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Nuclear hyperfine coupling constants of aluminium monoiodide determined by Fourier-transform microwave spectroscopy
Chemical Physics Letters 423 (2006) 327–330 www.elsevier.com/locate/cplett
Nuclear hyperfine coupling constants of aluminium monoiodide determined by Fourier-transform microwave spectroscopy Nicholas R. Walker, Simon G. Francis, Joshua J. Rowlands, Anthony C. Legon
*
School of Chemistry, University of Bristol, Bristol, BS8 1TS, UK Received 24 January 2006; in final form 17 March 2006 Available online 27 March 2006
Abstract The ground-state rotational spectrum of 27Al127I has been investigated by Fourier-transform microwave spectroscopy. AlI was generated by reaction of laser-ablated aluminium vapour with methyl iodide. The rotational constant (B0), nuclear quadrupole coupling I I constants ðvAl aa ; vaa Þ and the nuclear spin-rotation constant of iodine ðC bb Þ have been re-determined with high precision. The nuclear Al;I spin-rotation constant of aluminium ðC Al Þ, the nuclear spin–spin constants ðDAl;I Þ and the dependence of the coupling constant aa ; d bb Al,I Al;I I I I vaa on J ðvJ Þ were determined. Daa and d agree with calculated values and vJ is consistent in sign and magnitude with the known dependence of vIaa on vibrational state. 2006 Elsevier B.V. All rights reserved.
1. Introduction The first investigation of an aluminium monohalide by microwave spectroscopy was performed by Lide [1]. Rotational and centrifugal distortion constants were determined for AlF in addition to a nuclear quadrupole coupling constant for the aluminium atom. Gordy and co-workers [2,3] later applied millimetre-wave spectroscopy to determine rotational and centrifugal distortion constants for AlF, AlCl, AlBr and AlI. More complete descriptions of nuclear hyperfine structure in spectra of the aluminium monohalides have since been provided by microwave spectroscopy. A study of AlI by To¨rring et al. [4] yielded nuclear quadrupole coupling constants for aluminium and iodine, and a nuclear spin-rotation constant for iodine. Gerry and coworkers used a Fourier-transform microwave (FT-MW) instrument to provide nuclear quadrupole and spin-rotation constants associated with each atom and nuclear spin–spin constants for both AlCl and AlBr [5,6]. The investigation of the ground-state rotational spectrum of AlI by FT-MW spectroscopy is reported in this Letter. *
Corresponding author. Fax: +44 117 925 1295. E-mail address: [email protected] (A.C. Legon).
0009-2614/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2006.03.044
The intrinsically high resolution of the technique has now allowed the determination of the nuclear spin-rotation constant of aluminium ðC Al bb Þ, the tensor and scalar nuclear Al,I spin–spin coupling constants ðDAl;I , respectively) aa and d and the rotational state dependence of the nuclear quadrupole coupling constant of iodine that arises from centrifugal distortion ðvIJ Þ. In addition, the rotational constant I (B0), the nuclear quadrupole coupling constants ðvAl aa ,vaa Þ of aluminium and iodine, and the nuclear spin-rotation constant of iodine ðC Ibb Þ have been established with significantly improved precision. 2. Experimental The experimental apparatus comprises a laser-vaporisation and supersonic-nozzle source coupled to a Balle-Flygare, Fourier-transform microwave spectrometer. The microwave spectrometer is described in several previous papers [5,7,8]; therefore only a brief description will be provided here. The cavity consists of two spherical aluminium mirrors (diameter = 35 cm; radius of curvature = 84 cm) separated by approximately 70 cm. A gas mixture containing methyl iodide and argon is ejected from the orifice of a pulsed nozzle (General Valve, Series 9) and passes over the
328
N.R. Walker et al. / Chemical Physics Letters 423 (2006) 327–330
