Journal of Molecular Spectroscopy 269 (2011) 231–235 Contents lists available at ScienceDirect Journal of Molecular Spectroscopy journal homepage: www.elsevier.com/locate/jms Fourier transform microwave spectroscopy of LiCCH, NaCCH, and KCCH: Quadrupole hyperfine interactions in alkali monoacetylides P.M. Sheridan a,⇑, M.K.L. Binns a, M. Sun b, J. Min b, M.P. Bucchino b, D.T. Halfen b, L.M. Ziurys b a b Department of Chemistry and Biochemistry, Canisius College, Buffalo, NY 14208, United States Department of Chemistry, Department of Astronomy and Steward Observatory, University of Arizona, Tucson, AZ 85721, United States a r t i c l e i n f o Article history: Received 13 June 2011 In revised form 21 July 2011 Available online 2 August 2011 Keywords: Fourier transform microwave spectroscopy Metal acetylides Quadrupole coupling constants Laser ablation Discharge assisted a b s t r a c t The alkali metal monoacetylides LiCCH, NaCCH, and KCCH and their deuterium isotopologues have been investigated using Fourier transform microwave (FTMW) spectroscopy in the frequency range 5–37 GHz. The molecules were synthesized in a supersonic expansion by the reaction of metal vapor, produced by laser ablation, with acetylene or DCCD. Use of target rods of the pure metal and a DC discharge immediately following the laser interaction region were significant factors in molecule production. Multiple rotational transitions were recorded for all species, except where only the J = 1 ? 0 line was accessible (Li species). Quadrupole hyperfine interactions arising from the metal nuclei were resolved in each molecule, as well as those from the deuterium nucleus in the deuterated isotopologues. From a combined analysis with previous millimeter-wave data, refined rotational constants were determined for these species, as well as 7Li, 23Na, 39K, and D eQq parameters. The values of the metal quadrupole coupling constants are comparable to those of the alkali halides and hydroxides, indicating a similar degree of ionic character in the metal–ligand bond. Ó 2011 Elsevier Inc. All rights reserved. 1. Introduction Molecular hyperfine parameters can provide insight into chemical bonding [1–3]. For example, quadrupole coupling constants have been used to gauge the ionic/covalent character of alkali metal-containing compounds, such as fluorides [4–6], chlorides [7–9], hydroxides [10–12] and borohydrides [13]. Typically, Fourier transform microwave (FTMW) and molecular beam resonance spectroscopic techniques have been employed to measure the hyperfine parameters of such species, where they have been generated in the gas phase by heating or ablating the solid salt. This gasphase production method, however, limits the type of ligand that can be attached. As a result, hyperfine parameters for a number of alkali metal-containing species such as the amides [14,15], monomethyls [16] and hydrosulfides [17,18] have not yet been measured, despite the existence of extensive millimeter-wave measurements. Another class of compound for which hyperfine parameters have not yet been established is the alkali monoacetylides: LiCCH, NaCCH and KCCH. Their rotational spectra have been recorded at millimeter wavelengths [19–22], and these studies clearly indicate linear geometries for these molecules. Because these measurements ⇑ Corresponding author. Address: Department of Chemistry and Biochemistry, Canisius College, 2001 Main Street, Buffalo, NY 14208, United States. Fax: +1 716 888 3112. E-mail address: [email protected] (P.M. Sheridan). 