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Dipole moments of CH3F in the ν3 and ν6 vibrational excited states from the Stark effect
Journal of Quantitative Spectroscopy & Radiative Transfer 148 (2014) 213–220
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Dipole moments of CH3F in the ν3 and ν6 vibrational excited states from the Stark effect J. Koubek n, P. Kania, Š. Urban Institute of Chemical Technology Prague, Department of Analytical Chemistry, Technická 5, 16628 Prague, Czech Republic
a r t i c l e i n f o
abstract
Article history: Received 17 January 2014 Received in revised form 20 May 2014 Accepted 7 July 2014 Available online 15 July 2014
Both the parallel and perpendicular rotational Stark components of the methyl fluoride J, k, l: 2, 71, 0’1, 71, 0 and 2, 71, ∓1’1, 71, ∓1 lines in the ν3 and ν6 excited vibrational states were measured in the microwave region of ca 100 GHz at the Stark fields in the range of ca 150–1100 V/cm. The analysis of the Stark components was complicated by unexpected hyperfine structure patterns spanning a few MHz, which were observed for MJ components with large Stark shifts (4300 MHz), most probably due to an enhancement through the Stark effect. The permanent electric dipole moments for these two vibrational states were derived from selected separated hyperfine components of the Stark components: μ3 ¼ 1.90345(46) D, μ6 ¼ 1.86394(32) D (the expanded uncertainties are given with the coverage factor k¼ 2). The significant perturbational second-order Stark contributions were simply eliminated using a Stark component difference approach. Third-order Stark contributions were included in the analysis, and higher-order Stark contributions and polarizability contributions were neglected since they are inconsequential in this study. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Stark rotational combination differences Dipole moment Microwave spectroscopy Vibrational excited states Methyl fluoride Hyperfine splitting enhanced through the Stark effect
1. Introduction Along with carbonyl sulfide and acetonitrile, methyl fluoride is one of the most frequently used molecules for the calibration of Stark cells in rotational spectroscopy. The reference value of its dipole moment of 1.85840(7) D for J, K: 1, 1 rotational state was given by Marshall and Muenter using molecular beams [1]. The absorption Stark spectra of J, k: 2, 71’1, 71 ground state rotational transition at high voltage were measured in the millimeter wave region to conduct such a calibration. While performing this routine calibration, the observed spectra featured more lines then the expected single Stark components. The revealed structure is assumed to be a magnetic hyperfine structure enhanced by the Stark effect at high electric fields. The splittings are observable in the cases of Stark
n
Corresponding author. Tel.: þ420 220 443 823. E-mail address: [email protected] (J. Koubek).
http://dx.doi.org/10.1016/j.jqsrt.2014.07.006 0022-4073/& 2014 Elsevier Ltd. All rights reserved.
components with a large Stark shift. At a voltage of 900 V, for instance, five hyperfine components induced by the Stark effect were observed, see Fig. 1. Nevertheless at 1000 V, three additional lines interfered with the hyperfine pattern in the region of ca 101,665 MHz. These three lines located ca at 101,670.3 MHz, 101,674.6 MHz, and 101,676.3 MHz were assigned as the Stark components of J, k: 2, 0’1, 0 line of the ν6 first excited vibrational state. Hirota et al. in their microwave study on rotational transitions in the ν2, ν3, ν5 and ν6 states [2] observed a strong Coriolis interaction between the ν2 and ν5 states for J: 2’1 transitions and discussed the direct l-doubling transitions with J ranging from 2 to 6 while they did not observe any significant Coriolis effect between the ν3 and ν6 states for J: 1’0 and 2’1 rotational transitions. The observed Stark splitting being due mainly to the second-order contributions features small shifts and thus no further hyperfine splitting. Since the experimental value of the dipole moment of the CH3F in the ν6 state was available in the literature with an accuracy [3] that could be further
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Fig. 1. Hyperfine splittings in CH3F induced by the Stark effect with higher voltages of 900 V and 1000 V: ground state J, k: 2, 7 1’1, 7 1 Stark perpendicular transitions with MJ ¼ 1, ΔMJ ¼ þ 1 on the left, with MJ ¼ þ 1, ΔMJ ¼ 1 on the right. Pressure: 7 μbar, temperature: 296 K. The lower line intensities over 102 GHz are due to the lower performance of the Schottky detector. The three lines marked by arrows are the Stark components of ν6 J, k: 2, 0’1, 0 transition, split through the second-order contributions of the Stark effect (see Fig. 3).
improved using the microwave technique, a set of transitions was measured and this molecular property determined. The used difference approach (a form of Stark rotational combination differences) for the treatment (to remove eventual contributions) of the second-order Stark effect is detailed in the text with respect to another type of difference method for Stark measurements applied by Gadhi et al. [4] in their study on acetonitrile. The centrifugal distortion effect on the value of the dipole moment was evaluated to be below our experimental uncertainty for the measured low J (J¼1) transitions [5,6]. Due to an overlap of the actual experimental frequency interval with the ν3 rotational transitions at ca 100.7 GHz, the Stark spectra were measured and analyzed also for this a1 vibrational symmetry species. The obtained values for μ6 and μ3 are confronted with the results of three previous Laser Stark studies [3,6,7].
2. Experimental details The absorption Stark spectra of methyl fluoride (99.5% purity) with a pressure of 7 15 μbar were recorded at ca 101 GHz using a Stark module (with both parallel (ΔMJ ¼0) and perpendicular (ΔMJ ¼ 71) set-ups possible) and the semiconductor millimeter wave high resolution spectrometer at the ICT Prague [8,9], using frequency modulation and the back and forth scanning of the frequency range. The lines were measured and analyzed
in both directions; the line centers used for dipole moment calculation were the mean values from the two directions. The Stark module consists of a stable DC voltage generator Fluke 5440B (0–1100 V, factory claimed stability 10 ppm) and two ca 150 cm 8 cm 1 cm finely polished stainless steel plates placed in a free path glass absorption cell [10]. The distance d separating the electrodes, set by finely machined quartz blocks, was deduced as 0.978234 (47) cm (combined uncertainty) from the difference of the measured Stark shift of a hyperfine component of the two J, k, MJ: 2, 71, 0’1, 71, 1 and J, k, MJ: 2, 71, 0’1, 71, 1 GS perpendicular Stark lines under three voltages from 1000 to 1100 V (see Fig. 1) and from the calibration value of the dipole moment [1]. The experimental conditions (generated DC voltage, pressure (710%) in the cell (Leybold CTR 91), temperature of the cell (Fe/Cu–Ni thermocouple), modulation depth of the FM probing signal, frequency step between scanning points and number of averaged data in each scanning direction) of the measured lines are described in Table 1. 3. Analysis Since the selected perpendicular rotational transitions in the ν3 (symmetry a1) and ν6 (symmetry e) vibrational states do not manifest any further observable splitting under the experimental conditions used, neither do they undergo l-type doubling, and the standard ground state perturbation equations up to third order are used to
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Table 1 Parameters of the Stark measurements. Vib. mode
Stark transitions J, k, l, MJ: 2, 71, 0 (ν3)/∓1 (ν6), MJ0 ’1, 7 1, 0 (ν3)/∓1 (ν6), MJ″
ν3
All MJ: MJ: MJ: MJ: MJ:
7 1’0 and 7 2’ 71 1’0 and 2’ 1 1’0 and 2’1 1’0 and 2’ 1 1’0 and 2’1
All MJ: MJ: MJ: MJ: MJ: MJ:
7 1’0 and 7 2’ 71 7 1’0 and 7 2’ 71 1’0 and 2’ 1 1’0 and 2’1 1’0 and 2’ 1 1’0 and 2’1
ν6
U [V]
p [μbar]
T [1C]
Modulation depth [kHz]
Frequency step [kHz]
Number of scans
0 30 150 150 300 300
7 7 7 7 15 15
55 55 55 55 55 55
100 100 100 100 150 150
27 20 23 24 30 30
40 22 198 236 216 247
0 10 20 150 150 300 300
7 7 7 7 7 15 15
23 23 23 45 45 45 45
200 200 200 150 150 200 200
89 89 89 24 24 25 27
30 50 50 297 391 292 354
Vib. mode
Stark transitions J, k, l, MJ: 2, 71, 0 (ν3)/∓1 (ν6), MJ’1, 7 1, 0 (ν3)/∓1 (ν6), MJ
U [V]
p [μbar]
T [1C]
Modulation Depth [kHz]
Frequency step [kHz]
Number of scans
ν3
MJ ¼ 1 MJ ¼ 1
1075 1075
15 15
55 55
200 200
30 30
3364 3730
ν6
MJ ¼ 1 MJ ¼ 1
1075 1075
15 15
55 55
200 200
32 32
5799 5124
describe the shifts of the Stark components (Eq. (1)) in the symmetric top without a quadrupole interaction [11,12]. The same model was applied also in the case of the Stark spectra with a resolved hyperfine pattern where the frequency of the components denoted as C in Fig. 4 was estimated to coincide with a Stark non-split component.
