Theoretical Predictionof the Rotational Constants

forProtonated Methanol

(CH3OH2+):

A Missing Player in Hot Core Chemistry

David E. Woon

Overview

• Laboratory measurement of the rotational spectra of CH3OH2

+ would benefit from accurate theoretical predictions of:

rotational constants A0, B0, C0 fundamental frequencies i

barrier heights for internal rotation and inversion

• Models indicate that protonated methanol (CH3OH2

+) is likely to be an important interstellar species. Astronomical searches are not possible until rotational data is available.

• The theoretical approach was formulated via benchmark calculations on methylamine (CH3NH2). [see RH08]

computationally demanding

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)

i = i + ( xii, xij ) - anharmonicities B0 = Be – ½ i

B - rotation-vibration interaction constants

(similar for A and C)

• Perturbation theory was used for anharmonic shifts:

Vibrational Modes - Stretches

OH2 s-str (1) OH2 a-str (10)

CO str (8)

CH3 d-str (2) CH3 s-str (3) CH3 a-str (11)

Vibrational Modes – Bends and Torsion

CH3 d-def (5)

CH3 s-def (6)

CH3 a-def (12)

OH2 scis (4) OH2 wag (9) OH2 twist (13)

CH3 rock (7) CH3 rock (14)

torsion (15)

CH3NH2 – Fundamental Frequencies

Mode (A’)

AVDZ AVTZ AVQZ

B3LYPCCSD(T)/

AVQZ-H(f)Error

-157NH2 s-str -158 -156 3361 -13-153CH3 d-str -99 -72 2961 +47-121CH3 s-str -163 -154 2820 +24-33NH2 scis 132 184 1623 +227-29CH3 d-def -35 -34 1473 +1-18CH3 s-def -10 5 1430 +36-46CH3 rock -50 -49 1130 0-27CN str -26 -26 1044 -3-74NH2 wag 132 92 780 +165

Experiment

4 A’ modes have well-behaved anharmonic shifts and small errors.5 A’ modes have ill-behaved anharmonic shifts and large errors.

Mode (A”)

AVDZ AVTZ AVQZ

B3LYP

CH3NH2 – Fundamental Frequencies

-170NH2 a-str -168 -161 3427 -1-161CH3 a-str -130 -180 2985 +48-34CH3 a-def -53 -44 1485 -3-49NH2 twist -44 -39 1335 -20-29CH3 rock -20 -15 972 -13-51torsion -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.

CCSD(T)/ AVQZ-H(f)ErrorExperime

nt

• While perturbation theory has difficulties treating some modes, basis set analysis provides a useful diagnostic tool.

CH3OH2+ – Fundamental

Frequencies

Mode (A’)

AVDZ AVTZ AVQZ

B3LYP

CCSD(T)/ AVQZ-H(f)

-179OH2 s-str -175 -175 3492-152CH3 d-str -136 -134 3093-124CH3 s-str -76 -73 3023-33OH2 scis -53 -42 1653-34CH3 d-def -40 -39 1451-29CH3 s-def -14 -13 1461-54CH3 rock -16 -63 1121-46CO str -47 -49 790-116OH2 wag -88 -130 610

CH3OH2+ – Fundamental

Frequencies

Mode (A’)

AVDZ AVTZ AVQZ

B3LYP

CCSD(T)/ AVQZ-H(f)

-193OH2 a-str -189 -198 3550-154CH3 a-str -137 -133 3100-40CH3 a-def -42 -41 1455-47OH2 twist -49 -50 1250-26CH3 rock -18 -26 918-17torsion -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.

CH3NH2 – Rotational Constants

Ae

rotational constant or error (GHz)Be Ce

re: CCSD(T)/AVQZ+CVDZ

104.151

22.803 21.926

aIlyushin et al., J Mol Spectrosc 229, 170, 2005.

A0

103.156

Experimenta

B0 C0

22.169 21.291

re: CCSD(T)/AVQZ+CVDZ

103.085

22.543 21.666-0.071 +0.37

4+0.37

5e: CCSD(T)/AVQZ-fanh: B3LYP/AVQZ

CH3OH2+ – Rotational Constants

Ae

rotational constant (GHz)

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 20.093e: CCSD(T)/AVQZ-fanh: B3LYP/AVQZ

CH3OH2+ – Hindered Motions

rotation

inversion

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

CH3NH2 ……………………

1366 1688, 2081, 1943

CH3OH2+

………………….440

calc experiment

Conclusions and Acknowledgments

• This work predicted fundamental frequencies, rotational constants, and barrier heights for CH3OH2

+:

– 8-11 of the i’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.