Classical Mechanics of Dipolar Asymmetric Top Molecules in Collinear Static Electric and Nonresonant Linearly Polarized Laser Fields: Energy-Momentum Diagrams, Bifurcations and Accessible Configuration Space

Abstract

We study classical energy-momentum (E-m) diagrams for rotational motion of dipolar asymmetric top molecules in strong external fields. Static electric fields, nonresonant linearly polarized laser fields, and collinear combinations of the two are investigated. We treat specifically the molecules iodobenzene (a nearly prolate asymmetric top), pyridazine (nearly oblate asymmetric top), and iodopentafluorobenzene (intermediate case). The location of relative equilibria in the E-m plane and associated bifurcations are determined by straightforward calculation, with analytical results given where possible. In cases where analytical solutions cannot be obtained, we resort to numerical solutions, while keeping a geometrical picture of the nature of the solutions to the fore. The classification we obtain of the topology of classically allowed rotor configuration space regions in the E-m diagram is of potential use in characterization of energy eigenstates of the corresponding quantum mechanical problem.

Phase space structures governing reaction dynamics in rotating molecules

“…Let u, v be some canonical coordinates for the positive signed symplectic structure w + and q µ , p µ , 1 µ 3N − 6, be any choice of Figure 1. (u, v) coordinate lines on the angular momentum sphere for (a) the definition of (u, v) in (30) and (b) the definition of (u, v) in (38).…”

“…The dynamics near the first two can be studied in terms of the coordinates (u, v) defined according to (30) where they correspond to the points (0, 0) (for J = (r, 0, 0)), (π, 0) (for J = (−r, 0, 0)), (π/2, 0) (for J = (0, r, 0)) and (3π/2, 0) (for J = (0, −r, 0)) (see figure 2(a)). The dynamics near the relative equilibria J = (0, 0, ±r) (and again J = (0, ±r, 0)) can be studied in terms of (u, v) defined according to (38) where they correspond to the points the points (0, 0) (for J = (0, 0, r)), (π, 0) (for J = (0, 0, −r)), (π/2, 0) (for J = (0, r, 0)) and (3π/2, 0) (for J = (0, −r, 0)) (see figure 2(b)). The reduced Hamiltonian has local maxima at J = (±r, 0, 0) which correspond to rotations in either direction about the principal axis with the smallest moment of inertia, and minima at J = (0, 0, ±r) which correspond to rotations in either direction about the principal axis with the largest moment of inertia.…”

The bifurcation analysis and the Conley index in mechanics

“…Бифуркационную диаграмму в некоторых работах называют также диаграммой Смейла [13] или диаграммой энергии-момента [17] в зависимости от области исследований. Некото-рые авторы (см., например, [17]) метод анализа устойчивости на основе бифуркационной диаграммы называют также методом энергии-момента.…”

Laser-induced molecular alignment in the presence of chaotic rotational dynamics

“…Section III is devoted to an investigation of chaos in asymmetric top molecules interacting with an electric field. Although there are a few earlier works that indicate the presence of chaos in this system [41][42][43][44] , they concentrate on slightly different systems or aspects of the dynamics. Hence, it was necessary to establish a better background of our object of study.…”