Fragmentation Dynamics of Singly Ionized Homogeneous Rare Gas Trimers

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

Department of Physics, UDepartment of Physics, University of Ostrava, Ostrava, Czech Republicniversity of Ostrava, Ostrava, 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 with the whole DIM basis (HWD)M. Amarouche, F. X.Gadea, J. Durup, Chem. Phys. 130 (1989) 145-157 - multi-electronic-state molecular dynamics

DIM MethodF. O. Ellison, J. Am. Chem. Soc. 85 (1963), 3540.P. J. Kuntz & J. Valldorf, Z. Phys. D (1987), 8, 195.

Diatomic inputsNeutral 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.

DIM + SO [M. Amarouche et al., J. Chem. Phys. 88 (1988) 1010]The DIM model with inclusion of the spin-orbit coupling. [J. S. Cohen and B. Schneider, J. Chem. Phys. 64 (1974) 3230].DIM + SO + ID-ID [M. Amarouche et al., J. Chem. Phys. 88 (1988) 1010]. Inclusion of the most important three-body forces corresponding to the interaction of two atomic dipoles induced by a positive charge localized on a third atom.

DIM extensions

SIMULATION I: Fragmentation of the Rg3+ cluster after sudden ionisation

++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 static equilibrium configuration is vibrationallyexcited.

*3 3Rg Rg

0 20000 40000 60000 80000 1000000,00

0,01

0,02

0,03

0,04

0,05

0,06

0,07

0,08

No

rma

lise

d c

ou

nt

Time of decay [fs]

Ar3+

Kr3+

Xe3+

Diabatic Ionisationfrom E

V = E

dis

Model:DIM + SO + ID - ID

Now, the trimer is suddenly ionised.(Red colour indicates positive charge localized on an atom in case diabatic Ionisation).

After dynamic equilibrisation the heated cluster has a random configuration different from initial one.

The molecular dynamics continues up to 105 fs.

In case of a cluster decay indicationthe dynamics is stopped.

Results 1: Role of spin-orbit coupling (SO), induced dipole - induced dipole interaction (ID-ID) and initial vibrational excitation (Ev) in Ar3+ decay

Results 2: Comparison Ar3+, Kr3+ and Xe3+ decay.

Initial heating of clusters to vibrational energy EV shortens time of decay, especially for disociation limit energy Edis, which is energy released in decay of neutral trimer on dimer and monomer. Energy E0 represent estimate of basic quantum vibration (“zero vibration”).

Table of average values

Average values: <Q> - electric charge single Ar emitted, EKER – kinetic energy released, Evib, Erot, Etr – vibration, rotation and translation energy (REM – Ar2 remainder, EMIT – Ar emitted)

* A. Bastida, N. Halberdstat, J.A. Beswick, F.X. Gadéa, U. Buck, R. Galonska, C. Lauenstein, Chem. Phys. Lett. 249 (1996)1-6

The spin orbit coupling has major influence on decay. Time of decay is higher if SO is on. On the contrary a role of induced dipole – induced dipole interaction is not relevant.

For Ev=E0 none or sporadic fragmentations of Kr and Xe trimer ions are observed up to 105 fs. More frequent decay was found for higher initial vibrational excitation. For Ev = Edis a fragmentation of

population of the Ar3+ is very quick in

comparison with Kr and Xe cases.

Rare gas

Model

Ev [eV]

<Q> [e]

EvibION

[eV]

EvibREM

[eV]

ErotREM

[eV]

EtrREM

[eV]

EtrEMIT

[eV]

EKER

[eV]

Ar DIM Ev = E0

0.0044 0,24193 0,07447 0,02074 0,01693 0,01278 0,02556 0,03834

Ar DIM + SO Ev = E0

0.0044 0,27091 0,04452 0,01173 0,01134 0,00715 0,01431 0,02146

Ar DIM + SO + ID-ID Ev = E0

0.0044 0,27334 0,04363 0,01158 0,01113 0,00697 0,01395 0,02092

Ar DIM + SO + ID-ID Ev = 3E0

0.0132 0,28089 0,04349 0,01079 0,01106 0,00722 0,01444 0,02166

Ar DIM + SO + ID-ID Ev = Edis

0.0247 0,28078 0,0416 0,01117 0,00991 0,00684 0,01369 0,02053

Ar

Experiment*

0,018 (Eint)

