Physical Chemistry Chemical Physics

Pure rotational spectra of LuF and LuCl

Stephen A. Cooke*, Christine Krumrey and Michael C. L. Gerry*
Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancouver, BC, Canada V6T 1Z1. E-mail: mgerry@chem.ubc.ca

The pure rotational spectra of two isotopic species of LuF and three of LuCl have been measured in the frequency range 5–17 GHz using a cavity pulsed jet Fourier transform microwave spectrometer. The samples were prepared by laser ablation of Lu metal in the presence of SF₆ or Cl₂, and stabilized in supersonic jets of Ar. Spectra of molecules in states having v = 0, 1, and 2 have been measured, to produce rotational constants and centrifugal distortion constants, along with hyperfine constants for all the nuclei. Dunham-type fits for LuCl produced a Born–Oppenheimer breakdown parameter for Cl. Although a theoretical calculation showed that Lu in LuCl should have a significant field shift effect parameter, it could not be determined from the spectrum. Equilibrium internuclear distances, r_e, and dissociation energies have been evaluated for both molecules. The nuclear quadrupole coupling constants are discussed in terms of the molecular electronic structure.

Although the lutetium monohalides, LuX (X = F, Cl, Br, I), are rare, there are nonetheless reports in the literature of electronic spectra of all four. For the last three (LuCl, LuBr, LuI) two electronic transitions have been observed for each, but only at vibrational resolution;¹ no rotationally resolved spectra have thus far been reported.

The electronic spectrum of LuF, however, has been studied at high resolution in considerable detail. Around 150 bands have been observed, comprising nine systems, in the wavelength range 3000–8000 .^2–5 Each band is remarkably regular, with a dearth of perturbations.

The ground electronic state is X ¹⁺, with most observed excited states being ¹ or ¹. No ³ or ³ states in Hunds case (a) could be identified. From rotationally resolved spectra it was possible to do global fits^3,4 to produce quite accurate spectroscopic constants for several states, and particularly for the ground vibronic state. Values for the equilibrium internuclear distance r_e were obtained.³ Subsequently hyperfine structure in the B ¹–X ¹ band has yielded several hyperfine parameters,⁶ including an estimate of the ¹⁷⁵Lu nuclear quadrupole coupling constant eQq(¹⁷⁵Lu) as –2918(600) MHz. From the contributions of F to the hyperfine structure, the ionic character of LuF was deduced to be >95%.

In spite of all these results there is still much more information to be obtained from the spectra of these molecules. For all of them except the fluoride there are no high resolution data and the bond lengths are unknown. Lutetium has two isotopes, and spectra of isotopomers containing only one have been observed. The rare isotope ¹⁷⁶Lu (2.59% abundant) has nuclear spin I = 7, one of the largest known. Both isotopes have very large nuclear quadrupole moments, so that eQq(Lu) values larger than the rotational constants are entirely possible.

The Lu-containing molecules are also of astrophysical interest. Some of the lanthanide ions were detected in the optical spectrum of Arcturus⁷ and in Przybylskis holmium star⁸ as well as in HR6958, a star with a peculiar chemical composition.⁹ Sneden et al.¹⁰ have recently found spectroscopic evidence of Lu along with some other heavy metals in the atmosphere of the extremely metal-poor galactic halo giant CS 22892-052. Lu was also observed by Johnson and Bolte¹¹ very recently in CS 31062-050. This search was performed with three different terrestrial telescopes and the Hubble Space Telescope, mostly with high-resolution spectrometers. According to astro- and elementary physical theories Lu is formed in neutron capture processes within long-lived low- and intermediate-mass stars. From there the nucleosynthetic material is injected into the interstellar medium,^12,13 where it is available for the synthesis of corresponding molecular compounds.

In this paper we report the high resolution rotational spectra of LuF and LuCl in their electronic ground states. The measurements were made using a cavity pulsed jet Fourier transform microwave (FTMW) spectrometer of the Balle–Flygare type.^14,15 The samples were prepared via a laser ablation technique we have now used for many studies.^16–19 Spectra have been recorded for two isotopomers of LuF and three of LuCl in their ground vibrational states; for the isotopomers containing ¹⁷⁵Lu, spectra of vibrationally excited molecules have also been measured. Rotational constants, hyperfine constants and internuclear distances have been determined. The results are supported by theoretical calculations with the density functional theory method.

Because a detailed description of the spectrometer used in these experiments has been given earlier,^15,16 only essential features are presented here.