0022-2852/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2011.07.008 occurred at high frequencies, however, hyperfine structure, which would chiefly arise from quadrupole coupling, was not observed. Information regarding the degree of ionic/covalent bonding character between the metal and the CCH group could only be speculated from the structural parameters. Recently, the first experimental observation of monomeric copper acetylide, CuCCH, has been reported [23]. The pure rotational spectra of several isotopologues of this molecule were recorded using the FTMW and millimeter-wave spectrometers of the Ziurys group. CuCCH was successfully synthesized in the supersonic nozzle of the FTMW instrument, using the newly developed technique of discharge-assisted laser ablation. Building on the success of this study, we have employed discharge-assisted laser ablation to produce LiCCH, NaCCH, KCCH and their deuterium isotopologues, and to measure their microwave spectra. To conduct this study, specially-designed alkali metal ‘‘rods’’ were fabricated, which, to the best of our knowledge, is a novel approach. Quadrupole hyperfine structure was resolved in the spectra arising from the metals and the deuterium nuclei. In this paper, we present these data, analysis of the spectra, and an interpretation of the quadrupole constants. 2. Experimental The FTMW spectrometer of the Ziurys group [24] was used to measure the microwave spectra of LiCCH, NaCCH, KCCH and their 232 P.M. Sheridan et al. / Journal of Molecular Spectroscopy 269 (2011) 231–235 deuterium isotopologues in the range 5–37 GHz. The instrument has been described in detail elsewhere. Briefly, the Balle–Flygare type instrument [25] consists of a typical Fabry–Perot cavity that contains two spherical aluminum mirrors in a near confocal arrangement, housed in a cryo-pumped vacuum chamber. Antennas are embedded in opposite mirrors for the injection and detection of microwave radiation. A supersonic jet is introduced into the cavity by a pulsed valve, aligned 40° relative to the optical axis. Time domain signals are recorded over a 400 kHz frequency range, from which spectra with 2 kHz resolution are created via a fast Fourier transform. Transitions appear as Doppler doublets with a full width at half maximum of 5 kHz (resolved features) and transition frequencies were taken as the doublet average. In previous microwave experiments for alkali metal-containing species a sufficient gas-phase quantity of the molecule was produced by either heating the solid salt such as LiCl [7] or by laser ablating the solid salt such as NaCl [11]. In this work, the synthetic scheme employed laser ablation of the pure metal. Producing a target rod of an alkali metal is problematic, so instead a 3 cm notch was machined in an aluminum rod, with a diameter 2 mm smaller than the rod itself. A thin piece of the solid metal was then tightly pressed into the notch. For better adhesion, the lithium piece was mounted with superglue, but not for potassium or sodium, as contact with the glue produced an explosion, even under an argon atmosphere. Once inserted in the ablation housing, only the alkali metal-coated portion of the rod was exposed to the laser beam as the rod was rotated and translated. To produce the alkali metal acetylides, discharge assisted laser ablation was employed. The pure alkali metal vapor was ablated in the presence of a 0.3% mixture of acetylene in argon. A gas backing pressure of 40 psi was used and the pulsed valve was opened for 500 ls. The second harmonic (532 nm) of a Nd:YAG laser (200 mJ per pulse, 10 Hz repetition rate) was used to ablate the alkali metal surface 990 ls after the pulse valve was opened. A DC discharge of 1000 V was applied for a duration of 1000 ls after the opening of the valve. Typically, 250–1000 shots were averaged per frequency step. It should be noted that the alkali metal acetylides could be produced without the dc discharge; however, the resulting spectra were considerably weaker, by at least a factor of 10. The mechanism by which the discharge increases molecular production has not yet been definitively established; it has been speculated that the discharge may be breaking up clusters, or further activating the metal atoms from the ablation source. The deuterium isotopologues of each alkali metal acetylide were synthesized using the same conditions, with DCCD (99% enrichment, Cambridge Isotope Labs) substituted for acetylene. 