The pure rotational spectra of the lanthanum monohalides, LaF, LaCl, LaBr, LaI

Journal of Molecular Spectroscopy 218 (2003) 169–179 www.elsevier.com/locate/jms

The pure rotational spectra of the lanthanum monohalides, LaF, LaCl, LaBr, LaIq Daryl S. Rubinoff, Corey J. Evans, and Michael C.L. Gerry* Department of Chemistry, The University of British Columbia, 2036 Main Mall, Vancouver, BC, Canada V6T 1Z1 Received 31 May 2002; in revised form 18 November 2002

Abstract Pure rotational spectra have been measured for all the major isotopomers of the lanthanum monohalides, LaF, LaCl, LaBr, and LaI, in their ground and (except for La81 Br) excited vibrational states. The spectra were observed with a cavity pulsed jet Fourier transform microwave spectrometer in the frequency range 5–24 GHz. The molecules were prepared by laser ablation of La metal and allowing the resulting plasma to react with SF6 , Cl2 , Br2 , or CH3 I precursor in an Ar carrier gas of the pulsed jet. For LaBr this is the first reported spectrum of any kind. Rotational constants, centrifugal distortion constants, nuclear quadrupole coupling constants, and nuclear spin–rotation constants have been determined for all the molecules. Accurate equilibrium (re ) internuclear distances have given an indication of where the Born–Oppenheimer approximation is beginning to fail. From the centrifugal distortion constants and vibration–rotation ðae ) constants good estimates of the harmonic vibration frequencies and bond dissociation energies have been obtained. The halogen nuclear quadrupole coupling constants indicate the molecules to be highly ionic. Ó 2003 Elsevier Science (USA). All rights reserved.

1. Introduction The monohalides of lanthanum (LaF, LaCl, LaBr, LaI) have been subject to varying amounts of spectroscopic study. Of these, the fluoride, LaF, has received the most attention. For it, the first assigned measurements were of several rotationally analysed visible absorption bands by Barrow et al. [1]. These results were later ascribed to both triplet and singlet manifolds: Schall et al. [2] confirmed that the ground state is X 1 Rþ and determined the energies of several excited electronic states, including the lowest lying triplet state a3 D1 (1432 cm1 ). Several other investigations into the electronic states of LaF have since followed [3–7], including evaluation of the equilibrium rotational constant and internuclear distance [7]. Multiconfiguration ligand field calculations, ab initio pseudopotential calculations, and relativistic ab initio SCF and correlated calculations have also been carried out [8–10], and give results which agree with experimentally derived values. q Supplementary data for this article are available on ScienceDirect. * Corresponding author. Fax: +1-604-822-2847. E-mail address: [email protected] (M.C.L. Gerry).

The spectroscopy of LaCl has been far less extensively studied. The only published spectroscopic work is a rotational analysis by Xin and Klynning [11] of an infrared band system observed in the thermal emission spectrum. Although these authors obtained equilibrium rotational constants for several vibronic states, they could not decide whether ground state has 3 D or 1 R symmetry, though they tentatively chose 1 R as a result of the work of Schall et al. [2] and Langhoff et al. [8b]. The a3 D–X 1 R separation, though unknown, was predicted to be rather small because of the strong triplet transitions to a3 D, and by comparison with LaF [2]. The spectra of the remaining two compounds, LaBr and LaI, have received very little attention. The only report is of laser induced fluorescence (LIF) data of LaI [12], which provided preliminary rovibrational information on four low lying states, with the lowest two being X 1 R and a3 D (1064.33 cm1 ). Equilibrium rotational constants and bond lengths were evaluated for the ground vibronic state. There is no previous report of a spectrum of any kind for LaBr. Recently we have reported the pure rotational spectra of the halides of the lightest two Group 3 metals, Sc and Y [13–18], with the only one missing being ScI. Where possible, equilibrium geometries have been measured.

0022-2852/03/$ - see front matter Ó 2003 Elsevier Science (USA). All rights reserved. doi:10.1016/S0022-2852(02)00081-4

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A useful conclusion from the study of the Sc halides has been that nuclear quadrupole coupling constants of transition metals can be interpreted only cautiously: simple treatments can lead to erroneous deductions, and correct interpretation is most reliably carried out using only ab initio calculations [17]. Indeed, recently the latter approach has been taken: high level ab initio calculations combined with experimental nuclear quadrupole coupling constants from [17,18] have produced a significantly improved value for the nuclear quadrupole moment of 45 Sc [19]. The present paper extends this work to the four monohalides of the third Group 3 metal, La. Rotational constants have been determined for all four molecules in the ground and excited vibrational states, from which equilibrium geometries have been calculated. Hyperfine parameters have been evaluated.

