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The rotational spectrum of NCCCNC in excited vibrational states
17 March 2000
Chemical Physics Letters 319 Ž2000. 265–272 www.elsevier.nlrlocatercplett
The rotational spectrum of NCCCNC in excited vibrational states A. Huckauf a
c
a,b,)
, A. Guarnieri
a,b
, C. Bartel c , D. Lentz
c
Institut fur ¨ Physikalische Chemie der Christian-Albrechts-UniÕersitat ¨ zu Kiel, Ludewig-Meyn-Straße 8, D-24098 Kiel, Germany b Technische Fakultat ¨ der Christian-Albrechts-UniÕersitat ¨ zu Kiel, Lehrstuhl fur ¨ Hochfrequenztechnik, Kaiserstraße 2, D-24143 Kiel, Germany Fachbereich Biologie, Chemie, Pharmazie, Institut fur ¨ Chemie - Anorganische und Analytische Chemie, Freie UniÕersitat ¨ Berlin, Fabeckstrasse 34-36, D-14195 Berlin, Germany Received 17 January 2000; in final form 27 January 2000
Abstract Rotational transitions of the linear molecule 3-isocyano-2-propynenitrile, NCCCNC, have been measured in the frequency range from 75 up to 120 GHz and assigned to the excited vibrational bending states Žy6 y 7 y 8 y 9 . s Ž0002., Ž0003., Ž0004., Ž0011., and Ž0020.. The analysis of the spectrum extends the spectroscopic data for NCCCNC by adding various newly determined rotational and rovibrational constants. q 2000 Elsevier Science B.V. All rights reserved.
1. Introduction Long linear molecules are typically rather flexible with respect to bending motions, and this flexibility manifests itself in low bending vibrational frequencies and large population factors for the associated levels. Thus the rotational spectra of these molecules are characterised by a rich vibrational satellite structure well suited for testing vibration–rotation theory by means of microwave and millimetre-wave spectroscopic investigations. 3-Isocyano-2-propynenitrile was described for the first time as late as 1993, when Smith et al. suc-
) Corresponding author. Technische Fakultat ¨ der Christian-Albrechts-Universitat ¨ zu Kiel, Lehrstuhl fur ¨ Hochfrequenztechnik, Kaiserstraße 2, D-24143 Kiel, Germany. Fax: q49-431-7757-2453; e-mail: [email protected]
ceeded in producing this interesting molecule through UV laser photoisomerisation of dicyanoacetylene isolated in an argon matrix w1,2x. In the course of the cited works all five stretching vibrational fundamentals n 1 through n4 and various combination and overtone bands were observed. Both the identification and the assignments were confirmed through the theoretical investigations by Botschwina et al., who reported a multitude of ab initio calculated data for NCCCNC, among others harmonic Ž v i . and anharmonic Ž n i . vibrational wavenumbers and rotational Ž Be , B0 , and De ., vibration–rotation coupling Ž a i . and l-type doubling Ž qt and qt J . constants w3–5x. Quite recently CB and DL could contrive a method carefully directed to produce 3-isocyano-2-propynenitrile virtually without any impurities by vacuum pyrolysis of a suitable precursor. This first chemical synthesis of NCCCNC was reported previously w6,7x. The linear molecule was characterised through millimetre-wave and Fourier-transform in-
0009-2614r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 0 0 . 0 0 1 4 7 - 0
266
A. Huckauf et al.r Chemical Physics Letters 319 (2000) 265–272
frared FTIR spectroscopy in combination with coupled-cluster calculations. The molecular structure, derived from the rotational constants of ten isotopomers, and the first three stretching vibrational fundamentals n 1 through n 3 were reported. In a previous Letter w8x we reported the millimetre-wave spectrum of NCCCNC in the vibrational states Žy 6 y 7 y 8 y 9 . s Ž0000., Ž0001., Ž0010., Ž0100., and Ž1000.. The present Letter is concerned with the assignment and the analysis of additional vibrational states, Ž0002., Ž0003., Ž0004., Ž0011., and Ž0020., which extend the spectroscopic data for NCCCNC by adding various newly determined rotational and rovibrational constants. Fig. 1 shows the vibrational energy levels of NCCCNC, representing the states that have been investigated in our previous work w8x as well as those which are subject of this Letter.
2. Experimental The precursor substance, wŽ CO . 5 Cr Ž NC – CCl5CF–CN.x, was synthesised at the Free University of Berlin as described in Refs. w6,7x. 3-Isocyano-2-propynenitrile was obtained from this chromium complex by vacuum pyrolysis at 2408C. The products ŽNCCCNC and – probably – a very small amount of NC–CCl5CF–CN. were condensed in a liquid-nitrogen trap, which was passed by the carbon monoxide released during the pyrolysis. The measurements described in this Letter were performed in the 75–120 GHz range using a PC-controlled millimetre-wave spectrometer operating in the source modulation mode. Millimetre waves were obtained from a Ku- or K-band backward wave oscillator ŽHP 8695A or HP 8696A. combined with an active frequency multiplier Žtripler HP 83556A or sextupler HP 83558A.. The BWO was phase-locked against a frequency synthesiser ŽPTS 500. which was controlled by a standard frequency of 10 MHz Žaccuracy: "1 Hz. provided by a GPS receiver. The free-space absorption cell consisted of a 10 cm diameter glass tube, 2.40 m in length and capped at the ends with Teflon collimating lenses. Low-noise detection was achieved by a liquid-helium-cooled InSb bolometer Ž‘Putley detector’.. The accuracy of the frequency measurements carried out at room temperature Ž288C. at a pressure of 1–3 Pa varies with the line strength: Strong lines were measured with an accuracy of "5 kHz Žchecked through OCS Lines., weaker lines needed higher pressure reducing the accuracy to "25 kHz.
3. Theoretical background
Fig. 1. Vibrational energy levels of NCCCNC up to 600 cmy1 . The rotational spectra of states represented by bold lines are analysed in the present work; thin lines are used for states which have not been analysed so far.
The theory concerning excited bending states of linear molecules is well established. It has been studied by many investigators, e.g., Amat et al. w9x and Winnewisser and Winnewisser w10x. For our analysis we adopted a slightly modified version of the effective Hamiltonian proposed by Yamada, Birss and Aliev ŽYBA. w11x, which summarises the rovibrational interactions in a very compact form. Since
A. Huckauf et al.r Chemical Physics Letters 319 (2000) 265–272
the details are given in the original paper, we will only recall its essential features and describe the modifications we made: The Hamiltonian used for the analysis is given by Hˆr s hˆ d q hˆ 0 q hˆ 2 ,
Ž 1.
with hˆ d s Gyq
Ý x LŽ t t . pˆ zŽ t . pˆ zŽ t . X
tFt
X
X
q By q
Ý d JL Ž t t . pˆ z Ž t . pˆ z Ž t . ž Jˆ2 y Jˆz2 / X
tFt
X
X
2
y Dy Jˆ2 y Jˆz2 q Hy Jˆ2 y Jˆz2
ž
hˆ 0 s
/
ž
3
/
,
Ž 2.
Ý Ž rt t q rt t J Jˆ2 . X
t-t
X
X
= Lˆ qqŽ t . Lˆ yyŽ tX . q Lˆ yyŽ t . Lˆ qqŽ tX . ,
ž
/
Ž 3.
and hˆ 2 s
1 2
Ý ž qt q qt J Jˆ2 q qt J J Jˆ4 / t
= Lˆ qqŽ t . Jˆy2 q Lˆ yyŽ t . Jˆq2 .
