Substitution structure of cyanogen, NCCN, from high-resolution far infrared spectra

Journal of Molecular Spectroscopy 218 (2003) 246–255 www.elsevier.com/locate/jms

Substitution structure of cyanogen, NCCN, from high-resolution far infrared spectraq John C. Grecu,a,1 Brenda P. Winnewisser,a,b,* and Manfred Winnewissera,b b

a Physikalisch-Chemisches Institut, Justus-Liebig-Universit€at Giessen, D-35392 Gießen, Germany Department of Physics, The Ohio State University, 174 West 18th Avenue, Columbus, OH 43210, USA

Received 12 November 2002

Abstract The lowest lying vibrational bands of the gas-phase spectra of cyanogen, NCCN, and four of its isotopomers, 15 NCCN, N CCN, 15 NCC15 N, and N13 C13 CN, were recorded with a Fourier transform interferometer. The resolution was limited by the maximum optical path difference (MOPD) attainable with the interferometer to FWHM ¼ 0:0012 cm1 . Rovibrational transitions of the m5 ( 230 cm1 ) and also the m2 –m5 ( 610 cm1 ) band systems were assigned for all five isotopomers. The use of an effective Hamiltonian for linear molecules to fit the data yielded precise spectroscopic vibrational and rotational constants for the vibrational states ðv1 v2 v3 v4 v5 Þ or ðv4 v5 Þ ¼ ð00Þ, (01), (02), (03), and (01000). These data include the first rotationally resolved transitions involving (01000). Complete substitution (rs ) structures of cyanogen, based on both single and double isotopic substitution of the parent species, were calculated. The derived structure is rCC ¼ 138:48ð17Þ pm and rCN ¼ 115:66ð13Þ pm. The two rs structures coincide within the errors due to remaining contributions of zero-point vibrations. Ó 2003 Elsevier Science (USA). All rights reserved. 13

Keywords: Substitution structure; Isotopomers; Internuclear distances

1. Introduction The linear molecules cyanogen (NCCN), isocyanogen (CNCN), and diisocyanogen (CNNC) represent the non-cyclic CN-dimers. These have been studied extensively by both experimental [1–7] and theoretical spectroscopists [8–12]. Since these three molecules are connected by one potential surface, as calculated ab initio for example by Sunil et al. [8], the interconversion of one CN-dimer to an isomer may be regarded as a prototype for intramolecular motion in a linear, fouratomic molecule. A similar case is found with the interconversion of vinylidene and acetylene [13]. In order to evaluate the potential function it is necessary to characterize the ground electronic state of all isomers. q Supplementary data for this article are available on ScienceDirect. * Corresponding author. Fax: +614-292-7557. E-mail address: [email protected] (B.P. Winnewisser). 1 Part of this authorÕs dissertation, Justus-Liebig-Universit€at Gießen, D26.

This requires building up the term value diagram systematically, starting with the lowest rovibrational levels, with close collaboration between theoretical ab initio and experimental spectroscopy. Ab initio calculations of the spectroscopic properties of the (CN)-dimers and their isotopomers are given in great detail in [14–17]. The calculated parameters were valuable in the present work when assigning spectra in dense spectral regions. From the experimental side, it has been determined that the highest energy isomer, diisocyanogen, CNNC, is rather unstable. It has only been detected so far in a solid argon matrix [3]. Therefore, no rotationally resolved data are available for this species. The situation is different concerning isocyanogen and cyanogen, since they are stable species at low pressures (mbar region) and moderate temperatures (up to 500 K) [1,18]. Thus, these two molecules may be investigated by means of high resolution spectroscopy under equilibrium conditions. The substitution structure of isocyanogen was recently determined [2] and the vibrational states of the main species [4,5] and of the isotopomer C15 NC15 N [6,7]

0022-2852/03/$ - see front matter Ó 2003 Elsevier Science (USA). All rights reserved. doi:10.1016/S0022-2852(02)00092-9