surface of an aluminium rod from which material is ablated by the focussed pulse of 532 nm radiation from a Nd:YAG laser. The delay between the nozzle and vaporisation laser pulses is set to ensure optimal generation of AlI. The gas mixture then enters the Fabry–Perot cavity through an orifice in the centre of the stationary mirror. This parallel propagation of the gas and microwave pulses enhances the resolution of the instrument but increases the wellknown Doppler splitting of each hyperfine component into two peaks. The line frequency is determined by finding the average of the frequencies of the Doppler components. Molecules are excited to higher rotational states by the microwave pulse if the transition from the lower state is resonant or nearly resonant with the radiation and subsequently undergo relaxation by spontaneous coherent emission at the transition frequency. This free induction decay is detected and Fourier-transformed to yield a plot of emission intensity against frequency. The experimental cycle described above is repeated and averaged as necessary to obtain a satisfactory signal-to-noise ratio for measured lines. All frequency measurements are referenced to an external source that is accurate to one part in 1012. Individual hyperfine components had a full width at half height of 5 kHz and their frequencies were consequently measured with an estimated accuracy of 0.5 kHz. 3. Results 3.1. Spectroscopic analysis The spectroscopic constants obtained in the earlier work of Wyse and Gordy [3] and To¨rring et al. [4] were used for the initial prediction of the only rotational transitions (J = 1 0 and 2 1) of AlI that fall within the frequency range of the spectrometer. These parameters were sufficiently accurate that spectral lines could be identified without extensive searching. The strongest lines were visible after only a single experimental cycle. The hyperfine structure was very rich because the nuclei 27Al and 127I have spin quantum numbers IAl = 3/2 and II = 5/2, respectively and significant electric quadrupole moments. Frequencies of 95 hyperfine components were measured for transitions in the v = 0 vibrational state. Fig. 1 contains an example of two hyperfine components in the J = 2 1 transition. Pickett’s program SPFIT [9] was used to fit the measured line frequencies. The Hamiltonian chosen was as follows: X 1 X H ¼H R QX : V X þ I X CX J 6 X¼Al;I X¼Al;I þ I Al DAl;I I I þ dAl;I I Al I I
ð1Þ
where HR is that appropriate to the semi-rigid diatomic rotor and the next term accounts for the coupling of the spin angular momenta IX of nucleus X to the rotational angular momentum J through the interaction of nuclear electric quadrupole moment QX with the electric field gradient VX at nucleus X. The next three terms are
Fig. 1. Two hyperfine components in the J = 2 1 transition of 27Al127I, recorded after 200 experimental cycles. The line assignments are given as F 01 F 001 ; F 0 F 00 . Each component appears as the Doppler doublet indicated (see text for discussion).
P X much smaller. The term X¼Al;I I X C J describes the spin-rotation coupling of each of the two nuclei while the final two terms are concerned with spin–spin coupling of the dipolar tensorial (through-space) and scalar (through-bond) type, respectively. The coupling scheme J + II = F1; F1 + IAl = F was used. For a diatomic moleX X Al;I cule, only the components vX aa ¼ eQV aa , C bb and Daa of the various coupling tensors are determinable, although we found it necessary to allow for the dependence of vI on rotational state J through the term vIaa ðJ Þ ¼ vIaa ð0Þþ vIJ J ðJ þ 1Þ [10]. Table 1 shows the values of these quantities together with the rotational constant B0, the centrifugal distortion constant DJ and the scalar (through-bond)
Table 1 Evaluated spectroscopic constants of AlI compared with those from earlier microwave and millimetre-wave spectroscopic studies Spectroscopic
This work
Ref. [4]
Ref. [3]
B0/MHz DJ · 103/MHz vIaa ð0Þ=MHzb vIJ 103 =MHzc vAl aa =MHz C Ibb 103 =MHz 3 C Al bb 10 =MHz 3 10 =MHz DAl;I aa Al;I 3 daa 10 =MHz Nd rr.m.s/kHze
3520.187637(17) 1.9536a 309.5633(7) 1.28(18) 25.6171(7) 13.8670(22) 3.565(28) 0.653(33) 0.225(16) 89 0.38
3520.1867(20) 1.9536a 309.565(100)
3520.1876(7) 1.9536(3) 334(10)
a
25.50(10) 13.3(10)
Fixed at value provided in Ref. [3]. This is the value for the rotationless (J = 0) state. See text for discussion. c This term accounts for the dependence of the conventional coupling constant on J. See text for discussion. d Number of hyperfine components included in the fit. e Root-mean-square deviation of the fit. b