The instrument¹⁵ contains a Fabry–Perot cavity consisting of two spherical mirrors, 38.4 cm radius of curvature and 24 cm in diameter, approximately 30 cm apart. One mirror is fixed and the other can be moved to tune the cavity. A pulsed nozzle (General Valve, Series 9) is mounted in the fixed mirror, from which samples entrained in a noble gas (usually Ar or Ne) are injected into the cavity. This arrangement gives optimum sensitivity and resolution. However, because the jet travels parallel to the axis of propagation of the microwaves, all lines are doubled by the Doppler effect. The microwave synthesizer is referenced to a Loran C frequency standard accurate to one part in 10¹⁰. The frequency range of the experiments was 5–17 GHz. Observed line widths were 7–10 kHz fwhm, and the estimated measurement accuracy of the lines is ±1 kHz.

Details of the laser ablation system are in ref. 16. A 5 mm diameter lutetium rod (HEFA Rare Earth Canada) was held in a stainless steel nozzle cap 5 mm from the outlet of the pulsed nozzle. It was ablated with the fundamental (1064 nm) of a Nd:YAG laser. LuF and LuCl were prepared by the reaction of the resulting plasma with 0.1% SF₆ or Cl₂, respectively, in Ar at backing pressures of 5–7 atm. The resulting mixture was injected into the microwave cavity as a supersonic jet, which had the effects of stabilizing the LuF and LuCl molecules in a collision free environment and of reducing their rotational temperatures to a few degrees Kelvin.

Calculations have been performed using the Amsterdam Density Functional (ADF) routine.^20–23 The method, based on density functional theory (DFT), employs an all electron basis set (QZ4P) of Slater-type orbitals (STOs). For both components of the diatomic species the statistical average of orbital potentials (SAOP)²⁴ model was also applied. A method very recently developed by Cooke et al.²⁵ provides single point calculations presenting the electron density at the Lu nucleus in LuF and LuCl, at different internuclear distances in the range of 1–4 . Single point calculations were also used to generate potential functions for the molecules, predict their equilibrium internuclear distances and provide electron densities needed to determine nuclear shift effects. In addition the vibrational frequencies were calculated by applying the VIBROT program using the potential energy provided by the DFT computations.

The initial search for pure rotational transitions of LuF used the rotational constant of ¹⁷⁵LuF in ref. 3. The strongest Lu hyperfine component of the J = 1–0 transition near 16256 MHz was found within 65 kHz of the prediction. Using a predicted eQq(¹⁷⁵Lu) value from the DFT calculations, the remaining two components were easily found. The lines were strong, and visible within 5 pulses. Their assignments were confirmed by the extra splittings due to nuclear spin–rotation coupling of ¹⁹F. The central ¹⁷⁵Lu hyperfine component is in Fig. 1. Lines of molecules in the v = 1 and v = 2 excited vibrational states were similarly easily assigned and measured.

	Fig. 1 Section of power spectrum of the J= 1–0, v= 0 transition of 175LuF obtained using 150 averaging cycles. 4k data points were recorded and the power spectrum is shown as a 4k transformation.

To assign lines of ¹⁷⁶LuF (2.59% abundant) an r₀ geometry, plus a scaled value of eQq(¹⁷⁶Lu), both from the ¹⁷⁵LuF results, provided an excellent prediction. Lines of this isotopomer required 1800 pulses for a usable signal-to-noise ratio. Overall, only the J = 1–0 transition was available in the frequency range of our spectrometer. For ¹⁷⁶LuF, lines of molecules only in the state v = 0 were found.

The measured line frequencies and assigned quantum numbers for both isotopomers are in Table 1. The quantum number assignments follow the coupling scheme J + I_Lu = F₁ and F₁ + I_F = F.

