190 Acta Chim. Slov. 2008, 55, 190–200 Scientific paper Anharmonic Vibrational Properties of Chlorocarbonyl Ketene Conformers Using Second-order Perturbation Theory Ved Prakash Gupta* and Abhishek Kumar Mishra Department of Physics, University of Lucknow, Lucknow 226007, India * Corresponding author: E-mail:vpgpt1@yahoo.co.in Received: 24-08-2007 Abstract The present paper reports main results of a comprehensive study of the structure and vibrational spectra of the stable conformers of chlorocarbonyl ketene computed using second-order perturbation theory treatment based on quadratic, cubic and semidiagonal quartic force constants. It is found that the s-trans conformer is more stable than the s-cis conformer by ?0.69 kcal/mol. The vibrationally averaged bond lengths and bond angles, both for the cis and trans confor-mers, are within 0.005 Å and 0.14°, respectively, of the equilibrium geometry. The ab initio and DFT based anharmonic vibrational analysis using second-order perturbation theory provides reliable frequencies (r.m.s. deviation ±20 cm–1) and assignments to the vibrational bands. DFT calculations using the same method and basis function for the harmonic frequencies and anharmonic corrections give frequencies in better agreement with the experimental values than those in which the harmonic frequencies from a high level quantum mechanical method (B97-1/aug-cc-pVTZ) are coupled with anharmonic corrections from a cheap model (B3LYP/6-31+G**); the r.m.s. deviation in the latter case is ±47 cm–1. The errors in the calculation of the fundamental modes are reflected in the overtones and combination bands. Some spectros-copic constants namely, the anharmonic constants, rotational constants and rotation-vibration coupling constants of the two conformers have been calculated by density functional theory and compared with literature, where available. Keywords: Chlorocarbonyl ketene; Conformers; Anharmonic frequencies; Spectroscopic constants; DFT; Perturbation theory 1. Introduction Ketenes are fascinating and versatile reactive intermediates in a variety of reactions.1–4 Substituted ketenes are highly reactive species with properties often different from those of ketene itself and as such have prompted a number of mechanistic5 and theoretical studies.6,7 In an earlier communication,8 we have reported quantum chemical studies on the effect of substituents on structural, chemical and spectroscopic characteristics of di-substitu-ted ketenes. Pietri et al.9 have reported photolysis of chlo-roformyl ketene resulting in the formation of carbon suboxide and explained the reaction path on the basis of ab initio calculations. Brown et al.10 have suggested the possible existence of high-carbon content compounds like ke-tenes in the interstellar space. We have earlier reported11,12 results of anharmonic vibrational analysis of some cyanides and related molecules of astrophysical significance. Apart from the inherent interest in more thoroughly cha- racterizing a chemically interesting group of rather unstable molecule, the spectral data are potentially important as a basis for future astrophysical studies of such molecules. Badawi et al.13–15 have computed vibrational spectra of some substituted ketenes in the harmonic approximation and have also drawn conclusion about their structural stability. However, significant mismatch between the experimental and their calculated frequencies due to the neglect of anharmonicity raises doubt about their vibrational assignments. Several effective approaches going beyond the harmonic levels have been adopted during the last years to account for the anharmonicity effects. These include Car-Parrinello molecular dynamics (CPMD) method of Jezier-ska et al.,16 a mixed quantum-classical density matrix evolution (DME) method of Mavri and Grdadolnik17 limited to quantization of the OH motion in one dimension and variational method of Stare and Mavri18 for numerical solving of the vibrational time-independent Schrodinger Gupta and Mishra: Anharmonic Vibrational Properties of Chlorocarbonyl Ketene Conformers ... Acta Chim. Slov. 2008, 55, 190–200 191 equation in one and two dimensions. For small molecules converged rovibrational levels have been obtained by fully variational methods of Bowman et al.19–22 However, for large molecules the variational vibrational SCF (VSCF)23 and second-order perturbation 24,25,30 treatments have been the most successful approaches. The second-order perturbation theory (PT2) provides closed expressions for most of the spectroscopic parameters required for the analysis of the experimental frequencies. However, for correct results, this approach requires complete quartic development which is the most practical representation of the potential for large molecules. As noticed by Handy et al.26,27 and Barone,30 the predictions by the second-order perturbation theory after the inclusion of the quartic potential derivable from analytical second derivatives can be closer to experiment than their variational counterparts. We have earlier reported16 the vibrationally averaged structure and the results of anharmonic analysis of the vibrational spectrum of ketene by density functional theory using second order perturbation theory. In the present communication, we are reporting the results of anharmo-nic analysis of the vibrational spectra of the cis and trans conformers of chlorocarbonyl ketene using ab initio and DFT methods. 