The pure rotational spectrum of ScBr

Abstract

The pure rotational spectra of Sc⁷⁹Br and Sc⁸¹Br have been measured in two vibrational states (v=0 and 1) in the 5–24 GHz spectral region, using a cavity pulsed jet Fourier transform microwave spectrometer. The samples were prepared by ablating Sc metal in the presence of Br₂ contained in the Ar backing gas of the jet. The equilibrium internuclear distance r_e has been determined along with estimates for the harmonic vibration frequency ω_e and the dissociation energy, D_e. Nuclear quadrupole coupling constants and spin–rotation constants have been determined for both Sc and Br. The ionic character of the ScBr bond is estimated to be ∽95%. Magnetic shieldings for both nuclei have been estimated.

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1 Introduction

Scandium is the first of the transition metals, so its atoms have only one d-electron in the ground electronic state. Interest in its compounds thus arises because they can be considered as prototypes for understanding the role that d-orbitals play in chemical bonding.

The spectra and structures of scandium monochloride (ScCl) and scandium monofluoride (ScF) have been the subject of many theoretical and experimental studies.¹ The latter have generally been carried out using electronic spectroscopic techniques. Recently the pure rotational spectra of ScCl and ScF have been measured in this laboratory using a Fourier transform microwave (FTMW) spectrometer.² The results showed that the hyperfine structures in the spectra, particularly of the metal, are difficult to interpret using just simple bonding arguments. Investigation of the other scandium monohalides may help in improving our understanding of transition metal bonding. Of the scandium monohalides, scandium monobromide (ScBr) is the least studied spectroscopically. No high-resolution studies on ScBr have been previously reported. Fischell et al.³ measured radiation lifetimes and gave estimates of rotational constants for three electronic states. Langhoff et al.⁴ have reported theoretical values of the spectroscopic constants in the X ¹Σ⁺ and a¹Δ electronic states.

In this paper we report the first measurement of the pure rotational spectrum of ScBr. Rotational transitions have been measured for Sc⁷⁹Br and Sc⁸¹Br, in the ground and first excited vibrational states. Rotational and centrifugal distortion constants have been determined and have been used to evaluate the equilibrium bond distance, r_e, and to estimate the harmonic vibration frequency and dissociation energy. The determined hyperfine parameters have been used to investigate further the nature of the bonding in the molecule.

2 Experimental procedure

The pure rotational spectrum of ScBr was measured using a Balle–Flygare type Fourier transform spectrometer,⁵ that has been described in detail elsewhere.⁶ The spectrometer consists of a cavity formed by two spherical aluminium mirrors 28 cm in diameter and with 38.4 cm radius of curvature, held approximately 30 cm apart. One mirror is fixed, while the other is used to tune the cavity to the microwave excitation frequency. A scandium rod (Goodfellow, 92% scandium, 8% tantalum) was held near the center of the fixed mirror by a stainless steel nozzle cap 5 mm from the orifice of a General Valve series-9 pulsed nozzle.⁷ The scandium metal was ablated by the radiation from the second harmonic of a Nd:YAG laser (532 nm), in the presence of a Br₂/Ar gas mixture, which was then supersonically expanded into the cavity via a 5 mm diameter nozzle. This arrangement resulted in each line being split into two Doppler components since the propagation of the microwave radiation was parallel to that of the supersonic beam. The use of such a parallel configuration results in improved sensitivity and resolution.⁶ The measurement accuracy is estimated to be better than ±1 kHz. For well resolved lines the frequency was obtained by averaging the frequencies of the Doppler components in the frequency domain spectrum. For closely spaced or overlapped lines, the frequencies were obtained by fitting directly to the time domain signals⁸ to eliminate effects of line shape distortion in the power spectrum.

As was found for ScF and ScCl (ref. 2) the best signals were obtained with very small concentrations of Br₂ precursor. For ScBr, the optimal gas mixture consisted of 0.003% Br₂ in Ar (achieved by successive dilutions) at a stagnation pressure of 5–6 atm. Typically 4000–10000 averaging cycles were required for each measurement to obtain adequate signal-to-noise.