2. Experimental methods A Balle–Flygare type pulsed jet cavity Fourier transform microwave (FTMW) spectrometer [20] was used in these experiments. Since it has been described in detail earlier [21], only a short description will be given here. Briefly, the spectrometer contains a Fabry–Perot microwave cavity made up from two spherical mirrors 24 cm in diameter, 38.4 cm radius of curvature, separated by about 30 cm. One mirror is fixed, while the other is movable in order to tune the cavity to the microwave excitation frequency. A pulsed nozzle (General Value, Series 9) is mounted in the fixed mirror, so that samples entrained in jets of argon or neon travel parallel to the direction of microwave propagation. As a result all lines are split into two Doppler components, whose frequencies are averaged to obtain the rest frequencies. The microwave synthesizer is continuously referenced to a Loran C frequency standard, which is accurate to one part in 1010 . The spectra were measured in the frequency range 5–24 GHz. With the FWHM of the observed lines 7–10 kHz, the measurement accuracy of the observed transitions is estimated to be better than 1 kHz. The gas-phase lanthanum halides were prepared using the laser ablation system described earlier [22]. The second harmonic of a Nd:YAG laser (532 nm) was used to ablate a 5 mm-diameter La rod (Alfa AESAR, 99.9%) held in a stainless steel nozzle cap 5 mm from the orifice of the pulsed nozzle. The La monohalides were produced by the reaction of the ablated metal with an appropriate precursor contained in 5–7 bar of Ar. The best signals were obtained when the precursor gases and their concentrations for LaF, LaCl, LaBr, and LaI were, respectively: SF6 , 0.01%; Cl2 , 0.01%; Br2 , 0.006%; CH3 I, 0.01%. The very small concentrations were needed to minimize the formation of the La trihalides.

3. Observed spectra and assignments 3.1. LaF The transition frequencies of ground state (v ¼ 0) LaF were predicted using the values of the ground state rotational constant (B0 ) and centrifugal distortion constant (D0 ) obtained in an earlier electronic study [7]. The first lines of LaF were found within 10 MHz of this prediction, and consisted of two overlapping Doppler pairs split by spin–rotation coupling due to F. The lines were strong, requiring only 250 averaging cycles for an excellent signal-to-noise ratio; they are shown in Fig. 1. Further searching quickly revealed the remaining hyperfine components due to nuclear quadrupole coupling of 139 La (99.91% abundance, I ¼ 7=2). The corresponding transitions of the v ¼ 1 and v ¼ 2 excited vibrational states were also easily found, and required no more than 2000 cycles. Only the J ¼ 1–0 transition was available in the frequency range of our spectrometer. Its line frequencies and assigned quantum numbers are in the Supplementary Data, for all three observed vibrational states. Quantum number assignments follow the coupling scheme J þ ILa ¼ F1 ; F1 þ IF ¼ F.

Fig. 1. The J ¼ 1–0, F1 ¼ 9=2–7=2 transitions of 139 La19 F (v ¼ 0), showing the effect of 19 F spin–rotation coupling, obtained with 250 averaging cycles. The microwave excitation frequency was 14742.928 MHz operating at a pulse width of 0.4 ls. 4K data points were recorded at 50 ns sampling intervals; 8K transform is shown here.

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3.2. LaCl

3.3. LaBr

The ground vibrational state rotational transition frequencies of La35 Cl were initially predicted using the equilibrium spectroscopic constants of Xin and Klynning [11]. Those of La37 Cl were then predicted by mass scaling the rotational constant of La35 Cl. Transitions of each isotopomer were found within a few MHz of their predicted frequencies. They were significantly weaker than those of LaF, chiefly because of Cl quadrupole splitting plus isotope splitting, and required around 3500 averaging cycles for a usable signal-to-noise ratio; an example is in Fig. 2. They were assigned according to the coupling scheme J þ ILa ¼ F1 ; F1 þ ICl ¼ F. Several rotational transitions were observed for the two isotopomers; their frequencies and assignments are also in Supplementary Data. Transitions of the first excited vibrational state were considerably weaker than those observed for the ground state, and required as many as 16 000 averaging cycles to obtain a usable signal-to-noise ratio. Many of the rotational transitions observed in the ground state were painstakingly also recorded in the v ¼ 1 state for both isotopomers. Their frequencies are also in Supplementary Data.

