Transcript mss09_MI11_H2.ppt

DETERMINATION
OF THE IONIZATION AND DISSOCIATION ENERGIES
OF THE HYDROGEN MOLECULE
Jinjun Liu,1 Edcel J. Salumbides,2
Urs Hollenstein,1 Jeroen C. J. Koelemeij,2 Kjeld S. E. Eikema,2
Wim Ubachs,2 and Frédéric Merkt1
1
Laboratorium für Physikalische Chemie, ETH-Zürich,
8093 Zürich, Switzerland
2
Department of Physics and Astronomy, Laser Centre, Vrije Universiteit,
De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
Motivation




The hydrogen molecule is an important system for testing
molecular quantum mechanics.
The ionization energy (E i) and dissociation energy (D0) of H2 are
benchmark quantities for ab initio calculations.
The precision of both the experimental and theoretical values for
E i(H2) and D0(H2) has been improved by more than an order of
magnitude over the past three decades and the latest ones are:

Experimental: E i(H2)exp=124417.476(12) cm−1 [2]

Theoretical:
E i(H2)cal =124417.491 cm−1
[4]
D0(H2)exp=36 118.062(10) cm−1 [3]
D0(H2)cal =36 118.069 cm−1
New experimental determination of E i(H2) and/or D0(H2) with
improved precision would represent a more stringent test for
future theoretical calculations.
[2] A. de Lange, E. Reinhold, and W. Ubachs, Phys. Rev. A 65, 064501 (2002).
[3] Y. P. Zhang, C. H. Cheng, J. T. Kim, J. Stanojevic, and E. E. Eyler, Phys. Rev. Lett. 92, 203003 (2004).
[4] L. Wolniewicz, J. Chem. Phys. 103, 1792 (1995).
[4]
Energy level diagram
X  2g (   0, N   1,center)
Ei (ortho-H 2 )
Ei (H 2 )  Ei (para-H 2 )
binding
energy
(7)
(6)
X  2g (   0, N   0)
(5)
nlN N
54 p11 ( S  0), F  0  2
51d 11 (G   1/ 2), F  0
(4)
(3)
X  2g (   0, N   1, G   1/ 2), F   1/ 2
N
2
EF 1g (  0)
1
0
397 nm
202 nm
(2)
2
X  (  0)
1