N.R. Walker et al. / Chemical Physics Letters 423 (2006) 327–330
spin–spin coupling constant dAl,I obtained in the final cycle of the least-squares fit. Included in Table 1 for comparison are constants available from the earlier studies. The frequencies and assignments of all spectral lines observed are provided as supplementary data. Only when the spin–spin interactions and the J dependence of vI were included was it possible to obtain a fit whose RMS deviation (0.38 kHz) was commensurate with the estimated accuracy of frequency measurement (0.5 kHz). The centrifugal distortion constant was initially released in fits using the model Hamiltonian of Eq. (1) in order to allow comparison with the earlier work of Wyse and Gordy [3]. A value of 1.9736(135) kHz was obtained for DJ. This value is less precise (by two orders of magnitude) than that determined by Wyse et al., a result consistent with the different frequency ranges explored by the two works. The tuneable range of the spectrometer in the current investigation allows measurements of lines from only two J + 1 J transitions of AlI, while seventeen higher J transitions with much larger contributions from centrifugal distortion were accessible by Wyse and Gordy [3]. Nevertheless, the values determined from the two studies are in reasonable agreement, being within two standard deviations of each other. Owing to its greater precision, DJ was held constant at the value determined by Wyse and Gordy [3] in all subsequent fits to ensure hyperfine constants of optimal accuracy. The B0, and C Ibb values determined here reproduce those available from previous studies to within the experimental uncertainties. 3.2. Interpretation of the tensor and scalar nuclear spin–spin Al;I coupling constants ðDAl;I Þ aa ; d As is the case for previous spectroscopic studies of the aluminium monohalides [5,6], the FT-MW technique yields the most precise measurements for every hyperfine parameter measured. Even the small tensor and scalar nuclear Al;I spin–spin constants, Daa and dAl,I, are reasonably welldetermined. If the contribution from the axial component of the electron-coupled (through-bond) spin–spin coupling tensor is assumed negligible, DAl;I is directly related to the bond aa length through Eq. (2), where h is the Planck constant, l0 is the permeability of a vacuum, lN is the nuclear magneton, gAl and gI are the nuclear g factors for the Al and I nuclei [11], respectively, and r is the instantaneous value of the Al–I internuclear distance: 2 l0 2 1 Al;I Daa lN gAl gI 3 ¼ ð2Þ h 4p r 0;0 Al;I To calculate Daa from Eq. (2), we require the expectation va3 lue Ær æ0,0. The rotational constant B0 leads directly to the 1=2 operationally defined bond length r0 ¼ hr2 i0;0 ¼ 3 3 ˚ If we assume that r0 hr i0;0 , then Eq. (2) leads 2:5401 A. Al;I to the result Daa ¼ 0:769 kHz. This is in satisfactory agreement with the experimentally measured value of 0.653(55) kHz, given the assumption made. Fits to test
329
the precision of dAl,I demonstrated that the parameter was Al;I not changed significantly by holding Daa at this calculated value. The through-bond coupling constant dAl,I is in excellent agreement with that (208 Hz) calculated using a DFT with the B3LYP functional and a 6-31G basis set for Al and 3-21G for I in the GAUSSIAN electronic structure package [12]. 3.3. Nuclear quadrupole coupling constants The nuclear quadrupole coupling constant of aluminium, vAl ¨ rring et al. [4] to within aa , is consistent with the result of To the experimental uncertainties. The same is true for the iodine coupling constant vIaa , but the value of this quantity differs somewhat from that provided by the millimetre-wave 0 study [3]. Only rotational transitions with J > 22 were probed during the latter work, thereby explaining the lower precision of vIaa . The current experiment has further allowed the dependence of the nuclear quadrupole coupling constant of iodine on J that arises from centrifugal distortion to be quantified through determination of vIJ . In a given rotational state J, the effective nuclear quadrupole coupling constant v is related to the coupling constant v(0) of the rotationless state by the expression vaa ðJ Þ ¼ vaa ð0Þ þ vJ J ðJ þ 1Þ.