2. Methodology The potential energy function for an anharmonic oscillator may be written as ~T,fAsj +7S/msM + ^tZ/*«5'5A5' + (1) {SJrepresent a displacement internal coordinate and f.., f.-k and fijkl etc. are the quadratic, cubic and quartic etc. force constants. Using the Dunham potential functions, the energy of an anharmonic oscillator is given by *«........=%v°{n'+ìy%x'{"-+ì)i">+ì} (2) where Xii and Xik are the diagonal and non-diagonal anhar-monicity constants. While Xii characterizes anharmonicity of the given vibration, the coefficients Xik characterize coupling between different normal modes resulting from anharmonicity and are determined from cubic and quartic force constants. The fundamental frequencies of the an-harmonic oscillator are given by (3) The rotational – vibrational couplings may be determined in terms of the rotational, and rotation-vibration interaction constants. The anharmonic force fields and spectroscopic constants have been calculated by using the second order Perturbation theory (PT2) implemented in Gaussian03W29 software. The implementation of a fully automated code for the building of anharmonic force constants and their use in a second-order perturbative evaluation of vibrorota-tional parameters has been described in details by Barone.30 Anharmonic force fields are computed by exploiting the linear relationship between normal and cartesian displacement coordinates. The second-derivative matrix over normal modes is given as O = L+ M"1/2 F M"1/2 L where M is the diagonal matrix of atomic masses, and L is the matrix of (columnwise) eigenvectors of the mass weighted cartesian force constant matrix M–1/2 FM–1/2. Starting from analytical second derivatives, the third and semidiagonal fourth derivatives needed for second-order perturbation have been computed by a finite difference approach which scales linearly with the number of modes. A tight geometry optimization with residual gradients less than 10–7 hartree/bohrs (or radian) is a mandatory prerequisite for reliable anharmonic analysis irrespective of the specific quantum mechanical method (RHF or DFT). The vibrational Hamiltonian H is taken as a sum of zeroth vib order harmonic term (H°vib) and successive terms containing the contributions of cubic, quartic etc., components of the potential (Hvib = H°vib + H1vib + H2vib). The second order term includes a kinetic contribution arising from the vibrational angular momentum. Starting from the solutions |vo) of the harmonic problem the vibrational wave functions |vi) = |v0) +Ivi1) +|v2i) are obtained by the second-order perturbation theory. The vibrotational Hamiltonian Hvibrot obtained by adding the rotational energy term is used to get the vibrotational eigen functions and energies. The calculations were conducted using B3LYP and B97-1 procedures with 6-31+G**, 6-311++G** and aug-cc-p-VTZ basis sets involving diffuse functions and polarization functions and by ab initio method RHF/6-311++G**. The suggestion of Barone18 that best results can be obtained by using hybrid functionals (B3LYP, B97-1 etc) and large basis sets combined with anharmonic corrections using less expensive method B3LYP/6-31+G* was also tested. The forms of vibrations were analyzed using the software GaussView version 2.0.31 3. Results and Discussion The experimental infrared spectrum of chlorocar-bonyl ketene at 10 K in argon and xenon matrices has been reported by Pietri et al.9 during a photo-isomeriza-tion study. They assigned the two sets of absorption bands showing opposite behavior during the photo-iso-merization experiment to the s-cis and s-trans confor- Gupta and Mishra: Anharmonic Vibrational Properties of Chlorocarbonyl Ketene Conformers ... Acta Chim. Slov. 2008, 55, 190–200 mers. Quantum chemical calculations using MP2/D95* were also conducted by these authors to obtain molecular geometries of the s-cis and s-trans conformers in the electronic ground and first excited states. Spectral assignments to some prominent absorption peaks of the two conformers were also given. No experimental data seems to be available for the molecular geometry of the stable conformers of chlorocarbonyl ketene. Al-Saadi and Ba-dawi13,32 predicted molecular geometries of the two rotational isomers of chlorocarbonyl ketene using B3LYP/6-311++G** and MP2/6-311++G** calculations and compared them with the experimental geometries of an analogous molecule propenoyl chloride from electron diffrac-tion33 and microwave34 measurements. Discrepancies are observed in the values of the geometrical parameters reported by these authors in the two publications.13, 32 No anharmonic analysis has so far been reported in the literature for the vibrational spectra of chlorocarbonyl ketene. The results of our anharmonic calculations on the s-cis and s-trans conformers of chlorocarbonyl ketene using HF and density functional methods are given in Tables 1–6. The numbering on atoms in these tables are in accordance with Figures 1a and 1b for the s-trans ans s-cis conformers, respectively. The optimized and vibratio-nally averaged geometrical parameters, harmonic and an-harmonic vibrational frequencies and spectroscopic constants of the s-cis and s-trans conformers of chlorocar-bonyl ketene are being discussed separately. A reasonab- Fig. 1 s-trans (a) and s-cis (b) conformers of chlorocarbonyl ketene le agreement with the experimental frequencies has, in general, been obtained. 