J – J	F1 – F1	F – F	v = 0	Obs. – calc.a	v = 1	Obs. – calc.a	v = 2	Obs. – calc.a
175Lu19F
1 – 0	7/2–7/2	3–3	15 300.7307	0.7	15 212.6081	–0.3	15 124.6638	0.9
	7/2–7/2	4–4	15 300.7383	–0.7	15 212.6175	0.3	15 124.6711	–0.9
	9/2–7/2	4–3	16 256.0931	–1.6	16 160.6626	–1.7	16 065.4542	–2.3
	9/2–7/2	5–4	16 256.1358	1.6	16 160.7047	1.7	16 065.4978	2.3
	5/2–7/2	3–4	16 543.5898	1.9	16 445.9238	2.2	16 348.5631	2.7
	5/2–7/2	2–3	16 543.5898	–1.9	16 445.9493	–2.2	16 348.5487	–2.7
176Lu19F
1–0	7–7	13/2–13/2	15 153.2464	2.3
	7–7	15/2–15/2	15 153.2464	–2.3
	8–7	15/2–13/2	16 353.2600	–1.5
	8–7	17/2–15/2	16 353.3002	1.5
	6–7	13/2–15/2	16 529.2830	1.8
	6–7	11/2–13/2	16 529.3120	–1.8
a Observed frequency – frequency calculated using the constants of Table 2 (values in kHz).

Preliminary to the Dunham-type fits described below, state-by-state analyses were carried out for each isotopomer in each vibrational state. The program used was Picketts global least squares program SPFIT,²⁶ and the Hamiltonian was:

= rot + quad + spin–rot

(1)

r = Bv2 – Dv4

(2)

quad = (2)Lu(2)Lu + (2)hal(2)hal

(3)

spin–rot = CI(Lu)ÎLu· + CI(X)ÎX·

(4)

Because the only previously reported spectrum of LuCl showed no rotational structure, the DFT calclulation was first used to predict r_e and _e, and hence a value for the rotational constant of ¹⁷⁵Lu³⁵Cl in the ground vibrational state. A value of eQq(¹⁷⁵Lu) from the DFT calculation was scaled by the ratio of the experimental and predicted values for LuF to predict the basic ¹⁷⁵Lu hyperfine patterns. The initial search for transitions produced signals for J = 2–1 within 80 MHz of the prediction. Again the lines were strong, and visible this time after 20 cycles. An example is in Fig. 2. Mass scaling, plus use of a DFT _e value, produced excellent predictions of lines of less abundant isotopomers and of vibrationally excited molecules.

Lines of the J = 1–0 and 2–1 transitions of ¹⁷⁵Lu³⁵Cl (states v = 0, 1, 2), and ¹⁷⁵Lu³⁷Cl (states v = 0, 1), and of J = 2–1 of ¹⁷⁶Lu³⁵Cl (state v = 0) were measured and assigned. The coupling scheme used was J + I_Lu = F₁ and F₁ + I_Cl = F. The measured frequencies and their assignments are in Tables 3 and 4.

As with LuF, preliminary state-by-state analyses were carried out for each observed isotopomer and vibrational state of LuCl. The program was again SPFIT. The fitted constants were the rotational and centrifugal distortion constants, plus nuclear quadrupole and nuclear spin–rotation coupling constants of both Lu and Cl. The results are in Table 5.

	Fig. 2 Section of power spectrum of the J= 1–0, v= 0 transition of 175Lu35Cl obtained using 1776 averaging cycles. 4k data points were recorded and the power spectrum is shown as a 4k transformation.

J–J	F1–F1	F–F	v = 0	Obs. – calc.a	v = 1	Obs. – calc.a	v = 2	Obs. – calc.a
1–0	7/2–7/2	5–5	5548.6994	–0.5
		3–3	5548.7688	0.3
		4–4	5548.8152	–0.5
	9/2–7/2	5–4	6374.4979	1.2	6348.4542	0.0
		4–3	6374.5240	–0.7	6348.4896	–1.0
		6–5	6374.5941	0.4	6348.5791	–0.6
		3–2	6374.6173	0.3	6348.6126	2.0
	5/2–7/2	3–4	6628.0479	–0.2	6600.5705	–0.0
		4–5	6628.0905	–0.3	6600.6258	–0.4
2–1	9/2–9/2	3–3	11 663.3913	1.3
		6–6	11 663.4167	–0.9	11 617.5186	0.6	11 571.6791	1.5
		4–4	11 663.4726	2.1	11 617.5879	1.0
		5–5	11 663.4955	–0.7	11 617.6198	–0.3	11 571.7629	–1.5
	7/2–9/2	2–3	11 759.0501	–0.1
		5–6	11 759.0986	–0.1	11 712.6029	0.0
		3–4	11 759.1960	1.5
		4–5	11 759.2454	1.1	11 712.7918	0.2
	5/2–5/2	1–1	11 941.3773	–0.9
		4–4	11 941.4521	–1.1	11 893.9875	–0.3
		3–3	11 941.5748	–2.2	11 894.1477	–0.8
	11/2–9/2	6–5	12 387.3144	0.0	12 337.3351	–1.5	12 287.4381	–3.6
		7–6	12 387.3481	–2.2	12 337.38100	–1.8	12 287.4855	3.6
	9/2–7/2	5–4	12 489.1772	–0.1	12 438.6109	0.2
		4–3	12 489.2271	0.4	12 438.6760	1.0
		6–5	12 489.3132	1.8	12 438.7860	1.7
		3–2	12 489.3556	0.2	12 438.8413	–0.9
	3/2–5/2	3–4	12 490.6881	–1.8	12 440.1338	–2.5	12 389.6583	0.0
	7/2–7/2	4–4	12 584.9270	1.7	12 533.7838	1.6
		3–3	12 584.9517	1.1
		5–5	12 584.9926	0.1	12 533.8707	1.6
		2–2	12 584.0143	–1.3
a Observed frequency – frequency calculated with the constants of Table 5 (values in kHz).

