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The Lamb-dip spectrum of phosphine: The nuclear hyperfine structure due to hydrogen and phosphorus
Journal of Molecular Spectroscopy 239 (2006) 64–70 www.elsevier.com/locate/jms
The Lamb-dip spectrum of phosphine: The nuclear hyperfine structure due to hydrogen and phosphorus Gabriele Cazzoli *, Cristina Puzzarini Dipartimento di Chimica ‘‘G. Ciamician’’, Universita` di Bologna, Via Selmi 2, I-40126 Bologna, Italy Received 17 March 2006; in revised form 30 May 2006 Available online 6 June 2006
Abstract For the first time, the hyperfine structure of the rotational J = 1 ‹ 0 (K = 0) and J = 2 ‹ 1 (K = 0, 1) transitions of phosphine has been resolved by using microwave spectroscopy. To this purpose, the Lamb-dip technique has been employed. In addition, the J = 3 ‹ 2 (K = 0, 1, 2) transition has been recorded at Doppler resolution. The present investigation allowed us to provide accurate values for most of the hyperfine constants as well as ground state rotational parameters. 2006 Elsevier Inc. All rights reserved. Keywords: Lamb-dip spectroscopy; Rotational spectrum; Hyperfine structure; Phosphine
1. Introduction The first microwave measurements of the J = 1 ‹ 0 (K = 0) and J = 2 ‹ 1 (K = 0, 1) transitions of phosphine were carried out long time ago in Gordy’s group [1,2] with an accuracy of 0.04 MHz for the first and an accuracy of about 0.2 MHz for the latest [2]. In Ref. [2] the B0, DJ and DJK constants were determined for the first time employing microwave data only. Subsequently, the ‘‘forbidden’’ rotational spectra of PH3 (DJ = 0, DK = ±3) were investigated by Chu and Oka [3] and then by Helms and Gordy [4]. These measurements allowed the first determination of the C0 and DK rotational parameters. In the following years, observations of rotational and ‘‘forbidden’’ rotational spectra were extended up 1 THz by Belov et al. [5,6] allowing the improvement of the rotational parameters determined so far as well as the determination of sextic and octic centrifugal distortion constants [6]. In 1985, a re-analysis of all the data available in the literature was performed by Tarrago and Dang Nhu employing a new formulation which accounts for the DK = ±3 and ±6
*
Corresponding author. Fax: +39 051 209 9456. E-mail address: [email protected] (G. Cazzoli).
0022-2852/$ - see front matter 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2006.05.019
resonance terms through diagonalization of the energy matrix [7]. As far as the hyperfine parameters are concerned, in 1971 Davies et al. observed the electric resonance spectrum of phosphine at zero electric field for the three rotational states J = 4, 5 and 7 with K = 3; in addition, the J = K = 1 and J = K = 2 spectra were recorded at several values for the electric field [8]. All these measurements allowed the accurate evaluation of the electric dipole moment as well as of the determinable spin–rotation constants of 31P and H, where the adjective ‘‘determinable’’ refers to those hyperfine parameters that can be evaluated by conventional spectroscopic techniques. Finally, it should be noted that the observations carried out by both Gordy’s group and Davies and co-workers showed that inversion doubling must be negligible for phosphine: it was estimated to be less than 1 kHz. Similarly, no evidence of inversion doubling has been found in the present investigation. 2. Experimental details To resolve the hyperfine structure (hfs) due to the 31P and H nuclei of the J = 1 ‹ 0 and J = 2 ‹ 1 rotational transitions of phosphine, PH3, the Lamb-dip technique
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Fig. 1. The J = 10 ‹ 00 transition of PH3. The simulations of the spectrum containing only hyperfine components, only ghost transitions and both hyperfine components and crossing resonances are reported together with the experimental spectrum recorded at P = 0.2 mTorr employing a modulation depth of 8 kHz.
Fig. 2. The J = 2 ‹ 1 transition of PH3 is shown: the top panel reports the K = 0 component, the lower panel reports the K = 1 component. The K = 0 spectrum has been recorded at a pressure of 0.2 mTorr and with a modulation depth of 9 kHz. The K = 1 spectrum has been recorded at a pressure of 0.2 mTorr and with a modulation depth of 36 kHz. The asterisks mark the most relevant cross-over transitions.
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has been used. To this purpose, a frequency modulated computer-controlled spectrometer has been employed using a conventional free space cell, as shown in Ref. [9]. To increase the sensitivity of the spectrometer as well as the Lamb-dip effect the radiation path has been doubled (for details see Ref. [10]). A detailed description of the spectrometer is given in Ref. [11], whereas an extensive description of our experimental set up for performing sub-Doppler resolution spectroscopy can be found in various previous papers [12–15]. Therefore, here, we shortly report the main details related to the present investigation. The millimeter and submillimeter-wave sources employed are either frequency multipliers driven by gunn diode oscillators or gunn diodes themselves covering, on the whole, the frequency range 80–800 GHz. The source is phaselocked to a Rubidium frequency standard, and the frequency modulation is obtained by sine-wave modulating the 90 MHz local oscillator of the synchronization loop. A liquid Helium-cooled InSb detector has been used and its output is processed by means of a Lock-in amplifier tuned at twice the modulation frequency, so that the second derivative of the natural line profile has been recorded. The Lamb-dip measurements have been carried out at pressures of about 0.2 mTorr. Such low values of working pressure have been chosen in order to minimize as much as possible the dip widths as well as to avoid pressure frequency shift effects. The modulation depth used has been adjusted in the ranges 6–36 kHz according to the experimental conditions and the transition under consideration. As concerns the modulation frequency, it has been kept fixed at 1.666 kHz. In addition, in order to have narrow and not distorted dips, the source power has adequately been reduced. As far as the J = 3 ‹ 2 (K = 0, 1, 2) transition is concerned, its spectrum has been observed at Doppler resolution and recorded at low values of pressure (0.2–0.5 mTorr) employing a modulation depth and frequency of 800 kHz (1.6 MHz when the complete K structure has been recorded) and 1.666 kHz, respectively. Samples of phosphine have been prepared from the reaction between calcium phosphide (Ca3P2) and water. Figs. 1–3 provide some examples of the transitions observed and of the resolution obtained. More in details, Fig. 1 reports the hyperfine structure of the J = 1 ‹ 0 transition, Fig. 2 the hyperfine structure of the K = 0 and K = 1 components of the J = 2 ‹ 1 transition, and Fig. 3 the K structure of the J = 3 ‹ 2 transition. It should be noted that for the J = 1 ‹ 0 and J = 2 ‹ 1 transitions the resolution obtained is definitely higher with respect to that shown in Figs. 1 and 2 when the various parts of the hfs have been recorded into details (essentially using lower modulation depth values). 3. Analysis of the spectra The various hyperfine components result from the DF1, DF = +1, 0, 1 selection rules, where F1 and F are the hyperfine quantum numbers coming from the coupling
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Fig. 3. The K structure of the J = 3 ‹ 2 transition of PH3 is shown. The spectrum has been recorded at P = 0.5 mTorr and with a modulation depth of 1.6 MHz.
