Feng Zhang, Theodore S. Dibble

Chemistry Department, State University of New YorkCollege of Environmental Science and Forestry (SUNY-ESF)

Impact of tunneling on H-migration of n-propylperoxy radical

ICCK, MIT, 07/10/2011-07/14/2011

RH + ▪ OH

R▪

HO2 + alkene

O2 O2

ROO▪

QOOH

▪OH + products ▪OOQOOH

O2

2▪OH + products

Scheme of alkane auto-ignition (<1000 K)

H-migration

HO2 elimination

(or ▪H, O)

tunneling

)()()( TkTTk clQM

Goals

Tunneling treatment in literature: 1D model (Wigner or Eckart)

Use multidimensional treatment to get tunneling right;

Give guidance on 1D tunneling models for peroxy radicals.

OO

HO2

OOH

OOH

+

..

. 1, 5 H-migration

1, 4 H-migration

HO2 elimination

(R1)

(R2)

(R3)

Tunneling treatments

V0

V1

~Wiger

),,(~ 10 VVEckartEckart

~~

Reaction coordinate

V

VMEP

ZPE

VaG

~~

Reaction coordinate

V

VMEP

ZPE

VaG

),(~ curvatureV GamultiDDmulti

Methodologies

Benchmark: CCSD(T)/maug-cc-pVTZ//M052X/6-311+G(2df,2p)

1. Ab initio calculations

2. Tunneling treatment and rate constant calculation

VaG requires vibrational analysis along the whole path!

Select DFT method based on the benchmark

Calculate rate constants with multidimensional tunneling

Select DFT and basis set with least error

0.0

0.5

1.0

1.5

2.0

2.5

M05

2X/6-

31+G(d

,p)

M05

2X/6-

31+G(2

df,2p)

M05

2X/6-

311+

G(2d,2p

)

M05

2X/M

G3S

M06

2X/6-

31+G(d

,p)

M06

2X/M

G3S

B3LYP/M

G3S

B3PW

91/M

G3S

BMK/M

G3S

MPW

3PBE/M

G3S

B1B95

/MG

3S

CAM-B

3LYP/M

G3S

CBS-QB3

Mea

n U

nsi

gned

Err

or(k

cal/

mol

)

1,5 H-migration

1,4 H-migration: B3LYP/MG3S

HO2 elimination: B1B95/MG3S

1,5 H-migraion: M052X/MG3S

MG3S=6-311+g(2df,2p) for C,H, O

The “lucky” benchmark

1,5 H-migration 1,4 H-shift HO2 elimination method

E0 Erxn MUE E0 Erxn MUE E0 Erxn MUE

Focal pointa 24.5 16.1 0.0 32.7 13.4 0.0 30.1 17.5 0.0

CCSD(T)/maug-cc-PVTZb

24.7 16.1 0.1 33.2 13.9 0.5 30.1 16.8 0.3

M052X/MG3S 25.3 17.3 1.0 35.1 14.4 1.7 33.9 19.3 2.8

B3LYP/MG3S 24.5 18.7 1.3 33.0 14.6 0.7 26.9 14.1 3.3

B1B95/MG3S 24.6 20.0 2.1 32.7 16.5 1.5 29.1 16.2 1.1

CBS-QB3 23.8 15.9 0.4 32.1 13.7 0.4 30.90 18.2 0.7

a From Prof. Allen’s talk this morning!

Reaction paths

TS-15 (1836 cm-1)

TS-14 (2172 cm-1)

TS-e (1027 cm-1)

1

3

5

7

9

500 600 700 800 900 1000

T(K)

Tun

neli

ng c

oeff

icie

nt

R3

Multidimensional tunneling coefficients

R1

R2

OO

HO2

OOH

OOH

+

..

. R1

R2

R3

cl

QM

k

k

Comparison of tunneling treatments for 1,4 H-migration

Comparison of tunneling treatments for 1,5 H-migration

Reaction coordinate (amu1/2*Å)

Rate constants in the high pressure limit

SRG: J. Phys. Chem. A 114, 5689, 2010

HCD:J. Phys. Chem. A 114, 6594, 2010

Summary

High pressure limiting rate constants were computed for H-migration, HO2 elimination of n-propyl peroxy radical.

Wigner’s formula largely underestimates tunneling. Eckart potential gives reasonable predictions.

First multidimensional tunneling treatment of these reactions in alkyl peroxy radical

Acknowledgements

Prof. Donald G. Truhlar, Dr. Jingjing Zheng

U.S. Department of Energy

Thanks for your attention!

Internal rotation in CH3CH2CH2OO▪

Reactant TS-15s TS-14s TS-e

)(

)()(

tanRe TQ

TQTk

tac

TS

-200

0

200

400

600

800

1000

Hindered rotor treatment

Torsion Eigenvalue Summation(TES) method

n

nm

m nBmAAV sincos)( 0

0

200

400

600

800

1000

0 60 120 180 240 300 360

Torsional angle(degree)

Poten

tial En

ergy(cm-1)

0

1

2

3

4

5

-2 0 2 4 6

logP(Torr)

500 K

700 K

1,4 H-shift

1,5 H-shift

logΓ

Pressure dependence of Eckart tunneling coefficient

1atm