Microwave spectrum of the GeCl radical

Journal of Molecular Spectroscopy 251 (2008) 369–373

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Microwave spectrum of the GeCl radical Keiichi Tanaka *, Hiroaki Honjou, Masaki J. Tsuchiya, Takehiko Tanaka 1 Department of Chemistry, Faculty of Sciences, Kyushu University, Hakozaki, Higashiku, Fukuoka 812-8581, Japan

a r t i c l e

i n f o

Article history: Received 24 January 2008 In revised form 8 April 2008 Available online 22 April 2008 Keywords: Microwave spectrum GeCl radical Rotational constant K-doubling constant Equilibrium structure

a b s t r a c t Microwave spectrum of the GeCl radical in the ground vibronic state was observed for the 2P1/2 as well as 2 P3/2 spin substate. The GeCl radical was generated in a free-space absorption cell by a dc discharge in GeCl4 diluted with Ar. The observed spectra were subjected to a least-squares analysis to yield accurate molecular constants; those of the most abundant isotopomer 74Ge35Cl are as follows; B0 = 4535.91396(70) MHz, D0 = 2.5413(13) kHz, AD0 = 4.87595(37) MHz, jp0j = 17.87(31) MHz, jq0j = 4.06(18) MHz, and jp0 + 2q0j = 25.984(39) MHz, where uncertainties given in parentheses correspond to one standard deviation. The absolute signs of p0 and q0 are indeterminable, although they have the same sign. The equilibrium rotational constant Be and the vibration–rotation interaction constant ae were derived by analyzing the mass dependence of the B0 constants for seven isotopomers. The equilibrium bond length was determined to be re = 2.163739(23) Å. Ó 2008 Published by Elsevier Inc.

1. Introduction The present paper reports the microwave spectrum of the germanium monochloride radical GeCl in the 2P1/2 as well as 2P3/2 spin substate of the ground vibronic state. This species has not been investigated by microwave spectroscopy, although it has been applied to several Group 14 halide radicals; CF [1], CCl [2], SiF [3], SiCl [4], and GeF [5]. The electronic spectrum of GeCl has been observed by several authors in the ultraviolet [6–12] and visible regions [13–15]. The resonance enhanced multiphoton ionization (REMPI) spectroscopy was also reported [16]. Rotational analyses have been performed, yielding rotational as well as vibrational constants [9–12]. Zyrnicki [9] reported the rotational analysis of the 0–0 band of the a4R3/2– X2P3/2 subsystem, and Mishra and Khanna [10] the B2R+–X2Pr system. Badowski and Zyrnicki [11] obtained accurate rotational constants from analyses of the 0–0 and 0–2 bands belonging to B2R+–X2P1/2 and 0–0, 0–1, and 0–2 bands belonging to B2R+– X2P3/2. Mahieu et al. [12] reported rotational analyses of six vibrational bands attributed to the B2R+–X2Pr system for the most abundant isotopomer 74Ge35Cl. It has been established by these optical studies that the ground electronic state of GeCl is 2Pr following Hund’s coupling case (a) and the spin–orbit splitting between the 2 P3/2 and 2P1/2 substates is about 973 cm1 [11,12]. The K-doubling constant p in the ground vibronic state has been reported in Refs. [11] and [12] as 0.0102(2) and 0.001774(25) cm1, respectively, which disagree in the magnitude as well as in the sign.