ž
/
Ž 4.
This Hamiltonian differs slightly from that given in w11x, as some higher-order terms which were found not to be necessary to reproduce the experimental data were omitted in order to reduce the complexity of the Hamiltonian: We neglected the terms h JL Žin hˆ d ., rt tX J J Žin hˆ 0 ., and qt L and some crossterms Žin hˆ 2 .; furthermore we ignored the term hˆ 4 which represents the D l s "4 interaction. On the other hand, we decided to include the constant qt J J Žin hˆ 2 . which is not part of the original YBA Hamiltonian, though this constant could be determined only for the Ž0100. state. The notation for states and wavefunctions also follows a proposal of Yamada et al. w11–14x, but in order to avoid any misunderstanding, we give an explanation of the nomenclature in Appendix A.
267
absorption lines belonging to the states Ž0002., Ž0003., Ž0004., Ž0011. and Ž0020. rather easily. Starting from the ground state lines, broad scans towards higher frequencies were taken. The spectra obtained in this way revealed the extended vibrational satellite structure which characterises the rotational spectra of longer linear molecules. Paying attention to the different linestrengths and comparing the experimental with some simulated spectra we were able to identify the lines of the higher excited vibrational bending states without any particular difficulty. The simulated spectra were based upon molecular constants that were determined in our previous study w8x, in particular on the parameters a t and bt which describe the vibrational dependence of the rotational constant B and the centrifugal distortion constant D, respectively: For the Ž0002. state, e.g., we presumed B99 s B0 y 2 a 9 s 1415.967437 MHz and D 99 s D 0 y 2b 9 s 38.0159 Hz, which turned out to be rather close to the actual values of 1415.98315 MHz and 38.42 Hz, respectively. The dominant lines belong to n 9 levels, for which vibration satellites up to y s 4 could be detected. For the second lowest vibration, n 8 , only the fundamental Ž0010. and the second excited state Ž0020. could be observed. Only one combination state, Ž0011., could be clearly identified. For all other states of this type, only parts of the satellite structure could be identified, so that we were not able to include these states in our analysis. It is noteworthy that all attempts to identify absorption lines of the fundamental of the lowest vibrational stretching state, n 5 , failed, though we carefully scanned the corresponding frequency ranges, making use of the rotational constant predicted by ab initio methods w3,4x. With respect to its vibrational energy of 610.1 cmy1 w1,2x the rotational transitions of the y 5 s 1 state should be clearly observable. So it may be assumed that the y 5 s 1 state is involved in a resonance system, which could not be identified so far.
4. Observed spectrum and assignments Since the rotational and rovibrational constants of NCCCNC in the excited vibrational bending states Ž0001. and Ž0010. have already been determined in our previous work w8x, we could find and identify the
5. Analysis The rotational spectra were observed and analysed in the excited vibrational bending states Žy 6 y 7 y 8 y 9 .
A. Huckauf et al.r Chemical Physics Letters 319 (2000) 265–272
268
Table 1 Observed and calculated frequencies Žin MHz. of NCCCNC J
Ž0003.1y
nobs 26 27 28 29 30 31 32 33
76552.169 79387.034 82221.914 85056.707 87891.429 90726.121 93560.813 96395.410
Ž0003.1q oyc y0.007 y0.021 0.022 0.021 y0.008 y0.021 0.013 y0.001
Ž0004. 0
nobs 76687.155 79526.965 82366.762 85206.518 88046.169 90885.806 93725.397 96564.921
Ž0003. 3y oyc 0.010 y0.014 y0.003 0.017 y0.016 y0.010 0.005 0.010
Ž0004. 2y
nobs
87970.946 90808.628 93646.264 96483.884
Ž0003. 3q oyc
y0.027 0.002 y0.002 y0.009
nobs
87971.270 90808.942 93646.636 96484.299
oyc
0.034 0.007 0.010 y0.012
Ž0004. 4 "
Ž0004. 2q
26 27 28 29
76767.545 79609.231 82450.807 85292.140 Ž0011. 0y
y0.008 y0.021 0.017 y0.022
76780.792 79624.121 82467.403 85310.645 Ž0011. 0q
0.022 0.020 0.015 0.016
76797.623 79642.833 82488.187 85333.603 Ž0011. 2y
0.010 y0.023 y0.002 y0.011
76779.233 79622.786 82466.355 85309.910 Ž0011. 2q
0.003 y0.015 0.000 0.010
26 27 28 29 30 31 32 33 34 35 36
76445.438 79276.416 82107.386 84938.355 87769.214 90600.072 93430.917 96261.671 99092.417 101923.133 104753.735
y0.003 y0.024 y0.018 0.022 y0.012 y0.009 0.020 y0.003 0.008 0.030 y0.018
76442.817 79273.516 82104.222 84934.835 87765.384 90595.902 93426.365 96256.686 99087.019 101917.259 104747.471
0.008 y0.018 0.015 0.011 y0.001 0.014 0.034 y0.026 y0.011 y0.024 0.002
76449.373 79280.714 82112.025 84943.318 87774.546 90605.796 93437.039 96268.238 99099.436 101930.602 104761.776
y0.028 y0.001 0.011 0.022 y0.015 y0.012 0.003 y0.008 0.001 y0.003 0.023
76451.689 79283.252 82114.818 84946.404 87777.958 90609.556 93441.108 96272.709 99104.366 101935.889 104767.557
0.029 0.018 0.007 0.013 y0.015 y0.003 y0.039 y0.029 0.034 y0.039 0.031
26 27 28 29 30 31 32 33 34 35 36
Ž0002. 0 76454.565 79285.531 82116.454 84947.316 87778.028 90608.727 93439.335 96269.820 99100.272 101930.602 104760.915
0.019 0.001 0.011 0.034 y0.016 y0.001 0.005 y0.030 y0.012 y0.029 0.026
Ž0002. 2y 76458.375 79289.933 82121.451 84952.966 87784.421 90615.852 93447.271 96278.673 99110.048 101941.321 104772.661
0.011 0.015 0.004 0.017 y0.002 y0.017 y0.014 0.002 0.022 y0.027 0.024
Ž0002. 2q 76463.869 79296.044 82128.258 84960.484 87792.777 90625.048 93457.301 96289.625 99121.993 101954.357 104786.703
y0.014 y0.026 y0.020 y0.023 0.021 0.021 y0.019 y0.010 0.020 0.024 y0.014
Ž0020. 0 26 27 28 29 30 31 32 33 34 35 36
76427.068 79257.496 82087.844 84918.203 87748.503 90578.814 93409.063 96239.279 99069.484 101899.636 104729.773
Ž0020. 2y y0.017 0.015 y0.007 0.008 y0.008 0.015 0.006 y0.005 0.004 y0.008 y0.002
Ž0020. 2q
79263.274 82093.858 84924.427 87754.930 90585.457
0.015 0.007 0.009 y0.029 y0.017
79263.455 82094.098 84924.700 87755.220 90585.764
y0.010 0.018 0.028 y0.019 y0.017
96246.400 99076.837 101907.253 104737.643
y0.018 y0.010 0.008 0.030
96246.795 99077.253 101907.692 104738.073
0.008 0.003 0.009 y0.015
A. Huckauf et al.r Chemical Physics Letters 319 (2000) 265–272
s Ž0002., Ž0003., Ž0004., Ž0011., and Ž0020.. The analysis of the data was performed in two different ways: Firstly we have determined effective constants for each l substate by fitting the observed rotational transition frequencies to the frequency formula
n s 2 Beff Ž J q 1 . y4Deff Ž J q 1 . 3
3
3
q Heff Ž J q 1 . Ž J q 2 . y J 3 .
