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The infrared spectrum of the AsD radical in its X3Σ− state, recorded by laser magnetic resonance
Journal of Molecular Spectroscopy 232 (2005) 167–173 www.elsevier.com/locate/jms
The infrared spectrum of the AsD radical in its X3R state, recorded by laser magnetic resonance Jesu´s Flores-Mijangos 1, Heiko Ganser 2, John M. Brown * The Physical and Theoretical Chemistry Laboratory, Department of Chemistry, South Parks Road, Oxford OX1 3QZ, UK Received 10 February 2005; in revised form 22 March 2005 Available online 12 May 2005
Abstract The infrared spectrum of the AsD radical in the X3R ground state has been recorded using CO laser magnetic resonance. The radical was formed by the reaction between D atoms and arsenic powder. Low-N transitions in the fundamental band and in the (2– 1) and (3–2) hot bands have been detected. Hyperfine structure from the 75As nucleus (I = 3/2) is seen on many of the resonances. These measurements have been combined with information from previous measurements of rotational transitions at sub-millimeter wavelengths [H. Fujiwara, K. Kobayashi, H. Ozeki, S. Saito, A.I. Jaman, J. Chem. Soc. Faraday Trans. 93 (1997) 1045–1051] to determine an extended and improved set of molecular parameters for 75AsD. Comparison is made with corresponding parameter values for AsH. 2005 Elsevier Inc. All rights reserved. Keywords: Spectroscopy; Free radicals; Laser magnetic resonance; Arsenic deuteride
1. Introduction The Group 5 (pnicogen) hydrides, NH, PH, AsH, SbH, and BiH, have been extensively studied by a variety of spectroscopic techniques. These include rotational, vibration–rotation, and electronic spectroscopy, all performed at high resolution. In many cases, the corresponding spectra of the deuteride have also been recorded and analyzed. An exception to this statement is the infrared spectrum of AsD radical which has not yet been observed. Accordingly, we have remedied this omission by recording the spectrum by CO laser magnetic resonance (LMR).
*
Corresponding author. Fax: +44 1865 275410. E-mail address: [email protected] (J.M. Brown). 1 Post-doctoral visitor from Instituto de Ciencias Nucleares, UNAM, Me´xico, D.F. 2 Present address: Asselner Hellweg 241, 44319 Dortmund, Germany. 0022-2852/$ - see front matter 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2005.04.001
The first spectroscopic observation of AsH was by Dixon et al. [1,2] who studied the A3P–X3R transition of both AsH and AsD in the mid-ultraviolet. It was almost 20 years later that the first rotational and vibrational spectra of AsH were recorded, by far-infrared LMR [3] and by infrared diode laser spectroscopy [4], respectively. The former study has been followed by an investigation of the rotational spectra of AsH and AsD at sub-millimeter wavelengths [5] and the latter has been extended by a study of the LMR spectrum of AsH in the infrared [6]. In addition, the b1R+–X3R electronic transition of AsH has been recorded by Arens and Richter [7]. More recently, the a1D–X3R transition of both AsH and AsD has been studied by Beutel et al. [8]. AsH has also been the subject of several recent theoretical studies [9–13], many of them designed to test effective core potentials for the inclusion of relativistic effects. These calculations are particularly useful for the interpretation of electronic transitions in AsH [8,13]. The aim of the present work was to record vibration– rotation transitions of AsD in its ground 3R state using
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CO LMR spectroscopy and so to determine or refine its rotational, vibrational and fine structure parameters (the rotational and fine structure parameters for AsD in the v = 0 vibrational level have been accurately determined in the sub-millimeter study [5]). This objective has been achieved; the vibrational constants xe, xexe, and xeye have been determined for the first time. The values determined for the various parameters make an interesting comparison with those obtained by isotopic scaling from the corresponding parameters of AsH.
2. Experimental details The AsD radicals were produced by the reaction between deuterium atoms and arsenic powder in the intracavity absorption cell of a CO LMR spectrometer; the arrangement was similar to the used to form AsH in our earlier study [6]. Deuterium atoms were produced in a 100 W microwave discharge through D2O vapour at a pressure of 100 mTorr flowing in a quartz tube. The products of the discharge were introduced into the cell through a Teflon sleeve directly onto the arsenic powder (Aldrich, 99.999%), which was glued to a PTFE sheet wrapped round to cover the lower half of the cell. The ends of the cell were purged with helium at a partial pressure of 5 mTorr to keep the calcium fluoride Brewster windows clean. The cell was cleaned whenever the arsenic powder was replaced which was necessary after about 5 h of experiment. The CO LMR spectrometer used in this study has been described elsewhere [14]. The CO laser was operated on selected lines towards the bottom end of its wavenumber range between 1400 and 1500 cm1. The absorption signals were Zeeman-modulated at 50 kHz and detected at twice this frequency with a lock-in amplifier.
3. Results and analysis 3.1. LMR observations; v = 1 ‹ 0 fundamental band Initial searches for lines in the v = 1–0 band AsD in the X3R state were based on predictions of transition frequencies at zero magnetic field, using molecular parameters from references [5] and [6], the latter scaled by the appropriate isotopic ratios [15] from those for AsH. Coincidences were sought on CO laser lines that fell with about 0.6 cm1 of the predicted transitions, using both parallel (DMJ = 0) and perpendicular (DMJ = 1) laser polarizations. The signals were relatively strong; most showed a quartet structure as a result of the 75As nuclear hyperfine structure (I = 3/2; the 2H hyperfine structure was not resolved). The transitions detected are summarized in Table 1. A representative
Table 1 Summary of mid-infrared LMR observations of the AsD free radical in its X3R state Transition
CO laser line
~mlaser ðcm1 Þ
v=1‹0 R33 (2)a Q23 (2) P22 (2) P22 (3)
23P (13) 24P (11) 24P (15) 25P (10)
1511.2354 1493.8127 1480.0923 1472.9135
v =2 ‹ 1 R22 (1) Q32 (U) P33 (3)
25P (11) 25P (15) 26P (13)
1469.6011 1456.0198 1438.8064
v =3 ‹ 2 R33 (2) Q23 (2)
27P (8) 27P (13)
1431.0183 1414.8045
a
The value of N00 is given in parentheses.