J.C. Grecu et al. / Journal of Molecular Spectroscopy 218 (2003) 246–255

have been characterized up to a term value of 3000 cm1 above the vibrational ground state. No substitution structure of NCCN has been reported, and only very little is known about the isotopomers. Only two publications in the literature present rotationally resolved spectra of cyanogen isotopomers: the first presents pure rotational Raman transitions of 15 NCC15 N up to J ¼ 69 in the vibrational ground state [19] and the second study reports rovibrational transitions of 15 NCC15 N and 15 NCCN in the mid-infrared [20]. This report is an experimental contribution to the characterization of the structure of the most stable compound in the CN-dimer family, cyanogen, in its ground electronic state, on the basis of rotationally resolved infrared spectral data of five isotopic species, including the parent species. Although rotationally resolved rovibrational spectra enable us to obtain the rotational constants of non-polar molecules, it is nearly impossible in the case of cyanogen to assign the transitions of its isotopomers in natural abundance, as pointed out previously in [21]. The situation changed fundamentally with the syntheses of isotopically pure samples of 15 NCCN, N13 CCN, 15 NCC15 N, and N13 C13 CN [22]. We have now measured the high resolution far infrared gas-phase spectra of the main species and the four isotopomers of cyanogen with a Fourier transform interferometer. Rovibrational transitions within the m5 band and the m2 –m5 difference band systems were evaluated for each isotopomer. The results of the analysis of the m5 band system of the main species were given in a previous paper [21]. Corresponding analyses of the m2 –m5 band of that species and both bands of the four other isotopomers are reported here. These data represent the first rotationally resolved data characterizing the v2 ¼ 1 state. The assignments of the fundamental band provided us with the rotational constants of the vibrational ground state, B0 for each isotopomer. These data allow us to determine the first rs structure of isocyanogen, NCCN. Two complete rs structures could be calculated, one with single and the second with double isotopic substitution.

2. Far infrared measurements The NCCN sample in natural isotopic abundance was synthesized by oxidation of potassium cyanide with copper(II) sulfate in aqueous solution [18]. The crude gaseous product was dried and the impurities CO2 , HCN, and HNCO were removed by reaction with solid sodium hydroxide [22]. After this procedure no impurities are found in the low resolution infrared spectrum, as seen in Fig. 1. The syntheses of the isotopically pure samples 15 NCCN, N13 CCN, 15 NCC15 N, and N13 C13 CN

247

Fig. 1. Low resolution (2 cm1 ) infrared spectrum of NCCN from 400 to 3200 cm1 . The designations of the band systems and their band centers are given.

are described in [22]. The isotopic enrichment was 98% or better for all species. The infrared gas-phase spectra of the m5 band system for the four isotopomers, and the m2 –m5 band system for all isotopic species including the main species, were obtained using the Gießen Bruker IFS 120 HR interferometer [23]. As we were working with very low pressures (Doppler limit), the resolution in the wavenumber range of all the spectra was limited by the maximum optical path difference (MOPD). The full width at half maximum of the corresponding unapodized sine function is FWHM ¼ 0:6=ðMOPDÞ ¼ 0:0012 cm1 . In the 200–300 cm1 region a mercury lamp was used as a radiation source, a 6 lm mylar film beam splitter was employed, and the aperture had a diameter of 3.15 mm. The rather large aperture ensured that the intensity of far infrared radiation reaching the sample and detector was sufficient to achieve a signal-to-noise ratio of  6–8 : 1 with one scan. However, the resulting self-apodization of the interferogram reduced the effective resolution to  0:0024 cm1 . The path length was 300 cm and the sample pressure 25 Pa. The absorption cell windows were made of wedged polyethylene. The spectral region was limited by a cold optical filter to 0–390 cm1 . The infrared radiation was detected by a liquid helium cooled silicon bolometer. A total of 180 interferograms were coadded in six blocks of 30 scans each. Signal-to-noise ratios of the coadded spectra vary between 80:1 and 100:1. Pure rotational lines of residual water vapor were used for internal wavenumber calibration with the reference positions taken from [24]. The accuracy of this calibration procedure is 1  104 cm1 . In the upper wavenumber region, 550–810 cm1 , a globar source, a germanium coated KBr beam splitter, and unwedged caesium iodide cell windows were used. The diameter of the aperture, 2 mm, was small enough

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to prevent self-apodization, so that the maximum unapodized resolution was achieved. After passing an optical filter (0–990 cm1 ) the radiation was detected by a Ge:Cu chip at liquid helium temperature. In this region 300 coadded interferograms were recorded, and the signal-to-noise ratio was comparable to that achieved in the far infrared region. The sample pressure was 77.5 Pa. Calibration was made externally using rovibrational OCS lines, whereby the reference values were taken from [25]. The wavenumber accuracy of the external calibration is 1  104 cm1 . Each spectrum was zero-filled by a factor 4 and ratioed against a low resolution, post-transform zero-filled background spectrum which was recorded with the empty absorption cell directly after each sample measurement. The line positions were evaluated with a peakfinder program [26] by fitting a second-order polynomial using the five points adjacent to each minimum in the transmittance spectrum.