3. 1. Conformational Analysis The optimized and vibrationally averaged molecular geometries, dipole moments and total energies of the strans and s-cis conformers of chlorocarbonyl ketene using B97-1/6-311++ G**, B97-1/aug-cc-pVTZ, B3LYP/6-31+G**, MP2/6-311++G** and RHF/6-311++G** methods are given in Tables 1(a) and 1(b), respectively. The tables also contain theoretical values of bond lengths and bond angles given in the literature9,15 and the experimental values for an analogous molecule propenoyl chloride.33,34 It is found that all the theoretical methods presently used give almost identical geometries which are within 0.03 Å in bond length and 3° in bond angle of the experimental geometry of propenoyl chloride. The vibrationally averaged bond lengths for the two conformers are within 0.001–0.005 Å of the optimized parameters, as in the case of ketene.28 Our DFT and MP2 calculations confirm the experimental findings of Pietri et al.9 that the s-trans conformer is more stable than the s-cis conformer. This is in contrast to the findings of Badawi et al.15 that the s-cis conformer is the more stable of the two conformers by about 0.23 kcal/mol. The calculated enthalpy difference 0.69 kcal/mol. (B97-1/6-311++G**) between the s-cis and s-trans conformers, after incorporating zero-point energy correction, is in better agreement with the experimental estimate of 0.9–1.3 kcal/mol.9 in comparison to the theoretical predictions of 0.55 and 0.24 kcal/mol. by Pietri et al.9 and Badawi et al.,15 respectively. The geometries of the s-cis and s-trans conformers do not differ significantly except in the angles C2C1C4 and C4C1H5. While the angle C2C1C4 of the s-cis conformer is about 4° shorter, the angle C4C1H5 is larger by about 3° than the corresponding angles in the s-trans conformer. 3. 2. Harmonic and Anharmonic Fundamental Modes Two types of calculations were performed to obtain the frequencies and intensities of the fundamental modes, overtones and combination bands for the s-cis and s-trans conformers of chlorocarbonyl ketene. In the first case, the usual homogeneous model was adopted and both the harmonic frequencies and anharmonic corrections were calculated by using the same method and basis set viz. B97-1/6-311++G**, B3LYP/6-31+G** and RHF/6-311++ G**. In the second case, following Barone,30 the harmonic frequencies computed at a high level of quantum mechanical method and basis set (B97-1/aug-cc-pVTZ) were coupled with anharmonic corrections computed by a cheap model (B3LYP/6-31+G**). The results of calculations together with the experimental frequencies for the s-trans and s-cis conformers are given in Tables 2 and 3, respectively. Gupta and Mishra: Anharmonic Vibrational Properties of Chlorocarbonyl Ketene Conformers ... Table 1(a): Molecular geometry, cupole moment and total energy of s-trans conformer of chlorocarbonyl ketene Bond length/ B97-1/6 -311++G** B97- 1/aug-cc-p vtz B3LYP/6-31+G** MP2/ 6- -311++G** RHF/6- -311++G** Exptl. Literature Bond angle Opt. Aver. Opt. Aver. Opt. Aver. Opt. Aver. Opt. Aver. Valuesa [9] [15] O C -C M 4 1.4486 1.4531 1.4445 1.4476 1.4477 1.4522 1.4475 1.4520 1.4498 1.4538 1.476 1.454 1.466 e S C -C M 2 1.3333 1.3357 1.3321 1.3331 1.3354 1.3376 1.3394 1.3404 1.3239 1.3265 1.345 1.346 1.330 & c2=o3 1.1492 1.1483 1.1481 1.1441 1.1582 1.1572 1.1575 1.1563 1.1215 1.1204 - 1.172 1.153 p. co C,-H5 1.0848 1.0822 1.0828 1.0790 1.0852 1.0829 1.0834 1.0786 1.0723 1.0697 1.084 1.078 1.107 c4=o6 1.1872 1.1875 1.1867 1.1852 1.1954 1.1958 1.1969 1.1958 1.1650 1.1650 1.192 1.209 1.207 C4-C17 1.836 1.8418 1.8326 1.8389 1.8319 1.8383 1.8069 1.8120 1.7873 1.7936 1.816 1.811 1.746 •-t C C C 122.91 122.81 122.37 122.48 123.16 123.13 121.85 121.81 123.30 123.26 122.6 126.6 121.1 CjC203 180.0 176.98 180.0 176.71 180.0 176.95 180.00 176.92 180.0 177.29 - 180.0 178.7 H5CjC4 119.10 119.13 119.55 119.52 118.87 118.90 119.74 119.71 119.04 119.01 - 120.1 121.4 a- o6c4c, 127.25 127.30 127.50 127.50 126.66 126.73 126.50 126.64 125.96 126.02 127.2 126.6 124.0 3 7 4 1 112.62 112.56 112.08 112.03 113.14 113.07 112.94 112.93 114.20 114.17 116.3 112.5 113.9 O C C C 180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 S' V^lnV^yjV^ i -^^-^ 180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 - 180.0 180.0 H (Debye) 3.0489 3.0460 3.0460 2.9888 2.9849 2.7 s E (a.u.) -725.51647 -725.55205 -725.55248 -724.39376 -723.46747 -724.2621 -725.61893 S' s a 3 "values obtained from a microwave experiment for a similar molecule propenoyl chloride Ref. [33]. to g. S' Table 1(b): Molecular geometry, dipole