深圳研究生院SHENZHEN GRADUATE SCHOOL

How to Get the Binding Energy by Mass Spectrometry 

Speaker: Tianyu Sun

Advisor: Prof. Wu Dr. Zhang

2

Empedocles (490–430 BC, Greek) said:“ Love will bring about the element hate will separate the element”

Preface

love

hate

3

Preface

Binding energy

我做了这么久计算和有机机理，对化学理解就是“能量和电子的分配”

4

Preface

O

HO

OHOPd

O

O

NO

OHOPd

O

O

NO

AcOH substrate OHOPd

O

O

NO

substrate

in organometallic reactions, the key reactive intermediates are coordinatively unsaturated transition metal–ligand complexes that have an open site by loss of one or more ligands.

These unsaturated intermediates are good catalysts because they are reactive

But transient and difficult to study

such information would enable predictions of the feasibility of desired reaction

5

PrefaceThe methods to get the binding energy:

photoelectron spectroscopy

Time resolved infrared spectroscopy

ion beam studies of endothermic reactions

flowing afterglow

kinetic energy release distributions

Energy resolved collision induced dissociation

1aser-powered homogeneous pyrolysis

guided ion beam mass spectrometry

Quantum chemistry……

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Outline Kinetic theory of gases

maxwell speed distributionClassic Collision Theory

cross section Determination of cross section by MS

threshold energy (阈能 ) Determination of Binding Energy

Doppler broadeningthe relative velocity distributionthe models of cross section

Equipmention beam energyguided ion beampressure

Future work summary

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kinetic theory of gasesIdeal gas

maxwell velocity distribution

vdekTmnvdvf

NdN kT

mv 3223

32

)2()(

v

v+dv

Often we more care about speed, no velocity!

maxwell speed distribution

dvekTmnv

dvvfvdvvFNdN

kTmv22

32

2

2

)2(4

)(4)(

vdvf 3)( the number of particles with velocity between and + in per unit volumev v vd

8

maxwell speed distribution

dvekTmnvdvvF

NdN kT

mv22

32

2

)2(4)(

kinetic theory of gases

9

Classic Collision Theory

b

θ

A

B

ur

dAB

ur is the relative speed between particle A and particle B

dAB=rA+rB

2

21

rr u μ is the reduced mass ba

ba

mmmm

cAB

rrrr dbuu )1()sin1(2

1)cos(21

2

2222

εc is the threshold energy, if ε’r > εc, the reaction can happen!

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Classic Collision Theory

)1(22

r

cABr db

cAB

rr d

b )1( 2

2

b

θ

A

B

ur

dAB

cAB

rr db )1( 2

2

br :reaction radius

)1(22

r

cABrr db

define σr the reaction cross section

quantum states

11

Determination of cross section by MSUsing mass spectrometer can get the Ion intensities for reaction

+++++I0

+ + + + Massspectrometer

Ip(ArH+)

+ + +IR(Ar+)

gas cell

At a low pressureJust single collison

P. B. Armentrout ,J. Chern. Phys., 83, 166 (1985)

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Determination of cross section by MSat low pressure, just single collison

first order reaction

)exp()(

ln)(

)(

)(

)()(

1

1

0 10

1

1

1

tkaxa

tkxa

a

dtkxa

dx

dtkxa

dx

xakdtdx

xakdt

xad

tx

)exp()( nlIII totPRR

l is the effective path lengthn is the density

nl tσtot k1

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Taylor expansion

IR≈(IR+ΣIP)(1- σtotnl)

Determination of cross section by MS

)exp()( nlIII totPRR

At low pressure

PR III 0

)/( pPtotp II

Individual product cross sections σp

nlII pp 0/ σp→ threshold energy

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Determination of Binding Energy

++++ ++++

gas cell gas cell

target molecule: stationary target molecule: Doppler broadening

high ion beam energy low ion beam energy

high low

the σ is a function of Elab

the relative velocity is important

Elab»kT Elab<kT

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Determination of Binding Energy

center of mass(cm)

V0

mmonoenergetic ion beam

M

v

target molecule

Vcm

m

M

V

V0(cm)

v(cm)

VmM

mcmv

VmM

McmV

VcmvcmV

)(

)(

)()(

0

0

2

)(2 VMmMmE

if v=0

labEMm

MmVMm

ME )(21

)(200

E0 is nominal center of mass energy

how to get the relative velocity?

