Isabelle Kleinera and Jon T. Hougenb COMPETITION BETWEEN TWO LARGE-AMPLITUDE MOTION MODELS: NEW HYBRID HAMILTONIAN VERSUS OLD PURE-TUNNELING HAMILTONIAN 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) 2015: In 2-methyl malonaldehyde: Internal rotation = methyl-group rotation Back-and-forth motion = hydrogen-atom transfer Kleiner and Hougen JPC 2015 2016: In CH3-NH2: Internal rotation = methyl-group rotation Back-and-forth motion = amino-group inversion

Intramolecular hydrogen transfer Internal rotation of a methyl rotor 2015: 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

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 traditional tunneling Hamiltonian formalism*. Its two main deficiencies (which the hybrid program is supposed to fix) are: -It cannot treat torsional states near or above the top of the barrier. -It cannot treat the tunneling components of two different torsional states with one set of parameters. *N. Ohashi, J. T. Hougen, J. Mol. Spectrosc. 121 (1987) 474-501.

Fit more than one vibrational state simultaneously 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. Ohashi et al, Ilyushin et al … BREAKTHROUGH: NEW DATASET Accurate rovibrational energies for the first excited torsional state of methylamine I. Gulaczyk, M. Kreglewski, V.-M. Horneman, JMS 2016 high resolution IR spectrum : 40 - 360 cm-1. Over 11,700 transitions with a resolution of 0.00125 cm-1 for 0 ≤ K ≤ 17 and K ≤ J ≤ 40, 143 parameters (88 for vt = 1, 55 parameters for the GS vt = 0). Standard deviation vt = 1-0 : 0.00079 cm-1 (0.31 MHz for the MW)

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

Different ordering scheme for the parameters 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 Different ordering scheme for the parameters n = t + r + w Diagonal g terms: w = 0 cos3, (JxJz+JzJx), cos6a Off-diagonal W terms : w = 2 cos6a Off-diagonal Pg terms : w = 2 PgJy

ntrw Operator & Coefficient Block in H Par. Value (cm-1) RAM system 2200 P2 * F LL, RR 15.140592 (49) ½(1  cos3) * V3 LL, RR 695.847 (18)   2110 PJz * (-2F)* r LL, RR 0.64935834 (14) unitless PJx * AXG LL, RR 0.13615 (11) 2020 Jx2 * B LL, RR 0.72559581 (81) Jy2 * C LL, RR 0.75613097 (21) ! Jz2 * A LL, RR 3.4409804 (4) {Jx Jz }* DAB LL, RR -0.066205 (47)   2002 1 * WAG2. LR, RL -0.681 (21) _________________________________________________________   3012 PJy * WCPG LR, RL 0. ________________________________________________________

Fitting vt= 0 and 1 together ….progress from last year! _ _________________________________________________ Last year (J ≤20) This year (J ≤40, 69 parameters) Lines wrms Lines wrms MW A-species 542 13.8 1251 3.67 MW E-species 656 23.0 1446 3.28 ___________________________________________ Lines wrms Lines wrms Weight Pure rot vt = 0-0 FIR lines vt=0-0 [1] 351 2.54 688 0.85 0.0007 cm-1 vt=1-1 [1] 86 1.38 GSCD from FIR 99 0.94 ----- ----- 0.0010 cm-1 Vt = 1-0 FIR [3] 411 50.7 11684 1.99 0.00047 cm-1 MW lines vt =0-0 [1,2] 1198 19.4 2485 3.42 MW lines vt =1-1 [1,2] not fitted 212 3.94 [1] Ohashi et al JMS 1988, 1989 [2] Ilyushin et al JMS 2005,[3] Gulaczyk et al JMS 2016

Comparing our fit with Gulaczyk et al 2016 _ _________________________________________________ Gulaczyk et al Our fit (69 parameters) Nber parameters 55 vt=0 69 88 vt=1 ___________________________________________ Lines rms Lines rms vt = 0-0 FIR [1] 689 0.00059 cm-1 vt = 1-1 FIR [1] 86 0.00089 86 0.00097 cm-1 vt = 1-0 FIR [3] 11716 0.00079 11684 0.00067 cm-1 MW lines vt =0-0 2487 0.27 MHz MW lines vt =1-1 212 0.31 MHz 212 1.25 MHz [1] Ohashi et al JMS 1988, 1989 [2] Ilyushin et al JMS 2005,[3] Gulaczyk et al JMS 2016

Future work and conclusions The hybrid model seems to be useful to treat two torsional states simultaneously in a two-dimensional large amplitude problem, but about three ? After cleaning up the dataset: Add higher order terms (reduction of the Hamiltonian like Tsunekawa et al did on methanol would be useful) - Convergence problems related to the non-linearity (statistical and mathematical research would be useful) - Predict and fit vt=1, 2 states of methylamine (FIR and MW data)