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Theoretical Prediction of the Rotational Constants for Protonated Methanol (CH 3 OH 2 + ):

Theoretical Prediction of the Rotational Constants for Protonated Methanol (CH 3 OH 2 + ): A Missing Player in Hot Core Chemistry David E. Woon.

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Theoretical Prediction of the Rotational Constants for Protonated Methanol (CH 3 OH 2 + ):

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  1. Theoretical Prediction of the Rotational Constants for Protonated Methanol (CH3OH2+): A Missing Player in Hot Core Chemistry David E. Woon

  2. Models indicate that protonated methanol (CH3OH2+) is likely to be an important interstellar species. Astronomical searches are not possible until rotational data is available. • Laboratory measurement of the rotational spectra of CH3OH2+ would benefit from accurate theoretical predictions of: computationally demanding • rotational constants  A0, B0, C0 • fundamental frequencies ni • barrier heights for internal rotation and inversion Overview • The theoretical approach was formulated via benchmark calculations on methylamine (CH3NH2). [see RH08]

  3. Perturbation theory was used for anharmonic shifts: • ni = wi + S ( xii, xij ) - anharmonicities • B0 = Be – ½ S aiB - rotation-vibration interaction constants (similar for A and C) Theoretical Treatment • Equilibrium structures: all-electron CCSD(T) employing aug-cc-pVQZ sets plus sp core-valence functions (C&O) from cc-pCVDZ sets (MOLPRO, 398 basis functions) • Harmonic frequencies: valence-electron CCSD(T) with aug-cc-pVQZ sets without the H f function (MOLPRO, 320 basis functions) • Anharmonic corrections: as large as B3LYP/aug-cc-pVQZ (GAUSSIAN 03, 390 basis functions)

  4. OH2 s-str (n1) OH2 a-str(n10) CO str(n8) CH3 d-str (n2) CH3 s-str (n3) CH3 a-str (n11) Vibrational Modes - Stretches

  5. OH2 scis (n4) OH2 wag(n9) OH2 twist(n13) CH3 d-def (n5) CH3 s-def (n6) CH3 a-def (n12) CH3 rock (n7) CH3 rock (n14) torsion (n15) Vibrational Modes – Bends and Torsion

  6. 4 A’ modes have well-behaved anharmonic shifts and small errors. 5 A’ modes have ill-behaved anharmonic shifts and large errors. CH3NH2 – Fundamental Frequencies B3LYP CCSD(T)/ AVQZ-H(f) AVDZ AVTZ AVQZ Mode (A’) wn wn wn Experiment Error NH2 s-str -157 -158 -156 3361 -13 CH3 d-str -153 -99 -72 2961 +47 CH3 s-str -121 -163 -154 2820 +24 NH2 scis -33 132 184 1623 +227 CH3 d-def -29 -35 -34 1473 +1 CH3 s-def -18 -10 5 1430 +36 CH3 rock -46 -50 -49 1130 0 CN str -27 -26 -26 1044 -3 NH2 wag -74 132 92 780 +165

  7. 4 A” modes have well-behaved anharmonic shifts and small errors. 1 A” mode has an ill-behaved anharmonic shift and large error. CH3NH2 – Fundamental Frequencies B3LYP CCSD(T)/ AVQZ-H(f) AVDZ AVTZ AVQZ Mode (A”) wn wn wn Experiment Error NH2 a-str -170 -168 -161 3427 -1 CH3 a-str -161 -130 -180 2985 +48 CH3 a-def -34 -53 -44 1485 -3 NH2 twist -49 -44 -39 1335 -20 CH3 rock -29 -20 -15 972 -13 torsion -51 -49 -43 268 -15 • While perturbation theory has difficulties treating some modes, basis set analysis provides a useful diagnostic tool.

  8. CH3OH2+ – Fundamental Frequencies B3LYP AVDZ AVTZ AVQZ CCSD(T)/ AVQZ-H(f) Mode (A’) wn wn wn OH2 s-str -179 -175 -175 3492 CH3 d-str -152 -136 -134 3093 CH3 s-str -124 -76 -73 3023 OH2 scis -33 -53 -42 1653 CH3 d-def -34 -40 -39 1451 CH3 s-def -29 -14 -13 1461 CH3 rock -54 -16 -63 1121 CO str -46 -47 -49 790 OH2 wag -116 -88 -130 610

  9. 8 modes have well-behaved anharmonic shifts. 3 modes have small AVTZ-AVQZ changes in anharmonic shifts. 4 modes have ill-behaved anharmonic shifts. CH3OH2+ – Fundamental Frequencies B3LYP AVDZ AVTZ AVQZ CCSD(T)/ AVQZ-H(f) Mode (A’) wn wn wn OH2 a-str -193 -189 -198 3550 CH3 a-str -154 -137 -133 3100 CH3 a-def -40 -42 -41 1455 OH2 twist -47 -49 -50 1250 CH3 rock -26 -18 -26 918 torsion -17 -27 -2 235 • CH3OH2+ appears to be modestly better behaved than CH3NH2.

  10. rotational constant or error (GHz) Ae Be Ce re: CCSD(T)/AVQZ+CVDZ 104.151 22.803 21.926 A0 B0 C0 Experimenta 103.156 22.169 21.291 re: CCSD(T)/AVQZ+CVDZ 103.085 22.543 21.666 we: CCSD(T)/AVQZ-f -0.071 +0.374 +0.375 anh: B3LYP/AVQZ aIlyushin et al., J Mol Spectrosc 229, 170, 2005. CH3NH2 – Rotational Constants

  11. CH3OH2+ – Rotational Constants rotational constant (GHz) Ae Be Ce re: CCSD(T)/AVQZ+CVDZ 104.882 21.324 20.493 A0 B0 C0 re: CCSD(T)/AVQZ+CVDZ 104.065 20.917 20.093 we: CCSD(T)/AVQZ-f anh: B3LYP/AVQZ

  12. inversion rotation CH3OH2+ – Hindered Motions

  13. barrier height (cm-1) internal rotation calc experiment CH3NH2 …………………… 536 684.1, 718.4 CH3OH2+ …………………. 249 inversion calc experiment CH3NH2 …………………… 1366 1688, 2081, 1943 CH3OH2+ …………………. 440 CH3OH2+ – Barrier Heights • Barrier heights were computed at the CCSD(T) level with aug-cc-pVQZ sets with the H f and C/O g functions omitted, with B3LYP/aug-cc-pVQZ ZPE corrections.

  14. Conclusions and Acknowledgments • This work predicted fundamental frequencies, rotational constants, and barrier heights for CH3OH2+: • 8-11 of the ni’s are expected to be within 15 cm-1 of experiment-al values. • B0 and C0 may be within ~300 MHz of the experimental values. • Low and comparable barrier heights for internal rotation and inversion indicate that hindered motions will need to be treated very carefully in the analysis of rotational spectra. • THANKS to Prof. Ben McCall and Dr. Susanna Widicus-Weaver for a challenging problem and to Dr. Thom H. Dunning, Jr. for resources and financial support.

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