Dynamics of excited rare gas cluster cationsDynamics of excited rare gas cluster cations

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. 203/04/2146)rant. no. 203/04/2146)

Method for numerical simulation: Hemiquantal dynamics [1]

++3 2 +Rg Rg Rg3 3 eRg Rg

EXCITATION

*3 3Rg Rg

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

After MC equilibration the heated cluster had a random configuration different from the initial one (a distorted triangle). In the next step the trimer was suddenly ionised to energy level Ei from the cation trimer energy spectrum. This state is initial state for MD simulations. For each energy level we studied the count of fragmentations from 2000 trajectories up to 105 fs of real process time.

PRAHA

OSTRAVA

Fragmentation of rare gas trimers in adiabatic states after sudden ionisation

The first column of the figures on the left represent the histograms of the time of decay for argon, krypton and xenon. Curves for adiabatic levels higher than basic level are shifted along the vertical axis (blue lines mark zero value). The second column contain mosaics of quaternions of the graphs which show numbers of decays and mean values of the decay time, electric charge of evaporated single atom and kinetic energy of released atoms.

Model with initial vibrational excitation to Ek = E0

For argon trimers a frequent and quick fragmentation has been observed (see figure on the left) from each energy level with exception of E13 level (no decay) and the nearest neighbouring levels (sporadic and slow decay).

For krypton trimers we observe frequent fragmentation from the first three levels. For level E7 and for level E13 and higher no decay has been observed.

In case of xenon trimers a fragmentation has been detected only from basic level up to time 100 ps, thus for next studies model with higher heating of the neutral clusters was used.

Model with initial vibrational excitation to Ek = Edis

For argon trimers the massive decay can be observed from each energy level. From level E15 and E17 even the fragmentation to the single atoms has been detected. Maximal mean time of decay for standard channel (decay to dimer and single atom) was found for E15.

For krypton and xenon trimers one can see similar situation (decay for all levels with exception E15 for xenon), but the mean decay time is longer, fragmentation to the single atoms has been detected from level E11 and E17, and mean time of decay (as function of level number) has two local maxima for level E9 and E15.

Interesting result of our studies is stability of trimer cation (or existence of long living state) in some adiabatic states.*

*Private communication: Metastable decay (time of decay about 40μs) of the krypton trimer cations was observed in experiment [K.Gluch et al, J.Chem Phys. 120 (2004), 2686]

Model:DIM ● diatomics-in-molecules [2, 3] models of intra-cluster interactions + SO ● inclusion of the spin-orbit coupling [4]

+ ID-ID ● inclusion of three-body induced dipole – induced dipole interactions [5]

[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].

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

0,00070

0,00075

Ar+

3 - Model:

DIM + SO + ID-IDE

v = E

dis

No

rma

lise

d C

ou

nt

Decay Time [fs]

E01 E03 E05 E07 E09 E11 E13 E15

channel 3 E17

channel 3

E01 E03 E05 E07 E09 E11 E13 E15 E15 E17 E170

500

1000

1500

2000

88710

12

12

1684

458

2000

2000

1999

2000

2000

2000

Ar+ 3 Model:

DIM + SO + ID-IDE

v = E

dis 3Ar

Nu

mb

er o

f d

ecay

s

Initial Energy level

3 Ar

E01 E03 E05 E07 E09 E11 E13 E15 E15 E17 E170

10000

20000

30000

40000

50000

60000

3Ar 3Ar

Mea

n D

ecay

Tim

e [f

s]

Initial Energy level

E01 E03 E05 E07 E09 E11 E13 E15 E15 E17 E17

0,00

0,25

0,50

0,75

1,00

(Ar2+Ar)+

(3Ar)+

Ar+3

3Ar3Ar

Mea

n E

vap

ora

ted

Ch

arg

e [e

]

Initial Energy level

Ar+3

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

0,025

0,050

0,075

0,100

3 Ar

3Ar

Mea

n K

inet

ic E

ner

gy

of

Eva

po

rate

d A

tom

[eV

]

Initial Energy level

1000 10000 100000-0,00010

-0,00005

0,00000

0,00005

0,000100,00015

0,00020

0,00025

0,00030

0,00035

0,00040

0,00045

0,00050

0,000550,00060

0,00065

0,00070

0,00075

0,00080

Kr+

3 - Model:

DIM + SO + ID-IDE

v = E

dis

No

rma

lise

d C

ou

nt

Decay Time [fs]

E01 E03 E05 E07 E09 E11

channel 3 E13 E15 E17

channel 3

E01 E03 E05 E07 E09 E11 E11 E13 E15 E17 E170

500

1000

1500

2000

121

807

4

661

552

1372

1358

164417

28192020

00

3Kr

3Kr

Kr+ 3 Model:

DIM + SO + ID-IDE

v = E

dis

Nu

mb

er o

f d

ecay

s

Initial Energy level

E01 E03 E05 E07 E09 E11 E11 E13 E15 E17 E170

10000

20000

30000

40000

50000

60000

3Kr3Kr

Mea

n D

ecay

Tim

e [f

s]

