Application of the hybrid program for fitting microwave and far-infrared spectrum of methyl amine Isabelle Kleinera and Jon T. Hougenb aLISA, Université de Paris Est and CNRS, Créteil, F-94010, France bSensor Science Division, NIST, Gaithersburg, MD 20899, USA

Hybrid program for methylamine-type molecules. What is a “methylamine-like molecule”? = A molecule with 2 Large Amplitude Motions: 1 internal rotation motion (rotatory) 1 back-and-forth motion (oscillatory) Last year: In 2-methyl malonaldehyde (see next slide): Internal rotation = methyl-group rotation Back-and-forth motion = hydrogen-atom transfer This year: In CH3-NH2: Internal rotation = methyl-group rotation Back-and-forth motion = amino-group inversion

Intramolecular hydrogen transfer Internal rotation of a methyl rotor Last year: Two large-amplitude motions in methyl malonaldehyde: Intramolecular hydrogen transfer Internal rotation of a methyl rotor C4 C6 C5 O7 H9 H11 H10 C12 H3 H2 H1 O8 (123)(45)(78)(9,10) Intramolecular hydrogen transfer induces a tautomerization in the ring, which then triggers a 60 degree internal rotation of the methyl rotor. Kleiner and Hougen, JPC 2015

Successful solution of the specific 2-methylmalonaldehyde problem -With the hybrid formalism we fit the 2-MMA-d0 and -d1 fits from Ilyushin et al. JMS (2008) with the same quality -the -OH vs -OD discrepancy has been greatly reduced: V3 values from the old pure tunneling and the new hybrid formalism 2-MMA-OH 2-MMA-OD Diff. Pure tunneling formalism: V3 = 399 cm-1 V3 = 311 cm-1 88 cm-1 Hybrid formalism: V3 = 302 cm-1 V3 = 315.5 cm-1 15 cm-1 .

Why do we need a hybrid program ? Up to now, the rotational levels of methylamine-like molecules have been fit nearly to measurement error by a pure tunneling Hamiltonian formalism*. Its two main deficiencies (which the hybrid program is supposed to fix) are: -It cannot treat vibrational states near or above the top of the barrier to any tunneling motion. -It cannot treat the tunneling components of two different vibrational states at the same time. *N. Ohashi, J. T. Hougen, J. Mol. Spectrosc. 121 (1987) 474-501.

This year : Fit more than one vibrational state simultaneously Try to get a global fit of CH3NH2 rotational levels in the vtorsion = 0 and 1 states with vinversion = 0. Much of this MW and FIR data is already in the literature.

Theoretical approach of the “hybrid” program For internal rotation RAM Hamiltonian of Herbst et al (1984): F(PJz)2 + ½V3(1 cos3), + higher order torsion-rotation terms as found in the BELGI code. For the motion in a double-well potential (-NH2 inversion or H transfer motion), a tunneling formalism, where H = T + V is replaced with one tunneling splitting parameter + higher-order torsion- rotation corrections. ‘s BELGI

Theoretical approach of the “hybrid” program Interaction terms include all G12 group-theoretically allowed products of powers of the basic operators: Torsional motion: Pk, cos3m, sin3n, Back-and-forth motion: P,  Rotational motion: Jxp, Jyq, Jzr e.g., Operators Occur in blocks P2, cos6, Jx2, Jy2, Jz2 LL, RR, LR, RL cos3, (JxJz+JzJx) LL, RR PJy LR, RL ‘s BELGI

Present status of the fit Relatively good fit of vt=0 levels = MW + GS combination differences Lines wrms Weight ______________________________________________________ Pure rot vt = 0-0 FIR lines [1] 360 1.44 0.0007 cm-1 GSCD from FIR 99 1.36 0.0010 cm-1 MW lines [1,2] 1254 8.3 [1] Ohashi et al JMS 1987 and references herein [2] Motyenko et al A&A 2014 and references herein

Fitting vt= 0 and 1 together ….still a problem! _ _________________________________________________ Lines wrms MW A-species 542 13.8 MW E-species 656 23.0 ________________________________________________ Lines rms Weight Pure rot vt = 0-0 FIR lines [1] 351 2.54 0.0007 cm-1 GSCD from FIR 99 0.94 0.0010 cm-1 Vt = 1-0 FIR [1] 411 50.7 0.0006 cm-1 MW lines [1,2] 1198 19.4

Possible reasons for this fitting problem 1) is the hybrid model correct , can it handle this problem??? 2) Missing high order terms in the BELGI type term and/or in the interaction tunneling-internal rotation necessary to fit vt=1-0 3) assignments errors or uncompatibility between vt =0 and 1 in the literature dataset, labeling problems going from the tunneling formalism to the hybrid formalism 4) truncation error due to two step diagonalisation or programming errors

