The microwave spectrum of the 1,2-difluorobenzene dimer

Chemical Physics 283 (2002) 289–296 www.elsevier.com/locate/chemphys

The microwave spectrum of the 1,2-difluorobenzene dimer T. Goly, U. Spoerel, W. Stahl * Institut f€ ur Physikalische Chemie, Rheinisch-Westf€alische Technische Hochschule Aachen, Templergraben 59, D-52056 Aachen, Germany Received 2 February 2002

Abstract Using a pulsed molecular beam FT microwave spectrometer the pure rotational spectrum of the 1,2-difluorobenzene dimer has been recorded in the frequency range from 3 to 26.5 GHz. Only c-type transitions were found. Each line is split into two tunneling components separated by 110 kHz. The center frequencies were fitted to yield the rotational constants A ¼ 671:874764(55) MHz, B ¼ 498:955865(79) MHz, and C ¼ 456:933056(98) MHz. Moreover, all quartic and some sextic centrifugal distortion constants (Watson’s S reduction) were determined. In the complex the ring planes  between them. Both rings are rotated by an angle of 130.3° against are assumed to be parallel with a distance of 3.45 A each other. Ó 2002 Elsevier Science B.V. All rights reserved.

1. Introduction While searching for the 1,2-difluorobenzene (oDFB) argon complex [1] in 1992 some 10 doublets split by 110 kHz were found which could neither be assigned to the o-DFB monomer nor to its argon complex. One year later we were looking for lines of the o-DFB neon complex. For this purpose neon was used as carrier gas and again 110 kHz doublets were found. Some of them turned out to be identical with those observe earlier with argon. Finally we found that they could also be observed in helium as well with the best signal-to-noise ratio. However, they clearly required the presence of o-DFB and first ideas evolved that the doublets might be attributed to the o-DFB dimer. In total,

*

Corresponding author. Tel.: +49-241-80-94724; fax: +49241-80-92365. E-mail address: [email protected] (W. Stahl).

some 180 doublet, all split by 105–115 kHz, could be recorded. These lines, not assigned at that time, formed regular series with a difference of 1343 MHz between the lines. Double resonance experiments showed that two subsequent lines within these series had one energy level in common, whereas between two different series no common levels were found. Attempts to assign the spectrum failed since we still had some wrong ideas about the geometry of the dimer and we therefore did not realize that there is only one dipole component in c-direction. The situation changed in 1998 when we made some ab initio calculations in order to estimate which structure could be the most stable one. It turned out that also configurations with parallel ring planes and the monomers rotated against each other had to be taken into account. For symmetry reasons in such a dimer geometry, depending on the rotational angle, only one dipole component either along the inertial c-axis or the baxis exists. This information enabled us to finally

0301-0104/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 0 1 0 4 ( 0 2 ) 0 0 5 0 0 - 1

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Table 1 Measured lines of the o-DFB dimer. Observed frequency mo ; calculated frequency mc , tunneling splitting Dmtun Upper state

Lower state

J

Ka

Kc

J

Ka

Kc

3 4 5 6 6 7 7 8 8 9 9 10 10 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 4 4 5 6 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16

3 4 5 6 6 7 7 8 8 9 9 10 10 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 3 3 4 5 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15

1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 2 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2

2 3 4 5 5 6 6 7 7 8 8 9 9 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 3 3 4 5 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15

2 3 4 5 5 6 6 7 7 8 8 9 9 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 2 2 3 4 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14

1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 2 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2

mo (MHz)

mo –mc (kHz)

Dmtun (kHz)

3841.1983 5181.6776 6525.7383 7869.3706 7869.3706 9212.9984 9212.9984 10556.5911 10556.5911 11900.1512 11900.1512 13243.6782 13243.6782 15930.6268 15930.6268 17274.0454 17274.0454 18617.4251 18617.4251 19960.7634 19960.7634 21304.0635 21304.0635 22647.3120 22647.3120 23990.5196 23990.5196 25333.6797 25333.6797 4780.6633 4808.6565 6141.2434 7482.8491 8826.7487 10170.2153 10170.2153 11513.6055 11513.6055 12856.9137 12856.9137 14200.1468 14200.1468 15543.3072 15543.3072 16886.3962 16886.3962 18229.4125 18229.4125 19572.3563 19572.3563 20915.2283 20915.2283