3. Results The ground electronic state of the alkali metal acetylides is 1R+. Their spectra are therefore quite simple, except for the possible presence of quadrupole coupling and nuclear spin-rotation interactions of the alkali metal nuclei (I = 3/2 for Li, Na and K). Such hyperfine interactions were predicted for the acetylides on the basis of the alkali fluorides. Using these predictions, a 10 MHz frequency region was initially searched, centered on a given rotational transition. Only the J = 1 ? 0 transition could be observed for the lighter species LiCCH with this instrument; for NaCCH and KCCH the search focused on the J = 3 ? 2 rotational transition, because of greater instrument sensitivity at these frequencies (27.1 GHz and 17.8 GHz, respectively). After the most intense hyperfine components of these data were assigned, predictions were made for other rotational transitions and the spectra recorded. A similar process was conducted for the deuterium isotopologues. Table 1 lists the rotational transitions recorded for the alkali metal acetylides. As the table shows, each transition consists of multiple hyperfine components, labeled by quantum number F, where F = J + I. For LiCCH, three individual hyperfine components Table 1 e 1 Rþ .a Observed rotational transitions (in MHz) for MCCH X LiCCH F0 ? F00 mobs mobs mcalc 1 0 1.5 2.5 0.5 1.5 1.5 1.5 21088.214 21088.121 21088.043 0.001 0.002 0.000 2 1 1.5 2.5 1.5 0.5 3.5 2.5 1.5 0.5 3 2 4 3 a NaCCH J0 ? J00 mobs KCCH mobs mcalc mobs mobs mcalc 9018.782 9020.601 9022.052 0.001 0.002 0.001 5940.287 5942.000 5943.363 0.004 0.003 0.005 0.5 2.5 2.5 0.5 2.5 1.5 1.5 1.5 18038.587 18038.740 18040.037 18040.403 18040.559 18040.559 18041.854 18043.671 0.000 0.002 0.003 0.000 0.001 0.001 0.002 0.001 11881.554 11881.702 11882.925 11883.269 11883.417 11883.417 11884.641 11886.354 0.001 0.003 0.001 0.003 0.004 0.004 0.003 0.003 3.5 2.5 2.5 1.5 4.5 3.5 2.5 1.5 1.5 3.5 3.5 1.5 0.5 3.5 2.5 2.5 1.5 2.5 27058.706 0.001 27060.073 27060.073 27060.524 27060.524 27061.369 27061.886 0.002 0.002 0.003 0.003 0.001 0.001 17823.165 17823.962 17824.455 17824.455 17824.880 17824.880 17825.680 17826.167 17827.392 0.004 0.001 0.004 0.004 0.005 0.005 0.005 0.002 0.003 4.5 3.5 2.5 4.5 5.5 3.5 2.5 4.5 2.5 1.5 3.5 4.5 3.5 2.5 36078.498 36080.109 36080.109 36080.321 36080.321 0.004 0.002 0.002 0.003 0.003 36081.928 0.005 23764.538 23766.053 23766.053 23766.251 23766.251 23766.852 23767.766 0.006 0.006 0.006 0.005 0.005 0.005 0.005 Complete line list including millimeter-wave data available as Supplemental material. P.M. Sheridan et al. / Journal of Molecular Spectroscopy 269 (2011) 231–235 were measured in the J = 1 ? 0 transition, and four transitions were recorded for NaCCH and KCCH (J = 1 ? 0 through 4 ? 3), totaling 19 and 21 hyperfine components, respectively. For LiCCD, seven individual hyperfine components were measured, but only in the J = 1 ? 0 transition. The J = 1 ? 0 through 4 ? 3 transitions were recorded for NaCCD and KCCD, with a total of 16 and 30 hyperfine components observed, respectively. The transition frequencies for the deuterated species are found in the Supplemental Section of the journal. A spectrum of the J = 1 ? 0 transition of LiCCH near 21 GHz is shown in Fig. 1. The Doppler doublets for each hyperfine component are labeled by brackets. Three hyperfine features are visible, but one Doppler component of the F = 0.5 ? 1.5 line is blended with the F = 2.5 ? 1.5 transition. Fig. 2 shows the J = 1 ? 0 transition of NaCCH near 9 GHz; there are two frequency gaps in the figure to display all three hyperfine components. The J = 2 ? 1 transition near 12 GHz of KCCH is displayed in Fig. 3. Eight hyperfine transitions are visible in these data, with the strongest component consisting of two blended features (F = 3.5 ? 2.5 and F = 2.5 ? 1.5). Fig. 4 shows the J = 1 ? 