Transcript First principles modelling of Krn+ cations (n = 1

Fragmentation Dynamics of Singly Ionized
Homogeneous Rare Gas Trimers
PRAHA
Daniel Hrivňák, Ivan Janeček and René Kalus
OSTRAVA
Department of Physics, University of Ostrava, Ostrava, Czech Republic
Supported by the Grant Agency of the Czech Republic (grant. 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
n
n
n
Hˆ DIM   Hˆ ab  (n  2) Hˆ a
a 1 b  a
a 1
SIMULATION I:
Rg3  Rg
Diatomic inputs
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.
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.
+
Rg3
Fragmentation of the

3
Rg3  Rg  e
*
3
After dynamic equilibrisation
the heated cluster
has a random configuration
different from initial one.
A neutral trimer
in static equilibrium
configuration
is vibrationally
excited.
cluster after sudden ionisation
Rg   Rg2 + Rg 

+
3
Now, the trimer is suddenly ionised.
(Red colour indicates positive charge
localized on an atom in case diabatic
Ionisation).
Results 1:
Role of spin-orbit coupling (SO), induced dipole - induced
dipole interaction (ID-ID) and initial vibrational excitation
(Ev) in Ar3+ decay
The molecular dynamics
continues up to 105 fs.
Results 2:
Table of average values
Rare Model
gas
Comparison Ar3+, Kr3+ and Xe3+ decay.
Ar
0,10
0,08
DIM,
Ev = E0
DIM + SO,
Ev = E0
DIM + SO + ID- ID, Ev = E0
0,06
DIM + SO + ID- ID, Ev = 3 E0
0,04
DIM + SO + ID- ID, Ev = Edis
0,02
0,00
-0,02
0
20000
40000
60000
80000
100000
0,08

0,07
Diabatic Ionisation
from EV = Edis
0,06
Model:
DIM + SO + ID - ID
0,05



0,04
+
Ar3
Kr3+
+
Xe3



0,03

0,02
 




0,01








 
0,00
Time of decay [fs]

0
20000

 

  
























 




 
 
40000
60000
80000
100000
Time of decay [fs]
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.
SIMULATION II:
For Ev = Edis a fragmentation of
population of the Ar3+ is very quick in
comparison with Kr and Xe cases.
Stable configuration of the Rg3
on the basic electronic level.
Kinetic energy of fragments [eV]
Vibrationally excited Rg3+ cluster
on the basic electronic level.
+
DIM
DIM+SO
DIM+SO+ID-ID
Experiment
Xenon
2.1
SO constant = 0.874 eV
1.4
E(2P1/2) – E(2P3/2) = 1.311 eV
0.7
D0(Xe3+)
0.0
1.4
2.1
2.8
3.5
4.2
4.9
= 1.245 eV
5.6
Symmetric fragmentation ratio [%]
Kinetic energy distribution [eV]
Photon energy [eV]
Medium atom
Left-hand atom
Right-hand atom
1.0
0.8
0.6
0.4
0.2
0.0
70
DIM+SO+ID-ID, 100 K
Experiment
60
50
40
30
20
10
0
1.5
2.0
2.5
3.0
3.5
4.0
Photon energy [eV]
1.5
2.0
2.5
3.0
3.5
Photon energy [eV]
4.0
Ar
4.5
EvibION
[eV]
ErotREM
[eV]
EtrREM
[eV]
EtrEMIT
[eV]
EKER
[eV]
0.0044 0,24193 0,07447 0,02074 0,01693 0,01278 0,02556 0,03834
0.0044 0,27091 0,04452 0,01173 0,01134 0,00715 0,01431 0,02146
0.0044 0,27334 0,04363 0,01158 0,01113 0,00697 0,01395 0,02092
0.0132 0,28089 0,04349 0,01079 0,01106 0,00722 0,01444 0,02166
0.0247 0,28078 0,0416
0,018
(Eint)
0,01117 0,00991 0,00684 0,01369 0,02053
0,30
Xe
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
+
Rg3
cluster
Dissociation
The same configuration as
previous one. Cluster is excited
to the higher electronic level.
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 spinorbit splitting of the Rg+ ion to the two
states 2P1/2 and 2P3/2 with some
energetical gap.
Cluster is decayed to
the single atoms.
Argon
SO constant = 0.117 eV
E(2P1/2) – E(2P3/2) = 0.175 eV
D0(Ar3+) = 1.592 eV
4.2
DIM+SO
DIM
DIM+SO+ID-ID
Experiment
3.5
2.8
2.1
1.4
0.7
0.0
1.4
2.1
2.8
3.5
4.2
4.9
5.6
Photon energy [eV]
0.7
DIM+SO, 50 K
Experiment
0.6
0.5
0.4
0.3
0.2
0.1
1.5
2.0
2.5
3.0
3.5
4.0
Photon energy [eV]
4.5
4.5
5.0
5.5
1.8
Medium atom
Left-hand atom
Right-hand atom
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
1.5
1Experiment:
EvibREM
[eV]
DIM + SO + 0.0347 0,19284 0,02307 0,00656 0,00567 0,00362 0,00723 0,01085
ID-ID
Ev = Edis
DIM + SO + 0.0487 0,16045 0,02542 0,00726 0,00571 0,00415 0,00831 0,01246
ID-ID
Ev = Edis
Kr
Photon absorption
hn
2.8
Ar
Photodissociation of the vibrationally excited
Heating
3.5
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.
Symmetric fragmebtation ratio [%]
0,12
Normalised count
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”).
Diabatic ionisation
Influence of
additional interaction and initial heating
0,14
Ar
Normalised count
Ar3
<Q>
[e]
Ev
[eV]
DIM
Ev = E0
DIM + SO
Ev = E0
DIM + SO +
ID-ID
Ev = E0
DIM + SO +
ID-ID
Ev = 3E0
DIM + SO +
ID-ID
Ev = Edis
Experiment*
Ar
Ar
0,16
+
In case of a cluster decay indication
the dynamics is stopped.
Kinetic energy of fragments [eV]
F. O. Ellison, J. Am. Chem. Soc. 85 (1963), 3540.
P. J. Kuntz & J. Valldorf, Z. Phys. D (1987), 8, 195.
DIM extensions
Kinetic energy distribution [eV]
DIM Method
Haberland, Hofmann, and Issendorff, J. Chem. Phys. 103, 3450 (1995).
2.0
2.5
3.0
3.5
4.0
Photon energy [eV]
4.5
5.0
5.5