moment and tota energy of s-cis conformer of chlorocarbonyl ketene ^ Bond length/ B97-1/6 -311++G** B97- 1/aug-cc-p vtz B3LYP/6-31+G** MP2/ 6- -311++G** RHF/6- -311++G** Exptl. Literature o £ Bond angle Opt. Aver. Opt. Aver. Opt. Aver. Opt. Aver. Opt. Aver. Valuesa [9] [15] S" 3 C -C M 4 1.4553 1.4608 1.4516 1.4528 1.4528 1.4590 1.4528 1.4544 1.4514 1.456 1.484 1.459 1.466 TO a 3- C -C M 2 1.3339 1.3359 1.3322 1.3402 1.3402 1.3381 1.3402 1.3440 1.3273 1.3298 1.339 1.347 1.322 c2=o3 1.1486 1.1467 1.1479 1.1572 1.1572 1.1558 1.1572 1.1559 1.1202 1.1184 - 1.172 1.150 s C,-H5 1.0817 1.0783 1.0795 1.0804 1.0804 1.0794 1.0804 1.0802 1.0690 1.0659 - 1.085 1.108 ^ c4=o6 1.1909 1.1926 1.1901 1.2016 1.2016 1.2010 1.2016 1.2021 1.1699 1.1711 1.192 1.214 1.211 TO C4-C17 1.8176 1.8209 1.8160 1.7850 1.7850 1.8186 1.7850 1.7881 1.7720 1.7766 1.772 1.788 1.755 TO C C C V-4V—1V'2 118.69 118.55 118.60 117.10 117.10 118.69 117.10 117.11 117.47 117.37 123.4 127.1 121.0 TO CjC203 180.0 179.32 180.0 179.74 179.74 179.16 179.74 179.72 180.0 178.81 - 180.0 179.6 H5CjC4 122.79 122.93 122.82 121.20 121.20 122.83 121.20 121.35 123.86 124.0 - 124.0 121.2 o6c4c, 128.49 128.47 128.50 127.59 127.59 127.97 127.59 127.63 127.17 127.24 125.2 127.1 124.3 3 7 4 1 110.86 110.86 110.66 111.20 111.20 111.34 111.20 111.16 112.40 112.34 111.8 115.5 113.0 TO 2 O C C C 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Cl^CjH;; 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 - 0.0 0.0 li (Debye) 3.2485 3.1118 3.2628 3.4809 3.3399 2.7 E (a.u.) -725.51540 -725.54899 -725.55166 -724.39319 -723.46814 -724.26123 -725.61870 "values obtained from an electron diffraction experiment for a similar molecule, propenoyl chloride Ref. [32]. Table 2: Vibrational frequencies, intensities and assignments of s-trans conformer of chlorocarbonyl ketene Freq- Exptla B97-1/6- -311++G** B3LYP/C -3+G** RHF/6-311++G** B971/aug-cc -pvtzb Assignments uencies Arg an Harmonic Anhar- Harmonic Anhar- Harmonic \nhar- Harmonic Anhar- monic monic monic monic Vobs Int V cale Int. V cale V cale Int. V cale cale Int V cale V seal cale Int. V cale A' V! - - 3196.8 22.9 3027.3 3215.7 22.0 3066.5 3370.3 22.9 3250.7 2990.6 3237.8 20.9 3088.8 C-H str. v, 2160 100 2249.6 768.4 2206.6 2233.5 756.9 2186.6 2401.5 1201.0 2368.8 2175.6 2302.1 754.5 2255.2 CCO as str. v, 1785 53 1862.6 665.1 1834.9 1850.2 639.7 1821.3 2009.1 930.8 1987.1 1828.1 1907.5 654.3 1878.6 C=0 str. ^ 1376 5 1389.9 53.8 1365.6 1400.8 51.8 1367.5 1507.8 79.3 1480.6 1362.1 1413.0 54.8 1379.7 C=C str., C-H i.p. bend v, 1125 10 1138.0 98.3 1118.2 1149.8 108.7 1125.1 1229.8 173.0 1194.5 1098.9 1144.2 97.5 1119.5 C-H i.p. bend, C=C str. v* 1051 10 1078.6 179.8 1041.3 1087.3 167.8 1086.4 1175.1 200.6 1148.5 1056.6 1095.2 171.7 1094.3 C-C str., C-H i.p. bend v, - 628.8 5.7 611.6 625.7 5.7 611.2 717.6 23.2 713.6 656.5 613.5 0.1 599.0 CCCdef., CCO i.p. bend V8 587 10 585.7 106.6 582.2 582.2 107.5 574.2 642.6 95.1 633.9 583.2 579.3 118.2 571.3 CCO def., C-Cl str., C-H i.p. bend v„ - - 413.9 8.1 411.7 409.0 9.1 403.8 478.7 2.5 474.3 436.4 405.2 9.1 400.0 C-Cl str., C=0 i.p. bend V!0 - - 351.1 5.8 347.1 351.4 6.3 348.9 398.7 9.4 396.6 364.9 328.3 4.3 325.8 CCO i.p. def. Vll - - 131.1 1.5 126.8 130.4 1.7 128.7 144.1 2.8 143.0 131.6 113.9 2.3 112.2 C-Cl i.p. bend, CCO i.p. bend A" Vp 684 9 697.0 44.1 673.0 700.1 50.2 684.8 779.4 75.8 769.4 707.8 687.7 51.03 672.4 CCH o.p. bend,C-Cl wag vn 558 6 572.1 12.4 562.2 556.6 17.9 550.2 653.6 18.4 647.0 595.2 534.9 19.59 528.5 CCO o.p. def., C-H o.p. bend VH - 526.8 11.8 493.6 524.9 4.4 515.2 569.2 13.0 558.8 514.1 507.8 3.13 498.1 C-H o.p. bend V15 - 115.1 5.0 111.2 116.5 5.4 114.5 121.6 5.76 119.9 110.3 51.5 5.63 49.5 Asym. torsion * Scaling factor =0.92 a Ref. [9] b anharmonic corrections in B3LYP/6-31+G* Table 3: Vibrational frequencies, intensities and assignments for s-cis chlorocarbonyl ketene Freq- Exptla B97-1/6- -311++G** B3LYP/6-3+G** RHF/6-311++G** B971/aug-cc -pvtzb Assignments uencies Argon Harmonic Anhar- Harmonic Anhar- Harmonic Anhar- Harmonic Anhar- monic monic monic monic Vobs Int V cale Int. V cale V cale Int. V cale V cale Int V cale V seal V eale Int. V eale A' V! - - 3227.6 28.7 3062.4 3245.6 26.7 3099.9 3407.7 27.8 3286.0 3023.1 3226.7 26.4 3080.9 C-H str. v, 2158 100 2249.8 933.1 2205.9 2231.9 907.3 2188.8 2403.8 1381.2 2369.0 2179.5 2234.6 37.3 2190.8 C=C=0 asym. Str. v, 1748 80 1833.5 377.5 1784.5 1819.7 357.9 1777.9 1973.8 480.4 1940.9 1785.5 1823.0 333.8 1781.4 C=0 str. ^ 1361 65 1383.8 261.2 1359.6 1399.4 256.0 1373.5 1503.5 377.9 1464.8 1347.7 1380.3 252.8 1354.4 C=C=0 sym. str. v, 1113 6 1120.3 4.3 1100.4 1128.5 5.9 1160.2 1206.8 35.6 1171.1 1100.8 1115.5 3.5 1139.7 C-H i.p. bend v* 1004 23 1016.4 184.6 992.5 1026.0 184.4 1007.5 110.4 229.4 1091.2 1003.9 1014.9 172.9 996.2 C-C str. v, 827 - 839.6 230.7 825.9 834.1 229.0 819.6 938.7 233.1 925.1 851.1 835.5 219.9 821.0 C-C-C def., C-C=0 def. VK - - 515.4 29.5 508.5 506.4 30.2 500.9 578.7 36.1 573.1 527.1 513.6 1.5 508.2 C=C=0 i.p. bend v„ - - 438.7 12.1 434.4 432.9 13.5 428.9 499.3 6.7 495.3 455.7 433.9 12.1 430.0 CI C O def., C-Cl str. V!0 - - 311.2 4.2 309.3 