ΔνStark ðJ; k; l; MJ ; ΔMJ Þ ¼ νStark ðJ; k; l; MJ ; ΔMJ Þ νðJ; k; lÞ 3
¼ ∑ ΔνStark; i ðJ; k; l; M J ; ΔM J Þ i¼1
ð1Þ
The following perturbation equations were obtained after substitution for the J and k quantum numbers:
ΔνStark; 1 ðJ ¼ 1; k ¼ 7 1; l ¼ 0ðν0 ; ν3 Þ μU 2MJ 8 1 or 8 1ðν6 Þ; M J ; ΔM J ¼ 7 1Þ ¼ hd
6
ð2Þ
ΔνStark; 2 ðJ ¼ 1; k ¼ 7 1; l ¼ 0ðν0 ; ν3 Þ or 8 1ðν6 Þ; M J ; ΔM J ¼ 7 1Þ ¼
1 μU 2 811 314MJ 2 8 250MJ 2B hd 7560
ð3Þ
ΔνStark; 3 ðJ ¼ 1; k ¼ 7 1; l ¼ 0ðν0 ; ν3 Þ or 8 1ðν6 Þ; M J ; ΔM J ¼ 7 1Þ ¼
1 2B2
! 3 ( 1 MJ 2 4 MJ 2 MJ hd 3 480
μU
þ ðMJ 7 1Þ
9 ðM J 71Þ2 4 ðM J 7 1Þ2 8505 480
ΔνStark; 1 ðJ ¼ 1; k ¼ 7 1; l ¼ 0ðν0 ; ν3 Þ μU M J or 8 1ðν6 Þ; M J ; ΔM J ¼ 0Þ ¼ hd 3
!) ð4Þ
ð5Þ
ΔνStark; 2 ðJ ¼ 1; k ¼ 7 1; l ¼ 0ðν0 ; ν3 Þ or 8 1ðν6 Þ; M J ; ΔM J ¼ 0Þ
! 1 μU 2 3ð4 M J 2 Þ 8ð9 M J 2 Þ ¼ 2B hd 40 945
ΔνStark; 3 ðJ ¼ 1; k ¼ 7 1; l ¼ 0ðν0 ; ν3 Þ or 8 1ðν6 Þ; M J ; ΔM J ¼ 0Þ ¼
1
μU
2B2 hd
3
MJ
9 M J 2 4 MJ 2 1 MJ 2 þ 8505 240 3
ð6Þ
! ð7Þ
where the symbols ν(J, k, l), μ and B stand for the field-free frequency of the rotational line, the corresponding dipole moments and rotational constants in the ground (ν0), ν3 or ν6 vibrational states, respectively. The CODATA2010 [13] values for the fundamental constants were used in the calculations. For the voltages of 150 and 300 V used in this analysis, the estimated second-order contributions to the Stark shift for the considered lines range from 13 to 180 kHz and are significant in the total value of the Stark shift. The third-order contributions as well as their uncertainties are estimated to be below 0.1 kHz and do not need to be taken into account in this study. However, for a voltage of 1075 V, the Stark thirdorder contributions were no longer negligible, and these contributions were subtracted from the experimental frequencies. Since the third-order shifts are small (up to 11 kHz) and the uncertainty of calculation of their value insignificant at the level of kHz units, such subtraction in this case introduces no significant correlation in the dipole moment determination. The shifts, presented in Tables 2 and 3, were calculated using the ground state dipole moment from [1], the μ3 and μ6 values from this study and rotational constants B0 ¼25,536.14755(26) MHz from [14], B3 ¼25,197.570(20)
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Table 2 Calculated shifts (μ3 ¼1.90345(23) D, μ6 ¼1.86394(16) D, μGS ¼ 1.85840(7) D, d ¼ 0.978234(47) cm) and their uncertainties (in MHz) for selected J, k, l, MJ: 2, 7 1, 0 (GS, ν3)/∓1 (ν6), MJ0 ’1, 7 1, 0 (GS, ν3)/∓1 (ν6), MJ″ Stark transitions in three vibrational states. Vib. state
Transition
Voltage of 150 V (E ¼153.338(7) V/cm)
Voltage of 300 V (E¼ 306.675(15) V/cm)
ΔνStark [MHz]
ΔνStark,1 [MHz]
ΔνStark,2 [MHz]
ΔνStark [MHz]
ΔνStark,1 [MHz]
ΔνStark,2 [MHz]
GS
MJ: MJ: MJ: MJ:
1’0 2’ 1 1’0 2’1
23.866(2) 23.896(2) 23.952(2) 23.922(2)
23.909(2) 23.909(2) 23.909(2) 23.909(2)
0.043(0) 0.013(0) 0.043(0) 0.013(0)
47.645(3) 47.765(3) 47.991(3) 47.870(3)
47.818(3) 47.818(3) 47.818(3) 47.818(3)
0.173(0) 0.053(0) 0.173(0) 0.053(0)
ν3
MJ: MJ: MJ: MJ:
1’0 2’ 1 1’0 2’1
24.443(3) 24.475(3) 24.535(3) 24.502(3)
24.489(3) 24.489(3) 24.489(3) 24.489(3)
0.046(0) 0.014(0) 0.046(0) 0.014(0)
48.793(6) 48.921(6) 49.161(6) 49.033(6)
48.977(6) 48.977(6) 48.977(6) 48.977(6)
0.184(0) 0.056(0) 0.184(0) 0.056(0)
ν6
MJ: MJ: MJ: MJ:
1’0 2’ 1 1’0 2’1
23.937(2) 23.967(2) 24.024(2) 23.994(2)
23.980(2) 23.980(2) 23.980(2) 23.980(2)
0.044(0) 0.013(0) 0.044(0) 0.013(0)
47.786(5) 47.907(5) 48.135(5) 48.014(4)
47.960(5) 47.960(5) 47.960(5) 47.960(4)
0.175(0) 0.053(0) 0.175(0) 0.053 (0)
Table 3 Calculated shifts and their uncertainties (in MHz) for selected J, k, l, MJ: 2, 71, 0 (GS, ν3)/∓1 (ν6), MJ’1, 71, 0 (GS, ν3)/∓1 (ν6), MJ parallel Stark transitions in three vibrational states. Vib. state
Transition
Voltage of 1075 V (E¼ 1098.919(54) V/cm) ΔνStark [MHz]
ΔνStark,1 [MHz]
ΔνStark,2 [MHz]
ΔνStark,3 [MHz]
GS
MJ: 1’1 MJ: 1’ 1
344.388(21) 340.982(21)
342.695(21) 342.695(21)
1.703(0) 1.703(0)
0.010(0) 0.010(0)
ν3
MJ: 1’1 MJ: 1’ 1
352.802(46) 349.181(45)
351.002(46) 351.002(46)
1.810(0) 1.810(0)
0.011(0) 0.011(0)
ν6
MJ: 1’1 MJ: 1’ 1
345.427(34) 341.986(34)
343.716(34) 343.716(34)
1.721(0) 1.721(0)
0.010(0) 0.010(0)
MHz and B6 ¼25,418.917(47) MHz from [2]. The combined uncertainties of the shift values were calculated using the Kragten method [15]. Rather than analyzing the specific Stark shifts, the frequency differences of the selected Stark lines were used to derive the dipole moment values. Gadhi et al. [4] had already used the frequency differences of the Stark components sharing the same J and k quantum numbers in their Stark Lamb dip experiment on acetonitrile in order to eliminate the uncertainty of the rotational and centrifugal distortion spectroscopic constants in their calculation of the pure rotational line frequencies and to eliminate also some other systematic errors. Their approach helped treat the dipole and quadrupole-moment perturbational terms. In our study on a molecule without a quadrupole interaction, the main reason to analyze the differences between the selected Stark components is not the elimination of the reference rotational transition frequency from the treatment. Actually, this quantity is measurable in our experiment with better uncertainty than any Stark component frequency due to a better signal to noise ratio and no uncertainty propagation from the zero Stark field. Moreover, an evaluation of experimental Stark shifts already diminishes substantially or even eliminates some systematic flaws (possible biases due to failures in frequency calibration, in reference rotational line frequency calculation, in line frequency pressure dependence