g
1
Ei (ortho-H 2 )  (2)  (3)  (4)  (5)  (6)
0
Ei (H 2 )  Ei (para-H 2 )  (1)  Ei (ortho-H 2 )  (7)
(1)
Experimental setup
54 p
EF 1g
X 1g
202 nm   0.4 cm-1
397 nm   20 MHz
Beam 1
Beam 2
Absolute frequency calibration
Frequency comb at VU
NIR Doppler-free saturation
absorption spectroscopy of I2
at VU & ETH
Relative frequency calibration
He-Ne stabilized etalon
Coherent 899-29 Ti:Sa Ring Laser
PD1
PD2
Lock-in / Piezo Driver/
Oscillator / RF Rriver
Polarization
Stabilized He-Ne
AOM
PZT Confocal Fabry-Perot Cavity
Photoionization spectra of H2
nlN N ( S )
54 p11 (0)
54 p12 (0)
Sample spectrum with calibration
Measurement of Doppler shift
Beam 1
Beam 2
52 MHz
12604.96
12604.97
12604.98
fundamental 54p
12604.99
12605.00
12605.01
-1
EF laser wavenumber (cm )
12605.02
Statistics
beam1
beam2
(beam1+beam2)/2
fundamental 54p
-1
EF laser wavenumber (cm )
12605.0000
mean value
12604.9995
12604.9990
12604.99879(10) cm−1
12604.9985
12604.9980
12604.9975
0
2
4
6
8
10
12
# measurement
14
16
18
Corrections and error budget
54 p11 ( S  0, center)  EF 1 g (  0, N  1)
= 25209.99756  (0.00022)statistical  (0.00007)systematic cm-1
= 25209.99756(29) cm-1
Determination of E i(H2)
[5] S. Hannemann, E. J. Salumbides, S. Witte, R. T. Zinkstok, E. J. van Duijn, K. S. E. Eikema, and W. Ubachs, Phys. Rev. A 74,
062514 (2006).
[6] A. Osterwalder, A. W¨uest, F. Merkt, and Ch. Jungen, J. Chem. Phys. 121, 11810 (2004).
[8] D. E. Jennings, S. L. Bragg, and J.W. Brault, Astrophys. J. 282, L85 (1984).
[9] V. I. Korobov, Physical Review A 73, 024502 (2006).
[10] V. I. Korobov, Physical Review A 74, 052506 (2006).
[11] V. I. Korobov, Physical Review A 77, 022509 (2008).
[25] J.-P. Karr, F. Bielsa, A. Douillet, J. P. Gutierrez, V. I. Korobov, and L. Hilico, Phys. Rev. A 77, 063410 (2008).
History of determination of E i(H2)
0.54
1.8
theoretical
experimental
0.53
0.52
-1
Ei(H2)-124417 (cm )
1.6
1.4
1.2
0.51
this work
0.50
0.49
-1
Ei(H2)-124417 (cm )
0.48
0.47
1.0
0.46
1988
1992
0.8
1996
2000
2004
year
0.6
0.4
0.2
0.0
-0.2
[4] L. Wolniewicz, J. Chem. Phys. 103, 1792 (1995).
[24] G. Herzberg and Ch. Jungen, J. Mol. Spectrosc. 41, 425 1972.
[33] G. Herzberg, Phys. Rev. Lett. 23, 1081 (1969).
1970
1980
1990
year
2000
2010
2008
Dissociation energy of H2
D0 (H 2 )=Ei (H 2 )+D0 (H 2+ )-Ei (H)
=Ei (H 2 )+[Ei (H 2+ )-Ei (H)]-Ei (H)
=Ei (H 2 )+Ei (H 2+ )-2Ei (H)
Dissociation energy of H2


The latest experimental and theoretical values for
D0(H2) are:

Experimental: D0(H2)exp=36118.062(10) cm−1 [3]

Theoretical:
D0(H2)cal =36118.069 cm−1
[4]
New determination of D0(H2)
E i(H2)exp =124417.49111(43) cm-1
E i(H2+)cal=131058.1219761(10) cm-1
E i(H)cal =109678.7717414(18) cm-1
D0(H2) =E i(H2)+E i(H2+)-2E i(H)
[9-11]
= 36118.06962(37) cm-1
[3] Y. P. Zhang, C. H. Cheng, J. T. Kim, J. Stanojevic, and E. E. Eyler, Phys. Rev. Lett. 92, 203003 (2004).
[4] L. Wolniewicz, J. Chem. Phys. 103, 1792 (1995).
[9] V.I. Korobov, Phys. Rev. A 73, 024502 (2006).
[10] V.I. Korobov, Phys. Rev. A 74, 052506 (2006).
[11] V.I. Korobov, Phys. Rev. A 77, 022509 (2008).
Conclusions and future work
1 
 54 p11 ( S  0, center)  EF  g (  0, N  1)
= 25209.99756  (0.00022)statistical  (0.00007)systematic cm -1
-1
 Ei (ortho-H 2 )=124357.23797(36) cm
Ei (H 2 )  Ei (para-H 2 )=124417.49113(37) cm-1
v.s. 124417.491 cm-1 from ab initio calculations.
 D0 (H 2 )  36118.06962(37) cm-1
v.s. 36118.069 cm-1 from ab initio calculations.
Published in:
J. Chem. Phys. 130(17), 174306 (2009)

D2 and HD
Acknowledgments

Merkt Group
(ETH Zurich)

Ubachs Group
(VU Amsterdam)
Merkt Group
$ Swiss National Science Foundation $
Edcel J. Salumbides

Dr. H. Knöckel
(Hannover)
$ ERC Single Investigator Award $