ð3Þ
The difference dvaa = vaa(J) vaa(0) can then be written as dvaa
dvaa dr; dr
ð4Þ
where dr is the extension of the bond through centrifugal distortion. If dvaa/dr is known, Eq. (4) can be used to obtain dvaa and thence vJ as follows. The rotational constant of a diatomic molecule in a ro-vibrational state (v, J) in which centrifugal distortion is significant can be written as: Beff ¼ Bv DJ J ðJ þ 1Þ
ð5Þ
Recalling the operational definition of the effective bond length rv in a vibrational state v h 1 h 2 r ; Bv ¼ 2 ¼ ð6Þ 8p l r2 v;v 8p2 l v and writing reff = rv + dr, Eq. (5) becomes h Beff ¼ Bv DJ J ðJ þ 1Þ ¼ 2 ðrv þ drÞ2 8p l h 2dr 2dr ¼ 2 r2 1 þ ¼ B 1 þ v 8p l v rv rv
ð7Þ
Ignoring higher terms in the expansion, this rearranges to give dr
rv DJ J ðJ þ 1Þ ; 2Bv
which, when combined with Eq. (4), leads to rv DJ J ðJ þ 1Þ dvaa dvaa 2Bv dr and thence with Eq. (3) to give the required result
ð8Þ
ð9Þ
330
vJ
N.R. Walker et al. / Chemical Physics Letters 423 (2006) 327–330
r v DJ 2Bv
dvaa . dr
ð10Þ
To estimate dvaa/dr for AlI, we can use the results of To¨rring et al. [4], who measured the variation of both B and v with v. Their values of Bv, taken together with the operational definition of rv through Eq. (6), give r0 = ˚ , r1 = 2.546156 A ˚ , r2 = 2.552217 A ˚ and r3 = 2.540115 A ˚ . The variation is so close to linear that we can 2.558300 A ˚ 1. The same authors establish from write dv/dr 0.00604A I the variation of vaa with v that dvIaa =dv 4:314 0:100 MHz. Thus, to a reasonable degree of approximation,
been evaluated for the first time for this molecule. The tensor nuclear spin–spin coupling constant DAl;I aa is consistent with the bond length of the molecule, while the scalar constant dAl,I is in good agreement with a DFT calculated value. The correction vIJ to the nuclear quadrupole coupling constant of iodine arising from centrifugal distortion, is satisfactorily accounted for by a simple model in which the vibrational dependence of the rotational constant and the iodine nuclear quadrupole coupling constant from the previous work of To¨rring et al. [4] are the input data. Acknowledgements
1
˚ . dvIaa =dr ¼ ðdvIaa =dvÞðdv=drÞ 714:2 MHz A Using this value in Eq. (10) with B0 = 3520.1876 MHz, ˚ , we obtain DJ = 1.9536 kHz and r0 = 2.54011 A I vJ ¼ 0:50 kHz for the v = 0 state, which should be compared with the observed value of 1.28(18) kHz. Given the approximations involved, this is satisfactory agreement in sign and magnitude. The corresponding calculation for Al yields vJ(Al) = 0.02 kHz. We found that this quantity was too small to determine, given the present accuracy of frequency measurement. 4. Conclusions The ground-state rotational spectrum of AlI has been measured by FT-MW spectroscopy. The rotational constant (B0), nuclear quadrupole coupling constants I ðvAl aa ; vaa Þ of aluminium and iodine and the nuclear spinrotation constant of iodine ðC Ibb Þ have been determined with higher precision than previously. The nuclear spinrotation constant of aluminium ðC Al bb Þ, the tensor and scalar Al;I nuclear spin–spin coupling constants ðDAl;I Þ and the aa ; d J-dependent part of the nuclear quadrupole coupling constant of iodine arising from centrifugal distortion ðvIJ Þ have
The authors thank the Engineering and Physical Sciences Research Council for supporting this work. N.R.W. thanks the Royal Society for the award of a Royal Society University Research Fellowship. We are pleased to acknowledge Dr. Craig Butts for the calculation of the scalar coupling constant dAl,I. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
[12]
D.R. Lide, J. Chem. Phys. 42 (1965) 1013. F.C. Wyse, W. Gordy, E.F. Pearson, J. Chem. Phys. 52 (1970) 3887. F.C. Wyse, W. Gordy, J. Chem. Phys. 56 (1972) 2130. T. To¨rring, E. Tiemann, Z. Hœft, Z Naturforsch. 289A (1973) 1062. K.D. Hensel, C. Styger, W. Ja¨ger, A.J. Merer, M.C.L. Gerry, J. Chem. Phys. 99 (1993) 3320. K.A. Walker, M.C.L. Gerry, J. Mol. Spectrosc. 193 (1999) 224. T.J. Balle, W.H. Flygare, Rev. Sci. Instrum. 52 (1981) 33. S.G. Batten, A.G. Ward, A.C. Legon, J. Mol. Struct. 300 (2006) 780. H.M. Pickett, J. Mol. Spectrosc. 148 (1991) 371. J.T. Hougen, J. Chem. Phys. 57 (1972) 4207. IUPAC Quantities, Units and Symbols in Physical Chemistry, prepared by Ian Mills, Tomislav Cvitas, Klaus Homann, Nikola Kallay and Kozo Kuchitsu, second edn., Blackwell Science Oxford, 1993, p. 9104. M.J. Frisch et al., GAUSSIAN 03, Revision B.04, Gaussian, Inc., Pittsburgh, PA, 2003.
