1. Reinvestigation of the ground and first torsional states of methylformate M. Carvajal, Universidad of Huelva (Spain) F. Willaert and J. Demaison, Université de Lille (France) I.Kleiner, CNRS, Université Paris 7 et 12 (France)

2. Chemical structure, principal axes and direction of the dipole moment of methyl formate [R. F. Curl, J. Chem. Phys. 30, 1529-1536 (1959)]. The a-b plane is a plane of symmetry

3. Interstellar Detection of Methyl Formate, HC(O)OCH3 Typical hot core molecule. It is very abundant in massive star-forming regions. It was detected first in Sgr B2 by R. D. Brown, J. G. Crofts, P. D. Godfrey, F. F. Gardner, B. J. Robinson, and J. B. Whiteoak, Discovery of Interstellar Methyl Formate Astrophys. J. 197, L29–L31 (1975). Discovery of Interstellar Methyl Formate Also detected toward low-mass star-forming regions: S. Cazaux, A. G. G. M. Tielens, C. Ceccarelli, A. Castets, V. Wakelam, E. Caux, B. Parise, D. Teyssier, The Hot Core around the Low-mass Protostar IRAS 16293-2422: Scoundrels Rule! Astrophys. J. 593, L51–L55 (2003). The Hot Core around the Low-mass Protostar IRAS 16293-2422: Scoundrels Rule! v t = 1 detected in Orion for the first time! K. Kobayashi, K. Ogata, S. Tsunekawa, and S. Takano, Torsionally Excited Methyl Formate in Orion KL Astrophys. J. 657, L17–L19 (2007). Torsionally Excited Methyl Formate in Orion KL

4. -[BRO75] R.D. Brown, J.G. Crofts, F.F. Gardner, P.D. Godfrey, B.J. Robinson, J.B. Whiteoak, Astrophys. J. 197, L29-L31 (1975). -[BAU79] A. Bauder, J. Phys. Chem. Ref. Data 8, 583-618 (1979). -[DEM83] J. Demaison, D. Boucher, A. Dubrulle, B.P. Van Eijck, J. Mol. Spectrosc. 102, 260-263 (1983). -[PLU84] G.M. Plummer, G.A. Blake, E. Herbst, F.C. De Lucia, Astrophys. J. Suppl. 55, 633-656 (1984). -[PLU86] G.M. Plummer, E. Herbst, F.C. De Lucia, G.A. Blake, Astrophys. J. Suppl. 60, 949-961 (1986) -[OES99] L.C. Oesterling, S. Albert, F.C. De Lucia, K.V.L.N. Sastry, E. Herbst, Astrophys. J. 521, 255-260 (1999). PREVIOUS STUDIES

5. [TYAM04] Tsunekawa Lab, Toyama University (Japan) Global Fit of Rotational Transitions of Methyl Formate (HCOOCH3) in the Ground and First Excited Torsional States, K. Ogata, H. Odashima, K. Takagi, and S. Tsunekawa, J. Mol. Spectrosc. 225, 14-32 (2004). RMS = 1.96, 3862 lines, 69 parameters Analysis of Rotational Transitions of Methyl Formate in the Ground and First Excited Torsional States, H. Odashima, K. Ogata,Y. Karakawa, K. Takagi, and S. Tsunekawa, Molecules 8, 139-145 (2003). The Microwave Spectrum of Methyl Formate (HCOOCH3) in the Frequency Range from 7 to 200 GHz, Y. Karakawa, K. Oka, H. Odashima, K.Takagi, and S. Tsunekawa, J. Mol. Spectrosc. 210, 196-212 (2001).