The transition frequencies of La79 Br and La81 Br were predicted by mass scaling and comparing ratios of the accurate rotational constants of the scandium, yttrium, and lanthanum monohalides from present and earlier microwave spectroscopic studies [13–18], and, where these were not available, from electronic spectra [5,11,12,23]. As with LaF and LaCl, transitions of LaBr were readily found within a few MHz of their predicted frequencies. Assignments were confirmed by predicting and measuring several rotational transitions of both isotopomers. For the ground vibrational state (v ¼ 0) the line intensities were comparable to those of La35 Cl in the same state. However, those of the first excited vibrational state (v ¼ 1) were very weak, and data were collected only for La79 Br. A group of relatively strong lines of the J ¼ 3–2 rotational transition of La81 Br (v ¼ 0) is shown in Fig. 3. The measured frequencies and their assignments for all measured lines are in Supplementary Data. Again the coupling scheme was J þ ILa ¼ F1 ; F1 þ IBr ¼ F.

Fig. 2. The J ¼ 3–2, F1 ¼ 7=2–5=2 transitions of 139 La35 Cl (v ¼ 0), obtained with 3500 averaging cycles. The microwave excitation frequency was 17351.600 MHz operating at a pulse width of 0.4 ls. 4K data points were recorded at 50 ns sampling intervals, 8K transform is shown here.

Fig. 3. Selected hyperfine components of J ¼ 3–2 of 139 La81 Br (v ¼ 0), obtained with 4000 averaging cycles. The microwave excitation frequency was 8421.240 MHz operating at a pulse width of 0.4 ls. 4K data points were recorded at 50 ns sampling intervals; 8K transform is shown here.

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3.4. LaI

J 2  Dv b J4; H^rot ¼ Bv b

ð2Þ

The rotational transition frequencies of LaI were predicted using the values of Bv and Dv reported by Effantin et al. [12]. Lines of the ground vibrational state were again found within a few MHz of their predictions. With the added splittings due to the large nuclear spin of 127 I (I ¼ 5=2) the lines were even weaker than those of LaBr. Even so, it was possible to assign transitions of vibrationally excited molecules. Fig. 4 depicts a hyperfine component of one transition of LaI in its v ¼ 1 state: even after 15 000 averaging cycles the signal-to-noise level was still low. In this case, the quadrupole coupling constants of La and I are of the same order of magnitude, so the transition frequencies were assigned using the ‘‘parallel’’ scheme ILa þ II ¼ I; I þ J ¼ F. Again the measured transition frequencies and their assignments are in Supplementary Data.

1  ^ ð2Þ ^ ð2Þ ^ ð2Þ ^ ð2Þ  H^quadrupole ¼ V Q þ V x Qx ; 6 La La

ð3Þ

^ þ CX ^IX  J ^: H^spin–rot ¼ CLa^ILa  J

ð4Þ

4. Analysis of the spectra The Hamiltonian used to analyse all the observed spectra is H^ ¼ H^rot þ H^quadrupole þ H^spin–rot ;

ð1Þ

Fig. 4. Example hyperfine components recorded for the J ¼ 6–5 transition of 139 La127 I (v ¼ 1), obtained with 15 000 averaging cycles. The microwave excitation frequency was 10994.625 MHz operating at a pulse width of 0.2 ls. 4K data points were recorded at 50 ns sampling intervals; 8K transform is shown here.

Here, Bv and Dv are rotational and centrifugal distortion constants for vibrational state v. The determined parameters from Eq. (3) were eQqv (La) and eQqv (X), the nuclear quadrupole coupling constants of La and halogen, respectively, also in vibrational state v. CLa and CX are nuclear spin–rotation constants for La and halogen; they are also vibrational state-dependent. Because this Hamiltonian produced uncertainties in the spectral fits which were comparable to or less than the measurement uncertainties (see Supplementary Data), nuclear spin– spin coupling was not included in the Hamiltonian. The transitions in each vibrational state of each molecule were fit separately using PickettÕs global program SPFIT [24] to the constants in Eqs. (1)–(4). For LaF, since only one rotational transition was observed, the centrifugal distortion constant was fixed to the value calculated from [7]; furthermore, since IF ¼ 1=2, the 19 F nucleus has zero quadrupole moment, making eQqðF Þ automatically zero. Otherwise all the constants were obtained for all the molecules in all observed states. The results are in Tables 1–4, in comparison, where relevant for LaF, LaCl, and LaI, with the most precise values from the literature. It is clear from Tables 1–4 that very precise and accurate constants have been obtained for all four molecules. For the rotational constants of LaF, LaCl, and LaI, the precision is greatly improved over that of earlier results. Although for LaCl and LaI the present values agree well (to within 2 and 1 standard deviation, respectively) with those in the literature, the same cannot he said for LaF, where the deviations are beyond 4 standard deviations. The reasons for this are unclear. The earlier constants [7] would produce rotational transition frequencies too high by 100  20 kHz, which is well outside the accuracy of the microwave measurements. Even worse discrepancies were found earlier with results from the same laboratory for ScCl [17] and YI [16]. We are forced to conclude that there is a problem in the earlier results, possibly a calibration error or a systematic error arising from their fitting methods. The distortion constants, however, do agree with the earlier values. For La35 Cl, whereas the present work produced only the four lowest J transitions, Xin and Klynning [11] recorded ‘‘J-value regions up to 200.’’ Accordingly, it is not surprising that their distortion constants, for both the v ¼ 0 and v ¼ 1 states, are more precise. As a result of the supersonic expansion used to create these molecules, and thus the low sample