* Corresponding author. Fax: +81 92 642 2607. E-mail address: [email protected] (K. Tanaka). 1 Emeritus professor of Kyushu University. 0022-2852/$ - see front matter Ó 2008 Published by Elsevier Inc. doi:10.1016/j.jms.2008.04.007

The electronic states, potential energy curves, and spectroscopic properties of the GeCl radical were calculated by Liao and Balasubramanian [17]. Their ab initio calculations using the CASSCF method in FOCI level gave the bond length and electric dipole moment in the X2Pr state as follows; re = 2.228 Å and le = 2.224 D. In the present study, we observed microwave transitions of the GeCl radical generated in a discharge of germanium tetrachloride GeCl4 diluted with argon, including those in the 2P3/2 substate, which is almost 1000 cm1 above the 2P1/2 substate. We obtained accurate molecular constants in the ground vibronic state from the present work, including precise values of the K-doubling constants p0 and q0. The equilibrium bond length re is determined from the equilibrium constant Be obtained by analyzing the mass dependence of the rotational constants for seven isotopomers. 2. Experimental details A 83 kHz source modulation spectrometer equipped with a 1.6 m long free-space absorption cell at Kyushu University, of which details have been described in our previous paper [18], was used for the present measurement. We predicted the frequencies of pure rotational transitions in the 2P1/2 substate of the GeCl radical by using the molecular constants transferred from those of the B–X system [12]. The J = 15.5–14.5 transition of 74Ge35Cl was first searched for in the frequency region around 140 GHz, using a glow discharge of pure germanium tetrachloride GeCl4. A large number of strong absorption lines with a lifetime which seemed rather longer than that expected for the GeCl radical were observed. Most of the observed lines were identified as due to germanium dichloride GeCl2 [18]. Because magnetic dipole moments generated by the electronic orbital motion and electron spin

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K. Tanaka et al. / Journal of Molecular Spectroscopy 251 (2008) 369–373

almost cancel in the 2P1/2 substate (the g-factor is estimated to be less than 103), the Zeeman effect could not be used to distinguish the lines of the radical from those of GeCl2. We expected that the lifetime of the GeCl radical is much shorter than that of GeCl2, and we tried to separate the lines of the radical from those of GeCl2 by observing the decay of the signal when the discharge was switched off. The method worked well, and we found a pair of short-lived absorption lines which were seemingly a K doublet at 140 465 MHz and 140 490 MHz, 200 MHz above the predicted frequencies. Fig. 1 shows the J = 15.5–14.5 transition of 74Ge35Cl in the 2P1/2 substate split into a doublet with a splitting of about 25 MHz. Experimental conditions were then optimized by monitoring the strength of these signals. Optimum pressures were 25 mTorr for GeCl4 and 50 mTorr for Ar; dilution with Ar suppressed the intensity of the GeCl2 lines to about 1/4, leaving the GeCl signals intact. The dc discharge current was optimized at 50 mA. Under these optimum conditions, we searched for other transitions in the region of 104–168 GHz, and found seven more pairs of shortlived lines of 74Ge35Cl with splittings of about 25 MHz. The corresponding transitions of six other isotopomers (72Ge35Cl, 70Ge35Cl, 76 Ge35Cl, 74Ge37Cl, 72Ge37Cl, 70Ge37Cl) were then searched for in the region of 104–172 GHz, and 84 more lines were assigned, to confirm the isotopomer assignment. We could not detect isotopomers less abundant than 70Ge37Cl, nor the 73Ge35Cl species, of which the line strength is distributed among hyperfine components caused by the 73Ge nuclear spin I = 9/2 so that individual lines are too weak, although the natural abundance of this species is comparable to that of the 76Ge35Cl species. The microwave spectrum of the GeCl radical in the 2P3/2 substate was observed by accident while we tried to detect the germanium monochloride cation GeCl+ by using a hollow cathode discharge in GeCl4 diluted with Ar. We have shown that a hollow cathode discharge is a useful method to generate Group 14–17 diatomic cations, SiF+ [19], SiCl+ [20], GeF+ [21,22]. In the present study, we used a 60 cm long hollow cathode made of stainless steel sheet and a 2 mm diameter stainless steel rod as an anode. These electrodes were placed with a separation of 10 cm between them in an absorption cell made of a Pyrex glass tube with a diameter of 10 cm. Around the cell was wound a solenoid of enameled wire which provided an axial magnetic field of 5.5 Gauss/A. The cell could be cooled by circulating liquid nitrogen. We observed at 143 252 MHz a line which was sensitively affected by the applied magnetic field. Since we have learned in our previous studies [19–22] that the lines of cations generated

