Fragmentation Dynamics of Singly Ionised Homogeneous Rare Gas Trimers from Adiabatic States

Ivan JaneIvan Janeček ,ček , Daniel HrivňákDaniel Hrivňák, , and René Kalusand René Kalus

Department of Physics, UDepartment of Physics, University of Ostrava,niversity of Ostrava,Ostrava, Czech RepublicOstrava, Czech Republic

Supported by the Grant Agency of the Czech Republic (Supported by the Grant Agency of the Czech Republic (ggrant. no. 203/02/1204)rant. no. 203/02/1204)

THEORY: Hemiquantal dynamics and extended DIM method

Neutral diatoms: empirical data Ar2 – R. A. Aziz, J. Chem. Phys. 99 (1993), 4518.Singly charged diatoms: computed ab initio by I. Paidarová and F. X. Gadéa (1996)The spin-orbit constant used is of empirical origin.

Simulation: Fragmentation of the Rg3+ cluster after sudden ionisation from energy level Ei.

++3 2 +Rg Rg Rg3 3 eRg Rg

DIM ab a1 1

ˆ ˆ ˆ( 2)n n n

a b a a

H H n H

A neutral trimer in the static equilibrium configuration (equilateral triangle) is vibrationallyexcited .

*3 3Rg Rg

E01 E03 E05 E07 E09 E11 E11 E13 E15 E17 E170

500

1000

1500

2000

Xe+ 3 Model:

DIM+SO+ID-IDHeating: DL

Xe3 3Xe

Dec

ay N

um

ber

Initial Energy level

3Xe

E01 E03 E05 E07 E09 E11 E11 E13 E15 E17 E170

10000

20000

30000

40000

50000

60000

Xe3

3Xe3Xe

Mea

n D

ecay

Tim

e

Initial Energy level

E01 E03 E05 E07 E09 E11 E11 E13 E15 E17 E17

0,00

0,25

0,50

0,75

1,00

(Xe2+Xe)+

(3Xe)+

Xe+3

Xe3

3Xe3Xe

Mea

n E

vap

ora

ted

Ch

arg

e

Initial Energy level

Xe+3

E01 E03 E05 E07 E09 E11 E11 E13 E15 E17 E170,000

0,025

0,050

0,075

0,100

Xe3

3Xe3Xe

Mea

n K

inet

ic E

ner

gy

of

Eva

po

rate

d A

tom

[eV

]

Initial Energy level

1000 10000 100000

0,00000

0,00005

0,00010

0,00015

0,00020

0,00025

0,00030

0,00035

0,00040

0,00045

0,00050

0,00055

0,00060

0,00065

Xe+

3 - Model:

DIM+SO+ID-IDHeating: DL

No

rma

lise

d C

ou

nt

Decay Time [fs]

E01 E03 E05 E07 E09 E11

channel 3 E13 E17

Now, the trimer is suddenly ionised to energy level Ei from the cation trimer energy spectrum.

After MC equilibration the heated cluster has a random configuration different from the initial one(a distorted triangle).

The molecular dynamics runs up to 105 fs.

As soon as a cluster decay is indicated,the calculations is stopped.

PRAHA

OSTRAVA

Model: DIM + SO + ID-ID*

The initial state of the neutral cluster: equilibrium geometry, zero angular momentum, nonzero vibrational kinetic energy Ek. The initial state of the ion cluster: energy level Ei, where i = 1, 3, 5, 7, 9, 11, 13, 15, 17 (double degeneration).

* From diabatic decay simulations we know that the spin orbit coupling has major influence on the time of decay, wherefore DIM model with the inclusion of the SO coupling is used, ID-ID interaction does not seem to be relevant in this case.

Results: Fragmentation of Xe3+ cluster after sudden ionisation

Field of study: Rare gas cation trimers of Ar, Kr, Xe (= Rg) with initial kinetic energy Ek from the zero point vibration energy E0

to the dissociation limit (DL) energy Edl (dissociation of the Rg3 to Rg2 and Rg). At present trimers Rg3

+ are studied. However, fragmentation of larger Rgn+ clusters (n>3) can also be computed.