spectrum recorded at Doppler-limited resolution is shown in Fig. 1. The spectrum consists of the one detectable Zeeman component of the R33 (2) transition (N = 3 ‹ 2, J = 2 ‹ 1) recorded in parallel polarization; the four hyperfine components are clearly resolved. The other signals shown in the scan arise from some other, so far unidentified paramagnetic species; it is quite likely that it is AsD2 (see below). Fig. 2 shows another Zeeman component, this time from the P22 (3) transition. This transition is more slowly tuning and the As hyperfine structure is not resolvable with Doppler-limited linewidths. The structure can be seen however by the observation of saturation (Lamb) dips as shown in the figure. 3.2. Observations of the v = 2 ‹ 1 and 3 ‹ 2 hot bands Earlier work using the reaction between H atoms and arsenic [6] showed that the AsH radical was formed in excited vibrational levels as well as in the v = 0 level. We therefore looked for hot band transitions in AsD, using the estimated value for xexe scaled from that of AsH [6]. Transitions were detected in both the (2–1) and (3–2) hot bands with reasonable signal-to-noise ratios. These observations are also summarized in Table 2. Fig. 3 shows two Zeeman components, each with 75As hyperfine structure, arising from the R22 (1) transition in the (2–1) hot band. 3.3. Assignments and fitting of data The observed resonances were assigned in a straightforward manner by comparison with the predictions of a computer program. The assignments were fully substantiated by the details of the Zeeman pattern which consists of the resonant field, the relative intensity, the sign of the tuning rate and the linewidth (in mT) of the observed resonance. The details of the measurements
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169
Fig. 1. Part of the mid-IR LMR spectrum of the AsD radical in its X3R state, recorded at Doppler-limited resolution. The CO laser line is the 23P (13) line at 1511.2354 cm1 and the vibration–rotation transition involved is the R33 (2) line of the v = 1–0 band. The quartet at 425 mT is the MJ = 1 ‹ 1 Zeeman component of this transition showing resolved 75As nuclear hyperfine structure. The other, somewhat weaker features at lower field are associated with another molecule, most probably AsD2 (see text).
Fig. 2. Part of the mid-IR LMR spectrum of the AsD radical in its X3R state. The CO laser line is the 25P (10) line at 1472.9135 cm1 and the vibration–rotation transition involved is the P22 (3) line of v = 1 ‹ 0 band. The spectrum is recorded at sub-Doppler resolution through the observation of saturation (Lamb) dips; this allows the 75As nuclear hyperfine structure to be resolved on this slowly tuning transition. The figure shows the MJ = 1 ‹ 1 Zeeman component.
and their assignments are given in Table 2. The values of the tuning rates dm/dBz, which are also given, are those calculated by the computer program. The data were fitted with an effective Hamiltonian of the form H eff ¼ H ss þ H sr þ H rot þ H cd þ H hfs þ H Q þ H Z .
ð1Þ
The explicit forms of the spin–spin, spin–rotation, rotation, centrifugal distortion, magnetic hyperfine, electric quadrupole coupling, and Zeeman Hamiltonians have been given elsewhere [16,17]. The matrix representation in the computer program has been constructed in a HundÕs case (a) basis set. The vibrational dependence of the parameters of Heff are described by [14] 2
P v ¼ P e þ aP ðv þ 1=2Þ þ bP ðv þ 1=2Þ þ
ð2Þ
so that aB is opposite in sign to HerzbergÕs ae [15]. In the fit, some of the parameters were constrained to values obtained in other studies. For example, several parameters have been determined very accurately in the earlier millimeter-wave study of AsD in the v = 0 level, much more so than we could hope to achieve in the infrared LMR spectrum. These are the rotational and centrifugal
constants (B and D), the spin-rotation parameter and its centrifugal distortion correction (c and cD), the centrifugal distortion correction to the spin–spin parameter (kD) and the 75As nuclear hyperfine parameters (b, c, eqQ, and CI). In addition, we are not able to determine the spin–spin parameter k itself very accurately because we have not detected any transitions in which the spin quantum number R formally changes. We have therefore constrained the value of this parameter to that determined by Beutel et al. [8]. No vibrational dependence of the 75As hyperfine parameters was detectable in the fit. The fit was, however, quite sensitive to the detailed vibrational dependence of the spin–spin parameter k. Beutel et al. [8] modeled this as a simple linear dependence with the parameter ak even though their experimental values showed significant quadratic behavior. We found that the fit of our data was significantly improved by inclusion of the quadratic dependence. We therefore constrained the two parameters ak and bk in our fit to the values obtained by isotopic scaling of the values for AsH where the spin splittings are better determined [6], see Table 3 (ak l1/2 and bk l1, where l is the reduced mass of the molecule).