in a hollow cathode discharge lose intensity with the applied magnetic field, we took this line as a candidate of a GeCl+ line. However, this was disapproved because we could observe expected absorption lines neither 2B above nor 2B below, where B is the rotational constant estimated for the GeCl+ cation, which should have integral rotational quantum numbers. Meanwhile it was proved that the carrier of the 143 252 MHz signal is a diatomic species composed of 70Ge and 35Cl by the observation of isotopically related lines due to the species containing 72Ge and 74Ge. It also turned out by the confirmation of the lines located 2B above and 2B below that half-integral rotational quantum numbers are assigned to them. Finally these signals were identified as due to the GeCl radical in the 2P3/2 substate, because the magnetic-field effect could be explained by the Zeeman effect. In this measurement, the optimum conditions were pressures of 10 mTorr for GeCl4 and 100 mTorr for Ar and a dc discharge current of 500 mA. The strength of lines in the 2P3/2 substate increased with the discharge current until it was saturated around 500 mA, in contrast to the intensity of lines in the 2P1/2 substate which reached a peak at about 50 mA. The cathode was kept at low temperatures by close contact with the cell wall; the temperature was about 60 °C as measured on the outer surface. Finally, five lines were observed for each of the three isotopomers (74Ge35Cl, 72Ge35Cl, 70Ge35Cl) in the 2P3/2 substate. Fig. 2 shows the J = 18.5–17.5 transition in the 2P3/2 substate of 74Ge35Cl, in which the lower trace shows the signal broadened by the Zeeman effect with a magnetic field of 100 Gauss. Table 1 summarizes all observed frequencies of the GeCl radical in the ground vibronic state for the 2P1/2 as well as 2P3/2 substate. No hyperfine splittings due to the chlorine nuclear spin were resolved for the lines observed in the present measurement.

Fig. 1. The J = 15.5–14.5 transition of 74Ge35Cl in the 2P1/2 spin substate with K doubling. The e/f parity assignment is chosen by assuming that p0 + 2q0 is positive. See text. The radical was produced in the positive column of a dc glow discharge with a current of 50 mA through a flowing mixture of 25 mTorr GeCl4 and 50 mTorr Ar.

Fig. 2. The J = 18.5–17.5 transition of 74Ge35Cl in the 2P3/2 spin substate. Top trace: spectrum observed with no external magnetic field. Bottom trace: spectrum broadened by the Zeeman effect with a magnetic field of 100 G. The radical was produced in a hollow cathode discharge with a current of 500 mA through a mixture of 10 mTorr GeCl4 and 100 mTorr Ar.

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K. Tanaka et al. / Journal of Molecular Spectroscopy 251 (2008) 369–373 Table 1 Millimeter-wave spectrum of GeCl J0 –J00 74

Ge35Cl

P1/2 11.5–10.5

13.5–12.5 14.5–13.5 15.5–14.5 16.5–15.5 17.5–16.5 18.5–17.5 Ge35Cl

72

Ge35Cl

P3/2 14.5–13.5 15.5–14.5 16.5–15.5 17.5–16.5 18.5–17.5 P1/2 11.5–10.5

14.5–13.5 15.5–14.5 16.5–15.5 17.5–16.5 18.5–17.5

70

Ge35Cl

P3/2 14.5–13.5 15.5–14.5 16.5–15.5 17.5–16.5 18.5–17.5 P1/2 11.5–10.5

14.5–13.5 15.5–14.5 16.5–15.5 17.5–16.5 18.5–17.5

76

Ge35Cl

104225.410 104250.922 113286.620 113312.036 122347.072 122372.336 131406.696 131431.845 140465.385 140490.454 149523.170 149548.146 158579.994 158604.808 167635.693 167660.401