Ž 5.
The results, which might be useful for future IR spectroscopic investigations, are given in Tables 1 and 2. Secondly we have analysed the individual vibrational states Žincluding all l substates of a given state simultaneously. by use of a least-squares fitting program which sets up a matrix representation of the
269
Hamiltonian described in Section 3 and calculates its eigenvalues by a numerical diagonalisation procedure. The difference between the eigenvalues of two consecutive quantum numbers J gives the absorption frequency. The analysis of a total amount of 150 absorption frequencies resulted in the determination of the rotational, centrifugal distortion, vibration–rotation interaction, and l-type doubling constants given in Table 3. Since some parameters of our previous investigation w8x were employed in our present analysis, too, we recall those constants in Table 3 in order to facilitate the understanding. Some higher-order terms which were found not to be necessary to reproduce the experimental data were omitted in the analysis and do not appear in the table. Because certain information is not contained in the observed spectra, some constants had to be fixed.
Table 2 Effective rotational constants for individual vibrational substates of NCCCNC a State
Beff ŽMHz.
Deff ŽHz.
Heff ŽmHz.
s Fit ŽkHz.
Ž0000. 0q Ž0001.1y Ž0001.1q Ž0002. 0q Ž0002. 2y Ž0002. 2q Ž0003.1y Ž0003.1q Ž0003. 3y Ž0003. 3q Ž0004. 0q Ž0004. 2y Ž0004. 2q Ž0004. 4 " Ž0010.1y Ž0010.1q Ž0011. 0y Ž0011. 0q Ž0011. 2y Ž0011. 2q Ž0020. 0q Ž0020. 2y Ž0020. 2q Ž0100.1y Ž0100.1q Ž1000.1y Ž1000.1q
1409.975279Ž19. 1412.349175Ž22. 1413.593688Ž24. 1415.98156Ž69. 1415.95185Ž48. 1415.95303Ž63. 1417.72370Ž80. 1420.23484Ž55. 1418.9143Ž24. 1418.9141Ž14. 1421.9849Ž33. 1421.96221Ž27. 1421.9706Ž23. 1421.8620Ž16. 1412.424768Ž21. 1413.029186Ž26. 1415.72994Ž48. 1415.72321Ž50. 1415.76376Ž41. 1415.76532Ž71. 1415.37241Ž30. 1415.47157Ž63. 1415.47212Ž56. 1411.779021Ž24. 1412.161141Ž25. 1411.750924Ž26. 1412.101569Ž23.
34.5485Ž28. 35.6918Ž51. 36.8733Ž57. 107.45Ž32. 38.50Ž22. y30.68Ž29. 62.35Ž41. 70.30Ž29. 14.5Ž11. 11.83Ž67. 249.5Ž20. 65.64Ž16. y142.3Ž14. 16.78Ž97. 35.0693Ž48. 35.3831Ž64. 50.62Ž22. 79.29Ž23. 23.46Ž19. y4.39Ž33. 38.42Ž14. 35.92Ž28. 33.82Ž25. 34.9292Ž43. 35.0330Ž46. 34.8405Ž52. 34.8933Ž47.
2.15Ž13. 2.04Ž30. 3.01Ž34.
4.165 b 4.202 b 4.511b 27.161 18.801 24.878 19.863 13.796 20.840 12.701 28.998 2.372 19.920 14.134 3.950 b 4.733 b 18.784 19.564 15.923 28.014 11.616 21.606 19.122 4.578 b 4.831b 4.968 b 4.359 b
a b
Uncertainties Žin parentheses. are 1 s in the last significant digit. Fitted by use of previously published w8x measurement data.
3.87Ž29. 2.43Ž39.
0.58Ž22. 2.82Ž25. 1.89Ž29. 1.77Ž25.
A. Huckauf et al.r Chemical Physics Letters 319 (2000) 265–272
270
Table 3 Experimental rovibrational constants for individual vibrational states of NCCCNC a Constant
By ŽMHz. a t ŽMHz. c Dy ŽHz. bt ŽHz. c Hy ŽmHz. qt ŽMHz. q J t ŽHz. q J J t ŽmHz. s Fit ŽkHz. No. of lines
By ŽMHz. a t ŽMHz. c Dy ŽHz. bt ŽHz. c q8 ŽMHz. qJ8 ŽHz. q9 ŽMHz. qJ9 ŽHz. d J LŽ88. ŽkHz. d J LŽ89. ŽkHz. d J LŽ99. ŽkHz. x LŽ88. ŽGHz. x LŽ89. ŽGHz. x LŽ99. ŽGHz. r 89 ŽGHz. r J 89 ŽkHz. s Fit ŽkHz. No. of lines
Vibrational state Ž0000. b
Ž0001. b
Ž0010. b
Ž0100. b
Ž1000. b
1409.975279Ž19.
1412.971358Ž17. y2.996079Ž26. 36.2822Ž39. y1.7337Ž48. 2.50Ž23. 1.244467Ž26. y1.1659Ž15.
1412.726909Ž18. y2.751630Ž26. 35.2275Ž42. y0.6790Ž50. 3.23Ž25. 0.604484Ž27. y0.3372Ž16.
1411.970011Ž17. y1.994731Ž26. 34.9811Ž31. y0.4326Ž42. 1.70Ž16. 0.382122Ž34. y0.1041Ž63. 2.25Ž33. 4.659 62
1411.926177Ž17. y1.950897Ž26. 34.8669Ž34. y0.3185Ž44. 1.83Ž19. 0.350652Ž27. y0.0550Ž14.
34.5485Ž28. 2.15Ž13.
4.165 46
4.447 66
4.612 63
4.602 60
Ž0002.
Ž0003.
Ž0004.
Ž0011.
Ž0020.
1415.98315Ž34. y6.00787Ž34. 38.42Ž14. y3.87Ž14.
1418.98753Ž55. y9.01225Ž55. 39.52Ž32. y4.98Ž32.
1421.99344Ž83. y12.01816Ž83. 41.26Ž50. y6.71Ž50.
1415.72856Ž27. y5.75328Ž27. 37.24Ž12. y2.70Ž12. 0.604484 y0.3372 1.244467 y1.1659 24.800 17.94Ž28. y7.953 40.19 9.625Ž32. 6.9475 y6.313Ž16. y3.450Ž98. 21.281 44
1415.37238Ž28. y5.39710Ž28. 36.06Ž12. y1.51Ž12. 0.604484 y0.3372
1.249014 y1.4841
y7.953Ž56.
6.9475Ž47.
20.498 33
1.25356Ž51. y1.80Ž26.
y8.33Ž15.
6.884Ž58.
17.828 24
1.258109 y2.1207
y8.225Ž10.
6.8991Ž18.
16.328 20
24.800Ž47.
40.19Ž82.