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Table 2 Details of the mid-infrared LMR spectrum of the AsD in its X3R state MI
a
M 0J
v=1‹0 R33 (2) 3/2 0 1/2 1/2 3/2 3/2 1 1/2 1/2 3/2 3/2 2 1/2 1/2 3/2 Q23 (2) 3/2 1 1/2 1/2 3/2 3/2 0 1/2 1/2 3/2 P22 (2) 3/2 1/2 1/2 3/2 3/2 1/2 1/2 3/2 P22 (3) 3/2 1/2 1/2 3/2 3/2 1/2 1/2 3/2 3/2 1/2 1/2 3/2 3/2 1/2 1/2 3/2 3/2 1/2 1/2 3/2 1/2 3/2
M 00J
1
1
1
0
1
1
0
1
1
2
1
1
0
2
2
1
1
2
3
0
1
v=2‹1 R22 (1) 3/2 0 1/2 1/2 3/2 3/2 1
1
1
Bobsb (mT)
o cc (·104 cm1)
T.R. (MHz/G)
mlaser = 1511.2354 cm1 399.64d 0.86 386.51d 1.27 371.51d 0.58 355.04d 2.74 436.27 0.92 427.01 0.15 416.99 0.75 406.14 1.91 484.21d 1.68 479.57d 1.33 475.56d 1.09 471.49d 0.38
0.9998 1.0128 1.0181 1.0203 0.9032 0.9092 0.9127 0.9139 0.7983 0.8005 0.8012 0.8003
mlaser = 1493.8127 cm1 786.31d 0.64 774.76d 0.09 d 762.33 0.14 748.97d 0.89 1094.94d 1.09 1074.23d 1.13 1055.25d 0.93 1037.94d 0.64
1.3449 1.3444 1.3443 1.3449 0.9663 0.9667 0.9675 0.9686
mlaser = 1480.0923 cm1 855.33 0.96 843.22 0.14 831.49 0.74 820.10 1.00 1242.99 5.56 1231.38 4.15 1219.73 3.23 1207.85 2.10
1.5066 1.5055 1.5048 1.5045 1.0552 1.0544 1.0539 1.0537
mlaser = 1472.9135 cm1 240.02 1.96 229.08 0.20 217.40 0.43 204.12 1.94 349.62d 0.008 338.66d 0.47 326.55d 0.82 314.03d 0.36 354.85d 0.86 343.51d 0.13 331.44d 0.22 318.85d 0.35 d 692.19 0.95 680.57d 0.38 668.08d 0.08 654.25d 0.42 689.30d 2.25 673.88d 1.53 661.40d 1.00 652.01d 0.91 642.10d 0.74 629.71d 1.06
0.6753 0.6755 0.6776 0.6827 0.4573 0.4576 0.4579 0.4587 0.4448 0.4445 0.4452 0.4471 0.2238 0.2238 0.2240 0.2242 0.2281 0.2280 0.2279 0.2280 0.2410 0.2408
mlaser = 1469.6011 cm1 650.25 3.22 638.08 3.75 626.06 5.28 614.60 5.73 948.84 1.72
1.4816 1.4801 1.4793 1.4792 1.0268
Table 2 (continued) MI
a
M 0J M 00J Bobsb (mT)
1/2 1/2 3/2
937.10 925.67 913.83
o cc (·104 cm1) 0.66 1.00 0.22
T.R. (MHz/G) 1.0258 1.0253 1.0252
mlaser = 1456.0198 cm1 306.83 3.30 294.28 3.00 283.02 3.91 272.92 5.16 0 419.16 2.31 401.86 3.36 384.04 3.67 365.75 4.07 1 1067.94d 0.48 1071.73d 0.60 1075.55d 0.98 1079.31d 1.44
1.4173 1.4183 1.4214 1.4251 1.0481 1.0446 1.0432 1.0446 0.3929 0.3935 0.3940 0.3943
mlaser = 1438.8064 cm1 471.69 0.64 447.75 0.64 427.01 1.55 408.28 2.29 1 1 510.72 0.46 493.27 0.42 479.20 0.25 465.36 0.73 1 2 553.78d 1.06 549.38d 0.66 542.62d 0.93 534.05d 1.37
1.0393 1.0260 1.0218 1.0234 0.9449 0.9302 0.9299 0.9302 0.8565 0.8534 0.8499 0.8470
v=3‹2 R33 (2) mlaser = 1431.0183 cm1 3/2 1 1 1222.47 2.37 1/2 1208.48 2.11 1/2 1194.43 0.85 3/2 1180.73 0.70 3/2 2 1 1358.75 3.05 3/2 1342.15 2.83
0.9260 0.9252 0.9250 0.9252 0.8374 0.8369
mlaser = 1414.8045 cm1 1 0 1056.94 2.42 1044.22 3.50 1032.55 4.85 1021.55 7.96 0 1 1437.17 6.76 1420.99 4.41 1404.14 4.42 1385.65 2.95
1.4736 1.4731 1.4730 1.4732 1.0897 1.0886 1.0878 1.0873
Q32 (1) 3/2 1/2 1/2 3/2 3/2 1/2 1/2 3/2 3/2 1/2 1/2 3/2 P33 (3) 3/2 1/2 1/2 3/2 3/2 1/2 1/2 3/2 3/2 1/2 1/2 3/2
Q23 (2) 3/2 1/2 1/2 3/2 3/2 1/2 1/2 3/2 a b c d
0
1
1
1
1
0
DMI = 0. Flux density not calibrated. mlaser mcalc. Resonance observed as a saturation (Lamb) dip.
In the least-squares fit, the basis set was truncated without loss in accuracy at DJ = ±2. Each datum was ascribed a weight equal to the inverse of the experimental uncertainty. The experimental uncertainties were estimated to be as follows: Doppler-limited peaks were assigned an uncertainty of 1 · 103 cm1 while Lambdip spectra were assigned a smaller uncertainty of 3 · 104 cm1. The standard deviation of the fit relative
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171
Fig. 3. Part of the mid-IR LMR spectrum of the AsD radical in its X3R state, recorded at Doppler-limited resolution. The CO laser line involved is the 25P (11) line at 1469.6011 cm1 and the vibration–rotation transition is the R22(1) line of the v = 2 ‹ 1 hot band. The two Zeeman components are MJ = 0 ‹ 1 (290 mT) and MJ = 1 ‹ 0 (400 mT) of this transition, each showing resolved 75As nuclear hyperfine structure. Table 3 Molecular parameters for
75
AsD in the X3R state
Parameters This worka m0 xexe xeye B0 aB D0 · 105 k0 ak bk kD · 105 c0 ac cD · 105 b b+c eqQ CI · 106 gS gel gN
1495.304836(50) 19.89666(13) 0.013756(23) 3.66838534 0.0765423(74) 8.609 58.8078 0.0558b 0.0106b 3.999 0.1394194 0.005451(53) 1.308 0.0048868 0.0110783 0.0032819 9.44 2.0020 0.01229(56) 0.959647c
Fujiwara et al. [5] Beutel et al. [8]
3.66838534(50) 8.609(13)
3.999(70) 0.1394194(60) 1.308(50) 0.0048868(18) 0.0110783(40) 0.0032819(53) 9.44(40)
3.668262(9) 0.07653(8) 8.54 58.8078(3) 0.026(6) 3.6(2) 0.13940(4) 0.0053(3) 1.34(3)
Values quoted in cm1, except for g-factors; the number in parentheses corresponds to one standard deviation of the least-squares fit, in units of the last quoted decimal place. b Values calculated using the isotopic scaling factors from the ak and bk values of AsH [6]. c Value quoted in terms of the nuclear magneton lN. a
to experimental uncertainty was 0.3319, a value which is more than satisfactory. The parameter values obtained in the final fit, including the v = 2 ‹ 1 and v = 3 ‹ 2 hot band data, are given in Table 3. The residuals of the experimental measurements obtained in this fit are given in Table 2, along with the calculated tuning rates dm/dBz.