calculation, etc.). The main advantage of the difference approach is a possible elimination of the Stark secondorder terms from the derivation of the dipole moment and an extension of the Stark frequency interval by a factor of two approximately at the given voltage. Such an approach is equivalent to analyzing the difference between the shifts of those components that are symmetrical (a different sign of quantum number MJ, the same absolute value of the Stark shift) in the first order since the second-order contributions of their components have the same values and are canceled as can be seen from Eqs. (3) and (6), and Tables 2 and 3. It should be mentioned that these components of symmetrical lines in perpendicular Stark orientation are not resolved in our spectra due to the lower values of the differences of their second-order Stark shifts as compared to the line widths. The Coriolis ν3–ν6 interaction generally contribute to the centrifugal distortion and mix the corresponding vibrational wavefunctions; however, for the low quantum numbers involved in our experiment, these effects are expected to be low. The centrifugal distortion evaluation using Freund’s parameters [6] or Cosléou's parameters [5] gives values of 10 5 D and 2 to 5 10 5 D, respectively, which would be covered by the uncertainty evaluated as ca 4 10 4 D in our determination of the dipole moments. The dipole moments were therefore determined from experimental Stark component–frequency differences
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Fig. 2. The ν3 CH3F J: 2’1 rotational transitions (lower part, k ¼ 0 at 100,788.21 MHz (no observable Stark effect); k ¼ 71, l ¼0 at 100,786.14 MHz (a)) and their perpendicular Stark spectra (in both lower and upper parts). The intensive pairs of the Stark components of k ¼ 7 1, l ¼0 line, symmetrical in their shifts (MJ: 1’0 along with MJ: 2’ 1 at lower frequency, MJ: 1’0 along with MJ: 2’1 at higher frequency), are marked b1, b2, …, d2 for the different Stark voltages applied (30 V (b1, b2), 150 V (c1, c2) and 300 V (d1, d2)).
using Eqs. (8) and (9), based on the first-order Stark term. hd μi ¼ 3 νStark ðJ ¼ 1; k ¼ 71; l ¼ 0ðν3 Þ U or 8 1ðν6 Þ; M J ¼ 0=þ 1; ΔM J ¼ 1= þ 1Þ νStark ðJ ¼ 1; k ¼ 71; l ¼ 0ðν3 Þ or
8 1ðν6 Þ; M J ¼ 0= 1; ΔM J ¼ þ 1= 1Þ
ð8Þ
3 hd ν ðJ ¼ 1; k ¼ 7 1; l ¼ 0ðν3 Þ 2 U Stark or 8 1ðν6 Þ; M J ¼ þ1; ΔM J ¼ 0Þ
μi ¼
νStark ðJ ¼ 1; k ¼ 71; l ¼ 0ðν3 Þ or
8 1ðν6 Þ; M J ¼ 1; ΔM J ¼ 0Þ
ð9Þ
Also, the relative uncertainty of these frequency differences is lower than the relative uncertainty of the Stark shift, which helps reduce the combined uncertainty that was evaluated following the Eurachem Guide [15]. As mentioned above, in the case of components with large shifts, the very small third-order contribution (that does not cancel out like the second-order contribution does) was also included in the analysis. The observed spectra feature a more or less pronounced line profile asymmetry due to several effects. The observed line profile asymmetry in the case of broadened lines with medium Stark shifts as in Figs. 2 and 3 (Stark voltage 150 V, resp. 300 V) is caused by the differences of the Stark second-order contributions to different MJ components (ca 30 kHz, resp. 120 kHz – see
Table 2) and possibly by the hyperfine structure. The separations are too small to be resolved, yet large enough to bias the line center frequency that causes significant flaws in the determination of dipole moments from such data. The calculated uncertainties for the perpendicular Stark components for a voltage of 150 V and 300 V (see Table 4) do not account for this systematic bias and are therefore underestimated. The dipole moments determined from these lines with medium Stark shifts are hence systematically biased. The bias gets larger when the second-order differences and hyperfine separations increase with the voltage applied while the splitting pattern remains unresolved due to the relatively large line widths. The biased results are presented for illustration in Table 4. After this first analysis, the isolated parallel Stark components that have a reasonable intensity and a faster Stark shift were selected and a much larger number of spectra were integrated to observe the resolved hyperfine pattern. The observed isolated hyperfine lines for components with a large Stark shift feature as well a line profile asymmetry – the one generated by electric field inhomogeneity (see the ground-state perpendicular Stark spectra in Fig. 1). This inhomogeneity is assumed not to be very important – the spectra would not be observable at all in such a case of a high electric field – but it might have a slight contribution in the line position determination. The uncertainty of all the determined line position frequencies was doubled in the calculation of the frequency difference
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Fig. 3. The ν6 CH3F J: 2’1 rotational transitions (lower part, k ¼0, l ¼ 7 1 at 101,673.7 MHz (no observable Stark effect); k ¼ 7 1, l ¼∓1 at 101,667.45 MHz; k ¼ 7 1, l¼ 7 1 doublet at 101,693.8 MHz and 101,658.6 MHz) and their perpendicular Stark components (in both lower and upper parts). The intensive pairs of Stark components of k ¼ 7 1, l ¼∓1 line (a), symmetrical in their shifts (MJ: 1’0 along with MJ: 2’ 1 at lower frequency, MJ ¼: 1’0 along with MJ: 2’1 at higher frequency), are marked b1, b2, …, e2 for the different Stark voltages applied (10 V (b1, b2), 20 V (c1, c2), 150 V (d1, d2) and 300 V (e1, e2)).
