RESULTS I: Comparison for the different rare-gases Xenon SO constant = 0.874 eV E( 2 P 1/2 ) – E(...
1
RESULTS I: Comparison for the different rare-gases Xenon SO constant = 0.874 eV E( 2 P 1/2 ) – E( 2 P 3/2 ) = 1.311 eV D 0 (Xe 3 + ) = 1.245 eV 1 Experiment: Haberland, Hofmann, and Issendorff, J. Chem. Phys. 103, 3450 (1995). A general fragmentation pattern from experiment 1 is confirmed by our theoretical calculations at low temperatures 2 . The middle atom obtains only a small velocity, two remaining outer atoms gain high velocities of 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. The spin-orbit splitting of the Rg + ion to the two states 2 P 1/2 and 2 P 3/2 plays an essential role in the theoretical and experimental results. Argon SO constant = 0.117 eV E( 2 P 1/2 ) – E( 2 P 3/2 ) = 0.175 eV D 0 (Ar 3 + ) = 1.592 eV 1.5 2.0 2.5 3.0 3.5 4.0 4.5 0.0 0.2 0.4 0.6 0.8 D IM +SO E xperim ent Ar 3 + Kr 3 + P h o to n en erg y [eV ] Xe 3 + 0.0 0.2 0.4 0.6 0.8 S ym m e tric d e c a y ra tio 0.0 0.2 0.4 0.6 0.8 Photodissociation of Rare-Gas Trimer Cations Daniel Hrivňák Daniel Hrivňák a a , , René Kalus René Kalus a a , Florent X. Gadéa , Florent X. Gadéa b b a a Department of Physics, U Department of Physics, U niversity of Ostrava, Ostrava, Czech Republic niversity of Ostrava, Ostrava, Czech Republic b b The Nanoscience Groupe, CEMES, CNRS, Tolouse, France The Nanoscience Groupe, CEMES, CNRS, Tolouse, France F F inancial support inancial support : : the Grant Agency of the Czech Republic ( the Grant Agency of the Czech Republic ( g g rant rant s s No. 203/02/1204 No. 203/02/1204 and 203/04/2146 and 203/04/2146 ), ), Ministry of Ministry of Education of the Czech Education of the Czech Republic (grant No. 1N04125) Republic (grant No. 1N04125) . . OSTRAVA Krypton SO constant = 0.444 eV E( 2 P 1/2 ) – E( 2 P 3/2 ) = 0.666 eV D 0 (Kr 3 + ) = 1.375 eV 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 DIM D IM +SO E xperim ent T o ta lkin e tic e n e rg y o ffra g m e n ts [e V ] P h o to n e n e rg y [e V ] 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Xe + 3 Kr + 3 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Ar + 3 Stable configuration of the Rg 3 + on the ground electronic level. Vibrationally excited Rg 3 + cluster on the ground electronic level. The same configuration as previous one. Cluster is excited to a higher electronic level. h Photon absorption (standard formula) Heating (Metropolis Monte Carlo) Dissociation (molecular dynamics) Asymmetric decay SIMULATION Symmetric decay Cluster decays to single fragments following two main channels. Indication of the charge localization: THEORY Hemiquantal dynamics with the whole DIM basis (HWD) M. Amarouche, F. X.Gadea, J. Durup, Chem. Phys. 130 (1989) 145-157 - meanfield molecular dynamics DIM Method F. O. Ellison, J. Am. Chem. Soc. 85 (1963), 3540. P. J. Kuntz & J. Valldorf, Z. Phys. D (1987), 8, 195. Diatomic inputs Neutral diatoms - empirical data: Ar 2 – R. A. Aziz, J. Chem. Phys. 99 (1993), 4518. Kr 2 – A. K. Dham et al., Mol. Phys. 67 (1989) 1291. Xe 2 – A. K. Dham et al., Chem. Phys. 142 (1990) 173. Singly charged diatoms: computed ab initio by I. Paidarová and F. X. Gadéa (1996, 2003, 2001) 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 DIM ab a 1 1 ˆ ˆ ˆ ( 2) n n n a b a a H H n H 2 Vibrational temperature of the clusters before simulated photon absorption is 150 K for the plots above. Kinetic energy release Symmetric decay ratio RESULTS II: Temperature effects in Xe 3 + cation 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 S ym m e tric d e c a y ra tio P h o to n en erg y [eV ] 150 K 200 K 300 K 400 K E xp erim