The ring closure reaction of C4H3 with acetylene to give phenyl radical is one proposed mechanism for the formation of the first aromatic ring in hydrocarbon combustion. There are two low-lying isomers of C4H3; 1-dehydro-buta-l-ene-3-yne (n-C4H3) and 2-dehydro-buta-l-ene-3-yne (iso-C4H3). It has been proposed that only n-C4H3 reacts with acetylene to give phenyl radical, and since iso-C4H3 is more stable than n-C4H3, formation of phenyl radical by this mechanism is unlikely. We report restricted Hartree-Fock (RHF) plus singles and doubles configuration interaction calculations with a Davidson's correction (RHF+1+2+Q) using the Dunning correlation consistent polarized valence double zeta basis set (cc-pVDZ) for stationary point structures along the reaction pathway for the reactions of n-C4H3 and iso-C4H3 with acetylene. n-C4H3 plus acetylene (9.4) has a small entrance channel barrier (17.7) (all energetics in parentheses are in kcal/mol with respect to iso-C4H3 plus acetylene) and the subsequent closure steps leading to phenyl radical (-91.9) are downhill with respect to the entrance channel barrier. Iso-C4H3 Plus acetylene also has an entrance channel barrier (14.9) and there is a downhill pathway to 1-dehydro-fulvene (-55.0). 1-dehydro-fulvene can rearrange to 6-dehydro-fulvene (-60.3) by a 1,3-hydrogen shift over a barrier (4.0), which is still below the entrance channel barrier, from which rearrangement to phenyl radical can occur by a downhill pathway. Thus, both n-C4H3 and iso-C4H3 can react with acetylene to give phenyl radical with small barriers

Walch, Stephen P.

English

NASA Technical Reports Server

207259
Characterization of the minimum energy paths for the ring closure
reactions of C4H 3 with acetylene
Stephen P. Walch
Thermosciences Institute, NASA Ames Research Center, Moffett Field, California 94035-1000
(Received 23 March 1995; accepted 14 August 1995)
The ring closure reaction of C4H 3 with acetylene to give phenyl radical is one proposed mechanism
for the formation of the first aromatic ring in hydrocarbon combustion. There are two low-lying
isomers of C4H 3; l-dehydro-buta-l-ene-3-yne (n-C4H3) and 2-dehydro-buta- 1-ene-3-yne
(iso-C4H3). It has been proposed that only n-Call3 reacts with acetylene to give phenyl radical, and
since iso-C4H 3 is more stable than n-C4H3, formation of phenyl radical by this mechanism is
unlikely. We report restricted Hartree-Fock (RHF) plus singles and doubles configuration
interaction calculations with a Davidson's correction (RHF+I+2+Q) using the Dunning
correlation consistent polarized valence double zeta basis set (cc-pVDZ) for stationary point
structures along the reaction pathway for the reactions of n-C4H 3 and iso-C4H 3 with acetylene.
n-C4H 3 plus acetylene (9.4) has a small entrance channel barrier (17.7) (all energetics in parentheses
are in kcal/mol with respect to iso-C4H 3 plus acetylene) and the subsequent closure steps leading to
phenyl radical (-91.9) are downhill with respect to the entrance channel barrier. Iso-C4H 3 plus
acetylene also has an entrance channel barrier (14.9) and there is a downhill pathway to
l-dehydro-fulvene (-55.0). 1-dehydro-fulvene can rearrange to 6-dehydro-fulvene (-60.3) by a
1,3-hydrogen shift over a barrier (4.0), which is still below the entrance channel barrier, from which
rearrangement to phenyl radical can occur by a downhill pathway. Thus, both n-C4H3 and iso-C4H 3
can react with acetylene to give phenyl radical with small barriers. © 1995 American Institute of
Physics.
I. INTRODUCTION II. COMPUTATIONAL DETAILS
The formation of the first aromatic ring (phenyl radical)
is widely believed to be the rate limiting step in the forma-
tion of soot in hydrocarbon combustion. One mechanism for
the formation of phenyl radical involves the stepwise addi-
tion of acetylenes) One possible pathway is the reaction of
the vinyl radical with acetylene to give C4H 3 followed by
subsequent addition of another acetylene and ring closure to
give phenyl radical. Another pathway to C4H3 is the reaction
of vinylidene with acetylene to give vinylacetylene
(buta-l-ene-3-yne), 2 which can be converted to C4H 3 (1- or
2-dehydro-buta-l-ene-3-yne) by abstraction of a hydrogen.
