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Effective chromophore potential, dissipative trajectories, and vibrational energy relaxation: in Ar matrix
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Image of FIG. 1.
FIG. 1.

Potential-energy scheme of free for the electronic ground state , a covalent state , and a charges-transfer state . Pump and probe transitions are indicated by the solid arrows. The probe photon energy fits the - difference energy at and determines . (b) Excitation spectrum of in solid Ar, reproduced from Ref. 5 with narrow zero-phonon lines (ZPLs) accompanied by rather broad phonon sidebands (PSBs).

Image of FIG. 2.
FIG. 2.

Pump-probe spectra with fixed and varied from 500 to . The solid lines 1 and 2 with arrows indicate the out- and inwards moving vibrational wave packet on the -state potential surface. The solid lines 3 and 4 with arrows indicate that the wave packet is detected at the turning point.

Image of FIG. 3.
FIG. 3.

Pump-probe spectra with fixed and varied from 357 to . The solid lines and arrows are analog to Fig. 2. The dashed lines indicate splitting induced by coherent phonons and are not subject of further investigation (Refs. 12 and 13).

Image of FIG. 4.
FIG. 4.

Pump-probe spectra used to determine the round trip times . The lower three spectra are resonantly probed (see text); the upper two not (see text).

Image of FIG. 5.
FIG. 5.

Squared vibrational frequencies vs the -state energy . The dashed line between the arrows gives the fit to the ZPL in the excitation spectrum of Ref. 5. The solid squares are deduced from the round-trip times in the pump-probe spectra (see Table I). The solid lines (a) and(b) represent linear fits for a Morse oscillator according to Eq. (3.1) with parameters listed in Table II.

Image of FIG. 6.
FIG. 6.

(a) Scheme of the wave-packet motion including vibrational energy relaxation. The probe window position is marked by and and the solid arrow. The wave packet is excited at time 0, moves towards the outer turning point through the probe window at 1, and looses the energy in the collision with the matrix, and is once more detected in the probe window at time 2 and continues to and 3. (b) Solid line: RKR surface of . Thin solid line: free potential (Ref. 21). Short dashed line: free plus interactions with head-on atoms sitting at (nearest-neighbor distance in a undisturbed Ar lattice). Dashed line: free plus interactions with head-on atoms sitting at distance from the molecular center. (c) Scheme of the molecule with the internuclear distance and the two “head-on” Ar atoms sitting in distance from the molecular center.

Image of FIG. 7.
FIG. 7.

Trajectory for a wave packet with for . (a) The pump-probe spectra for different show the in- and outward motions of the vibrational wave packet indicated for the first two maxima by the dashed lines (arrows indicate the direction). Each corresponds to a distinct (Table III). (b) The are plotted vs delay times of the maxima (open circles). The velocity of the returning wave packet is fitted to the value as the dashed line. A numerical propagation of a free molecule wave packet with the same excitation conditions is given as the gray scale plot.

Image of FIG. 8.
FIG. 8.

Energy relaxation rates for different molecules in rare-gas solids as a function of excess energy over the gas phase dissociation limit . Given in units are the rates for (solid squares) and (solid triangles). The rates for are furthermore given in units of per wave-packet vibrational period at the excitation wavelength as open circles.


Generic image for table
Table I.

-state periods vs energy. The pump wavelength is transformed to a pump quantum energy . Using the -state absorption spectrum, the mean energy of the wave packet is calculated. is the vibrational energy of the wave packet in the state. The oscillation period is taken from pump-probe spectra using the probe resonance condition at , where indicates a two-photon probe process.

Generic image for table
Table II.

Morse fits for vibrational frequencies following Eq. (3.1). Case (a) refers to the values from 0 to in Fig. 5, whereas case (b) refers to the values above . Only the values of part (a) can be interpreted as parameters of a real Morse oscillator (see text).

Generic image for table
Table III.

for different . The construction is carried out via the probe resonance condition. The values are from the experimental RKR potential from Fig. 6.

Generic image for table
Table IV.

Morse parameters for and obtained fitting the potentials in Refs. 37 and 38.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Effective chromophore potential, dissipative trajectories, and vibrational energy relaxation: Br2 in Ar matrix