Nuclear hyperfine coupling constants of aluminium monoiodide determined by Fourier-transform microwave spectroscopy Nicholas R. Walker, Simon G. Francis, Joshua J. Rowlands, Anthony C. Legon
*
School of Chemistry, University of Bristol, Bristol, BS8 1TS, UK Received 24 January 2006; in final form 17 March 2006 Available online 27 March 2006
Abstract The ground-state rotational spectrum of 27Al127I has been investigated by Fourier-transform microwave spectroscopy. AlI was generated by reaction of laser-ablated aluminium vapour with methyl iodide. The rotational constant (B0), nuclear quadrupole coupling I I constants ðvAl aa ; vaa Þ and the nuclear spin-rotation constant of iodine ðC bb Þ have been re-determined with high precision. The nuclear Al;I spin-rotation constant of aluminium ðC Al Þ, the nuclear spin–spin constants ðDAl;I Þ and the dependence of the coupling constant aa ; d bb Al,I Al;I I I I vaa on J ðvJ Þ were determined. Daa and d agree with calculated values and vJ is consistent in sign and magnitude with the known dependence of vIaa on vibrational state. 2006 Elsevier B.V. All rights reserved.
1. Introduction The first investigation of an aluminium monohalide by microwave spectroscopy was performed by Lide [1]. Rotational and centrifugal distortion constants were determined for AlF in addition to a nuclear quadrupole coupling constant for the aluminium atom. Gordy and co-workers [2,3] later applied millimetre-wave spectroscopy to determine rotational and centrifugal distortion constants for AlF, AlCl, AlBr and AlI. More complete descriptions of nuclear hyperfine structure in spectra of the aluminium monohalides have since been provided by microwave spectroscopy. A study of AlI by To¨rring et al. [4] yielded nuclear quadrupole coupling constants for aluminium and iodine, and a nuclear spin-rotation constant for iodine. Gerry and coworkers used a Fourier-transform microwave (FT-MW) instrument to provide nuclear quadrupole and spin-rotation constants associated with each atom and nuclear spin–spin constants for both AlCl and AlBr [5,6]. The investigation of the ground-state rotational spectrum of AlI by FT-MW spectroscopy is reported in this Letter. *
Corresponding author. Fax: +44 117 925 1295. E-mail address: [email protected] (A.C. Legon).