Note that reaction of acetylene with itself does not occur by
any low energy pathway, and vinylidene is 43 kcal/mol
above acetylene; 2'3 thus, the formation of vinylacetylene
from two acetylenes requires a moderate activation energy.
The structure and properties of C4H 3 have been studied by
Ha and Gey 4 using PUMP4/6-31G** theory. They find two
low-lying isomers 1-dehydro-buta- l-ene-3-yne (n-C4H3) and
2-dehydro-buta-1-ene-3-yne (iso-C4H3). Iso-C4H 3 is found to
be 7.3 kcal/mol below n-C4H3 (including zero-point effects).
Miller and Melius 5 also noted that iso-CaH 3 is thermody-
namically more stable than n-C4H 3 and thus most of the
CnH 3 should be in the form of the iso isomer even at com-
bustion temperatures. Thus, it is of interest to study the re-
action of both iso-C4H 3 and n-CnH 3 with acetylene, as dis-
cussed herein.
In Sec. II the technical details of the calculations are
discussed, while Sec. III discusses the results, and Sec. IV
concludes the paper.
Two different basis sets were used in these calculations.
The stationary points were located with restricted Hartree-
Fock (RHF) derivative calculations using the valence double
zeta set of Dunning and Hay. 6 The basis set for C is the
(9s5p)l[3s2p] basis and the H basis is (4s)l[2s], i.e., the
polarization functions are omitted. The subsequent internally
contracted configuration interaction (ICCI) calculations were
based on the RHF reference wave function and used the
Dunning correlation consistent polarized valence double zeta
basis set. 7
The geometry optimizations used the SIRIUS ABACUS
system of programs, 8 while the ICCI calculations were car-
ried out with MOLPRO. 9'10 All electrons were correlated ex-
cept for the C ls like electrons. A multireference analog of
the Davidson's correction u was added to the ICCI energies
and is denoted by + Q.
III. DISCUSSION
Table I(a) shows the computed ICCI energies of the sta-
tionary point structures for the reaction of iso-C4H 3 with
acetylene, while Table I(b) shows the same information for
the reaction of n-C4H 3 with acetylene. The computed har-
monic frequencies are given in Tables AIa and AIb of the
PAPS material. 12 The zero point effects were estimated as
!/2 the sum of the harmonic frequencies and these are in-
cluded in the relative energies, which are given in the last
column of Tables I(a) and I(b). Finally, the Cartesian coordi-
nates for the stationary points are given in Tables Alia and
Allb of the PAPS material.
8544 J. Chem. Phys. 103 (19), 15 November1995 0021-9606/95/103(19)/8544/4/$6.00 © 1995American Instituteof Physics
https://ntrs.nasa.gov/search.jsp?R=19980037545 2020-06-15T23:48:37+00:00Z
Stephen P. Walch: MEP for reactions of C4H3 with acetylene 8545
TABLE I. (a) Computed energies for stationary points on the iso-C4H 3 plus
C2H2 surface. _ (b) Computed energies for stationary points on the n-Call3
plus C2H 2 surface, b
sp2 min2 sp4
Geometry ICCI (ICCI + Q + 230.) ZPE AE
(a)
reac -230.551 40(-0.685 46) 0.075 38 0.0
spl -230.530 32(-0.668 48) 0.082 08 14.9
mini -230.612 79(-0.742 74) 0.087 99 -28.0
sp3 -230.602 14(-0.733 03) 0.085 70 -23.4
min3 -230.612 50(-0.742 39) 0.087 84 -27.9
sp6 -230.586 35(- 0.719 08) 0.086 60 - 14.1
min6 -230.657 85(-0.789 94) 0.092 23 -55.0
sp7 -230.553 15(-0.688 29) 0.084 52 4.0
min7 -230.665 83(-0.797 63) 0.091 41 -60.3
sp8 -230.601 10(-0.734 03) 0.086 29 -23.6
min8 -230.610 98(-0.741 16) 0.087 99 -27.0
sp9 -230.529 84(-0.664 82) 0.082 95 17.7
rain9 -230.659 85(-0.791 56) 0.091 76 -56.3
spl0 -230.587 26(-0.720 29) 0.086 40 - 14.9
minl0 -230.618 72(-0.748 86) 0.086 78 -32.6
(h)
reactants -230.537 98(-0.671 01) 0.075 87 9.4
sp2 -230.530 09(-0.663 57) 0.081 72 17.7
min2 -230.605 13(-0.737 60) 0.088 29 -24.6
sp4 -230.595 01(-0.728 48) 0.085 96 -20.4
rain4 -230.610 98(-0.741 16) 0.087 99 -27.0
sp5 -230.589 19(-0.729 47) 0.087 62 - 19.9
min5 -230.720 30(-0.850 62) 0.094 09 -91.9
"Energies in a.u. except for AE which is the relative energy in kcal/mol with
respect to iso-C4H3+C2H 2 including zero point energy.