en t 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 To ta l k in e tic e n e rg y o f fra g m e n ts [e V ] P h o to n en erg y [eV ] 150 K 200 K 300 K 400 K E xp erim en t Kinetic energy release Symmetric decay ratio Computational model: DIM+SO+ID- ID(dmp). ID-ID interaction is damped properly for short distances (I. Last, T. F. George, J. Chem. Phys. 93 (1990) 8925). Structural changes (Monte Carlo simulation) 3 Structural number = Q 1 – Q 2 + Q 3 (- Q 4 ) (0: dimer or tetramer core, 0.5: trimer core). CONCLUSIONS Generally, a very good agreement between experimental and computed data has been obtained. The HWD-dynamics, based on the DIM approach, is well suited for analysis of this problem. Inclusion of the spin-orbit coupling to the computational model is necessary. The general experimental fragmentation pattern has been confirmed by our calculations in the temperature range 150 K – 400 K. The total kinetic energy of the photodissociation fragments increases linearly with energy of the photon, but there is a discrete down-jump for a sharply defined photon energy. This jump is clearly caused by pumping of the kinetic energy to the energy of the charged fragment (transition between 2 P 3/2 and 2 P 1/2 state). The experimental curves of the symmetric decay ratio differ partially from our curves computed at low temperatures in the region of the higher photon energies. In the case of xenon, this difference vanishes for the simulation temperature about 300 K, but a good agreement in the intensity of the main peak is now disturbed. Plausible explanation of this problem will require further calculations. Temperature induced structural changes are the most suspicious in the problem mentioned above. In the case of the xenon 2 Core atoms = atoms with the non-negligible charge. 1 Lindeman coefficient = (0: solid phase, 1: liquid phase). 2 2 1 1 1 2 ( 1) N N ij ij i j i ij R R NN R 0 50 100 150 200 250 300 0.20 0.25 0.30 0.35 0.40 0.45 0.50 S tru ctu raln u m b er 3 Tem p eratu re [K ] 2.6 2.7 2.8 2.9 3.0 N u m b e r o f c o re a to ms 2 0.0 0.2 0.4 0.6 0.8 L ind em an co efficien t 1
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Transcript of RESULTS I: Comparison for the different rare-gases Xenon SO constant = 0.874 eV E( 2 P 1/2 ) – E(...
RESULTS I: Comparison for the different rare-gases
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 is confirmed by our theoretical calculations at low temperatures2. The middle atom obtains only a small velocity, two remaining outer atoms gain high velocities of 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. The spin-orbit splitting of the Rg+ ion to the two states 2P1/2 and 2P3/2 plays an essential role in the theoretical and experimental results.
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
0.0
0.2
0.4
0.6
0.8
DIM+SO Experiment
Ar3
+
Kr3
+
Photon energy [eV]
Xe3
+
0.0
0.2
0.4
0.6
0.8
Sy
mm
etr
ic d
ec
ay
ra
tio
0.0
0.2
0.4
0.6
0.8
Photodissociation of Rare-Gas Trimer CationsDaniel HrivňákDaniel Hrivňákaa, , René KalusRené Kalusaa, Florent X. Gadéa, Florent X. Gadéabb
aa Department of Physics, UDepartment of Physics, University of Ostrava, Ostrava, Czech Republicniversity of Ostrava, Ostrava, Czech Republic
bb The Nanoscience Groupe, CEMES, CNRS, Tolouse, FranceThe Nanoscience Groupe, CEMES, CNRS, Tolouse, France
FFinancial supportinancial support:: the Grant Agency of the Czech Republic ( the Grant Agency of the Czech Republic (ggrantrantss No. 203/02/1204 No. 203/02/1204 and 203/04/2146 and 203/04/2146),), Ministry ofMinistry of Education of the Czech Republic (grant No. 1N04125)Education of the Czech Republic (grant No. 1N04125)..
