J. Chem. Chem. Eng. 6 (2012) 563-573
Mechanism and Kinetic of Free Radical Reactions for
Propane Using theoretical Calculations
Abbas A- Ali Drea*1 and Nadia Izet2
1. Department of Chemistry, College of Science, Babylon University, post box No.4, Hilla-Iraq
2. Department of Chemistry, College of Education for Girls, AL-Kufa University, Al Najafe-Iraq
Received: May 27, 2012 / Accepted: June 15, 2012 / Published: June 25, 2012.
Abstract: Quantum calculation method has been used to understand and investigate the free radical reactions of propane with
hydroxyl radical in vacuum through modern quantum mechanics that is package on hyperchem 8.02 program. Optimized structures
and structural reactivates have been studied through bond stability and angles using DFT calculation based on the basis set 6-31G*.
Energetic properties have been calculated like total energy, Gibbs free energy, entropy, heat of formation, and rate constant for all
chemical species that’s participate in the suggested reaction mechanism. Reaction mechanism and rate determining step had been
suggested according to calculation of energy barrier values, and compares between the suggested competitive reactions for each
probable reaction step. Suggested structures and the probable transition states have been studied.
Key words: Free radicals, reaction mechanism, theoretical chemistry, quantum mechanics, rate determining step.
1. Introduction?
Free radicals reactions are very important for
different industrial processes. Controlling on the
reaction condition must be understood the mechanism
and kinetic model. Chain reaction involving free
radicals can usually be classified into three distinct
processes, which is initiation, propagation, and
termination steps [1, 2]. The application of
mathematical and theoretical principles can be used to
solve the chemical problems in industries and other
applications. That’s helps us to determine, calculate,
and study new concepts, compounds, reactions and
mechanisms. Such way is very useful with compounds
that require special expensive technique to study the
mechanism, such as free radicals reactions to decrease
testing time and maintenance costs in service.
Quantum calculation methods are classified under
three major categories that is ab-inatio electronic
*
Corresponding author: Abbas A-Ali Drea, Associate
Professor, research field: quantum mechanics of chemistry.
E-mail: aadreab@yahoo.com.
structure method, semi-empirical methods and
molecular mechanics [3-5]. DFT (density functional
theory) is the most commonly method of electronic
structure calculation in quantum chemistry. That has
been proven to be an important tool in modern
quantum chemistry by the approach of Kahu-sham.
Because its ability included some effects of electron
correlation, computational cost was reduced greatly [6, 7].
Propane gas can be interred into different chemical
process to produced different chemical products
through free radical mechanism reaction. This
chemical reaction can be controlled under the studying
the rate determination step. It is consisted the
concentrations and pressures or reactant species in this
slow determining step [8, 9].
In the present work we are interested in using
different methods of semi-empirical, DFT calculation
to estimate the optimized structure of reactants,
transition state and products. The suggested structure
for chemical species are get on through potential
energy surface, zero point energy, and
IR–frequencies calculation. Net equation of reaction
DDAVID PUBLISHING
564 Mechanism and Kinetic of Free Radical Reactions for Propane Using theoretical Calculations
mechanism investigation comes out depending on
energy barrier estimation values for different reaction
probabilities and zero point energy with first
imaginary frequency for transition state. Enthalpy
formation of reactant for all most probable
subsequent steps is carried out of enthalpy change
value to final reaction.
2. Methods of Calculations
All theoretical calculations in this work were
performed using the co-implemented methods in the
Hyperchem package 8.02 [6]. All suggested structures
of free radicals reactions mechanisms have been
optimized by DFT, 6-31G(d), 6-31G(d, p),
B3LYP/6-31G** [10, 11].
Frequencies of proposed transition state structures
have been calculated at 6-31G*/UHF for
characterization of the nature of stationary points and
ZPE (zero point energy) calculations to compute the
quantum energies of these reactions. Rate constant
values for the most probable reactions have been
calculated by DFT and 6-31G* to estimate the rate
determination step for ethane gas with hydroxyl
radical.
3. Results and Discussion
Photolysis of gaseous hydrogen peroxide occurs
shorter than 320 nm [12]. Fig. 1 shows the structure
for electronic properties of hydrogen peroxide and
hydroxyl radical molecules. The bond lengths of O-H
and O-O bond of hydrogen peroxide molecule are
0.99 ? and 1.47 ?, respectively. The bond angle of
O-O-H bond is 97.5°, with torsion angle equal to 180°.
