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An IAM Calculation of the Torsional–Rotational Term Values for Three Isotopic Species of Ethyl Mercaptan
Journal of Molecular Spectroscopy 201, 321–322 (2000) doi:10.1006/jmsp.2000.8102, available online at http://www.idealibrary.com on
NOTE An IAM Calculation of the Torsional–Rotational Term Values for Three Isotopic Species of Ethyl Mercaptan Two and one-half decades ago Schmidt and Quade reported their results of the microwave spectroscopic studies of CH 3CH 2SH, CH 3CH 2SD, and CH 2DCH 2SH, both methyl symmetric and asymmetric conformations for the latter species, and first excited state spectra for both trans- and gaucheCH 3CH 2SH and CH 3CH 2SD (1). Spectra for both the trans and gauche conformations were identified, assigned, and analyzed. Among the things determined from the analyses were the gauche tunneling energy, a molecular structure that was good for both conformations, components of the electric dipole moment, the x–y and x–z product of inertial coefficients D and E, the V 3 methyl barrier to internal rotation for trans-CH 3CH 2SH, the gauche–trans, gauche– gauche, and trans–trans energy differences from relative intensity measurements, and the potential energy coefficients for the hydroxyl internal rotation. Recently we have used an internal axis method (IAM) (2) for calculation of the torsional–rotational term values for five isotopic species of ethyl alcohol (3). The results were as much negative as positive in the sense that the IAM, with its seven inertial constants plus three potential energy coefficients, did not in any way improve the spectral analyses over the parametric methods of analysis (4) based upon the isolation of the trans and gauche effective rotational blocks within the context of the framework fixed-axis method (FFAM) (5). The positive feature was that the so-called nonrigidity terms could be evaluated and improved values were obtained for the gauche tunneling energy in conjunction with the hydroxyl internal-rotation potential energy coefficients. The same situation has been found to be the case for the ethyl mercaptan. The results of our analyses are given in Tables 1 and 2. Table 1 contains the new potential energy coefficients, selected torsional energy differences, and the nonrigidity constants ⌬A, ⌬B, ⌬C. Again, V 3 ⫽ 444 cm ⫺1 has been fixed at the CH 3SH value (6), consistent with our work on the methyl and ethyl alcohols. Table 2 compares our nonrigidity ⌬A, ⌬B, ⌬C with ⌬A, ⌬B, ⌬C calculated from the structure within the context of a rigid-rotor molecule from the empirical A, B, C. The differences in these quantities are due to the averaging over the ␣-dependence of the rotational coefficients with the torsional wavefunctions. For the ethyl mercaptans, there was not as complete data for symCH 2DCH 2SH and CH 3CH 2SD as there was for the ethyl alcohols of the preceding paper; especially for the c-dipole transitions with regards to selection rules in K ⫺1 . For these species, independent equations for ⌬A ⫹ , ⌬A ⫺ , and ⌬ did not exist. However, the tunneling for the ethyl mercaptans is much, much smaller than for the ethyl alcohols. The coupled equations for ⌬A ⫹ , ⌬A ⫺ , and ⌬ indicate that these quantities are good to better than 0.1 MHz in Table 1 for the assumed molecular structure. For CH 3CH 2SH, these quantities are better still, more on the order of 0.05 MHz as are the ⌬B and ⌬C for all species. In the analyses, the molecular structure determined by Schmidt (1) was used, which incorporated a tilt of 3.16° as determined from his rigid-rotor analysis. In the determination of the potential energy coefficients, V 3 was again fixed and the torsional term values with excited states were used. For CH 3CH 2SH, these term values from the infrared work are no better than ⫾10 cm ⫺1 and the calculated values in Table 1 are within these limits. In the case of CH3CH 2SD, the IAM gives the splitting of the ⫹ and ⫺ a-dipole lines to be on the order of 0.04 MHz or less except for the 322 4 2 21 and 3 21 4 2 20 lines which were predicted to be split by 1.30 MHz. Similarly the 423 4 3 22 and
TABLE 1 Potential Energy and Nonrigidity Coefficients for CH 3CH 2SH, CH 3CH 2SD, and sym CH 2DCH 2SH
4 22 4 3 21 lines were predicted to be split by 1.75 MHz. These calculated splittings have an interesting origin. For CH3CH 2SD, the tunneling energy is on the order of 70 MHz. At the same time, the splitting of the K ⫺1 ⫽ 2 Wang states is for J ⫽ 2, 7 MHz; for J ⫽ 3, 36 MHz; and for J ⫽ 4, 112 MHz. The operator z␣pP z not only mixes the gauche ⫹ and ⫺ states but also the K ⫺1 ⫽ 2 Wang states. Since the splitting of the Wang states for K ⫺1 ⫽ 2 is comparable to the tunneling energy, the K ⫺1 ⫽ 2 transitions for ⫹ and ⫺ should be split by a small amount from the pP z interaction. The fact that Schmidt did not observe this small internal rotation splitting indicates that it is suppressed by other terms in the Hamiltonian such as centrifugal distortion. Depending upon the symmetry, sign, and size of the centrifugal distortion, it can either enhance or suppressed this effect. Apparently it is such as to cause it to be suppressed. In conclusion, we wish to point out that an FFAM analysis for CH 3CH 2SD should not proceed in the same manner as for CH 3CH 2SH, sym-CH 2DCH 2SH, and the ethyl alcohols where the tunneling energy is large compared to the contributions to the rotational energies from the x–y and x–z product of inertia terms. When the tunneling is small, as it is for CH 3CH 2SD, the approach that has been used successfully for phenol (7) should be used. In the present case, rather than making small rotation about the x-axis, small rotations about the zand y-axes should be made to remove the products of inertia after the transformation to the localized basis in the effective rotational Hamiltonian. Even
321 0022-2852/00 $35.00 Copyright © 2000 by Academic Press All rights of reproduction in any form reserved.
