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

2. Overview
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:
rotational constants  A0, B0, C0
fundamental frequencies  ni
barrier heights for internal rotation and inversion
computationally demanding
The theoretical approach was formulated via benchmark calculations on methylamine (CH3NH2). [see RH08]

3. 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)
ni = wi + S ( xii, xij ) - anharmonicities
B0 = Be – ½ S aiB - rotation-vibration interaction constants
(similar for A and C)
Perturbation theory was used for anharmonic shifts:

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

5. Vibrational Modes – Bends and Torsion
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)

6. 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
CN str
-27
-26
-26
1044 -3
NH2 wag
-74
132 92
780
+165
4 A’ modes have well-behaved anharmonic shifts and small errors.
5 A’ modes have ill-behaved anharmonic shifts and large errors.

7. 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
4 A” modes have well-behaved anharmonic shifts and small errors.
1 A” mode has an ill-behaved anharmonic shift and large error.
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. 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
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+ appears to be modestly better behaved than CH3NH2.

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

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

12. CH3OH2+ – Hindered Motions
rotation
inversion

13. 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.
barrier height (cm-1)
calc
CH3NH2 ……………………
536
internal rotation
experiment
684.1, 718.4
CH3OH2+ ………………….
249
inversion
1366
1688, 2081, 1943
440

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.