J–J	F1–F1	F–F	v = 0	Obs. – calc.a	v = 1	Obs. – calc.a
175Lu37Cl
1–0	9/2–7/2	5–4	6098.8361	1.7
		4–3	6098.8555	–0.8
		6–5	6098.9121	2.7
		3–2	6098.9271	–1.0
	5/2–7/2	3–4	6352.8041	–0.7
		2–3	6352.8214	–3.0
		4–5	6352.8394	1.1
2–1	9/2–9/2	4–4	11 110.8369	2.8
	11/2–9/2	6–5	11 834.7735	–3.0	11 788.1075	–0.2
		7–6	11 834.8017	–2.4	11 788.1430	0.2
	9/2–7/2	5–4	11 936.4994	–0.2
		4–3	11 936.5406	2.6
	3/2–5/2	3–4	11 938.0727	–5.3
	7/2–7/2	5–5	12 033.7404	1.0
	5/2–7/2	3–4	12 468.4457	3.6
		1–2	12 468.4715	0.8
176Lu35Cl
2–1	8–8	19/2–19/2	11 577.4157	1.3
	9–8	19/2–17/2	12 415.4210	–1.5
		21/2–19/2	12 415.4531	–2.7
	5–6	13/2–15/2	12 478.4696	–1.4
	7–7	17/2–17/2	12 561.0464	–0.8
	8–7	17/2–15/2	12 616.8306	1.4
		13/2–11/2	12 616.9563	3.0
	6–7	13/2–11/2	12 942.6297	0.8
a Observed frequency – frequency calculated with the constants of Table 5 (values in kHz).

It is possible to use the rotational constants in Tables 2 and 5 to determine values of the equilibrium internuclear distance r_e. However, such a procedure ignores the possibility of Born–Oppenheimer breakdown (BOB), which recently has been found to be significant for a large number of metal-containing diatomic molecules. These have included ZrO and ZrS,²⁷ HfO,²⁸ HfS,²⁹ BiN,³⁰ PtSi,³¹ SbN and SbP,¹⁸ and PtS.¹⁷ It thus seemed appropriate to check whether BOB has an effect on the spectra of LuF and LuCl.

Accordingly, for both molecules, were carried out using the energy expression^32–34 for isotopomer of diatomic molecule AB in a ¹ electronic state:

(5)

(6)

Eqns. (5) and (6) do not consider hyperfine structure. Accordingly, to apply them to LuF and LuCl it was necessary to calculate unsplit line frequencies, with hyperfine structure removed, for each observed rotational transition. This was done using the rotational constants and centrifugal distortion constants of Tables 2 and 5, retaining enough significant figures to reproduce the experimental accuracies.

Unfortunately, because of lack of data BOB could not be detected for LuF. With four measured transitions, a fit could be obtained only for U₀₁, U₁₁, and U₂₁, with U₀₂ fixed at its value derived from the distortion constant D_e found in the literature.⁴ The results are given in Table 6, which shows well-determined values for the parameters. Values are also presented for Y₀₁, Y₀₂, Y₁₁, and Y₂₁, plus r_e (discussed in Section 6(a)), for the two isotopomers.

	U01/u MHz	U02/u2 MHz	U11/u3/2 MHz	U21/u2 MHz	Lu01	01F
LuF	137 505.300(15)	–1.771a	–3322.784(122)	15.49(17)	0a	0a
	Y01/MHz	103Y02/MHz	Y11/MHz	103Y21/MHz
	Be	–103De	–e	103e	re/
175LuF	8023.7399	–6.03	–46.836 91	52.75	1.917 118 15
176LuF	8019.2640	–6.02	–46.797 72	52.69	1.917 118 14
a Fixed value.