3 Results

The three lowest frequency rotational transitions (J=1–0, 2–1 and 3–2) of the ground vibrational state of ScBr were available for study in the frequency range of the spectrometer (5–24 GHz). Since no accurate experimentally determined rotational constant was available the theoretical r_e value from ref. 4 was used to estimate B₀ of Sc⁷⁹Br. To decrease the search range the r_e value of ScBr was refined by using the r_e values from ScF and ScCl,² and comparing them against their theoretical values from ref. 4. Lines from the J=2–1 transition of Sc⁷⁹Br were found within 200 MHz of the predicted frequency. As with ScF and ScCl² the lines were very weak, even after careful optimization of the experimental conditions. There are several possible reasons for this: (a) problems with ablating Sc metal, (b) ScX₃ being more stable than the monomeric species, ScX, and/or (c) an uneven surface on the Sc rod.

Confirmation that we were observing ScBr was obtained by the prediction and measurement of lines from Sc⁸¹Br. In total, lines were measured and assigned to the J=1–0, 2–1 and 3–2 transitions of the ground vibrational state for both Sc⁷⁹Br and Sc⁸¹Br. For the first excited vibrational state, lines were measured and assigned to the J=2–1 and 3–2 transitions for both isotopomers. Since the nuclear quadrupole coupling constants of ⁴⁵Sc(I=7/2, 100%) and ⁷⁹Br(I=3/2, 50.53%) and ⁸¹Br(I=3/2, 49.46%) are comparable in magnitude, a ‘‘parallel ’’ coupling scheme was employed in the assignments: I=I₁+I₂; F=I+J. Measured frequencies and their assignments are available as supplementary data.† The lines were fitted to within experimental uncertainty using Pickett’s weighted-least squares program SPFIT.⁹ The Hamiltonian was

H=H_rot+H_elecquad+H_spin–rotn (1)

where

H_rot=B₀J²−D₀J⁴ (2)

H_spin–rotn=C_I(Sc)I_Sc·J+C_I(Br)I_Br·J (4)

The results of the fits are listed in Table 1. The ground state effective bond distances (r₀) are 2.3833167(9) and 2.3833042(9) Å for Sc⁷⁹Br and Sc⁸¹Br, respectively. No effect of nuclear spin–spin coupling was found.

Table 1 Molecular constants for ScBr in MHz^a

Parameters	Sc^79Br(v=0)	Sc^79Br(v=1)	Sc^81Br(v=0)	Sc^81Br(v=1)
a Numbers in parentheses are one standard deviation in units of least significant figure.
Bv	3106.49059(11)	3093.59139(17)	3078.68584(12)	3065.95999(18)
Dv×10^3	1.169(8)	1.143(11)	1.148(11)	1.167(12)
eQq(Sc)	65.2558(32)	65.1139(81)	65.2597(38)	65.1129(70)
eQq(Br)	39.0857(24)	41.0992(51)	32.6438(19)	34.3215(66)
CI(Sc)×10^2	2.0478(62)	2.133(12)	2.0244(61)	2.105(23)
CI(Br)×10^2	1.706(16)	1.691(24)	1.824(17)	1.795(24)

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4 Analysis

(a) Hyperfine constants

The ratios of the hyperfine parameters found for Sc⁷⁹Br and Sc⁸¹Br can be related to the ratios of certain nuclear and molecular properties. In particular, the spin–rotation constant C_I is proportional to the product g_IB, where g_I is the nuclear g-factor. Thus the ratios of C_I and g_IB for two isotopomers should be the same. These are given for both Sc and Br in Table 2; the agreement is well within the uncertainties.