schemes F1 = J + IP and F = F1 + Itot, where IP is the nuclear spin of the phosphorus atom and I tot ¼ I H1 þ I H2 þ I H3 is the sum of the nuclear spins of the three H nuclei. The corresponding hamiltonian can be written as: H ¼ HROT þ HSR þ HSS ;
ð1Þ
where HROT is the rotational part of the hamiltonian operator [16]. HSR ¼ P HSR þ H HSR ;
ð2Þ
is the spin–rotation hamiltonian [17,18]: L
HSR ¼ þIL C I ðLÞJ;
ð3Þ
where L denotes H or P. Finally, HSS is the spin–spin hamiltonian [17,18] HSS ¼ þIL DIM ;
ð4Þ
where L and M are H and/or P. The relevant terms are due to H–H and P–H spin–spin interactions and can be described by the following expressions [19–21]: D1 ¼ gP gH l2N ½1 2 sin2 ðc=2Þ=r3PH ;
ð5Þ
gP gH l2N 2 sin2 ðc=2Þ=r3PH ;
ð6Þ
D2 ¼
3
D3 ¼ g2H l2N ½2rPH sinðc=2Þ ;
ð7Þ
where lN is the nuclear magneton and rPH and c are the geometrical parameters, i.e., the PH bond distance and the \HPH bond angle, respectively. As proved by Eqs. (5)–(7), the direct spin–spin interaction constants essentially depend on the molecular structure considered and on the g factors of the nuclei involved (gP for phosphorus and gH for hydrogen); therefore, they can be estimated a priori. For phosphine, D1, D2 and D3 have been found to be not negligible: 1.06, 18.3 and 13.8 kHz, respectively (value obtained employing the experimental equilibrium geometry
[4]). It should be mentioned that what are actually determinable from our fit are 3D1, 0.5D2 and +1.5D3. As far as the indirect, electron-coupled, part of spin–spin interaction is concerned, it should be noted that highly correlated ab initio calculations confirmed, as expected, that it is entirely negligible since it provides contributions largely lower than 1 kHz [22]. As concerns the spectra analysis, first of all, it is worth noting that the hyperfine component frequencies have been determined by a line profile analysis (see Ref. [11]) instead of fitting the experimental data points to a parabolic function as usually done in laboratory spectroscopy. Due to the relative high number of interacting nuclei, in most cases, the spectra is characterized by multiplets instead of isolated lines. Consequently, all the lines forming the multiplet should be considered at the same time in the fitting procedure. The situation is further complicated by the presence of crossing resonances, the so-called ghost transitions. As well known, this effect is due to the saturation of overlapping gaussian profiles of two or more transitions with a common level [23,24], and it was observed in our laboratory many times (see for example Ref. [25] and references therein). In order to correctly retrieve the hyperfine component frequencies, the ghost transitions should be taken into account in the line profile analysis. Consequently, in the first place, it has been found necessary to make a prediction of the spectra containing only the hyperfine components, spectra containing only the ghost transitions and spectra containing both hyperfine components and crossing resonances. This allowed us to understand how the real spectra have been modified by the presence of the ghost transitions and to correctly take them into account in the line profile analysis. For predicting the hyperfine pattern of the rotational spectra we made use of the spin–rotation parameters from Ref. [8] and of the spin–spin constants estimated as previously explained. The required rotational and centrifugal distortion constants were available in the literature [7]. Consequently, the hyperfine pattern of the rotational spectra could be quite accurately predicted. The spectra containing only the ghost transitions have been predicted by evaluating the frequencies and intensities of all possible cross-over resonances. As well-known, the frequency mij of a ghost transition is given by the arithmetic mean of the frequencies mi and mj of the interacting hyperfine components: mij = (mi + mj)/2 [23,24]. As concerns the intensities, they have been determined starting from the intensities of the interacting transitions and employing Eq. (8) of Ref. [26]. Finally, the resulting spectra could be predicted by putting together the hyperfine and ghost frequencies with their relative intensities. Making use of the predicted resulting spectra as starting points, the line profile analysis has been performed as described into details in Ref. [27] for H13CN. A graphical example of the prediction of spectra is provided by Fig. 1 which reports the J = 10 ‹ 00 transition: in addition to the experimental spectrum, calculated spectra are also given. More precisely, the spectrum reporting only the hyperfine components,
G. Cazzoli, C. Puzzarini / Journal of Molecular Spectroscopy 239 (2006) 64–70 Table 1 Rotational J 0K 0
67
J 00K 00 transitions of PH3a
J0
K0
F 01
F0
J00
