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)

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

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 FormateAstrophys. J. 197, L29–L31 (1975).

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).

vt = 1 detected in Orion for the first time!K. Kobayashi, K. Ogata, S. Tsunekawa, and S. Takano,

Torsionally Excited Methyl Formate in Orion KLAstrophys. J. 657, L17–L19 (2007).

-[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

[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).

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)

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

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?

-A fairly asymmetric top ( = - 0.78 ) combined with an internal rotation methyl top

V3 ≈ 371 cm-1 , F ≈ 5.49 cm-1

-clustering of the transitions with the same Kc quantum number for high J, low Ka values.

-a rather large number of torsionally dependent contributions to this term of the form

P2(Pb

2-Pc2), cos3 (Pb

2-Pc2) ….

-a small =0.084 parameter : F(P – Pa)2 : same labeling scheme as for acetic acid

the +Ka E-species levels belonging to even values of vt lie below the ‑Ka levels, and the +Ka E species levels belonging to odd values of vt lie above the ‑Ka levels for all values of |Ka| from 1 to 18.

RHO AXIS METHODKirtman (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 -2FpxJx and -2FpyJy terms.

The new « z RAM » axis is along the vector (x = y = 0)

Advantages:

Htor = F(P2 –Jz) + V() is diagonal in K, can be diagonalized first

Then

Hrot and Hint can be diagonalized

Hint= P2P2, P

2Pa2, cos(3)P2, cos(3)Pa

2 (Pb

2-Pc2)Cos(3), (Pb

2-Pc2)P

2

(PaPb+PbPa) sin3

Table 1. Root-Mean-Square (rms) Deviations From the Global Fita of Transitions Involving vt = 0 and 1 Torsional Energy Levels of Methylformate (H12COOCH3).

Number of parameters 49

Number of lines 4270

rms of the 3496 MW vt=0-0 lines 0.0940 MHz

rms of the 774 MW vt=1-1 lines 0.0836 MHz

rms of the 2181 A symmetry lines 0.0906 MHz

rms of the 2089 E symmetry lines 0.0939 MHz

Sourceb Rangec (GHz) vt, Jmax, Kmaxd Number of linese Uncertaintiesf (MHz) rmsg (MHz)

Brown around 1.6 0,1,1 2 0.003 0.0029

Bauder 8-58 0,40,10 51 0.020 0.0267

LILLE PluE PluA DeMa TYAM

567-669 200-352 216-506 150-313 7-200

0,62,22 0,30,15 0,40,18 0,28,12 0,40,17

1,18,7

434 147 97 44 2591

0.050h

0.0778

TYAM 7-200

7

Oest 250-510 0,43,18 897 0.200i 0.1340

0.116 MHz

0.148 MHz

69

Present Ogata et al

3862

7 4- 86210.149000 1050 6 4-

one path 86210.149

7 4- -124272.418000 1050 7 5+ 7 5+ 86029.804000 1250 6 5+ 6 5+ 124453.104000 1050 6 4-

another path 86210.490

residual of the loop= 0.341 MHz

8 4- 193802.722000 1050 7 3- 7 3- -8910.032000 1020 6 4-

one path 184892.690

8 4- -124022.550000 1050 8 5+ 8 5+ 98432.916000 1050 7 5+ 7 5+ 86029.804000 1250 6 5+ 6 5+ 124453.104000 1050 6 4-

another path 184893.274

residual of the loop= 0.584 MHz

EXEMPLES OF BAD « CD-LOOPS »

9 3+ 110887.060000 1050 8 3+ 8 3+ 98611.212000 1050 7 3+

one path 209498.272

9 3+ 79432.518000 1050 9 2- 9 2- 124838.325000 1050 8 1- 8 1- -38975.936000 1050 8 2+ 8 2+ 44202.818000 1050 7 3+

another path 209497.725

residual of the loop= 0.547 MHz

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.

RAM PAM PAMa

A(MHz) 17640.0910 19939.5304 19848.5032

B(MHz) 9240.9676 6954.4483 7006.1251

C(MHz)Dab(MHz)

5309.8769-4945.9580

5309.87690.0

5351.30170.0

<(i,a) 52.989 58.568

<(i,b) 37.011 31.432

<(i,c) 90.000 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).

Intensity calculations: Dipole moment components in Debye in the principal axis system (PAM) and in the RHO axis system (RAM).

RAM PAMa

a +1.765 +1.63

b -0.067 +0.68

A Experimental value from A. Bauder, J. Phys. Chem. Ref. Data 8, 583-618 (1979).

