore the geometry of the phase space, and to use energy momentum diagrams to classify the motions of the rotor. For $\beta \ne 0$ the system is non-integrable showing mostly regular dynamics in the high-energy (free-rotor) and low-energy (pendular) limits; for energy near the tilted fields barrier the phase space is highly chaotic with degree of chaos increasing with $\beta$ between 0 and $\pi/2$. Periodic orbits and bifurcation diagrams are obtained from symmetry lines and their iterations under the Poincar\'{e} map. These bifurcation diagrams are used to observe the changes in the basic structure of the phase space as $\beta$ changes between collinear and perpendicular fields. Some quantum eigenstates are localized near stable or unstable periodic orbits showing tori quantization or scarring respectively.
For asymmetric top molecules only the case of collinear fields is treated. In parallel fields $m$ is a constant of the motion and it is possible to define an effective potential $V_m(\theta,\psi)$. In an $E$-$m$ diagram the equilibrium solutions of $V_m(\theta,\psi)$ are curves that enclose regions of qualitatively different accessible $\theta$-$\psi$ configuration space. Interestingly these regions can be used to classify the quantum eigenstates.
For plane rotors primitive semiclassical mechanics is used to calculate the rotational excitation caused by laser pulses. Depending on the pulse intensity and duration several methods are employed from the analytical sudden approximation to primitive semiclassical initial value representation (IVR) integrals. The calculated transition probabilities are in good agreement with the quantum probabilities considering the simplicity of the methods. In the case of plane rotors in electric fields we calculate energy spectra, orientation ($\left<\cos\varphi\right>$), and alignment ($\left<\cos^2\varphi\right>$), using the Herman-Kluk propagator in terms of periodic coherent states. These results are in good agreement with the quantum analogues although the number of trajectories used is discouragingly large. For diatomic rotors in tilted fields, the HK propagator was used to calculate energy spectra with good agreement for high-energy and not very dense eigenspectra. Some steps are taken towards the development of HK-type propagator for rotational coherent states.

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**Description**

Committee: Greg Ezra (chair), Ben Widom, Roger Loring

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**Sponsorship**

Cornell University,
Department of Chemistry and Chemical Biology

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**Date Issued**

2005-06-21#####
**Subject**

classical mechanics; semiclassical mechanics; molecular rotors; combined fields; control rotational degrees of freedom; monodromy

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**Type**

dissertation or thesis