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A reinvestigation of the hyperfine structure in fluoroform
CHEMICAL
Vdume26,number4
A REINVESTIGATION
PHYSICS
LETTERS
OF THE HYPERFINE
J.M.H. REIJNDERS, Fwisch Laboratorium.
15June1974
STRUCTURE
A.W. ELLENBROEK
IN FLUOROFORM
and A. DYMANUS
Katholieke Uttiwrsiteit. Nijrrtegen. The Netherhds
Received 16 April 1974
The hyperfine structure of theJ = 1 - 0 rotational transition of the CFsH and CFsD molecules hzas been reinvestigated with a high resolution beam maser spectrometer equipped with a nozzle source. Considerable gain in SIN ratio compared with previous measurements performed with a normal effuser source is obtained. The experimental results eliminate discrepancies between the results of previous investigations.
1. Introduction
of Kukolich et al. [2] on CF,D were not used for this check because some weak lines were not observed
Hyperfine structure of the J= 1 + 0 rotational transition of CF,H was studied by Kukolich et al. [ 1,2] and by Reijnders et al. [3]. Poor signal to noise (S/N) ratio of the CF3H spectrum combined with a low confidence level in the least squares analysis led to contradictory and confusing results both for the interaction constants and for the assignment of the spectra. The rather low confidence level (*O%) for the least squares analysis of the CF,H spectrum, where the number of hyperfine lines approaches the number of coupling constants to be varied in the fit, is illustrated by the three “good” fits [l-3]. Our first measurements [3] were performed with an ordinary
in their measurements. Their analysis was consequently subject to a low confidence level, which may explain the two different “good” fits which Kukolich et al. [ 1, 21 obtained for essentially the same spectrum.
effuser source with signal averaging in a computer average transients (CAT, Technical Measurements
2. The measurements
The spectrometer is a single cavity molecular beam maser similar to that of Verhoeven and Dymanus [S] except for the source and the vacuum system. The vacuum chamber consists of three independently pumped units: a nozzle exhaust chamber, a buffer chamber and a detector chamber containing the state selector and a reflection-type cylindrical TMoIo cavity. A single hole nozzle with a diameter of 48fi driven by pressures in the range of 300 to 1000 torr is used. The position of the nozzle is adjustable in three perpendicular directions. A skimmer with a diameter of 1 mm and a full inner angle of 75” separates the nozzle exhaust chamber from the buffer chamber. The molecular beam enters the detector chamber through a diaphragm with an opening of IO mm (equal to the diameter of the state selector)_ Witn this set-up a gain in S/N ratio of about 20 compared with a normal effuser source has been obtained. for the-fluoroform spectrum (ref. [3] ; this work, fig. I). This gain comes from ‘, (i) h&her beam intensity and-@) enhancement of the
of
Corporation [4])_ This method implied very long integration times (2-5 hours). Recently a significant (about 20X) improvement in the S/N ratio has been obtained with a powerful nozzle source, which makes the sampling with the CAT unnecessary_ The results obtained with this source agree with the new results of Kukolich et al. [2], which they obtained after a remeasurement of the CF,H spectrum and a correction of the sign of the spin-spin interaction in some off-diagonal matrix elements. As the confidence level -for the derived.coupling constants for CF3H is rather Idti also the J= 1 + 0 rotational trarsition of CFjD has been measured.in brder to have a check. The results
:.
,- _.47(l
:.-.
._:‘:
..
-..
._::
.‘.
c . .
:
_
__
:.
.:.
.::
-. TV_‘. --
::-
.. .
j . ...:
‘: _J .:
y
_. ,
.:
.,
::
..
.,
..
_,
._.
__
Volume 26, number 4
CHEMICAL PHYSICS LETTERS
15 June 1974
a):
T I -10
I
1
-20
-30
"0
, 10
-10
20
30 kHz
*y-J/u;\ vo
43
-90
-m
-60
-5~
-40
-30
-20
-10
10
m
30
Ln
50
60 t*z
scale in kHz relative to ~0 of the hyperfine structure of theJ = 1 - 0 rotational transition of (3) CF3H. where vo = 20.697 695 WI) GHz and (b) CF3D, where vo = 19.842 212 S(2) GHz. The vertical bars represent the positions and relative intensities for the case of conventional microwave spectroscopy of the spectra c&olated with the best-fit COUpling constants. Fig. 1. Recordings
with frequency
of the lower (rotational) nozzle expansion.
population
states by the
Recorder traces of the J = 1 --z 0 rotational transition of CF,H and CF,D are shown in fig. I_ A slight increase in resonance line width (half width of 2.8 kHz compared with the effuser result of 2.5 kHz) illustrates that the velocity distribution in a nozzle beam is shifted towards higher velocities. The now cleaily observable CFSH hyperfine line at about -34 kHz (relative to vo) was not detected by us with the effuser source in spite of long (300 runs) and careful searching with the CAT [3]. Appaiently low frequenCY noise components which are proportional to VQ with 0
:.