to determine the dipole moment. We assume that this treatment is useful for not underestimating the contribution of the inhomogeneity to the dipole moment determination. The values of the permanent electric dipole moments in the two vibrationally excited states and their expanded combined uncertainties calculated with a coverage factor of k ¼2 were determined from the spectra with larger Stark shifts and with a resolved hyperfine structure (parallel transitions in Table 4, hyperfine components marked C in Fig. 4), as μ3 ¼1.90345(46) D and μ6 ¼ 1.86394(32) D. 4. Discussion Our determined value of the dipole moment for the ν6 state falls in the uncertainty interval of the result by Duxbury [3]: 1.859(5) D whose lower value measured for relatively high J of the measured QQ(6,4) transitions is most probably due to the rotational dependence of the dipole moment. The value for the ν3 state falls between the values provided by the two Laser Stark studies: Brewer [7] gives a value of 1.9009(10) D and Freund et al. [6] present a value of 1.9054(6) D. Brewer determined the dipole moment using the QQ(12,2) transition (J¼12) and his result is obviously affected by centrifugal distortion as mentioned in Ref. [6] that used QP(J,K), QQ(J,K) and QR(J,K) transitions
mostly with J values up to 6. The respective values of these two Laser Stark experiments are roughly consistent. The rotational dependence of the dipole moment was estimated as μJ ¼4.42 10 6 D, μK ¼3 10 6 D by Freund et al. using “diatomic” approximation that was obtained from the ground state centrifugal distortion relations [16,17]. These estimated values led to the assumption that the rotational contributions of up to J ¼6 and K ¼5 could be estimated maximally by 3 10 4 D; therefore, they were neglected in their evaluation of the dipole moments in the excited states. These estimated rotational dependence parameters explained the difference between their value and Brewer's only partially [6]. The Cosléou et al. [5] study on 13CH3F discussed a minimal isotopic difference of the ground state μJ and μK values between 13CH3F and 12 CH3F and obtained a different set of these parameters for the ground state: μJ ¼1.1 4.4 10 5 D and μK ¼ 3.7 10 5 D. These ground parameters are one order higher than was estimated by Freund [6] for the ν3 excited state; in addition, the μK differs by sign. Besides this, we would expect even larger rotational contributions to the dipole moment in the vibrationally excited state than in the ground state due to the effect of the Coriolis interaction between the ν3 and ν6 states [5] that provides an additional contribution to the centrifugal distortion rotational dependence of the ν3 dipole moment. Given the discussion above, the uncertainty of the ν3 dipole moment
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Fig. 4. The ν3 resp. ν6 CH3F parallel Stark components of J: 2’1 rotational transitions under field 1098.919(54) V/cm (voltage 1075 V applied on Stark cell), with resolved hyperfine structure. The hyperfine components labeled C were used in dipole moment determination. Table 4 Measured frequencies of selected J, k, l, MJ: 2, 7 1, 0 (ν3)/∓1 (ν6), MJ0 ’ 1, 7 1, 0 (ν3)/∓1 (ν6), MJ″ perpendicular Stark transitions, resp. hyperfine components denoted as C in Fig. 4 for parallel Stark transitions. Vib. state
U/d [V/cm]
Line Frequency [MHz]
Frequency difference [MHz]
MJ: 1’0, 2’ 1
MJ: 1’0, 2’1
Dipole moment [D]
ν3
153.25(15) 306.50(29)
100,761.760(25) 100,737.444(50)
100,810.603(25) 100,835.109(50)
48.843(71) 97.67(14)
1.8982(27) 1.8978(27)
ν6
153.25(15) 306.50(29)
101,643.550(25) 101,619.747(50)
101,691.446(25) 101,715.406(50)
47.896(71) 95.66(14)
1.8614(27) 1.8589(27)
MJ: 1’ 1
MJ: 1’1
ν3
1098.919(54)
100,437.003(21)
101,138.984(15)
701.981(52)
1.90345(23)
ν6
1098.919(54)
101,325.526(16)
102,012.940(17)
687.413(47)
1.86394(16)
determination in Ref. [6] is very likely underestimated from our point of view. Also the enhanced hyperfine splitting of the Stark level energies could bias the result. If not entirely resolved, this hyperfine structure could broaden the Stark component and even slightly shift off center due to profile asymmetry, altering thus the derivation of the dipole moment. This can be observed in the asymmetry of the upper lines in Figs. 2 and 3 and in the bias of the corresponding results in Table 4. The paper by Freund et al. [6] mentions that “an appreciable number of lines have been left unassigned”. It might be speculated whether some of these lines could be such resolved hyperfine components enhanced via the
Stark effect due to the presence of very high intensities of the electrical field. These structures might, on the other hand, not be resolved enough in the rovibrational transitions measured in that study as it is in the rotational transitions in the particular vibration state measured in absorption microwave spectroscopy using lower gas pressures where this effect was observed1 (see the ca 15 MHz hyperfine splitting at ca 1 kV/cm in Fig. 1). The analysis of
1 Poster H17 “Hyperfine Splittings in CH3F Induced by the Stark Effect” was presented by the authors at the 22th International Conference on High Resolution Molecular Spectroscopy in Prague in September 2012.
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this hyperfine-like pattern in the microwave domain remains the subject of our present research. 5. Conclusion Using the absorption Stark spectra, the permanent electric dipole moments in the ν3 and ν6 excited vibrational states of methyl fluoride were derived. The obtained values (with a coverage factor of k ¼2) μ3 ¼ 1.90345(46) D and μ6 ¼1.86394(32) D can help calculate the dipole moment surfaces [18] and can contribute to the remote temperature determination from the intensities of the rotational lines.
Acknowledgments The work was supported through the Czech Science Foundation (Grants P206/10/2182 and P206/10/P481). References [1] Marshall MD, Muenter JS. The electric dipole moment of methyl fluoride. J Mol Spectrosc 1980;83:279–82. [2] Hirota E, Tanaka T, Saito S. Second-order Coriolis resonance between ν2 and ν5 of CH3F by microwave spectroscopy. J Mol Spectrosc 1976;63:478–84. [3] Duxbury G, Kato H. Optical-optical double resonance spectra of CH3F and CD3F using isotopic CO2 lasers. Chem Phys 1982;66:161–7. [4] Gadhi J, Lahrouni A, Legrand J, Demaison J. Moment dipolaire de CH3CN. J Chim Phys 1995;92:1984–92.