The situation was more favourable for LuCl. In this case there are nine available measured transitions. Their frequencies could be used only cautiously, because they had to be calculated from the rotational and distortion constants derived using SPFIT as discussed in Section 4 above. There was no problem for ¹⁷⁵Lu³⁵Cl in the states v = 0 and 1, or for ¹⁷⁵Lu³⁷Cl in the state v = 0; for each of these situations two rotational transitions were measured and a full set of constants was derived. For ¹⁷⁵Lu³⁵Cl (v = 2), ¹⁷⁶Lu³⁵Cl (v = 0) and ¹⁷⁵Lu³⁷Cl (v = 1) only one transition was found. Accordingly, a value for the distortion constant had to be assumed, but this was not a problem in obtaining the unsplit line frequency, because any error would be absorbed by the rotational constant. However, for the first two isotopomers, a value for C_I(Cl) also had to be assumed. Although its value was estimated by scaling from known values with the rotational constants and nuclear g-factors, and was hence reasonable, its contribution was 1–2 kHz to the transition frequencies. These data were accordingly weighted down by a factor of 4 in the Dunham-type fit. For ¹⁷⁵Lu³⁷Cl (v = 1) every parameter except the rotational constant had to be assumed, making these measurements useless in the Dunham-type fit; they were omitted.

Even then, the small data set meant that a fairly complex procedure had to be carried out. An initial fit to eqns. (5) and (6) including U₀₁, U₁₁, U₀₂, and U₂₁ was performed, but omitting all BOB parameters; an unacceptable rms deviation of 10 kHz was obtained. A second fit released in addition ^Lu₀₁ and ^Cl₀₁. This drastically reduced the rms deviation to less than 1 kHz, and produced two seemingly good BOB parameters. However, ^Lu₀₁ was strongly correlated with U₀₁, so two new fits were done, in which only one of ^Lu₀₁ or ^Cl₀₁ was released, with the other set to zero. The value for ^Lu₀₁ changed drastically, and was still correlated with U₀₁. The value of ^Cl₀₁ held firm and was well determined. The rms value was 2 kHz, which was acceptable. The result with ^Lu₀₁ = 0 is presented in Table 7 as Method A.

However, ^Lu₀₁ is unlikely to be zero. Accordingly a new fit was carried out assuming ^Lu₀₁ ^Cl₀₁.^17,32 The results are in Table 7, (Method B), which also contains values for Y₀₁, Y₀₂, Y₁₁,and Y₂₁, plus equilibrium internuclear distances evaluated from Y₀₁ for each isotopomer. The isotopic variation of r_e is comparable to that found in other molecules, such as ZrO,²⁷ HfS²⁹ and PtSi.³¹

	U01/u MHz	U02/u2 MHz	U11/u3/2 MHz	U21/u2 MHz	Lu01	Cl01
Method A (VLu01 = 0)a
	89 729.38(16)b	–1.008(47)	–1946.30(15)	7.20(30)	0c	–2.96(12)
Method B (VLu01 = 0)a
	89 730.22(16)	–1.010(47)	–1946.29(15)	7.19(30)	–2.97d	–2.97(12)
	Y01/MHz	103Y02/MHz	Y11/MHz	103Y21/MHz
	Be	–103De	–e	103e	re/
175Lu35Cl	3078.7500	–1.191	–12.370 73	8.45	2.373 2930
175Lu37Cl	2940.1391	–1.086	–11.544 74	7.70	2.373 2900
176Lu35Cl	3075.8296	–1.189	–12.353 14	8.43	2.373 2929
Method C (VLu01 = 2.4 × 10–6 fm2)e
	01 = 89 730.24(16)f	–1.011(47)	–1946.28(15)	7.18(30)	–2.98d	–2.98(12)
a VLu01 was fixed at this value in the fit.  b Numbers in parentheses are one standard deviation in units of the least significant figures.  c Lu01 was fixed at zero in Method A.  d Lu01 was held fixed at Cl01 in Methods B and C.  e This VLu01 value, obtained from the DFT calculations, was fixed in the fit.  f This value is 01, related to U01 by eqn. (9).