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Table 1 Molecular constants determined for LaF (MHz)a Parameter

v¼0

Literature valueb

v¼1

Literature valueb

v¼2

Literature valueb

Bv Dv 103 CLa 103 CF 103 eQqv (La)

7367.86720(24) 5.43221c 9.53(13) 35.6(10) )143.9287(50)

7367.915(10) 5.43221(30)

7331.21163(24) 5.44608c 9.80(13) 35.4(10) )142.7527(50)

7331.264(10) 5.44608(30)

7294.52501(24) 5.45994c 9.95(13) 35.4(10) )141.5909(50)

7294.586(10) 5.45994(30)

a

One standard deviation in parentheses, in units of least significant digit. Ref. [7]. c Dv is fixed at the value from [7]. b

Table 2 Molecular constants determined for LaCl (MHz)a Parameter

La35 Cl (v ¼ 0)

Literature valueb

La35 Cl (v ¼ 1)

Literature valueb

La37 Cl (v ¼ 0)

La37 Cl (v ¼ 1)

Bv Dv 103 CLa 103 CCl 103 eQqv (La) eQqv (Cl)

2893.564961(70) 0.9302(34) 13.011(54) 2.71(12) )132.6047(16) )0.9501(24)

2893.687(60) 0.9361(12)

2882.66003(13) 0.9315(88) 13.100(76) 2.64(19) )131.8885(26) )1.1674(30)

2882.775(59) 0.9382(12)

2768.80586(11) 0.8481(69) 12.503(57) 1.73(15) )132.6127(17) )0.7496(28)

2758.5987(11) 0.835(53) 13.21(36) 1.83(37) )131.991(60) )0.8935(99)

a b

One standard deviation in parentheses, in units of least significant digit. Ref. [11].

Table 3 Molecular constants determined for LaBr (MHz)a Parameter

La79 Br (v ¼ 0)

La79 Br (v ¼ 1)

La81 Br (v ¼ 0)

Bv Dv 103 CLa 103 CBr 103 eQqv (La) eQqv (Br)

1425.726965(30) 0.23223(60) 8.694(35) 6.957(57) )125.3037(28) 13.6242(21)

1421.69045(58) 0.2280(58) 9.55(72) 7.59(23) )124.94(11) 14.969(42)

1403.294661(33) 0.22560(68) 8.552(36) 7.405(64) )125.2999(46) 11.3750(22)

a

One standard deviation in parentheses, in units of least significant digit.

Table 4 Molecular constants determined for LaI (MHz)a Parameter

v¼0

Literature valueb

v¼1

Literature valueb

Bv Dv 103 CLa 103 CI 103 eQq(La) eQq(I)

918.384255(66) 0.10076(78) 9.53(13) 5.79(11) )117.546(28) )81.197(23)

918.47(12) 0.1031(9)

916.15771(24) 0.1095(32) 8.30(31) 5.63(30) )117.43(11) )84.889(78)

916.21(12)

a b

One standard deviation in parentheses, in units of least significant digit. Ref. [12].

temperatures, it can be inferred that the observed spectra were due to molecules in the ground electronic state. In all cases the patterns are those of a 1 þ R state, thus confirming the deduction of Xin and Klynning [11] for LaCl that its ground state has this configuration.

5. Discussion 5.1. Equilibrium bond distances For a diatomic molecule the vibrational dependence of the rotational constants Bv can be expressed as:

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   2 1 1 Bv ¼ B e  a e v þ   þ ce v þ 2 2

Equilibrium bond lengths re were calculated from the Be values, using the fundamental constants recommended by CODATA in the 1998 paper by Mohr and Taylor [27]. The equation was

ð5Þ

where Be is the equilibrium rotational constant, and ae and ce are vibration–rotation constants. For each observed isotopomer (except La81 Br) the three parameters in Eq. (5) were determined. For LaF, where constants for three vibrational states have been evaluated, Eq. (5) was used directly. For La35 Cl, La79 Br, and LaI, for which constants for only two vibrational states have been determined, two methods were used. For the first, ce was set to zero; for the second, it was set at 103 ae , a value typical of the alkali halides [25,26], but about double the LaF value. The resulting values are given in Tables 5–9. The Be values for which ce was set to zero are in the columns labeled Method M1 and Method M3; those for which ce 6¼ 0 are in the columns labeled Method M2 and Method M4. These methods are discussed below. The available literature values for LaF, La35 Cl and LaI are also in Tables 5–9.