K00
F 001
F00
Frequency (MHz)
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1
1/2 1/2 (1/2,1/2) 1/2 1/2 1/2 (1/2,3/2) (1/2,3/2) (1/2,3/2) (1/2,3/2) 3/2 (3/2,3/2) (3/2,3/2) 3/2 3/2 3/2 3/2 3/2 3/2 3/2 3/2 3/2 3/2 3/2 3/2 3/2 (3/2,5/2) 3/2 (3/2,5/2) (3/2,5/2) (3/2,5/2) (3/2,5/2) (3/2,5/2) (3/2,5/2) (3/2,5/2) 3/2 3/2 3/2 (3/2,5/2) (3/2,3/2) (3/2,3/2) (3/2,3/2) (3/2,3/2) (3/2,3/2) 5/2 5/2 5/2 5/2 5/2 (5/2,5/2) (5/2,5/2) (5/2,5/2) (5/2,5/2) 5/2 (5/2,5/2) (5/2,5/2) 5/2 5/2 3/2 3/2 3/2 3/2 3/2 (3/2,5/2)
2 2 (2,1)b (2,1)b 1 1 (2,2)b (2,1)b (2,2)b (2,1)b 3 (3,2)b (3,1)b 0 2 2 1 1 3 2 2 0 1 1 1 2 (3,4)b 3 (3,2)b (0,2)b (0,1)b (1,2)b (1,1)b (1,2)b (1,1)b 2 0 1 (2,2)b (3,2)b (3,1)b (2,0)b (2,1)b (2,2)b 4 2 2 1 1 (4,3)b (4,2)b (3,2)b (3,1)b 3 (2,1)b (1,1)b 1 1 2 1 1 2 1 (2,2)b
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1
1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 (3/2,1/2) (3/2,1/2) (3/2,1/2) (3/2,1/2) (3/2,1/2) (3/2,1/2) (3/2,1/2) (3/2,1/2) 3/2 1/2 3/2 3/2 3/2 3/2 3/2 3/2 3/2 1/2 1/2 1/2 3/2 1/2 1/2 1/2 1/2 1/2 3/2 3/2 3/2 3/2 3/2 3/2 3/2 3/2 3/2 (3/2,3/2) 3/2 3/2 (3/2,3/2) (3/2,3/2) (3/2,1/2) (3/2,1/2) (3/2,1/2) (3/2,1/2) (3/2,1/2) 3/2
1 2 1 2 2 1 1 1 2 2 2 2 2 1 1 2 1 2 (3,2)b (1,2)b (2,2)b (1,1)b (1,1)b (2,1)b (0,1)b (3,1)b 3 2 3 1 1 1 1 2 2 1 1 1 3 2 2 1 1 1 3 1 2 1 0 3 3 2 2 (2,3)b 1 2 (1,2)b (1,0)b (1,1)b (1,1)b (1,0)b (2,1)b (2,1)b 1
266944.3911(7) 0.20 ’’ ’’ 266944.3997(10) 0.31 ’’ ’’ 266944.4090(8) 0.12 ’’ ’’ 266944.4862(10) 1.02 ’’ ’’ ’’ ’’ ’’ ’’ 266944.5573(4) 0.12 266944.5704(10) 0.01 ’’ ’’ 266944.5830(4) 0.03 ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ 533794.4658(10) 0.04 533794.4887(10) 0.19 ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ 533794.5240(10) 0.65 533794.5468(10) 0.29 ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ 533794.5711(10) 1.11 ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ 533794.6665(10) 0.19 533794.6865(10) 0.40 ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ 533815.1259(10) 0.46 ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ 533815.1888(15) 0.60 (continued on next page)
o c (kHz)
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Table 1 (continued ) J0
K0
2 2 2 2 2 2 2 2 2 2 2 3 3 3 4 4 4 4
1 1 1 1 1 1 1 1 1 1 1 0 1 2 0 1 2 3 a b c
F 01
F0 b
(3/2,5/2) (3/2,5/2) (3/2,5/2) (3/2,5/2) (3/2,5/2) 3/2 3/2 3/2 3/2 5/2 5/2
(1,2) (2,3)b (1,3)b (2,2)b (1,2)b 1 1 2 1 2 3
J00
K00
F 001
F00
Frequency (MHz)
o c (kHz)
1 1 1 1 1 1 1 1 1 1 1 2 2 2 3 3 3 3
1 1 1 1 1 1 1 1 1 1 1 0 1 2 0 1 2 3
3/2 3/2 3/2 3/2 3/2 (1/2,1/2) 1/2 1/2 1/2 3/2 3/2
1 2 2 2 2 (0,1)b 0 1 1 1 2
’’ ’’ ’’ ’’ ’’ ’’ 533815.2139(10) ’’ ’’ 533815.3291(6) ’’ 800456.217(6) 800487.115(11) 800579.914(8) 1066835.850(200)c 1066876.900(200)c 1067000.330(200)c 1067206.260(200)c
’’ ’’ ’’ ’’ ’’ ’’ 0.01 ’’ ’’ 0.02 ’’ 0.17 2.74 2.06 57.45 45.22 159.73 134.61
Quotation marks (’’) in Table cells correspond to the numerical values given above them, and thus denote unresolved hyperfine components. Cross-over transitions: the quantum numbers of the generating hf components are given. Ref. [6].
that reporting only the crossing resonances and that reporting both of them are depicted. Therefore, this figure clearly provides an example of how the ghost transitions affect the observed spectrum.
As concerns the J = 3 ‹ 2 (K = 0, 1, 2) transition, since the hyperfine structure has not been resolved, the frequencies have been obtained by fitting the experimental data points to a parabolic function.
Table 2 Spectroscopic constants of PH3 Constant
This work
Belov et al. (1981)a
Tarrago and Dang Nhu (1985)b
MBER (1971)c
Ab initio resultsd
B0 (MHz) C0 (MHz) DJ (MHz) DJK (MHz) DK (MHz) LJ (kHz) LJK (kHz) LKJ (kHz) LK (kHz) LJJJK (Hz) LJJKK (Hz) LJKKK (Hz) CN(31P) (kHz) CK(31P) (kHz) (Cx + Cy)/2(H) (kHz) (Cx Cy)/4(H) (kHz) Cz(H) (kHz) Cxz(H) (kHz) Czx(H) (kHz) 3D1(P–H) (kHz) 0.5D2(P–H) (kHz) +1.5D3(H–H) (kHz)
133480.128989(95) 117489.436e 3.936901(36) 5.17102(44) — 0.4157(39) 1.237(85) 1.34(27) — — — — 115.35(12) 115.0(14) 7.57(13) — 7.69f — — 3.05(62) 9.15g 25.3(19)
133480.129(34) 117488.694(207) 3.9396(37) 5.1790(16) 4.1270(313) 0.545(132) 1.4411(40) 0.820(235) 3.984(935) 0.102(4) 0.22(14) 30.51(673) — — — — — — — — — —
133480.1264(65) 117489.436(10) 3.93789(99) 5.17239(12) 4.23895(55) 0.488(46) 1.44204(72) 1.7650(13) 0.485(11) 0.1163(13) — — — — — — — — — — — —
— — — — — — — — — — — — 114.90(13) 116.38(32) 8.01(8) — 7.69(19) — — — — —
— — — — — — — — — — — — 114.43 114.37 7.86 3.09 7.66 6.69 7.97
v2 a b c d e f g
0.45 Ref. [6]. Ref. [7]. Ref. [8]. Ref. [22]: vibrationally averaged values computed at the CCSD(T)/cc-pwCVQZ level (correlating all electrons but 1s of P). Fixed at the value given in Ref. [7]. Fixed at the value reported in Ref. [8]. Fixed at the calculated value. See text.