There is an additional concern. Because Lu is a heavy atom, it is possible that the spectrum may be significantly affected by nuclear field shift effects. These arise because the Lu nucleus can no longer be considered a point charge, but to have a volume. To account for this possibility eqn. (6) for Y₀₁ was modified to:³⁴

(7)

(8)

01 = U01(1 + VLu01r2Lu).

(9)

A new fit was then carried out, using eqns. (5) and (7). This required that a reference isotopomer be chosen;³⁴ this was ¹⁷⁵Lu³⁵Cl. In this case r²_LuLu in eqn. (7) is the change in mean square nuclear charge radius of Lu on isotopic substitution (here from ¹⁷⁵Lu to ¹⁷⁶Lu); it is also available from tables.³⁶ ₀₁ is that of the reference isotopomer ¹⁷⁵Lu³⁵Cl. Because of insufficient data, V^Lu₀₁ was fixed at a value estimated using eqn. (8), with (d^Lu_el/dr)_re evaluated from the results of the DFT calculations²⁵ described in section 3 above.

The final fit was thus to ₀₁, U₁₁, U₀₂, U₂₁, and ^Cl₀₁, with ^Lu₀₁ constrained to ^Cl₀₁, and V^Lu₀₁ fixed at 2.4 × 10^–6 fm^–2 from the DFT calculation. The result is in Table 7 (Method C).

In Table 7 the constants from Methods A and B show that U₀₁ varies as ^Lu₀₁ is varied, in keeping with the high correlation between these constants found in the initial fits. Thus fixing ^Lu₀₁ at a reasonable value should produce an improved U₀₁. It appears from the result of Method C that the data are insensitive to field shift effects, even though V^Lu₀₁ is not insignificant (see below). This leads to the conclusion that because the fitting parameter of Method C is ₀₁, then the value of U₀₁ from Method B (which is numerically the same) is simply an effective value, without a specific physical meaning.

Table 8 gives a comparison of the results of the Dunham-type fits with those of several related molecules. Clearly only limited results could be obtained for LuF. The situation was better for LuCl, for which ^Cl₀₁ could be determined, thus confirming the presence of Born–Oppenheimer breakdown. However, neither ^Lu₀₁ nor V^Lu₀₁ could be obtained directly from the spectrum, and both were fixed in the fits. The former was assumed to be ^Cl₀₁ ± 1, and the latter was the theoretical value. Comparison with the other results in Table 8 indicates that both fixed values are reasonable, and gives confidence that the most physically reasonable values available for ₀₁ and U₀₁ have been obtained.

AB	01A	01B	107VA01/fm–2	U01/u MHz	Ref.
LuF	—	—		137 505.300(15)a	This work
LuCl	–2.96b	–2.96(12)		89 730.23(16)	This workb
LuCl	–3(1)c	–2.98(12)	24d	89 724.02(36)c	This workf
				01 = 89 730.25(29)c
ZrO	–4.872(39)	–6.1888(25)		172 480.086(98)	27
ZrS	–5.325(82)	–6.523(39)		108 670.07(19)	27
HfO	–3.40(57)	–5.656(23)		170 239.68(18)g	28
HfS	–4.18(53)	–5.820(49)		108 708.38(27)	29
PtSi	10.75(68)	–2.99(4)		118 923.32(33)h	31
PtSi	–3(1)c	–2.99(4)	–72(12)	118 952.7(47)e
				01 = 118 927.94(54)
			–110d		25
PtS	–42.60(74)	–62.466(49)		121 604.07(30)h	17
PtS	–62.5(10)c	–62.46(5)	–104(9)	121 647.1(20)e
				01 = 121 610.91(50)
			–84d		25
TlCl	–18.96(200)	–1.243(49)		81 857.0(1)g	45
TlCl	–0.5i	–1.257(73)	40.9(55)		46
			88.0d		25
PbS	–12.94(141)	–1.997(71)		96 642.20(50)g	45
PbSh	–1.333i	–1.988(70)	26.38(51)		46
			34.5d		25
BiN	—	–2.788(19)		135 003.18(10)h	30
BiN	–2.8(10)c	–2.788(19)	32d	134 991.08(45)e
				01 = 135 004.17(10)
a The numbers in parentheses are one standard deviation in units of the least signficant figures.  b Values obtained using Method B (see text).  c This is an estimated value and uncertainty based on the assumption that A01 = B01 ± 1. The uncertainties in 01 and U01 reflect this assumption.  d Value obtained using DFT following the method outlined in ref. 25. For LuCl and BiN the calculated value was used directly to obtain 01 and U01.  e Value obtained from 01 using eqn. (9).  f Value obtained using Method C (see text).  g This value for U01 has been calculated from the data given in the corresponding reference.  h In this fit nuclear field shift effects were neglected.  i This value was held fixed in the fitting procedure. See ref. 34 for details of the fitting procedure used.