322
NOTE
TABLE 2 Comparison of Nonrigidity Contributions from the IAM and Rigid Rotor Analyses
2. M. Liu and C. R. Quade, J. Mol. Spectrosc. 146, 238 –251 (1991). 3. C. R. Quade, M. Liu, and C. F. Su, 201, 319 –322 (2000). 4. (a) J. C. Pearson, K. V. L. N. Sastry, M. Winnewisser, E. Herbst, and F. C. De Lucia, J. Chem. Phys. Ref. Data 24, 1–32 (1995); (b) J. C. Pearson, K. V. L. N. Sastry, E. Herbst, and F. C. De Lucia, J. Mol. Spectrosc. 175, 246 –261 (1996). 5. C. R. Quade and C. C. Lin, J. Chem. Phys. 38, 540 –550 (1963). 6. (a) T. Kojima and T. Nishikawa, J. Phys. Soc. Jpn. 12, 680 – 686 (1957); (b) T. Kojima, J. Phys. Soc. Jpn. 15, 1284 –1291 (1960). 7. C. R. Quade, J. Chem. Phys. 48, 5490 –5493 (1968). C. Richard Quade* Mujian Liu* Chun Fu Su†
in the FFAM, the near-resonance between the tunneling and K ⫺1 ⫽ 2 splittings must be taken into account.
REFERENCES 1. R. E. Schmidt and C. R. Quade, J. Chem. Phys. 62, 3864 –3874 (1975).
*Department of Physics Texas Tech University Lubbock, Texas 79409 †Department of Physics Mississippi State University Mississippi State, Mississippi 39762
Received December 28, 1999; in revised form February 23, 2000
Copyright © 2000 by Academic Press
NOTE An IAM Calculation of the Torsional–Rotational Term Values for Three Isotopic Species of Ethyl Mercaptan Two and one-half decades ago Schmidt and Quade reported their results of the microwave spectroscopic studies of CH 3CH 2SH, CH 3CH 2SD, and CH 2DCH 2SH, both methyl symmetric and asymmetric conformations for the latter species, and first excited state spectra for both trans- and gaucheCH 3CH 2SH and CH 3CH 2SD (1). Spectra for both the trans and gauche conformations were identified, assigned, and analyzed. Among the things determined from the analyses were the gauche tunneling energy, a molecular structure that was good for both conformations, components of the electric dipole moment, the x–y and x–z product of inertial coefficients D and E, the V 3 methyl barrier to internal rotation for trans-CH 3CH 2SH, the gauche–trans, gauche– gauche, and trans–trans energy differences from relative intensity measurements, and the potential energy coefficients for the hydroxyl internal rotation. Recently we have used an internal axis method (IAM) (2) for calculation of the torsional–rotational term values for five isotopic species of ethyl alcohol (3). The results were as much negative as positive in the sense that the IAM, with its seven inertial constants plus three potential energy coefficients, did not in any way improve the spectral analyses over the parametric methods of analysis (4) based upon the isolation of the trans and gauche effective rotational blocks within the context of the framework fixed-axis method (FFAM) (5). The positive feature was that the so-called nonrigidity terms could be evaluated and improved values were obtained for the gauche tunneling energy in conjunction with the hydroxyl internal-rotation potential energy coefficients. The same situation has been found to be the case for the ethyl mercaptan. The results of our analyses are given in Tables 1 and 2. Table 1 contains the new potential energy coefficients, selected torsional energy differences, and the nonrigidity constants ⌬A, ⌬B, ⌬C. Again, V 3 ⫽ 444 cm ⫺1 has been fixed at the CH 3SH value (6), consistent with our work on the methyl and ethyl alcohols. Table 2 compares our nonrigidity ⌬A, ⌬B, ⌬C with ⌬A, ⌬B, ⌬C calculated from the structure within the context of a rigid-rotor molecule from the empirical A, B, C. The differences in these quantities are due to the averaging over the ␣-dependence of the rotational coefficients with the torsional wavefunctions. For the ethyl mercaptans, there was not as complete data for symCH 2DCH 2SH and CH 3CH 2SD as there was for the ethyl alcohols of the preceding paper; especially for the c-dipole transitions with regards to selection rules in K ⫺1 . For these species, independent equations for ⌬A ⫹ , ⌬A ⫺ , and ⌬ did not exist. However, the tunneling for the ethyl mercaptans is much, much