Theoretical Study of Rotational Spectroscopy of Acetonitrile-d3 in the Ground and Different Excited Vibrational States

Journal of Chemistry, May 2019

The millimeter-wave rotational spectra of the ground and excited vibrational states v8 = 1 and v8 = 2 of the symmetric top molecule CD3CN have been analyzed again. The l = ± 1 in v8 =1, l = 0 and l = ± 2 series in v8 = 2 states have been assigned respectively. The assignment and analysis of the measurements with a least – squares procedure have made it possible to obtain the rotational, quartic and sextic centrifugal distortion constants with more reliable and higher accuracy. Analysis of the v8 = 2 state gave the following rotational parameters: Aζ = 62218.96 MHz and xll = 87527.70 MHz. Investigation in v8 = 2 state indicates that l-resonance is observed for this molecule around k=xℓℓ

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Theoretical Study of Rotational Spectroscopy of Acetonitrile-d3 in the Ground and Different Excited Vibrational States

CODEN ECJHAO E-Journal of Chemistry Vol. 5 0973-4945 Theoretical Study of Rotational Spectroscopy of Acetonitrile-d3 in the Ground and Different Excited Vibrational States MOTAMEDI 0 MASOUD 0 MORADI 0 PARINAZ 0 0 Department of Chemistry, Faculty of Science, University of Kurdistan , Sanandaj , Iran The millimeter-wave rotational spectra of the ground and excited vibrational states v8 = 1 and v8 = 2 of the symmetric top molecule CD3CN have been analyzed again. The l = ? 1 in v8 =1, l = 0 and l = ? 2 series in v8 = 2 states have been assigned respectively. The assignment and analysis of the measurements with a least - squares procedure have made it possible to obtain the rotational, quartic and sextic centrifugal distortion constants with more reliable and higher accuracy. Analysis of the v8 = 2 state gave the following rotational parameters: A? = 62218.96 MHz and x?? = 87527.70 MHz. Investigation in v8 = 2 state indicates that l-resonance is observed for this molecule around k = x ll + (A ? B) ? 2A? ? 4 . A? ? (A ? B) - http://www.e-journals.net Introduction Ground state The frequency of rotational transition k, J ? k, J + 1 in the ground and non-degenerate vibrational states may be written as: ? = 2B(J + 1) - 4DJ(J + 1)3 ? 2DJk(J + 1) k2 + HJ(J + 1)3[(J + 1)3 - J3] + 4HJk(J + 1)3k2 + 2HkJ(J + 1)k4 (1) In equation (1), the DJ, DJk, Dk are quartic and HJ, HJk, HkJ are sextic centrifugal distortion terms respectively. The measurements of ground state were combined to each other 2,4. A weighted leastsquares method5 was used to fit the mixed frequencies for low and high J values. The results of refinement are listed in Table 1. The parameters derived from the fit are given in Table 4 and compared with v8 = 1 and v8 = 2 states. The spectra in this state is simple, so the different k values (k = 0,1,2,3,4...) for each J transition are assigned easily. The centrifugal distortion produces a band head to high frequency at k = 0, with a spread to lower frequency with higher k. If |k| values are plotted against frequency for this state, the Fortrat diagram is produced which is shown in (Fig. 1). In this diagram the splitting increase as k increases and this is due to the DJk parameter. In other words the term -2DJk(J + 1)k2 has the effect of separating the (J + 1) components of each (J + 1) - J transition. 