The distribution of electronic density are
homogenously on the atoms, where both of oxygen
atoms contained negative density are provided with
red color, while the hydrogen atoms contained
positive density
Tube view with bond lengths (?) of
hydrogen peroxide
Ball and cylinder with atomic charge of
hydrogen peroxide
Electrostatic potential surface of
hydrogen peroxide
Ball and cylinder with atomic charge of
hydroxyl radical
Tube view with bond lengths (?) and Basis
set of hydroxyl radical
Electrostatic potential surface of hydroxyl
radical
Fig. 1 Energy properties of hydrogen peroxide and hydroxyl radical calculated using DFT through 6-31G** full/UHF.
Mechanism and Kinetic of Free Radical Reactions for Propane Using theoretical Calculations 565
are provided with green color. The librated hydroxyl
radical react with propane molecules, due the highly
reactivity react toward reactions [13, 14]. Recorded
values at two different methods of calculation are
shown in Table 1.
The splitting of hydrogen peroxide molecule forms
two hydroxyl radicals OH? occurs with energy barrier
equal to 67 kCal/mol calculated using DFT through
6-31G**. This radical enters into the photoreaction
that leads to the sequence reaction of propane
molecule. PES (potential energy stability) has been
investigated for the two bonds of peroxide to estimate
the reactivity toward photolysis reaction. Fig. 2
illustrates the stability energy curve of bonds. Fig. 2
illustrates that O-O is more active than O-H bond. The
O-O bond is broken down at 2.97 ? (-93,516.08
kCal/mol), but O-H bond is broken down at 2.49 ?
(-93,494 kCal/mol).
The investigation for Chemical reactivity in
propane molecule has been carried out through the
calculation of atomic charge, bond length, electrostatic
potential, HOMO and LUMO orbital. Geometry
optimization of propane molecule is shown in Fig. 3.
Electrostatic potential mapping employed to
distinguish regions on the surface which are electron
rich (subject to electrophilic attack providing with red
color (carbon atom) from which are electron poor
(subject to nucleophilic attack providing with green
color (hydrogen atom).
The HOMO (highest occupied molecule orbital) is
the orbital that primary acts as electron donor (Lewis
base ) concentrated of carbon atom providing with red
color, and the lowest unoccupied molecular orbital is
the orbital that largely act as the electron accepter
(Lewis acid ) concentrated of hydrogen atom
providing with green color [15-17]. The results show
that the negative charge of oxygen of hydroxyl radical
can attach the positive charge atom in propane
molecule and same opposing thing for positive
hydrogen atom of hydroxyl radical. Table 2 is shown
the comparative of atomic charge, bond length and
bond angle in the propane molecule. Table 3 shows
Table 1 Structural properties in units of kCal/mol calculated by DFT through 6-31G* and 6-31G** basis set using UHF
calculation method.
?H at 298.15K ?S
at 298.15 K
?G
at 298.15 K
Correlation
energy
Molecule Basis set Total energy
6-31G* -93,639.33 -391.42 -93,653.4 0.053 -93,637.61 H2O2 6-31G** -93,644.97 -399.79 -93,659.1 0.053 -93,643.31
6-31G* -46,782.34 -138.182 -46,792.8 0.04 -46,780.88 .
OH
6-31G** -46,785.21 142.45 -46,795 0.04 -46,783.03
Fig. 2 Potential energy stability curve of hydrogen peroxide’s bonds calculated using DFT through 6-31G**.
566 Mechanism and Kinetic of Free Radical Reactions for Propane Using theoretical Calculations
Ball and cylinder with atomic charge Tube view with bond lengths (?)
Basis se Number of atom
Highest occupied molecular orbital Lowest unoccupied molecular orbital
Electrostatic potential 3D
Fig. 3 Energy properties of propane calculated using DFT through 6-31G** full/UHF.
Mechanism and Kinetic of Free Radical Reactions for Propane Using theoretical Calculations 567
accuracy of the calculated result depends on the type
of calculations. The results show that the stable
geometry of propane molecule has a minimal total
energy value equaled to -74,711.83 that calculated by
B3LYP/6-31G*.