30 2 7 15 15 16 29 11 12 19 16 5 20 9 5 13

e+f e+f e+f e+f e+f

131601.881 140673.079 149743.434 158812.735 167880.921

38 23 18 13 40

e f e f e f e f e f e f e f e f

105154.441 105180.234 114296.342 114321.955 123437.437 123462.869 132577.717 132603.073 141717.099 141742.396 150855.590 150880.739 159992.982 160018.084 169129.357 169154.304

23 269d 22 153d 12 7 26 7 41 0 13 8 11 12 32 3

e+f e+f e+f e+f e+f

132774.915 141927.031 151078.336 160228.205 169377.206

22d 18 210d 8 7

e f e f e f e f e f e f e f e f

106135.688 106161.490 115362.914 115388.685 124589.378 124615.023 133814.890 133840.483 143039.501 143065.022 152263.157 152288.575 161485.797 161511.084 170707.291 170732.488

18 84d 15 4 73d 13 30 9 1 4 9 3 7 7 19 7

e+f e+f e+f e+f e+f

134014.072 143251.762 152488.163 161723.611 170958.093

246d 15 91d 75 83

e f e f

121313.607 121338.641 130296.698 130321.680

J0 –J00

Paritya

Observedb

15.5–14.5

e f e f e f e f

139279.047 139303.855 148260.222 148285.002 157240.633 157265.272 166219.874 166244.503

103d 29 40 51 39 17 8 28

e f e f e f e f e f e f e f e f

109138.187 109162.696 117866.970 117891.402 126595.055 126619.263 135322.200 135346.307 144048.489 144072.594 152773.954 152797.888 161498.229 161522.212 170221.569 170245.370

104d 22 74d 39 20 22 7 75 13 4 91d 12 7 52 8 22

e f e f e f e f e f e f

110147.889 110172.539 118957.451 118981.807 136574.040 136598.368 145381.008 145405.358 154187.127 154211.223 162992.153 163016.217

29 1 36 148d 7 27 32 55 25 37 8 8

e f e f e f e f e f e f

120109.495 120133.836 129003.411 129028.328 137896.606 137921.193 146788.794 146813.370 155680.019 155704.472 164570.275 164594.617

28 430d 32 162d 37d 18 8 28 18 28d 15 10

16.5–15.5 17.5–16.5 18.5–17.5 74

Ge37Cl

P1/2 12.5–11.5 13.5–12.5 14.5–13.5 15.5–14.5 16.5–15.5 17.5–16.5 18.5–17.5 19.5–18.5

2

P1/2 13.5–12.5 14.5–13.5

Ge37Cl

2

P1/2 12.5–11.5 13.5–12.5 15.5–14.5 16.5–15.5 17.5–16.5 18.5–17.5

70

Ge37Cl

2

P1/2 13.5–12.5

15.5–14.5 16.5–15.5 17.5–16.5

2

P3/2 14.5–13.5 15.5–14.5 16.5–15.5 17.5–16.5 18.5–17.5

72

14 1 3 11

O–Cc

2

14.5–13.5

2

13.5–12.5

Ge35Cl

e f e f e f e f e f e f e f e f

2

12.5–11.5

70

O–Cc

2

13.5–12.5

Ge35Cl

Observedb

2

12.5–11.5

72

Paritya

2

12.5–11.5

74

Table 1 (continued)

18.5–17.5

a The e/f parity assignment is chosen by assuming that p0 + 2q0 is positive: see text. b In units of MHz. c Observed minus calculated frequency in units of kHz. d Not weighted in the analysis.