16.141 29
a Uncertainties Žin parentheses. are 1 s in the last significant digit. If no uncertainty is given, the corresponding parameter was fixed Žsee text.. b Refitted from the data of our previous investigation w8x. c Calculated according to the simplified expressions a t s B0 y By and bt s D 0 y Dy , respectively.
In Table 3 one can easily distinguish between fixed and fitted parameters because for the latter the standard deviations are given in parentheses. For the Ž0002. and Ž0004. states, e.g., the constants q9 and q J 9 were fixed at values obtained by linear interpolation and extrapolation of the corresponding Ž0001. and Ž0003. constants, and for the Ž0011. state, the constants x LŽ89. and d JLŽ89. were fitted, whereas the constants x LŽ88. , x LŽ99. , d JLŽ88. , and d JLŽ99. had to be fixed at the values obtained from the analyses of the Ž0002. and Ž0020. states, respectively. The molecular constants which have been determined for the higher excited vibrational states do not
reveal any unexpected characteristics, but some topics seem to be worth mentioning: In contrast to our previous investigation w8x, we have not been able to determine any P 6 term Ž Hy or q J J t . for the higher excited vibrational states, because in this study the range of our data was much smaller and the measurements were taken at lower J values. However, these constants turned out to be very small for the vibrational states studied previously w8x, and it can be assumed that they are in the same order for the newly investigated states. The fact that x LŽ99. has a positive and d JLŽ99. a negative value confirms that NCCCNC is a well-be-
A. Huckauf et al.r Chemical Physics Letters 319 (2000) 265–272
271
haved linear molecule – for a quasi-linear molecule, the signs of these constants must be opposite w15x. Finally, it should be pointed out that we assumed the constants q6 through q9 to have positive values as discussed in w8x.
In the simplified notation employed in this Letter the l substates are expressed as Žy6 y 7 y 8 y 9 . l " Žthe inclusion of l t or l tX is superfluous in the case of the vibrational states which are the subject of this Letter., where the sign in the superscript indicates the positive or the negative linear combination:
Acknowledgements
Ž 0001.
1"
<1 Ž 1 . ; J ,1 " :
1
A.G. and A.H. would like to thank Prof. Dr.-Ing. ŽLehrstuhl fur R. Knochel ¨ ¨ Hochfrequenztechnik, Technische Fakultat ¨ der Universitat ¨ Kiel. for research support. Furthermore we are indebted to the workshop of the Technische Fakultat ¨ for manufacturing of millimetre-wave components and other indispensable devices without which this investigation could not have been made. The work at Kiel was supported by the Deutsche Forschungsgemeinschaft DFG ŽGU 128r15-1., the work at Berlin by the Fonds der Chemischen Industrie and the Deutsche Forschungsgemeinschaft DFG ŽLE 423r9-2..
s
< :< : '2 Ž 1 Ž 1. ; J ,1 " 1 Ž y1. ; J ,y 1 .
Ž A.5 .
Žanalogous for the l substates of the Ž0010., Ž0100., and Ž1000. states., 0 Ž 0002. <2 Ž 0 . ; J ,0: ,
Ž 0002.
2"
<2 Ž 2 . ; J ,2 " :
1
s
Ž A.6 .
< : < : '2 Ž 2 Ž 2. ; J ,2 " 2 Ž y2. ; J ,y 2 .
Ž A.7 .
Žanalogous for the l substates of the Ž0020. state.,
Ž 0003.
1"
<3 Ž 1 . ; J ,1 " :
1
s Appendix A. Nomenclature of states and wavefunctions A vibrational state where two bending modes y t s n, y tX s m are simultaneously excited contains Ž n q 1.Ž m q 1. substates. Each substate is characterized by n, m, J, and l, where J is the total angular momentum and l its projection along the symmetry axis with l s l t q l tX , Ž A.1 . l t s yn, yn q 2, . . . , n y 2, n ,
Ž A-2.
and l tX s ym, ym q 2, . . . , m y 2, m .
Ž A.3 .
For a given J value the substates can be identified with a set of symmetrised linear combinations in a basis of Ž n q 1 .Ž m q 1 . functions line < Õt Ž l t .,ÕtX Ž l tX .; J,l :, each of which is the product of two two-dimensional harmonic oscillator functions and a symmetric top function: < n Ž l t . ,m Ž l tX . ; J ,l " :
Ž 0003.
<3 Ž 3 . ; J ,3 " :
< : < : '2 Ž 3 Ž 3. ; J ,3 " 3 Ž y3. ; J ,y 3 . , Ž A.9 .
0 Ž 0004. <4 Ž 0 . ; J ,0: ,
Ž 0004.
2"
Ž A.10 .
<4 Ž 2 . ; J ,2 " :
1
s
< : < : '2 Ž 4 Ž 2. ; J ,2 " 4 Ž y2. ; J ,y 2 . , Ž A.11 .
Ž 0004.
4"
<4 Ž 4 . ; J ,4 " :
1
s
< : < : '2 Ž 4 Ž 4. ; J ,4 " 4 Ž y4. ; J ,y 4 . , Ž A.12 .
Ž 0011.
0"
<1 Ž 1 . ,1 Ž y1 . ; J ,0 " :
1
s
< : '2 Ž 1 Ž 1. ,1 Ž y1. ; J ,0
"<1 Ž y1 . ,1 Ž 1 . ; J ,0: . ,
Ž 0011.
2"
Ž A.13 .
<1 Ž 1 . ,1 Ž y1 . ; J ,2 " :
1
< : '2 Ž n Ž l t . ,m Ž l t . ; J ,l
s
X
"< n Ž yl t . ,m Ž yl tX . ; J ,y l : . .
3"
1
s
1
s
< : < : '2 Ž 3 Ž 1. ; J ,1 " 3 Ž y1. ; J ,y 1 . , Ž A.8 .
Ž A.4 .
< : '2 Ž 1 Ž 1. ,1 Ž 1. ; J ,2
"<1 Ž y1 . ,1 Ž y1 . ; J ,y 2: . .
Ž A.14 .
272
A. Huckauf et al.r Chemical Physics Letters 319 (2000) 265–272
References w8x w1x A.M. Smith, G. Schallmoser, A. Thoma, V.E. Bondybey, J. Chem. Phys. 98 Ž3. Ž1992. 1776. w2x A.M. Smith, V.E. Bondybey, M. Horn, P. Botschwina, J. Chem. Phys. 100 Ž2. Ž1994. 765. w3x P. Botschwina, M. Horn, J. Flugge, S. Seeger, J. Chem. Soc., ¨ Faraday Trans. 89 Ž13. Ž1993. 2219. w4x M. Horn, P. Botschwina, J. Flugge, Theor. Chim. Acta 88 ¨ Ž1994. 1. ¨ Heyl, M. Horn, Poster F17, 15th Int. w5x P. Botschwina, A. Colloq. on High Resolution Molecular Spectroscopy, Glasgow, Sept. 1997. ¨ Heyl, w6x C. Bartel, P. Botschwina, H. Burger, A. Guarnieri, A. ¨ A. Huckauf, D. Lentz, T. Merzliak, E.B. Mkadmi, Angew. Chem. 110 Ž1998. 3036. ¨ Heyl, w7x C. Bartel, P. Botschwina, H. Burger, A. Guarnieri, A. ¨
w9x w10x w11x w12x w13x w14x w15x
A. Huckauf, D. Lentz, T. Merzliak, E.B. Mkadmi, Angew. Chem., Int. Ed. Engl. 37 Ž1998. 2879. ¨ Heyl, P. Potschwina, C. Bartel, A. Huckauf, A. Guarnieri, A. D. Lentz, Chem. Phys. Lett. 303 Ž1999. 607. G. Amat, H.H. Nielsen, G. Tarrago, Rotation–Vibration of Polyatomic Molecules, Dekker, New York, 1971. M. Winnewisser, B.P. Winnewiser, J. Mol. Spectrosc. 41 Ž1972. 143. K.M.T. Yamada, F.W. Birss, M.R. Aliev, J. Mol. Spectrosc. 112 Ž1985. 347. K.M.T. Yamada, R.A. Creswell, J. Mol. Spectrosc. 116 Ž1986. 384. G.M. Plummer, D. Mauer, K.M.T. Yamada, K. Moller, J. ¨ Mol. Spectrosc. 130 Ž1988. 407. M. Niedenhoff, K.M.T. Yamada, J. Mol. Spectrosc. 157 Ž1993. 182. K. Yamada, M. Winnewisser, Z. Naturforsch. A 31 Ž1976. 139.
