Molecular Spectroscopy Symposium 2009 22-26 June 2009 The Submillimeter Spectrum of the Ground Torsional State of CH 2 DOH J.C. PEARSON, C.S. BRAUER, S

Molecular Spectroscopy Symposium 2009 22-26 June 2009

The Submillimeter Spectrum of the Ground Torsional State of CH2DOH

J.C. PEARSON, C.S. BRAUER, S. YU and B.J. DROUINJ.C. PEARSON, C.S. BRAUER, S. YU and B.J. DROUIN

Jet Propulsion Laboratory, California Institute of Jet Propulsion Laboratory, California Institute of

Technology, 4800 Oak Grove Dr, Pasadena, CA 91109Technology, 4800 Oak Grove Dr, Pasadena, CA 91109

2Molecular Spectroscopy Symposium 2009 22-26 June 2009

Why CHWhy CH22DOH When CHDOH When CH33OH Is Hard Enough?OH Is Hard Enough?

CH2DOH was first discovered in the ISM by Jacq et al., 1993, A&A 271, 276

Methanol in the ISM is known to be made on grains

– Gas phase chemistry cannot reproduce observed abundance (Geppert et al., 2006, Faraday Discuss 133, 177)

On grain surface D is efficiently incorporated in the Methyl group (Nagaoka et al., 2005, ApJ 624, L29 & Nagaoka et al., 2007, J. Phys. Chem. A 111, 3016)

– Cold ISM conditions makes CH2DOH, CD2HOH and CD3OH (Parise et al., 2002, A&A 393, L49 & Parise et al., 2004, A&A 416, 159)

– CD3OH was observed to be ~1% of methanol column in IRAS 16293 (Parise et al., 2004, A&A 416,159)

CH2DOH is potentially an excellent tracer of star formation history and cold ISM material processing (Parise et al., 2006, A&A 453, 949)

– It is believed that D enriched species on grain surface evaporate first once star formation starts

– Correctly interpreting observational data requires frequencies, partition functions and line strengths


Asymmetric Internal RotationAsymmetric Internal Rotation

C3V symmetry is broken by D in Methyl Group

– CS is the only symmetry

Torsional wave functions A’ or even and A” or odd upon inversion Rotational wave functions are also ‘+’ and ‘-’

A, E1, E2 in C3V becomes e0, e1 and o1 where each is an asymmetric top

– Interactions are allowed under the CS group

– Same symmetry interactions are c-symmetry or x-symmetry

– Opposite symmetry interaction are a-symmetry or b-symmetry

– Every torsional m state is allowed to interact with all others Avoided crossing torsional cusps between all wave functions

– A state in C3V maps to unpaired number of nodes in asymmetric case

Selection rules become

– Same symmetry transitions are a-type and b-type

– Different symmetry transitions are c-type

– All are allowed and observed and many are very strong


CH2DOH Barrier

0

100

200

300

400

500

0 100 200 300

Torsional Angle

cm

-1

The result is a trans (e0), a gauche+ (e1) and a gauche- (o1)ground state with Cs symmetry about 0 degrees (trans D)

Barrier With D-In-Plane Global MinimumBarrier With D-In-Plane Global Minimum


Symmetry Cs Group either DCO plane or COH planeSelection rules:

e to e a- or b-typeo to o a- or b-typee to o c- or x-typeo to e c- or x-type

(x is Ka=0,2,4... & Kc=0,2,4...)

OC

H

HH

D

CCSS Selection Rules Selection Rules


CC3V3V to C to CSS Torsional Wave Functions Torsional Wave Functions

C3V Internal rotation

-1.5

-1

-0.5

0

0.5

1

1.5

0 5 10 15 20 25

K value

Rel

ativ

e T

ors

ion

co

ntr

ibu

tio

n

A state

E1 state

E2 State

Asymmetric Internal Rotation

-1.5

-1

-0.5

0

0.5

1

1.5

0 5 10 15 20 25

K value

Rel

ativ

e T

ors

ion

Co

ntr

ibu

tio

n

e0

e1

o1

All torsional m states interact resulting in avoided crossing within each torsionalState grouping as well as between each torsional grouping

Avoided crossing cusp occur regularly


Level OrderingLevel Ordering

Breaking the C3V symmetry does make level ordering easier

– Ordering for a given K is e0, e1 and o1 in increasing energy

– This will apply to excited states as well

Reduced Enengy Levels

0

2

4

6

8

10

12

14

16

18

0 1 2 3 4 5 6 7 8

K

cm-1

Derived Levels

e0

e1

o1


Low KLow Kaa Levels Levels

ch2doh low K levels

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

0 5 10 15 20 25 30

J

Re

lati

ve

En

erg

y

e0 k=0

e0 k=1 lower

e0 k=1 upper

e0 k=2 lower

e0 k=2 upper

e1 k=0

e1 k=1 lower

e1 k=1 upper

e1 k=2 lower

e1 k=2 upper

o1 k=0

o1 k=1 lower

o1 k=1 upper

o1 k=2 lower

o1 k=2 upper

e0 k=3 lower


Extra Transitions and D Spin EffectsExtra Transitions and D Spin Effects

3 3

4

4 55 6

K=3 o1 to K=2 e1 Q branch c-type

53,3 e1- 52,4 e0

J2,J-1

J2,J-2

J3,J-2

J3,J-3

Like E-statemixing in C3V


Spectra near 0.9 THzSpectra near 0.9 THz

1

23

1=e0 K=6-52=o1 K=5 to e1 K=43=e1 K=6-5


Data SetData Set

Literature data most below 120 GHz– Accuracy 10-200 kHz

FTMW from U. of A below 12 GHz– Better than 10kHz resolved D splitting

A few unassigned Stark lines from NIST to 120 GHz– 50-200kHz

FASSST spectra 129-172, 180-360– 200 kHz

JPL spectrum from 75-92, 172-180, spots between 247 and 400, 400-730, 780-930, 968-1050, 1060-1200, 1218-1226, 1580-1625 GHz– 50-150 kHz