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4. Results and discussion The retrieved hyperfine components of the J = 1 ‹ 0 (K = 0) and J = 2 ‹ 1 (K = 0, 1) rotational transitions of PH3 are given in Table 1. As previously explained, they have been obtained from the line profile analysis, and the values reported have been obtained as averages of a set of measurements, and two times the standard deviation (2r) has been employed as uncertainty. In order to get information on those hyperfine components that are too weak to be observed, the ghost transitions generated by them have also been taken into account in the fitting procedure. The K-structure frequencies of the J = 3 ‹ 2 (K = 0, 1, 2) transition, obtained in the present work, are also reported in Table 1; even in this case, the frequency values have been obtained as averages of a set of measurements and 2r has been employed as frequency uncertainty. Our frequency values plus the J = 4 ‹ 3, with K = 0, 1, 2, 3, transition frequencies from Ref. [6] have then been included in a least-square fit in which each line has been weighted proportionally to the inverse square of its experimental uncertainty. For unresolved hyperfine components, the calculated frequencies have been determined using intensity-weighted averages. Ghost transitions have been included as averages of the hyperfine components from which they arise. The fit has been carried out with Pickett’s SPCAT/SPFIT program [28]. In Table 2, our results (first column) are also compared with those available in the literature. From this Table, it is evident that, as concerns spectroscopic parameters, our results are in good agreement with those from Refs. [6,7], but it is worth noting that our measurements allowed us to largely improve some constants such as B0 and DJ. As far as the hyperfine parameters are concerned, in Ref. [8] Davies et al obtained accurate results from molecular beam electric resonance (MBER) spectroscopy. In
69
Table 2 these results (last column) are compared to ours. From this comparison we can notice an overall good agreement for all constants: they agree within 2–3 times the given uncertainties. A few considerations should be drawn: on one hand, our resolution allowed us to obtain CN of 31P and (Cx + Cy)/2 of H with an accuracy comparable to MBER spectroscopy; on the other hand, the Lamb-dip spectra observed did not provide any information on Cz of H, which has therefore kept fixed at the value from Ref. [8]. With respect to CK of 31P, its large uncertainty is due to the fact that only the few K = 1 hf components of the J = 2 ‹ 1 transition contribute to its evaluation. Furthermore, it should be noticed that the off-diagonal terms of spin–rotation tensor of H not only cannot be determined but also do not affect the determination of the other hyperfine parameters (if they are kept fixed in the fitting procedure at the corresponding ab initio values [22]). As concerns the spin–spin interaction, it is worth noting that, to our knowledge, the present investigation provides the first determination of the D1 and D3 constants. The importance of including spin–spin interaction in our spectra analysis is graphically demonstrated by Fig. 4, which reports the J = 10 ‹ 00 transition of PH3 and shows how the various hyperfine parameters affect the observed spectra. Starting from the top we notice how the inclusion of the various hyperfine parameters modifies the hyperfine pattern. In particular, this figure shows how the D1 and D3 spin–spin interaction constants affect the hyperfine structure: it is clear that these interactions cannot be neglected. In order to test the vibrational effects on the calculated spin–spin parameters, in particular with respect to D2 that we could not experimentally determine, we also evaluated the D1, D2 and D3 constants by employing a vibrational averaged molecular structure instead of the equilibrium one in Eqs. (5)–(7). We noticed that for all
Fig. 4. The J = 10 ‹ 00 transition of PH3. In addition to the experimental spectrum, the contributions of each hyperfine parameter to the hyperfine pattern are also depicted. Starting from the top (unperturbed transition: ‘‘no hfs’’ spectrum) the effect of the inclusion of each relevant hyperfine constant is shown: (1) only CN(31P), (2) CN(31P) + (Cx(H) + Cy(H)), (3) CN(31P) + (Cx(H) + Cy(H)) + D1(P–H), (4) CN(31P) + (Cx(H) + Cy(H)) + D1(P–H) + D3(H–H).
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parameters the absolute value decreased by 3.5–4.5%. Therefore, we can consider these calculated constants affected by an uncertainty of about 5%, which seems to be a conservative estimate of the zero-point effects. Consequently, the 0.5D2 parameter reported in Table 2 may be better estimated to be 9.2(5) kHz. 5. Conclusions In the present investigation we have shown that employing the Lamb-dip technique it is possible to resolve the hyperfine structure due to 31P and H. It is worth noting that we were able to determine CN of 31P and (Cx + Cy)/ 2 of H with an accuracy comparable to MBER spectroscopy. Furthermore, our study reports the first experimental determination of the D1 and D3 spin–spin parameters and shows that spin–spin interactions should be taken into account in the hyperfine structure analysis. As far as the rotational parameters are concerned, it is important to notice that, on one hand, our results are in good agreement with those available in the literature, but, on the other hand, our measurements allowed us to largely improve some constants such as B0 and DJ. Acknowledgment This work has been supported by MIUR (ex-40%), CNR and University of Bologna (funds for selected research topics and ex-60% funds). References [1] [2] [3] [4] [5]
C.A. Burrus, A. Jache, W. Gordy, Phys. Rev. 95 (1954) 706–708. P. Helminger, W. Gordy, Phys. Rev. 188 (1969) 100–108. F.Y. Chu, T. Oka, J. Chem. Phys. 60 (1974) 4612–4618. D.A. Helms, W. Gordy, J. Mol. Spectrosc. 66 (1977) 206–218. S.P. Belov, A.V. Burenin, L.I. Gershtein, A.F. Krupnov, V.N. Markov, A.V. Maslovsky, S.M. Shapin, J. Mol. Spectrosc. 86 (1981) 184–192.