OSTRAVA
Krypton
SO constant = 0.444 eV
E(2P1/2) – E(2P3/2) = 0.666 eV
D0(Kr3+) = 1.375 eV
1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
DIM DIM+SO Experiment
To
tal k
ine
tic e
ne
rgy
of f
rag
me
nts
[eV
]
Photon energy [eV]
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Xe+
3
Kr+
3
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Ar+
3
Stable configuration of the Rg3
+ on the ground electronic level.
Vibrationally excited Rg3
+ cluster on the ground electronic level.
The same configuration as previous one. Cluster is excited to a higher electronic level.
h Photon absorption (standard formula)
Heating(Metropolis
Monte Carlo)
Dissociation(molecular dynamics)
Asymmetric decay
SIMULATION
Symmetric decay Cluster decays to single fragments following two main channels.
Indication of the charge localization:
THEORY Hemiquantal dynamics with the whole DIM basis (HWD)M. Amarouche, F. X.Gadea, J. Durup, Chem. Phys. 130 (1989) 145-157 - meanfield 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.Kr2 – A. K. Dham et al., Mol. Phys. 67 (1989) 1291.Xe2 – A. K. Dham et al., Chem. Phys. 142 (1990) 173. Singly charged diatoms: computed ab initio by I. Paidarová and F. X. Gadéa (1996, 2003, 2001)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
DIM ab a1 1
ˆ ˆ ˆ( 2)n n n
a b a a
H H n H
2Vibrational temperature of the clusters before simulated photon absorption is 150 K for the plots above.
Kinetic energy release Symmetric decay ratio
RESULTS II: Temperature effects in Xe3+ cation
1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Sy
mm
etr
ic d
ec
ay
ra
tio
Photon energy [eV]
150 K 200 K 300 K 400 K Experiment
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
To
tal
kin
eti
c e
ne
rgy
of
fra
gm
en
ts [
eV
]
Photon energy [eV]
150 K 200 K 300 K 400 K Experiment
Kinetic energy release
Symmetric decay ratio
Computational model: DIM+SO+ID-ID(dmp).ID-ID interaction is damped properly for short distances
(I. Last, T. F. George, J. Chem. Phys. 93 (1990) 8925).
Structural changes(Monte Carlo simulation)
3Structural number = Q1 – Q2 + Q3 (- Q4) (0: dimer or tetramer core, 0.5: trimer core).
CONCLUSIONS Generally, a very good agreement between experimental and computed data has been obtained. The HWD-dynamics, based on the DIM approach, is well suited for analysis of this problem.
Inclusion of the spin-orbit coupling to the computational model is necessary.
The general experimental fragmentation pattern has been confirmed by our calculations in the temperature range 150 K – 400 K.
The total kinetic energy of the photodissociation fragments increases linearly with energy of the photon, but there is a discrete down-jump for a sharply defined photon energy. This jump is clearly caused by pumping of the kinetic energy to the energy of the charged fragment (transition between 2P3/2 and 2P1/2 state).
The experimental curves of the symmetric decay ratio differ partially from our curves computed at low temperatures in the region of the higher photon energies. In the case of xenon, this difference vanishes for the simulation temperature about 300 K, but a good agreement in the intensity of the main peak is now disturbed. Plausible explanation of this problem will require further calculations.
Temperature induced structural changes are the most suspicious in the problem mentioned above. In the case of the xenon trimer, the phase changes to a liquid phase seems to occur at temperatures about 220 K. A charged dimer core with one neutral atom attached appears for the higher temperatures with the non-negligible probability.
2Core atoms = atoms with the non-negligible charge.
1Lindeman coefficient = (0: solid phase, 1: liquid phase).
221
1 1
2
( 1)
N Ni j i j
i j i i j
R R
N N R
0 50 100 150 200 250 3000.20
0.25
0.30
0.35
0.40
0.45
0.50
Str
uct
ura
l nu
mb
er3
Temperature [K]
2.6
2.7
2.8
2.9
3.0
Nu
mb
er o
f co
re a
tom
s2
0.0
0.2
0.4
0.6
0.8
Lin
dem
an c
oef
fici
ent1