0009-2614/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2006.03.044
The intrinsically high resolution of the technique has now allowed the determination of the nuclear spin-rotation constant of aluminium ðC Al bb Þ, the tensor and scalar nuclear Al,I spin–spin coupling constants ðDAl;I , respectively) aa and d and the rotational state dependence of the nuclear quadrupole coupling constant of iodine that arises from centrifugal distortion ðvIJ Þ. In addition, the rotational constant I (B0), the nuclear quadrupole coupling constants ðvAl aa ,vaa Þ of aluminium and iodine, and the nuclear spin-rotation constant of iodine ðC Ibb Þ have been established with significantly improved precision. 2. Experimental The experimental apparatus comprises a laser-vaporisation and supersonic-nozzle source coupled to a Balle-Flygare, Fourier-transform microwave spectrometer. The microwave spectrometer is described in several previous papers [5,7,8]; therefore only a brief description will be provided here. The cavity consists of two spherical aluminium mirrors (diameter = 35 cm; radius of curvature = 84 cm) separated by approximately 70 cm. A gas mixture containing methyl iodide and argon is ejected from the orifice of a pulsed nozzle (General Valve, Series 9) and passes over the
328
N.R. Walker et al. / Chemical Physics Letters 423 (2006) 327–330
surface of an aluminium rod from which material is ablated by the focussed pulse of 532 nm radiation from a Nd:YAG laser. The delay between the nozzle and vaporisation laser pulses is set to ensure optimal generation of AlI. The gas mixture then enters the Fabry–Perot cavity through an orifice in the centre of the stationary mirror. This parallel propagation of the gas and microwave pulses enhances the resolution of the instrument but increases the wellknown Doppler splitting of each hyperfine component into two peaks. The line frequency is determined by finding the average of the frequencies of the Doppler components. Molecules are excited to higher rotational states by the microwave pulse if the transition from the lower state is resonant or nearly resonant with the radiation and subsequently undergo relaxation by spontaneous coherent emission at the transition frequency. This free induction decay is detected and Fourier-transformed to yield a plot of emission intensity against frequency. The experimental cycle described above is repeated and averaged as necessary to obtain a satisfactory signal-to-noise ratio for measured lines. All frequency measurements are referenced to an external source that is accurate to one part in 1012. Individual hyperfine components had a full width at half height of 5 kHz and their frequencies were consequently measured with an estimated accuracy of 0.5 kHz. 3. Results 3.1. Spectroscopic analysis The spectroscopic constants obtained in the earlier work of Wyse and Gordy [3] and To¨rring et al. [4] were used for the initial prediction of the only rotational transitions (J = 1 0 and 2 1) of AlI that fall within the frequency range of the spectrometer. These parameters were sufficiently accurate that spectral lines could be identified without extensive searching. The strongest lines were visible after only a single experimental cycle. The hyperfine structure was very rich because the nuclei 27Al and 127I have spin quantum numbers IAl = 3/2 and II = 5/2, respectively and significant electric quadrupole moments. Frequencies of 95 hyperfine components were measured for transitions in the v = 0 vibrational state. Fig. 1 contains an example of two hyperfine components in the J = 2 1 transition. Pickett’s program SPFIT [9] was used to fit the measured line frequencies. The Hamiltonian chosen was as follows: X 1 X H ¼H R QX : V X þ I X CX J 6 X¼Al;I X¼Al;I þ I Al DAl;I I I þ dAl;I I Al I I
ð1Þ
where HR is that appropriate to the semi-rigid diatomic rotor and the next term accounts for the coupling of the spin angular momenta IX of nucleus X to the rotational angular momentum J through the interaction of nuclear electric quadrupole moment QX with the electric field gradient VX at nucleus X. The next three terms are
Fig. 1. Two hyperfine components in the J = 2 1 transition of 27Al127I, recorded after 200 experimental cycles. The line assignments are given as F 01 F 001 ; F 0 F 00 . Each component appears as the Doppler doublet indicated (see text for discussion).
P X much smaller. The term X¼Al;I I X C J describes the spin-rotation coupling of each of the two nuclei while the final two terms are concerned with spin–spin coupling of the dipolar tensorial (through-space) and scalar (through-bond) type, respectively. The coupling scheme J + II = F1; F1 + IAl = F was used. For a diatomic moleX X Al;I cule, only the components vX aa ¼ eQV aa , C bb and Daa of the various coupling tensors are determinable, although we found it necessary to allow for the dependence of vI on rotational state J through the term vIaa ðJ Þ ¼ vIaa ð0Þþ vIJ J ðJ þ 1Þ [10]. Table 1 shows the values of these quantities together with the rotational constant B0, the centrifugal distortion constant DJ and the scalar (through-bond)