312.8 4.5 311.5 342.2 3.7 340.8 313.5 309.5 4.3 308.3 CCI def. Vll - - 132.3 3.1 130.1 133.0 3.2 131.7 151.3 3.7 150.1 138.1 131.1 2.9 130.1 C=C=0 i.p. bend A" V12 660 10 669.3 34.8 657.5 672.2 43.3 664.1 761.9 70.2 754.6 694.3 671.7 31.2 663.7 C-C-H o.p. bend, C-Cl wag vn - - 571.6 3.2 559.9 559.2 25.6 549.9 654.5 8.8 645.9 594.2 570.6 0.6 561.4 C=C=0 o.p. bend VH 531 vw 550.6 28.1 517.7 556.1 2.0 547.0 589.1 30.5 579.1 532.8 554.5 513.6 545.5 C-H o.p. bend V15 - - 92.0 2.6 87.8 92.9 2.8 92.8 100.4 2.4 99.2 91.2 90.9 2.3 91.1 Asymm. Torsion « Scaling factor =0.92 a Ref. [9] b anharmonic corrections in B3LYP/6-31+G fc# Table 4: Overtones and combination bands (cm ') of s-trans and s-cis conformers of chlorocarbonyl ketene s-trans s-cis B97-1/6 -311++G** B3LYP/6 -31+G** RHF/6- -311++G** Assignment B97-1/6- -311++G** B3LYP/6 -31+G** RHF/6- -311++G** Assig nment Harm- Anhar- Harm- Anhar- Harm- Anhar- Scaled Harm- Anhar- Harm- Anhar- Harm- Anhar- Scaled onic monic onic monic oninc monic Anhar onic monic onic monic onic monic Anhar 4499.2 4390.2 4467.0 4359.5 4803.1 4702.2 4326.0 2v2 4499.6 4387.0 4464.0 4355.8 4807.6 4707.4 4330.8 2v2 725.2 3645.1 3700.5 3616.8 4018.2 3951.2 3635.1 2v3 3667.1 3543.8 3639.4 3530.0 3947.7 3858.6 3549.9 2v3 2276.0 2234.9 2299.7 2244.1 2459.6 2410.8 2217.9 2v5 2767.6 2702.5 2798.8 2730.0 3007.1 2910.5 2677.6 2v4 2157.3 2078.0 2174.6 2134.4 2350.1 2292.2 2108.8 2v6 2240.7 2166.0 2257.0 2317.9 2413.6 2336.6 2146.9 2v5 1171.4 1165.1 1164.4 1148.9 1285.2 1265.9 1164.6 2v8 2032.8 1980..2 2052.1 2009.7 2220.7 2177.6 2003.4 2v6 1394.0 1341.4 1400.2 1384.0 1558.9 1540.2 1416.9 2v12 1679.1 1649.3 1668.2 1636.6 1157.5 1145.3 1053.7 2v8 1144.1 1124.8 1113.1 1100.5 1307.1 1293.8 1190.3 2v13 4083.4 3989.4 4051.7 3966.2 4377.7 4305.3 3960.9 v2 + v3 4112.2 4040.3 4083.7 4011.1 4410.6 4348.1 4000.2 v2 + v3 3633.6 3554.1 3631.4 3549.9 3907.4 3820.4 3514.8 v2 + v4 3387.6 3324.9 3383.7 3314.5 3631.3 3567.8 3282.4 V2+V5 3266.2 3195.3 3258.0 3194.3 3514.2 3454.3 3177.9 V2+V6 3328.2 3242.1 3320.8 3254.3 3576.6 3505.3 3224.9 V2+V6 3089.4 3028.5 3066.1 3004.1 3342.5 3287.0 3024.0 v2 + v7 2835.3 2789.0 2815.7 2765.5 3044.1 2996.5 2756.8 v2 + v8 2765.2 2709.9 2738.4 2686.2 2982.6 2934.6 2699.8 v2 + v8 2821.7 2759.6 2790.1 2733.4 3055.1 3000.7 2760.6 V2 + V13 2821.4 2757.7 2791.2 2737.6 3058.3 3003.8 2763.5 V2 + V13 3000.6 2954.4 3000.1 2946.7 3238.9 3197.4 2941.6 v3+v5 3217.4 3142.3 3219.1 3149.8 3477.4 3404.1 3131.8 v2 + v4 2941.2 2874.1 2937.5 2889.2 3184.2 3135.1 2884.3 V3+V6 2850.0 2754.7 2845.7 2771.3 3084.2 3021.7 2779.9 V3+V6 2491.3 2449.4 2475.9 2436.0 2726.7 2707.5 2490.9 v3+v7 2673.1 2595.0 2653.8 2589.9 2912.6 2864.0 2634.9 v3+v7 2448.3 2418.2 2432.4 2396.6 2651.7 2622.6 2412.8 v3+v8 2502.8 2439.5 2491.9 2439.7 2735.8 2693.7 2478.2 V3 + V12 2559.6 2506.4 2550.3 2507.8 2788.5 2754.2 2533.9 V3 +V12 2400.2 2346.7 2425.7 2375.3 2613.9 2551.4 2347.3 V3+V6 2216.6 2158.9 2237.2 2196.7 2404.0 2351.3 2163.2 V5+V6 2223.4 2187.8 2233.5 2194.5 2442.3 2378.6 2188.3 v3+v7 1723.7 1700.9 1732.1 1694.1 1872.4 1840.7 1693.4 V5+V8 1856.0 1832.3 1860.1 1833.0 2049.1 2018.9 1857.3 v3+v7 1664.4 1622.0 1669.5 1641.1 1818.7 1781.8 1639.2 V6+V8 1508.8 1482.4 1506.3 1482.9 1700.7 1678.7 1544.4 V3 + V12 700.8 964.8 698.7 693.4 764.2 752.9 692.7 V8+V15 1122.2 1061.0 1115.3 1081.8 1243.6 1240.9 1141.6 v3+v14 1098.9 1068.3 1081.5 1047.0 1222.8 1228.6 1130.3 V13+V14 607.4 596.1 599.3 593.9 679.2 672.4 618.6 v3+v8 Acta Chim. Slov. 2008, 55, 190–200 197 It follows from these tables that, both in the case of the s-cis as well as s-trans conformers, the calculated harmonic frequencies from density functional theory need significant scaling for agreement with the experimental values. The corresponding anharmonic frequencies on the other hand are quite close to the experimental values within ±20 cm–1 and do not need further scaling. The ab ini-tio frequencies using Hartree-Fock formalism with 6-311++G** basis set show large deviations from the experimental values, both in the harmonic as well as anharmo-nic approximations. The anharmonic frequencies in this case need scaling by a factor of 0.92 to match with the experimental frequencies within ±20 cm–1. It also follows from Tables 2 and 3 that coupling of anharmonic correction from a cheap model B3LYP/6-31+G** with harmonic frequencies from B97-1/aug-cc-pVTZ, as in ref. 30, does not give satisfactory agreement with the experimental values; the r.m.s deviation in this case is ±47 cm–1. It may thus be concluded that calculations using the same method and basis set for harmonic frequencies and anhar-monic corrections is superior to the one using different methods and basis sets for the two parts. Both the s-cis and s-trans conformations of chloro-carbonyl ketene belong to Cs symmetry groups and have 11A’ + 4A’’ normal modes. The assignment of these normal vibrational modes for the s-trans and s-cis confor-mers are given Tables 2 and 3, respectively. Our assignment of vibrational bands, both of the s-cis and s-trans conformers, are in closer agreement with those of Pietri et al.9 rather than of Badawi et al.15 Calculated frequencies of Badawi