Association ReactionStudies of Alkali Metal Ions and

Dimethoxy ethane (DXE)

Hideya Koizumi and P. B. ArmentroutUniversity of Utah

+

Objectives• R. Dunbar has measured BDEs by association

reactions in an FT-ICR • Here, we investigate the kinetic energy

dependence of association reaction by GIBMS• Alkali metal cation and DXE association reaction

is chosen because the only product is the long-lived association complex

• We want to develop methods to obtain the BDE for the association reaction cross section

• The results test our use of statistical theory

Potential Energy SurfaceM+DXE*

M+ + DXE

Association

UnimolecularDissociation

C ID

Guided Ion Beam Mass Spectrospcopy(Efrim)

10 cm

SchematicsAssociation Reaction

M+ + DXEAssociation

M+(DXE)*

Long lived Complex

Dissociation

The lifetime of the complex can be calculated from the energy dependent unimolecular decay rate constant k

Required conditions for obtaining good experimental data1) Complex has to be long lived (more than flight time )to be detected2) No collisional stabilization by multiple collisions

(pressure dependence)

Basically, M+DXE(E) = LGS(E) exp[-k(E)]

Pressure Dependence

Na++ DXE

Energy(CM, eV)0.1 1

Cro

ss S

ectio

ns(1

0-16 cm

2 )

0.1

1

10

100

Energy(Lab, eV)0.1 1

0.100 mTorr 0.059 mTorr 0.026 mTorr 0.000 mTorr

Na+DXE

M+ + DXE

Energy (CM, eV)0.1 1

Cro

ss S

ectio

ns (1

0-16 cm

2 )

0.1

1

10

100

Li+

Na+

K+

LGS

2.50 (0.19)

1.64 (0.04)

1.23 (0.04)

BDEs (eV) from CID values and theory (More et al.)

1.35

1.79

2.65

Modeling the cross sectionsIn all models, the only adjustable parameter is E0

• Statistical distribution of total angular momentum (AM)(by Rodgers, Ervin, Armentrout)

Usual method used for CID (Fix n and 0 to give LGS)Problem: AM is not conserved

2) Explicit conservation of orbital AMUse impact parameter distribution

It conserves AM for the complex (w/ stationary target approx.)Approximation L’ = L’’ (No Coupling to rotations); |J | << |L |

3) Rigorous Statistical Theory (Phase Space Theory)(by Chesnavich, Bowers) Explicitly conserve angular momentum (Coupling allowed)

Distribution of Total Angular Momentum of the Energized Molecule

J

J Dis

tribu

tion

StatisticalOrbital AMConservation& PST

Centrifugal acceleration

Jmax

Deceleration

Na+ + DXE

Energy (CM, eV)0.1 1

Cro

ss S

ectio

ns (1

0-16 cm

2 )

0.1

1

10

100

Energy (Lab, eV)0.1 1

Na+DXE

LGS

CID 1.64 (0.04) eV

Statistical 1.78 ± 0.12

Orbital AM conservation

1.75 ± 0.11

PST 2.20 ± 0.17 !

! Means work in progress

Na+ + DXE

Energy (CM, eV)0.1 1

Cro

ss S

ectio

ns (1

0-16 cm

2 )

0.1

1

10

100

Energy (Lab, eV)0.1 1

Na+DXE

LGS

Na+

E0=1.64eV

E0=1.75 eV

E0=1.86 eV

Very conservative Error chosen for time being

ModelOrbital AM conservation

K+ + DXE

Energy (CM, eV)0.1 1

Cro

ss S

ectio

ns (1

0-16 cm

2 )

0.1

1

10

100

Energy (Lab, eV)0.1 1

K+DXE

LGS

K+

CID 1.23 (0.04) eV

Statistical 1.28 ± 0.10

Orbital AMConservation 1.28 ± 0.10

PST 1.62 ± 0.08 !

Li+ + DXE

Energy (CM, eV)0.1 1

Cro

ss S

ectio

ns (1

0-16 cm

2 )

1

10

100

Energy (Lab, eV)0.1 1

Li+DXE

LGS

CID 2.50 (0.19) eV

Statistical 2.45 ± 0.35

Orbital AM conservation

2.40 ± 0.3

PST 3.00 ± 0.4 !

CID Theory Statistical Orbital AM conservation

Phase Space Theory (!)

Li+ +DXE

2.50(0.19)

2.65 2.45(0.35)

2.40(0.3)

3.00(0.4)

Na+ +DXE

1.64(0.04)

1.79 1.78(0.12)

1.75(0.11)

2.20(0.17)

K+ +DXE

1.23(0.04)

1.39 1.28(0.10)

1.28(0.10)

1.62(0.08)

SummaryEnergy dependence of the cross section is well

charactorized with all modelThe association reaction analysis (Statistical and

Orbital AM conservation) nearly reproduce the bond dissociation energy obtained by CID

The dynamic range of this analysis is established to be fairly large

Work In ProgressBetter implementation of Statistically rigorous PSTin this example.

Oblate & TS switching & etc

Acknowledgement

• Group Members• Prof. P. B. Armentrout• Prof. K. M. Ervin• Thank you for listening!!This work is supported by NSF#

One Possible reason of poor performance of statistically rigorous PST

• Maybe the complex rotating fastFragments of TS (large |L |) stop rotating • Better approximated by TTS1) Barrierless TS switching (K dependent)

( Chesnavitch & Bowers)1) Note (Tightness of TS is depend on |L |) Allow TS switch for even small K but large L

K

J

L|L | large enough thatTS is better considered to be Tight TS

What about Sphere approximation?

Sphere is very good approximation!

(Chesnavich&Bowers)

atom-oblateatom-prolate

What about Centrifugel distortion of M+DXE complex?Our calculation shows that change of rotational energy is much less than 5% in all case [Li < Na < K]

QuestionDoes rotational phase space dynamically restricted?

PST always prefer to dissociate with low value of orbital angular momentum no matter how fast the complex rotate.