4. Discussion Measurement of lines in the v = (1–0), (2–1), and (3– 2) bands of the 75AsD radical have been made by infra-
red LMR spectroscopy and analyzed to determine the vibrational dependencies of several molecular parameters. In particular, accurate values for m10, xexe, and xeye have been determined for the first time. These values, given in Table 3, imply a value for the harmonic wavenumber xe of 1535.1431(24) cm1. For comparison, the isotopically scaled values from the vibrational parameters for AsH [6] are 1534.8266, 19.8865, and 0.01465 cm1. There is, in particular, a significant difference between the experimental and scaled values for xe; this is a manifestation of the breakdown of the Born–Oppenheimer approximation. Watson [18] has introduced a dimensionless parameter DA kl to describe both the non-adiabatic and Dunham corrections from atom A to the isotopic scaling factors for the Dunham coefficient Ykl. In the case of the harmonic wavenumber of AsH, the value for DH 10 is determined from the present observations to be 0.7574. Values are also determined for the vibrational dependencies of the rotational constant B and the spin–rotation parameter c, see Table 3. These values are in good agreement with those determined earlier by Beutel et al. [8] but are more accurate. Harmonic and anharmonic vibrational parameters for all members of the Group V diatomic hydrides have now been determined experimentally. The best values that are currently available (for the dominant isotopomers) are collected in Table 4. The trend in the harmonic wavenumber xe down the group is in accord with a steady reduction in the force constant. There is an intriguing change in sign of the second harmonic parameter xeye between PH and AsH which presumably reflects a systematic change in shape of the potential energy function. The fact that BiH does not conform to this general pattern is probably not significant; for this molecule, vibrational intervals have only been measured for the lowest spin component, 3 R 0 [22]. LMR data also provide information on the magnetic properties of the AsD radical. In the present study, we have chosen to constrain the electron spin g-factor gS to the relativistically adjusted value of 2.0020 [24].
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Table 4 Vibrational parameters (in cm1) for the Group V diatomic hydrides in their X3R states Molecule 14
NH PH 75 AsH 121 SbH 209 BiH 14 ND 32 PD 75 AsD 121 SbD 209 BiD 32
a b c
m0 a
3125.57178(14) 2276.20901(51) 2076.92528(89) 1854.17310(18) 1635.75219(40)b 2315.23753(23) 1653.2909(48) 1495.304836(50) 1331.25546(21) 1173.35513(4)b
xe
xexe
xeye
Ref.
3282.721(99) 2363.774(36) 2155.5026(20) 1921.8348(28) 1699.51700(42) 2399.126(30) 1698.6046(48) 1535.14286(28) 1365.4829(50) 1205.42257(34)
79.042(80) 43.907(27) 39.22272(87) 33.6591(22) 31.92533(35) 42.106(21) 22.72071(22) 19.89666(13) 17.0781(37) 16.05000(21)
0.367(23) 0.1059(73) 0.04058(13) 0.20556(48) 0.03825(11) 0.1203(54) 0.0393c 0.013756(23) 0.02171(80) 0.013017(37)
[19] [20] [6] [21] [22] [20] [23] Present work [21] [22]
The figures in parentheses are the authorsÕ estimate of uncertainty (lr) in units of the last quoted decimal place. The values for BiH and BiD refer to the lowest spin component, with X = 0, only. Value scaled from the corresponding parameter for PH.
With this assumption, the data imply that the value for the anisotropic correction to the electron spin g factor, gl, is 0.01229(56). This is in only moderately good agreement with the value of 0.0190 predicted from CurlÕs relationship [25] gl ¼ c=ð2BÞ.
H.G. thanks the Leverhulme Trust for financial support. We are also grateful to Jeni Tod for assistance with some of the measurements.
ð3Þ
CurlÕs relationship is based on the admixture of remote electronic states of the same multiplicity into the state in question (in this case the admixture of excited triplet states into the X3R state). It does not however take account of the spin–orbit mixing of the b1R+ state into the ground state, a mixing which is responsible for the large spin–spin splitting of 115.8 cm1 in the X3R state. The effect of this mixing is to introduce some singlet character into the X = 0+ component of the ground state but not into the X = ±1 components (at least not directly). Such differential mixing can be modeled as an additional contribution to gl dgl ¼ ð1 c1 ÞgS ;
ð4Þ
where c1 ¼ ½1 þ j2k=ðE3 R E1 R Þj
Acknowledgments
1=2
.
ð5Þ
In the case of AsD (and AsH), the extra contribution to gl can be calculated to be 0.0082, leading to an improved value for gl of 0.0108, in much better agreement with the experimental value. Several other resonances were observed in this work that could not be assigned to the AsD radical in either its X3R or its a 1D states; a typical example is shown in Fig. 1. In most cases, these resonances showed the 75 As quartet hyperfine structure implying that the molecule contains a single As atom. The most likely carrier is AsD2; both the symmetric m1 and anti-symmetric m3 stretching vibrations are expected to fall in this wavenumber region. Similar resonances were observed in the previous LMR study of AsH [6].