[5] Cosléou J, Cacciani P, Herlemont F, Khelkhal M, Lecointre J, Pracna P. Rotational dependence of the dipole moment of 13CH3F. Phys Chem Chem Phys 2004;6:352–7. [6] Freund SM, Duxbury G, Romheld M, Tiedje JT, Oka T. Laser Stark spectroscopy in the 10 μm region: the ν3 bands of CH3F. J Mol Spectrosc 1974;52:38–57. [7] Brewer RG. Precision determination of CH3F dipole moment by nonlinear infrared spectroscopy. Phys Rev Lett 1970;25:1639–41. [8] Kania P, Stříteská L, Šimečková M, Urban Š. Pressure shifts of acetonitrile ground state parameters. J Mol Struct 2006;795:209–18. [9] Nová Stříteská L, Šimečková M, Kania P, Musil P, Kolesniková L, Koubek J, Urban Š. Precise ground state molecular parameters of chloromethane. J Mol Struct 2009;919:89–93. [10] Koubek J, Boulet C, Perrin A, Urban Š, Hartmann J-M. Line-mixing between rotational Stark components of CH3F self-perturbed and perturbed by helium: experimental results and IOS analysis. J Mol Spectrosc 2011;266:12–20. [11] Gordy W, Cook RL. Microwave molecular spectra. New York: John Wiley & Sons; 1984. [12] Meerts WL, Ozier I, Dymanus A. The molecular beam electric resonance spectrum of OPF3. Can J Phys 1979;57:1163–73. [13] Mohr PJ, Taylor BN, Newell DB. CODATA recommended values of the fundamental physical constants. J Phys Chem Ref Data 2010;41: 043109–84. [14] Papoušek D, Hsu YC, Chen HS, Pracna P, Klee S, Winnewisser M. Far infrared spectrum and ground state parameters of 12CH3F. J Mol Spectrosc 1993;159:33–41. [15] Eurachem/CITAC guide: Quantifying uncertainty in analytical measurement; 2012. [16] Watson JKG. Forbidden rotational spectra of polyatomic molecules. J Mol Spectrosc 1971;40:536–44. [17] Aliev MR, Watson JKG. Higher-order effects in the vibration–rotation spectra of semirigid molecules. In: Narahari Rao K, editor. Molecular spectroscopy, modern research, vol.III. Orlando: Academic Press; 1985. [18] Nikitin AV, Rey M, Tyuterev VG. Rotational and vibrational energy levels of methyl fluoride calculated from a new potential energy surface. J Mol Spectrosc 2012;274:28–34.
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Journal of Quantitative Spectroscopy & Radiative Transfer journal homepage: www.elsevier.com/locate/jqsrt
Dipole moments of CH3F in the ν3 and ν6 vibrational excited states from the Stark effect J. Koubek n, P. Kania, Š. Urban Institute of Chemical Technology Prague, Department of Analytical Chemistry, Technická 5, 16628 Prague, Czech Republic
a r t i c l e i n f o
abstract
Article history: Received 17 January 2014 Received in revised form 20 May 2014 Accepted 7 July 2014 Available online 15 July 2014
Both the parallel and perpendicular rotational Stark components of the methyl fluoride J, k, l: 2, 71, 0’1, 71, 0 and 2, 71, ∓1’1, 71, ∓1 lines in the ν3 and ν6 excited vibrational states were measured in the microwave region of ca 100 GHz at the Stark fields in the range of ca 150–1100 V/cm. The analysis of the Stark components was complicated by unexpected hyperfine structure patterns spanning a few MHz, which were observed for MJ components with large Stark shifts (4300 MHz), most probably due to an enhancement through the Stark effect. The permanent electric dipole moments for these two vibrational states were derived from selected separated hyperfine components of the Stark components: μ3 ¼ 1.90345(46) D, μ6 ¼ 1.86394(32) D (the expanded uncertainties are given with the coverage factor k¼ 2). The significant perturbational second-order Stark contributions were simply eliminated using a Stark component difference approach. Third-order Stark contributions were included in the analysis, and higher-order Stark contributions and polarizability contributions were neglected since they are inconsequential in this study. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Stark rotational combination differences Dipole moment Microwave spectroscopy Vibrational excited states Methyl fluoride Hyperfine splitting enhanced through the Stark effect
1. Introduction Along with carbonyl sulfide and acetonitrile, methyl fluoride is one of the most frequently used molecules for the calibration of Stark cells in rotational spectroscopy. The reference value of its dipole moment of 1.85840(7) D for J, K: 1, 1 rotational state was given by Marshall and Muenter using molecular beams [1]. The absorption Stark spectra of J, k: 2, 71’1, 71 ground state rotational transition at high voltage were measured in the millimeter wave region to conduct such a calibration. While performing this routine calibration, the observed spectra featured more lines then the expected single Stark components. The revealed structure is assumed to be a magnetic hyperfine structure enhanced by the Stark effect at high electric fields. The splittings are observable in the cases of Stark
n
Corresponding author. Tel.: þ420 220 443 823. E-mail address: [email protected] (J. Koubek).
http://dx.doi.org/10.1016/j.jqsrt.2014.07.006 0022-4073/& 2014 Elsevier Ltd. All rights reserved.
components with a large Stark shift. At a voltage of 900 V, for instance, five hyperfine components induced by the Stark effect were observed, see Fig. 1. Nevertheless at 1000 V, three additional lines interfered with the hyperfine pattern in the region of ca 101,665 MHz. These three lines located ca at 101,670.3 MHz, 101,674.6 MHz, and 101,676.3 MHz were assigned as the Stark components of J, k: 2, 0’1, 0 line of the ν6 first excited vibrational state. Hirota et al. in their microwave study on rotational transitions in the ν2, ν3, ν5 and ν6 states [2] observed a strong Coriolis interaction between the ν2 and ν5 states for J: 2’1 transitions and discussed the direct l-doubling transitions with J ranging from 2 to 6 while they did not observe any significant Coriolis effect between the ν3 and ν6 states for J: 1’0 and 2’1 rotational transitions. The observed Stark splitting being due mainly to the second-order contributions features small shifts and thus no further hyperfine splitting. Since the experimental value of the dipole moment of the CH3F in the ν6 state was available in the literature with an accuracy [3] that could be further
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Fig. 1. Hyperfine splittings in CH3F induced by the Stark effect with higher voltages of 900 V and 1000 V: ground state J, k: 2, 7 1’1, 7 1 Stark perpendicular transitions with MJ ¼ 1, ΔMJ ¼ þ 1 on the left, with MJ ¼ þ 1, ΔMJ ¼ 1 on the right. Pressure: 7 μbar, temperature: 296 K. The lower line intensities over 102 GHz are due to the lower performance of the Schottky detector. The three lines marked by arrows are the Stark components of ν6 J, k: 2, 0’1, 0 transition, split through the second-order contributions of the Stark effect (see Fig. 3).
improved using the microwave technique, a set of transitions was measured and this molecular property determined. The used difference approach (a form of Stark rotational combination differences) for the treatment (to remove eventual contributions) of the second-order Stark effect is detailed in the text with respect to another type of difference method for Stark measurements applied by Gadhi et al. [4] in their study on acetonitrile. The centrifugal distortion effect on the value of the dipole moment was evaluated to be below our experimental uncertainty for the measured low J (J¼1) transitions [5,6]. Due to an overlap of the actual experimental frequency interval with the ν3 rotational transitions at ca 100.7 GHz, the Stark spectra were measured and analyzed also for this a1 vibrational symmetry species. The obtained values for μ6 and μ3 are confronted with the results of three previous Laser Stark studies [3,6,7].
