theoretical prediction of the rotational constants for protonated methanol (ch 3 oh 2 + ):
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Theoretical Prediction of the Rotational Constants for Protonated Methanol (CH 3 OH 2 + ): A Missing Player in Hot Core Chemistry David E. Woon. - PowerPoint PPT PresentationTRANSCRIPT
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.