0,30

Kr DIM + SO + ID-ID Ev = Edis

0.0347 0,19284 0,02307 0,00656 0,00567 0,00362 0,00723 0,01085

Xe DIM + SO + ID-ID Ev = Edis

0.0487 0,16045 0,02542 0,00726 0,00571 0,00415 0,00831 0,01246

0 20000 40000 60000 80000 100000-0,02

0,00

0,02

0,04

0,06

0,08

0,10

0,12

0,14

0,16

DIM, Ev = E

0

DIM + SO, Ev = E

0

DIM + SO + ID- ID, Ev = E

0

DIM + SO + ID- ID, Ev = 3 E

0

DIM + SO + ID- ID, Ev = E

dis

No

rma

lise

d c

ou

nt

Time of decay [fs]

Ar3

Diabatic ionisationInfluence of additional interaction and initial heating

PRAHA

OSTRAVA

SIMULATION II: Photodissociation of the vibrationally excited Rg3+ cluster

Stable configuration of the Rg3+

on the basic electronic level.

Vibrationally excited Rg3+ cluster

on the basic electronic level.

The same configuration as previous one. Cluster is excited to the higher electronic level.

h

Photon absorptionHeating Dissociation

Cluster is decayed to the single atoms.

1.4 2.1 2.8 3.5 4.2 4.9 5.6

0.0

0.7

1.4

2.1

2.8

3.5

Kin

etic

en

erg

y o

f fr

agm

ents

[eV

]

Photon energy [eV]

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

1.5 2.0 2.5 3.0 3.5 4.0 4.5

0.0

0.2

0.4

0.6

0.8

1.0

Photon energy [eV]

Medium atom Left-hand atom Right-hand atom

Kin

eti

c e

ne

rgy

dis

trib

uti

on

[e

V]

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Sy

mm

etr

ic f

rag

me

bta

tio

n r

ati

o [

%]

Photon energy [eV]

DIM+SO, 50 K Experiment

1.4 2.1 2.8 3.5 4.2 4.9 5.6

0.0

0.7

1.4

2.1

2.8

3.5

4.2

Kin

eti

c e

ne

rgy

of

fra

gm

en

ts [

eV

]

Photon energy [eV]

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

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

Kin

eti

c e

ne

rgy

dis

trib

uti

on

[e

V]

Photon energy [eV]

Medium atom Left-hand atom Right-hand atom

Xenon

SO constant = 0.874 eV

E(2P1/2) – E(2P3/2) = 1.311 eV

D0(Xe3+) = 1.245 eV

1Experiment: Haberland, Hofmann, and Issendorff, J. Chem. Phys. 103, 3450 (1995).

A general fragmentation pattern from experiment1, confirmed by our theoretical calculations at low temperatures: the middle atom obtains only a small velocity, two remaining outer atoms gain high velocities in opposite directions.

The positive charge is usually localized on one of the fast outer atoms (the asymmetric fragmentation), but localization of the charge on the slow middle atom (the symmetric case) is observed too.

An essential role in the theoretical and experimental results plays the spin-orbit splitting of the Rg+ ion to the two states 2P1/2 and 2P3/2 with some energetical gap.

Argon

SO constant = 0.117 eV

E(2P1/2) – E(2P3/2) = 0.175 eV

D0(Ar3+) = 1.592 eV

1.5 2.0 2.5 3.0 3.5 4.0 4.5

0

10

20

30

40

50

60

70 DIM+SO+ID-ID, 100 K Experiment

Sym

met

ric

frag

men

tati

on

rat

io [

%]

Photon energy [eV]