Þ ¼ C½Be ðMHzÞlðuÞ 1=2 ; re ðA

ð6Þ

 MHz1=2 u1=2 [28], and l is where C ¼ 710:9001379(25) A the reduced mass of the molecule in atomic mass units. The atomic masses from the 1993 compilation of Audi and Wapstra [29] were used to produce re values by Methods M1 and M2 in Tables 5–9. Given that method M2 includes values of ce in the determinations, the re values obtained using it are probably the most accurate. The very high precision of both the rotational constants and the bond lengths means that great care must be taken in determining the uncertainties in the re values. The precision of the rotational constants reflects the frequency measurement accuracy of FTMW spectroscopy. In the determination of re using Eq. (6), the accuracies of the fundamental constants are now so high

Table 5 Equilibrium molecular constants and vibrational parameters calculated for LaFa Parameter

Literature valueb

Present work M2c

Be (MHz) ae (MHz) ce (kHz) ) re (A xe (cm1 ) xe xe (cm1 ) De (eV)

M4c 7386.18335(55) 36.62453(90) )15.52(29)

2.02337583(8)

2.02335060(8) 574.948(25) 2.11302(14) 4.84909(53)

7386.231(10) 36.62510(36) )13.185(42) 2.0233693(14)d 575.20538(11) 2.133415(33) 4.807033(74)e

a

One standard deviation in parentheses, in units of least significant digit. Ref. [7]. c M2 and M4 represent methods of calculating the rotational constants and bond lengths as described in the text. d Calculated from Be of [7] using atomic masses. e Calculated from constants in [7]. b

Table 6 Equilibrium molecular constants and vibrational parameters calculated for La35 Cla Parameter

Be (MHz) ae (MHz) ) re (A xe (cm1 ) xe xe (cm1 ) De (eV) a

Literature valueb

Present work M1c

M2c

M3c

M4c

2899.01743(12) 10.90494(14) 2.49804506(7)

2899.02561(12) 10.926745(70) 2.49804153(7) 341.43(62)d;e 1.0014(25)e 3.608(16)e

2899.01743(12) 10.90494(14) 2.49803040(7)

2899.02561(12) 10.926745(70) 2.49802688(7)

2899.14(6) 10.9121(9) 2.49799(3)f 341.603(1) 0.9797(5) 3.692(2)g

One standard deviation in parentheses, in units of least significant digit. Ref. [11]. c M1, M2, M3, and M4 represent methods of determining the rotational constants and bond lengths for LaCl (see text). d xe is determined using D0 in place of De . e Rotational constants from M2 used to evaluate these constants. f Calculated from Be of in [11] using atomic masses. g Calculated from constants in [11]. b

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Table 7 Equilibrium molecular constants and vibrational parameters calculated for La37 Cla Parameter

Be (MHz) ae (MHz) ) re (A xe (cm1 ) xe xe (cm1 ) De (eV)

Present work M1b

M2b

M3b

M4b

2773.90946(59) 10.2072(11) 2.4980401(3)

2773.91711(59) 10.22761(11) 2.4980367(3) 334.7(14)c;d 0.9610(53)d 3.613(36)d

2773.90946(59) 10.2072(11) 2.4980266(3)

2773.91711(59) 10.22761(11) 2.4980231(3)

a

One standard deviation in parentheses, in units of least significant digit. M1, M2, M3, and M4 represent methods of determining the rotational constants and bond lengths for LaCl (see text). c xe is determined using D0 in place of De . d Rotational constants from M2 used to evaluate these constants. b

Table 8 Equilibrium molecular constants and vibrational parameters calculated for La79 Bra Parameter

M1b

M2b

M3b

M4b

Be (MHz) ae (MHz) ) re (A xe (cm1 ) xe xe (cm1 ) De (eV)

1427.74522(29) 4.03651(58) 2.6520810(3)

1427.74825(29) 4.044587(30) 2.6520781(3) 236.17(31)c;d 0.5317(10)d 3.252(10)d

1427.74522(29) 4.03651(58) 2.6520770(3)

1427.74825(29) 4.044587(30) 2.6520742(3)

a

One standard deviation in parentheses, in units of least significant digit. M1, M2, M3, and M4 represent methods of determining the rotational constants (see text). c xe is determined using fixed value of D0 . d Rotational constants from M2 are used to evaluate these constants. b