)0.1 0.1 0.1 )0.4 )4.5 0.1 )0.2 0.0 0.0 )0.1 )0.1 )0.0 )0.0 )0.2 )0.2 )0.3 )0.3 )0.2 )0.2 )0.7 )0.7 3.0 3.0 )0.9 )0.9 )0.2 )0.2 0.1 0.1 )0.1 )0.1 0.2 0.5 0.7 2.0 )1.9 0.2 )0.1 0.1 0.0 0.1 0.1 )0.1 )0.1 0.2 0.2 )0.3 )0.3 )0.7 )0.7 0.5 0.5

110.2 110.0 110.3 109.3 109.3 108.7 108.7 109.8 109.8 109.5 109.5 108.6 108.6 107.2 107.2 107.8 107.8 107.4 107.4 106.2 106.2 107.5 107.5 101.7 101.7 106.0 106.0 105.0 105.0 113.5 112.9 110.2 109.5 109.4 109.2 109.2 109.0 109.0 108.3 108.3 109.4 109.4 109.3 109.3 107.9 107.9 107.8 107.8 105.4 105.4 109.9 109.9

T. Goly et al. / Chemical Physics 283 (2002) 289–296

291

Table 1 (continued) Upper state

Lower state

J

Ka

Kc

J

Ka

Kc

18 18 19 19 5 5 6 6 7 8 8 9 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 5 8 9 10 10 11 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 7

17 17 18 18 3 3 4 4 5 6 6 7 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 2 5 6 7 7 8 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 3

1 2 1 2 2 3 2 3 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 4 4 3 3 4 3 3 3 4 3 4 3 4 3 4 3 4 3 4 3 4 4

17 17 18 18 4 4 5 5 6 7 7 8 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 4 7 8 9 9 10 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 6

16 16 17 17 2 2 3 3 4 5 5 6 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 1 4 5 6 6 7 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 2

1 2 1 2 2 3 2 3 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 4 4 3 3 4 3 3 3 4 3 4 3 4 3 4 3 4 3 4 3 4 4

mo (MHz)

mo –mc (kHz)

Dmtun (kHz)

23600.7441 23600.7441 24943.3883 24943.3883 5713.1685 5786.5945 7086.3093 7102.2793 8440.5881 9783.3112 9783.5729 11126.9560 12470.2473 13813.3530 13813.3530 15156.3203 15156.3203 16499.1632 16499.1632 17841.8908 17841.8908 19184.5061 19184.5061 20527.0115 20527.0115 21869.4091 21869.4091 23211.6999 23211.6999 24553.8734 24553.8734 5566.3531 9397.8745 10738.4888 12082.8890 12083.0171 13426.3026 14769.3124 16112.0771 16112.0771 17454.6421 17454.6421 18797.0314 18797.0314 20139.2600 20139.2600 21481.3331 21481.3331 22823.2577 22823.2577 24165.0390 24165.0390 7567.2049

)0.9 )0.9 )0.8 )0.8 )4.0 0.0 0.1 0.2 0.6 0.5 0.0 0.3 )0.8 0.1 )0.1 0.3 0.2 )0.2 )0.2 )0.0 )0.0 )0.2 )0.2 )0.4 )0.4 0.5 0.5 3.2 3.2 )2.6 )2.6 0.5 0.3 0.1 0.3 0.1 6.5 0.4 )0.1 )0.2 )0.4 )0.4 )0.7 )0.7 0.3 0.3 )0.0 )0.0 0.7 0.7 4.6 4.6 )0.3

109.2 109.2 108.2 108.2 119.9 110.1 109.7 109.3 110.2 109.9 109.9 109.5 109.8 109.2 109.2 108.0 108.0 108.0 108.0 107.3 107.3 110.0 110.0 108.0 108.0 107.2 107.2 109.3 109.3 107.0 107.0 112.0 110.5 109.9 109.4 109.0 109.8 109.7 108.3 108.3 108.7 108.7 108.7 108.7 111.3 111.3 108.4 108.4 112.3 112.3 116.3 116.3 109.9

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Table 1 (continued) Upper state

Lower state

J

Ka

Kc

J

Ka

Kc

9 9 10 11 11 13 13 14 14 15 15 17 17 18 18 19 19 7 9 9 10 10 11 12 17 17 18 18 19 19 20 20 7 9 10 10 11 11 12 14 16 17 17 18 18 19 19 20 20 21 21 9 9

5 5 6 7 7 9 9 10 10 11 11 13 13 14 14 15 15 2 4 4 5 5 6 7 12 12 13 13 14 14 15 15 1 3 4 4 5 5 6 8 10 11 11 12 12 13 13 14 14 15 15 2 2

4 5 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 5 5 6 5 6 5 5 5 6 5 6 5 6 5 6 6 6 6 7 6 7 6 6 7 6 7 6 7 6 7 6 7 6 7 7 8