Table 1 Evaluated spectroscopic constants of AlI compared with those from earlier microwave and millimetre-wave spectroscopic studies Spectroscopic
This work
Ref. [4]
Ref. [3]
B0/MHz DJ · 103/MHz vIaa ð0Þ=MHzb vIJ 103 =MHzc vAl aa =MHz C Ibb 103 =MHz 3 C Al bb 10 =MHz 3 10 =MHz DAl;I aa Al;I 3 daa 10 =MHz Nd rr.m.s/kHze
3520.187637(17) 1.9536a 309.5633(7) 1.28(18) 25.6171(7) 13.8670(22) 3.565(28) 0.653(33) 0.225(16) 89 0.38
3520.1867(20) 1.9536a 309.565(100)
3520.1876(7) 1.9536(3) 334(10)
a
25.50(10) 13.3(10)
Fixed at value provided in Ref. [3]. This is the value for the rotationless (J = 0) state. See text for discussion. c This term accounts for the dependence of the conventional coupling constant on J. See text for discussion. d Number of hyperfine components included in the fit. e Root-mean-square deviation of the fit. b
N.R. Walker et al. / Chemical Physics Letters 423 (2006) 327–330
spin–spin coupling constant dAl,I obtained in the final cycle of the least-squares fit. Included in Table 1 for comparison are constants available from the earlier studies. The frequencies and assignments of all spectral lines observed are provided as supplementary data. Only when the spin–spin interactions and the J dependence of vI were included was it possible to obtain a fit whose RMS deviation (0.38 kHz) was commensurate with the estimated accuracy of frequency measurement (0.5 kHz). The centrifugal distortion constant was initially released in fits using the model Hamiltonian of Eq. (1) in order to allow comparison with the earlier work of Wyse and Gordy [3]. A value of 1.9736(135) kHz was obtained for DJ. This value is less precise (by two orders of magnitude) than that determined by Wyse et al., a result consistent with the different frequency ranges explored by the two works. The tuneable range of the spectrometer in the current investigation allows measurements of lines from only two J + 1 J transitions of AlI, while seventeen higher J transitions with much larger contributions from centrifugal distortion were accessible by Wyse and Gordy [3]. Nevertheless, the values determined from the two studies are in reasonable agreement, being within two standard deviations of each other. Owing to its greater precision, DJ was held constant at the value determined by Wyse and Gordy [3] in all subsequent fits to ensure hyperfine constants of optimal accuracy. The B0, and C Ibb values determined here reproduce those available from previous studies to within the experimental uncertainties. 3.2. Interpretation of the tensor and scalar nuclear spin–spin Al;I coupling constants ðDAl;I Þ aa ; d As is the case for previous spectroscopic studies of the aluminium monohalides [5,6], the FT-MW technique yields the most precise measurements for every hyperfine parameter measured. Even the small tensor and scalar nuclear Al;I spin–spin constants, Daa and dAl,I, are reasonably welldetermined. If the contribution from the axial component of the electron-coupled (through-bond) spin–spin coupling tensor is assumed negligible, DAl;I is directly related to the bond aa length through Eq. (2), where h is the Planck constant, l0 is the permeability of a vacuum, lN is the nuclear magneton, gAl and gI are the nuclear g factors for the Al and I nuclei [11], respectively, and r is the instantaneous value of the Al–I internuclear distance: 2 l0 2 1 Al;I Daa lN gAl gI 3 ¼ ð2Þ h 4p r 0;0 Al;I To calculate Daa from Eq. (2), we require the expectation va3 lue Ær æ0,0. The rotational constant B0 leads directly to the 1=2 operationally defined bond length r0 ¼ hr2 i0;0 ¼ 3 3 ˚ If we assume that r0 hr i0;0 , then Eq. (2) leads 2:5401 A. Al;I to the result Daa ¼ 0:769 kHz. This is in satisfactory agreement with the experimentally measured value of 0.653(55) kHz, given the assumption made. Fits to test
329
the precision of dAl,I demonstrated that the parameter was Al;I not changed significantly by holding Daa at this calculated value. The through-bond coupling constant dAl,I is in excellent agreement with that (208 Hz) calculated using a DFT with the B3LYP functional and a 6-31G basis set for Al and 3-21G for I in the GAUSSIAN electronic structure package [12]. 3.3. Nuclear quadrupole coupling constants The nuclear quadrupole coupling constant of aluminium, vAl ¨ rring et al. [4] to within aa , is consistent with the result of To the experimental uncertainties. The same is true for the iodine coupling constant vIaa , but the value of this quantity differs somewhat from that provided by the millimetre-wave 0 study [3]. Only rotational transitions with J > 22 were probed during the latter work, thereby explaining the lower precision of vIaa . The current experiment has further allowed the dependence of the nuclear quadrupole coupling constant of iodine on J that arises from centrifugal distortion to be quantified through determination of vIJ . In a given rotational state J, the effective nuclear quadrupole coupling constant v is related to the coupling constant v(0) of the rotationless state by the expression vaa ðJ Þ ¼ vaa ð0Þ þ vJ J ðJ þ 1Þ.