Table 9 Equilibrium molecular constants and vibrational parameters calculated for LaIa Parameter

Be (MHz) ae (MHz) ) re (A xe (cm1 ) xe xe (cm1 ) De (eV)

Literature valueb

Present work M1c

M2c

M3c

M4c

919.49753(15) 2.22654(24) 2.8788573(2)

919.49920(15) 2.230995(66) 2.8788547(2) 189.5(19)e 0.3753(54)e 2.965(74)e

919.49753(15) 2.22654(24) 2.8788567(2)

919.49920(15) 2.230995(66) 2.8788541(2)

919.60(12) 2.257(3) 2.87870(19)d 184.43(2)f 0.334(1)f

a

One standard deviation in parentheses, in units of least significant digit. Ref. [12]. c M1, M2, M3, and M4 represent methods of determining the rotational constants and bond lengths for LaI (see text). d Calculated from Be of [12] using atomic masses. e Rotational constants from M2 are used to evaluate these constants. f Apparent ground state effective vibrational frequencies. b

that the uncertainty in C is negligible; accordingly, only the errors in the atomic masses and rotational constants were considered in obtaining the uncertainties in the re values given in Tables 5–9. Determining the true accuracy of such precise re values is somewhat more awkward. There are so many significant figures that the possibility exists that several are outside the validity of the Born–Oppenheimer approximation. In the first place, although the uncertainty

of ce is less than 2% for LaF, it is nearer 50% for LaCl, LaBr, and LaI (given the probable accuracy of the ap proximation). This produces an uncertainty of 106 A in re for these three molecules. Secondly the experimentally determined Be values are in reality Dunham Y01 ðDÞ values, and a Dunham correction DY01 should be applied [30]. The value of this correction depends on the value of ce which is reliably determined only for LaF; it,  and is probably similar for all molecules. too, is 106 A

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It is also relevant to consider where breakdown of the Born–Oppenheimer approximation is starting to occur. A standard test is to compare re values for different isotopomers. In the present case this can be done only for La35 Cl and La37 Cl, whose re values differ by . This is an order of magnitude greater than 4 106 A the uncertainties from the atomic masses and the measurements (Tables 6 and 7), and somewhat larger than the uncertainties due to the uncertainties in ce described above (though the latter are systematic, and should be the same for both isotopomers). Thus the isotopic variations represent the uncertainties of the re values within the Born–Oppenheimer approximation. Born–Oppenheimer breakdown (BOB) results chiefly through adiabatic and non-adiabatic mechanisms [30]. It was shown recently [28] that where non-adiabatic effects dominate, the point at which these effects become clear can be obtained by substituting ionic masses for atomic masses in the re bond length determination. This was done in the present work, where method M3 replaced M1, and method M4 replaced M2. For LaCl the variation found for re using this procedure ) was rather larger than that found by (1:4 105 A ) (Tables 6 and 7). varying the atomic mass (4 106 A This would imply, but by no means proves, that the dominant cause of BOB in LaCl is non-adiabatic, but that it is counterbalanced by a significant adiabatic contribution. When ionic masses are substituted for atomic masses  for LaF, 1:4 105 A  the changes in re are 2:5 105 A  for La79 Br, and 6 107 A  for LaI. for LaCl, 4 106 A Except for LaI, in all cases the changes are at least an order of magnitude bigger than the statistical uncertainties, so the effect appears to be real. Non-adiabatic effects arise through excitations to excited electronic states, so if the molecule has low lying excited states the effect is expected to be more pronounced. This is indeed the case for the LaX molecules where the a3 D states of LaF and LaI are only 1432 and 1064 cm1 , respectively, above the ground state [5,12], and a similar situation is expected for LaCl [11]. A very similar situation was recently found for ZrO and ZrS [31].

where De is the equilibrium centrifugal distortion constant, which can be obtained using an equation analogous to Eq. (5):   1 : ð9Þ Dv ¼ De  be v þ 2 This was used for LaF and LaI, where the vibrational dependences of Dv are clear (Table 1). For the other two molecules, De was approximated to D0 . The resulting vibration wavenumbers are in Tables 5–9, with literature values for comparison where available. For LaF and La35 Cl the differences between the calculated values and those derived directly from experiment are better than 2%, a remarkable result considering both the Kratzer and Pekeris relations are approximations. For LaI the agreement is only moderate, with xe xe differing from the literature value by more than 11%. It has also been possible to estimate the dissociation energies, De , using [34]: De ¼

x2e 4xe xe

The results are also in Tables 5–9. With no experimental results available for comparison, De was also estimated where possible from the xe and xe xe values in the literature; these results are also in Tables 5–9. 5.3. Hyperfine coupling constants The halogen nuclear quadrupole coupling constants (NQCC) of the ground state lanthanum monohalides are summarized in Table 10, in comparison with the values for the corresponding alkali metal and alkaline earth monohalides. All the values are small, with the magnitudes changing in the order MCl < MBr < MI, in keeping with the trends in the halogen quadrupole moments. The values are typical of those of highly ionic molecules. The ionic characters of LaCl, LaBr, and LaI can be estimated from their respective halogen NQCCs using the equation [34]: ie ¼ 1 þ