PES (potential energy stability) has been
investigated for the three bonds of propane. Fig. 4
illustrates the stability energy curve for C-C, C1-H4
and C2-H7 bond. The C-C bond is broken down at
3.033 A?
(-73,428.914 kCal/mol), C1-H4 bond is
broken down at 2.520999 A?
(-73,437.828 kCal/mol),
but C2-H7bond is broken down at 2.525001 A?
(73,443.562 kCal/mol).
There are several properties for transition state
Table 2 Comparing atomic charge, bond length and bond angle in the propane molecule.
?Hf ?G? ?S? ? Molecular orbital energy Method Total energy ZPE
LUMO HOMO ?Egap
PM3 -11,060.28 64.08 3.71 -11.5 14.5 -11,012.6 0.065 -10,993.23
6-31G** -73,043.78 61.09 2.71 -6.077 8.78 -73,044.6 0.039 -73,032.98
-74,711.83 64.7 2.05 -8.716 10.766 -74,712.7 0.039 -74,701.08 B3LYP//
6-31G**
Table 3 Energy properties of propane in units of kCal/mol calculated by DFT based on 6-31G**and B3LYP/6-31G** using
UHF calculation.
Angle bond Torsion of angle Atomic charge
H9-C3-C2 112.223° H9-C3-C2-H8 57.77° C1, C3 -0.368
H10-C3-C2 111.074° H9-C3-C2-C1 180° C2 -0.208
H8-C2-C3 109.632° H10-C3-C2-C8 62.75° H5, H6, H10, H11 0.119
H 0.118 C1-C2-C3 112.405° H7-C2-C1-H4 -57.7851 9, H4
H4-C1-H5 107.623° - - H7, H8 0.112
Fig. 4 Investigation of bond stability of Propane molecule bonds toward the free radical reactions.
568 Mechanism and Kinetic of Free Radical Reactions for Propane Using theoretical Calculations
forming to the reaction of hydroxyl radical with
propane molecule depending upon the effective side
towards the attachment hydroxyl radical. The first
step is initiation that depends on the transition state
with high probability to give up stable product with
low energy barrier compared with other probable
transition state. The main kinds reactions of the
reacted hydroxyl radical with propane is substitution
reaction, abstraction reaction and causing nine
transition state.
Hydrogen abstraction reaction occur when the OH
radical attack directly and abstract the medial
hydrogen atom to produce secondary propyl radical
and water, as seen Eq. 1. The transition state structure
for this channel is TS1. Hydrogen abstraction reaction
occur when the OH radical can attack directly and
abstract the terminal hydrogen atom to produce
primary propyl radical and water, as seen in Eq. (2).
The transition state structure for this channel is TS2,
TS3 and TS7. The substitution reaction can be occurs
in three different suggested path way, the first
probable of substitution include the OH radical attacks
the C position, the opposite hydrogen atom substituted
by OH radical to produce propanol and hydrogen
radical atom according to Eq. (3). The transition state
for this channel is TS4, TS8, the second probable of
substitution reaction included the OH radical.
Fig. 5 is shown the geometry optimized of these
transition states. All the transition state structure has been
presented. Table 4 is shown the energetic properties
TS1 TS2 TS3
TS4 TS5 TS6
TS7 TS8 TS9
Fig. 5 Ball and cylinder view for suggested transition states calculated using DFT through 6-31G** full/UHF.
Mechanism and Kinetic of Free Radical Reactions for Propane Using theoretical Calculations 569
Table 4 Energetic values of proposed transition states calculated by DFT through 6-31G** full UHF at kCal/mol units.
?Hf?
at 298.15 k
?S?
at 298.15 k
?G?
at 298.15 k TS Total energy Energy barrier ZPE IR. Freq.
TS1 -105,542.32 117.17 11.41 - -105,486 0.064 -105,466.93
TS2 -105,541.74 68,162.61 17.46 - -105,559 0.064 -105,539.93
TS3 -105,529.12 -2.5 29.96 - -105,559 0.064 -105,539.93
TS4 -105,540.36 3,202.79 35.51 - -105,558 0.064 -105,538.93
TS5 -105,553.07 43.50 25.07 - -105,570 0.064 -105,550.93
TS6 -105,538.77 97,322.19 28.196 - -105,556 0.064 -105,536
TS7 -105,534.75 95,268.87 19.99 - -105,545 0.064 -105,525.93
TS8 -105,544.35 3,023.941 22.69 - -105,536 0.064 -105,516.93
TS9 -105,593.69 22,695.35 24.99 - -105,540 0.064 -105,520.93
of these transition states, according to transition state
calculation. The third attacks the C-C from the end.