Approximately 6500 lines assigned to J=40 Ka=8,9,8 – Transitions within and between all states

– A-type e0-e1 are weak as expected

– Some b- and c-type branches are weak both between and within states

Higher Ka lines K=4 or more are well modeled by power series in J(J+1) and asymmetry if present

12Molecular Spectroscopy Symposium 2009 22-26 June 2009Columbus 2000 #6

Barrier to Internal RotationBarrier to Internal Rotation

Splitting at K=0 is not a good indication of barrier height

– Torsional wave functions in e1 and o1 are at “cusp”

Barrier is determined by average splitting between e1 and o1

– Average energy difference is 5.4 cm-1

– Difference at K=0 is 3.397171

Parameters used in eyeball fit– E0=5.387 cm-1

– E1=1.99 cm-1

– Rho=0.152

Pure Cosine series does not account for interactions between states

o1-e1 energy

0

1

2

3

4

5

6

7

8

0 2 4 6 8 10

K

cm-1 o1-e1

E0-E1cos(2*pi*rho*k)


Assignment TechniqueAssignment Technique

Step 1 assign aR branches by identifying K origin

– Does not assign torsional state

Step 2 identify Q branches connecting R-branches

– Create ladders to e0 J=0

– Apply selection rules for asymmetry split lines

Step 3a identify b- and c-type P and R branches

– 9 possibilities for b- and c-type with same Ka’s

Step 3b identify any weaker lines K=2,3 e0-e1 a-types etc….

Step 4a fit with “empirical” IAM at low K

– Issues with correlation of K constants

Step 4b fit with power series to identify blends, typos etc..

– Including 2x2 for level crossings

Step 5 fit with improved IAM (in work)

Step 6 properly rotate dipole to account for D in e0

– Use in IAM finder for approximate geometric projections

Step 7 repeat for excited torsional state


Based on procedure proposed by H. Pickett, 1997, J. Chem. Phys. 107, 6732.

H=pTGp-pTGCTP-PTCGp+PTCGCTP+PTmP+V

– p = Vibrational Angular momentum vector (N)

– P = Rotational Angular momentum vector

– G = Inverse mass of vibration (N by N matrix)

– C = Vibrational Angular momentum coupling (3 by N)

– m = Inverse moment of Inertia tensor

– V = Sum of potential and psudopotential terms

Internal Axis System Approach:

– Successive rotations until Cz is not a function of torsion and Cx and Cy are zero

Fit constants and empirically add higher order terms

– No true methanol like Hamiltonian

IAM CalculationsIAM Calculations


IAM AnalysisIAM Analysis

Matthieu Equation Solver “IAMCALC” starts with methanol structure including best guess at torsional path

Takes Fourier Series from “MOIAM”– Solves H=(p-K)F(p-K)+V in a free rotor basis set exp(im)

Generates “Rotational” Hamiltonian– Ev, Ev*C, Av-(Bv+Cv)/2, Av-(Bv+Cv)/2*C, (Bv+Cv)/2, (Bv+Cv)/2*C,

– (Bv-Cv)/4, (Bv-Cv)/4*C, Dvab, Dvab*C,

Generates interaction Hamiltonian– Av”v’-(Bv”v’+Cv”v’)/2*(C or S), (Bv”v’+Cv”v’)/2*(C or S),

– (Bv”v’-Cv”v’)/4*(C or S), Dv”v’ab*(C or S), Dv”v’ac (S or C),

– Dv”v’bc (S or C)

C is cos(2N(K)/3), S is sin(2N(K)/3)

C is even under CS, S is odd under CS

Generates dipole parameters for a, b and c components assuming components fixed in frame and top


Remaining WorkRemaining Work

Understand line shapes

– Extra b-type or c-type transition (like extra E state lines in C3V)

Complete D nuclear coupling analysis

– Possible to resolve in some pre-stellar cores

Complete IAM analysis

– Verify assignments to higher J (more than 26)

Complete dipole analysis

– Compare with observed intensities

Attempt to transfer to excited torsional states

– Torsional effects much larger


Acknowledgements

Support for this work, part of the NASA Herschel Science Center Theoretical Research/Laboratory Astrophysics Program, was provided by NASA through a contract issued by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA."

This work was performed at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration

Thanks to Frank De Lucia and Rebecca Harlan for FASSST surveys taken at OSU

Thanks to Richard Suenram for his Stark data.

Thanks to Stephen Kukolich for use of his FTMW system

Thanks to Herb Pickett for numerous useful discussion on internal rotation

Documents

Molecular Spectroscopy Symposium 2009 22-26 June 2009 The Submillimeter Spectrum of the Ground Torsional State of CH 2 DOH J.C. PEARSON, C.S. BRAUER, S