Chemical Physics Letters 319 Ž2000. 265–272 www.elsevier.nlrlocatercplett
The rotational spectrum of NCCCNC in excited vibrational states A. Huckauf a
c
a,b,)
, A. Guarnieri
a,b
, C. Bartel c , D. Lentz
c
Institut fur ¨ Physikalische Chemie der Christian-Albrechts-UniÕersitat ¨ zu Kiel, Ludewig-Meyn-Straße 8, D-24098 Kiel, Germany b Technische Fakultat ¨ der Christian-Albrechts-UniÕersitat ¨ zu Kiel, Lehrstuhl fur ¨ Hochfrequenztechnik, Kaiserstraße 2, D-24143 Kiel, Germany Fachbereich Biologie, Chemie, Pharmazie, Institut fur ¨ Chemie - Anorganische und Analytische Chemie, Freie UniÕersitat ¨ Berlin, Fabeckstrasse 34-36, D-14195 Berlin, Germany Received 17 January 2000; in final form 27 January 2000
Abstract Rotational transitions of the linear molecule 3-isocyano-2-propynenitrile, NCCCNC, have been measured in the frequency range from 75 up to 120 GHz and assigned to the excited vibrational bending states Žy6 y 7 y 8 y 9 . s Ž0002., Ž0003., Ž0004., Ž0011., and Ž0020.. The analysis of the spectrum extends the spectroscopic data for NCCCNC by adding various newly determined rotational and rovibrational constants. q 2000 Elsevier Science B.V. All rights reserved.
1. Introduction Long linear molecules are typically rather flexible with respect to bending motions, and this flexibility manifests itself in low bending vibrational frequencies and large population factors for the associated levels. Thus the rotational spectra of these molecules are characterised by a rich vibrational satellite structure well suited for testing vibration–rotation theory by means of microwave and millimetre-wave spectroscopic investigations. 3-Isocyano-2-propynenitrile was described for the first time as late as 1993, when Smith et al. suc-
) Corresponding author. Technische Fakultat ¨ der Christian-Albrechts-Universitat ¨ zu Kiel, Lehrstuhl fur ¨ Hochfrequenztechnik, Kaiserstraße 2, D-24143 Kiel, Germany. Fax: q49-431-7757-2453; e-mail: [email protected]
ceeded in producing this interesting molecule through UV laser photoisomerisation of dicyanoacetylene isolated in an argon matrix w1,2x. In the course of the cited works all five stretching vibrational fundamentals n 1 through n4 and various combination and overtone bands were observed. Both the identification and the assignments were confirmed through the theoretical investigations by Botschwina et al., who reported a multitude of ab initio calculated data for NCCCNC, among others harmonic Ž v i . and anharmonic Ž n i . vibrational wavenumbers and rotational Ž Be , B0 , and De ., vibration–rotation coupling Ž a i . and l-type doubling Ž qt and qt J . constants w3–5x. Quite recently CB and DL could contrive a method carefully directed to produce 3-isocyano-2-propynenitrile virtually without any impurities by vacuum pyrolysis of a suitable precursor. This first chemical synthesis of NCCCNC was reported previously w6,7x. The linear molecule was characterised through millimetre-wave and Fourier-transform in-
0009-2614r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 0 0 . 0 0 1 4 7 - 0
266
A. Huckauf et al.r Chemical Physics Letters 319 (2000) 265–272
frared FTIR spectroscopy in combination with coupled-cluster calculations. The molecular structure, derived from the rotational constants of ten isotopomers, and the first three stretching vibrational fundamentals n 1 through n 3 were reported. In a previous Letter w8x we reported the millimetre-wave spectrum of NCCCNC in the vibrational states Žy 6 y 7 y 8 y 9 . s Ž0000., Ž0001., Ž0010., Ž0100., and Ž1000.. The present Letter is concerned with the assignment and the analysis of additional vibrational states, Ž0002., Ž0003., Ž0004., Ž0011., and Ž0020., which extend the spectroscopic data for NCCCNC by adding various newly determined rotational and rovibrational constants. Fig. 1 shows the vibrational energy levels of NCCCNC, representing the states that have been investigated in our previous work w8x as well as those which are subject of this Letter.
2. Experimental The precursor substance, wŽ CO . 5 Cr Ž NC – CCl5CF–CN.x, was synthesised at the Free University of Berlin as described in Refs. w6,7x. 3-Isocyano-2-propynenitrile was obtained from this chromium complex by vacuum pyrolysis at 2408C. The products ŽNCCCNC and – probably – a very small amount of NC–CCl5CF–CN. were condensed in a liquid-nitrogen trap, which was passed by the carbon monoxide released during the pyrolysis. The measurements described in this Letter were performed in the 75–120 GHz range using a PC-controlled millimetre-wave spectrometer operating in the source modulation mode. Millimetre waves were obtained from a Ku- or K-band backward wave oscillator ŽHP 8695A or HP 8696A. combined with an active frequency multiplier Žtripler HP 83556A or sextupler HP 83558A.. The BWO was phase-locked against a frequency synthesiser ŽPTS 500. which was controlled by a standard frequency of 10 MHz Žaccuracy: "1 Hz. provided by a GPS receiver. The free-space absorption cell consisted of a 10 cm diameter glass tube, 2.40 m in length and capped at the ends with Teflon collimating lenses. Low-noise detection was achieved by a liquid-helium-cooled InSb bolometer Ž‘Putley detector’.. The accuracy of the frequency measurements carried out at room temperature Ž288C. at a pressure of 1–3 Pa varies with the line strength: Strong lines were measured with an accuracy of "5 kHz Žchecked through OCS Lines., weaker lines needed higher pressure reducing the accuracy to "25 kHz.
3. Theoretical background
Fig. 1. Vibrational energy levels of NCCCNC up to 600 cmy1 . The rotational spectra of states represented by bold lines are analysed in the present work; thin lines are used for states which have not been analysed so far.