PAMb

a

RAMRAM

RAMRAM

RAMb

a

)cos()sin(

)sin()cos(

0 13 12 2 - 0 12 12 1 - 159524.527 159524.498 0.050 0.029 0.941545E-06 174.6104 169.2893 TYAM 0 14 12 3 - 0 13 12 2 - 171847.894 171847.888 0.050 0.006 0.415686E-03 180.3427 174.6104 TYAM 0 15 12 4 - 0 14 12 3 - 184182.917 184182.863 0.050 0.054 0.142133E+02 186.4863 180.3427 TYAM 0 16 12 5 - 0 15 12 4 - 196530.329 196530.253 0.050 0.076 0.169486E+02 193.0419 186.4863 TYAM 0 17 12 6 - 0 16 12 5 - 0.000 208890.891 0.000 0.000 0.121638E+02 200.0097 193.0419 PRED 0 18 12 7 - 0 17 12 6 - 0.000 221265.618 0.000 0.000 0.218135E+02 207.3904 200.0097 PRED 0 19 12 8 - 0 18 12 7 - 0.000 233655.287 0.000 0.000 0.300867E+02 215.1843 207.3904 PRED 0 20 12 9 - 0 19 12 8 - 0.000 246060.762 0.000 0.000 0.340316E+02 223.3920 215.1843 PRED 0 21 12 10 - 0 20 12 9 - 258482.908 258482.928 0.100 -0.020 0.376121E+02 232.0140 223.3920 Oest 0 22 12 11 - 0 21 12 10 - 270922.873 270922.686 0.100 0.187 0.411140E+02 241.0510 232.0140 Oest 0 23 12 12 - 0 22 12 11 - 283381.081 283380.968 0.100 0.113 0.445385E+02 250.5036 241.0510 Oest 0 24 12 13 - 0 23 12 12 - 295858.682 295858.734 0.100 -0.052 0.479014E+02 260.3724 250.5036 Oest 0 25 12 14 - 0 24 12 13 - 0.000 308356.984 0.000 0.000 0.512101E+02 270.6581 260.3724 PRED 0 26 12 15 - 0 25 12 14 - 0.000 320876.762 0.000 0.000 0.544712E+02 281.3614 270.6581 PRED 0 27 12 16 - 0 26 12 15 - 0.000 333419.167 0.000 0.000 0.576901E+02 292.4830 281.3614 PRED 0 28 12 17 - 0 27 12 16 - 0.000 345985.358 0.000 0.000 0.608715E+02 304.0239 292.4830 PRED 0 29 12 18 - 0 28 12 17 - 0.000 358576.569 0.000 0.000 0.640196E+02 315.9847 304.0239 PRED 0 30 12 19 - 0 29 12 18 - 0.000 371194.117 0.000 0.000 0.671377E+02 328.3664 315.9847 PRED 0 31 12 20 - 0 30 12 19 - 0.000 383839.413 0.000 0.000 0.702291E+02 341.1699 328.3664 PRED 0 32 12 21 - 0 31 12 20 - 0.000 396513.974 0.000 0.000 0.732964E+02 354.3962 341.1699 PRED 0 33 12 22 - 0 32 12 21 - 0.000 409219.426 0.000 0.000 0.763419E+02 368.0463 354.3962 PRED 0 34 12 23 - 0 33 12 22 - 0.000 421957.507 0.000 0.000 0.793679E+02 382.1213 368.0463 PRED 0 35 12 24 - 0 34 12 23 - 0.000 434730.049 0.000 0.000 0.823760E+02 396.6223 382.1213 PRED 0 36 12 25 - 0 35 12 24 - 0.000 447538.947 0.000 0.000 0.853681E+02 411.5506 396.6223 PRED 0 37 12 26 - 0 36 12 25 - 0.000 460386.084 0.000 0.000 0.883455E+02 426.9074 411.5506 PRED 0 38 12 27 - 0 37 12 26 - 473273.027 473273.222 0.100 -0.195 0.913096E+02 442.6941 426.9074 Oest 0 39 12 28 - 0 38 12 27 - 486201.663 486201.802 0.100 -0.139 0.942615E+02 458.9121 442.6941 Oest 0 40 12 29 - 0 39 12 28 - 499172.684 499172.675 0.100 0.009 0.972024E+02 475.5627 458.9121 Oest 0 41 12 30 - 0 40 12 29 - 0.000 512185.700 0.000 0.000 0.100133E+03 492.6473 475.5627 PRED 0 42 12 31 - 0 41 12 30 - 0.000 525239.232 0.000 0.000 0.103055E+03 510.1674 492.6473 PRED 0 43 12 32 - 0 42 12 31 - 0.000 538329.474 0.000 0.000 0.105967E+03 528.1242 510.1674 PRED 0 44 12 33 - 0 43 12 32 - 0.000 551449.747 0.000 0.000 0.108872E+03 546.5186 528.1242 PRED 0 45 12 34 - 0 44 12 33 - 0.000 564589.729 0.000 0.000 0.111769E+03 565.3513 546.5186 PRED 0 46 12 35 - 0 45 12 34 - 577734.850 577734.801 0.050 0.049 0.114658E+03 584.6224 565.3513 NEW 0 47 12 36 - 0 46 12 35 - 590865.664 590865.627 0.050 0.037 0.117540E+03 604.3316 584.6224 NEW 0 48 12 37 - 0 47 12 36 - 0.000 603958.161 0.000 0.000 0.120413E+03 624.4774 604.3316 PRED 0 49 12 38 - 0 48 12 37 - 0.000 616984.199 0.000 0.000 0.123277E+03 645.0578 624.4774 PRED 0 50 12 39 - 0 49 12 38 - 0.000 629912.548 0.000 0.000 0.126131E+03 666.0694 645.0578 PRED 0 51 12 40 - 0 50 12 39 - 642710.706 642710.759 0.050 -0.053 0.128973E+03 687.5080 666.0694 NEW 0 52 12 41 - 0 51 12 40 - 0.000 655347.248 0.000 0.000 0.131802E+03 709.3680 687.5080 PRED 0 53 12 42 - 0 52 12 41 - 0.000 667793.567 0.000 0.000 0.134616E+03 731.6432 709.3680 PRED 0 54 12 43 - 0 53 12 42 - 0.000 680026.517 0.000 0.000 0.137415E+03 754.3264 731.6432 PRED 0 55 12 44 - 0 54 12 43 - 0.000 692029.857 0.000 0.000 0.140199E+03 777.4101 754.3264 PRED 0 56 12 45 - 0 55 12 44 - 0.000 703795.428 0.000 0.000 0.142967E+03 800.8862 777.4101 PRED 0 57 12 46 - 0 56 12 45 - 0.000 715323.554 0.000 0.000 0.145721E+03 824.7468 800.8862 PRED 0 58 12 47 - 0 57 12 46 - 0.000 726622.776 0.000 0.000 0.148463E+03 848.9843 824.7468 PRED 0 59 12 48 - 0 58 12 47 - 0.000 737708.661 0.000 0.000 0.151196E+03 873.5916 848.9843 PRED 0 60 12 49 - 0 59 12 48 - 0.000 748602.639 0.000 0.000 0.153923E+03 898.5623 873.5916 PRED