ð3Þ
The difference dvaa = vaa(J) vaa(0) can then be written as dvaa
dvaa dr; dr
ð4Þ
where dr is the extension of the bond through centrifugal distortion. If dvaa/dr is known, Eq. (4) can be used to obtain dvaa and thence vJ as follows. The rotational constant of a diatomic molecule in a ro-vibrational state (v, J) in which centrifugal distortion is significant can be written as: Beff ¼ Bv DJ J ðJ þ 1Þ
ð5Þ
Recalling the operational definition of the effective bond length rv in a vibrational state v h 1 h 2 r ; Bv ¼ 2 ¼ ð6Þ 8p l r2 v;v 8p2 l v and writing reff = rv + dr, Eq. (5) becomes h Beff ¼ Bv DJ J ðJ þ 1Þ ¼ 2 ðrv þ drÞ2 8p l h 2dr 2dr ¼ 2 r2 1 þ ¼ B 1 þ v 8p l v rv rv
ð7Þ
Ignoring higher terms in the expansion, this rearranges to give dr
rv DJ J ðJ þ 1Þ ; 2Bv
which, when combined with Eq. (4), leads to rv DJ J ðJ þ 1Þ dvaa dvaa 2Bv dr and thence with Eq. (3) to give the required result
ð8Þ
ð9Þ
330
vJ
N.R. Walker et al. / Chemical Physics Letters 423 (2006) 327–330
r v DJ 2Bv
dvaa . dr
ð10Þ
To estimate dvaa/dr for AlI, we can use the results of To¨rring et al. [4], who measured the variation of both B and v with v. Their values of Bv, taken together with the operational definition of rv through Eq. (6), give r0 = ˚ , r1 = 2.546156 A ˚ , r2 = 2.552217 A ˚ and r3 = 2.540115 A ˚ . The variation is so close to linear that we can 2.558300 A ˚ 1. The same authors establish from write dv/dr 0.00604A I the variation of vaa with v that dvIaa =dv 4:314 0:100 MHz. Thus, to a reasonable degree of approximation,
been evaluated for the first time for this molecule. The tensor nuclear spin–spin coupling constant DAl;I aa is consistent with the bond length of the molecule, while the scalar constant dAl,I is in good agreement with a DFT calculated value. The correction vIJ to the nuclear quadrupole coupling constant of iodine arising from centrifugal distortion, is satisfactorily accounted for by a simple model in which the vibrational dependence of the rotational constant and the iodine nuclear quadrupole coupling constant from the previous work of To¨rring et al. [4] are the input data. Acknowledgements
1
˚ . dvIaa =dr ¼ ðdvIaa =dvÞðdv=drÞ 714:2 MHz A Using this value in Eq. (10) with B0 = 3520.1876 MHz, ˚ , we obtain DJ = 1.9536 kHz and r0 = 2.54011 A I vJ ¼ 0:50 kHz for the v = 0 state, which should be compared with the observed value of 1.28(18) kHz. Given the approximations involved, this is satisfactory agreement in sign and magnitude. The corresponding calculation for Al yields vJ(Al) = 0.02 kHz. We found that this quantity was too small to determine, given the present accuracy of frequency measurement. 4. Conclusions The ground-state rotational spectrum of AlI has been measured by FT-MW spectroscopy. The rotational constant (B0), nuclear quadrupole coupling constants I ðvAl aa ; vaa Þ of aluminium and iodine and the nuclear spinrotation constant of iodine ðC Ibb Þ have been determined with higher precision than previously. The nuclear spinrotation constant of aluminium ðC Al bb Þ, the tensor and scalar Al;I nuclear spin–spin coupling constants ðDAl;I Þ and the aa ; d J-dependent part of the nuclear quadrupole coupling constant of iodine arising from centrifugal distortion ðvIJ Þ have
The authors thank the Engineering and Physical Sciences Research Council for supporting this work. N.R.W. thanks the Royal Society for the award of a Royal Society University Research Fellowship. We are pleased to acknowledge Dr. Craig Butts for the calculation of the scalar coupling constant dAl,I. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
[12]
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