It was initially surprising that the V^Lu₀₁ -dependence is so slight. Table 8 shows that although V^Lu₀₁ is one of the smallest examples known, it is not much smaller than V₀₁^Pb in PbS or V₀₁^Tl in TlCl, which have significant effects on the apparent values of ₀₁^Pb or ₀₁^Tl, respectively. For both of these molecules (and also for PtSi and PtS) there are significant differences between the two ₀₁ⁱ values when V₀₁ⁱ is omitted from the fit, which can be accounted for if V₀₁ⁱ is included. Since determinations of both ^Lu₀₁ and V^Lu₀₁ in LuCl depend on the isotopic substitution ¹⁷⁵Lu to ¹⁷⁶Lu the insensitivity of the spectrum to these parameters is likely due to the weak observed spectrum of ¹⁷⁶Lu³⁵Cl. (It should be added parenthetically that a fit to V^Lu₀₁ with ^Lu₀₁ fixed does give a fit. However, the value obtained, V^Lu₀₁ = –2.6 × 10^–5 fm², is of the wrong order of magnitude and has the wrong sign.)

Equilibrium internuclear distances r_e have been evaluated for both molecules. Several possible methods were available, all of which give precise, but slightly differing values. Accordingly it is necessary to be clear on how the values were obtained, and what they mean.

One approach is to use the Y₀₁ values in Tables 6 and 7 to calculate r_e of each isotopomer from

(10)

(11)

For LuF, two values of r_e, one for each isotopomer, are given in Table 6. They must be viewed with caution. They ignore the possibility of Born–Oppenheimer breakdown, because the breakdown terms could not be determined from the spectrum. Furthermore, this means the two values of r_e must be the same, as they are. In the absence of BOB or field shift parameters, this is as far as one can go for LuF.

For LuCl (see Table 7), the values for the three isotopomers seem reasonable; their variations of 10^–6 give a measure of how well the Born–Oppenheimer approximation holds for this molecule. In addition, an isotope-independent Born–Oppenheimer bond length can be obtained. It is given by³⁹

(12)

To estimate an uncertainty in r_e^BO, separate fits of the data were carried out varying ^Lu₀₁ by ± 1.³² The uncertainty in r_e^BO in Table 9 reflects the variation obtained.

Molecule	re/	Comment
LuF	1.917 118 15(11)a	Experimental re for 175Lu19F
	1.9165(2)	Ref. 3
	1.9237	DFT calculation; this work
LuCl	2.373 2930(21)	Experimental re for 175Lu35Cl
	2.373 3088(47)b	rBOe
	2.3825	DFT calculation; this work
a Numbers in parentheses are one standard deviation in units of the least significant figures.  b Obtained from U01 derived using Method C (Table 7). The uncertainty reflects the range of assumed values of Lu01 = –3 ± 1.

For both LuF and LuCl the vibrational frequency, anharmonicity constant and dissociation energy _e have been estimated using the following equations^40,41 which assume a Morse potential:

(13)

(14)

(15)

For LuF there is excellent agreement between the present and literature values of both _e and _ex_e. Since the literature values were obtained directly from the vibrational energies² it appears that the Morse potential applies well to the molecule. In turn this inspires confidence in the calculated dissociation energy. The agreement with literature values for LuCl is poorer because the literature values are uncertain. However, it is not unreasonable to assume that the Morse potential applies in this case as well, making the present values reliable. For both molecules the DFT values of _e agree well with experiment. The agreement for _ex_e is poorer.

The implication appears to be that although the DFT potential functions are reasonable overall, they are not so good in detail. This appears also to be reflected in the DFT values of r_e (Table 9).

Parameter		LuF	LuCl
e/cm–1	This work	618(12)a	337(1)
	Literature	611b	350–387c
	DFT	623	329
exe/cm–1	This work	2.82(8)	1.048(4)
	Literature	2.68b	0.78–1.76c
	DFT	4.02	3.01
e/kJ mol–1	This work	405(19)	324(2)
e/eV	This work	4.19(20)	3.35(2)
e/eV	Literature	3.451(16)d	—
a Numbers in parentheses are one standard deviation in units of the least significant figures.  b Calculated from Table 2 of ref. 2.  c Ref. 1.  d Ref. 47.