Table 2 Comparison of hyperfine constants for ScBr^a

	CI(^79Br)/CI(^81Br)	CI(Sc in Sc^79Br)/CI(Sc in Sc^81Br)	eQg(^79Br)/eQq(^81Br)
a Numbers in parentheses are one standard deviation in units of least significant figure.b Literature values are the ratios of gIB for CI, and of the nuclear quadrupole moments for eQq.c Ref. 14.d Inverse ratio of reduced masses of Sc^79Br and Sc^81Br.e Ref. 10.
v=0	0.935(12)	1.0116(43)	1.19734(10)
v=1	0.953(19)	1.020(13)	1.19747(27)
Equilibrium	1.19726(18)
Lit. value^b	0.939995(2)^c	1.0090^d	1.197050(1)^e

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The ratio of the nuclear quadrupole coupling constants should be that of the quadrupole moments of ⁷⁹Br and ⁸¹Br. However, within experimental error, this is not the case for the constants for v=0 and v=1 state, as shown in Table 2. To examine the vibrational dependence of the nuclear quadrupolecoupling constants, an expansion in terms of vibrational con tributions was made:

eQq_v=eQq_e+α_eQq(v+1/2) (5)

where eQq_e is the equilibrium nuclear quadrupole coupling constant and α_eQq is the vibration–rotation correction term. Using the nuclear quadrupole coupling constants obtained in the ground and first excited vibrational states, the following two expressions have been derived:

eQq_v(⁷⁹Br)=38.0789(36)+2.0135(56)(v+1/2)

eQq_v(⁸¹Br)=31.8049(38)+1.6777(68)(v+1/2)

The ratio of the eQq_e values of Sc⁷⁹Br and Sc⁸¹Br now agrees with the ratio of the quadrupole moments within experimental error: evidently vibrational effects cause significant distortion of the field gradients of Br.^11,12

(i) Nuclear quadrupole coupling constants.. The ionic character of the ScBr bond can be calculated from the bromine nuclear quadrupole coupling constant, eQq(Br). If contributions from the d-orbitals of the Br atom are neglected in the bonding orbitals, the ionic character can be related to the coupling constants by:

i_c=1+eQq₀(Br)/eQq₄₁₀(Br) (6)

where eQq₄₁₀(Br) is the quadrupole coupling constant for a singly occupied 4p_z orbital of atomic bromine [eQq₄₁₀(⁷⁹Br)=−769.76 MHz¹³]. The result is i_c=94.9%, indicating an almost entirely ionic ScBr bond. Table 3 compares the ionic character calculated by this method with those of several alkali and alkaline earth metal monobromides, and of ScCl and YBr. For the Sc and Y derivatives, the results follow the expected periodic trends in electronegativity, with ScBr less ionic than ScCl and YBr. It is interesting to note that the ionicity of ScBr is comparable to that of NaCl (i_c= 94.8%),¹⁷ which is widely considered to be fully ionic.

Table 3 Comparison of i_c for Sc⁷⁹Br and some related species

Sc^79Br	Y^79Br^a	Mg^79Br^b	Na^79Br^c	Ca^79Br^d	Sc^35Cl
a Ref. 14.b Ref. 15.c Ref. 16.d Ref. 12.e eQq(^35Cl) and ionic character from ref. 2.f Ionic character, defined by eqn. (6).
eQq0(^79Br)/MHz	39.087	12.935	110.313	58.6080	20.015	−3.786^e
ic (%)^f	94.9	98.3	85.7	92.5	97.4	96.6^e

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Table 4 shows that the value of eQq(Sc) in ScBr is very close to, though somewhat smaller than, the corresponding values in ScO (ref. 18), ScF and ScCl.² On the surface this would seem to imply that the electronic structures near the Sc nucleus are essentially the same for all four molecules. Though this is probably true for the halides, other factors must also be considered. ScO has one fewer valence electron than the halides; the similarity between its eQq value and those of the halides must have a significant contribution from the fact that the HOMO (from which the extra electron has been removed) has a large amount of Sc 4s character, which does not contribute to eQq.¹⁹ Given the ionic character of ScBr, and the fact that Br is less electronegative than F or Cl it might be expected that amongst the halides the valence electron density on Sc would be highest for ScBr. Ab initio calculations for ScF and ScCl in ref. 2 are consistent with this view. Unfortunately a simple application of the modified Townes–Dailey theory, also discussed in ref. 2, would lead to a higher eQq(Sc) value for ScBr than for the other two halides. However, the ab initio results also predict directly reasonable values for the eQq(Sc) values of ScO, ScF and ScCl, including correct trends. Attempts to account for variations in eQq(Sc) values between the molecules (including ScBr) using a simple picture appear not to be fruitful.