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The infrared spectrum of the AsD radical in its X3R state, recorded by laser magnetic resonance Jesu´s Flores-Mijangos 1, Heiko Ganser 2, John M. Brown * The Physical and Theoretical Chemistry Laboratory, Department of Chemistry, South Parks Road, Oxford OX1 3QZ, UK Received 10 February 2005; in revised form 22 March 2005 Available online 12 May 2005
Abstract The infrared spectrum of the AsD radical in the X3R ground state has been recorded using CO laser magnetic resonance. The radical was formed by the reaction between D atoms and arsenic powder. Low-N transitions in the fundamental band and in the (2– 1) and (3–2) hot bands have been detected. Hyperfine structure from the 75As nucleus (I = 3/2) is seen on many of the resonances. These measurements have been combined with information from previous measurements of rotational transitions at sub-millimeter wavelengths [H. Fujiwara, K. Kobayashi, H. Ozeki, S. Saito, A.I. Jaman, J. Chem. Soc. Faraday Trans. 93 (1997) 1045–1051] to determine an extended and improved set of molecular parameters for 75AsD. Comparison is made with corresponding parameter values for AsH. 2005 Elsevier Inc. All rights reserved. Keywords: Spectroscopy; Free radicals; Laser magnetic resonance; Arsenic deuteride
1. Introduction The Group 5 (pnicogen) hydrides, NH, PH, AsH, SbH, and BiH, have been extensively studied by a variety of spectroscopic techniques. These include rotational, vibration–rotation, and electronic spectroscopy, all performed at high resolution. In many cases, the corresponding spectra of the deuteride have also been recorded and analyzed. An exception to this statement is the infrared spectrum of AsD radical which has not yet been observed. Accordingly, we have remedied this omission by recording the spectrum by CO laser magnetic resonance (LMR).
*
Corresponding author. Fax: +44 1865 275410. E-mail address: [email protected] (J.M. Brown). 1 Post-doctoral visitor from Instituto de Ciencias Nucleares, UNAM, Me´xico, D.F. 2 Present address: Asselner Hellweg 241, 44319 Dortmund, Germany. 0022-2852/$ - see front matter 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2005.04.001
The first spectroscopic observation of AsH was by Dixon et al. [1,2] who studied the A3P–X3R transition of both AsH and AsD in the mid-ultraviolet. It was almost 20 years later that the first rotational and vibrational spectra of AsH were recorded, by far-infrared LMR [3] and by infrared diode laser spectroscopy [4], respectively. The former study has been followed by an investigation of the rotational spectra of AsH and AsD at sub-millimeter wavelengths [5] and the latter has been extended by a study of the LMR spectrum of AsH in the infrared [6]. In addition, the b1R+–X3R electronic transition of AsH has been recorded by Arens and Richter [7]. More recently, the a1D–X3R transition of both AsH and AsD has been studied by Beutel et al. [8]. AsH has also been the subject of several recent theoretical studies [9–13], many of them designed to test effective core potentials for the inclusion of relativistic effects. These calculations are particularly useful for the interpretation of electronic transitions in AsH [8,13]. The aim of the present work was to record vibration– rotation transitions of AsD in its ground 3R state using
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CO LMR spectroscopy and so to determine or refine its rotational, vibrational and fine structure parameters (the rotational and fine structure parameters for AsD in the v = 0 vibrational level have been accurately determined in the sub-millimeter study [5]). This objective has been achieved; the vibrational constants xe, xexe, and xeye have been determined for the first time. The values determined for the various parameters make an interesting comparison with those obtained by isotopic scaling from the corresponding parameters of AsH.
2. Experimental details The AsD radicals were produced by the reaction between deuterium atoms and arsenic powder in the intracavity absorption cell of a CO LMR spectrometer; the arrangement was similar to the used to form AsH in our earlier study [6]. Deuterium atoms were produced in a 100 W microwave discharge through D2O vapour at a pressure of 100 mTorr flowing in a quartz tube. The products of the discharge were introduced into the cell through a Teflon sleeve directly onto the arsenic powder (Aldrich, 99.999%), which was glued to a PTFE sheet wrapped round to cover the lower half of the cell. The ends of the cell were purged with helium at a partial pressure of 5 mTorr to keep the calcium fluoride Brewster windows clean. The cell was cleaned whenever the arsenic powder was replaced which was necessary after about 5 h of experiment. The CO LMR spectrometer used in this study has been described elsewhere [14]. The CO laser was operated on selected lines towards the bottom end of its wavenumber range between 1400 and 1500 cm1. The absorption signals were Zeeman-modulated at 50 kHz and detected at twice this frequency with a lock-in amplifier.
3. Results and analysis 3.1. LMR observations; v = 1 ‹ 0 fundamental band Initial searches for lines in the v = 1–0 band AsD in the X3R state were based on predictions of transition frequencies at zero magnetic field, using molecular parameters from references [5] and [6], the latter scaled by the appropriate isotopic ratios [15] from those for AsH. Coincidences were sought on CO laser lines that fell with about 0.6 cm1 of the predicted transitions, using both parallel (DMJ = 0) and perpendicular (DMJ = 1) laser polarizations. The signals were relatively strong; most showed a quartet structure as a result of the 75As nuclear hyperfine structure (I = 3/2; the 2H hyperfine structure was not resolved). The transitions detected are summarized in Table 1. A representative
Table 1 Summary of mid-infrared LMR observations of the AsD free radical in its X3R state Transition
CO laser line
~mlaser ðcm1 Þ
v=1‹0 R33 (2)a Q23 (2) P22 (2) P22 (3)
23P (13) 24P (11) 24P (15) 25P (10)
1511.2354 1493.8127 1480.0923 1472.9135
v =2 ‹ 1 R22 (1) Q32 (U) P33 (3)
25P (11) 25P (15) 26P (13)
1469.6011 1456.0198 1438.8064
v =3 ‹ 2 R33 (2) Q23 (2)
27P (8) 27P (13)
1431.0183 1414.8045
a
The value of N00 is given in parentheses.