3. Analysis and results The effective Hamiltonian used for the present analysis is of a standard form for a diatomic molecule in the 2P electronic state, 1 H ¼ B0 ðN 2x þ N 2y Þ  D0 ðN 2x þ N 2y Þ2 þ A0 Lz Sz þ AD0 ½Lz Sz ; N 2x þ N 2y þ 2 p0 q0 2  ðLþþ S N  þ L Sþ N þ Þ þ ðLþþ N  þ L N 2þ Þ; ð1Þ 2 2 where B0 is the rotational constant, D0 the centrifugal distortion constant, A0 the spin–orbit coupling constant, and AD0 represents the centrifugal distortion of the spin–orbit coupling. The terms proportional to p0 and q0 cause K-type splittings, where L++ and L are operators connecting the eigenstates of Lz as follows;

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L jK ¼ 1i ¼ jK ¼ 1i:

ð2Þ

It is noted that the sign of the p0 as well as q0 constant depends on the assignment of the e/f parity to the K doublets. If e and f parities are assigned to low- and high-frequency components, respectively, we obtain p0 = 17.87(31), q0 = 4.06(18), and p0 + 2q0 = 25.984(39) MHz for the 74Ge35Cl species, whereas the reverse assignment results in p0 = 17.87(31), q0 = 4.06(18), and p0 + 2q0 = 25.984(39) MHz. There occur no changes in the absolute values of p0 and q0. Also, other spectroscopic constants remain unchanged. The e/f parity assignment corresponding to the positive value of p0 + 2q0 is given in Fig. 1 and Table 1.

Although explicit expressions of matrix elements may be found in many places, e.g., Eqs. (36)–(38) in Ref. [23] (also consult Ref. [24] and Hirota’s textbook [25]), they are given here for convenience in later sections.   1 1 H11 ¼ A0 þ 3D0 þ B0 þ 3D0 þ AD0 ðX 2  2Þ  D0 X 4 ð3Þ 2 2     1 1 1 H22 ¼  A0 þ D0 þ B0  D0  AD0 X 2  D0 X 4  q0 þ p0 X ð4Þ 2 2 2  pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 H12 ¼ H21 ¼  B0  2D0 ðX 2  1Þ  q0 X X2  1 ð5Þ 2 2

4. Discussion

2

In Eqs. (3–5), the subscripts 1 and 2 correspond to P3/2 and P1/2, respectively, and X = J + 1/2. As for , the upper and lower signs are for e and f parities, respectively. The observed frequencies in Table 1 for the 74Ge35Cl isotopomer were subjected to a least-squares fitting, in which the spectroscopic constants B0, D0, AD0, p0, and q0 were optimized. The spin– orbit coupling constant A0 was fixed at 973 cm1, which was reported in Ref. [12]. The same fitting procedure was applied to the spectra of the 72Ge35Cl and 70Ge35Cl species. For the species 76 Ge35Cl, 74Ge37Cl, 72Ge37Cl, and 70Ge37Cl, for which only the transitions in the 2P1/2 substate have been observed, the AD0 constant was fixed in addition to A0. The fixed values of AD0 were estimated by assuming that the AD0 constant is inversely proportional to the reduced mass. For example, the AD0 constant of 72Ge37Cl may be estimated by AD0 ð72 Ge37 ClÞ ¼ AD0 ð74 Ge35 ClÞ 

lð74 Ge35 ClÞ lð72 Ge37 ClÞ

¼ 4:74065 MHz:

The present analysis of the microwave spectrum gave accurate molecular constants in the ground vibronic state for seven different isotopomers of GeCl. Precise values of the K-doubling constants p0 and q0 were also determined. However, an ambiguous assignment of the e/f parity to K-doublet components resulted in the ambiguity in the absolute signs of the K-doubling constants, so that Table 2 lists jp0j, jq0j, and jp0 + 2q0j. Since the terms proportional to p0 and q0 have opposite signs in the energy matrices for e and f levels, as seen in Eqs. (3–5), we obtain exactly the same energy level scheme if the signs of p0 and q0 are inverted simultaneously, although the assignment of the e/f parity is reversed. Therefore, the e/f parity is indeterminable solely from the microwave spectrum. The determination is possible if high-resolution electronic spectrum connecting the present 2P state with a 2R state is observed, provided that it is certain whether the 2R state is 2R+ or 2  R . In fact, from rotational analyses of the B2R+–X2Pr system, Badowski and Zyrnicki [11] and Mahieu et al. [12] obtained the p constant as 0.0102(2) and 0.001774(25) cm1, respectively, which should be compared with the p0 + 2q0 value in the present study, whose absolute value is about 0.00085 cm1. Unfortunately, both reported values are inconsistent with the present result, and could not be used for the determination of the sign of p0 + 2q0. We have attempted without success to find what causes the discrepancy, although we confirmed that it is not due to the use of different forms of the effective Hamiltonian. The rotational constant B0 of 74Ge35Cl in Table 2, 4535.91396(70) MHz, is slightly different from the previous results, 4533.58 ± 0.050 MHz by Badowski and Zyrnicki [11] and 4527.7 ± 3.0 MHz by Mahieu et al. [12]. The ground-state rotational constant B0 is expressed by the equilibrium rotational constant Be and the vibration–rotation interaction constant ae as