.-
...
:._
‘..- .-_:.
spectrum of CFjD which were not detected by Kukolich et al. [ 1, 21 are now clearly observable.
hyperfine
3. Discussion of the results
As discussed in a previous paper [3] the hyperfine in terms of the spin-rotation coupling constants @J, @ , and the spin-spin c&pLing constants dJFKF’,and d $ f)- For the analysis of the CF3D spectrum the same detinitions for the spin-rotation and ipin-spin coupling constants are used but with H replaced by D. In addition.there is alSo t& quadspole injeraction due to. ‘the deuteron quadrupole rno.&ek in CFi D..The: .. ‘. h<onia&H~ of.t&is interacjion is written as a y’.... ..::;.; 471 ‘. :_ ; ‘1 ,:..: -’ ..,. -. : ; _- .-’ ‘-. ‘..( ,;_ .._.--.. ., : _..._ ., .., .: ,.._ ._.. ., ‘Z.‘. : : .. ,_::... . .... :-..-. ,.., ;. ‘. :. -_.’ .: ..-.-.. .‘.‘:... ;;.’ ; .. :. .‘,., _. . spectrum of CF,H can be interpieted
Volume 26, number 4
CHEMICAL PHYSICS LETTERS
15 June 1974
Table 1 Observed
andcaltu~tedfiequenciesofthe
Calculated
312 312 312 112 112 312
F
reIative intensity
0 1 2 1 2 3
1 3 5 3 5 7f
J= l+
0 transition of CFaH. All values are in kHz relative to V,J= 20.697 695 4(2) GHz
Observed intensity this work
Calculated frequency ref. [2]
this work
ref. [2j
this work
-
-37.93 -33.93 -8.81 4.55 13.30 14.18
-38.2 -33.9 -8.8 5.2 13.8 14.2
-33.87 -8.81 3.67 14.X 14.15
-34.1(2) -8.8(l) 4.3(10) 13.8(5) 13.8(S)
3 6 3 20
Observed frequency
Table 2
Observedand calculated frequencies of the J= 1 -t 0 transition of CFSD. All values are in kHz relative to vo = 19.842 212 S(2) GHz Calculated relative intensity
F
0 2 2 2 2 1 1 1
312 l/2 312 512 712 l/2 312
Observed intensity this work 1.3 0.6 2.5 5.0 9.0
4 : 6 8 2 4 6
512
Calculated frequency
8.0
Observed frequency
ref. [2]
this work
ref. (21
this work
-87.39 -37.90 -27.00 -8.24 4.68 38.67 40.94
-87.1 -38.4 -26.; -8.5 4.7 38.4 40.4
-87.4 -
50.76
50.6
-87.1(11) -38.2(15) -26.4(10) -8.7(g) 4.9(7) 39.8(20) 39.8(20) 5 OA(8)
12.0
-8.2 4.7 39.8 39.8 SO.4
Table 3 Hyperfine coupling constants for theJ = 1 -L 0 rotational transition in fluoroform. CFJH
All values are in kHz
CFJD
ref. [ 1]
ref. [2]
ref. [3]
this work
-
-
_
-
l&2(45) 24.X30) -6.283 7.012
31.2(18) -2.0(15) -6.283
10.6(10) O-0(10) -6.275
31-l(4) -3-O(6) -6.275
7.012
7.009
a) N isH for CFiH and D for CFBD.
7.009
ref. [l]
ref. [2]
this work
-34.16(40) 13.8(30) 3S(lO) -6.283 1.076
-34.18(20) 28.X18) O.O(lO) -6.283 1.076
-34.10(40) 29-O(9) -0.16(40) -6.275 1.076 :
b) Calculated from the known molecular geometry [ 7 1.
product: H, = Q(D)*V(d)
e@g
,
where-d(D) is the quadrupole tensor-of the deuteron and V(D) the gradient tensor of the electric field at. :,.the. positibn.of the deuteronr The coupling constantCD).Ff the quad&pole interaction is-defined as: @%K .:
:, .:.