The opposite methyl can be substituted by the OH
radical to produce ethanol and methyl radical, as
seen in Eq. 4. The transition state for this channel is
TS5 and TS9. The third probable of substitution
reaction included the substation OH radical by ethyl
group to produce methanol and ethyl radical. The
transition state for this channel TS6 transition state
has the lowest energy barrier value of formation
equal to -2.5 kCal/mol and the medium value of ZPE
to produce their product. This meaning that TS3
needed in a faster rate than the other propable
transition state and needed short time to occurs
[18-20].
The proposed mechanism must be involved all
(hydroxylation) reaction that occur with different
species for the path way of reactions. Table 5
represents some of energetic properties of proposed
structure of propane hydroxylation reaction, this result
shows that the molecule increased in size, and the
energy became negative increased [21]. Table 6 shows
that compares all of different competitive reactions
according to the energy barrier value of reaction.
There are some competitive reactions that differ in
energy barrier. The lowest energy barrier reaction will
occur at high probability, compared with other
competitive reactions [22]. Therefore, the suggestion
of propane mechanism is represented in Fig. 1.
Enthalapy of most of reaction probability is exothermic
Table 5 Energy values of suggested chemical species that’s participate in the reaction mechanism calculated DFT through
6-31G*/UHF by kCal/mol units.
?Hf ?G? at 298.15 ?S? at 298.15 ? at 298.15 IR.
Freq. Reaction compound Total energy ZPE
H2O -42,352.37 5.57 + -42,364.8 0.047 -42,350.79
C2H5C*H2 -63,175.54 26.21 - -63,191.7 0.06 -63,173.8
CH3C*H2CH3 -63,178.20 26.12 - -63,194.3 0.06 -63,176.42
CH -105,392.5 31.66 - -105,409 0.063 -105,390.23 3CH2CH2OH
CH3CHCH2 -63,022.58 22.21 - -63,038.5 0.06 -63,020.62
C -126,415.31 58.66 - -126,434 0.067 -126,414.03 6H12
CH3C*H(CH2)3CH3 -126,215.16 52.97 - -126,233 0.067 -126,213.03
CH -105,189.72 18.5 - -105,207 0.06 -105,189.12 3C*HCH2OH
CH3CHCHOH -105,035.26 26.72 - -105,052 0.062 -105,033.52
CH -105,034.17 24.32 - -105,051 0.062 -105,032.52 2CHCH2OH
CH3CH(OH)CH2OH -147,404.64 31.08 - -147,422 0.065 -147,402.63
CH -168,426.74 55.05 - -168,445 0.068 -168,424.74 3CH(C3H7)CH2OH
C4H9C*HCH2OH -168,224.757 23.32 - -168,243 0.069 -168,222.44
C4H9CHCHOH -168,071.18 48.92 - -168,090 0.068 -168,069.74
C -168,066.35 48.8 - -168,082 0.068 -168,061.74 3H7CHCHCH2OH
570 Mechanism and Kinetic of Free Radical Reactions for Propane Using theoretical Calculations
Table 5 (coutinued)
C3H7C*(CH3)CH2OH -168,227.38 88.97 - -168,247 0.068 -168,226.74
C5H11C(O)H -166,921.46 49.57 - -166,940 0.068 -166,919.74
C4H9CH(OH) C*HOH -208,781 11.21 - -208,800 0.07 -208,779.14
C -208,806 58.57 - -208,826 0.07 -208,805.14 4H9C*HCH(OH)2
C4H9CH(C3H7) C*HOH -229,654.35 79.7 - -229,674 0.072 -229,652.54
C -229,628.82 52.21 - -229,649 0.071 -229,627.84 5H11CH(C3H7)(O*)
C5H11C*H(OH) -167,064.80 53.07 - -167,083 0.069 -167,062.45
C -208,824.15 50.95 - -208,836 0.07 -208,815.14 5H11C*H(OOH)
C5H11C*H(OC3H7) -229,663.12 80.86 - -229,683 0.072 -229,661.54
C -167,055.54 32.54 - -167,070 0.068 -167,055.74 5H11CH2(O*)
C5H11CH2OH -167,260.32 58.26 - -167,279 0.068 -167,258.74
C -209,000 58.94 - -209,020 0.07 -208,999.14 5H11CH2(OOH)
C5H11CH2(OC3H7) -229,857.85 84.69 - -229,877 0.072 -229,855.54
Table 6 Reaction probabilities of free radical sequences mechanism calculated using DFT 6-31G*/UHF at kCal/mol units.