20 15 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 8 2 8 3 8 4 8 5 8 6 8 7 9 0 9 1 9 2 9 3 9 4 9 5 9 6 9 7 9 8 9 9 13 0 13 1 13 2 13 3 13 4 13 5 13 6 13 7 13 8 13 9 13 10 13 11 13 12 14 0 14 1 14 2 14 3 14 4 14 5 14 6 14 7 14 8 14 10 14 11 14 14 24 0 24 1 24 2 24 3 24 4 61. 24 5 392589.2160 62. 24 6 392528.9370 63. 24 9 392282.1430 64. 24 12 391937.3780 65. 24 14 391653.3740 66. 24 15 391495.2650 67. 24 18 390957.0190 68. 24 21 390323.1870 69. 43 0 690562.2000 70. 43 1 690552.5000 71. 43 2 690523.7000 72. 43 3 690476.4000 73. 43 4 690409.7000 74. 43 5 690323.7000 75. 43 6 690219.1000 76. 43 7 690095.6000 77. 43 8 689952.9000 78. 43 9 689791.2000 79. 43 10 689610.7000 80. 43 11 689411.7000 81. 43 12 689192.8000 82. 43 13 688956.0000 83. 45 13 720183.2000 84. 45 14 719916.6000 85. 45 15 719630.3000 86. 48 0 768782.4000 87. 48 1 768771.8000 88. 48 2 768740.5000 89. 48 3 768687.7000 90. 48 4 768613.6000 91. 48 5 768518.4000 92. 48 6 768402.4000 93. 48 7 768265.4000 94. 48 8 768107.1000 95. 48 9 767928.2000 96. 48 12 767265.0000 97. 65 7 1033397.0400 98. 65 8 1033188.9000 99. 65 9 1032952.4000 100. 65 10 1032689.0000 101. 65 11 1032397.2000 102. 65 12 1032078.2000 103. 65 13 1031732.2000 -0.0982 0.0120 -0.0001 0.0150 -0.0365 -0.0341 0.1488 -0.0122 0.3273 0.1648 -0.0251 0.3511 0.3822 0.1527 0.3427 0.6277 0.6790 0.6632 0.7427 1.1753 0.5144 0.7090 -0.0958 0.0947 0.0336 -0.7826 -0.8151 -0.4148 -0.3893 -0.5509 -0.7168 -0.6094 -0.4557 -0.5880 -0.3431 -0.6908 0.0385 0.3809 0.0101 0.3296 -0.2238 -0.5201 -0.4357 Sigma = 0.309662; 103 Transitions in fit Sigma. w = 0.841528; 98 Degrees of freedom v8 = 1 State The ro-vibrational Hamiltonian for excited degenerate vibrational states is set up as a matrix in basis states which are products of harmonic oscillator and rigid-rotator functions. This may be transformed to a new effective Hamiltonian in which the off-diagonal matrix elements which connect different vibrational states are eliminated. The result is to produce a series of blocks in the Hamiltonian matrix, there being one such block for each vibrational state. Each such block may be regarded as the effective Hamiltonian for that vibrational state. The diagonal elements of this effective Hamiltonian is given by Eq(2). Jkl H Jkl = (B + B3l2 )J(J + 1) + (A ? B)k 2 ? 2A?kl 1 ? [J(J + 1) ? k(k m 1)] 2 (2k + 1) For singly excited degenerate vibrational states the effective Hamiltonian when set up as above is of order (4J + 2). In this new basis the Hamiltonian blocks off into factors which good quantum number for the problem although k ? l t or alternatively kl t ? 1 , remains a good quantum number. Levels with kl t ? 1 = 3n , where n is an integer, may be shown to have A1 or A2 symmetry whilst all others are of E symmetry7-11. The selection rules are such that for transitions due to the ?z component of the dipole then ?J=?1 and A1?A2 and E?E. For a doubly-degenerate state vt = 1, the q t+ matrix elements given in equation (3) produce a first-order splitting of the A1A2 levels with kl t ? 