0 transition of LiCCD. Again, the hyperfine components appear as Doppler doublets and are indicated by brackets. The spectrum is clearly more complex than that of LiCCH (Fig. 1), because of the deuterium nucleus. Hyperfine components are therefore labeled by F1 and F, where F1 = J + I1 (I1 refers to the alkali metal) and F = F1 + I2 (I2 refers to the deuterium). The spectra of the alkali-metal acetylides were fit to a 1R+ effective Hamiltonian of the following form [3] b eff ¼ H b rot þ H b eQq H 233 Fig. 2. Spectrum of the three hyperfine components of the J = 1 ? 0 rotational transition of NaCCH near 9 GHz, measured in this work. The Doppler doublets are indicated by brackets and the hyperfine components are labeled by the F quantum number. Unlike the J = 1 ? 0 transition of LiCCH, each individual hyperfine component is clearly resolved and two frequency breaks are needed to display all three features. This spectrum is a composite of three, 400 kHz wide scans, with 250 shots averaged per scan. ð1Þ b rot contains rotational and centrifugal distortion paramewhere H b eQq describes the quadrupole interactions. The nuclear ters and H spin-rotation coupling was also initially considered in the analysis, but the corresponding constant, CI, could not be reliably determined within a 3r uncertainty. For each species, a combined least squares fit of the FTMW and the previously measured millimeter-wave data, weighted by uncertainties of 5 kHz and 50 kHz, respectively, was performed using SPFIT [26]. For the deuterated molecules, an additional term was included to account for the deuterium quadrupole coupling. Spectroscopic parameters for each monoacetylide species are listed in Tables 2 and 3. Rotational constants from the previous Fig. 3. Spectra of the J = 2 ? 1 rotational transition of KCCH near 12 GHz. Eight hyperfine components, arising from the 39K nucleus and labeled by the F quantum number, are visible in the data. Doppler doublets are indicated by brackets. Six of the hyperfine components appear as single features but the F = 3.5 ? 2.5 and F = 2.5 ? 1.5 components are blended. The spectrum is a composite of five scans, each 400 kHz wide, with 250–1600 shots averaged per scan. millimeter-wave work are also included in the tables for comparison. For each acetylide, the rotational constants determined in this analysis are in good agreement with those of the previous millimeter studies. In some cases, such as NaCCD, higher-order centrifugal distortion constants could also be established. The quadrupole coupling constants, eQq, were determined for the first time for the metal and deuterium nuclei, as well. The rms of each combined fit is consistent with the accuracy of the FTMW and millimeter-wave instruments. Residuals for the millimeter-wave transitions are available as Supplemental material. 4. Discussion Fig. 1. Spectrum of the J = 1 ? 0 rotational transition of LiCCH measured in this work near 21 GHz. Three closely-spaced hyperfine components, arising from the 7Li nucleus and labeled by the F quantum number, are visible in the data. Doppler doublets are indicated by brackets. This spectrum is a single, 400 kHz wide scan, created from a 1500 shot average. Table 4 lists the metal quadrupole coupling constants for several alkali-metal containing molecules, namely the fluorides, chlorides, hydroxides and borohydrides. The metal quadrupole coupling 234 P.M. Sheridan et al. / Journal of Molecular Spectroscopy 269 (2011) 231–235 Table 4 Quadrupole coupling constants for alkali species (in MHz). 7 Species a c d e f g h i j Fig. 4. Spectra of the J = 1 ? 