?Hf Reactant Product Energy barrier ?
CH3CH2CH3+*OH CH3CH2C*H2+H2O 107.61 -1.71
CH3C*HCH3 42.5 -2.62
CH3CH2C*H2 CH3CHCH2+H* 14.69 -18.22
*OH CH3CH2CH2OH 896.8 -73.55
CH3CH2C*H2+ C2H5CH3 C6H12+H*
C2H5C*H2 C6H12 2,704.76 -66.43
CH C2H5C*H2 C4H9C*HCH3 18.89 -18.61 3CHCH2+
*OH CH3C*HCH2OH 11.17 -26.22
CH3CHCHOH+H* 84.98 -16.4
CH3C*HCH2OH
CH 28.07 -15.3 2CHCH2OH+H*
CH 70.21 -70.63 *OH 3CH(OH)CH2OH
CH3C*HCH2OH+ C2H5C*H2 CH3CH(C3H7)CH2OH 6,951.84 -61.22
C3H8 CH3CH(C3H7)CH2OH+H* 2,212.98
CH 110.49 CH2CHCH2OH+ *OH 2OHC*HCH2OH
C2H5C*H2 C4H9C*HCH2OH -3.52 -16.12
?Hf Reactant Product Energy barrier ?
C 33.06 -19.74 4H9CHCHOH
C4H9C*HCH2OH C3H7 CHCHCH2OH 50.18 -11.74
C 395.7 -4.3 3H7C* (CH3)CH2OH
C4H9CHCHOH C5H11CH(O) 42.03 -19
C 400.94 -46.52 4H9C*HCH(OH)2 *OH
C4H9CHCHOH+ C4H9CH(OH) C*HOH 254.64 -20.52
C 56.37 -34.28 C2H5C*H2 4H9CH(C3H7) C*HOH
C5H11CH2(O*) -34.98 +30.9 H*
C5H11CH(O)+
C5H11C*HOH -16 +23.79
C5H11CH(C3H7)(O*) 68.73 +9.42
C2H5C*H2 C5H11C*H(OC3H7) 4,502.1 -24.28
*OH C5H11C*H(OOH) 94.72 -37.52
C5H 25.71 -25.9 C5H11CH2O* + H* 11CH2OH
C2H5C*H2 C5H11CH2(OC3H7) 3,948 -82.28
C 2,819.43 -85.52 *OH 5H11CH2(OOH)
Mechanism and Kinetic of Free Radical Reactions for Propane Using theoretical Calculations 571
and that’s to be characterized by high rate constant,
due to relation between heat of formation, entropy and
free energy. Decreases of enthalpy cause decrease of
free energy, but increase of rate constant [23, 24]. In
two reactions represented by Eqs. (9) and (11), that
have low value of rate constant form the endothermic
reaction. The net equation consisted two mole of
propane reacted with mole of hydrogen peroxide to
produce one mole of water and one mole of Hexanol.
The reaction is exothermic to give up.