8 8 9 10 10 12 12 13 13 14 14 16 16 17 17 18 18 6 8 8 9 9 10 11 16 16 17 17 18 18 19 19 6 8 9 9 10 10 11 13 15 16 16 17 17 18 18 19 19 20 20 8 8

4 4 5 6 6 8 8 9 9 10 10 12 12 13 13 14 14 1 3 3 4 4 5 6 11 11 12 12 13 13 14 14 0 2 3 3 4 4 5 7 9 10 10 11 11 12 12 13 13 14 14 1 1

4 5 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 5 5 6 5 6 5 5 5 6 5 6 5 6 5 6 6 6 6 7 6 7 6 6 7 6 7 6 7 6 7 6 7 6 7 7 8

mo (MHz)

mo –mc (kHz)

Dmtun (kHz)

10334.2207 10356.3150 11694.6952 13037.5342 13038.0298 15724.6037 15724.6037 17067.2761 17067.2761 18409.6337 18409.6337 21093.5980 21093.5980 22435.2549 22435.2549 23776.7158 23776.7158 7387.5403 9858.0758 10026.4904 11266.2967 11318.0491 12638.8952 13990.1580 20705.8842 20705.8842 22047.4366 22047.4366 23388.7130 23388.7130 24729.7313 24729.7313 7561.7826 9501.6512 10768.4569 11026.3944 12181.9050 12286.1545 13578.7657 16287.7354 18975.3278 20317.6250 20317.6250 21659.3765 21659.3765 23000.6880 23000.6880 24341.6283 24341.6283 25682.2321 25682.2321 9575.9941 9862.6145

0.2 )0.2 )0.1 0.8 0.4 0.8 )5.5 )0.8 )1.4 0.3 0.3 )0.4 )0.4 )2.3 )2.3 )2.5 )2.5 )0.8 0.8 )0.3 )0.1 )0.2 )0.5 )0.7 1.5 1.5 )1.8 )1.9 )0.8 )0.8 )0.9 )0.9 )0.3 0.2 )0.1 )0.3 )0.3 )0.5 )0.3 )0.3 )2.7 0.1 )1.2 0.9 0.8 1.2 1.2 3.1 3.1 )0.4 )0.4 )0.6 )0.6

109.8 109.9 110.3 110.4 110.1 116.8 116.8 109.3 109.3 108.1 108.1 106.4 106.4 108.2 108.2 112.6 112.6 110.6 110.8 110.3 110.1 110.4 110.4 110.9 108.2 108.2 106.9 106.9 107.5 107.5 111.3 111.3 111.1 110.6 110.9 110.8 111.4 111.4 111.1 110.2 109.5 108.2 108.2 114.8 114.8 108.5 108.5 106.1 106.1 107.0 107.0 111.1 113.1

T. Goly et al. / Chemical Physics 283 (2002) 289–296

293

Table 1 (continued) Upper state

Lower state

J

Ka

Kc

J

Ka

Kc

10 10 11 11 12 14 14 15 17 19 19 9 10 10 11 12 12 13 14 15 16 17 19 20 20 10 11 13 13 15 15 16 11 12 13 15 13 16 15 15 11 6 8 8 11 13 16

3 3 4 4 5 7 7 8 3 12 12 1 2 2 3 4 4 5 6 7 8 9 11 12 12 1 2 4 4 6 6 7 1 2 3 5 2 5 3 2 4 2 1 2 4 3 4

7 8 7 8 8 7 8 8 15 7 8 8 8 9 8 8 9 9 8 9 9 8 9 8 9 9 10 9 10 9 10 10 10 10 11 10 11 11 13 13 7 4 7 6 7 10 12

9 9 10 10 11 13 13 14 16 18 18 8 9 9 10 11 11 12 13 14 15 16 18 19 19 9 10 12 12 14 14 15 10 11 12 14 12 15 14 14 10 5 7 7 10 12 15

2 2 3 3 4 6 6 7 2 11 11 0 1 1 2 3 3 4 5 6 7 8 10 11 11 0 1 3 3 5 5 6 0 1 2 4 1 4 2 1 5 3 2 3 5 4 5

7 8 7 8 8 7 8 8 15 7 8 8 8 9 8 8 9 9 8 9 9 8 9 8 9 9 10 9 10 9 10 10 10 10 11 10 11 11 13 13 5 2 5 4 5 8 10

mo (MHz)

mo –mc (kHz)

Dmtun (kHz)