spectrum recorded at Doppler-limited resolution is shown in Fig. 1. The spectrum consists of the one detectable Zeeman component of the R33 (2) transition (N = 3 ‹ 2, J = 2 ‹ 1) recorded in parallel polarization; the four hyperfine components are clearly resolved. The other signals shown in the scan arise from some other, so far unidentified paramagnetic species; it is quite likely that it is AsD2 (see below). Fig. 2 shows another Zeeman component, this time from the P22 (3) transition. This transition is more slowly tuning and the As hyperfine structure is not resolvable with Doppler-limited linewidths. The structure can be seen however by the observation of saturation (Lamb) dips as shown in the figure. 3.2. Observations of the v = 2 ‹ 1 and 3 ‹ 2 hot bands Earlier work using the reaction between H atoms and arsenic [6] showed that the AsH radical was formed in excited vibrational levels as well as in the v = 0 level. We therefore looked for hot band transitions in AsD, using the estimated value for xexe scaled from that of AsH [6]. Transitions were detected in both the (2–1) and (3–2) hot bands with reasonable signal-to-noise ratios. These observations are also summarized in Table 2. Fig. 3 shows two Zeeman components, each with 75As hyperfine structure, arising from the R22 (1) transition in the (2–1) hot band. 3.3. Assignments and fitting of data The observed resonances were assigned in a straightforward manner by comparison with the predictions of a computer program. The assignments were fully substantiated by the details of the Zeeman pattern which consists of the resonant field, the relative intensity, the sign of the tuning rate and the linewidth (in mT) of the observed resonance. The details of the measurements
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169
Fig. 1. Part of the mid-IR LMR spectrum of the AsD radical in its X3R state, recorded at Doppler-limited resolution. The CO laser line is the 23P (13) line at 1511.2354 cm1 and the vibration–rotation transition involved is the R33 (2) line of the v = 1–0 band. The quartet at 425 mT is the MJ = 1 ‹ 1 Zeeman component of this transition showing resolved 75As nuclear hyperfine structure. The other, somewhat weaker features at lower field are associated with another molecule, most probably AsD2 (see text).
Fig. 2. Part of the mid-IR LMR spectrum of the AsD radical in its X3R state. The CO laser line is the 25P (10) line at 1472.9135 cm1 and the vibration–rotation transition involved is the P22 (3) line of v = 1 ‹ 0 band. The spectrum is recorded at sub-Doppler resolution through the observation of saturation (Lamb) dips; this allows the 75As nuclear hyperfine structure to be resolved on this slowly tuning transition. The figure shows the MJ = 1 ‹ 1 Zeeman component.
and their assignments are given in Table 2. The values of the tuning rates dm/dBz, which are also given, are those calculated by the computer program. The data were fitted with an effective Hamiltonian of the form H eff ¼ H ss þ H sr þ H rot þ H cd þ H hfs þ H Q þ H Z .
ð1Þ
The explicit forms of the spin–spin, spin–rotation, rotation, centrifugal distortion, magnetic hyperfine, electric quadrupole coupling, and Zeeman Hamiltonians have been given elsewhere [16,17]. The matrix representation in the computer program has been constructed in a HundÕs case (a) basis set. The vibrational dependence of the parameters of Heff are described by [14] 2
P v ¼ P e þ aP ðv þ 1=2Þ þ bP ðv þ 1=2Þ þ
ð2Þ
so that aB is opposite in sign to HerzbergÕs ae [15]. In the fit, some of the parameters were constrained to values obtained in other studies. For example, several parameters have been determined very accurately in the earlier millimeter-wave study of AsD in the v = 0 level, much more so than we could hope to achieve in the infrared LMR spectrum. These are the rotational and centrifugal
constants (B and D), the spin-rotation parameter and its centrifugal distortion correction (c and cD), the centrifugal distortion correction to the spin–spin parameter (kD) and the 75As nuclear hyperfine parameters (b, c, eqQ, and CI). In addition, we are not able to determine the spin–spin parameter k itself very accurately because we have not detected any transitions in which the spin quantum number R formally changes. We have therefore constrained the value of this parameter to that determined by Beutel et al. [8]. No vibrational dependence of the 75As hyperfine parameters was detectable in the fit. The fit was, however, quite sensitive to the detailed vibrational dependence of the spin–spin parameter k. Beutel et al. [8] modeled this as a simple linear dependence with the parameter ak even though their experimental values showed significant quadratic behavior. We found that the fit of our data was significantly improved by inclusion of the quadratic dependence. We therefore constrained the two parameters ak and bk in our fit to the values obtained by isotopic scaling of the values for AsH where the spin splittings are better determined [6], see Table 3 (ak l1/2 and bk l1, where l is the reduced mass of the molecule).
