DETERMINATION DETERMINATION

OF THE IONIZATION AND DISSOCIATION ENERGIES OF THE IONIZATION AND DISSOCIATION ENERGIES

OF THE HYDROGEN MOLECULEOF THE HYDROGEN MOLECULEJinjun 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, Switzerland2 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] D0(H2)exp=36 118.062(10) cm−1 [3] Theoretical: E i(H2)cal =124417.491 cm−1 [4] D0(H2)cal =36 118.069 cm−1 [4]

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).

Energy level diagram

1 ( 0)gX

1 ( 0)gEF 2

2 ( 0, 1, 1/ 2), 1/ 2gX N G F

NnlN

N

2 ( 0, 1,center)gX N

2 ( 0, 0)gX N

(7)

(1)

(2)

(3)(4)

(5)

(6)

154 1 ( 0), 0 2p S F

151 1 ( 1/ 2), 0d G F

1

0

2

1

0

397 nm202 nm

i2

(ort

ho-H

)E

i2

i2

(H)

(par

a-H

)E

E

i 2

i 2 i 2 i 2

(ortho-H ) (2) (3) (4) (5) (6)

(H ) (para-H ) (1) (ortho-H ) (7)

E

E E E

bin

din

gen

erg

y

Experimental setup

54p

202 nm 397 nm

1 gX

1 gEF

Beam 1 Beam 2

20 MHz

-10.4 cm

Absolute frequency calibration

NIR Doppler-free saturation absorption spectroscopy of I2

at VU & ETH

Frequency comb at VU

Coherent 899-29 Ti:Sa Ring Laser

PD1

PD2

Lock-in / Piezo Driver/Oscillator / RF Rriver

PolarizationStabilized He-Ne

AOM

PZTConfocal Fabry-Perot Cavity

Relative frequency calibrationHe-Ne stabilized etalon

Photoionization spectra of H2

N ( )nlN S

154 1 (0)p

254 1 (0)p

Sample spectrum with calibration

Measurement of Doppler shift

12604.96 12604.97 12604.98 12604.99 12605.00 12605.01 12605.02

fundamental 54p EF laser wavenumber (cm-1)

52 MHz

Beam 1 Beam 2

Statistics

0 2 4 6 8 10 12 14 16 1812604.9975

12604.9980

12604.9985

12604.9990

12604.9995

12605.0000

fun

da

me

nta

l 54p

EF

lase

r w

ave

nu

mb

er

(cm

-1)

# measurement

beam1

beam2

(beam1

+beam2

)/2

mean value

12604.99879(10) cm−1

Corrections and error budget

11

-1statistical systematic

-1

54 1 ( 0, center) ( 0, 1)

= 25209.99756 (0.00022) (0.00007) cm

= 25209.99756(29) cm

gp S EF N

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)

[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 2000 2010

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

1988 1992 1996 2000 2004 20080.46

0.47

0.48

0.49

0.50

0.51

0.52

0.53

0.54

Ei(H

2)-

12

44

17

(cm

-1)

year

theoretical experimental

Ei(H

2)-

1244

17 (

cm-1)

year

this work

Dissociation energy of H2

+0 2 i 2 0 2 i

+i 2 i 2 i i

+i 2 i 2 i

D (H )= (H )+D (H )- (H)

= (H )+[ (H )- (H)]- (H)

= (H )+ (H )-2 (H)

E E

E E E E

E E E

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 [9-11]

E i(H)cal =109678.7717414(18) cm-1

D0(H2) =E i(H2)+E i(H2+)-2E i(H)

= 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

Published in: J. Chem. Phys. 130(17), 174306 (2009)

-10 2

-1

(H ) 36118.06962(37) cm

v.s. 36118.069 cm from calculations.

D

ab initio

11

-1statistical systematic

54 1 ( 0, center) ( 0, 1)

= 25209.99756 (0.00022) (0.00007) cm

gp S EF N

-1i 2

-1i 2 i 2

-1

(ortho-H )=124357.23797(36) cm

(H ) (para-H )=124417.49113(37) cm

v.s. 124417.491 cm from calculations.

E

E E

ab initio

D2 and HD

Acknowledgments Merkt Group (ETH Zurich) Ubachs Group (VU Amsterdam)

Dr. H. Knöckel (Hannover)

Edcel J. Salumbides

Merkt Group

$ Swiss National Science Foundation $

$ ERC Single Investigator Award $