The theory concerning excited bending states of linear molecules is well established. It has been studied by many investigators, e.g., Amat et al. w9x and Winnewisser and Winnewisser w10x. For our analysis we adopted a slightly modified version of the effective Hamiltonian proposed by Yamada, Birss and Aliev ŽYBA. w11x, which summarises the rovibrational interactions in a very compact form. Since
A. Huckauf et al.r Chemical Physics Letters 319 (2000) 265–272
the details are given in the original paper, we will only recall its essential features and describe the modifications we made: The Hamiltonian used for the analysis is given by Hˆr s hˆ d q hˆ 0 q hˆ 2 ,
Ž 1.
with hˆ d s Gyq
Ý x LŽ t t . pˆ zŽ t . pˆ zŽ t . X
tFt
X
X
q By q
Ý d JL Ž t t . pˆ z Ž t . pˆ z Ž t . ž Jˆ2 y Jˆz2 / X
tFt
X
X
2
y Dy Jˆ2 y Jˆz2 q Hy Jˆ2 y Jˆz2
ž
hˆ 0 s
/
ž
3
/
,
Ž 2.
Ý Ž rt t q rt t J Jˆ2 . X
t-t
X
X
= Lˆ qqŽ t . Lˆ yyŽ tX . q Lˆ yyŽ t . Lˆ qqŽ tX . ,
ž
/
Ž 3.
and hˆ 2 s
1 2
Ý ž qt q qt J Jˆ2 q qt J J Jˆ4 / t
= Lˆ qqŽ t . Jˆy2 q Lˆ yyŽ t . Jˆq2 .
ž
/
Ž 4.
This Hamiltonian differs slightly from that given in w11x, as some higher-order terms which were found not to be necessary to reproduce the experimental data were omitted in order to reduce the complexity of the Hamiltonian: We neglected the terms h JL Žin hˆ d ., rt tX J J Žin hˆ 0 ., and qt L and some crossterms Žin hˆ 2 .; furthermore we ignored the term hˆ 4 which represents the D l s "4 interaction. On the other hand, we decided to include the constant qt J J Žin hˆ 2 . which is not part of the original YBA Hamiltonian, though this constant could be determined only for the Ž0100. state. The notation for states and wavefunctions also follows a proposal of Yamada et al. w11–14x, but in order to avoid any misunderstanding, we give an explanation of the nomenclature in Appendix A.
267
absorption lines belonging to the states Ž0002., Ž0003., Ž0004., Ž0011. and Ž0020. rather easily. Starting from the ground state lines, broad scans towards higher frequencies were taken. The spectra obtained in this way revealed the extended vibrational satellite structure which characterises the rotational spectra of longer linear molecules. Paying attention to the different linestrengths and comparing the experimental with some simulated spectra we were able to identify the lines of the higher excited vibrational bending states without any particular difficulty. The simulated spectra were based upon molecular constants that were determined in our previous study w8x, in particular on the parameters a t and bt which describe the vibrational dependence of the rotational constant B and the centrifugal distortion constant D, respectively: For the Ž0002. state, e.g., we presumed B99 s B0 y 2 a 9 s 1415.967437 MHz and D 99 s D 0 y 2b 9 s 38.0159 Hz, which turned out to be rather close to the actual values of 1415.98315 MHz and 38.42 Hz, respectively. The dominant lines belong to n 9 levels, for which vibration satellites up to y s 4 could be detected. For the second lowest vibration, n 8 , only the fundamental Ž0010. and the second excited state Ž0020. could be observed. Only one combination state, Ž0011., could be clearly identified. For all other states of this type, only parts of the satellite structure could be identified, so that we were not able to include these states in our analysis. It is noteworthy that all attempts to identify absorption lines of the fundamental of the lowest vibrational stretching state, n 5 , failed, though we carefully scanned the corresponding frequency ranges, making use of the rotational constant predicted by ab initio methods w3,4x. With respect to its vibrational energy of 610.1 cmy1 w1,2x the rotational transitions of the y 5 s 1 state should be clearly observable. So it may be assumed that the y 5 s 1 state is involved in a resonance system, which could not be identified so far.
4. Observed spectrum and assignments Since the rotational and rovibrational constants of NCCCNC in the excited vibrational bending states Ž0001. and Ž0010. have already been determined in our previous work w8x, we could find and identify the
5. Analysis The rotational spectra were observed and analysed in the excited vibrational bending states Žy 6 y 7 y 8 y 9 .
A. Huckauf et al.r Chemical Physics Letters 319 (2000) 265–272
268
Table 1 Observed and calculated frequencies Žin MHz. of NCCCNC J
Ž0003.1y
nobs 26 27 28 29 30 31 32 33
76552.169 79387.034 82221.914 85056.707 87891.429 90726.121 93560.813 96395.410
Ž0003.1q oyc y0.007 y0.021 0.022 0.021 y0.008 y0.021 0.013 y0.001
Ž0004. 0
nobs 76687.155 79526.965 82366.762 85206.518 88046.169 90885.806 93725.397 96564.921
Ž0003. 3y oyc 0.010 y0.014 y0.003 0.017 y0.016 y0.010 0.005 0.010
Ž0004. 2y
nobs
87970.946 90808.628 93646.264 96483.884
Ž0003. 3q oyc
y0.027 0.002 y0.002 y0.009
nobs
87971.270 90808.942 93646.636 96484.299
oyc
0.034 0.007 0.010 y0.012
Ž0004. 4 "
Ž0004. 2q
26 27 28 29
76767.545 79609.231 82450.807 85292.140 Ž0011. 0y
y0.008 y0.021 0.017 y0.022
76780.792 79624.121 82467.403 85310.645 Ž0011. 0q
0.022 0.020 0.015 0.016
76797.623 79642.833 82488.187 85333.603 Ž0011. 2y
0.010 y0.023 y0.002 y0.011
76779.233 79622.786 82466.355 85309.910 Ž0011. 2q
0.003 y0.015 0.000 0.010
26 27 28 29 30 31 32 33 34 35 36
76445.438 79276.416 82107.386 84938.355 87769.214 90600.072 93430.917 96261.671 99092.417 101923.133 104753.735
y0.003 y0.024 y0.018 0.022 y0.012 y0.009 0.020 y0.003 0.008 0.030 y0.018
76442.817 79273.516 82104.222 84934.835 87765.384 90595.902 93426.365 96256.686 99087.019 101917.259 104747.471
0.008 y0.018 0.015 0.011 y0.001 0.014 0.034 y0.026 y0.011 y0.024 0.002
76449.373 79280.714 82112.025 84943.318 87774.546 90605.796 93437.039 96268.238 99099.436 101930.602 104761.776
y0.028 y0.001 0.011 0.022 y0.015 y0.012 0.003 y0.008 0.001 y0.003 0.023
76451.689 79283.252 82114.818 84946.404 87777.958 90609.556 93441.108 96272.709 99104.366 101935.889 104767.557
0.029 0.018 0.007 0.013 y0.015 y0.003 y0.039 y0.029 0.034 y0.039 0.031
26 27 28 29 30 31 32 33 34 35 36
Ž0002. 0 76454.565 79285.531 82116.454 84947.316 87778.028 90608.727 93439.335 96269.820 99100.272 101930.602 104760.915
0.019 0.001 0.011 0.034 y0.016 y0.001 0.005 y0.030 y0.012 y0.029 0.026
Ž0002. 2y 76458.375 79289.933 82121.451 84952.966 87784.421 90615.852 93447.271 96278.673 99110.048 101941.321 104772.661
0.011 0.015 0.004 0.017 y0.002 y0.017 y0.014 0.002 0.022 y0.027 0.024
Ž0002. 2q 76463.869 79296.044 82128.258 84960.484 87792.777 90625.048 93457.301 96289.625 99121.993 101954.357 104786.703
y0.014 y0.026 y0.020 y0.023 0.021 0.021 y0.019 y0.010 0.020 0.024 y0.014
Ž0020. 0 26 27 28 29 30 31 32 33 34 35 36
76427.068 79257.496 82087.844 84918.203 87748.503 90578.814 93409.063 96239.279 99069.484 101899.636 104729.773
Ž0020. 2y y0.017 0.015 y0.007 0.008 y0.008 0.015 0.006 y0.005 0.004 y0.008 y0.002
Ž0020. 2q
79263.274 82093.858 84924.427 87754.930 90585.457
0.015 0.007 0.009 y0.029 y0.017
79263.455 82094.098 84924.700 87755.220 90585.764
y0.010 0.018 0.028 y0.019 y0.017
96246.400 99076.837 101907.253 104737.643
y0.018 y0.010 0.008 0.030
96246.795 99077.253 101907.692 104738.073
0.008 0.003 0.009 y0.015
A. Huckauf et al.r Chemical Physics Letters 319 (2000) 265–272
s Ž0002., Ž0003., Ž0004., Ž0011., and Ž0020.. The analysis of the data was performed in two different ways: Firstly we have determined effective constants for each l substate by fitting the observed rotational transition frequencies to the frequency formula
n s 2 Beff Ž J q 1 . y4Deff Ž J q 1 . 3
3
3
q Heff Ž J q 1 . Ž J q 2 . y J 3 .