:. - .I,:..
= -eQ
J(J-i-i j-3ir2 (.r+1)(2&3)
a2Hm ar2_
’
where &$(D)/az2 is the &adient.of the electric field along the molecular symmetry axis z; 4(D) is the : potential due to the surrouriding :eiectrdniti and ylear ,. : . . .. ;_ _, :.‘.. :. .~
Volume 26, number 4
CHEhllCAL PHYSICS LETTERS
1SJunel974
charge distribution at the position of the deuteron, The best-fit coupling consranrs obtained From a
References
Ieast-squares analysis of the observed spectra (tables 1 and 2) are shown in table 3 together with the results of previous investi tions. The ratio of the spin-rotation constants Cf?i7 of CF$ and CF$ agrees within
[ 11 S-G. Kukolich, A.C. Neison and D.J. Ruben, 3, Mol.
the experimental error with the ratio of the rotational constants expressed in the cerrtre frequencies u. of the transitions studied (tables I and 2). The same ap
pIies to the ratio CJ%‘jC>T if also the ratio of the magnetic g-values for the proton and the deuteron is taken into account. FinaiIy there is a good agreement between the present results and the new resuits of the MIT group, which were obtained after a remeasurement of the CF3H spectrum and a reassignment of the CF,D data [2)_
Spectrp. 40 (1971) 33. [2] S.G. Kukolich and D.J.Ruben, J. Mol. Spectry.44 (t972) 607. 13) JXH. Reijnders, A.W. Eltenbruek and A. Dymanus, Cfiem. Phys. Letters 17 (1972) 351. [4f J. Verhoeven, Thesis. Katbolieke Universiteit, N$jme~en, The Netherlands (1969). ISI J. Verhoeven and A. Dymanus. 3. Cbem. Phys. 52 (1970)
3222. f6I V. Radeka, Proceedings ISPRA, Nuclear Electronic SYmnosium 119691. 171 S.N. Gosh, R.Trambarulo 20 0952) 60.5.
and W. Cordy, J. Chem. Phys.
Vdume26,number4
A REINVESTIGATION
PHYSICS
LETTERS
OF THE HYPERFINE
J.M.H. REIJNDERS, Fwisch Laboratorium.
15June1974
STRUCTURE
A.W. ELLENBROEK
IN FLUOROFORM
and A. DYMANUS
Katholieke Uttiwrsiteit. Nijrrtegen. The Netherhds
Received 16 April 1974
The hyperfine structure of theJ = 1 - 0 rotational transition of the CFsH and CFsD molecules hzas been reinvestigated with a high resolution beam maser spectrometer equipped with a nozzle source. Considerable gain in SIN ratio compared with previous measurements performed with a normal effuser source is obtained. The experimental results eliminate discrepancies between the results of previous investigations.
1. Introduction
of Kukolich et al. [2] on CF,D were not used for this check because some weak lines were not observed
Hyperfine structure of the J= 1 + 0 rotational transition of CF,H was studied by Kukolich et al. [ 1,2] and by Reijnders et al. [3]. Poor signal to noise (S/N) ratio of the CF3H spectrum combined with a low confidence level in the least squares analysis led to contradictory and confusing results both for the interaction constants and for the assignment of the spectra. The rather low confidence level (*O%) for the least squares analysis of the CF,H spectrum, where the number of hyperfine lines approaches the number of coupling constants to be varied in the fit, is illustrated by the three “good” fits [l-3]. Our first measurements [3] were performed with an ordinary
in their measurements. Their analysis was consequently subject to a low confidence level, which may explain the two different “good” fits which Kukolich et al. [ 1, 21 obtained for essentially the same spectrum.
