Molecular Spectroscopy Symposium June 2009 The Submillimeter Spectrum of the Ground Torsional State of CH 2 DOH J.C. PEARSON, C.S. BRAUER, S. YU and B.J. DROUIN Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Dr, Pasadena, CA 91109

2 Molecular Spectroscopy Symposium June 2009 Why CH 2 DOH When CH 3 OH Is Hard Enough? CH 2 DOH 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 CH 2 DOH, CD 2 HOH and CD 3 OH (Parise et al., 2002, A&A 393, L49 & Parise et al., 2004, A&A 416, 159) –CD 3 OH was observed to be ~1% of methanol column in IRAS (Parise et al., 2004, A&A 416,159) CH 2 DOH 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

3 Molecular Spectroscopy Symposium June 2009 Asymmetric Internal Rotation C 3V symmetry is broken by D in Methyl Group –C S 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 C 3V becomes e 0, e 1 and o 1 where each is an asymmetric top –Interactions are allowed under the C S 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 C 3V 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

4 Molecular Spectroscopy Symposium June 2009 The result is a trans (e 0 ), a gauche+ (e 1 ) and a gauche- (o 1 ) ground state with C s symmetry about 0 degrees (trans D) Barrier With D-In-Plane Global Minimum

5 Molecular Spectroscopy Symposium June 2009 Symmetry Cs Group either DCO plane or COH plane Selection rules: e to e a- or b-type o to o a- or b-type e to o c- or x-type o to e c- or x-type (x is  K a =0,2,4... &  K c =0,2,4...) OC H H H D C S Selection Rules

6 Molecular Spectroscopy Symposium June 2009 C 3V to C S Torsional Wave Functions All torsional m states interact resulting in avoided crossing within each torsional State grouping as well as between each torsional grouping Avoided crossing cusp occur regularly

7 Molecular Spectroscopy Symposium June 2009 Level Ordering Breaking the C 3V symmetry does make level ordering easier –Ordering for a given K is e 0, e 1 and o 1 in increasing energy –This will apply to excited states as well e0e0 e1e1 o1o1

8 Molecular Spectroscopy Symposium June 2009 Low K a Levels

9 Molecular Spectroscopy Symposium June 2009 Extra Transitions and D Spin Effects K=3 o 1 to K=2 e 1 Q branch c-type 5 3,3 e ,4 e 0 J 2,J-1 J 2,J-2 J 3,J-2 J 3,J-3 Like E-state mixing in C 3V

10 Molecular Spectroscopy Symposium June 2009 Spectra near 0.9 THz =e 0 K=6-5 2=o 1 K=5 to e 1 K=4 3=e 1 K=6-5

11 Molecular Spectroscopy Symposium June 2009 Data Set Literature data most below 120 GHz –Accuracy 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 , –200 kHz JPL spectrum from 75-92, , spots between 247 and 400, , , , , , GHz – 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

12 Molecular Spectroscopy Symposium June 2009 Columbus 2000 #6 Barrier 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 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

13 Molecular Spectroscopy Symposium June 2009 Assignment Technique Step 1 assign a R branches by identifying K origin –Does not assign torsional state Step 2 identify Q branches connecting R-branches –Create ladders to e 0 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 K a ’s Step 3b identify any weaker lines  K=2,3 e 0 -e 1 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 e 0 –Use in IAM finder for approximate geometric projections Step 7 repeat for excited torsional state

14 Molecular Spectroscopy Symposium June 2009 Based on procedure proposed by H. Pickett, 1997, J. Chem. Phys. 107, H=p T Gp-p T GC T P-P T CGp+P T CGC T P+P T mP+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 Calculations

15 Molecular Spectroscopy Symposium June 2009 IAM 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 C S, S is odd under C S Generates dipole parameters for a, b and c components assuming components fixed in frame and top

16 Molecular Spectroscopy Symposium June 2009 Remaining Work Understand line shapes –Extra b-type or c-type transition (like extra E state lines in C 3V ) 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

17 Molecular Spectroscopy Symposium June 2009 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