Ž 5.
The results, which might be useful for future IR spectroscopic investigations, are given in Tables 1 and 2. Secondly we have analysed the individual vibrational states Žincluding all l substates of a given state simultaneously. by use of a least-squares fitting program which sets up a matrix representation of the
269
Hamiltonian described in Section 3 and calculates its eigenvalues by a numerical diagonalisation procedure. The difference between the eigenvalues of two consecutive quantum numbers J gives the absorption frequency. The analysis of a total amount of 150 absorption frequencies resulted in the determination of the rotational, centrifugal distortion, vibration–rotation interaction, and l-type doubling constants given in Table 3. Since some parameters of our previous investigation w8x were employed in our present analysis, too, we recall those constants in Table 3 in order to facilitate the understanding. Some higher-order terms which were found not to be necessary to reproduce the experimental data were omitted in the analysis and do not appear in the table. Because certain information is not contained in the observed spectra, some constants had to be fixed.
Table 2 Effective rotational constants for individual vibrational substates of NCCCNC a State
Beff ŽMHz.
Deff ŽHz.
Heff ŽmHz.
s Fit ŽkHz.
Ž0000. 0q Ž0001.1y Ž0001.1q Ž0002. 0q Ž0002. 2y Ž0002. 2q Ž0003.1y Ž0003.1q Ž0003. 3y Ž0003. 3q Ž0004. 0q Ž0004. 2y Ž0004. 2q Ž0004. 4 " Ž0010.1y Ž0010.1q Ž0011. 0y Ž0011. 0q Ž0011. 2y Ž0011. 2q Ž0020. 0q Ž0020. 2y Ž0020. 2q Ž0100.1y Ž0100.1q Ž1000.1y Ž1000.1q
1409.975279Ž19. 1412.349175Ž22. 1413.593688Ž24. 1415.98156Ž69. 1415.95185Ž48. 1415.95303Ž63. 1417.72370Ž80. 1420.23484Ž55. 1418.9143Ž24. 1418.9141Ž14. 1421.9849Ž33. 1421.96221Ž27. 1421.9706Ž23. 1421.8620Ž16. 1412.424768Ž21. 1413.029186Ž26. 1415.72994Ž48. 1415.72321Ž50. 1415.76376Ž41. 1415.76532Ž71. 1415.37241Ž30. 1415.47157Ž63. 1415.47212Ž56. 1411.779021Ž24. 1412.161141Ž25. 1411.750924Ž26. 1412.101569Ž23.
34.5485Ž28. 35.6918Ž51. 36.8733Ž57. 107.45Ž32. 38.50Ž22. y30.68Ž29. 62.35Ž41. 70.30Ž29. 14.5Ž11. 11.83Ž67. 249.5Ž20. 65.64Ž16. y142.3Ž14. 16.78Ž97. 35.0693Ž48. 35.3831Ž64. 50.62Ž22. 79.29Ž23. 23.46Ž19. y4.39Ž33. 38.42Ž14. 35.92Ž28. 33.82Ž25. 34.9292Ž43. 35.0330Ž46. 34.8405Ž52. 34.8933Ž47.
2.15Ž13. 2.04Ž30. 3.01Ž34.
4.165 b 4.202 b 4.511b 27.161 18.801 24.878 19.863 13.796 20.840 12.701 28.998 2.372 19.920 14.134 3.950 b 4.733 b 18.784 19.564 15.923 28.014 11.616 21.606 19.122 4.578 b 4.831b 4.968 b 4.359 b
a b
Uncertainties Žin parentheses. are 1 s in the last significant digit. Fitted by use of previously published w8x measurement data.
3.87Ž29. 2.43Ž39.
0.58Ž22. 2.82Ž25. 1.89Ž29. 1.77Ž25.
A. Huckauf et al.r Chemical Physics Letters 319 (2000) 265–272
270
Table 3 Experimental rovibrational constants for individual vibrational states of NCCCNC a Constant
By ŽMHz. a t ŽMHz. c Dy ŽHz. bt ŽHz. c Hy ŽmHz. qt ŽMHz. q J t ŽHz. q J J t ŽmHz. s Fit ŽkHz. No. of lines
By ŽMHz. a t ŽMHz. c Dy ŽHz. bt ŽHz. c q8 ŽMHz. qJ8 ŽHz. q9 ŽMHz. qJ9 ŽHz. d J LŽ88. ŽkHz. d J LŽ89. ŽkHz. d J LŽ99. ŽkHz. x LŽ88. ŽGHz. x LŽ89. ŽGHz. x LŽ99. ŽGHz. r 89 ŽGHz. r J 89 ŽkHz. s Fit ŽkHz. No. of lines
Vibrational state Ž0000. b
Ž0001. b
Ž0010. b
Ž0100. b
Ž1000. b
1409.975279Ž19.
1412.971358Ž17. y2.996079Ž26. 36.2822Ž39. y1.7337Ž48. 2.50Ž23. 1.244467Ž26. y1.1659Ž15.
1412.726909Ž18. y2.751630Ž26. 35.2275Ž42. y0.6790Ž50. 3.23Ž25. 0.604484Ž27. y0.3372Ž16.
1411.970011Ž17. y1.994731Ž26. 34.9811Ž31. y0.4326Ž42. 1.70Ž16. 0.382122Ž34. y0.1041Ž63. 2.25Ž33. 4.659 62
1411.926177Ž17. y1.950897Ž26. 34.8669Ž34. y0.3185Ž44. 1.83Ž19. 0.350652Ž27. y0.0550Ž14.
34.5485Ž28. 2.15Ž13.