6. OSU FASST MEASUREMENTS A. Maeda, I. Medvedev, E. Herbst, F. De Lucia and P. Groner FASSST spectrometer, ERHAM program Each torsional states is fitted by itself. (whereas in our approach all states are treated simultaneously)

7. Goals of this study were: Further studies of MF are needed because: 1)For astrophysical purposes: his formation mechanism is still not yet understood 2)Detection of torsional excited states informs on the temperature of the medium 3)The 500-600 GHz spectral range : interest for astronomers because the radiotelescopes in development (HERSCHEL, ALMA, SOFIA) will operate in this sub-millimeterwave range (and up to the FIR range)  accurate predictions (extended at high J and K) for methyl formate are needed 4) Even though the MW spectrum of MF is complex and dense, it is a rather small and well adapted to perform high level quantum chemical calculations.  “test” molecule to validate ab initio [Senent et al, 2005] and Density Functional Theory calculations by comparing them with experimental results (no precise equilibrium structure and barrier height calculated yet) : study in progress

8. NEW MEASUREMENTS FROM LILLE 567-669 GHz, accuracy 50 kHz 434 lines J up 62, K up to 22 (TYAM goes up to J = 40, K = 17) CHALLENGES -a relatively small rotational A constant (almost 0.6 cm -1 )  observation of very high J values (up to 70) -2 non-zero components of the dipole moment  both a-type and b-type transitions observed (  a = 1.63 Debye and  b = 0.68 Debye) -3 low frequencies modes: ( t = 130 cm -1, COC bending mode 12 = 318 cm -1, out-of-plane bending mode 17 = 332 cm -1 )  observation of rotational transitions within those levels populated at room temperature.  perturbations?

9. -A fairly asymmetric top (  = - 0.78 ) combined with an internal rotation methyl top V 3 ≈ 371 cm -1, F ≈ 5.49 cm -1 - clustering of the transitions with the same K c quantum number for high J, low K a values. -a rather large number of torsionally dependent contributions to this term of the form P  2 (P b 2 -P c 2 ), cos3  (P b 2 -P c 2 ) …. -a small  =0.084 parameter : F(P  –  P a ) 2 : same labeling scheme as for acetic acid the +K a E-species levels belonging to even values of v t lie below the ‑ K a levels, and the +K a E species levels belonging to odd values of v t lie above the ‑ K a levels for all values of |K a | from 1 to 18.

10. RHO AXIS METHOD Kirtman (1962), Lees and Baker (1968), Herbst et al (1984) Takes its name from the choice of axis system: related to the PAM by a rotation of an angle  RAM to eliminate the -2Fp   x J x and -2Fp   y J y terms. The new « z RAM » axis is along the  vector (  x =  y = 0) Advantages: H tor = F(P  2 –  J z ) + V(  ) is diagonal in K, can be diagonalized first Then H rot and H int can be diagonalized H int= P  2 P 2, P  2 P a 2, cos(3  )P 2, cos(3  )P a 2 (P b 2 -P c 2 )Cos(3  ), (P b 2 -P c 2 )P  2 (P a P b +P b P a ) sin3 

11. 0.116 MHz 0.148 MHz 69 Present Ogata et al 3862

12. EXEMPLES OF BAD « CD-LOOPS »

14. Rotational constants in the RHO axis system (RAM) and in the principal axis system (PAM). Angles between the principal axis and the methyl top axis. RAMPAMPAM a A(MHz)17640.091019939.530419848.5032 B(MHz)9240.96766954.44837006.1251 C(MHz) D ab (MHz) 5309.8769 -4945.9580 5309.8769 0.0 5351.3017 0.0 <(i,a)52.98958.568 <(i,b)37.01131.432 <(i,c)90.000  RAM 24.83 a a Calculation of the principal axis rotational constants from the molecular structure (MP2/VTZ) and of the angles in degrees between the principal axis (a,b,c) and the methyl top axis (i).

15. Intensity calculations: Dipole moment components in Debye in the principal axis system (PAM) and in the RHO axis system (RAM). RAMPAM a aa +1.765+1.63 bb -0.067+0.68 A Experimental value from A. Bauder, J. Phys. Chem. Ref. Data 8, 583-618 (1979).