ð6Þ

Similarly we obtain AD0(72Ge37Cl) = 4.73888 and 4.73906 MHz, respectively, using the observed values of 72Ge35Cl and 70Ge35Cl. The three estimated values are close to each other with an average deviation of 0.75 kHz. We adopt their average 4.73953 MHz as the value at which AD0 is fixed. It is noted that an error of 1 kHz in the fixed value of AD may cause an error of only 0.5 kHz in the optimized value of B0, and therefore we believe that the present fixed values are sufficiently accurate. The optimized spectroscopic constants are summarized in Table 2, with 1r uncertainties given in parentheses. The transition frequencies calculated from the optimized constants are compared with the observed frequencies, the differences being listed in the column ‘‘O–C” in Table 1. The standard deviations of the fit are given in Table 2 as rfit, which are consistent with the experimental accuracy. Table 2 also includes the values of p0 + 2q0, with the uncertainty calculated from the uncertainties of p0 and q0 combined with their correlation coefficient. The uncertainties of p0 + 2q0 are much smaller than those of p0 and q0 themselves, reflecting the fact that the K-type splittings of the transitions in the 2P1/2 substate are almost equal to p0 + 2q0, as seen from Eq. (4).

1 B0 ¼ Be  ae ; 2

ð7Þ

if higher-order terms are neglected. Since Be and ae have different isotopic dependence, being proportional to l1 and l3/2, respectively, where l is the reduced mass of the GeCl molecule, B0 values for seven isotopomers may be used to derive Be and ae. The Be and ae

Table 2 Spectroscopic constants of the GeCl radicala 74

Ge35Cl

72

70

76

B0 D0 AD0 jp0jc jq0jc

4535.91396(70) 2.5413(13) 4.87595(37) 17.87(31) 4.06(18)

4576.35148(87) 2.5877(15) 4.91764(42) 20.18(36) 2.86(20)

4619.0728(13) 2.6371(23) 4.96379(69) 19.44(53) 3.43(30)

4497.5834(16) 2.4963(28) 4.83355b 19.42(68) 3.07(39)

jp0 + 2q0jd

25.984(39)

25.903(48)

26.298(71)

25.564(96)

24.768(88)

25.102(90)

25.29(13)

MHz

rfit

22.6

21.5

35.4

33.8

36.8

36.1

29.9

kHz

a b c d

Ge35Cl

Ge35Cl

Ge35Cl

74

Ge37Cl

72

Ge37Cl

4369.7639(15) 2.3639(24) 4.69602b 19.28(60) 2.74(34)

4410.1976(16) 2.3956(29) 4.73953b 18.31(66) 3.40(37)

70

Ge37Cl

Unit

4452.9273(21) 2.4512(35) 4.78550b 19.38(85) 2.96(49)

MHz kHz MHz MHz MHz

Uncertainties in parentheses are 1r in units of the last digit. Fixed. See text. Absolute signs are not known except that p0 and q0 have the same sign. See text. Calculated from p0 and q0, where the uncertainty is estimated from the uncertainties of p0 and q0 combined with their correlation coefficient.