et al.,15 in most part, do not agree with the experimental values of chlorocarbonyl ketene.9 Pietri et al.9 assign a calculated band at 3214 cm–1 to C–H stretching mode. However, no such band appears in the experimental infrared spectra.9 Present anharmonic calculations for the s-cis and s-trans conformers predict this band at 3062.4 Table 5: Anharmonicity constants (cm–1) of s-trans and s-cis conformers of chlorocarbonyl ketene using DFT methods Trans Anhar. constts B97-1/6-311++G** CCK B3LYP/6-31+G** Cis CCK B97-1/6-311++G** B3LYP/6-31+G** X 1 1 -69.88 X 2 2 -11.46 X 3 3 -12.32 X 4 4 -7.37 X 5 5 -2.28 X 6 6 -2.27 X 7 7 -1.17 X 8 8 0.36 X 9 9 -0.73 X 10 10 0.04 Xin1 -0.57 X 12 12 -1.64 X 13 13 -0.54 X 14 14 -7.23 X 15 15 -0.20 X 1 4 4.17 X 1 5 -19.10 X 1 12 -12.27 X 1 14 -19.57 X 3 7 2.96 X 3 8 1.12 X 5 9 1.11 X 5 13 4.92 X 5 14 4.11 X 6 9 1.55 X 6 13 -22.86 X 6 14 -19.06 X 7 14 -8.29 X 7 15 -6.54 X 10 14 -1.17 X 11 12 0.08 X 12 13 -1.04 X 13 14 12.44 X 10 15 0.64 X 14 X 15 5.05 -63.64 -68.89 -11.23 -11.85 -12.94 -12.60 -7.39 -8.35 -2.99 -1.94 -2.45 -2.47 -0.88 -1.35 0.29 0.31 -1.26 -0.32 0.21 -0.06 0.29 0.05 -0.04 -0.49 0.06 5.90 -3.18 -8.44 -0.26 -0.59 3.04 5.29 -17.36 -19.29 -8.28 -6.08 -7.32 -24.82 3.44 -15.51 1.11 -0.40 0.88 0.05 3.07 -29.39 1.25 2.82 1.01 0.74 –4.64 -2.07 5.91 -3.81 -6.88 -1.21 -5.06 -0.11 1.49 0.27 0.10 -0.72 1.38 -2.23 -1.70 -1.40 0.51 1.11 5.10 -2.40 -63.33 -10.92 -12.94 -8.48 -1.23 -2.68 -1.33 -2.42 -0.003 -0.05 0.16 -0.04 -5.57 -14.58 -0.35 5.88 -17.52 -5.24 -1.55 -7.65 -0.26 0.06 33.94 70.40 0.81 -3.60 -3.67 -0.72 0.09 -0.13 -0.56 3.46 -15.16 1.06 -1.15 Gupta and Mishra: Anharmonic Vibrational Properties of Chlorocarbonyl Ketene Conformers ... 198 Acta Chim. Slov. 2008, 55, 190–200 Table 6: Rotational constants (MHz) including terms due to quartic centrifugal distortion constants and rotation-vibration coupling constants (MHz) of s-trans and s-cis conformers of chlorocarbonyl ketene Rotational constants (MHz) s-trans Ref. [15] Ref. [24] s-cis Ref. [15] Ref. [24] B97-1/ B3LYP/ B3LYP/6- B3LYP/6- B97-1/6-311 B3LYP/6- B3LYP/6- B3LYP/6- 6-311++G** 6-31+G** 311++G** 31++G** ++G** 31+G** 311++G** 311++G** Ao 4847.7 4838.7 3840 4845 9370.4 9380.7 3524 9405 Bo 2208.3 2185.7 2400 2203 1463.2 1456.6 2490 1464 Co 1517.2 1505.6 1476 1514 1265.6 1260.8 1459 1267 Rotation-vibration coupling constants (MHz) s-trans s-cis B97-1/6-311++G** B3LYP/6-31+G** B97-1/6-311++G** B3LYP/6-31+G** a b c a b c a b c a b c «1 22.69 2.80 3.52 23.24 2.80 3.55 10.17 3.03 2.43 9.06 2.99 2.38 cc2 2.57 6.43 3.28 2.90 6.44 3.32 72.13 2.44 3.14 71.80 2.55 3.02 a3 19.84 3.37 3.47 19.48 3.44 3.45 18.42 -1.35 -0.73 18.15 -1.39 -0.77 a4 -17.90 1.94 -0.67 -16.89 2.06 -0.48 47.03 -0.79 0.49 47.05 -0.55 0.66 a5 -30.44 -0.52 -3.16 -27.10 -0.22 -2.63 17.41 -1.58 -0.77 18.13 -1.51 -0.73 a6 17.56 3.09 4.53 18.35 3.01 4.47 10.29 4.16 3.95 12.56 4.38 4.15 «7 –42.94 0.22 -1.16 -33.64 0.17 -0.86 20.34 0.90 2.11 26.16 0.97 2.26 a8 5.46 -0.33 2.35 10.07 -0.23 2.55 59.73 2.21 0.63 65.79 2.30 0.68 a9 -13.29 0.71 -1.65 -11.42 0.70 -1.57 -0.04 0.57 0.76 9.11 0.71 1.00 10 -14.61 -3.50 -0.89 -12.34 -3.39 -0.55 -1.19 -2.24 0.91 0.95 -2.13 1.00 «11 -55.75 -3.42 2.64 -63.09 -3.37 2.74 -98.14 –4.75 -0.77 -100.05 –4.66 -0.76 12 –4.31 -0.25 -0.72 –4.77 -0.21 -0.80 20.63 0.25 -0.32 20.42 0.11 -0.42 13 39.38 -0.93 -1.21 29.23 -1.24 -1.45 –41.52 -1.54 -0.55 -15.51 0.66 -0.06 «14 21.93 0.55 1.18 21.82 0.77 1.37 -13.16 0.54 0.11 –44.69 -1.65 -0.36 «15 78.86 -2.77 -1.85 86.92 -2.65 -1.82 14.52 1.87 -3.68 23.03 1.78 -3.55 and 3066.5 cm–1 (Tables 2 and 3), respectively, in close vicinity to the 3070 cm–1 band in ketene which was assigned by us28 to C–H stretch mode. 3. 3. Overtones and Combination Bands Anharmonic analyses are performed using the second-order perturbation theory for asymmetric tops.35 Fermi resonances have been handled in the usual fashion. That is, near singular terms are eliminated from the expressions for the anharmonic constants Xij and final band origins are obtained by diagonalising the Fermi energy matrix. Some of the overtones and combination bands of the s-cis and s-trans conformers of chlorocarbonyl ketene are given in Table 4. No experimental values are available for these bands for comparison. The errors in the calculation of the fundamental modes are reflected in the overtones and combination bands. Thus, the results of B97-1/6-311++G** and B3LYP/6-311++G** in the anharmonic approximation are quite close to each other. RHF/ 6-311++G** calculations give very high values for these bands which compare with the DFT values only after sca- ling with a factor of 0.92. DFT calculations predict Fermi resonance between ?5 and 2?13 and ?4 and 2 ?12 frequencies of the s-trans conformer. The deperturbed values of these frequencies are 1119.7 and 1123.3 cm–1 and 1362.6 and 1344.3 cm–1, respectively. Similarly, in the case of the s-cis conformer, the Fermi resonance is expected between ?2 and 2?5 and ?5 and ?13 + ?14. The deperturbed values of these frequencies in B97-1/6-311++G** are 2205.0 and 2166.5 cm–1 and 1085.2 and 1076.2 cm–1 , respectively. 3. 