2. Experimental details The absorption Stark spectra of methyl fluoride (99.5% purity) with a pressure of 7 15 μbar were recorded at ca 101 GHz using a Stark module (with both parallel (ΔMJ ¼0) and perpendicular (ΔMJ ¼ 71) set-ups possible) and the semiconductor millimeter wave high resolution spectrometer at the ICT Prague [8,9], using frequency modulation and the back and forth scanning of the frequency range. The lines were measured and analyzed
in both directions; the line centers used for dipole moment calculation were the mean values from the two directions. The Stark module consists of a stable DC voltage generator Fluke 5440B (0–1100 V, factory claimed stability 10 ppm) and two ca 150 cm 8 cm 1 cm finely polished stainless steel plates placed in a free path glass absorption cell [10]. The distance d separating the electrodes, set by finely machined quartz blocks, was deduced as 0.978234 (47) cm (combined uncertainty) from the difference of the measured Stark shift of a hyperfine component of the two J, k, MJ: 2, 71, 0’1, 71, 1 and J, k, MJ: 2, 71, 0’1, 71, 1 GS perpendicular Stark lines under three voltages from 1000 to 1100 V (see Fig. 1) and from the calibration value of the dipole moment [1]. The experimental conditions (generated DC voltage, pressure (710%) in the cell (Leybold CTR 91), temperature of the cell (Fe/Cu–Ni thermocouple), modulation depth of the FM probing signal, frequency step between scanning points and number of averaged data in each scanning direction) of the measured lines are described in Table 1. 3. Analysis Since the selected perpendicular rotational transitions in the ν3 (symmetry a1) and ν6 (symmetry e) vibrational states do not manifest any further observable splitting under the experimental conditions used, neither do they undergo l-type doubling, and the standard ground state perturbation equations up to third order are used to
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215
Table 1 Parameters of the Stark measurements. Vib. mode
Stark transitions J, k, l, MJ: 2, 71, 0 (ν3)/∓1 (ν6), MJ0 ’1, 7 1, 0 (ν3)/∓1 (ν6), MJ″
ν3
All MJ: MJ: MJ: MJ: MJ:
7 1’0 and 7 2’ 71 1’0 and 2’ 1 1’0 and 2’1 1’0 and 2’ 1 1’0 and 2’1
All MJ: MJ: MJ: MJ: MJ: MJ:
7 1’0 and 7 2’ 71 7 1’0 and 7 2’ 71 1’0 and 2’ 1 1’0 and 2’1 1’0 and 2’ 1 1’0 and 2’1
ν6
U [V]
p [μbar]
T [1C]
Modulation depth [kHz]
Frequency step [kHz]
Number of scans
0 30 150 150 300 300
7 7 7 7 15 15
55 55 55 55 55 55
100 100 100 100 150 150
27 20 23 24 30 30
40 22 198 236 216 247
0 10 20 150 150 300 300
7 7 7 7 7 15 15
23 23 23 45 45 45 45
200 200 200 150 150 200 200
89 89 89 24 24 25 27
30 50 50 297 391 292 354
Vib. mode
Stark transitions J, k, l, MJ: 2, 71, 0 (ν3)/∓1 (ν6), MJ’1, 7 1, 0 (ν3)/∓1 (ν6), MJ
U [V]
p [μbar]
T [1C]
Modulation Depth [kHz]
Frequency step [kHz]
Number of scans
ν3
MJ ¼ 1 MJ ¼ 1
1075 1075
15 15
55 55
200 200
30 30
3364 3730
ν6
MJ ¼ 1 MJ ¼ 1
1075 1075
15 15
55 55
200 200
32 32
5799 5124
describe the shifts of the Stark components (Eq. (1)) in the symmetric top without a quadrupole interaction [11,12]. The same model was applied also in the case of the Stark spectra with a resolved hyperfine pattern where the frequency of the components denoted as C in Fig. 4 was estimated to coincide with a Stark non-split component.
ΔνStark ðJ; k; l; MJ ; ΔMJ Þ ¼ νStark ðJ; k; l; MJ ; ΔMJ Þ νðJ; k; lÞ 3
¼ ∑ ΔνStark; i ðJ; k; l; M J ; ΔM J Þ i¼1
ð1Þ
The following perturbation equations were obtained after substitution for the J and k quantum numbers:
ΔνStark; 1 ðJ ¼ 1; k ¼ 7 1; l ¼ 0ðν0 ; ν3 Þ μU 2MJ 8 1 or 8 1ðν6 Þ; M J ; ΔM J ¼ 7 1Þ ¼ hd
6
ð2Þ
ΔνStark; 2 ðJ ¼ 1; k ¼ 7 1; l ¼ 0ðν0 ; ν3 Þ or 8 1ðν6 Þ; M J ; ΔM J ¼ 7 1Þ ¼
1 μU 2 811 314MJ 2 8 250MJ 2B hd 7560
ð3Þ
ΔνStark; 3 ðJ ¼ 1; k ¼ 7 1; l ¼ 0ðν0 ; ν3 Þ or 8 1ðν6 Þ; M J ; ΔM J ¼ 7 1Þ ¼
1 2B2
! 3 ( 1 MJ 2 4 MJ 2 MJ hd 3 480
μU
þ ðMJ 7 1Þ
9 ðM J 71Þ2 4 ðM J 7 1Þ2 8505 480
ΔνStark; 1 ðJ ¼ 1; k ¼ 7 1; l ¼ 0ðν0 ; ν3 Þ μU M J or 8 1ðν6 Þ; M J ; ΔM J ¼ 0Þ ¼ hd 3
!) ð4Þ
ð5Þ
ΔνStark; 2 ðJ ¼ 1; k ¼ 7 1; l ¼ 0ðν0 ; ν3 Þ or 8 1ðν6 Þ; M J ; ΔM J ¼ 0Þ
! 1 μU 2 3ð4 M J 2 Þ 8ð9 M J 2 Þ ¼ 2B hd 40 945
ΔνStark; 3 ðJ ¼ 1; k ¼ 7 1; l ¼ 0ðν0 ; ν3 Þ or 8 1ðν6 Þ; M J ; ΔM J ¼ 0Þ ¼
1
μU
2B2 hd
3
MJ
9 M J 2 4 MJ 2 1 MJ 2 þ 8505 240 3
ð6Þ
! ð7Þ
where the symbols ν(J, k, l), μ and B stand for the field-free frequency of the rotational line, the corresponding dipole moments and rotational constants in the ground (ν0), ν3 or ν6 vibrational states, respectively. The CODATA2010 [13] values for the fundamental constants were used in the calculations. For the voltages of 150 and 300 V used in this analysis, the estimated second-order contributions to the Stark shift for the considered lines range from 13 to 180 kHz and are significant in the total value of the Stark shift. The third-order contributions as well as their uncertainties are estimated to be below 0.1 kHz and do not need to be taken into account in this study. However, for a voltage of 1075 V, the Stark thirdorder contributions were no longer negligible, and these contributions were subtracted from the experimental frequencies. Since the third-order shifts are small (up to 11 kHz) and the uncertainty of calculation of their value insignificant at the level of kHz units, such subtraction in this case introduces no significant correlation in the dipole moment determination. The shifts, presented in Tables 2 and 3, were calculated using the ground state dipole moment from [1], the μ3 and μ6 values from this study and rotational constants B0 ¼25,536.14755(26) MHz from [14], B3 ¼25,197.570(20)