[6] S.P. Belov, A.V. Burenin, O.L. Polyansky, S.M. Shapin, J. Mol. Spectrosc. 90 (1981) 571–589. [7] G. Tarrago, M. Dang Nhu, J. Mol. Spectrosc. 111 (1985) 425–439. [8] P.B. Davies, R.M. Neumann, S.C. Wofsy, W. Klemperer, J. Chem. Phys. 55 (1971) 3564–3568. [9] G. Cazzoli, L. Dore, J. Mol. Spectrosc. 143 (1990) 231–236. [10] L. Dore, C. Degli Esposti, A. Mazzavillani, G. Cazzoli, Chem. Phys. Lett. 300 (1999) 489–492. [11] G. Cazzoli, L. Dore, J. Mol. Spectrosc. 141 (1990) 49–58. [12] G. Cazzoli, C. Puzzarini, A.V. Lapinov, Astrophys. J. 592 (2003) L95–L98. [13] C. Puzzarini, L. Dore, G. Cazzoli, J. Mol. Spectrosc. 217 (2003) 19– 25. [14] G. Cazzoli, L. Dore, L. Cludi, C. Puzzarini, S. Beninati, J. Mol. Spectrosc. 215 (2002) 160–162. [15] G. Cazzoli, L. Dore, C. Puzzarini, S. Beninati, Phys. Chem. Chem. Phys. 4 (2002) 3575–3577. [16] W. Gordy, R.L. Cook, in: A. Weissberger (Ed.), Microwave Molecular Spectra, Third ed., Wiley, New York, 1984. [17] C.H. Townes, A.L. Schawlow, Microwave Spectroscopy, McGrawHill, New York, 1955. [18] W.H. Flygare, Chem. Rev. 74 (1974) 653–687. [19] J. Oddershede, I. Paidarova, V. Spirko, J. Mol. Spectrosc. 152 (1992) 342–354. [20] J.P. Gordon, Phys. Rev. 99 (1955) 1253–1263. [21] G.R. Gunther-Mohr, C.H. Townes, J.H. Van-Vleck, Phys. Rev. 94 (1954) 1191–1203. [22] C. Puzzarini, unpublished results. Note: from the literature it is well known that very reliable data (almost quantitative) for indirect spin–spin terms and spin–rotation constants can be evaluated from ab initio —at the CCSD(T) level of theory— calculations. [23] R.S. Winton, Observations and Applications of the Lamb-dip in Millimeter-Wave Molecular Spectroscopy, Ph.D. dissertation, Duke University, Durham, NC, 1972. [24] V.S. Letokhov, V.P. Chebotayev, Nonlinear Laser Spectroscopy, Springer-Verlag, Berlin/Heidelberg/New York, 1977, and references therein, pp. 238–242. [25] G. Cazzoli, C. Puzzarini, Phys. Chem. Chem. Phys. 6 (2004) 5133–5139. [26] G. Magerl, W. Schupita, J.M. Frye, W.A. Kreiner, T. Oka, J. Mol. Spectrosc. 107 (1984) 72–83. [27] G. Cazzoli, C. Puzzarini, J. Mol. Spectrosc. 233 (2005) 289–298. [28] H.M. Pickett, J. Mol. Spectrosc. 148 (1991) 371–377.
The Lamb-dip spectrum of phosphine: The nuclear hyperfine structure due to hydrogen and phosphorus Gabriele Cazzoli *, Cristina Puzzarini Dipartimento di Chimica ‘‘G. Ciamician’’, Universita` di Bologna, Via Selmi 2, I-40126 Bologna, Italy Received 17 March 2006; in revised form 30 May 2006 Available online 6 June 2006
Abstract For the first time, the hyperfine structure of the rotational J = 1 ‹ 0 (K = 0) and J = 2 ‹ 1 (K = 0, 1) transitions of phosphine has been resolved by using microwave spectroscopy. To this purpose, the Lamb-dip technique has been employed. In addition, the J = 3 ‹ 2 (K = 0, 1, 2) transition has been recorded at Doppler resolution. The present investigation allowed us to provide accurate values for most of the hyperfine constants as well as ground state rotational parameters. 2006 Elsevier Inc. All rights reserved. Keywords: Lamb-dip spectroscopy; Rotational spectrum; Hyperfine structure; Phosphine
1. Introduction The first microwave measurements of the J = 1 ‹ 0 (K = 0) and J = 2 ‹ 1 (K = 0, 1) transitions of phosphine were carried out long time ago in Gordy’s group [1,2] with an accuracy of 0.04 MHz for the first and an accuracy of about 0.2 MHz for the latest [2]. In Ref. [2] the B0, DJ and DJK constants were determined for the first time employing microwave data only. Subsequently, the ‘‘forbidden’’ rotational spectra of PH3 (DJ = 0, DK = ±3) were investigated by Chu and Oka [3] and then by Helms and Gordy [4]. These measurements allowed the first determination of the C0 and DK rotational parameters. In the following years, observations of rotational and ‘‘forbidden’’ rotational spectra were extended up 1 THz by Belov et al. [5,6] allowing the improvement of the rotational parameters determined so far as well as the determination of sextic and octic centrifugal distortion constants [6]. In 1985, a re-analysis of all the data available in the literature was performed by Tarrago and Dang Nhu employing a new formulation which accounts for the DK = ±3 and ±6
*
Corresponding author. Fax: +39 051 209 9456. E-mail address: [email protected] (G. Cazzoli).
0022-2852/$ - see front matter 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2006.05.019
resonance terms through diagonalization of the energy matrix [7]. As far as the hyperfine parameters are concerned, in 1971 Davies et al. observed the electric resonance spectrum of phosphine at zero electric field for the three rotational states J = 4, 5 and 7 with K = 3; in addition, the J = K = 1 and J = K = 2 spectra were recorded at several values for the electric field [8]. All these measurements allowed the accurate evaluation of the electric dipole moment as well as of the determinable spin–rotation constants of 31P and H, where the adjective ‘‘determinable’’ refers to those hyperfine parameters that can be evaluated by conventional spectroscopic techniques. Finally, it should be noted that the observations carried out by both Gordy’s group and Davies and co-workers showed that inversion doubling must be negligible for phosphine: it was estimated to be less than 1 kHz. Similarly, no evidence of inversion doubling has been found in the present investigation. 2. Experimental details To resolve the hyperfine structure (hfs) due to the 31P and H nuclei of the J = 1 ‹ 0 and J = 2 ‹ 1 rotational transitions of phosphine, PH3, the Lamb-dip technique
G. Cazzoli, C. Puzzarini / Journal of Molecular Spectroscopy 239 (2006) 64–70
Fig. 1. The J = 10 ‹ 00 transition of PH3. The simulations of the spectrum containing only hyperfine components, only ghost transitions and both hyperfine components and crossing resonances are reported together with the experimental spectrum recorded at P = 0.2 mTorr employing a modulation depth of 8 kHz.
Fig. 2. The J = 2 ‹ 1 transition of PH3 is shown: the top panel reports the K = 0 component, the lower panel reports the K = 1 component. The K = 0 spectrum has been recorded at a pressure of 0.2 mTorr and with a modulation depth of 9 kHz. The K = 1 spectrum has been recorded at a pressure of 0.2 mTorr and with a modulation depth of 36 kHz. The asterisks mark the most relevant cross-over transitions.