4. Spectroscopic Constants Spectroscopic constants namely, the anharmonic constants and rotational and rotation-vibrational coupling constants given in Tables 5 and 6, respectively, may be helpful in future experimentation as no such experimental data is currently available for the s-trans and s-cis confor-mers of chlorocarbonyl ketene which, as mentioned earlier, has astrophysical importance.10 It follows from Table 5 that B97-1/6-311++G** and B3LYP/6-31+G** calculations give a negative value for the diagonal anharmonic constants for the stretching mo- Gupta and Mishra: Anharmonic Vibrational Properties of Chlorocarbonyl Ketene Conformers ... Acta Chim. Slov. 2008, 55, 190–200 199 des of both the s-trans and s-cis conformers of chlorocar-bonyl ketene. However, in the case of frequencies ?8 and ?10, which have substantial contribution from C=C=O deformation modes, they have small positive values. Lower anharmonic frequencies in both the cases suggest that the cumulative effect of the anharmonic contributions from the non-diagonal terms exceed the contribution of the diagonal terms. A similar observation was made in the case of ketene28. The rotational constants of the s-trans and s-cis con-formers of chlorocarbonyl ketene, including terms due to quartic centrifugal distortion constants are given in Table 6 and compared with the values reported by Badawi et. al.15 and Al-Saadi et al.32 The table also contains rotationvibration coupling constants based on second order per-turbative vibrational treatment. Rotational constants obtained from different methods and basis sets agree with each other. Present values of rotational constants A0, B0, C0, which contain effects due to zero point vibrations and centrifugal distortions, are quite close to those reported by Al-Saadi et al.32 Badawi et al.,15 however, report very different values for the rotational constants and seem to be in error. 4. Conclusions Conformational and vibrational spectral studies have been conducted on the s-trans and s-cis conformers of chlorocarbonyl ketene by different ab initio and density functional theory methods. It is found that the s-trans conformer is more stable than the s-cis conformer by ?0.69 kcal/mol.; this value is in closer agreement with the experimental estimate 0.9–1.3 kcal/mol. than the other previously reported values.9,15 The vibrationally averaged bond lengths and bond angles, both for the cis and trans confor-mers, are within 0.005 Å and 0.14°, respectively, of the equilibrium geometry. The ab initio and DFT based an-harmonic vibrational analysis using second-order perturbation theory involving quartic, cubic and semidiagonal quartic force constants provides reliable frequencies (r.m.s. deviation ±20 cm–1) and assignments to the vibra-tional bands. DFT calculations using the same method and basis function for the harmonic frequencies and an-harmonic corrections give frequencies in better agreement with the experimental values than those in which the harmonic frequencies from a high level quantum mechanical method (B97-1/aug-cc-pVTZ) are coupled with anharmo-nic corrections from a cheap model (B3LYP/6-31+G**); the r.m.s. deviation in the latter case is ±47 cm–1. The errors in the calculation of the fundamental modes are reflected in the overtones and combination bands. Thus, the ab initio anharmonic frequencies from RHF/6-311++G** calculations needed scaling by a factor of 0.92 to match the DFT values. Some spectroscopic constants namely, the anharmonic constants, rotational constants and rota- tion-vibration coupling constants of the two conformers have been calculated by density functional theory and compared with literature, where available. 5. Supolementary Material Coriolis coupling constants (cm–1) and Nielsen´s centgrifugal distortion constants (MHz) for the s-trans and s-cis conformers of chlorocarbonyl ketene using B97-1/6-311++G** are given as supplementary material. 6. Acknowledgements A thankful acknowledgement is made of the financial support to this work by the Council of Scientific and Industrial Research (CSIR), New Delhi (India) through a major research project. 7. References 1. H. R. Seikaly, T. T. Tidwell, Tetrahedron 1986, 42, 2587–2613. 2. S. Niwayama, E. Adam Kallel, C. Sheu, K. N. Houk, J. Org. Chem. 1996, 61, 2517–2522. 3. C. Aubry, J. L. Holmes, J. Phys. Chem. 1997, 101, 5958– 5961. 4. W. Huang, D. Fang, K. Temple, T. T. Tidwell, J. Am. Chem. 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Handy, Chem. Phys. Lett. 2003, 373, 357–365. 28. V. P. Gupta, Spectrochimica Acta Part A 2005, 67, 870–876. 29. M. J. Frisch et al., Gaussian 03W, Gaussian Inc., Wallingford, CT 06092, USA,2003. 30. V. Barone, J. Chem. Phys. 2005, 122, 014108–014110. 31. A. Frisch, A. B. Nielsen, A. J. Holder, Gauss View W Version 2, Gaussian Inc., Pittsburgh, PA 151006, USA, 2000. 32. A. Al- Saadi, H. M. Badawi, J. Mol. Struct. (Theochem) 2002, 582, 11–23. 33. R. Kewley, D. C. Hemphill, R. F. Curl jr, J. Mol. Spectrosc. 1972, 44, 443–458. 34. K. Hagen, K. Hedberg, J. Am. Chem. Soc. 1984, 106, 6150– 6155. 