0 rotational transition of LiCCD near 19 GHz. In these data, a total of 15 hyperfine components, labeled by the F1 and F quantum numbers, respectively, are present, arising from the 7Li and D nuclei. Doppler doublets are indicated by brackets. The spectrum was generated by an average of 10 000 shots in a single 400 kHz wide scan. constant is small in magnitude for each species, which is consistent with an ionic description of the alkali metal–ligand bond [1–3]. For the acetylides, the magnitude of the eQq constant for a particular metal is very similar to those listed for the other ligands in Table 4. This comparison suggests that the acetylides possess a high degree of ionic metal–ligand bonding character similar to the halides, hydroxides and borohydrides. Covalent bonding character can often be examined using the electronegativity difference between two atoms in a bond [3]. This quantity is smaller between each alkali metal and carbon than between each alkali metal and fluorine or chlorine [3]. Because a decreasing electronegativity difference is associated with an increase in covalent bonding, the alkali metal–acetylide bond most 39 Na a MF M35Cl MOH MBH4 MCCH MCCD b 23 Li K b 0.41590 (12) 0.24993(50)d 0.2958(15)g 8.4401(15) 5.6698(60)e 7.584(52)h 3.385(31)i 7.264(20)j 7.442(47) j 0.378(47)j 0.272(37)j 7.932397(10)c 5.66583(3)f 7.454(52)h 4.256(24)i 6.856(18)j 6.873(14)j From Ref. [4]. From Ref. [5]. From Ref. [6]. From Ref. [7]. From Ref. [8]. From Ref. [9]. From Ref. [10]. From Ref. [11]. From Ref. [13]. This work. likely possess a greater degree of covalent character. Unfortunately, quantifying such character from alkali metal quadrupole coupling constants is difficult [27]. However, if it is assumed that there is some degree of sp hybridization on the metal atom in the acetylides, and that the hybridization forms the greatest contribution to the value of eQq for each metal, then the Townes–Dailey model can be used to quantitatively examine the covalent character of the metal–ligand bond. In the Townes–Dailey model, the metal quadrupole coupling constants can be expressed in terms of eQqn10, the coupling generated by an electron in a p orbital on the metal atom [1,27,28]: 1 eQq ¼ eQqn10 nnpr nnpp 2 ð2Þ The values of eQqn10 for the Li, Na, and K atoms are 0.29 MHz, 4.77 MHz and 4.79 MHz, respectively [29]. It is reasonable to assume that npp is zero for an alkali metal and hence npr is calculated Table 2 e 1 Rþ .a Spectroscopic constants (in MHz) for MCCH X a b c d e Parameter LiCCHb LiCCHc NaCCHb NaCCHd KCCHb KCCHe B D H L eQq (M) rms 10544.0915(32) 0.011375(11) 2.78(99) 108 10544.0909(46) 0.011373(14) 2.7(1.3) 108 4510.12329(86) 0.00282733(64) 4.12(14) 109 4510.116(10) 0.0028240(48) 3.63(70) 109 2970.8168(31) 0.0017560(13) 1.310(22) 108 2.73(13) 1013 0.378(47) 0.010 0.078 7.264(20) 0.032 0.083 2970.83066(77) 0.00176168(43) 1.403(10) 108 3.257(76) 1013 6.856(18) 0.077 0.038 Values in parenthesis are 3r standard deviations. This work. From Ref. [19]. The rms reflects a combined fit of ground vibrational state and m5 vibrational state rotational transitions. From Ref. [20]. The rms reflects a combined fit of ground vibrational state and m5 vibrational state rotational transitions. From Ref. [21]. The L constant is given as I in Ref. [20]. Table 3 e 1 Rþ .a Spectroscopic constants (in MHz) for MCCD X a b c d e Parameter LiCCDb LiCCDc NaCCDb NaCCDd KCCDb KCCDe B D H L eQq (M) eQq (D) rms 9622.8794(21) 0.0086090(18) 9622.8736(92) 0.0086047(69) 4181.19005(91) 0.00228463(95) 2.88(18) 109 4181.0949(59) 0.00225585(88) 2765.21740(58) 0.0014454(19) 9.78(36) 109 1.77(20) 1013 6.873(14) 0.157(20) 0.013 2764.999(14) 0.0013966(21) 4.97(11) 109 0.272(37) 0.152(33) 0.027 0.024 7.442(47) 0.193(48) 0.009 0.055 Values in parenthesis are 3r standard deviations. This work. From Ref. [19]. The rms reflects a combined fit of ground vibrational state and m5 vibrational state rotational transitions. From Ref. [20]. From Ref. [21]. 0.027 P.M. Sheridan et al. / Journal of Molecular Spectroscopy 269 (2011) 231–235 to be 1.3, 1.5 and 1.4 for LiCCH, NaCCH and KCCH, respectively. Since npr represents the number of electrons in the pr orbital on the metal atom, and the maximum value is 1, these values are not physical. Nevertheless, they suggest that hybridization is not the dominant contribution to eQq, and that the covalent character of the metal–ligand bond, even in the acetylides, is minimal. Polarization of the core electrons on the metal by the ligand most likely makes the dominant contribution to the value of eQq. The values of the deuterium quadrupole