??Hrea = -93.47 kCal/mol
H2O2 2*OH (1)
?Hrea = -11 kCal/mol, K1 = 9.8 × 1025 S-1
2CH3CH2CH3+2*OH 2CH3CH2C*H2+2H2O (2)
?HRea = -1.7 kCal/mol, K2 = 1.16 × 1015 S-1
CH3CH2C*H2 CH3CHCH2+H* (3)
?HRea = -18.22 kCal/mol, K3 = 3.8 × 1029 S-1
CH3CHCH2+*OH CH3C*HCH2OH (4)
?HRea = -26.22 kCal/mol, K4 = 4.17 × 1022 S-1
CH3C*HCH2O CH2CHCH2OH+H* (5)
?HRea = -15.3 kCal/mol, K5 = 3.42 × 1027 S-1
CH2CHCH2OH +CH3CH2C*H2 CH3CH2CH2CH2C*HCH2OH (6)
?HRea = -16.12 kCal/mol, K6 = 1.03 × 1013 S-1
CH3CH2CH2CH2C*HCH2OH CH3CH2CH2CH2CHCHOH (7)
?HRea = -19.74 kCal/mol, K7 = 4.58 × 1029 S-1
CH3CH2CH2CH2CHCHOH CH3CH2CH2CH2CH2CH(O) (8)
?HRea = -19 kCal/mol, K8 = 5.34 × 1026 S-1
CH3CH2CH2CH2CH2CH(O)+H* CH3CH2CH2CH2CH2CH2O* (9)
?HRea = + 30.9 kCal/mol, K9 = 5.25 × 10-18 S-1
CH3CH2CH2CH2CH2CH2O*+H* C6H13 (OH) (10)
?HRea = -29.39 kCal/mol, K10 = 1.19 × 1040 S-1
H*+H2O *OH+H2 (11)
?HRea = + 32.32 kCal/mol, K11 = 6.15 × 10-01S-1
H2O2+2CH3CH2CH3 H2+C6H13OH+H2O (12)
?HRea= -93.47
Rate = K1[H2O2] (13) Rate = K2[CH3CH2CH3][OH] (14)
Rate = K3[CH3CH2C*H2] (15) Rate = K4[CH3CHCH2][OH] (16)
Rate = K5[CH3C*HCH2OH] (17) Rate = K6[CH2CHCH2OH][CH3CH2C*H2] (18)
Rate = K7[C5H11C*HOH] (19) Rate = K8[C4H9CHCHOH] (20)
Rate = K9 [C5H11CHO][H*] (21) Rate = K10 [C5H11C*HOH][H*] (22)
??OH?
?? ? K??H?O?? ? K??CH?CH?CH???OH? ? K??CH?CHCH???OH? ? 0 (23)
[OH? ? K??H?O??
K??CH?CH?CH???K??CH?CHCH??
(24)
According to rate constant values, the rate
determining step (the step have highest energy of
transition state and lowest step from steps reactions)
[25] have been suggested depending on the steady
572 Mechanism and Kinetic of Free Radical Reactions for Propane Using theoretical Calculations
state approximation. It is represent the determination
of the effective concentration on the reaction rate. It
can be seen that hydrogen peroxide concentrations is
very important in the initiation of propane’s reactions
by the equation formula.
The reaction rate law for the investigated mechanism
can be derived according to the steady-state
approximation. The net rate of change of the
intermediates may be set equal to zero [9]. Since the
rate determined step is:
Rate ? K??OH??CH?CH?CH?? ?25?
Therfore it can be substituted Eq. (23) in Eq. (24) to
obtain the rate of determinated step accourding to
steady state approximation.
Rate ? K?K??H?O???CH?CH?CH??
K??CH?CH?CH???K??CH?CHCH??
(26)
At comparison position Eq. (26), the rate constant
K4 is larger than K2 (1022 ب 1015) and K4 is control
of reaction and can approximation position in Eq.
(27).
K2[CH3CH2CH3]+K4[CH3CHCH2] ?
K4[CH3CHCH2]
Rate ? K?K??H?O???CH?CH?CH??
K??CH?CHCH?? ,
?RateK/[H2O2][CH3CH2CH3],
K/ ? K?K?
K??CH?CHCH??
(27)
4. Conclusions
(1). The photolysis reaction of peroxide in gas
phase occurs with energy barrier equal to 67 kCal/mol.
(2). The stabilized structure of propane comes out
by total energy that’s equal to -74,711.83 kCal mol-1.
(3). The direct reaction of propane with hydroxyl
radical occurs through the probable third transition
state with lowest value of energy barrier (-2.5
kCal/mol) and the zero energy value (25.96
kCal/mol).
(4). The net equation is consisted from one mol of
hydrogen peroxide and two mol of propane to
produced one mol of water, and one mol of hexanol.
Since the reaction is exothermic with ? ?Hrea = -93.47
kCal/mol.
(5). The rate constant of rate determinate step is
represented by K/
= K?K?
K??CH?CHCH??
.
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