smaller than for the ethyl alcohols. The coupled equations for ⌬A ⫹ , ⌬A ⫺ , and ⌬ indicate that these quantities are good to better than 0.1 MHz in Table 1 for the assumed molecular structure. For CH 3CH 2SH, these quantities are better still, more on the order of 0.05 MHz as are the ⌬B and ⌬C for all species. In the analyses, the molecular structure determined by Schmidt (1) was used, which incorporated a tilt of 3.16° as determined from his rigid-rotor analysis. In the determination of the potential energy coefficients, V 3 was again fixed and the torsional term values with excited states were used. For CH 3CH 2SH, these term values from the infrared work are no better than ⫾10 cm ⫺1 and the calculated values in Table 1 are within these limits. In the case of CH3CH 2SD, the IAM gives the splitting of the ⫹ and ⫺ a-dipole lines to be on the order of 0.04 MHz or less except for the 322 4 2 21 and 3 21 4 2 20 lines which were predicted to be split by 1.30 MHz. Similarly the 423 4 3 22 and
TABLE 1 Potential Energy and Nonrigidity Coefficients for CH 3CH 2SH, CH 3CH 2SD, and sym CH 2DCH 2SH
4 22 4 3 21 lines were predicted to be split by 1.75 MHz. These calculated splittings have an interesting origin. For CH3CH 2SD, the tunneling energy is on the order of 70 MHz. At the same time, the splitting of the K ⫺1 ⫽ 2 Wang states is for J ⫽ 2, 7 MHz; for J ⫽ 3, 36 MHz; and for J ⫽ 4, 112 MHz. The operator z␣pP z not only mixes the gauche ⫹ and ⫺ states but also the K ⫺1 ⫽ 2 Wang states. Since the splitting of the Wang states for K ⫺1 ⫽ 2 is comparable to the tunneling energy, the K ⫺1 ⫽ 2 transitions for ⫹ and ⫺ should be split by a small amount from the pP z interaction. The fact that Schmidt did not observe this small internal rotation splitting indicates that it is suppressed by other terms in the Hamiltonian such as centrifugal distortion. Depending upon the symmetry, sign, and size of the centrifugal distortion, it can either enhance or suppressed this effect. Apparently it is such as to cause it to be suppressed. In conclusion, we wish to point out that an FFAM analysis for CH 3CH 2SD should not proceed in the same manner as for CH 3CH 2SH, sym-CH 2DCH 2SH, and the ethyl alcohols where the tunneling energy is large compared to the contributions to the rotational energies from the x–y and x–z product of inertia terms. When the tunneling is small, as it is for CH 3CH 2SD, the approach that has been used successfully for phenol (7) should be used. In the present case, rather than making small rotation about the x-axis, small rotations about the zand y-axes should be made to remove the products of inertia after the transformation to the localized basis in the effective rotational Hamiltonian. Even
321 0022-2852/00 $35.00 Copyright © 2000 by Academic Press All rights of reproduction in any form reserved.
322
NOTE
TABLE 2 Comparison of Nonrigidity Contributions from the IAM and Rigid Rotor Analyses
2. M. Liu and C. R. Quade, J. Mol. Spectrosc. 146, 238 –251 (1991). 3. C. R. Quade, M. Liu, and C. F. Su, 201, 319 –322 (2000). 4. (a) J. C. Pearson, K. V. L. N. Sastry, M. Winnewisser, E. Herbst, and F. C. De Lucia, J. Chem. Phys. Ref. Data 24, 1–32 (1995); (b) J. C. Pearson, K. V. L. N. Sastry, E. Herbst, and F. C. De Lucia, J. Mol. Spectrosc. 175, 246 –261 (1996). 5. C. R. Quade and C. C. Lin, J. Chem. Phys. 38, 540 –550 (1963). 6. (a) T. Kojima and T. Nishikawa, J. Phys. Soc. Jpn. 12, 680 – 686 (1957); (b) T. Kojima, J. Phys. Soc. Jpn. 15, 1284 –1291 (1960). 7. C. R. Quade, J. Chem. Phys. 48, 5490 –5493 (1968). C. Richard Quade* Mujian Liu* Chun Fu Su†
in the FFAM, the near-resonance between the tunneling and K ⫺1 ⫽ 2 splittings must be taken into account.
REFERENCES 1. R. E. Schmidt and C. R. Quade, J. Chem. Phys. 62, 3864 –3874 (1975).
*Department of Physics Texas Tech University Lubbock, Texas 79409 †Department of Physics Mississippi State University Mississippi State, Mississippi 39762
Received December 28, 1999; in revised form February 23, 2000
Copyright © 2000 by Academic Press