coupling constants for LiCCD, NaCCD and KCCD are 0.152(33) MHz, 0.193(48) MHz, and 0.157(20) MHz, respectively, which are essentially the same, within the reported uncertainties. For CuCCH, eQq(D) was determined to be 0.214(23) MHz [23], which overall is slightly larger in value. This small but significant variation likely results from increased metal–ligand covalent bonding character in CuCCH, which influences the electronic environment at the deuterium nucleus. Direct ablation of the pure metal appears to be a promising way of synthesizing alkali containing compounds in the gas phase. As mentioned previously, alkali metal quadrupole coupling constants have not yet been measured for the amides, monomethyls and hydrosulfides, and this method may offer an avenue to their synthesis and study. Surprisingly, the alkali eQq constants have not yet been measured for the deuterated alkali metal hydroxides either, a situation where use of the salt may have been the limiting factor. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] Acknowledgments [23] This research is supported by NSF-CHE-1057924. P.M.S. and M.K.L.B. would like to thank Canisius College for providing travel funds and the Ziurys group for the use of their spectrometer and their hospitality. [24] [25] [26] [27] [28] [29] Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.jms.2011.07.008. 235 C.H. Townes, B.P. Dailey, J. Chem. Phys. 17 (1949) 782–796. A.D. Buckingham, Trans. Faraday Soc. 58 (1962) 1277–1283. W. Gordy, R.L. Cook, Microwave Molecular Spectra, Wiley, New York, 1984. J. Cederberg, D. Olson, P. Soulen, K. Urberg, H. Ton, T. Steinbach, B. Mock, K. Jarausch, P. Haertel, M. Bresnahan, J. Mol. Spectrosc. 154 (1992) 43–50. C.D. Hollowell, A.J. Hebert, K. Street, J. Chem. Phys. 41 (1964) 3540–3545. G. Paquette, A. Kotz, J. Cederberg, D. Nitz, A. Kolan, D. Olson, K. Gunderson, S. Lindaas, S. Wick, J. Mol. Struct. 190 (1988) 143–148. T.F. Gallagher, R.C. Hilborn, N.F. Ramsey, J. Chem. Phys. 56 (1972) 5972–5979. F.H. De Leeuw, R. van Wachem, A. Dymanus, J. Chem. Phys. 53 (1970) 981–984. D. Nitz, J. Cederberg, A. Kotz, K. Hetzler, T. Aakre, T. Walhout, J. Mol. Spectrosc. 108 (1984) 6–16. D. McNaughton, L.M. Tack, B. Kleibömer, P.D. Godfrey, Struct. Chem. 5 (1994) 313–319. Y. Kawashima, R.D. Suenram, E. Hirota, J. Mol. Spectrosc. 175 (1996) 99–103. J. Cederberg, D. Olson, D. Rioux, T. Dillemuth, B. Borovsky, J. Larson, S. Cheah, M. Carlson, M. Stohler, J. Chem. Phys. 105 (1996) 3361–3365. Y. Kawashima, Y. Ohshima, Y. Endo, E. Hirota, J. Mol. Spectrosc. 174 (1995) 279–289. D.B. Grotjahn, P.M. Sheridan, I. Al-Jihad, L.M. Ziurys, J. Am. Chem. Soc. 123 (2001) 5489–5494. J. Xin, M.A. Brewster, L.M. Ziurys, Astrophys. J. 530 (2000) 323–328. D. Grotjahn, T.C. Pesch, M.A. Brewster, L.M. Ziurys, J. Am. Chem. Soc. 122 (2000) 4735–4741. A. Janczyk, L.M. Ziurys, Chem. Phys. Lett. 365 (2002) 514–524. E. Kagi, K. Kawaguchi, Astrophys. J. 491 (1997) L129–L132. A.J. Apponi, M.A. Brewster, L.M. Ziurys, Chem. Phys. Lett. 298 (1998) 161–169. M.A. Brewster, A.J. Apponi, J. Xin, L.M. Ziurys, Chem. Phys. Lett. 310 (1999) 411–422. J. Xin, L.M. Ziurys, Astrophys. J. 501 (1998) L151–L153. D.B. Grotjahn, A.J. Apponi, M.A. Brewster, J. Xin, L.M. Ziurys, Angew. Chem. Int. Ed. 37 (1998) 2678–2681. M. Sun, D.T. Halfen, J. Min, B. Harris, D.J. Clouthier, L.M. Ziurys, J. Chem. Phys. 133 (2010) 174301. M. Sun, A.J. Apponi, L.M. Ziurys, J. Chem. Phys. 130 (2009) 034309. T.J. Balle, W.H. Flygare, Rev. Sci. Instrum. 52 (1981) 33–45. H.M. Pickett, J. Mol. Spectrosc. 148 (1991) 371–377. A. Honig, M. Mandel, M.L. Stitch, C.H. Townes, Phys. Rev. 96 (1954) 629–642. K.A. Walker, M.C.L. Gerry, Chem. Phys. Lett. 301 (1999) 200–204. E.R. Cohen, T. Cvitas, J.G. Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, H.L. Strauss, M. Takami, A.J. Thor, Quantities, Units and Symbols in Physical Chemistry, IUPAC Green Book, 3rd ed., IUPAC & RSC Publishing, Cambridge, 2008 (2nd Printing).
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