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Computational investigation of the reaction of NO with imine, silanimine, and its substituted derivatives
Journal of Molecular Structure: THEOCHEM 772 (2006) 93–102 www.elsevier.com/locate/theochem
Computational investigation of the reaction of NO with imine, silanimine, and its substituted derivatives Hui-Lung Chen, Jia-Jen Ho
*
Department of Chemistry, National Taiwan Normal University, 88, Section 4, Tingchow Road, Taipei 116, Taiwan Received 7 April 2006; received in revised form 15 June 2006; accepted 21 June 2006 Available online 27 June 2006
Abstract The reaction mechanisms of HN@XH2 (X = C, Si) + NO were studied at the QCISD(T)/6-311++G(d,p)//B3LYP/6-311++G(d,p) level. The result indicated that the most favorable pathway of HN@CH2 + NO would lead to the formation of CH2N2 + OH with the calculated barrier of 44.41 kcal/mol, while in the reaction of HN@SiH2 + NO the most preferable pathway shifted to the production of H2SiOH + N2, a direct reduction of NO into a stable and nontoxic nitrogen molecule. The barrier of rate-determining step was calculated to be 18.90 kcal/mol, and it could be further decreased to 14.42 kcal/mol in the N-methyl substituted silanimine (CH3N@SiH2). It could be advantageous if it would act as a reactant in converting the reactive and toxic NO into a harmless N2 gas in several NO-producing combustion systems. The possible explanation to the differences between imine and silanimine toward the reaction with NO was provided. 2006 Elsevier B.V. All rights reserved. Keywords: Ab initio; NO; Imine; Silanimine; Donor–acceptor
Mechanism of the Thermal DeNOx reaction
1. Introduction The production of nitrogen oxides via the combustion of fossil fuels attracts great interest because they are considered as toxic pollutants to the atmosphere. In 1970s it was first reported by Richard Lyon that ammonium could rapidly and nearly quantitatively reduce NO to N2 and H2O if used in the presence of O2 at temperatures of 900–1100 C [1,2]. This new chemical reaction was quickly developed into what is called the Thermal DeNOx process and its development has been reported in a series of papers [3–11]. The model developed by Dean, DeGregoria, Hardy, and Lyon (the so called DDHL model [12]) consists of a set of reactions involving the nitrogenous species shown in the following scheme:
N2 + H2O NO
NH2
NH3
OH O
M
0166-1280/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2006.06.022
N2 + H
NH2 O2 OH O
NH3 + NO
NH2 M
HNO
NH O2
OH
H + NO
NO pathway
H2 O + NO
The key reaction in thermal DeNOx is the reaction between NH2 and NO, which has two major product channels:
NH2 + NO $ N2 + H2 O Corresponding author. Tel.: +886 2 29309085; fax: +886 2 29324249. E-mail address: [email protected] (J.-J. Ho).
N2 pathway
OH + NNH
NH2 + NO $ NNH + OH
*
NH3 + N2
a radical-producing channel a chain-terminating channel
Although the model proves to be successful at predicting actual field performance [13] the details of the reaction
94
H.-L. Chen, J.-J. Ho / Journal of Molecular Structure: THEOCHEM 772 (2006) 93–102
mechanism remain controversial. Several other studies [14–24] also have been conducted by using catalysts to eliminate the production of NOx, however, the diversity and complexity of these reaction mechanisms were still unknown. There were other important reaction mechanisms studied to reduce the emission of nitrogen oxides from internal-combustion engine, such as NCO + NO by Hershberger [25], and Lin et al. [26], and NCN + NO by Hershberger [27], and Chen et al. [28]. Theoretical studies on the mechanism of halogenated carbenes with NO, and methylidyne radical with NO2 were also performed by Liu [29], and Tao et al. [30]. Recently, several experimental studies about the reaction of nitric oxide (NO) with a series of organic compounds (such as amines, imines, enamines, and amidines) was also reported widely by Hrabie and Keefer et al. [31–36]. Our purpose of this study is to find the possible reactants which may react with NO to form the stable product such as N2 which is not harmful to our environment and possibly with lower energy barriers. The first portion of this paper focuses on imine to react with NO. We calculate most of the probable reaction pathways and plot the potential energy surfaces, find the possible pathway leading to stable N2, and perform transition barrier calculations. In the second portion we replace imine with silanimine and emphasizing on this N2 formation pathway, and find the barrier of rate-determining step is greatly reduced. We further replace the silanimine with substituted derivatives to compare the energy barriers, and the results are discussed. 2. Computational methods Ab initio molecular orbital calculations were carried out using the Gaussian 03 suite of programs [37]. The geomet-