5.2. Estimates of vibration frequencies and dissociation energies The harmonic vibration frequency, xe , and the anharmonicity constant, xe xe , were estimated using the equations of Kratzer [32] and Pekeris [33], respectively: sffiffiffiffiffiffiffiffi 4B3e ; ð7Þ xe ¼ De  xe xe ¼ Be

ae xe þ1 6B2e

2 ;

ð8Þ

ð10Þ

eQqðXÞ ; eQqn10 ðXÞ

ð11Þ

where eQqn10 (X) is the NQCC for a singly occupied npz orbital of the atomic halogen: eQq310 ð35 ClÞ ¼ 109:74 MHz, eQq410 ð79 BrÞ ¼ 769:76 MHz, and eQq510 ð127 IÞ ¼ 2292:71 MHz. Eq. (11) assumes zero hybridization on the halogens, and neglects screening corrections because the halide ion has a filled p-shell. The results are in Table 11, also in comparison with corresponding values for alkali metal and alkaline earth halides. The values for LaCl, LaBr, and LaI are 99.1, 98.2, and 96.5%, respectively. These are very large values. For comparison, the value for NaCl, which is generally regarded as fully ionic, is 94.9% [35]. Unfortunately, this treatment will not

D.S. Rubinoff et al. / Journal of Molecular Spectroscopy 218 (2003) 169–179

177

Table 10 Ground state halogen quadrupole coupling constants of lanthanum monohalides and related species eQq0 (MHz)

M35 Cl

M37 Cl

M79 Br

M81 Br

45

)3.7861(35)a )11.622(21)c )0.8216(43)e )0.9501(24) )1.002(4)h 3.96(84)j )5.6468(60)j

)2.9824(36)a

39.0857(24)b 110.3133(36)d 12.9352(16)f 13.6242(21) 20.015(7)i 7.15(46)j 58.06890(3)j

32.6438(19)b 92.1532(35)d 10.8017(16)f 11.3750(22) 16.714(6)i 5.54(41)j 48.50868(1)j

Sc 24 Mg 89 Y 139 La 40 Ca 88 Sr 23 Na 137 Ba 39 K 85 Rb 133 Cs

0.0559(4)j 0.774(9)j 1.76517(6)j

)0.621(20)e )0.7496(28) )0.810(4)h )4.4470(13)j 0.0449(3)j 1.39230(6)j

10.2383(7)j 3.50(29)j ) 6.47(16)j

8.5513(10)j 2.86(27)j

MI

)82.982(19)g )81.197(23) )131.84(4)j )54.42(47)j )262.1407(10)j )33.62(12)j )86.79(10)k )59.89(30)l )15.33(15)j

Metals are listed in order of decreasing Pauling electronegativity. a Ref. [17]. b Ref. [18]. c Ref. [36]. d Ref. [37]. e Ref. [13]. f Ref. [14]. g Ref. [16]. h Ref. [38]. i Ref. [39]. j Ref. [40]. k Ref. [41]. l Ref. [42].

Table 11 Calculated ionic characters of lanthanum monohalides and related speciesa ic (%)

M35 Cl

M37 Cl

M79 Br

45

96.5 89.4 99.3 99.1 99.1 103.6 94.9

96.6

94.9 85.7 98.3 98.2 97.4 99.1 92.5

94.9 85.7 98.3 98.2 97.4 99.1 92.5

98.7 99.5 100.8

98.7 99.6

Sc Mg 89 Y 139 La 40 Ca 88 Sr 23 Na 137 Ba 39 K 85 Rb 133 Cs 24

100.1 100.7 101.6

99.3 99.1 99.1 94.9 100.1 101.6

M81 Br

MI

96.4 96.5 94.2 97.6 88.6 98.5 96.2 97.4 99.3

Metals are listed in order of decreasing Pauling electronegativity. a Ionic character is determined using Eq. (10) with the halogen quadrupole coupling constants from Table 10.