Initial Energy level

E01 E03 E05 E07 E09 E11 E11 E13 E15 E17 E17

0,00

0,25

0,50

0,75

1,00

3Kr3Kr

(Kr2+Kr)+

(3Kr)+

Kr+3

Mea

n E

vap

ora

ted

Ch

arg

e [e

]

Initial Energy level

Kr+3

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

0,025

0,050

0,075

0,100

3Kr 3Kr

Mea

n K

inet

ic E

ner

gy

of

Eva

po

rate

d A

tom

[eV

]

Initial Energy level

1000 10000 100000-0,00005

0,00000

0,00005

0,00010

0,00015

0,00020

0,00025

0,00030

0,00035

0,00040

0,00045

0,00050

0,00055

Ar+

3 - Model:

DIM + SO + ID-IDE

v = E

0

No

rma

lise

d c

ou

nt

Decay Time [fs]

E01 E03 E05 E07 E09 E11 E15 E17

channel 3

/ 50

E01 E03 E05 E07 E09 E11 E13 E15 E17 E170

500

1000

1500

2000

1985

13

171

0

17

1997

1992

1972

2000

Ar+ 3 Model:

DIM + SO +ID-IDE

v = E

0

3Ar

Nu

mb

er o

f d

ecay

s

Initial Energy level

Ar3

2000

E01 E03 E05 E07 E09 E11 E13 E15 E17 E170

10000

20000

30000

40000

50000

60000

3ArAr3

Mea

n D

ecay

Tim

e [f

s]

Initial Energy level

>105 fs

E01 E03 E05 E07 E09 E11 E13 E15 E17 E17

0,00

0,25

0,50

0,75

1,00

3ArAr3

(Ar2+Ar)+

(3Ar)+

Ar+3

Mea

n E

vap

ora

ted

Ch

arg

e [e

]

Initial Energy level

Ar+3

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

0,025

0,050

0,075

0,100

3ArAr

3

Mea

n K

inet

ic E

ner

gy

of

Eva

po

rate

d A

tom

[eV

]

Initial Energy level Ar3

Kr3

Xe3

Neutral trimer

E0 [meV]

Edis

[meV] Emin

[meV]

Ar3 4.4 24.7 37

Kr3 4.5 34.7 52

Xe3 3.8 48.7 73

IONISATION FRAGMENTATIONMonte Carlo Simulation Molecular Dynamics Simulation

Neutral trimers in the static equilibrium configuration (equilateral triangle) were vibrationally excited to determined energy. In our models its value was from the zero point energy E0 to the dissociation limit energy Edis. The values of these energies for argon, krypton and xenon are presented in the table together with the global minimum energy Emin.

E01 E03 E05 E07 E09 E11 E11 E13 E15 E17 E170

500

1000

1500

2000

8

2750

772

383

1382

569

866

68376

6

2000

Xe+ 3 Model:

DIM + SO + ID-IDE

v = E

dis

Xe3 3Xe

Nu

mb

er o

f d

ecay

s

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 [f

s]

Initial Energy level

>105 fs

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 [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

Spin-orbit effects in photodissociation of ionised rare gas trimers

0

500

1000

1500

2000

1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0 5,50

500

1000

1500

2000

250 K

200 KKr3

+

150 K

Ave

rag

e li

fe-t

ime

[fs]

Photon energy [eV]

Ar3

+

Xe3

+

0

500

1000

1500

2000 DIM DIM+SO

1 2 3 4 5

0,0

0,1

0,2

0,3

0,4

0,5

0,6

150 K

Sym

me

tric

bra

nch

ing

ra

tio

Photon energy [eV]

Ar3

+

Xe3

+250 K

0,0

0,1

0,2

0,3

0,4

0,5

0,6

DIM DIM+SO DIM+SO+ID-ID Experiment

1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0

0

20

40

60

80

100

Re

lativ

e fr

eq

ue

ncy

co

un

t [%

]

Photon energy [ev]

DIM+SO

0

20

40

60

80

100

Channel 1 Channel 3

Xe3

+T=250 K

DIM

Indication of the charge localization:

Stable configuration of the Rg3+

on the ground electronic level. Vibrationally excited Rg3

+ cluster on the ground electronic level.

Cluster is excited to a higher electronic level.

Photon absorptionHeating (Metropolis

Monte Carlo)

Dissociation (MD)

Asymmetric decaySymmetric decay

Channel 3 (three evaporated atoms)

Channel 1(one evaporated atom)

Xenon

SO constant = 0.874 eV

E(2P1/2) – E(2P3/2) = 1.311 eV

D0(Xe3+) = 1.245 eV

Argon

SO constant = 0.117 eV

E(2P1/2) – E(2P3/2) = 0.175 eV

D0(Ar3+) = 1.592 eV

Krypton

SO constant = 0.444 eV

E(2P1/2) – E(2P3/2) = 0.666 eV

D0(Kr3+) = 1.375 eV

Experiment: Haberland, Hofmann, and Issendorff, J. Chem. Phys. 103, 3450 (1995). Next results: D. Hrivňák, R. Kalus, and F. X. Gadea, Europhys. Lett. 71 (1), pp. 42-48 (2005).