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 V3

• nlm Operator

Paramer

Present Work

220 (1-cos 3)/2 V3 370.924(113) 404 - P DJ 0.00000042854(455)

P F 5.49038(129) - PPa

2 DJK -0.0000019285(527)

211 PPa 0.08427127(723) -Pa4 DK 0.0000036534(594)

202 Pa2 ARAM 0.5884101(188) -2 P (Pb

- Pc) J 0.00000017990(227)

Pb2 BRAM 0.3082455(179) -{Pa

2 ,(Pb

- Pc)} 0.00000028824(900)

Pc2 CRAM 0.17711843(416) (Pa

3 Pb + Pb Pa3 ) Dab 0.0000020747(108)

(Pa Pb + Pb Pa) Dab -0.1649794(162) 642

(1-cos 6) P

Nv -0.0000507(127)

440 P k4 0.0004368(184) (1-cos 6)(Pb

- Pc c11 -0.0014751(202)

(1-cos 6)/2 V6 23.9018(636) 2 P(Pb

- Pc c3 0.00000045962(750)

431 PPa k3 -0.00012758(711) 624 (1-cos 3) P fv 0.00000009957(441)

422 PP Gv 0.000002709(432) (1-cos 3) (Pb

- Pc) P c2J 0.00000005483(445)

2P(Pb

- Pc) c1 0.000018117(264) (1-cos 3){Pa

2 , (Pb

- Pc)} c2K 0.00000024458(404)

sin3(Pa Pc + Pc Pa) Dac -0.0068896(540) 2PP

PP c1J

0.0000000017386(211)

(1-cos 3) P Fv -0.0025827(184) (1-cos 3) (Pa Pb + Pb Pa) P dabJ -0.00000012488(883)

(1-cos 3) Pa2 k5 0.0112949(386)

(1-cos 3) (Pa3 Pb + Pb Pa

3 )

dabK 0.00000019649(625)

(1-cos 3)(Pb- Pc

) c2 0.0012608(253) (1-cos 3) Pa2P k5J -0.0000005853(125)

(1-cos 3)(Pa Pb + Pb Pa) dab -0.0063031(176) 633 PPPa k3J 0.00000007061(198)

PPa

2 k2 -0.00002837(166) PPa

3 k3K -0.00000008230(461)

P(Pa Pb + Pb Pa)

ab -0.000008874(434) P{Pa , (Pb

- Pc)} c12 -0.00000006946(110)

413 PPa P Lv 0.000003932(110) P

{Pa , Pb} ab -0.000000061998(808)

PPa3 k1 -0.000000596(279) 606 P HJ

0.000000000000333(35)

P{Pa ,(Pb- Pc

)} c4 0.0000001100(561) PPa2 HJK

0.000000000015998(570)

P{Pa, Pb} b -0.000010141(145) PPa

4 HKJ

-0.00000000007620(187)

Pa6 HK

0.00000000009098(281)

826 (1-cos 3) (Pb

- Pc) P c2JJ

0.000000000001746(201)

844 2 P

(Pb- Pc

P c3J

-0.000000000029116(514)

N d

4270 (Jmax = 62)

s e

1.43 (49 Parameters)

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

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