1 = 0 . These give rise to the familiar l ? doublets . The remaining transitions show second-order splitting due to this term and these are called l ? resonance splitting. The perturbation expression for these splittings was first given by Grenier-Besson and Amat6 and the major term is reproduced below: ?? = - (q +t )2 (J +1)3 4[B ? A + A? ](kl t ?1) If (kl t ?1) ? 0. (2) (4) (5) Therefore the largest l ? resonance effects are to be found for transitions with low values of kl t ? 1. In our own analysis of the rotational spectra of CD3CN in this state we have used a least squares fitting program in which the transitions are calculated from energy levels obtained by setting up the A1, A2 and E blocks of the effective Hamiltonian and diagonalizing. There are then no model errors due to the adoption of perturbation theory. In this work, most of the frequencies which was measured by Cosleou, J et al3 and some of the observed frequencies by Weidong C et al12 have been mixed and refined them together by least square method5. By this program, the frequencies belong to the transitions J = 80 could not refined. Due to increasing of data from low and high J values the new results are more accuracy and reliable. The results of refinement are given in Table 2. The obtained parameters are listed in Table 4 and compared with other parameters. Table 2. The Results of Refinement of Observed Frequencies for CD3CN in the v8 = 1 State. S.No. J'' ? k Observed/ MHz Obs-Calc/ MHz Error /MHz 1* 2* 3* 4* 5* 6* 7* 8* 9* 10* 11* 12* 13* 14* 15* 16* 17* 18* 19* 20* 21* 22* 23* 24* 25* 26* 27* 28* 29* 30* 31* 32* 33* 34* 35* 36* 37* 38* 39* 40* 41* 42* 43* 44* 45* 46* 47* 48* 49* 50* 51* 52* 53* 54* 55* 56* 57* 58* 59* 60* 61* 62* 63* 64* 65* 66* 67* 68* 69* 70* 71* 72* 73* 74* 75* 76* 77* 78* 79* 80* 81* 82* 9 5 1 9 8 1 12 -10 -1 12 -7 -1 12 -4 -1 12 -1 -1 12 2 -1 12 5 -1 12 8 -1 12 11 -1 12 1 1 12 -12 -1 12 -9 -1 12 -6 -1 12 -3 -1 12 0 -1 12 3 -1 12 6 -1 12 9 -1 12 12 -1 12 -10 1 12 -7 1 12 2 1 12 5 1 12 8 1 12 11 1 17 -1 -1 17 1 1 17 -3 -1 24 -16 -1 24 -13 -1 24 -10 -1 24 -7 -1 24 -4 -1 24 -1 -1 24 2 -1 24 5 -1 24 8 -1 24 11 -1 24 14 -1 24 17 -1 24 1 1 24 -15 -1 24 -12 -1 24 -9 -1 24 -6 -1 83* 84* 85* 86* 87* 88* 89* 90* 91* 92* 93* 94* 95* 96* 97* 98* 99* 100* 101* 102* 103* 104* 105* 106* 107* 108* 109* 110* 111* 112* 113* 114* 115* 116* 117* 118* 119* 120* 121* 122* 123* 124* 125* 126* 127* 128* 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 65 65 65 65 65 65 65 65 65 65 65 65 65 -1 -1 1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 -1 -1 1 -1 1 -1 In order to explain the form of the spectra we need to consider the energy levels in v8 = 2 as given by the Hamiltonian matrix. The diagonal elements are: (6) (8) (9) via the qt+ term with those in the l = 2 series. This resonance will affect the frequencies of the |J, k,?l> ? |J + 1, k,?l> transitions. The maximum resonance occurs when the energies of the unperturbed states are equal: E (| J, k, l = 0 >) = E (| J, k + 2, l = 2 >) (7) After omitting terms, which are the same from both sides of equation (6), this occurs when: (A ? B)k2 = 4Xll + (A ? B)(k + 2)2 ? 4A?(k + 2) Hence k = xll + (A ? B) ? 