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K. Tanaka et al. / Journal of Molecular Spectroscopy 251 (2008) 369–373

constants as determined for the 74Ge35Cl species by a least-squares fitting of B0 for seven isotopomers are 4547.212(95) and 22.60(23) MHz, respectively. Although the observed B0 values of seven isotopomers are reproduced by the least-squares fitting with a standard deviation of 2.3 kHz, a strong statistical correlation between Be and ae (correlation coefficient of 99.996%) introduces large uncertainties in their values. In terms of the Dunham coefficients Ykl, B0 is given by B0 ¼ Y 01 þ

Y 11 Y 21 þ þ : 2 4

ð8Þ

Watson [26] presented the formula   me Ge me Cl Y kl ¼ lðk=2þlÞ U kl 1 þ Dkl þ Dkl M Ge M Cl

ð9Þ

for the isotopic dependence of the Dunham coefficients, where Ukl is the mass-independent Dunham coefficient, me the electron mass, Cl MGe and MCl atomic masses, and DGe kl and Dkl isotopically invariant parameters. The above analysis of ours to determine Be and ae correspond to the neglect of Y21 and higher-order terms as well as D parameters, and the results correspond to U01 = 107946.2(23) u MHz and U11 = 2614(22) u3/2 MHz. We also tried to determine DGe 01 and DCl 01 or U21, but no acceptable results were obtained. The equilibrium rotational constant obtained above, 4547.212(95) MHz, is larger than the reported result, 4530.73 MHz [12], by about 16.5 MHz, but the vibration–rotation interaction constant ae is in agreement with the previous value 22.78 MHz [12]. The equilibrium bond length re = 2.163739(23) Å is obtained from the present equilibrium rotational constant. This value agrees well with 2.1640 and 2.1620 Å reported for the 2P1/2 and 2P3/2 substates, respectively [11]. The ab initio calculation by Liao and Balasubramanian [17] gave a bond length which is longer by 0.064 Å than the present value. The present equilibrium bond length is about 0.0057 Å shorter than the equilibrium Ge–Cl distance in GeCl2, 2.169452(15) Å [18]. The harmonic vibrational frequency xe may be calculated from Be and De through the relation xe ¼ ð4B3e =De Þ1=2 :

Table 3 Summary of the constants derived for

Valuea

Unit

Be ae re xe xexe ke

4547.212(95) 22.60(23) 2.163739(23) 405.79(10) 1.569(22) 230.31(12)

MHz MHz Å cm1 cm1 N/m

a

Uncertainties in parentheses correspond to 1r in units of the last digit.

1.34 cm1, reported in Refs. [11] and [12], respectively. Some derived constants discussed above are summarized in Table 3 for convenience. The AD0 constant of 74Ge35Cl is determined as 4.87595(37) MHz, which is much more precise than the reported values, 8.57(6) MHz [11] and 7.90(10) MHz [12]. Acknowledgment The authors thank Professor Kozo Kuchitsu for reading the manuscript. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]

We obtain xe = 405.79(10) cm , where we use D0 instead of De. This value agrees with 408.75 cm1 determined by Mahieu et al. [12] as well as 405.41 and 406.28 cm1 for the 2P1/2 and 2P3/2 substates, respectively, reported by Badowski and Zyrnicki [11]. The force constant is calculated as ke = 230.31(12) N/m. This is stronger by about 11% than the Ge–Cl stretching force constant 206.6 N/m in GeCl2 [18], consistent with the shorter re distance. The relation

[14] [15] [16] [17] [18]

xe xe ¼ Be ð1 þ ae x e =6B2e Þ2

[23] [24] [25]

ð11Þ

derived by Pekeris [27] with the assumption of the Morse potential allows us to calculate the vibrational anharmonicity constant xexe = 1.569(22) cm1, which is compared with 1.917 cm1 and

Ge35Cl

Constant

ð10Þ 1

74

[19] [20] [21] [22]

[26] [27]

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