0 1 2 3 4 5 6 7 8 9 10 11 12

-1,4

-1,2

-1,0

-0,8

-0,6

-0,4

-0,2

0,0

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

En

erg

y [e

V]

Y3, X3=0 [ angstrem]

E01 E03 E05 E07 E09 E11

Init. Conf.

E13 E15 E17

We have computed 2000 trajectories for each energy level. For initial heating with Ek = E0 = 0.0038 eV we have observed no decay from either energy level up to time 100 ps. In the left figure the histogram (in form of the point graph) of the time of decay is plotted for Ek = Edl = 0.0487 eV. The y-scale is correct for basic energy level only. Curves for higher adiabatic levels are shifted along the vertical axis. The main way of the decay is a fragmentation to a dimer and a single atom. One can observe quick decay from the ground state and also from E11 level, where also the fragmentation to single atoms is observed (channel 3). On the other hand, no decay has been observed for E15 level. In the right picture one can see summary of some mean values .

Bottom contour plots show the potential energy surfaces of Xe3+ for levels E11 (left) and E15 (right) as a function of xy-coordinates of the third atom Xe for fixed positions

of the two remaining atoms (1 and 2). Their distance R12 = 4.45 angstrem, which is a mean value of the shortest side of Xe3 triangle after the equilibration phase. Small points correspond to Xe3

+ configurations obtained after this phase (These configurations are initial configuration for molecular dynamics on ion cluster). The red line is an approximate “lower boundary” of the configurations. Atoms 1 and 2 are situated on axis x and have equivalent distance from axis y. Coloured circles at axes show positions of the atoms in configuration corresponding to the potential energy surface minimum (PES E11- equilateral triangle, PES E15 – equilateral triangle and linear trimer). In the case of the initial adiabatic state E15 no decay has been observed for any initial configurations, in the case of the initial adiabatic state E11, on the contrary, a frequent fragmentation has been observed, the green points relate to the initial configuration without decay observed. For illustration, sections for x 3 = 0 are plotted for all the levels in the middle graph.

Hemiquantal, mean-field dynamics (HWD) [1] and recently developed extended diatomics-in-molecules (DIM) [2, 3] models of intra-cluster interactions with the inclusion of the spin-orbit coupling (DIM +SO) [4] and the most important three-body forces induced dipole – induced dipole interactions (DIM +SO + ID-ID) [5] are used to study fragmentation of argon, krypton and xenon trimer cations after a sudden ionization of respective vibrationally excited neutral trimers.

[1] M. Amarouche, F. X.Gadea, J. Durup, Chem. Phys. 130 (1989) 145-157 [2] F. O. Ellison, J. Am. Chem. Soc. 85 (1963), 3540.[3] P. J. Kuntz & J. Valldorf, Z. Phys. D (1987), 8, 195.[4] J. S. Cohen and B. Schneider, J. Chem. Phys. 64 (1974) 3230[5] M. Amarouche et al., J. Chem. Phys. 88 (1988) 1010].

0,62

0,48 0,380,28

-0,16

-0,22-0,24

-0,26

-0,28

-0,30

-0,32

-0,34

-0,36

-0,38-0,40

-0,42 -0,44

-0,46

-0,46

-0,47-0,48

0 2 4 6 8 100

2

4

6

8

10 Y3 Y3 B Ymin

Y3 [

an

gs

tre

m]

X3 [angstrem]

Xe+

3 E

11

DIM + SO + ID-IDE

k= E

dl

<R12

> = 4.45 angstrem

Minimum energyconfiguration

0,960,94

0,92

0,900,88

0,86

0,84

0,82 0,800,78 0,760,76

0,78

0,80

0,82

0,74

0,74

0 2 4 6 8 100

2

4

6

8

10

Minimum energyconfiguration

Xe+

3 E

15

DIM + SO + ID-IDE

k= E

dl

<R12

> = 4.45 angstrem

Y3 B B Ymin

Y3 [

an

gs

tre

m]

X3 [angstrem]