65
has been used. To this purpose, a frequency modulated computer-controlled spectrometer has been employed using a conventional free space cell, as shown in Ref. [9]. To increase the sensitivity of the spectrometer as well as the Lamb-dip effect the radiation path has been doubled (for details see Ref. [10]). A detailed description of the spectrometer is given in Ref. [11], whereas an extensive description of our experimental set up for performing sub-Doppler resolution spectroscopy can be found in various previous papers [12–15]. Therefore, here, we shortly report the main details related to the present investigation. The millimeter and submillimeter-wave sources employed are either frequency multipliers driven by gunn diode oscillators or gunn diodes themselves covering, on the whole, the frequency range 80–800 GHz. The source is phaselocked to a Rubidium frequency standard, and the frequency modulation is obtained by sine-wave modulating the 90 MHz local oscillator of the synchronization loop. A liquid Helium-cooled InSb detector has been used and its output is processed by means of a Lock-in amplifier tuned at twice the modulation frequency, so that the second derivative of the natural line profile has been recorded. The Lamb-dip measurements have been carried out at pressures of about 0.2 mTorr. Such low values of working pressure have been chosen in order to minimize as much as possible the dip widths as well as to avoid pressure frequency shift effects. The modulation depth used has been adjusted in the ranges 6–36 kHz according to the experimental conditions and the transition under consideration. As concerns the modulation frequency, it has been kept fixed at 1.666 kHz. In addition, in order to have narrow and not distorted dips, the source power has adequately been reduced. As far as the J = 3 ‹ 2 (K = 0, 1, 2) transition is concerned, its spectrum has been observed at Doppler resolution and recorded at low values of pressure (0.2–0.5 mTorr) employing a modulation depth and frequency of 800 kHz (1.6 MHz when the complete K structure has been recorded) and 1.666 kHz, respectively. Samples of phosphine have been prepared from the reaction between calcium phosphide (Ca3P2) and water. Figs. 1–3 provide some examples of the transitions observed and of the resolution obtained. More in details, Fig. 1 reports the hyperfine structure of the J = 1 ‹ 0 transition, Fig. 2 the hyperfine structure of the K = 0 and K = 1 components of the J = 2 ‹ 1 transition, and Fig. 3 the K structure of the J = 3 ‹ 2 transition. It should be noted that for the J = 1 ‹ 0 and J = 2 ‹ 1 transitions the resolution obtained is definitely higher with respect to that shown in Figs. 1 and 2 when the various parts of the hfs have been recorded into details (essentially using lower modulation depth values). 3. Analysis of the spectra The various hyperfine components result from the DF1, DF = +1, 0, 1 selection rules, where F1 and F are the hyperfine quantum numbers coming from the coupling
66
G. Cazzoli, C. Puzzarini / Journal of Molecular Spectroscopy 239 (2006) 64–70
Fig. 3. The K structure of the J = 3 ‹ 2 transition of PH3 is shown. The spectrum has been recorded at P = 0.5 mTorr and with a modulation depth of 1.6 MHz.
schemes F1 = J + IP and F = F1 + Itot, where IP is the nuclear spin of the phosphorus atom and I tot ¼ I H1 þ I H2 þ I H3 is the sum of the nuclear spins of the three H nuclei. The corresponding hamiltonian can be written as: H ¼ HROT þ HSR þ HSS ;
ð1Þ
where HROT is the rotational part of the hamiltonian operator [16]. HSR ¼ P HSR þ H HSR ;
ð2Þ
is the spin–rotation hamiltonian [17,18]: L
HSR ¼ þIL C I ðLÞJ;
ð3Þ
where L denotes H or P. Finally, HSS is the spin–spin hamiltonian [17,18] HSS ¼ þIL DIM ;
ð4Þ
where L and M are H and/or P. The relevant terms are due to H–H and P–H spin–spin interactions and can be described by the following expressions [19–21]: D1 ¼ gP gH l2N ½1 2 sin2 ðc=2Þ=r3PH ;
ð5Þ
gP gH l2N 2 sin2 ðc=2Þ=r3PH ;
ð6Þ
D2 ¼
3
D3 ¼ g2H l2N ½2rPH sinðc=2Þ ;
ð7Þ
where lN is the nuclear magneton and rPH and c are the geometrical parameters, i.e., the PH bond distance and the \HPH bond angle, respectively. As proved by Eqs. (5)–(7), the direct spin–spin interaction constants essentially depend on the molecular structure considered and on the g factors of the nuclei involved (gP for phosphorus and gH for hydrogen); therefore, they can be estimated a priori. For phosphine, D1, D2 and D3 have been found to be not negligible: 1.06, 18.3 and 13.8 kHz, respectively (value obtained employing the experimental equilibrium geometry
[4]). It should be mentioned that what are actually determinable from our fit are 3D1, 0.5D2 and +1.5D3. As far as the indirect, electron-coupled, part of spin–spin interaction is concerned, it should be noted that highly correlated ab initio calculations confirmed, as expected, that it is entirely negligible since it provides contributions largely lower than 1 kHz [22]. As concerns the spectra analysis, first of all, it is worth noting that the hyperfine component frequencies have been determined by a line profile analysis (see Ref. [11]) instead of fitting the experimental data points to a parabolic function as usually done in laboratory spectroscopy. Due to the relative high number of interacting nuclei, in most cases, the spectra is characterized by multiplets instead of isolated lines. Consequently, all the lines forming the multiplet should be considered at the same time in the fitting procedure. The situation is further complicated by the presence of crossing resonances, the so-called ghost transitions. As well known, this effect is due to the saturation of overlapping gaussian profiles of two or more transitions with a common level [23,24], and it was observed in our laboratory many times (see for example Ref. [25] and references therein). In order to correctly retrieve the hyperfine component frequencies, the ghost transitions should be taken into account in the line profile analysis. Consequently, in the first place, it has been found necessary to make a prediction of the spectra containing only the hyperfine components, spectra containing only the ghost transitions and spectra containing both hyperfine components and crossing resonances. This allowed us to understand how the real spectra have been modified by the presence of the ghost transitions and to correctly take them into account in the line profile analysis. For predicting the hyperfine pattern of the rotational spectra we made use of the spin–rotation parameters from Ref. [8] and of the spin–spin constants estimated as previously explained. The required rotational and centrifugal distortion constants were available in the literature [7]. Consequently, the hyperfine pattern of the rotational spectra could be quite accurately predicted. The spectra containing only the ghost transitions have been predicted by evaluating the frequencies and intensities of all possible cross-over resonances. As well-known, the frequency mij of a ghost transition is given by the arithmetic mean of the frequencies mi and mj of the interacting hyperfine components: mij = (mi + mj)/2 [23,24]. As concerns the intensities, they have been determined starting from the intensities of the interacting transitions and employing Eq. (8) of Ref. [26]. Finally, the resulting spectra could be predicted by putting together the hyperfine and ghost frequencies with their relative intensities. Making use of the predicted resulting spectra as starting points, the line profile analysis has been performed as described into details in Ref. [27] for H13CN. A graphical example of the prediction of spectra is provided by Fig. 1 which reports the J = 10 ‹ 00 transition: in addition to the experimental spectrum, calculated spectra are also given. More precisely, the spectrum reporting only the hyperfine components,
G. Cazzoli, C. Puzzarini / Journal of Molecular Spectroscopy 239 (2006) 64–70 Table 1 Rotational J 0K 0
67
J 00K 00 transitions of PH3a
J0
K0
F 01
F0
J00
K00
F 001
F00
Frequency (MHz)
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1
1/2 1/2 (1/2,1/2) 1/2 1/2 1/2 (1/2,3/2) (1/2,3/2) (1/2,3/2) (1/2,3/2) 3/2 (3/2,3/2) (3/2,3/2) 3/2 3/2 3/2 3/2 3/2 3/2 3/2 3/2 3/2 3/2 3/2 3/2 3/2 (3/2,5/2) 3/2 (3/2,5/2) (3/2,5/2) (3/2,5/2) (3/2,5/2) (3/2,5/2) (3/2,5/2) (3/2,5/2) 3/2 3/2 3/2 (3/2,5/2) (3/2,3/2) (3/2,3/2) (3/2,3/2) (3/2,3/2) (3/2,3/2) 5/2 5/2 5/2 5/2 5/2 (5/2,5/2) (5/2,5/2) (5/2,5/2) (5/2,5/2) 5/2 (5/2,5/2) (5/2,5/2) 5/2 5/2 3/2 3/2 3/2 3/2 3/2 (3/2,5/2)
2 2 (2,1)b (2,1)b 1 1 (2,2)b (2,1)b (2,2)b (2,1)b 3 (3,2)b (3,1)b 0 2 2 1 1 3 2 2 0 1 1 1 2 (3,4)b 3 (3,2)b (0,2)b (0,1)b (1,2)b (1,1)b (1,2)b (1,1)b 2 0 1 (2,2)b (3,2)b (3,1)b (2,0)b (2,1)b (2,2)b 4 2 2 1 1 (4,3)b (4,2)b (3,2)b (3,1)b 3 (2,1)b (1,1)b 1 1 2 1 1 2 1 (2,2)b
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1
1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 (3/2,1/2) (3/2,1/2) (3/2,1/2) (3/2,1/2) (3/2,1/2) (3/2,1/2) (3/2,1/2) (3/2,1/2) 3/2 1/2 3/2 3/2 3/2 3/2 3/2 3/2 3/2 1/2 1/2 1/2 3/2 1/2 1/2 1/2 1/2 1/2 3/2 3/2 3/2 3/2 3/2 3/2 3/2 3/2 3/2 (3/2,3/2) 3/2 3/2 (3/2,3/2) (3/2,3/2) (3/2,1/2) (3/2,1/2) (3/2,1/2) (3/2,1/2) (3/2,1/2) 3/2
1 2 1 2 2 1 1 1 2 2 2 2 2 1 1 2 1 2 (3,2)b (1,2)b (2,2)b (1,1)b (1,1)b (2,1)b (0,1)b (3,1)b 3 2 3 1 1 1 1 2 2 1 1 1 3 2 2 1 1 1 3 1 2 1 0 3 3 2 2 (2,3)b 1 2 (1,2)b (1,0)b (1,1)b (1,1)b (1,0)b (2,1)b (2,1)b 1
266944.3911(7) 0.20 ’’ ’’ 266944.3997(10) 0.31 ’’ ’’ 266944.4090(8) 0.12 ’’ ’’ 266944.4862(10) 1.02 ’’ ’’ ’’ ’’ ’’ ’’ 266944.5573(4) 0.12 266944.5704(10) 0.01 ’’ ’’ 266944.5830(4) 0.03 ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ 533794.4658(10) 0.04 533794.4887(10) 0.19 ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ 533794.5240(10) 0.65 533794.5468(10) 0.29 ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ 533794.5711(10) 1.11 ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ 533794.6665(10) 0.19 533794.6865(10) 0.40 ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ 533815.1259(10) 0.46 ’’ ’’ ’’ ’’ ’’ ’’ ’’ ’’ 533815.1888(15) 0.60 (continued on next page)
o c (kHz)
68
G. Cazzoli, C. Puzzarini / Journal of Molecular Spectroscopy 239 (2006) 64–70
Table 1 (continued ) J0
K0
2 2 2 2 2 2 2 2 2 2 2 3 3 3 4 4 4 4
1 1 1 1 1 1 1 1 1 1 1 0 1 2 0 1 2 3 a b c
F 01
F0 b
(3/2,5/2) (3/2,5/2) (3/2,5/2) (3/2,5/2) (3/2,5/2) 3/2 3/2 3/2 3/2 5/2 5/2
(1,2) (2,3)b (1,3)b (2,2)b (1,2)b 1 1 2 1 2 3
J00
K00
F 001
F00
Frequency (MHz)
o c (kHz)
1 1 1 1 1 1 1 1 1 1 1 2 2 2 3 3 3 3
1 1 1 1 1 1 1 1 1 1 1 0 1 2 0 1 2 3
3/2 3/2 3/2 3/2 3/2 (1/2,1/2) 1/2 1/2 1/2 3/2 3/2
1 2 2 2 2 (0,1)b 0 1 1 1 2
’’ ’’ ’’ ’’ ’’ ’’ 533815.2139(10) ’’ ’’ 533815.3291(6) ’’ 800456.217(6) 800487.115(11) 800579.914(8) 1066835.850(200)c 1066876.900(200)c 1067000.330(200)c 1067206.260(200)c
’’ ’’ ’’ ’’ ’’ ’’ 0.01 ’’ ’’ 0.02 ’’ 0.17 2.74 2.06 57.45 45.22 159.73 134.61
Quotation marks (’’) in Table cells correspond to the numerical values given above them, and thus denote unresolved hyperfine components. Cross-over transitions: the quantum numbers of the generating hf components are given. Ref. [6].
that reporting only the crossing resonances and that reporting both of them are depicted. Therefore, this figure clearly provides an example of how the ghost transitions affect the observed spectrum.
As concerns the J = 3 ‹ 2 (K = 0, 1, 2) transition, since the hyperfine structure has not been resolved, the frequencies have been obtained by fitting the experimental data points to a parabolic function.