17. Conclusions: Our global RAM fit represents some improvement over past studies but -a number of previously published lines show bad observed-calculated values. inadequate combination differences ( i.e. violate a “CD loop criterion”). Of all the “loops” checked, 12% of them (corresponding to 1747 energy levels) show indeed combination differences exceeding about 0.4 MHz. New experimental recordings are needed before trying to fit/predict at higher J !!! -no direct measurement of the torsional frequency  a strong correlation between F and V 3

18. nlmOperatorParamer Present Work 220 (1-cos 3  )/2 V3V3 370.924(113) 404- P  DJDJ 0.00000042854(455) PP F 5.49038(129) - P  P a 2 D JK -0.0000019285(527) 211P PaP Pa  0.08427127(723) -P a 4 DKDK 0.0000036534(594) 202Pa2Pa2 A RAM 0.5884101(188) -2 P  (P b  - P c  ) JJ 0.00000017990(227) Pb2Pb2 B RAM 0.3082455(179) -{P a 2,(P b  - P c  )}  0.00000028824(900) Pc2Pc2 C RAM 0.17711843(416) (P a 3 P b + P b P a 3 )D ab 0.0000020747(108) (P a P b + P b P a )D ab -0.1649794(162) 642 (1-cos 6  ) P  NvNv -0.0000507(127) 440PP k4k4 0.0004368(184) (1-cos 6  )(P b  - P c   c 11 -0.0014751(202) (1-cos 6  )/2 V6V6 23.9018(636) 2 P   (P b  - P c   c3c3 0.00000045962(750) 431PgPaPgPa k3k3 -0.00012758(711) 624 (1-cos 3  ) P  fvfv 0.00000009957(441) 422PgPPgP GvGv 0.000002709(432) (1-cos 3  ) (P b  - P c  ) P  c 2J 0.00000005483(445)

19. 2P   (P b  - P c  )c1c1 0.000018117(264) (1-cos 3  ){P a 2, (P b  - P c  )} c 2K 0.00000024458(404) sin3  (P a P c + P c P a ) D ac -0.0068896(540) 2P    P    P    P  c 1J 0.0000000017386(211) (1-cos 3  ) P  FvFv -0.0025827(184) (1-cos 3  ) (P a P b + P b P a ) P  d abJ -0.00000012488(883) (1-cos 3  ) P a 2 k5k5 0.0112949(386) (1-cos 3  ) (P a 3 P b + P b P a 3 ) d abK 0.00000019649(625) (1-cos 3  )(P b  - P c  ) c2c2 0.0012608(253) (1-cos 3  ) P a 2 P  k 5J -0.0000005853(125) (1-cos 3  )(P a P b + P b P a ) d ab -0.0063031(176) 633PP PaPP Pa k 3J 0.00000007061(198) PgPa2PgPa2 k2k2 -0.00002837(166) PPa3PPa3 k 3K -0.00000008230(461) P g   (P a P b + P b P a )  ab -0.000008874(434) P   {P a, (P b  - P c  )}c 12 -0.00000006946(110) 413P  P a P  LvLv 0.000003932(110) P   {P a , P b }  ab -0.000000061998(808) P g P a 3 k1k1 -0.000000596(279) 606PP HJHJ 0.000000000000333(35) P  {P a,(P b  - P c  )}c4c4 0.0000001100(561) P Pa2P Pa2 H JK 0.000000000015998(570)

20. P  {P a  , P b } bb -0.000010141(145) P  P a 4 H KJ -0.00000000007620(187) Pa6Pa6 HKHK 0.00000000009098(281) 826 (1-cos 3  ) (P b  - P c  ) P  c 2JJ 0.000000000001746(201) 844 2 P   (P b  - P c   P  c 3J -0.000000000029116(514) N d 4270 (J max = 62) s es e 1.43 (49 Parameters)

21. Ab Initio Study of the Rotational-Torsional Spectrum of Methyl Formate M. L. Senent, M. Villa, F. J. Meléndez, and R. Domínguez-Gómez The Astrophysical Journal, volume 627, part 1 (2005), pages 567–576

22. Methyl formate and laboratory measurement. Large amount found in Orion molecular cloud and recent researches have revealed that this molecule exists in the early stage of star-formation. The tsunekawa group reports the first observation of methyl formate in torsionally excited state (20 lines assigned around 97 GHz with Nobeyama 45 m radio telescope). Torsional motion requires higher energy and it indicates that the observed region is warmer. FROM: http://www.sci.u-toyama.ac.jp/phys/4ken/press/detailEN.html