Table 4 Sc nuclear quadrupole coupling constants of ScBr and related molecules^a

Molecule	eQq(Sc)/MHz
a Numbers in parentheses are one standard deviation in units of least significant figure.b Ref. 18.c Ref. 2.
ScO	72.240(5)^b
ScF	74.086(5)^c
ScCl	68.207(3)^c
ScBr	65.256(3)

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(ii) Nuclear spin–rotation constants.. For a diatomic molecule, the spin–rotation coupling constant, C_I, can be expressed as the sum of nuclear and electronic terms.^20,21

C_I=C_I^nucl+C_I^elec (7)

The nuclear part depends only on the nuclear positions, and for a diatomic molecule is given by²¹

where e is the charge on the proton, c is the speed of light, μ_N and g_I are the nuclear magneton and the g-factor of the nucleus, respectively, B is the rotational constant, r₁₂ is the internuclear separation and Z_l is the atomic number of the second nucleus. From eqn. (9) and (10) both parts of C_I were calculated and are listed in Table 5. From Table 5 we find the dominant contribution of C_I is given by C_I^elec.

Table 5 Nuclear and electronic contributions to the experimental spin–rotation constants and corresponding paramagnetic shieldings in ScBr^a

Sc				Br
CI/kHz	CI^nucl/kHz	CI^elec/kHz	σp/ppm	CI/kHz	CI^nucl/kHz	CI^elec/kHz	σp/ppm
a Numbers in parentheses are one standard deviation in units of least significant figure.
Sc^79Br	20.478(62)	−0.95	21.43(6)	−3107(9)	17.06(16)	−0.59	17.65(17)	−2476(23)
Sc^81Br	20.244(61)	−0.94	21.18(6)	−3098(9)	18.24(17)	−0.63	18.87(18)	−2396(22)

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The average magnetic shielding (σ_av) determines the chemical shift which is obtainable from NMR measurements. The parameter σ_av is composed of two parts,²² a diamagnetic part (σ_d) and a paramagnetic part (σ_p):

σ_av=σ_d+σ_p (9)

For a diatomic molecule, σ_p is directly proportional to C_I^elec.

For both nuclei of ScBr the values of σ_p have been calculated using eqn. (10). These results are listed in Table 5. A simple estimate of σ_d was given by Flygare et al.:^23,24

where σ_d(a) is the diamagnetic shielding for the atom and can be found in ref. 25. The values of σ_d(a) for Sc and Br are 1521.35 and 3121.19 ppm, respectively. Combining eqn. (9)– (11) we can calculate the average magnetic shieldings, including the paramagnetic and diamagnetic parts. These results are listed in Table 6.

Table 6 The magnetic shieldings of the nuclei in ScBr^a

Sc			Br
σp/ppm	σd/ppm	σav/ppm	σp/ppm	σd/ppm	σav/ppm
a Numbers in parentheses are one standard deviation in units of least significant figures.
Sc^79Br	−3107(9)	1659	−1448(9)	−2476(23)	3204	728(23)
Sc^81Br	−3098(9)	1659	−1439(9)	−2478(22)	3204	726(22)

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(b) Equilibrium structure of ScBr

The equilibrium rotational constants, B_e, of Sc⁷⁹Br and Sc⁸¹Br were evaluated using

B_v=B_e−α_e(v+1/2)+γ_e(v+1/2)² (12)

where B_v is the rotational constant for the v vibrational state, and α_e and γ_e are the vibration–rotation constants. The equilibrium structure was investigated using four different methods. For Method 1, γ_e was taken as zero and only B_e and α_e were evaluated. Since γ_e has not been determined experimentally, it was estimated by assuming the ratio of α_e and γ_e for ScBr is the same as found for ScCl.² With γ_e fixed at 0.0043 MHz, α_e and B_e were re-evaluated; this was Method 2. The results, including r_e values, from Methods 1 and 2 are listed in Table 7. The standard deviations in r_e are derived from the uncertainties in the atomic masses, rotational constants and fundamental constants.