3. Assignments and data reduction Throughout this paper the following notation and nomenclatures will be used: a vibrational state of cyanogen is designated by a complete set of vibrational quantum numbers fvg ¼ ðv1 v2 v3 v4 v5 Þ, or by the abbreviated form ðv4 v5 Þ if no stretching mode is excited. Each vibrational state with at least one bending mode excited includes one or more vibrational levels characterized by

the vibrational angular momentum quantum numbers l4 and l5 . These levels are designated by superscripts indicating the total vibrational angular momentum quantum number k ¼ l4 þ l5 . The vibrational state (02) thus consists of the levels ð02Þ0 and ð02Þ2 . Vibrational levels with k > 0 are split further due to l-type doubling or l-type resonance into vibrational sublevels indicated by the symmetry designation e or f . All corresponding subbands originating and ending in the same vibrational states constitute a vibrational band. Bands involving a given change in the quantum numbers of the same modes belong to a band system. The m5 band system of NCCN is a typical perpendicular band system of a linear molecule, as can be seen from the intense Q branches in Fig. 2. A description of the spectral structure and the assignments within this band system is given in [21] for the main species. The spectral structure remains essentially unchanged for the isotopomers. All assignments were carried out on a personal computer with the aid of the Gießen assignment programs for rovibrational transitions. The LOOMISWOOD program [27] was used for the P and R branches and QBRASS [28] for the Q branches. After the assignment of the fundamental band the combination differences of the sublevels ð01Þ1e and ð01Þ1f provided the basis of the assignment of the subbands of the next band in the m5 band system, ð02Þ ð01Þ. In successive steps all subbands of the bands up through ð03Þ ð02Þ were assigned for all four isotopomers.

Fig. 2. The Q-branch region of the m5 band system of NCCN. The vibrational assignment ðv4 v5 Þke;f of the Q branches and the location of their origins are indicated in the spectrum.

J.C. Grecu et al. / Journal of Molecular Spectroscopy 218 (2003) 246–255

The m2 –m5 band system is also a perpendicular band but, in contrast to the m5 band system, the Q branches all degrade towards decreasing wavenumbers, indicating a negative change of the rotational constants upon excitation, as seen in Fig. 3. Since it is a difference band, m2 –m5 is a very weak band system. Nevertheless the low intensity under the conditions of the recording was useful for observing the nuclear spin statistics for the various isotopomers, because the intensity distortion in a spectrum showing instrumentally limited resolution is less for weak transitions (see [29]). In Fig. 4 excerpts of the P-branch region of the three centrosymmetric isotopomers, NCCN, 15 NCC15 N, and N13 C13 CN, and for one asymmetric isotopomer, 15 NCCN, are shown. The predicted ratio for the statistical weights of even and odd J is 1:3 for 15 NCC15 N, 6:3 for NCCN, 21:15 for N13 C13 CN, and 1:1 for the asymmetric species. The predicted intensity alternation is clearly seen in the spectra in Fig. 4, thus confirming the identity of the carrier and showing the isotopic purity of the gas samples. Since the data for the vibrational state (01) are now known for all NCCN isotopomers from the m5 band system, the assignments in the m2 –m5 band system were straightforward, and the band ð01000Þ ð00001Þ could be assigned for all isotopomers. The data reduction ensued in two steps, as described in detail in [21]. First the assigned wavenumbers of each subband were fitted by a linear least-squares procedure to the common power series (ps) in J ðJ þ 1Þ, T ðv; J Þ ¼ Gc þ Bps J ðJ þ 1Þ  Dps ½J ðJ þ 1Þ 3

4

2

þ Hps ½J ðJ þ 1Þ þ Lps ½J ðJ þ 1Þ :

ð1Þ

T ðv; J Þ is the total term value of the rovibrational level, Gc the vibrational term value, Bps , Dps , Hps , and Lps are the rotational and centrifugal constants, respectively. All these spectroscopic constants are given in cm1 . The fitted power series constants of Eq. (1) are summarized in Tables 1–5. Since Eq. (1) cannot account for l-type

