COMPETITION BETWEEN TWO - PowerPoint Presentation

Slide1

COMPETITION BETWEEN TWO LARGE-AMPLITUDE MOTION MODELS: NEW HYBRID HAMILTONIAN VERSUS OLD PURE-TUNNELING HAMILTONIAN

Isabelle Kleinera and Jon T. HougenbaLISA, Université de Paris Est and CNRS, Créteil, F-94010, FrancebSensor Science Division, NIST, Gaithersburg, MD 20899, USASlide2

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 rotationBack-and-forth motion = hydrogen-atom transfer 2

2016

: In CH

3

-NH

2:Internal rotation = methyl-group rotationBack-and-forth motion = amino-group inversion

Kleiner

and

Hougen

JPC 2015Slide3

2015: Two

large-amplitude motions in methyl malonaldehyde: Intramolecular hydrogen transferInternal rotation of a methyl rotor Intramolecular hydrogen transfer induces a tautomerization in the ring, which then triggers a

60 degree internal rotation of the methyl rotor.

C

4

C

6

C

5

O

7

H

9

H

11

H

10

C

12

H

3

H

2

H1

C

4

C6

C5

O7

O8

H9

H11

H10

C12

H1

H3

H2

(123)(45)(78)(9,10)

O

8

Kleiner

and

Hougen

, JPC 2015Slide4

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.

4*N. Ohashi, J. T. Hougen, J. Mol. Spectrosc. 121 (1987) 474-501. Slide5

This year :

Fit more than one vibrational state simultaneouslyTry 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 DATASETAccurate rovibrational energies for the first excited torsional state of methylamineI.

Gulaczyk, M

.

Kreglewski, V

.

-M. Horneman, JMS 20165

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)Slide6

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

(-NH

2

inversion or

H

transfer motion), a tunneling formalism,

where H = T + V is replaced

with one tunneling splitting parameter +higher-order torsion-rotation corrections.

6Slide7

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:

J

x

p

, Jyq,

J

z

r

e.g., Operators Occur

in blocks

P



2

, cos6,

J

x2, Jy2

, Jz2

LL, RR, LR, RL cos3, (Jx

Jz+JzJ

x) LL, RR

PJy

LR, RL7

Different ordering scheme for the parameters

n =

t + r + wDiagonal

g terms: w = 0 cos3, (

JxJz+

JzJx), cos6

aOff-diagonal W terms : w = 2 cos6a

Off-diagonal Pg terms : w

= 2 PgJySlide8

ntrw

Operator & Coefficient Block in H Par. Value (cm-1) RAM system2200 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 Jx

2

* B LL, RR 0.72559581 (81)

J

y

2

* 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. ________________________________________________________

  Slide9

_ _________________________________________________ Last year (J ≤20)

This year (J ≤40, 69 parameters) Lines wrms Lines wrmsMW 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 1.38GSCD 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

Fitting

vt

= 0 and 1 together ….progress from last year!

[1]

Ohashi

et al JMS 1988, 1989

[2] Ilyushin et al JMS 2005,[3] Gulaczyk et al JMS 2016Slide10

_ _________________________________________________ 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-1vt = 1-1 FIR [1] 86 0.00089 86 0.00097 cm-1vt = 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

Comparing our fit with

Gulaczyk

et al 2016

[1]

Ohashi

et al JMS 1988, 1989

[2]

Ilyushin

et al JMS 2005,[3]

Gulaczyk et al JMS 2016Slide11

Future work and conclusions

The hybrid model seems to be useful to treattwo 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)