4.165 46
4.447 66
4.612 63
4.602 60
Ž0002.
Ž0003.
Ž0004.
Ž0011.
Ž0020.
1415.98315Ž34. y6.00787Ž34. 38.42Ž14. y3.87Ž14.
1418.98753Ž55. y9.01225Ž55. 39.52Ž32. y4.98Ž32.
1421.99344Ž83. y12.01816Ž83. 41.26Ž50. y6.71Ž50.
1415.72856Ž27. y5.75328Ž27. 37.24Ž12. y2.70Ž12. 0.604484 y0.3372 1.244467 y1.1659 24.800 17.94Ž28. y7.953 40.19 9.625Ž32. 6.9475 y6.313Ž16. y3.450Ž98. 21.281 44
1415.37238Ž28. y5.39710Ž28. 36.06Ž12. y1.51Ž12. 0.604484 y0.3372
1.249014 y1.4841
y7.953Ž56.
6.9475Ž47.
20.498 33
1.25356Ž51. y1.80Ž26.
y8.33Ž15.
6.884Ž58.
17.828 24
1.258109 y2.1207
y8.225Ž10.
6.8991Ž18.
16.328 20
24.800Ž47.
40.19Ž82.
16.141 29
a Uncertainties Žin parentheses. are 1 s in the last significant digit. If no uncertainty is given, the corresponding parameter was fixed Žsee text.. b Refitted from the data of our previous investigation w8x. c Calculated according to the simplified expressions a t s B0 y By and bt s D 0 y Dy , respectively.
In Table 3 one can easily distinguish between fixed and fitted parameters because for the latter the standard deviations are given in parentheses. For the Ž0002. and Ž0004. states, e.g., the constants q9 and q J 9 were fixed at values obtained by linear interpolation and extrapolation of the corresponding Ž0001. and Ž0003. constants, and for the Ž0011. state, the constants x LŽ89. and d JLŽ89. were fitted, whereas the constants x LŽ88. , x LŽ99. , d JLŽ88. , and d JLŽ99. had to be fixed at the values obtained from the analyses of the Ž0002. and Ž0020. states, respectively. The molecular constants which have been determined for the higher excited vibrational states do not
reveal any unexpected characteristics, but some topics seem to be worth mentioning: In contrast to our previous investigation w8x, we have not been able to determine any P 6 term Ž Hy or q J J t . for the higher excited vibrational states, because in this study the range of our data was much smaller and the measurements were taken at lower J values. However, these constants turned out to be very small for the vibrational states studied previously w8x, and it can be assumed that they are in the same order for the newly investigated states. The fact that x LŽ99. has a positive and d JLŽ99. a negative value confirms that NCCCNC is a well-be-
A. Huckauf et al.r Chemical Physics Letters 319 (2000) 265–272
271
haved linear molecule – for a quasi-linear molecule, the signs of these constants must be opposite w15x. Finally, it should be pointed out that we assumed the constants q6 through q9 to have positive values as discussed in w8x.
In the simplified notation employed in this Letter the l substates are expressed as Žy6 y 7 y 8 y 9 . l " Žthe inclusion of l t or l tX is superfluous in the case of the vibrational states which are the subject of this Letter., where the sign in the superscript indicates the positive or the negative linear combination:
Acknowledgements
Ž 0001.
1"
<1 Ž 1 . ; J ,1 " :
1
A.G. and A.H. would like to thank Prof. Dr.-Ing. ŽLehrstuhl fur R. Knochel ¨ ¨ Hochfrequenztechnik, Technische Fakultat ¨ der Universitat ¨ Kiel. for research support. Furthermore we are indebted to the workshop of the Technische Fakultat ¨ for manufacturing of millimetre-wave components and other indispensable devices without which this investigation could not have been made. The work at Kiel was supported by the Deutsche Forschungsgemeinschaft DFG ŽGU 128r15-1., the work at Berlin by the Fonds der Chemischen Industrie and the Deutsche Forschungsgemeinschaft DFG ŽLE 423r9-2..
s
< :< : '2 Ž 1 Ž 1. ; J ,1 " 1 Ž y1. ; J ,y 1 .
Ž A.5 .
Žanalogous for the l substates of the Ž0010., Ž0100., and Ž1000. states., 0 Ž 0002. <2 Ž 0 . ; J ,0: ,
Ž 0002.
2"
<2 Ž 2 . ; J ,2 " :
1
s
Ž A.6 .
< : < : '2 Ž 2 Ž 2. ; J ,2 " 2 Ž y2. ; J ,y 2 .
Ž A.7 .
Žanalogous for the l substates of the Ž0020. state.,
Ž 0003.
1"
<3 Ž 1 . ; J ,1 " :
1
s Appendix A. Nomenclature of states and wavefunctions A vibrational state where two bending modes y t s n, y tX s m are simultaneously excited contains Ž n q 1.Ž m q 1. substates. Each substate is characterized by n, m, J, and l, where J is the total angular momentum and l its projection along the symmetry axis with l s l t q l tX , Ž A.1 . l t s yn, yn q 2, . . . , n y 2, n ,
Ž A-2.
and l tX s ym, ym q 2, . . . , m y 2, m .
Ž A.3 .
For a given J value the substates can be identified with a set of symmetrised linear combinations in a basis of Ž n q 1 .Ž m q 1 . functions line < Õt Ž l t .,ÕtX Ž l tX .; J,l :, each of which is the product of two two-dimensional harmonic oscillator functions and a symmetric top function: < n Ž l t . ,m Ž l tX . ; J ,l " :
Ž 0003.
<3 Ž 3 . ; J ,3 " :
< : < : '2 Ž 3 Ž 3. ; J ,3 " 3 Ž y3. ; J ,y 3 . , Ž A.9 .
0 Ž 0004. <4 Ž 0 . ; J ,0: ,
Ž 0004.
2"
Ž A.10 .
<4 Ž 2 . ; J ,2 " :
1
s
< : < : '2 Ž 4 Ž 2. ; J ,2 " 4 Ž y2. ; J ,y 2 . , Ž A.11 .
Ž 0004.
4"
<4 Ž 4 . ; J ,4 " :
1
s
< : < : '2 Ž 4 Ž 4. ; J ,4 " 4 Ž y4. ; J ,y 4 . , Ž A.12 .
Ž 0011.
0"
<1 Ž 1 . ,1 Ž y1 . ; J ,0 " :
1
s
< : '2 Ž 1 Ž 1. ,1 Ž y1. ; J ,0
"<1 Ž y1 . ,1 Ž 1 . ; J ,0: . ,
Ž 0011.
2"
Ž A.13 .
<1 Ž 1 . ,1 Ž y1 . ; J ,2 " :
1
< : '2 Ž n Ž l t . ,m Ž l t . ; J ,l
s
X
"< n Ž yl t . ,m Ž yl tX . ; J ,y l : . .
3"
1
s
1
s
< : < : '2 Ž 3 Ž 1. ; J ,1 " 3 Ž y1. ; J ,y 1 . , Ž A.8 .
Ž A.4 .
< : '2 Ž 1 Ž 1. ,1 Ž 1. ; J ,2
"<1 Ž y1 . ,1 Ž y1 . ; J ,y 2: . .
Ž A.14 .
272
A. Huckauf et al.r Chemical Physics Letters 319 (2000) 265–272
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