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Table 2 Details of the mid-infrared LMR spectrum of the AsD in its X3R state MI
a
M 0J
v=1‹0 R33 (2) 3/2 0 1/2 1/2 3/2 3/2 1 1/2 1/2 3/2 3/2 2 1/2 1/2 3/2 Q23 (2) 3/2 1 1/2 1/2 3/2 3/2 0 1/2 1/2 3/2 P22 (2) 3/2 1/2 1/2 3/2 3/2 1/2 1/2 3/2 P22 (3) 3/2 1/2 1/2 3/2 3/2 1/2 1/2 3/2 3/2 1/2 1/2 3/2 3/2 1/2 1/2 3/2 3/2 1/2 1/2 3/2 1/2 3/2
M 00J
1
1
1
0
1
1
0
1
1
2
1
1
0
2
2
1
1
2
3
0
1
v=2‹1 R22 (1) 3/2 0 1/2 1/2 3/2 3/2 1
1
1
Bobsb (mT)
o cc (·104 cm1)
T.R. (MHz/G)
mlaser = 1511.2354 cm1 399.64d 0.86 386.51d 1.27 371.51d 0.58 355.04d 2.74 436.27 0.92 427.01 0.15 416.99 0.75 406.14 1.91 484.21d 1.68 479.57d 1.33 475.56d 1.09 471.49d 0.38
0.9998 1.0128 1.0181 1.0203 0.9032 0.9092 0.9127 0.9139 0.7983 0.8005 0.8012 0.8003
mlaser = 1493.8127 cm1 786.31d 0.64 774.76d 0.09 d 762.33 0.14 748.97d 0.89 1094.94d 1.09 1074.23d 1.13 1055.25d 0.93 1037.94d 0.64
1.3449 1.3444 1.3443 1.3449 0.9663 0.9667 0.9675 0.9686
mlaser = 1480.0923 cm1 855.33 0.96 843.22 0.14 831.49 0.74 820.10 1.00 1242.99 5.56 1231.38 4.15 1219.73 3.23 1207.85 2.10
1.5066 1.5055 1.5048 1.5045 1.0552 1.0544 1.0539 1.0537
mlaser = 1472.9135 cm1 240.02 1.96 229.08 0.20 217.40 0.43 204.12 1.94 349.62d 0.008 338.66d 0.47 326.55d 0.82 314.03d 0.36 354.85d 0.86 343.51d 0.13 331.44d 0.22 318.85d 0.35 d 692.19 0.95 680.57d 0.38 668.08d 0.08 654.25d 0.42 689.30d 2.25 673.88d 1.53 661.40d 1.00 652.01d 0.91 642.10d 0.74 629.71d 1.06
0.6753 0.6755 0.6776 0.6827 0.4573 0.4576 0.4579 0.4587 0.4448 0.4445 0.4452 0.4471 0.2238 0.2238 0.2240 0.2242 0.2281 0.2280 0.2279 0.2280 0.2410 0.2408
mlaser = 1469.6011 cm1 650.25 3.22 638.08 3.75 626.06 5.28 614.60 5.73 948.84 1.72
1.4816 1.4801 1.4793 1.4792 1.0268
Table 2 (continued) MI
a
M 0J M 00J Bobsb (mT)
1/2 1/2 3/2
937.10 925.67 913.83
o cc (·104 cm1) 0.66 1.00 0.22
T.R. (MHz/G) 1.0258 1.0253 1.0252
mlaser = 1456.0198 cm1 306.83 3.30 294.28 3.00 283.02 3.91 272.92 5.16 0 419.16 2.31 401.86 3.36 384.04 3.67 365.75 4.07 1 1067.94d 0.48 1071.73d 0.60 1075.55d 0.98 1079.31d 1.44
1.4173 1.4183 1.4214 1.4251 1.0481 1.0446 1.0432 1.0446 0.3929 0.3935 0.3940 0.3943
mlaser = 1438.8064 cm1 471.69 0.64 447.75 0.64 427.01 1.55 408.28 2.29 1 1 510.72 0.46 493.27 0.42 479.20 0.25 465.36 0.73 1 2 553.78d 1.06 549.38d 0.66 542.62d 0.93 534.05d 1.37
1.0393 1.0260 1.0218 1.0234 0.9449 0.9302 0.9299 0.9302 0.8565 0.8534 0.8499 0.8470
v=3‹2 R33 (2) mlaser = 1431.0183 cm1 3/2 1 1 1222.47 2.37 1/2 1208.48 2.11 1/2 1194.43 0.85 3/2 1180.73 0.70 3/2 2 1 1358.75 3.05 3/2 1342.15 2.83
0.9260 0.9252 0.9250 0.9252 0.8374 0.8369
mlaser = 1414.8045 cm1 1 0 1056.94 2.42 1044.22 3.50 1032.55 4.85 1021.55 7.96 0 1 1437.17 6.76 1420.99 4.41 1404.14 4.42 1385.65 2.95
1.4736 1.4731 1.4730 1.4732 1.0897 1.0886 1.0878 1.0873
Q32 (1) 3/2 1/2 1/2 3/2 3/2 1/2 1/2 3/2 3/2 1/2 1/2 3/2 P33 (3) 3/2 1/2 1/2 3/2 3/2 1/2 1/2 3/2 3/2 1/2 1/2 3/2
Q23 (2) 3/2 1/2 1/2 3/2 3/2 1/2 1/2 3/2 a b c d
0
1
1
1
1
0
DMI = 0. Flux density not calibrated. mlaser mcalc. Resonance observed as a saturation (Lamb) dip.
In the least-squares fit, the basis set was truncated without loss in accuracy at DJ = ±2. Each datum was ascribed a weight equal to the inverse of the experimental uncertainty. The experimental uncertainties were estimated to be as follows: Doppler-limited peaks were assigned an uncertainty of 1 · 103 cm1 while Lambdip spectra were assigned a smaller uncertainty of 3 · 104 cm1. The standard deviation of the fit relative
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171
Fig. 3. Part of the mid-IR LMR spectrum of the AsD radical in its X3R state, recorded at Doppler-limited resolution. The CO laser line involved is the 25P (11) line at 1469.6011 cm1 and the vibration–rotation transition is the R22(1) line of the v = 2 ‹ 1 hot band. The two Zeeman components are MJ = 0 ‹ 1 (290 mT) and MJ = 1 ‹ 0 (400 mT) of this transition, each showing resolved 75As nuclear hyperfine structure. Table 3 Molecular parameters for
75
AsD in the X3R state
Parameters This worka m0 xexe xeye B0 aB D0 · 105 k0 ak bk kD · 105 c0 ac cD · 105 b b+c eqQ CI · 106 gS gel gN
1495.304836(50) 19.89666(13) 0.013756(23) 3.66838534 0.0765423(74) 8.609 58.8078 0.0558b 0.0106b 3.999 0.1394194 0.005451(53) 1.308 0.0048868 0.0110783 0.0032819 9.44 2.0020 0.01229(56) 0.959647c
Fujiwara et al. [5] Beutel et al. [8]
3.66838534(50) 8.609(13)
3.999(70) 0.1394194(60) 1.308(50) 0.0048868(18) 0.0110783(40) 0.0032819(53) 9.44(40)
3.668262(9) 0.07653(8) 8.54 58.8078(3) 0.026(6) 3.6(2) 0.13940(4) 0.0053(3) 1.34(3)
Values quoted in cm1, except for g-factors; the number in parentheses corresponds to one standard deviation of the least-squares fit, in units of the last quoted decimal place. b Values calculated using the isotopic scaling factors from the ak and bk values of AsH [6]. c Value quoted in terms of the nuclear magneton lN. a
to experimental uncertainty was 0.3319, a value which is more than satisfactory. The parameter values obtained in the final fit, including the v = 2 ‹ 1 and v = 3 ‹ 2 hot band data, are given in Table 3. The residuals of the experimental measurements obtained in this fit are given in Table 2, along with the calculated tuning rates dm/dBz.