35. I. M. Mills in K. N.Rao and C. W. Mathews (Eds.), Molecular Spectroscopy – Modern Research, Academic, London 1972, p.1 Povzetek V prispevku obravnavamo kvantno kemijsko {tudijo struktur in vibracijskih spektrov za stabilne konformacije klorokar-bonil ketena. Ab initio izra~uni so bili izvedeni v okviru DFT pribli`ka upo{tevajo~ popravke drugega reda teorije motenj. Izkazalo se je, da je s-trans konformacija stabilnej{a kot s-cis konformacija za 0.69 kcal/mol. Povpre~na vibracijska dol`ina in kot, ki merita odmik odmik od ravnovesja, sta okoli 0.005 Å in 0.14°. Nekatere spektroskopske konstante, kot so anharmonska konstanta, rotacijska konstanta in rotacijsko-vibracijska sklopitvena konstanta so bile izra~una-ne za obe konformaciji v okviru DFT pribli`ka in primerjane s podatki iz literature. Gupta and Mishra: Anharmonic Vibrational Properties of Chlorocarbonyl Ketene Conformers ... Acta Chim. Slov. 2008, 55, 190–200 S201 Coriolis coupling constants Z(I,J) (cm–1) for trans-chlorocarbonyl ketene using B97-1/6-311++G** I J Z(I,J) I J Z(I,J) I J Z(I,J) X-Component Y-Component Z-Component 12 1 0.27851 12 1 0.52459 4 1 0.61378 12 2 -0.01762 12 2 -0.01618 4 2 -0.12471 12 3 -0.75576 12 3 0.15305 4 3 -0.07789 12 4 0.45949 12 4 -0.32105 5 1 -0.70704 12 5 -0.29309 12 5 -0.22957 5 2 0.04843 12 6 -0.06110 12 6 -0.60637 5 3 -0.39567 12 7 0.15758 12 7 -0.22307 5 4 0.08412 12 8 0.11834 12 8 0.33309 6 1 0.22958 12 9 0.05607 12 9 -0.04872 6 2 -0.33829 12 10 -0.08961 12 10 -0.11961 6 3 -0.55650 12 11 -0.01294 12 11 -0.01650 6 4 0.38226 13 1 0.08283 13 1 0.13384 6 5 0.32143 13 2 -0.95479 13 2 0.03892 7 1 0.15185 13 3 0.13960 13 3 -0.01522 7 2 0.71060 13 4 0.20772 13 4 -0.17091 7 3 -0.23437 13 5 0.04260 13 5 0.15043 7 4 -0.19740 13 6 -0.05304 13 6 -0.32991 7 5 -0.24506 13 7 -0.01336 13 7 0.77006 8 1 -0.13326 13 8 -0.09449 13 8 -0.21401 8 2 -0.08079 13 9 -0.01840 13 9 -0.08941 8 3 0.56671 13 10 0.06886 13 10 0.41415 8 4 0.27130 13 11 0.00817 13 11 -0.03688 8 6 -0.27821 14 1 0.36782 14 1 0.68296 8 7 -0.10273 14 2 0.19559 14 2 0.03536 9 2 -0.12690 14 3 0.49028 14 3 -0.07393 9 3 -0.31633 14 4 0.40267 14 4 -0.11754 9 4 -0.20772 14 5 -0.50199 14 5 0.53175 9 5 -0.11554 14 6 0.23588 14 6 0.35381 9 6 -0.08037 14 7 0.04292 14 7 -0.04699 9 7 -0.37831 14 8 -0.23474 14 8 -0.23603 9 8 -0.10846 14 9 -0.10957 14 9 0.06390 10 1 0.13962 14 10 0.20005 14 10 -0.20389 10 2 0.54996 14 11 0.08567 14 11 0.03890 10 4 0.39176 15 1 0.04478 15 1 0.09332 10 5 0.32518 15 2 -0.17880 15 2 0.01734 10 9 -0.55389 15 3 -0.30862 15 3 -0.00768 11 2 -0.16696 15 4 -0.62817 15 4 0.11840 11 3 -0.15392 15 5 -0.44628 15 5 0.20096 11 4 -0.36505 15 6 0.37470 15 6 0.20908 11 5 -0.22677 15 7 -0.09489 15 7 -0.09389 11 6 0.26687 15 8 -0.16685 15 8 0.46016 11 7 0.16669 15 9 -0.18548 15 9 -0.49812 11 8 -0.11859 15 10 0.24804 15 10 0.36728 11 9 -0.57267 15 11 0.06202 15 11 -0.53780 11 10 -0.32703 Gupta and Mishra: Anharmonic Vibrational Properties of Chlorocarbonyl Ketene Conformers ... S202 Acta Chim. Slov. 2008, 55, 190–200 Coriolis coupling constants Z(I,J) (cm–1) for cis- chlorocarbonyl ketene using B97-1/6-311++G** I J Z(I?J) I J Z(I?J) I J Z(I?J) X-Component Y-Component Z-Component 12 1 0.18315 12 1 0.34544 4 1 0.65381 12 2 -0.06893 12 2 0.21898 4 2 0.15854 12 3 0.52097 12 3 0.59934 4 3 0.29114 12 4 0.61464 12 4 -0.38719 5 1 -0.67227 12 5 -0.13136 12 5 -0.10169 5 2 -0.19541 12 6 -0.45197 12 6 0.00791 5 3 0.08994 12 7 -0.24864 12 7 0.52240 5 4 0.13316 12 8 -0.08354 12 8 0.16800 6 1 0.25928 12 9 -0.12818 12 9 -0.03567 6 2 -0.24993 12 10 0.07501 12 10 0.09946 6 3 -0.39453 12 11 -0.01089 12 11 0.03001 6 4 0.40812 13 1 -0.06299 13 1 -0.10303 6 5 0.34663 13 2 -0.53075 13 2 0.77514 7 2 0.41755 13 3 -0.05194 13 3 -0.21138 7 3 -0.72753 13 4 0.05249 13 4 0.08523 7 4 -0.27211 13 5 -0.02769 13 5 -0.26706 7 5 -0.28310 13 6 -0.13499 13 6 -0.22560 8 1 0.19897 13 7 0.56438 13 7 0.15073 8 2 -0.73613 13 8 -0.56755 13 8 -0.40990 8 3 -0.20424 13 9 -0.09707 13 9 -0.05325 8 4 -0.17435 13 10 -0.17968 13 10 -0.13333 8 6 0.09186 13 11 0.08691 13 11 0.05506 8 7 0.10719 14 1 0.41135 14 1 0.79542 9 2 -0.21730 14 2 -0.05982 14 2 -0.01203 9 3 -0.34096 14 3 -0.30098 14 3 -0.32135 9 4 -0.04405 14 4 0.44243 14 4 -0.20640 9 5 -0.06506 14 5 -0.51969 14 5 0.27030 9 6 -0.40016 14 6 0.36717 14 6 -0.26904 9 8 0.10430 14 7 0.24863 14 7 -0.17812 10 1 0.08949 14 8 0.23128 14 8 -0.18310 10 2 -0.18471 14 9 0.14039 14 9 -0.03860 10 4 -0.11154 14 10 0.03052 14 10 -0.04987 10 6 0.33956 15 1 0.05636 14 11 -0.08132 10 7 0.03160 15 2 -0.12572 15 1 0.09699 10 9 -0.63194 15 3 0.02357 15 2 0.18698 11 2 0.26274 15 4 -0.28538 15 3 0.02903 11 3 -0.21489 15 5 -0.39962 15 4 0.32965 11 4 0.38972 15 6 0.07748 15 5 0.52614 11 5 0.50018 15 7 -0.33403 15 6 0.39344 11 6 0.07803 15 8 -0.20968 15 7 0.11725 11 7 0.35704 15 9 -0.10334 15 9 -0.47519 11 8 0.23250 15 10 0.27316 15 10 -0.04138 11 9 -0.42559 15 11 0.70178 15 11 0.41620 11 10 0.18526 Nielsen’s centrifugal distortionconstants (MHz) for s-cis and s-trans conformers of chlorocarbnyl ketene using B97-1/6-311++G** Trans Cis DJ × 10–3 0.157053 0.103174 DJ K × 10–2 0.648810 0.413465 DK × 10–3 0.011333 0.037930 R5 × 10–3 -0.772086 -0.555614 R6 × 10–4 0.114969 0.011338 Gupta and Mishra: Anharmonic Vibrational Properties of Chlorocarbonyl Ketene Conformers ...