2A? A? ? (A ? B) This has been termed vibrational l - resonance to distinguish it from accidental resonances which can occur between energy levels not separated by the vibrational term Xll . The measurements for second vibrational excited state 3 were combined with a few measurements of Weidong C et al12 . A weighted least-squares method5 was used to fit the mixed frequencies for low and high J values. The results of refinement are listed in Table 3. The parameters derived from the fit are given in Table 4 and compared with others. 12* 13* 15* 16* 17* 18* 20* 21* 22* 23* 24* 25* 26* 27* 28* 29* 30* 31* 32* 33* 34* 35* 36* 37* 38* 39* 40* 41* 42* 43* 44* 45* 46* 47* 48* 49* 50* 51* 52* 53* 54* 55* 56* 57* 58* 59* 3 3 3 3 3 3 3 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 60* 61* 62* 63* 64* 65* 66* 67* 68* 69* 70* 71* 72* 73* 74* 75* 76* 77* 78* 79* 80* 81* 82* 83* 84* 85* 86* 87* 88* 89* 90* 91* 92* 93* 94* 95* 96* 97* 98* 99* 100* 101* 102* 103* 104* 105* 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 17 106* 107* 108* 109* 110* 111* 112* 113* 114* 115* 116* 117* 118* 119* 120* 121* 122* 123* 124* 125* 126* 127* 128* 129* 130* 131* 132* 133* 134* 135* 136* 137* 138* 139* 140* 141* 142* 143* 144* 145* 146* 147* 148* 149* 150* 151* 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 21 21 21 21 21 21 21 21 21 21 21 21 152* 153* 154* 155* 156* 157* 158* 159* 160* 161* 162* 163* 164* 165* 166* 167* 168* 169* 170* 171* 172* 173* 174* 175* 176* 177* 178* 179* 180* 181* 182* 183* 184* 185* 186* 187* 188* 189* 190* 191* 192* 193* 194* 195* 196* 197* 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 198* 199* 200* 201* 202* 203* 204* 205* 206* 207* 208* 209* 210* 211* 212* 213* 214* 215* 216* 217* 218* 219* 220* 221* 1 In all refinements the weights were taken to be ?2 , where ? is the estimated uncertainty in an observation and is given in the columned headed Error/MHz. In this experiment B0, DJ, DJk, HJk and, HkJ were determined for the ground state, v8 = 1 and v8 = 2 states of CD3CN with more reliable and high accuracy because they were determined for high J values, Table 4. In this table they are compared to parameters derived by previous work12 . HJk appears to be more important than HkJ in analysis of high J rotational spectrum of this particular molecule, and it seems that the HJ parameter is important for this molecule only at very high J values. The HJ parameters in the ground and v8 = 1 states were constrained to zero since For CD3CN, the Fortrat diagram for J = 65 Figure 3, |k - l| = (kl -1) was plotted rather than k against ? which are the positive and negative (kl-1) series. This diagram shows the 'l' 9 7 0 2 1 62 9 7 s e t a t S 2 ro ) ) ) ) .4 k 0*0 (163 )(56 )(77 )(14 )25 )6 )5 ) (56 )2 .9 (1 2 8 5 (1 (9 (1 65 5 (1 (9 3 ( N ) C3 )9 ) )6 .9 D k * (6 )96 )63 )11 183 )6 )3 )3 ) (5 )7 (9 rC 1 ro .6 4 (0 (51 (6 (9 (4 (13 (53 (28 65 (2 trfseeo v=8 itshw 78883 .008781 0* .218208 .111114 .825814 .-9110 .-4106 .62082 .330 . 3 8 1 7 3 5 123 .5195 .4651 0* 969 - . 8 1 2 2 6 The ?-type doubling interaction matrix elements must also be considered: Jkl H Jk ? 2, l ? 2 = 1 {q (0) ? q (1)J(J + 1) + q (2)J 2 (J + 1) 2 + q k k 2 } 4 (10) (12) 5. 6. 7 8. 9. 10. 11. 12. 13. 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Motamedi Masoud, Moradi Parinaz. Theoretical Study of Rotational Spectroscopy of Acetonitrile-d3 in the Ground and Different Excited Vibrational States, Journal of Chemistry, DOI: 10.1155/2008/253610