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Vibrational energy relaxation of large-amplitude vibrations in liquids
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10.1063/1.4733392
/content/aip/journal/jcp/137/2/10.1063/1.4733392
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/2/10.1063/1.4733392

Figures

Image of FIG. 1.
FIG. 1.

The perylene molecule and its 1au (“warping”) vibrational mode. (Upper picture) The equilibrium molecular geometry giving the numbering convention for the H atoms and showing how the mode rotates the two naphthalene halves about the molecular-frame X axis. (Lower picture) A schematic view of the normal mode (from a different angle) showing our molecular-frame coordinate axes and defining the vibrational angle θ between the two naphthalene planes (shown in red), the “lever arm” for the vibration R, and what we refer to as the amplitude of the vibration A.

Image of FIG. 2.
FIG. 2.

Schematic portrayal of the real parts of the instantaneous normal mode solvent bands of Ar-like liquids with solvent masses m v = 0.1, 1.0, 10 m Ar (roughly to scale). The arrows show the locations of two of the solute frequencies Ω considered in this paper.

Image of FIG. 3.
FIG. 3.

Equilibrium vibrational energy dynamics for the perylene warping mode in liquid argon when different frequencies (Ω/(2πc) = 12, 48, and 192 cm−1) are assigned to the mode. Shown here are the normalized total-vibrational-energy-fluctuation correlation functions, C(t), and their kinetic- and potential energy components C KK(t), C VV(t), and C KV(t), (denoted by E, K, V, and KV, respectively).

Image of FIG. 4.
FIG. 4.

The solution-phase equilibrium vibrational kinetic energy dynamics referred to in Fig. 3, viewed in the frequency domain. The results plotted are for three choices of solvent mass (m v = 0.1, 1.0, and 10.0 m Ar), and for both Ω/(2πc) = 48 and 192 cm−1. Arrows indicate where peaks would be located in the absence of solvent.

Image of FIG. 5.
FIG. 5.

Non-equilibrium relaxation of the average vibrational potential energy of perylene in liquid argon following a 1998 cm−1 = 24 kBT excitation of the warping mode. Results are plotted for three values of the warping frequency, Ω. Note the difference in scales between the upper and lower panels.

Image of FIG. 6.
FIG. 6.

Non-equilibrium solvent structural relaxation following excitation of the perylene warping mode in liquid argon. Here, we choose the warping-mode frequency to be Ω/(2πc) = 12 cm−1. This figure shows the evolution with time of the average number of solvent atoms in the innermost (rH–Ar < σ Ar–H) and outermost (σ Ar–H < rH–Ar < 1.5 σ Ar–H) halves of the first solvation shells of the perylene “corner” H atoms.89 (Upper panel) Results for different initial vibrational energies E vib (0): 125, 1998, and 3996 cm−1 (1.5, 24, and 48 kBT) with a normal Ar-mass solvent. (Lower panel) Results for different solvent masses (m v = 0.1, 1.0, and 10.0 m Ar) with a common initial vibrational energy E vib (0) = 1998 cm−1. The two large-dashed horizontal lines in each panel indicate the equilibrium number of solvent atoms in each region.

Image of FIG. 7.
FIG. 7.

Non-equilibrium solvent structural relaxation following excitation of the perylene warping mode in liquid argon. The details of the graph are the same as those shown in Fig. 6, except that here the warping mode frequency is chosen to be Ω/(2πc) = 48 cm−1.

Image of FIG. 8.
FIG. 8.

Non-equilibrium solvent structural relaxation following excitation of the perylene warping mode in liquid argon. The details of the graph are the same as those shown in Fig. 6, except that here the warping mode frequency is chosen to be Ω/(2πc) = 192 cm−1.

Image of FIG. 9.
FIG. 9.

Non-equilibrium vibrational energy relaxation following excitation of the perylene warping mode in liquid argon. The warping mode frequency is chosen to be Ω/(2πc) = 12 cm−1. (Top panel) Comparison of the non-equilibrium total vibrational energy response functions S(t) for different initial vibrational energies E vib (0): 125, 1998, and 3996 cm−1 (1.5, 24, and 48 kBT) (dashed lines), with the thermal, equilibrium, total vibrational energy fluctuation correlation function C(t) (solid line). (Bottom three panels) Comparison of the non-equilibrium total and kinetic energy vibrational energy response functions S(t) and KS(t) (for initial vibrational energy E vib (0) = 1998 cm−1) (dashed lines) with thermal equilibrium vibrational energy fluctuation correlation functions for different solvent masses m v (solid lines). The equilibrium results plotted are the total (C(t)), kinetic energy (K(t)≡C KK(t)), and potential energy (V(t)≡C VV(t)) correlation functions. Note that each of these lower three panels show five different curves; some of these curves are similar enough to one another that they are difficult to distinguish on this scale.

Image of FIG. 10.
FIG. 10.

Non-equilibrium vibrational energy relaxation following excitation of the perylene warping mode in liquid argon. The details of the graph are the same as those shown in Fig. 9, except that the warping mode frequency here is chosen to be Ω/(2πc) = 48 cm−1.

Image of FIG. 11.
FIG. 11.

Non-equilibrium vibrational energy relaxation following excitation of the perylene warping mode in liquid argon. The details of the graph are the same as those shown in Fig. 9, except that the warping mode frequency here is chosen to be Ω/(2πc) = 192 cm−1.

Tables

Generic image for table
Table I.

Hamiltonian parameters.

Generic image for table
Table II.

Average amplitudes of vibrational motion.a,b

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/content/aip/journal/jcp/137/2/10.1063/1.4733392
2012-07-12
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Vibrational energy relaxation of large-amplitude vibrations in liquids
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/2/10.1063/1.4733392
10.1063/1.4733392
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