249

doubling and resonance, in a second step a fit to an effective Hamiltonian for linear molecules was performed. The power series constants of Tables 1–5 were used to define starting values. The Hamiltonian as defined by Yamada et al. [30] has matrix elements of the form Ek;k ¼ hkjHjki


 ¼ Gv þ xk k 2 þ yk k 4 þ Bv þ dJk k 2 þ hlJ k 4 f0 ðk; kÞ
 2 3  Dv þ hJk k 2 f0 ðk; kÞ þ Hv f0 ðk; kÞ ; ð2Þ

Uk;kþ2 ¼ hkjHjk þ 2i ¼ 14½qt þ qtJ J ðJ þ 1Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ðn  kÞðn þ k þ 2Þf2 ðk; k þ 2Þ;

ð3Þ

Ul;lþ2 ¼ Ulþ2;l ; with Gv being the pure vibrational term value, xk and yk the higher-order contributions in k 2 to the vibrational term value, Bv the rotational constant of vibrational state v, dJk and hkJ the higher-order contributions in k 2 to the rotational constant, Dv and Hv the centrifugal constants, hJk the first-order contribution in k 2 to the centrifugal constant Dv , qt the l-type-doubling constant, and qtJ the J dependent contribution to the l-typedoubling. The factors f in Eqs. (2) and (3) are f0 ðk; kÞ ¼ J ðJ þ 1Þ  k 2 ; f2 ðk; k  2Þ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ½J ðJ þ 1Þ  kðk  1Þ ½J ðJ þ 1Þ þ ðk  1Þðk  2Þ : In Eqs. (2) and (3) only the terms which could be determined from the assigned transitions are given. The fits to the effective Hamiltonian were performed with the least-squares fitting program LINC. The derived spectroscopic constants are summarized in Table 6. The standard deviations of the fits are slightly higher than the wavenumber accuracy of the calibration. All lines of non-zero weight were weighted equally in the fit. A complete listing of the observed wavenumbers of all (except for two bands) assigned and fitted rovibrational transitions for each isotopomer are available in an Appendix which can be found on the Journal web site, or from the authors.

4. Complete substitution structure

Fig. 3. Q-branch of the m2 –m5 band of NCCN. The rotational assignments are indicated.

The knowledge of the rotational constant of the vibrational ground state, B0 , of the main species [21] and of the four isotopomers (Table 6) enabled us to calculate complete substitution (rs ) structures using the Kraitchman equation [31,32]. Since the structure of cyanogen is fully determined by two parameters, and it contains two sets of equivalent atoms we may use the available data to derive one rs structure with single and one with double substitution.

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J.C. Grecu et al. / Journal of Molecular Spectroscopy 218 (2003) 246–255

A

B

Fig. 4. Comparison of the P-branch region of the m2 –m5 band system of NCCN, statistics for the various isotopomers.

15

NCC15 N,

15

NCCN, and N13 C13 CN. Note the different spin

Table 1 Power series constantsa in cm1 for the observed subbands of NCCN Subband

m~c

B0ps B00ps

D0ps D00ps

m2 –m5 Band system ð00001Þ1e ð01000Þ0e

611.870487 (17)

ð01000Þ0e

611.870480 (22)

0.15679898 (27) 0.15751579 (27) 0.156798973 (27) 0.15773856

2.2004 (45) 2.1785 (46) 2.20653 (59) 2.2432

a

ð00001Þ1f

0 Hps 00 Hps

L0ps L00ps

#

r

112

91

70

95

Notation: #, number of transitions in fit; r, standard deviation of fit in cm1 106 ;  indicates that the parameter indicated was held fixed in the fit.