Table 7 Equilibrium parameters of ScBr^a

References
Parameters	M1^b	M2^b	M3^b	M4^b	Theo.^c	Expt.^d
a Numbers in parentheses are one standard deviation in units of least significant figure.b M1, M2, M3, and M4 stand for Methods 1, 2, 3 and 4 as discussed in the text, M2 and M4 use an estimated γe. Estimated uncertainties in re are derived from rotational constants, fundamental constants, and reduced masses.c Ref. 4, no isotope effect specified, average values are used.d Ref. 3.
Sc^79Br
αe/MHz	12.8992(2)	12.9078(2)	12.8992(2)	12.9078(2)
Be/MHz	3112.94019(15)	3112.94342(15)	3112.94019(15)	3112.94342(15)	2623
re/Å	2.3808465(10)	2.3808453(10)	2.3808435(10)	2.3808515(10)	2.432	2.60
Sc^81Br
αe/MHz	12.7259(2)	12.7345(2)	12.7259(2)	12.7345(2)
Be/MHz	3085.04877(15)	3085.05200(16)	3085.04877(15)	3085.05200(16)	2623
re/Å	2.3808451(10)	2.3808439(10)	2.3808423(10)	2.3808504(10)	2.432	2.60
ωe/cm^−1	338.8(11)	327	275(5)
ωexe/cm^−1	1.099(11)
De/eV	3.4	3.74

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Because of the high ionic character of ScBr (i_c=94.9%) the r_e distance was also calculated using ionic masses. The variation should give at least a rough idea of where breakdown of the Born–Oppenheimer approximation might be expected. Bond lengths obtained using ionic masses corresponding to Methods 1 and 2 are given under Methods 3 and 4, respectively, in Table 7.

The equilibrium bond lengths of Sc⁷⁹Br and Sc⁸¹Br show isotopic variation within their uncertainties ∽10⁻⁶ Å, indicating no observable Born–Oppenheimer breakdown. They also agree well with the theoretical r_e result of 2.43 Å (ref. 4) and are greatly improved over the value of Fischell et al.³ who estimated the ScBr bond length as 2.6 Å by using empirical rules.

The harmonic vibration frequency, ω_e, and the vibrational anharmonicity constant, ω_ex_e, of ScBr were estimated using the relations developed by Kratzer²⁶ and Pekeris,²⁷ respectively

where D_Je is the equilibrium centrifugal distortion constant, which is approximated as the ground state value. The disso ciation energy D_e can be approximated by the relation

These expressions have been found to provide reasonable estimates of the vibration frequency and dissociation energy for ScCl.² The results for ScBr are listed in Table 7. The calculated values of ω_e and D_e are in good agreement with the theoretical values from ref. 4. The discrepancy between the value of ω_e from this work and that from Fischell et al.³ arises because Fischell et al.³ overestimated the Sc–Br bond length in their analysis of the ScBr laser induced fluorescence spectrum. Their standard deviation of ±5 cm⁻¹ for ω_e is ambitious considering the number of approximations made in their analysis.

5 Conclusions

The microwave spectrum of ScBr has been measured for the first time to produce rotational and centrifugal distortion constants, along with nuclear quadrupole and spin–rotation coupling constants. The equilibrium bond distance and vibration frequency of ScBr have been determined. From the nuclear quadrupole coupling constants, the ScBr bond has been shown to be highly ionic, though slightly less so than the bonds in YBr and ScCl. The electronic structures at Sc in the scandium halides have been found to be similar.

Acknowledgements

This work has been supported by the Natural Sciences and Engineering Research Council of Canada, and by the Petroleum Research Fund administered by the American Chemical Society.

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Footnote

† Available as electronic supplementary information. See http://www.rsc.org/suppdata/cp/a9/a907769c.

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