effuser source with signal averaging in a computer average transients (CAT, Technical Measurements
2. The measurements
The spectrometer is a single cavity molecular beam maser similar to that of Verhoeven and Dymanus [S] except for the source and the vacuum system. The vacuum chamber consists of three independently pumped units: a nozzle exhaust chamber, a buffer chamber and a detector chamber containing the state selector and a reflection-type cylindrical TMoIo cavity. A single hole nozzle with a diameter of 48fi driven by pressures in the range of 300 to 1000 torr is used. The position of the nozzle is adjustable in three perpendicular directions. A skimmer with a diameter of 1 mm and a full inner angle of 75” separates the nozzle exhaust chamber from the buffer chamber. The molecular beam enters the detector chamber through a diaphragm with an opening of IO mm (equal to the diameter of the state selector)_ Witn this set-up a gain in S/N ratio of about 20 compared with a normal effuser source has been obtained. for the-fluoroform spectrum (ref. [3] ; this work, fig. I). This gain comes from ‘, (i) h&her beam intensity and-@) enhancement of the
of
Corporation [4])_ This method implied very long integration times (2-5 hours). Recently a significant (about 20X) improvement in the S/N ratio has been obtained with a powerful nozzle source, which makes the sampling with the CAT unnecessary_ The results obtained with this source agree with the new results of Kukolich et al. [2], which they obtained after a remeasurement of the CF,H spectrum and a correction of the sign of the spin-spin interaction in some off-diagonal matrix elements. As the confidence level -for the derived.coupling constants for CF3H is rather Idti also the J= 1 + 0 rotational trarsition of CFjD has been measured.in brder to have a check. The results
:.
,- _.47(l
:.-.
._:‘:
..
-..
._::
.‘.
c . .
:
_
__
:.
.:.
.::
-. TV_‘. --
::-
.. .
j . ...:
‘: _J .:
y
_. ,
.:
.,
::
..
.,
..
_,
._.
__
Volume 26, number 4
CHEMICAL PHYSICS LETTERS
15 June 1974
a):
T I -10
I
1
-20
-30
"0
, 10
-10
20
30 kHz
*y-J/u;\ vo
43
-90
-m
-60
-5~
-40
-30
-20
-10
10
m
30
Ln
50
60 t*z
scale in kHz relative to ~0 of the hyperfine structure of theJ = 1 - 0 rotational transition of (3) CF3H. where vo = 20.697 695 WI) GHz and (b) CF3D, where vo = 19.842 212 S(2) GHz. The vertical bars represent the positions and relative intensities for the case of conventional microwave spectroscopy of the spectra c&olated with the best-fit COUpling constants. Fig. 1. Recordings
with frequency
of the lower (rotational) nozzle expansion.
population
states by the
Recorder traces of the J = 1 --z 0 rotational transition of CF,H and CF,D are shown in fig. I_ A slight increase in resonance line width (half width of 2.8 kHz compared with the effuser result of 2.5 kHz) illustrates that the velocity distribution in a nozzle beam is shifted towards higher velocities. The now cleaily observable CFSH hyperfine line at about -34 kHz (relative to vo) was not detected by us with the effuser source in spite of long (300 runs) and careful searching with the CAT [3]. Appaiently low frequenCY noise components which are proportional to VQ with 0
:.
.-
...
:._
‘..- .-_:.
spectrum of CFjD which were not detected by Kukolich et al. [ 1, 21 are now clearly observable.
hyperfine
3. Discussion of the results
As discussed in a previous paper [3] the hyperfine in terms of the spin-rotation coupling constants @J, @ , and the spin-spin c&pLing constants dJFKF’,and d $ f)- For the analysis of the CF3D spectrum the same detinitions for the spin-rotation and ipin-spin coupling constants are used but with H replaced by D. In addition.there is alSo t& quadspole injeraction due to. ‘the deuteron quadrupole rno.&ek in CFi D..The: .. ‘. h<onia&H~ of.t&is interacjion is written as a y’.... ..::;.; 471 ‘. :_ ; ‘1 ,:..: -’ ..,. -. : ; _- .-’ ‘-. ‘..( ,;_ .._.--.. ., : _..._ ., .., .: ,.._ ._.. ., ‘Z.‘. : : .. ,_::... . .... :-..-. ,.., ;. ‘. :. -_.’ .: ..-.-.. .‘.‘:... ;;.’ ; .. :. .‘,., _. . spectrum of CF,H can be interpieted
