PowerPoint Poster Template

1
Kinetics of Phenyl Radical Addition to Butadiene
Using Quantum ChemistryA Theoretical and
Experimental Comparison of Reaction Rates
Huzeifa Ismail1, Bryan M. Wong1, William H.
Green, Jr.21Department Of Chemistry, 2Department
of Chemical Engineering, Massachusetts Institute
of Technology
Quantum Chemistry Continued
Introduction
Results - Continued
Modeling Pres. Dependence Cont.
The numerous reactions of phenyl radical (C6H5,
Fig. 1) are a current field of growing
technological and scientific interest. For
example, C6H5 is believed to be an essential
component in both combustion and in the formation
of fullerenes.1 Despite its importance, there
have been very limited theoretical and
experimental studies on the kinetics of C6H5
reactions. In this present work, we performed a
theoretical computational study on phenyl radical
addition to butadiene (C4H6) using first
principles in quantum chemistry.
Comparison to Experiment ? Experimental results
from collaborators Professor M.C. Lin and
Dr. Joonbum Park at Emory University Dept. of
Chemistry (Fig 8). ? Theoretical apparent
Arrhe- nius factor and activation energy
are in

• Transition state optimization
• very sensitive to initial
• geometries (Fig. 3)
• Rule of thumb
• Hammonds Postulate If
• (two states) have nearly
• the same energy content,
• their interconversion will

? vector of density of states for each isomer B
relaxation matrix R chemical activation flux
(assumed constant)

• ? Chemical activation, isomerization, and
  decomposition
• modeled by the master equation (Fig. 5)
• ? Solution is a function of the eigenvalues and
• eigenvectors of the 2140 2140 matrix, B4
• ? Total rate constants obtained by
  differentiating
• activated molecules according to energy

only involve a small reorganization of molecular
structure





Tbl. 1 Rate Parameters for All Rxns.
excellent agreement with experiment
values (Tbl. 2)
Kinetic parameters were calculated from
statistical mechanics to determine important
reactions under various pressure and temperature
conditions. The comparison with experimental data
from our collaborators show good agreement.
Statistical Approach to Reaction Dynamics
Experiment
Aexpt 3.31 ? 1012 cm3/mol s Eexpt 1.76
kcal AQRRK 3.34 ? 1012 cm3/mol s EQRRK
1.48 kcal
Canonical Transition State Theory High-pressure
limit rate constants calculated using
statistical mechanics

• Experiments carried out using the cavity
  ringdown
• spectrometric technique under slow-flow
  conditions
• with Ar as carrier gas
• C6H5 radical generated using Lambda Physik
• excimer laser at 248 nm with C6H5NO as
  precursor

Fig. 8 Apparent Rate Constants
Tbl. 2 Comparison of Aapp Eapp
Conclusions

• C6H5 probed using
• 504.8 nm excimer-
• pumped-tunable-dye
• laser.

Fig. 1 Phenyl Radical
? reaction path degeneracy ?(T) Wigner
tunneling correction factor at
temperature T QTS, QR partition function per
unit volume of the transition
state and reactants
respectively E0 zero-point corrected barrier
height

• Butadiene addition to phenyl radical is in the
  high-
• pressure limit for most temperatures and
  pressures
• Theoretical predictions of potential energy
  surfaces
• and reaction paths can provide useful insight
  in
• experimental research

Quantum Chemistry Methodology
Computational Model ? Potential Energy Surface
(PES) of C6H5 C4H6 explored using
GAUSSIAN 98 ? Vibrational frequencies and
geometries calculated using the B3LYP
density functional with the 6- 31G(d,p)
basis set Characterizing Stationary Points ?
Reactants and products local minima on PES
0 internal forces and 3N6 frequencies (Fig. 2)
References
Results
Modeling Pressure Dependent Rates
1. Frenklach, M. Clary, D. W. Gardiner, W. C.
Stein, S. E. Proc. Combust. Inst. 1984, 20,
887 2. Hammond, G.S. J. Am. Chem. Soc. 1955, 77,
334 3. Wong, B. M. Matheu, D. M. Green, W. H.,
Jr. J. Phys. Chem. A. 2003, 107, 6206 4. Bedanov,
V. M. Tsang, W. Zachariah, M. R. J. Phys. Chem.
1995, 99, 11452.
The Master Equation ? Gas-phase rate constants
dependent on both temper- ature and

• Transition states
• saddle points on
• PES
• 0 internal forces
• and 3N7 frequen-
• cies one imaginary
• frequency corre-
• sponds to the
• reaction coordinate

• pressure,
• k(T,P)
• Neglection
• of pressure-
• dependence
• can incur ser-
• ious errors in
• kinetic
• modeling3

Acknowledgements
Fig. 7 Potential Energy Surface for Phenyl
Butadiene
This work was supported by the Office of Basic
Energy Sciences. Office of Energy Research, U.S.
Dept. of Energy, under Grant No.
DE-FG02-98ER14914. We also gratefully acknowledge
Dr. Igor Tokmakov, Dr. Henning Richter, and
Joanna Yu for several helpful conversations.
? Major products are isomers in wells 3 and 4
4-phenyl-buten-3-yl and 1,4,9-trihydronaphtha
lene (Fig. 7) (Tbl. 1)
Fig. 5 Schematic for calculating
pressure-dependent rate constants
Fig. 2 Potential Energy Surface