J.C. Grecu et al. / Journal of Molecular Spectroscopy 218 (2003) 246–255

251

Table 2 Power series constantsa in cm1 for the observed subbands of N13 CCN Subband

m~c

B0ps B00ps

D0ps D00ps

m5 Band system ð00001Þ1e ð00000Þ0e

231.171800 (10)

ð00001Þ1f

ð00000Þ0e

231.171750 (32)

ð00002Þ2e

ð00001Þ1e

231.623048 (25)

ð00002Þ2f

ð00001Þ1f

231.622827 (16)

ð00002Þ0e

ð00001Þ1e

228.777462 (37)

ð00002Þ0e

ð00001Þ1f

228.777641 (26)

0.15681193 (13) 0.15639808 (13) 0.157035070 (29) 0.156398 0.15744360 (45) 0.15681199 (45) 0.15744520 (22) 0.15703556 (22) 0.15744992 (96) 0.15681280 (96) 0.157448506 (86) 0.15703556

2.1653 (12) 2.1039 (12) 2.21850 (47) 2.1 0.375 (18) 2.153 (19) 2.2983 (31) 2.2283 (31) 4.277 (46) 2.223 (47) 4.1413 (67) 2.222834

m2 –m5 Band system ð01000Þ0e ð00001Þ1e

609.071995 (14)

ð01000Þ0e

609.071980 (14)

0.15611649 (23) 0.15681263 (24) 0.156116148 (19) 0.15703556

2.2075 (51) 2.1765 (53) 2.20078 (48) 2.22834

a

ð00001Þ1f

0 Hps 00 Hps

L0ps L00ps

)761 (22) )30 (23)

922 (85) 130 (87) 625 (14)

)13.5 (52) )9.1 (54)

#

r

171

69

73

147

121

96

139

93

164

186

54

83

106

69

63

57

Notation: see footnote to Table 1.

Table 3 Power series constantsa in cm1 for the observed subbands of N13 C13 CN Subband

m~c

B0ps B00ps

D0ps D00ps

m5 Band system ð00001Þ1e ð00000Þ0e

228.818943 (10)

ð00002Þ2e

ð00001Þ1e

229.256490 (29)

ð00002Þ2f

ð00001Þ1f

229.2561666 (96)

ð00002Þ0e

ð00001Þ1e

226.583056 (59)

0.15609043 (12) 0.15568916 (12) 0.15670764 (74) 0.15608913 (76) 0.15671023 (11) 0.15631369 (11) 0.15671189 (95) 0.15608595 (97) 0.15671444 (14) 0.15631369 0.156313865 (25) 0.155689156 0.15720825 (42) 0.15670497 (43) 0.15722123 (64) 0.15671691 (63) 0.1569982 (12) 0.1567176 (13) 0.15699409 (57) 0.15670662 (60) 0.1574454 (20) 0.1567095 (21) 0.15744397 (19) 0.15671189

2.1544 (11) 2.09564 (100) 0.167 (39) 2.080 (41) 2.2787 (11) 2.2079 (11) 4.198 (22) 1.944 (23) 4.252 (11) 2.20789 2.21089 (38) 2.09563 1.4575 (57) 2.0158 (96) 1.9872 (75) 0.5217 (77) 3.069 (53) 4.451 (53) 2.827 (11) 0.100 (14) 3.041 (90) 2.192 (94) 3.120 (12) 4.19844

0.15541514 (50) 0.15609064 (50) 0.155414655 (25) 0.15631369

2.2061 (94) 2.1607 (95) 2.19399 (56) 2.2079

ð00002Þ0e

ð00001Þ1f

226.583410 (39)

ð00001Þ1f

ð00000Þ0e

228.818998 (31)

ð00003Þ3f

ð00002Þ2f

229.693153 (39)

ð00003Þ3e

ð00002Þ2e

229.693247 (58)

ð00003Þ1e

ð00002Þ0e

227.089348 (63)

ð00003Þ1e

ð00002Þ2e

224.415946 (51)

ð00003Þ1f

ð00002Þ2f

224.415956 (92)

ð00003Þ1f

ð00002Þ0e

227.088765 (62)

m2 –m5 Band system ð00001Þ1e ð01000Þ0e

605.924822 (31)

ð01000Þ0e

605.924854 (20)

a

ð00001Þ1f

Notation: see footnote to Table 1.