Volume 26, number 4
CHEMICAL PHYSICS LETTERS
15 June 1974
Table 1 Observed
andcaltu~tedfiequenciesofthe
Calculated
312 312 312 112 112 312
F
reIative intensity
0 1 2 1 2 3
1 3 5 3 5 7f
J= l+
0 transition of CFaH. All values are in kHz relative to V,J= 20.697 695 4(2) GHz
Observed intensity this work
Calculated frequency ref. [2]
this work
ref. [2j
this work
-
-37.93 -33.93 -8.81 4.55 13.30 14.18
-38.2 -33.9 -8.8 5.2 13.8 14.2
-33.87 -8.81 3.67 14.X 14.15
-34.1(2) -8.8(l) 4.3(10) 13.8(5) 13.8(S)
3 6 3 20
Observed frequency
Table 2
Observedand calculated frequencies of the J= 1 -t 0 transition of CFSD. All values are in kHz relative to vo = 19.842 212 S(2) GHz Calculated relative intensity
F
0 2 2 2 2 1 1 1
312 l/2 312 512 712 l/2 312
Observed intensity this work 1.3 0.6 2.5 5.0 9.0
4 : 6 8 2 4 6
512
Calculated frequency
8.0
Observed frequency
ref. [2]
this work
ref. (21
this work
-87.39 -37.90 -27.00 -8.24 4.68 38.67 40.94
-87.1 -38.4 -26.; -8.5 4.7 38.4 40.4
-87.4 -
50.76
50.6
-87.1(11) -38.2(15) -26.4(10) -8.7(g) 4.9(7) 39.8(20) 39.8(20) 5 OA(8)
12.0
-8.2 4.7 39.8 39.8 SO.4
Table 3 Hyperfine coupling constants for theJ = 1 -L 0 rotational transition in fluoroform. CFJH
All values are in kHz
CFJD
ref. [ 1]
ref. [2]
ref. [3]
this work
-
-
_
-
l&2(45) 24.X30) -6.283 7.012
31.2(18) -2.0(15) -6.283
10.6(10) O-0(10) -6.275
31-l(4) -3-O(6) -6.275
7.012
7.009
a) N isH for CFiH and D for CFBD.
7.009
ref. [l]
ref. [2]
this work
-34.16(40) 13.8(30) 3S(lO) -6.283 1.076
-34.18(20) 28.X18) O.O(lO) -6.283 1.076
-34.10(40) 29-O(9) -0.16(40) -6.275 1.076 :
b) Calculated from the known molecular geometry [ 7 1.
product: H, = Q(D)*V(d)
e@g
,
where-d(D) is the quadrupole tensor-of the deuteron and V(D) the gradient tensor of the electric field at. :,.the. positibn.of the deuteronr The coupling constantCD).Ff the quad&pole interaction is-defined as: @%K .:
:, .:.
:. - .I,:..
= -eQ
J(J-i-i j-3ir2 (.r+1)(2&3)
a2Hm ar2_
’
where &$(D)/az2 is the &adient.of the electric field along the molecular symmetry axis z; 4(D) is the : potential due to the surrouriding :eiectrdniti and ylear ,. : . . .. ;_ _, :.‘.. :. .~
Volume 26, number 4
CHEhllCAL PHYSICS LETTERS
1SJunel974
charge distribution at the position of the deuteron, The best-fit coupling consranrs obtained From a
References
Ieast-squares analysis of the observed spectra (tables 1 and 2) are shown in table 3 together with the results of previous investi tions. The ratio of the spin-rotation constants Cf?i7 of CF$ and CF$ agrees within
[ 11 S-G. Kukolich, A.C. Neison and D.J. Ruben, 3, Mol.
the experimental error with the ratio of the rotational constants expressed in the cerrtre frequencies u. of the transitions studied (tables I and 2). The same ap
pIies to the ratio CJ%‘jC>T if also the ratio of the magnetic g-values for the proton and the deuteron is taken into account. FinaiIy there is a good agreement between the present results and the new resuits of the MIT group, which were obtained after a remeasurement of the CF3H spectrum and a reassignment of the CF,D data [2)_
Spectrp. 40 (1971) 33. [2] S.G. Kukolich and D.J.Ruben, J. Mol. Spectry.44 (t972) 607. 13) JXH. Reijnders, A.W. Eltenbruek and A. Dymanus, Cfiem. Phys. Letters 17 (1972) 351. [4f J. Verhoeven, Thesis. Katbolieke Universiteit, N$jme~en, The Netherlands (1969). ISI J. Verhoeven and A. Dymanus. 3. Cbem. Phys. 52 (1970)
3222. f6I V. Radeka, Proceedings ISPRA, Nuclear Electronic SYmnosium 119691. 171 S.N. Gosh, R.Trambarulo 20 0952) 60.5.
and W. Cordy, J. Chem. Phys.