Table 2 Spectroscopic constants of PH3 Constant
This work
Belov et al. (1981)a
Tarrago and Dang Nhu (1985)b
MBER (1971)c
Ab initio resultsd
B0 (MHz) C0 (MHz) DJ (MHz) DJK (MHz) DK (MHz) LJ (kHz) LJK (kHz) LKJ (kHz) LK (kHz) LJJJK (Hz) LJJKK (Hz) LJKKK (Hz) CN(31P) (kHz) CK(31P) (kHz) (Cx + Cy)/2(H) (kHz) (Cx Cy)/4(H) (kHz) Cz(H) (kHz) Cxz(H) (kHz) Czx(H) (kHz) 3D1(P–H) (kHz) 0.5D2(P–H) (kHz) +1.5D3(H–H) (kHz)
133480.128989(95) 117489.436e 3.936901(36) 5.17102(44) — 0.4157(39) 1.237(85) 1.34(27) — — — — 115.35(12) 115.0(14) 7.57(13) — 7.69f — — 3.05(62) 9.15g 25.3(19)
133480.129(34) 117488.694(207) 3.9396(37) 5.1790(16) 4.1270(313) 0.545(132) 1.4411(40) 0.820(235) 3.984(935) 0.102(4) 0.22(14) 30.51(673) — — — — — — — — — —
133480.1264(65) 117489.436(10) 3.93789(99) 5.17239(12) 4.23895(55) 0.488(46) 1.44204(72) 1.7650(13) 0.485(11) 0.1163(13) — — — — — — — — — — — —
— — — — — — — — — — — — 114.90(13) 116.38(32) 8.01(8) — 7.69(19) — — — — —
— — — — — — — — — — — — 114.43 114.37 7.86 3.09 7.66 6.69 7.97
v2 a b c d e f g
0.45 Ref. [6]. Ref. [7]. Ref. [8]. Ref. [22]: vibrationally averaged values computed at the CCSD(T)/cc-pwCVQZ level (correlating all electrons but 1s of P). Fixed at the value given in Ref. [7]. Fixed at the value reported in Ref. [8]. Fixed at the calculated value. See text.
G. Cazzoli, C. Puzzarini / Journal of Molecular Spectroscopy 239 (2006) 64–70
4. Results and discussion The retrieved hyperfine components of the J = 1 ‹ 0 (K = 0) and J = 2 ‹ 1 (K = 0, 1) rotational transitions of PH3 are given in Table 1. As previously explained, they have been obtained from the line profile analysis, and the values reported have been obtained as averages of a set of measurements, and two times the standard deviation (2r) has been employed as uncertainty. In order to get information on those hyperfine components that are too weak to be observed, the ghost transitions generated by them have also been taken into account in the fitting procedure. The K-structure frequencies of the J = 3 ‹ 2 (K = 0, 1, 2) transition, obtained in the present work, are also reported in Table 1; even in this case, the frequency values have been obtained as averages of a set of measurements and 2r has been employed as frequency uncertainty. Our frequency values plus the J = 4 ‹ 3, with K = 0, 1, 2, 3, transition frequencies from Ref. [6] have then been included in a least-square fit in which each line has been weighted proportionally to the inverse square of its experimental uncertainty. For unresolved hyperfine components, the calculated frequencies have been determined using intensity-weighted averages. Ghost transitions have been included as averages of the hyperfine components from which they arise. The fit has been carried out with Pickett’s SPCAT/SPFIT program [28]. In Table 2, our results (first column) are also compared with those available in the literature. From this Table, it is evident that, as concerns spectroscopic parameters, our results are in good agreement with those from Refs. [6,7], but it is worth noting that our measurements allowed us to largely improve some constants such as B0 and DJ. As far as the hyperfine parameters are concerned, in Ref. [8] Davies et al obtained accurate results from molecular beam electric resonance (MBER) spectroscopy. In
69
Table 2 these results (last column) are compared to ours. From this comparison we can notice an overall good agreement for all constants: they agree within 2–3 times the given uncertainties. A few considerations should be drawn: on one hand, our resolution allowed us to obtain CN of 31P and (Cx + Cy)/2 of H with an accuracy comparable to MBER spectroscopy; on the other hand, the Lamb-dip spectra observed did not provide any information on Cz of H, which has therefore kept fixed at the value from Ref. [8]. With respect to CK of 31P, its large uncertainty is due to the fact that only the few K = 1 hf components of the J = 2 ‹ 1 transition contribute to its evaluation. Furthermore, it should be noticed that the off-diagonal terms of spin–rotation tensor of H not only cannot be determined but also do not affect the determination of the other hyperfine parameters (if they are kept fixed in the fitting procedure at the corresponding ab initio values [22]). As concerns the spin–spin interaction, it is worth noting that, to our knowledge, the present investigation provides the first determination of the D1 and D3 constants. The importance of including spin–spin interaction in our spectra analysis is graphically demonstrated by Fig. 4, which reports the J = 10 ‹ 00 transition of PH3 and shows how the various hyperfine parameters affect the observed spectra. Starting from the top we notice how the inclusion of the various hyperfine parameters modifies the hyperfine pattern. In particular, this figure shows how the D1 and D3 spin–spin interaction constants affect the hyperfine structure: it is clear that these interactions cannot be neglected. In order to test the vibrational effects on the calculated spin–spin parameters, in particular with respect to D2 that we could not experimentally determine, we also evaluated the D1, D2 and D3 constants by employing a vibrational averaged molecular structure instead of the equilibrium one in Eqs. (5)–(7). We noticed that for all
Fig. 4. The J = 10 ‹ 00 transition of PH3. In addition to the experimental spectrum, the contributions of each hyperfine parameter to the hyperfine pattern are also depicted. Starting from the top (unperturbed transition: ‘‘no hfs’’ spectrum) the effect of the inclusion of each relevant hyperfine constant is shown: (1) only CN(31P), (2) CN(31P) + (Cx(H) + Cy(H)), (3) CN(31P) + (Cx(H) + Cy(H)) + D1(P–H), (4) CN(31P) + (Cx(H) + Cy(H)) + D1(P–H) + D3(H–H).
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parameters the absolute value decreased by 3.5–4.5%. Therefore, we can consider these calculated constants affected by an uncertainty of about 5%, which seems to be a conservative estimate of the zero-point effects. Consequently, the 0.5D2 parameter reported in Table 2 may be better estimated to be 9.2(5) kHz. 5. Conclusions In the present investigation we have shown that employing the Lamb-dip technique it is possible to resolve the hyperfine structure due to 31P and H. It is worth noting that we were able to determine CN of 31P and (Cx + Cy)/ 2 of H with an accuracy comparable to MBER spectroscopy. Furthermore, our study reports the first experimental determination of the D1 and D3 spin–spin parameters and shows that spin–spin interactions should be taken into account in the hyperfine structure analysis. As far as the rotational parameters are concerned, it is important to notice that, on one hand, our results are in good agreement with those available in the literature, but, on the other hand, our measurements allowed us to largely improve some constants such as B0 and DJ. Acknowledgment This work has been supported by MIUR (ex-40%), CNR and University of Bologna (funds for selected research topics and ex-60% funds). References [1] [2] [3] [4] [5]
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