10524.6358 10917.9509 11696.0814 12043.3964 13264.2532 15883.8525 15895.5277 17239.5700 18582.3443 22612.0807 22612.0807 9816.3851 10711.1520 10959.3081 11590.5533 12656.4004 13078.4587 14255.8966 15416.0842 16846.7000 18189.0255 19533.6355 22221.8982 23563.8521 23563.8521 10934.2050 12059.5560 13659.2770 14131.1035 16307.7133 16495.0757 17799.4060 12046.5257 12993.3150 14173.1455 15816.5653 14123.4618 16796.0827 16374.5478 16360.0175 9107.9160 5004.0165 6953.6886 7051.5639 9107.9160 11656.2058 14400.3952

)0.1 )0.5 )0.0 )0.6 )0.6 )0.4 1.3 )0.6 )0.2 0.8 0.3 1.7 )0.2 )0.3 )0.1 0.1 )0.2 )0.1 )0.1 )1.0 0.3 2.4 )5.0 2.2 0.3 0.2 )1.1 )0.0 0.7 1.6 0.9 1.8 1.3 0.2 0.3 0.1 0.0 )0.1 0.1 0.2 0.1 )0.2 0.6 1.1 0.1 )1.0 )0.5

110.4 111.1 111.0 111.4 111.0 110.1 109.4 107.8 107.2 109.9 109.9 111.5 110.6 112.3 110.5 111.3 112.1 112.1 110.1 108.7 107.2 110.3 106.1 105.7 105.7 111.9 112.8 111.6 114.1 112.2 109.9 108.8 112.0 113.9 113.0 113.4 115.1 112.9 113.4 115.5 110.7 111.3 113.7 110.4 110.7 111.4 112.0

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assign all measured lines using the simple model of a rigid rotor including centrifugal distortion terms.

2. Experimental All experiments were carried out using a pulsed molecular beam FT microwave spectrometer as described in detail in [2]. The molecular beam was produced from a mixture of 1% o-DFB (Aldrich, Germany) in helium at a backing pressure of 200 kPa. All lines were split into Doppler doublets [3] with a separation of approximately 53 kHz at 10 GHz, i.e., the torsional doublets with a splitting of 110 kHz appeared as quartets in the spectrum. Double resonance experiments were carried out using the techniques described in [4].

Table 2 Rotational and centrifugal distortion constants of the o-DFB dimer A B C DJ DJK DK d1 d2 HJ HJJK HJKK HK h1 h2 h3

671.874764(55) MHz 498.955865(79) MHz 456.933056(98) MHz 0.23759(55) kHz 2.28546(140) kHz )2.44494(91) kHz )0.001701(250) kHz 0.026673(50) kHz )0.01105(150) Hz )0.0417(52) Hz 0.2037(66) Hz )0.14970(294) Hz 6.51(118) Hz 0.0(fixed) Hz 0.0(fixed) Hz

rms

1.23 kHz

Watson’s S reduction [5] and Ir representation used.

3. Analysis In a first step the torsional splitting were averaged to obtain hypothetical line centers. As described in the introduction, a number of lines were found which could be arranged within different series. Using the hypothesis that only a lc dipole component exists, these series had to be of the general types J þ 1J nþ1;n JJ n;n and J þ 1J nþ1;nþ1 JJ n;nþ1 with n ¼ 0; 1; 2; . . . At higher J values, where corresponding members of both types form unresolved K doublets, the separation between two lines is almost constant at 1343 MHz. These lines were easily identified. After a first fit, based on a rigid rotor Hamiltonian, the whole spectrum could be predicted sufficiently accurate to allow the assignment of all other transitions observed (Table 1). For a final fit, quartic and sextic centrifugal distortion terms had to be included in the Hamiltonian. We decided to use Watson’s S reduction [5] and the Ir representation as implemented in Pickett’s program SPFIT [6]. All measured lines, including some DKc ¼ 2 transitions, were included in the final fit yielding the rotational and centrifugal distortion constants given in Table 2. It should be mentioned that even after carefully searching for a- and b-type transitions, none of them could be found. Even if this does not rigor-

ously exclude the existence of la and lb dipole components, it indicates that they must be very much smaller than the lc component.