0 Hps 00 Hps

L0ps L00ps

)948 (62) )116 (67)

725 (15) )355 (20) 706 (23)

)402 (18) )580.7 (40) 408 (85) 1138 (87) )1034 )590 )210 )932

(13) (150) (160) (22)

#

r

173

67

119

127

157

58

186

317

54

126

77

141

138

170

154

300

169

263

87

155

139

287

53

218

116

167

60

77

19.50 (62)

16.7 (14)

)11.7 (46) )22.0 (47)

31.1 (89) 14.9 (97)

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J.C. Grecu et al. / Journal of Molecular Spectroscopy 218 (2003) 246–255

Table 4 Power series constantsa in cm1 for the observed subbands of

15

NCCN

Subband

m~c

B0ps B00ps

D0ps D00ps

m5 Band system ð00001Þ1e ð00000Þ0e

231.934789 (12)

ð00001Þ1f

ð00000Þ0e

231.934884 (39)

ð00002Þ2f

ð00001Þ1f

232.398125 (20)

ð00002Þ2e

ð00001Þ1e

232.398273 (37)

ð00002Þ0e

ð00001Þ1e

229.286090 (25)

0.15275693 (16) 0.15233973 (16) 0.152967887 (29) 0.15233973 0.15338134 (28) 0.15296743 (27) 0.15338125 (74) 0.15275728 (74) 0.15338494 (64) 0.15275754 (66)

2.0480 (17) 1.9865 (17) 2.09893 (40) 1.98648 2.1621 (33) 2.0956 (32) 0.640 (24) 2.074 (24) 3.771 (26) 2.097 (27)

m2 –m5 Band system ð01000Þ0e ð00001Þ1e

603.869355 (14)

ð01000Þ0e

603.869341 (12)

0.15205842 (24) 0.15275676 (25) 0.152058467 (17) 0.15296788

2.0621 (52) 2.0521 (55) 2.05658 (43) 2.098934

a

ð00001Þ1f

)488 34 590 68

L0ps L00ps

#

(24) (23) (31) (33)

r

159

77

78

178

157

130

148

188

143

136

109

72

63

50

Notation: see footnote to Table 1.

Table 5 Power series constantsa in cm1 for the observed subbands of

15

NCC15 N

Subband

m~c

B0ps B00ps

m5 Band system ð00001Þ1e ð00000Þ0e

230.149145 (10)

ð00001Þ1f

ð00000Þ0e

230.149127 (42)

ð00002Þ2e

ð00001Þ1e

230.609737 (33)

ð00002Þ2f

ð00001Þ1f

230.609519 (18)

ð00002Þ0e

ð00001Þ1e

227.426987 (34)

0.14810991 (13) 0.14770304 (13) 0.148309915 (31) 0.14770304 0.14871255 (58) 0.14810956 (58) 0.14871364 (22) 0.14830954 (22) 0.14871713 (58) 0.14811138 (58)

1.9172 (11) 1.8593 (11) 1.96648 (41) 1.8593 0.650 (18) 1.905 (18) 2.0239 (22) 1.9614 (22) 3.433 (13) 1.957 (13)

m2 –m5 Band system ð01000Þ0e ð00001Þ1e

595.834310 (14)

ð01000Þ0e

595.834308 (10)

0.14743036 (22) 0.14810960 (22) 0.147430680 (13) 0.14830991

1.9235 (45) 1.9205 (48) 1.92044 (33) 1.966485

a

0 Hps 00 Hps

ð00001Þ1f

D0ps D00ps

0 Hps 00 Hps

)441 (16) )11 (17)

459.1 (91) 30.3 (88)

L0ps L00ps

#

r

181

74

78

186

133

142

164

118

170

189

102

67

63

40

Notation: see footnote to Table 1.

For the rs structure on the basis of single isotopic substitution we use the rotational constants B0 of the main species and of the asymmetric isotopomers 15 NCCN and N13 CCN. The Kraitchman equation for this case is given by 2

jzs ðiÞj ¼

I00  I0 ; li

ð4Þ

where jzs ðiÞj is the absolute substitution coordinate of the atom i with respect to the center of mass of the parent species, and I0 and I00 are the moments of inertia for the parent and substituted species, respectively. The reduced mass li accounts for the change of the position of the center of mass upon substitution of nucleus i,

li ¼

MDMi ; M0

ð5Þ

M being the mass of the parent species, DMi the change of mass upon substitution of nucleus i, and M 0 the mass of the substituted species; all are given in unified atomic mass units (u). The moments of inertia were calculated from the rotational constants with the relation I ¼ h=8p2 B. The B0 values, the moments of inertia I0 , the masses mi and DMi , li and the resulting substitution coordinates are given in Table 7. The derived structure of NCCN upon single substitution is shown in Fig. 5. For an rs structure via double isotopic substitution, we have to use the B0 values of the main species,