4. Discussion Measurement of lines in the v = (1–0), (2–1), and (3– 2) bands of the 75AsD radical have been made by infra-
red LMR spectroscopy and analyzed to determine the vibrational dependencies of several molecular parameters. In particular, accurate values for m10, xexe, and xeye have been determined for the first time. These values, given in Table 3, imply a value for the harmonic wavenumber xe of 1535.1431(24) cm1. For comparison, the isotopically scaled values from the vibrational parameters for AsH [6] are 1534.8266, 19.8865, and 0.01465 cm1. There is, in particular, a significant difference between the experimental and scaled values for xe; this is a manifestation of the breakdown of the Born–Oppenheimer approximation. Watson [18] has introduced a dimensionless parameter DA kl to describe both the non-adiabatic and Dunham corrections from atom A to the isotopic scaling factors for the Dunham coefficient Ykl. In the case of the harmonic wavenumber of AsH, the value for DH 10 is determined from the present observations to be 0.7574. Values are also determined for the vibrational dependencies of the rotational constant B and the spin–rotation parameter c, see Table 3. These values are in good agreement with those determined earlier by Beutel et al. [8] but are more accurate. Harmonic and anharmonic vibrational parameters for all members of the Group V diatomic hydrides have now been determined experimentally. The best values that are currently available (for the dominant isotopomers) are collected in Table 4. The trend in the harmonic wavenumber xe down the group is in accord with a steady reduction in the force constant. There is an intriguing change in sign of the second harmonic parameter xeye between PH and AsH which presumably reflects a systematic change in shape of the potential energy function. The fact that BiH does not conform to this general pattern is probably not significant; for this molecule, vibrational intervals have only been measured for the lowest spin component, 3 R 0 [22]. LMR data also provide information on the magnetic properties of the AsD radical. In the present study, we have chosen to constrain the electron spin g-factor gS to the relativistically adjusted value of 2.0020 [24].
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Table 4 Vibrational parameters (in cm1) for the Group V diatomic hydrides in their X3R states Molecule 14
NH PH 75 AsH 121 SbH 209 BiH 14 ND 32 PD 75 AsD 121 SbD 209 BiD 32
a b c
m0 a
3125.57178(14) 2276.20901(51) 2076.92528(89) 1854.17310(18) 1635.75219(40)b 2315.23753(23) 1653.2909(48) 1495.304836(50) 1331.25546(21) 1173.35513(4)b
xe
xexe
xeye
Ref.
3282.721(99) 2363.774(36) 2155.5026(20) 1921.8348(28) 1699.51700(42) 2399.126(30) 1698.6046(48) 1535.14286(28) 1365.4829(50) 1205.42257(34)
79.042(80) 43.907(27) 39.22272(87) 33.6591(22) 31.92533(35) 42.106(21) 22.72071(22) 19.89666(13) 17.0781(37) 16.05000(21)
0.367(23) 0.1059(73) 0.04058(13) 0.20556(48) 0.03825(11) 0.1203(54) 0.0393c 0.013756(23) 0.02171(80) 0.013017(37)
[19] [20] [6] [21] [22] [20] [23] Present work [21] [22]
The figures in parentheses are the authorsÕ estimate of uncertainty (lr) in units of the last quoted decimal place. The values for BiH and BiD refer to the lowest spin component, with X = 0, only. Value scaled from the corresponding parameter for PH.
With this assumption, the data imply that the value for the anisotropic correction to the electron spin g factor, gl, is 0.01229(56). This is in only moderately good agreement with the value of 0.0190 predicted from CurlÕs relationship [25] gl ¼ c=ð2BÞ.
H.G. thanks the Leverhulme Trust for financial support. We are also grateful to Jeni Tod for assistance with some of the measurements.
ð3Þ
CurlÕs relationship is based on the admixture of remote electronic states of the same multiplicity into the state in question (in this case the admixture of excited triplet states into the X3R state). It does not however take account of the spin–orbit mixing of the b1R+ state into the ground state, a mixing which is responsible for the large spin–spin splitting of 115.8 cm1 in the X3R state. The effect of this mixing is to introduce some singlet character into the X = 0+ component of the ground state but not into the X = ±1 components (at least not directly). Such differential mixing can be modeled as an additional contribution to gl dgl ¼ ð1 c1 ÞgS ;
ð4Þ
where c1 ¼ ½1 þ j2k=ðE3 R E1 R Þj
Acknowledgments
1=2
.
ð5Þ
In the case of AsD (and AsH), the extra contribution to gl can be calculated to be 0.0082, leading to an improved value for gl of 0.0108, in much better agreement with the experimental value. Several other resonances were observed in this work that could not be assigned to the AsD radical in either its X3R or its a 1D states; a typical example is shown in Fig. 1. In most cases, these resonances showed the 75 As quartet hyperfine structure implying that the molecule contains a single As atom. The most likely carrier is AsD2; both the symmetric m1 and anti-symmetric m3 stretching vibrations are expected to fall in this wavenumber region. Similar resonances were observed in the previous LMR study of AsH [6].
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