Nuclear quadrupole coupling constants have been evaluated for both isotopes of Lu and Cl. The latter are presented in Table 11 in comparison with values for other diatomic metal halides. The eQq(Cl) values for LuCl are among the smallest known. They have been used to evaluate the ionic character i_c of LuCl using⁴²

(16)

Species	eQq0/MHz	Ionicity ic (%)	Bond length/	Dipole moment µ/D	Electronegativity difference48	Ref.a
175LuF		>95b	1.9175		2.71	Present study
175Lu35Cl	–0.647	99.4	2.3733		1.89	Present study
174YbF			2.0165	3.91	2.88	44
174Yb35Cl	–2.16	98.5	2.4883		2.06	44
LaCl	–0.950	99.1	2.4980		2.06	49
LaBr	13.624	98.2	2.6521		1.86	49
LaI	–81.197	96.5	2.8788		1.56	49
MgCl	–11.62	89.4	2.1991c		1.85	50
CaCl	–1.002	99.1	2.4390	4.27d	2.16	51
NaCl	–5.642	94.8e	2.3609f	9.002g	2.23	52
KCl	0.04	100	2.6668f	10.269h	2.34	42
a Or as stated otherwise.  b See ref. 6.  c See ref. 53.  d See ref. 54.  e See ref. 51.  f See ref. 55.  g See ref. 42.  h See ref. 56.

The magnitudes of the Lu nuclear quadrupole coupling constants for both isotopes are, as predicted, very large, being comparable to (in LuF) or larger than (in LuCl) the rotational constants. For LuF the value is much larger in magnitude than the approximate value obtained from the electronic spectrum.⁶ Tables 2 and 5 show a clear vibrational state dependence in eQq(¹⁷⁵Lu) for both LuF and LuCl. The constants have been fitted to the expression

(17)

Constanta	175LuF	175Lu35Cl
eQqe	–4976.6014(18)b	–4302.8074(43)
eQq	–38.1875(36)	–24.344(13)
eQq	–0.1240(16)	–0.0807(88)
a The parameters are defined in eqn. (17). The equilibrium value is eQqe  b Numbers in parentheses are one standard deviation in units of the least significant figures.

The electron configuration of free Lu⁺ is [Xe]4f¹⁴6s² (¹S₀), predicting a spherical electron density distribution and a Lu nuclear quadrupole coupling constant of zero. The nonzero eQq(Lu) values suggest that the anion (F^–, Cl^–) causes considerable distortion of the Lu⁺electron cloud. This distortion was recognized by Gotkis⁴³ in his electronic structure model for rare earth monohalides. He depicted Lu⁺ in its monohalides as containing a [Xe]4f¹⁴ core plus a -orbital localized on Lu and polarized away from the halide. (Gotkis calls this orbital _6s). Our own calculations confirm this and indicate that this orbital is 95% 6s plus 5% 5d_z².

LuF and LuCl comprise only the second set of rare earth halides whose rotational spectra have been reported (after the ytterbium halides⁴⁴). The laser ablation technique has been proven to be an ideal method to prepare them, and the spectra were generally strong. The rotational constants of ¹⁷⁵LuF are considerably more precise than the literature values; those for ¹⁷⁶LuF are the first reported. New, precise values of hyperfine constants of Lu and F have also been obtained. The experimental r_e value for ¹⁷⁵LuF is a major improvement over the literature value.

For LuCl this is the first high resolution spectrum ever reported, and a large set of precise spectroscopic constants has been obtained, including hyperfine constants for all nuclei. Experimental evidence for Born–Oppenheimer breakdown has been obtained. Although a significant Lu nuclear shift effect was predicted theoretically, it was found to have no influence on the observed spectrum. Equilibrium bond lengths r_e have been evaluated for each isotopomer, along with a Born–Oppenheimer bond length. The Cl nuclear quadrupole coupling constant shows LuCl to be highly ionic. The very large Lu quadrupole coupling constants are consistent with strong polarization of the Lu⁺ electron distribution by the anions.

Acknowledgements

This research has been supported by grants from the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Berliner Programm zur Förderung der Chancengleichheit für Frauen in Forschung und Lehre.

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