bEnergiees in a.u. except for AE which is the relative energy in kcal/mol
with respect to iso-C4H3+C2H 2 including zero point energy.
The stationary points structures for the reaction of
iso-C4H 3 with acetylene are shown in Fig. 1, while those for
the reaction of n-C4H 3 with acetylene are shown in Fig. 2.
Figure 3 shows the stationary point structures for the conver-
sp6 mln6 sp7 mln7
$p8 mln8 sp5 rain5
min4 sp5 min5
FIG. 2. Stationary point structures for the reaction of n-C4H3+C2H2--*C6H 5
(phenyl). The following nomenclature is used. Min2 and min4= l-dehydro-
hexa- 1,3-diene-5-yne. Min5 =phenyl radical.
sion of min6 to minl0. (Here structures denoted by min are
minima and structures denoted by sp are saddle points on the
potential energy surface.) The energetics for these processes
are shown in Figs. 4-6, respectively.
Consider first the entrance channel barriers for the reac-
tion of n-C4H 3 and iso-C4H 3 with acetylene, n-C4H 3 plus
acetylene is 9.4 kcal/mol above iso-CaH3 plus acetylene, but
the barrier to addition is 14.9 kcal/moi for iso-C4H 3 plus
acetylene and 8.3 kcal/mol for n-C4H 3 plus acetylene. The
higher barrier for iso-C4H 3 plus acetylene probably results
from larger nonbonding interactions between the two acety-
lenic groups, which come closer together in the iso-C4H 3
plus acetylene case. This is reflected in the larger angle be-
tween the acetylenic groups in Fig. 1 as compared to Fig. 2.
Addition of n-Call 3 to acetylene leads to min2. Inversion
about the CH group of C 1 interconverts min2 and min4 with
a barrier of 4.2 kcal/mol. Min4 closes to min5 (phenyi radi-
cal) with only a small barrier. Thus, this reaction path leads
to phenyl radical with no barrier other than the entrance
channel addition barrier.
Addition of iso-CaH 3 to acetylene leads to mini. Minl is
connected to rain3 by sp3. The conversion from mini to
sp9 min9
spiO minlO
FIG. 1. Stationary point structures for the reaction of
iso-C4H3+C2H2--,C6H 5 (phenyl). The following nomenclature is used. Mini
and min3=l-dehydro-3-methylene-penta-l-ene-4-yne. Min6=l-dehydro-
fulvene. Min7=6-dehydro-fulvene. Min8= l-dehydro-hexa-l,3-diene-5-yne
=Min4. Min5-phenyl radical. Structures designated by rain are minima on
the PES while structures designated by sp are saddle points. This convention
is also used for Figs. 2 and 3.
FIG. 3. Stationary point structures for the conversion of rain6 to mini0, The
following nomenclature is used. Min9=2-dehydro-fulvene. Minl0=2-
dehydro-hexa- 1,3-diene-5-yne.
J. Chem. Phys., Vol. 103, No. 19, 15 November 1995
8546 Stephen P.Walch: MEP for reactions of C4H 3 with acetylene
iso-C4H3+ C2H2--> C6H5
40.0
spl
sp7
.,o.o_,, .,n, /
rain6 _/
-80.0_ mln7
40.0
0,0
-40.0_
-80.0_
sp7 --> minl0
sp9
spl 0
min7 mln9
FIG. 4. Energetics from SDCI+Q calculations with the cc-pVDZ basis set
for iso-C4H3+C2H2-_C6H5(phenyl).