J.C. Grecu et al. / Journal of Molecular Spectroscopy 218 (2003) 246–255

253

Table 6 Spectroscopic constants in cm1 of the effective Hamiltonian for linear molecules [30] Constant

NCCN

N13 C13 CN

15

NCC15 N

15

NCCN

N13 CCN

(00000) B0 108 D0

0.15708769 (14) 2.1106 (16)

0.15568940 (14) 2.0926 (16)

0.14770309 (20) 1.8601 (17)

0.15233987 (20) 1.9831 (26)

0.15639994 (23) 2.1056 (13)

(00001) Gv Bv 108 Dv 104 qv 1010 q5J

233.879144 (23) 0.15762663 (14) 2.2051 (17) 2.22824 (23) )6.114 (80)

228.975169 (30) 0.15620203 (17) 2.1793 (16) 2.23482 (20) )5.665 (39)

230.297358 (25) 0.14820995 (18) 1.9423 (17) 1.99962 (17) )4.857 (29)

232.087692 (26) 0.15286201 (21) 2.0600 (26) 2.11046 (19) )5.250 (37)

231.328708 (15) 0.15692364 (12) 2.1958 (13) 2.23221 (11) )5.734 (29)

(00002) Gv xk Bv 107 dJk 108 Dv 1011 hJk 104 qv 1010 q5J

464.866405 (35) 0.9188296 (90) 0.15816380 (14) )5.29 (13) 2.2995 (19) 1.82 (38) 2.23295 (48) )5.978 (97)

455.402457 (42) 0.8248664 (91) 0.15671383 (17) )8.96 (11) 2.2763 (17) 0.76 (20) 2.23604 (35) )6.289 (63)

457.576299 (44) 0.944316 (11) 0.14871478 (18) )2.24 (15) 2.0303 (19)

461.220999 (43) 0.931361 (11) 0.15338296 (21) )4.04 (16) 2.1644 (27)

459.949456 (24) 0.8687310 (63) 0.15744772 (12) )7.405 (99) 2.2920 (15)

(00003) Gv xk Bv 107 dJk 108 Dv 1011 hJk 104 qv 1010 q5J

695.812505 (46) 0.9087167 (64) 0.15869847 (15) )6.74 (10) 2.3978 (29) 2.76 (37) 2.24088 (31) )6.14 (14)

681.831729 (50) 0.8168469 (59) 0.15722231 (17) )10.344 (51) 2.3536 (17) 5.843 (85) 2.24519 (14) )5.811 (30)

(00004) Gv xk 105 yk Bv 107 dJk 108 Dv 1011 hJk 104 qv 1010 q5J

925.850387 (51) 0.8976390 (11) 6.687 (68) 0.15923077 (6) )7.67 (5) 2.4751 (16) 5.00 (17) 2.24625 (87) )4.10 (34)

(01000)a Gv Bv 108 Dv

845.591933 (47) 0.156798315 (57) 2.1928 (13)

834.743754 (32) 0.15541484 (42) 2.1949 (10)

2.00468 (57) )5.176 (96)

2.11711 (69) )5.78 (12)

825.983446 (41) 0.14743078 (18) 1.9219 (19)

835.804172 (40) 0.15205821 (21) 2.0549 (28)

2.23667 (38) )6.137 (85)

840.243777 (25) 0.15611591 (12) 2.1975 (15)

Each vibrational state is indicated as ðv1 v2 v3 v4 v5 ). a The Fermi resonance between the states (01000) and ð00020Þ0 was not considered. 15

NCC15 N, and N13 C13 CN. The Kraitchman equation is now  1
0 2 jzs ðiÞj ¼ I  I0 ; ð6Þ 2Dmi 0

since the position of the center of mass remains unchanged. Table 7 summarizes the quantities used in Eq. (6) and the derived rs coordinates. The errors of the coordinates given in Table 7 ( 0.01 pm) are determined by the experimental error of the moments of inertia (3  1051 kg m2 ). However, as discussed by Watson [33], the rs structure compensates only part of the effect of zero-point vibrations on the

molecular structure. This model error of an rs coordinate, representing the probable range of its deviation from the re value, depends on the substituted nuclei and inversely on the distance of the substituted nuclei from the center of mass: Djzs j ¼

K ; jzs j

K ¼ 8 pm2 for

12

K ¼ 11 pm2 for

C ! 13 C;

14

N ! 15 N:

ð7Þ

This results in model errors of the substitution coordinates of Djzs jðCÞ ¼ 0:12 pm and Djzs jðNÞ ¼ 0:06 pm,

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J.C. Grecu et al. / Journal of Molecular Spectroscopy 218 (2003) 246–255

Table 7 Calculation of the subsitution coordinates jzs j for the nuclei of cyanogen Isotopomer

B0 ðcm1 Þ

Single isotopic substitution NCCN 0.15708769 (14) 0.15639994 (23) N13 CCN 15 NCCN 0.15233987 (20)

1046 I ðkg m2 Þ

1046 DI ðkg m2 Þ

M (u)

17.81984 (1) 17.89820 (2) 18.37521 (2)

0.07836 (3) 0.55537 (3)

52.006148040 (28) 53.009502830 (29) 53.003183972 (40)

Isotopomer

1027 M (kg)

1027 DM (kg)

1027 l (kg)

jzs j (pm)

NCCN N13 CCN 15 NCCN

86.358300(52) 88.024410 (53) 88.013917 (53)

1.666110 (74) 1.655617 (74)

1.635160 (12) 1.625039 (32)

69.234 (8) 184.899 (10)

Isotopomer

B0 ðcm1 Þ

1046 I ðkg m2 Þ

1046 DI ðkg m2 Þ

M (u)

17.81984 (1) 17.97988 (1) 18.95205 (2)

0.16004 (2) 1.13221 (3)

52.006148040 (28) 54.012857640 (35) 54.000217940 (43)

Double isotopic substitution NCCN 0.15708769 (14) N13 C13 CN 0.15568940 (14) 15 NCCN15 0.14770309 (20) Isotopomer

1027 M (kg)

1027 DM (kg)

jzs j (pm)

NCCN N13 C13 CN 15 NCCN15

86.358300 (52) 89.690521 (54) 89.669532 (54)

3.332221 (76) 3.311232 (76)

69.3022 (87) 184.9135 (69)

The atomic masses and fundamental constants used are those given in [35].

Table 8 Comparison of experimental (this work) and ab initio [15] calculated rotational constants of the ground vibrational state for isotopomers of cyanogen Isotopomer 13

N CCN 15 NCCN N13 C13 CN 15 NCCN15 Fig. 5. Derived substitution (rs ) structure of cyanogen. Substitution coordinates jzs j of the nuclei (lower labels) and the internuclear distances (upper labels) are given in pm. Numbers in parentheses indicate the errors in units of the last digit.

which are an order of magnitude larger than the experimental error, and these model errors are given in Fig 5.

5. Discussion In order to derive the complete substitution (rs ) structure of cyanogen we recorded high resolution spectra of the m5 and m2 –m5 band systems of four isotopomers, each in an isotopically pure sample. Rotationally resolved data for (01000) are presented here for the first time. However, for an analysis which would include the effect of the significant Fermi resonance between the levels ð20Þ0e and (01000), data for the level ð20Þ0e are required. Similarly, a full characterization of the (11) state requires data for the four substates ð11Þ0e;f and ð11Þ2e;f . Further experimental effort will be required to measure these levels.

B0 (exp) (MHz)

B0 (ab initio) (MHz)

4688.752 4567.034 4667.451 4428.027

4688.68 4567.02 4667.38 4428.04

(69) (60) (42) (60)

With the use of the resulting highly precise rotational constants of the ground vibrational state, B0 , we were able to calculate two complete substitution structures, on the basis of single and double substitution. Within the experimental errors of the moments of inertia (3  1051 kg m2 ) we found a slight increase of the internuclear distances for the doubly substituted species, as expected due to the larger residual effect of zero-point vibrations. This effect is consistent with the physical model of the substitution structure (see for example [33]). If the error due to residuals of zero-point vibrations is considered, as discussed in [34], the two substitution structures may be considered identical. Table 8 compares the rotational constants of the ground vibrational state with the results of ab initio calculations [15]. The ab initio values (given in the Erratum to [15]) are within less than 0.1 MHz of our experimental values. Comparing the rs structures of NCCN and CNCN we note that the distance between the two CN moities is 7 pm shorter in CNCN [1] than in NCCN. This indicates that the canonical form with a double bond between the CN groups plays a more dominant role for

J.C. Grecu et al. / Journal of Molecular Spectroscopy 218 (2003) 246–255

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