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Table 2 Calculated shifts (μ3 ¼1.90345(23) D, μ6 ¼1.86394(16) D, μGS ¼ 1.85840(7) D, d ¼ 0.978234(47) cm) and their uncertainties (in MHz) for selected J, k, l, MJ: 2, 7 1, 0 (GS, ν3)/∓1 (ν6), MJ0 ’1, 7 1, 0 (GS, ν3)/∓1 (ν6), MJ″ Stark transitions in three vibrational states. Vib. state
Transition
Voltage of 150 V (E ¼153.338(7) V/cm)
Voltage of 300 V (E¼ 306.675(15) V/cm)
ΔνStark [MHz]
ΔνStark,1 [MHz]
ΔνStark,2 [MHz]
ΔνStark [MHz]
ΔνStark,1 [MHz]
ΔνStark,2 [MHz]
GS
MJ: MJ: MJ: MJ:
1’0 2’ 1 1’0 2’1
23.866(2) 23.896(2) 23.952(2) 23.922(2)
23.909(2) 23.909(2) 23.909(2) 23.909(2)
0.043(0) 0.013(0) 0.043(0) 0.013(0)
47.645(3) 47.765(3) 47.991(3) 47.870(3)
47.818(3) 47.818(3) 47.818(3) 47.818(3)
0.173(0) 0.053(0) 0.173(0) 0.053(0)
ν3
MJ: MJ: MJ: MJ:
1’0 2’ 1 1’0 2’1
24.443(3) 24.475(3) 24.535(3) 24.502(3)
24.489(3) 24.489(3) 24.489(3) 24.489(3)
0.046(0) 0.014(0) 0.046(0) 0.014(0)
48.793(6) 48.921(6) 49.161(6) 49.033(6)
48.977(6) 48.977(6) 48.977(6) 48.977(6)
0.184(0) 0.056(0) 0.184(0) 0.056(0)
ν6
MJ: MJ: MJ: MJ:
1’0 2’ 1 1’0 2’1
23.937(2) 23.967(2) 24.024(2) 23.994(2)
23.980(2) 23.980(2) 23.980(2) 23.980(2)
0.044(0) 0.013(0) 0.044(0) 0.013(0)
47.786(5) 47.907(5) 48.135(5) 48.014(4)
47.960(5) 47.960(5) 47.960(5) 47.960(4)
0.175(0) 0.053(0) 0.175(0) 0.053 (0)
Table 3 Calculated shifts and their uncertainties (in MHz) for selected J, k, l, MJ: 2, 71, 0 (GS, ν3)/∓1 (ν6), MJ’1, 71, 0 (GS, ν3)/∓1 (ν6), MJ parallel Stark transitions in three vibrational states. Vib. state
Transition
Voltage of 1075 V (E¼ 1098.919(54) V/cm) ΔνStark [MHz]
ΔνStark,1 [MHz]
ΔνStark,2 [MHz]
ΔνStark,3 [MHz]
GS
MJ: 1’1 MJ: 1’ 1
344.388(21) 340.982(21)
342.695(21) 342.695(21)
1.703(0) 1.703(0)
0.010(0) 0.010(0)
ν3
MJ: 1’1 MJ: 1’ 1
352.802(46) 349.181(45)
351.002(46) 351.002(46)
1.810(0) 1.810(0)
0.011(0) 0.011(0)
ν6
MJ: 1’1 MJ: 1’ 1
345.427(34) 341.986(34)
343.716(34) 343.716(34)
1.721(0) 1.721(0)
0.010(0) 0.010(0)
MHz and B6 ¼25,418.917(47) MHz from [2]. The combined uncertainties of the shift values were calculated using the Kragten method [15]. Rather than analyzing the specific Stark shifts, the frequency differences of the selected Stark lines were used to derive the dipole moment values. Gadhi et al. [4] had already used the frequency differences of the Stark components sharing the same J and k quantum numbers in their Stark Lamb dip experiment on acetonitrile in order to eliminate the uncertainty of the rotational and centrifugal distortion spectroscopic constants in their calculation of the pure rotational line frequencies and to eliminate also some other systematic errors. Their approach helped treat the dipole and quadrupole-moment perturbational terms. In our study on a molecule without a quadrupole interaction, the main reason to analyze the differences between the selected Stark components is not the elimination of the reference rotational transition frequency from the treatment. Actually, this quantity is measurable in our experiment with better uncertainty than any Stark component frequency due to a better signal to noise ratio and no uncertainty propagation from the zero Stark field. Moreover, an evaluation of experimental Stark shifts already diminishes substantially or even eliminates some systematic flaws (possible biases due to failures in frequency calibration, in reference rotational line frequency calculation, in line frequency pressure dependence
calculation, etc.). The main advantage of the difference approach is a possible elimination of the Stark secondorder terms from the derivation of the dipole moment and an extension of the Stark frequency interval by a factor of two approximately at the given voltage. Such an approach is equivalent to analyzing the difference between the shifts of those components that are symmetrical (a different sign of quantum number MJ, the same absolute value of the Stark shift) in the first order since the second-order contributions of their components have the same values and are canceled as can be seen from Eqs. (3) and (6), and Tables 2 and 3. It should be mentioned that these components of symmetrical lines in perpendicular Stark orientation are not resolved in our spectra due to the lower values of the differences of their second-order Stark shifts as compared to the line widths. The Coriolis ν3–ν6 interaction generally contribute to the centrifugal distortion and mix the corresponding vibrational wavefunctions; however, for the low quantum numbers involved in our experiment, these effects are expected to be low. The centrifugal distortion evaluation using Freund’s parameters [6] or Cosléou's parameters [5] gives values of 10 5 D and 2 to 5 10 5 D, respectively, which would be covered by the uncertainty evaluated as ca 4 10 4 D in our determination of the dipole moments. The dipole moments were therefore determined from experimental Stark component–frequency differences
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217
Fig. 2. The ν3 CH3F J: 2’1 rotational transitions (lower part, k ¼ 0 at 100,788.21 MHz (no observable Stark effect); k ¼ 71, l ¼0 at 100,786.14 MHz (a)) and their perpendicular Stark spectra (in both lower and upper parts). The intensive pairs of the Stark components of k ¼ 7 1, l ¼0 line, symmetrical in their shifts (MJ: 1’0 along with MJ: 2’ 1 at lower frequency, MJ: 1’0 along with MJ: 2’1 at higher frequency), are marked b1, b2, …, d2 for the different Stark voltages applied (30 V (b1, b2), 150 V (c1, c2) and 300 V (d1, d2)).