min3 involves an inversion of the CH group about CI. This
involves only a 4.6 kcal/mol barrier. Sp6 connects min3 to
min6 (1-dehydro-fulvene). Sp7 is the saddle point for a 1,3-
hydrogen shift which connects min6 (l-dehydro-fulvene) to
min7 (5-dehydro-fulvene). This process involves a large bar-
rier; sp7 is 4 kcal/mol above iso-C4H 3 plus acetylene, but
still below the entrance channel saddle point, so this channel
is energetically accessible. Min7 can convert to min8 via
sp8. Min8 is the same structure as rain4 in the n-C4H3 plus
acetylene reaction pathway. This can then convert to phenyl
radical via a downhill pathway. Thus, both iso-C4H 3 plus
acetylene and n-CaH3plus acetylene can give phenyi radical
by pathways which involve no barriers, which are larger than
the entrance channel addition barriers.
Sp9 is a saddle point connecting mint to min9 (2-
dehydro-fulvene). Sp9 is 17.7 kcal/mol above iso-CaH 3 plus
acetylene, which is still below the entrance channel saddle
point. However, sp9 is a second order saddle point, i.e., it has
two negative eigenvalues [see Table l(a)] one of which leads
to symmetry breaking. Thus, there may be a lower energy
path to rain9 if the symmetry is lowered. This point was not
examined further in this work. Spl0 connects min9 to minl0.
n-C4H3 + CZH2 ---> C6H5
40.0
sp2
__ min2 sp4 sp5
0.0
-40.0 _
80.0_ _._5
-12O.0._...
FIG. 5. Energetics from SDCI+Q calculations with the cc-pVDZ basis set
for n-C4H3+C2H;t--*C6H 5 (phenyl).
FIG. 6. Energetics from SDCI+Q calculationswith the cc-pVDZ basis set
for the conversion of min6 to mini0.
IV. CONCLUSIONS
The ring closure reactions of i-dehydro-buta-l-ene-3-
yne (n-C4H3) and 2-dehydro-buta-l-ene-3-yne (iso-CaH3)
with acetylene have been studied using RHF plus singles and
doubles CI plus a Davidson's correction with the Dunning
cc-pVDZ basis set at stationary point structures determined
by RHF derivative calculations using a polarized valence
double zeta basis set. Zero-point effects were estimated
based on the RHF harmonic frequencies.
n-C4H 3plus acetylene (9.4) has a small entrance channel
barrier (17.7) (all energetics in parentheses are in kcal/mol
with respect to iso-C4H 3 plus acetylene) and the subsequent
closure steps leading to phenyl radical (-91.9) are downhill
with respect to the entrance channel barrier. Iso-CaH 3 plus
acetylene also has an entrance channel barrier (14.9) and
there is a downhill pathway to I-dehydro-fulvene (-55.0).
I-dehydro-fulvene can rearrange 6-dehydrofulvene (-60.3)
by a 1,3-hydrogen shift over a barrier (4.0), which is still
below the entrance channel barrier. 6-dehydro-fulvene can
rearrange to phenyl radical via 1-dehydro-hexa-l,3-diene-5-
yne (-27.0). Thus, both n-Call 3 and iso-C4H 3 can react with
acetylene to give phenyl radical with small barriers.
With respect to iso-CaH 3 plus acetylene, all of the open
structures (minl, min3, min8=min4, and minl0) are from
27.0 to 32.6 kcal/mol lower, while the dehydro-fulvene struc-
tures (min6, min7, and min9) are from 55.0 to 60.3 kcal/mol
lower, and the phenyl radical is 91.9 kcal/mol lower, respec-
tively. Thus, since all these structures can interconvert with
barriers below the entrance channel barrier, the ultimate
product is expected to be phenyl radical, although other C6H 5
species may still play a role as reactive intermediates.
ACKNOWLEDGMENTS
S.EW. was supported by NASA Cooperative Agreement
Number NCC2-478 to ELORET Institute and by NASA
Contract No. NAS2-14031 to ELORET.
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t2 See AIP document No. PAPS JCPSA6-103-8544-18 for 18 pages of tables
of supplemental material. Order by PAPS number and journal reference
from American Institute of Physics, Physics Auxilary Publication Service,
Carolyn Gehlbach, 500 Sunnyside Boulevard, Woodbury, New York
11797-2999. Fax: 516-576-2223; e-mail: janis@alp.org. The price is $1.50
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J. Chem. Phys., Vol. 103, No. 19, 15 November 1995


Characterization of the Minimum Energy Paths for the Ring Closure Reactions of C4H3 with Acetylene

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