4. Discussion We will now combine our experimental findings to get some information on the structure and the dynamics of the o-DFB dimer. To describe the relative orientation of the monomers to each other, six parameters are needed. These may considered as the three spatial components of the distance vector between the centers of mass of the monomers and three Euler angles for the rotation of one monomer with respect to the other one. Since we only have three pieces of information, i.e., the three rotational constants of the dimer, additional assumptions are necessary. From all possible geometries consistent with the rotational constants of the dimer, only those are relevant, which have only one (very strong) dipole component which points along the inertial c-axis of the dimer. This condition can be fulfilled, if the ring planes of both monomers are arranged parallel to each other. If we assume a  [7], a half-thickness of a benzene ring as 1.70 A . distance between the two rings would be 3.40 A For the sake of simplicity, we assume the centers

T. Goly et al. / Chemical Physics 283 (2002) 289–296

295

Fig. 1. Geometry of the o-DFB dimer. 1a and 1c show a proposed structure of one enantiomer, in a perspective view (a) and a projection on the bc-plane (c), respectively. Angle u is the rotation of one monomer unit around the monomer c-axis. 1b and 1d show the other enantiomer.

of mass of the monomers to be on top of each other, so that the monomer c-axis form the dimer a-axis. Independent of the dihedral angle 2u between the monomer a axes, the inertial moment IaC of the complex should be twice the inertial mo-

find ment IcM of 2 the monomer [8]. We  and 2 I M ¼ 763:49 uA 2 . This IaC ¼ 752:19 uA c corresponds to a deviation of only 1.5% with respect to IaC , which appears good enough for our purposes. After IaC has been used, two further

Table 3 Structural data and dipole moments of the o-DFB monomer and dimer Monomer [8]a A MHz B MHz C MHz 2 Ia u A 2 Ib uA 2 Ic uA  dA u Deg la D lb D lc D a

b b b

c c c

3263.527(3) 2227.885(2) 1323.856(2) 154.857 226.843 381.748 – – 2.59 (20) [9] 0.0 0.0

Mass of monomer mM ¼ 114:028 u. 2 . Conversion factor ¼ 505379:076 MHz uA c 1 D ¼ 3:33564  1030 Cm. d Excluded due to the observation of a pure c-type spectrum. b

Dimer 671.874764(55) 498.955865(79) 456.933056(98) 752.192 1012.873 1106.024 3.448 24.842d 0.0 4.72d 0.0

65.158 0.0 0.0 2.18

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pieces of information, IbC and IcC are still available. We will use them to determine the distance d between the ring planes and the dihedral angle 2u. Some simple manipulations lead us to the equations rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi IcC  IbC  2ðIbM þ IaM Þ d¼ ; mM   1 IcC  IbC u ¼ arccos ; 2 2ðIbM  IaM Þ with the mass mM and the moments of inertia IaM and IbM of the monomer. For the distance between . The soluthe ring planes we obtain d ¼ 3:448 A tion of u is not unique and two different angles, u1 ¼ 24:842° and u2 ¼ 65:158° are found. With u1 ¼ 24:842° (corresponding to a dihedral angle of 49.684°) the dimer would have only a strong dipole component along the dimer b-axis which disagrees with the experimental fact that a pure c-type spectrum was observed. In the other case with u2 ¼ 65:158° (dihedral angle 130.316°) vector addition of the monomer dipole moments lM a ¼ 2:59ð2Þ D [9] yields a total dipole moment of 2.18 D in c-direction, which is consistent with the spectrum. Therefore we assume that this geometry, which is shown in Fig. 1, is close to the true structure of the o-DFB dimer. It should be noted, that this structure is chiral and a tunneling between both enantiomers could explain the splitting of 110 kHz observed at all lines. However, since

there is not enough information on the tunneling path, no attempt was made to determine the torsional barrier. The assumptions and results of the structure considerations are compiled in Table 3.

Acknowledgements We thank the microwave group at the University of Kiel for many fruitful discussion. Funds from the Deutsche Forschungsgemeinschaft, the Fonds der Chemischen Industrie, and the Land Nordrhein-Westfalen a gratefully acknowledged.

References [1] E. Jochims, J.-U. Grabow, W. Stahl, J. Mol. Spectrosc. 158 (1992) 278. [2] U. Andresen, H. Dreizler, J.-U. Grabow, W. Stahl, Rev. Sci. Instrum. 61 (1990) 3694. [3] J.-U. Grabow, W. Stahl, Z. Naturforsch. 45a (1990) 1043. [4] U. W€ otzel, W. Stahl, H. M€ader, Can. J. Phys. 75 (1997) 821. [5] J.K.G. Watson, in: J.R. Durig (Ed.), Vibrational Spectra and Structure, vol. 6, Elsevier, Amsterdam, 1977, p. 1. [6] H.M. Pickett, J. Mol. Spectrosc. 148 (1991) 371. [7] W. Gordy, R.L. Cook, Microwave Molecular Spectra, Wiley, New York, 1984. [8] O.L. Stiefvater, Z. Naturforsch. 43a (1988) 147. [9] L. Nygaard, E.R. Hansen, R.L. Hansen, J. RastrupAndersen, G.O. Sørensen, Spectrochim. Acta 23A (1967) 2813.