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Determination of Binding Energythe thermal distribution of v gives rise to a distribution of V

V0

vV

V0-V

V0+V

dV0

dv

velocity space ρ: the volume of the red area to the volume of the whole shell of radius v

θ

vVVdV

dvvVdVdvVv

02

0 24)sin(sin2

G. J. SCHULZT, PHYS.REV., 32, 110 (1954).

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Determination of Binding Energy

the ratio of particles with relative velocity between V and V+dV

VV

VVdvvF

NdN 0

0)(

vVVdV

02

dvekTmnvdvvF kT

mv22

32

2

)2(4)(

VV

VVkTmv

dvekTmnv

vVVdV

NdN 0

0

2

223

2

0)2(42

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Determination of Binding Energy

VV

VVkTmv

dvekTmnv

vVVdV

NdN 0

0

2

223

2

0)2(42

integration gives:

dVVVkTMVV

kTM

VV

kTM

NdN )])(2exp())(2[exp()2(

20

20

0

21

dEEEfNdN ),( 0

It is convenient to introduce the parameters

mMm

kTE

kTE

00

dNdN )])(exp())([exp()4

1( 221

021

221

021

21

0

19

Determination of Binding Energy

dEEEEfEEEapp )(),()/()( 0

21

0 00

σapp(E0) is the apperent reaction cross section

dEEEfNdN ),( 0

convolution of σ(E)

The (E/Eo)1/2 factor accounts for the difference in the residence times of ions in the interaction region at different ion energies.

++++

target molecule: Doppler broadening

lowElab<kT

gas cell

low ion beam energy

P. B. Armentrout ,J. Chern. Phys., 83, 166 (1985)

relative kinetic energy disturbution

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Determination of Binding Energy

σ(E) is a function of threshold energy

)1(22

r

cABrr db

classic quantum

Step-Function Cross Section

Linear Cross Section

Inclined Step-Function Cross Section

Exponential Cross Section

the models of σ(E):

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Determination of Binding Energy

Peter Chen, J. Phys. Chem. A, Vol. 111, No. 30, 2007

dEEEEfEEEapp )(),()/()( 0

21

0 00

labEMm

MmVMm

ME )(21

)(200

E0 is nominal center of mass energy

σ0 is a scaling factorE the relative kinetic energyn an adjustable parameterquantum states(vibrational, rotational, and electronic)with energies Ei and populations gi

The σ0, n, and E0 parameters are fitted by least squares analysis

CRUNCH L-CID

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Determination of Binding Energy

dEEEEfEEEapp )(),()/()( 0

21

0 00

threshold energy

there are three types of reaction used to determine the binding energy of M+–L

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Equipment

The energy spread of Elab need to be very narrowBecause the cross section is a funtion of energy

++++

gas cell

Elab

The narrower , the better

dEEEEfEEEapp )(),()/()( 0

21

0 00

momentum analyzer serves to narrow the energy spread

P. B. Armentrout ,J. Chern. Phys., 83, 166 (1985)

V0

monoenergetic ion beam

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Equipment

So we need to trap the ionic products regardless of scattering angle.

+

+

detector

The scattering can reduce the signal

+

+

detector+

+

25

EquipmentUsing octopole to trap the ion

Travelling wave (T-wave) ion guide

adjacent rings have opposite phases of radio frequence voltage

the effective potential

26

EquipmentAt a low pressure, Just single collison

Pressures 6.5e-6 Pa can be used for cross section measurements.

2.25e-2 Pa

++++

gas cell

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Future research

Yu, J.-Q. Angew. Chem. Int. Ed. 2008, 47, 4882.)

COOH

NHBoc

COOH

NHBoc

COOH

NHBoc

COOH

NHBoc

COOH

NHBoc

COOH

NHBoc

ClCOOH

NHBoc

COOH

NHBoc

OCOOH

NHBoc

H

COOH

NHMe

COOH

NH2

CO2Me

NHBoc

COOH

N(Boc)2

COOH

BocN

COOH

NHPiv

COOH

NHFormyl

COOH

NHAc

COOH

HN

OMe

O

COOH

HN

O

O

CCl3

COOH

HN

O-(+)-Menthyl

O

COOH

HN

O-(-)-Menthyl

O

Ligand Yield[%] ee[%]Entry Ligand Yield[%] ee[%]Entry

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

63

60

69

85

60

66

83

47

65

n.r

n.r

90

52

70

72

80

81

83

85

88

---

---

86 0

74 7

63 6

58 7

53 6

74 80

88 79

89 85

87 85

91 87

N AA ligand

Pd(OAc)2 PdO

N

O

PGH

i-BuH

N

H Ph

Alkylation

RB(OH)2

NR

R

Pd II-Catalyzed Enantioselective Activation of C(sp2)-H and C(sp3)-H Bonds Using Monoprotected Amino Acids as Chiral Ligands

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Summary

dEEEEfEEEapp )(),()/()( 0

21

0 00

threshold energy

Determination of Binding Energy

Equipment

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Thanks for your attention