using Eqs. (8) and (9), based on the first-order Stark term. hd μi ¼ 3 νStark ðJ ¼ 1; k ¼ 71; l ¼ 0ðν3 Þ U or 8 1ðν6 Þ; M J ¼ 0=þ 1; ΔM J ¼ 1= þ 1Þ νStark ðJ ¼ 1; k ¼ 71; l ¼ 0ðν3 Þ or
8 1ðν6 Þ; M J ¼ 0= 1; ΔM J ¼ þ 1= 1Þ
ð8Þ
3 hd ν ðJ ¼ 1; k ¼ 7 1; l ¼ 0ðν3 Þ 2 U Stark or 8 1ðν6 Þ; M J ¼ þ1; ΔM J ¼ 0Þ
μi ¼
νStark ðJ ¼ 1; k ¼ 71; l ¼ 0ðν3 Þ or
8 1ðν6 Þ; M J ¼ 1; ΔM J ¼ 0Þ
ð9Þ
Also, the relative uncertainty of these frequency differences is lower than the relative uncertainty of the Stark shift, which helps reduce the combined uncertainty that was evaluated following the Eurachem Guide [15]. As mentioned above, in the case of components with large shifts, the very small third-order contribution (that does not cancel out like the second-order contribution does) was also included in the analysis. The observed spectra feature a more or less pronounced line profile asymmetry due to several effects. The observed line profile asymmetry in the case of broadened lines with medium Stark shifts as in Figs. 2 and 3 (Stark voltage 150 V, resp. 300 V) is caused by the differences of the Stark second-order contributions to different MJ components (ca 30 kHz, resp. 120 kHz – see
Table 2) and possibly by the hyperfine structure. The separations are too small to be resolved, yet large enough to bias the line center frequency that causes significant flaws in the determination of dipole moments from such data. The calculated uncertainties for the perpendicular Stark components for a voltage of 150 V and 300 V (see Table 4) do not account for this systematic bias and are therefore underestimated. The dipole moments determined from these lines with medium Stark shifts are hence systematically biased. The bias gets larger when the second-order differences and hyperfine separations increase with the voltage applied while the splitting pattern remains unresolved due to the relatively large line widths. The biased results are presented for illustration in Table 4. After this first analysis, the isolated parallel Stark components that have a reasonable intensity and a faster Stark shift were selected and a much larger number of spectra were integrated to observe the resolved hyperfine pattern. The observed isolated hyperfine lines for components with a large Stark shift feature as well a line profile asymmetry – the one generated by electric field inhomogeneity (see the ground-state perpendicular Stark spectra in Fig. 1). This inhomogeneity is assumed not to be very important – the spectra would not be observable at all in such a case of a high electric field – but it might have a slight contribution in the line position determination. The uncertainty of all the determined line position frequencies was doubled in the calculation of the frequency difference
218
J. Koubek et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 148 (2014) 213–220
Fig. 3. The ν6 CH3F J: 2’1 rotational transitions (lower part, k ¼0, l ¼ 7 1 at 101,673.7 MHz (no observable Stark effect); k ¼ 7 1, l ¼∓1 at 101,667.45 MHz; k ¼ 7 1, l¼ 7 1 doublet at 101,693.8 MHz and 101,658.6 MHz) and their perpendicular Stark components (in both lower and upper parts). The intensive pairs of Stark components of k ¼ 7 1, l ¼∓1 line (a), symmetrical in their shifts (MJ: 1’0 along with MJ: 2’ 1 at lower frequency, MJ ¼: 1’0 along with MJ: 2’1 at higher frequency), are marked b1, b2, …, e2 for the different Stark voltages applied (10 V (b1, b2), 20 V (c1, c2), 150 V (d1, d2) and 300 V (e1, e2)).
to determine the dipole moment. We assume that this treatment is useful for not underestimating the contribution of the inhomogeneity to the dipole moment determination. The values of the permanent electric dipole moments in the two vibrationally excited states and their expanded combined uncertainties calculated with a coverage factor of k ¼2 were determined from the spectra with larger Stark shifts and with a resolved hyperfine structure (parallel transitions in Table 4, hyperfine components marked C in Fig. 4), as μ3 ¼1.90345(46) D and μ6 ¼ 1.86394(32) D. 4. Discussion Our determined value of the dipole moment for the ν6 state falls in the uncertainty interval of the result by Duxbury [3]: 1.859(5) D whose lower value measured for relatively high J of the measured QQ(6,4) transitions is most probably due to the rotational dependence of the dipole moment. The value for the ν3 state falls between the values provided by the two Laser Stark studies: Brewer [7] gives a value of 1.9009(10) D and Freund et al. [6] present a value of 1.9054(6) D. Brewer determined the dipole moment using the QQ(12,2) transition (J¼12) and his result is obviously affected by centrifugal distortion as mentioned in Ref. [6] that used QP(J,K), QQ(J,K) and QR(J,K) transitions
mostly with J values up to 6. The respective values of these two Laser Stark experiments are roughly consistent. The rotational dependence of the dipole moment was estimated as μJ ¼4.42 10 6 D, μK ¼3 10 6 D by Freund et al. using “diatomic” approximation that was obtained from the ground state centrifugal distortion relations [16,17]. These estimated values led to the assumption that the rotational contributions of up to J ¼6 and K ¼5 could be estimated maximally by 3 10 4 D; therefore, they were neglected in their evaluation of the dipole moments in the excited states. These estimated rotational dependence parameters explained the difference between their value and Brewer's only partially [6]. The Cosléou et al. [5] study on 13CH3F discussed a minimal isotopic difference of the ground state μJ and μK values between 13CH3F and 12 CH3F and obtained a different set of these parameters for the ground state: μJ ¼1.1 4.4 10 5 D and μK ¼ 3.7 10 5 D. These ground parameters are one order higher than was estimated by Freund [6] for the ν3 excited state; in addition, the μK differs by sign. Besides this, we would expect even larger rotational contributions to the dipole moment in the vibrationally excited state than in the ground state due to the effect of the Coriolis interaction between the ν3 and ν6 states [5] that provides an additional contribution to the centrifugal distortion rotational dependence of the ν3 dipole moment. Given the discussion above, the uncertainty of the ν3 dipole moment
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219
Fig. 4. The ν3 resp. ν6 CH3F parallel Stark components of J: 2’1 rotational transitions under field 1098.919(54) V/cm (voltage 1075 V applied on Stark cell), with resolved hyperfine structure. The hyperfine components labeled C were used in dipole moment determination. Table 4 Measured frequencies of selected J, k, l, MJ: 2, 7 1, 0 (ν3)/∓1 (ν6), MJ0 ’ 1, 7 1, 0 (ν3)/∓1 (ν6), MJ″ perpendicular Stark transitions, resp. hyperfine components denoted as C in Fig. 4 for parallel Stark transitions. Vib. state
U/d [V/cm]
Line Frequency [MHz]
Frequency difference [MHz]
MJ: 1’0, 2’ 1
MJ: 1’0, 2’1
Dipole moment [D]
ν3
153.25(15) 306.50(29)
100,761.760(25) 100,737.444(50)
100,810.603(25) 100,835.109(50)
48.843(71) 97.67(14)
1.8982(27) 1.8978(27)
ν6
153.25(15) 306.50(29)
101,643.550(25) 101,619.747(50)
101,691.446(25) 101,715.406(50)
47.896(71) 95.66(14)
1.8614(27) 1.8589(27)
MJ: 1’ 1
MJ: 1’1
ν3
1098.919(54)
100,437.003(21)
101,138.984(15)
701.981(52)
1.90345(23)
ν6
1098.919(54)
101,325.526(16)
102,012.940(17)
687.413(47)
1.86394(16)
determination in Ref. [6] is very likely underestimated from our point of view. Also the enhanced hyperfine splitting of the Stark level energies could bias the result. If not entirely resolved, this hyperfine structure could broaden the Stark component and even slightly shift off center due to profile asymmetry, altering thus the derivation of the dipole moment. This can be observed in the asymmetry of the upper lines in Figs. 2 and 3 and in the bias of the corresponding results in Table 4. The paper by Freund et al. [6] mentions that “an appreciable number of lines have been left unassigned”. It might be speculated whether some of these lines could be such resolved hyperfine components enhanced via the
Stark effect due to the presence of very high intensities of the electrical field. These structures might, on the other hand, not be resolved enough in the rovibrational transitions measured in that study as it is in the rotational transitions in the particular vibration state measured in absorption microwave spectroscopy using lower gas pressures where this effect was observed1 (see the ca 15 MHz hyperfine splitting at ca 1 kV/cm in Fig. 1). The analysis of
1 Poster H17 “Hyperfine Splittings in CH3F Induced by the Stark Effect” was presented by the authors at the 22th International Conference on High Resolution Molecular Spectroscopy in Prague in September 2012.
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this hyperfine-like pattern in the microwave domain remains the subject of our present research. 5. Conclusion Using the absorption Stark spectra, the permanent electric dipole moments in the ν3 and ν6 excited vibrational states of methyl fluoride were derived. The obtained values (with a coverage factor of k ¼2) μ3 ¼ 1.90345(46) D and μ6 ¼1.86394(32) D can help calculate the dipole moment surfaces [18] and can contribute to the remote temperature determination from the intensities of the rotational lines.
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