work for LaF as 19 F has zero quadrupole moment. Nevertheless, on electronegativity arguments, it is reasonable to infer that LaF should be even more ionic than LaCl. The 139 La quadrupole coupling constants are in Table 12 in comparison with those of 45 Sc in the corresponding Sc halides. Results from the literature for LaO and ScO are also included. Several points stand out: (i) For the halides the ratio of a given LaX constant to that of the corresponding ScX is nearly the same for all X. (ii) This same ratio is NOT the ratio of the nuclear quadrupole moments [44] of 139 La to 45 Sc. (iii) Whereas the 45 Sc coupling constants of the halides and oxide are very close, this is not the case for the 139 La coupling

constants. It appears that although the change of the metal electron distribution is essentially the same on variation of the halogen, the absolute electron distribution at the nuclei of the two metals is quite different. In [17] the 45 Sc coupling constants were investigated using a straightforward Townes–Dailey-type approach which assumed the valence MOÕs to be the same in ScO and ScF. A plausible picture was obtained by adding an electron to the HOMO of ScO. However, when orbital populations from a preliminary ab initio calculation were used in this approach, the results strongly contradicted the above assumption for the 45 Sc coupling constants, even though they produced a plausible qualitative rationale for the halogen coupling constants. The

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D.S. Rubinoff et al. / Journal of Molecular Spectroscopy 218 (2003) 169–179

Table 12 Comparison of

139

La and

45

Sc quadrupole coupling constantsa

MX

eQq0 ð45 ScÞ (MHz)

eQq0 ð139 LaÞ (MHz)

M16 O M19 F M35 Cl M37 Cl M79 Br M81 Br M129 I

72.240(5)b 74.0861(51)d 68.2067(29)d 68.2062(29)d 65.2558(32)e 65.2597(38)e

)84.28273(51)c )143.9287(50) )132.6047(16) )132.6127(17) )125.3037(28) )125.2999(46) )117.546(28)

a

One standard deviation in parentheses, in units of least significant digit. b Ref. [43]. c Evaluated using PickettÕs exact fitting program, SPFIT [24], using measured transition frequencies in [46]. d Ref. [17]. e Ref. [18].

ab initio calculations did, however, produce field gradients which reproduced the 45 Sc coupling constants quite well. The conclusion drawn from these results was that discussion of transition metal coupling constants in terms of a simple Townes–Dailey-type approach must be viewed with great caution. With this result, there seems little point in pursuing a simple rationale for the 139 La coupling constants. A more sensible approach might be to follow the one taken recently for 91 Zr and 45 Sc: ab initio field gradients were calculated for both 91 ZrO=91 ZrS [45] and 45 ScX [19]. These field gradients, in conjunction with the eQq values from FTMW spectroscopy, were then used to improve the accuracy of the 91 Zr and 45 Sc nuclear quadrupole moments. A similar project would seem to be in order for 139 La, though in this case it will be more difficult, not least because relativistic effects will probably have to be taken into account. It should be noted that similar considerations apply to the nuclear spin–rotation constants. A proper accounting for these constants requires accurate knowledge of both the molecular wave functions and the electronic energy levels, for both of which current information is sparse. The accurate values obtained here should provide a sensitive test for future theoretical determinations.

6. Conclusions The pure rotational spectra of the lanthanum monohalides, LaF, LaCl, LaBr, and LaI have been measured for the first time. Transitions have been measured for all halogen isotopomers with 139 La, in their ground and one or more excited vibrational states, except for 139 La81 Br, for which only ground state data were recorded. Rotational constants and centrifugal distortion constants have been presented, along with the nuclear quadrupole coupling constants and nuclear

Table 13 Equilibrium bond lengths of lanthanum monohalides LaX

) re (A Present worka

LaF La35 Cl La37 Cl La79 Br LaI

b

2.02337553(8) 2.49804153(7) 2.4980367(3) 2.6520781(3) 2.8788547(2)

Literature 2.0233693(13)c 2.49799(3)d

2.87870(19)e

a

Equilibrium bond lengths from method M2. One standard deviation in parentheses, in units of least significant digit. c Calculated from constants in [7] using atomic masses. d Calculated from constants in [11] using atomic masses. e Calculated from constants in [12] using atomic masses. b

spin–rotation coupling constants of each molecule in each observed vibrational state. The ground electronic state of all the molecules studied has been confirmed as 1 þ R , based on the intensities and hyperfine patterns of the observed transitions. The rotational constants are the most accurate determined to date, and have produced correspondingly accurate equilibrium (re ) internuclear distances. The latter are summarized in Table 13, in comparison with literature values which indicate the degree of improvement from the present work. The isotopic variations  indicate the point at which the Born–Oppen106 A heimer approximation is losing its validity. The distortion constants have given good estimates of the vibration frequencies and dissociation energies. From the halogen nuclear quadrupole coupling constants the molecules have been found to be nearly fully ionic.

Acknowledgments This research has been supported by the Natural Sciences and Engineering Research Council of Canada.

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