Possible reasons for this fitting problem 2) Simplest possible explanation = not enough terms in H This hybrid program is a new approach, so we lack experience in what to do. We will continue to add terms, but there are some questions: (i) Determinable parameters for this approach have not been investigated. We have been assuming that it is essentially like in Tsunekawa et al paper, where terms with odd n in their nlm scheme can be neglected. Maybe this is not the case. (ii) Higher-order terms involving  and P terms may be more important than we think

Possible reasons for this fitting problem (suite) 3) There could be some unsuspected assignment inconsistency across vt=1, since in the tunneling formalism, the splitting parameters for vt=0 and vt=1 are not connected by a potential energy surface. We are not sure how to begin looking for such a possible inconsistency, since we are not quite sure what it even means. (i) But we will try fitting A,B 1, B2 levels without E1, E2 levels (similar to 1 top fits). (ii) We will try fitting vt=0 and vt=1 separately like the successful pure tunneling fits did and see which parameters change by a suspicious amount

Possible reasons for this fitting problem (suite) 4) There could be some errors in the code. We are constantly checking for these, using a J=6 energy-level program using a one-step diagonalization procedure (easy to program and easy to check).

Conclusions This problem is more difficult than expected We went too fast. Return back to the vt = 0 problem 2) we hope to report if ithe trouble is in the model or in the code in a later meeting

Additional slides

Diagram of Frameworks for the Pure Tunneling Formalism Diagram of Frameworks for the Hybrid Formalism 17

Theoretical Model: the global approach RAM = Rho Axis Method (axis system) for a Cs (plane) frame HRAM = Hrot + Htor + Hint + Hd.c. Torsional operators and potential function V(a) Constants 1 1-cos3a p2a Japa 1-cos6a p4a Jap3a V3/2 F r V6/2 k4 k3 J2 (B+C)/2* Fv Gv Lv Nv Mv k3J Ja2 A-(B+C)/2* k5 k2 k1 K2 K1 k3K Jb2 - Jc2 (B-C)/2* c2 c1 c4 c11 c3 c12 JaJb+JbJa Dab or Eab dab Dab dab6 DDab ddab Rotational Operators Rotational constants give the structure. Using the diagonalization of the inertial tensor, one can get the orientation angles of the CH3 group relative to the PAS = angle of torsion, r = couples internal rotation and global rotation, ratio of the moment of inertia of the top and the moment of inertia of the whole molecule Kirtman et al 1962 Lees and Baker, 1968 Herbst et al 1986 Hougen, Kleiner, Godefroid JMS 1994 18

Methylamine microwave and FIR literature (suite) 1) Microwave Spectrum of Methyl Amine: Assignment and Analysis of the First Torsional State Ohashi, Tsunekawa, Takagi and Hougen, JMS 1989 -add 30 new microwave vt = 1- 1 to the previously assigned -Fit 714 lines with 38 parameters for vt = 1 S = 0.75 MHz for the 216 MW data S = 0.00115 cm-1 for far-infrared pure rotational data vt = 1-1 S = 0.00100 cm-1 for upper state (vt = 1) combination differences from the far-infrared torsional band data 2) Far-Infrared Spectrum of Methyl Amine: Assignment of the Second Torsional State Oda and ohashi, JMS 1989 35 pure rotational transitions in vt = 2- 2 87 transitions vt = 2 -1

Methylamine data set from literature: tunneling formalism - Rotational spectroscopy of methylamine up to 2.6 THz Motiyenko, Ilyushin, Drouin, Yu, and Margulès, A&A 2014 vt = 0, 76 parameters, weighted rms deviation = 0.87, J ≤ 50 and Ka ≤ 20. 2563 MW lines, 96 vt=0 GSCD and 416 pure rotational lines from and FIR spectrum (Ohashi et al 1987) Previous works : Lide 1954; Shimoda et al. 1954; Hirakawa et al. 1956; Nishikawa 1957, Takagi & Kojima 1971, 1973, Kreglewski&Wlodarczak 1992; Ilyushin et al. 2005, Ilyushin & Lovas 2007, Ohashi 1987 …

Methylamine microwave and FIR literature (suite) Far-Infrared Spectrum and Ground State Constants of Methyl Amine, Ohashi, Takagi, Hougen Olson and Lafferty, JMS 1987 40 to 350 cm-1 by BOMEM Fourier transform spectroscopy with an apodized resolution of 0.005 cm-1 526 lines pure rotational spectrum vt = 0 – 0 (precision : 0.0007 cm-1) - 496 lines in fundamental torsional band vt = 1 – 0: cannot treat vt=0 and 1 together so they fit 96 ground state combination differences (precision : 0.0010 cm-1) 1000 energy differences for the ground state vt = 0 with 0 < K < 19 and J < 30 were fit to 30 molecular parameters S= 0.00063 cm-1