rical structures of all the reactants, intermediates, transition states, and the products were optimized by using hybrid density functional, B3LYP, method [38,39] with 6311++G(d,p) basis set. The calculated equilibrium structures (local minima and saddle points) were characterized by harmonic vibrational frequency calculations at the same level of theory. Zero-point energy (ZPE) correction was also considered at B3LYP/6-311++G(d,p) level. Intrinsic reaction coordinates (IRC) [40] calculations were performed at the same level of theory to actually establish the link between transition state and the intermediates. To further correct for electron correlation, single point calculations were carried out at the QCISD(T)/6311++G(d,p)//B3LYP/6-311++G(d,p) level of theory [41–44]. We referred to the work of Liu et al. [29] in which they used similar method of calculation QCISD(T)/6311G(df,p)//B3LYP/6-311G(d,p) and found that the spin contamination for NO radical was not severe (ÆS2æ = 0.76). We expanded the basis set by adding the diffuse functions for both heavy and light atoms. Also we tried several other methods to calculate the geometrical parameters and proton affinity of CH2NH molecule, as well as the dissociation energy of CH2N2 fi CH2 + N2 (where CH2N2 is among the important product in the titled reaction), which were all compared with the known observed values and the result was listed in Table 1. The best fit of various calculation methods to the observed values [45–51] was QCISD(T)/6-311++G(d,p)//B3LYP/6311++G (d,p). In addition, we also carried out the same method to calculate the reaction energy of the (1/2) C2H4 + (1/2) trans-N2H2 fi CH2@NH, and the result, DE = 8.91 kcal/mol, was in good agreement with the calculated value obtained by Oliveira et al. [47] (ca. 9.1 kcal/ mol, by W2 method). Consequently, QCISD(T)/
Table 1 The geometries (bond lengths and angles), proton affinities (PA) of the CH2@NH molecule and the dissociation energy of CH2N2 fi CH2 + N2 calculated at various levels of theory and some experimental and other calculated data available from the literature ˚) ˚) ˚) ˚) Level of theory C–N (A N–H (A Cis-C–H (A Trans-C–H (A \HNC Proton affinities Dissociation energies MP2/6-31G MP2/6-31+G* MP2/6-311++G** B3LYP/6-31G B3LYP/6-31+G* B3LYP/6-311++G** QCISD(T)/6-311+ +G**//B3LYP/6-311++G** Data from literature a b c d e f g h i
(kcal/mol)a
(kcal/mol)b
1.28 1.28 1.28 1.28 1.27 1.27
1.03 1.03 1.02 1.03 1.03 1.02
1.10 1.10 1.10 1.10 1.10 1.10
1.09 1.09 1.09 1.09 1.09 1.09
109.7 110.1 109.2 113.7 110.9 110.9
131.70 203.25 205.56 215.08 204.90 206.21 207.42
31.66 38.92 36.76 55.63 45.78 43.75 30.16
1.27c
1.02c
1.09c
1.09c
110.4c
206.2 ± 1.5d, 207.5(calcd.)e
<35f, <44g <41.7h, 25i
The energy difference between the cation CH2NH+ and the neutral CH2NH molecule. The energy difference between the CH2N2 and the CH2(a˜1A1) + N2 molecule. References [45]. References [46,47]. References [46,47]. References [48–51]. References [48–51]. References [48–51]. References [48–51].
H.-L. Chen, J.-J. Ho / Journal of Molecular Structure: THEOCHEM 772 (2006) 93–102
6-311++G(d,p)//B3LYP/6-311++G (d,p) accounts for our choice of calculation method in this study. Unless otherwise specified, the QCISD(T) single-point energies are used in the following discussions.
vibration energy (ZPE) correction is considered, and the energies relative to the reactants calculated at QCISD(T) levels are denoted as QRE. The highest transition barrier in the whole pathway from CR2 to product P3 will be 61.6 kcal/mol (TS11,QCISD(T)). There is another pathway leading to the same product from CR1 (CR1 fi TS1 fi 2 fi TS2 fi 3 fi TS3 fi 4 fi TS5 fi 5 fi TS8 fi 6 fi TS9 fi P3), with much higher energy barrier, 67.6 kcal/mol (TS8). Diazomethane, P1 products (CH2N2 + OH), could also be formed via the pathway of CR1 fi TS1 fi 2 fi TS2 fi 3 fi TS3 fi 4 fi TS5 fi 5 fi TS7 fi P1 with much smaller energy barriers, the highest one in the whole pathway is 44.41 kcal/mol (TS2). During our calculation we found two possible pathways leading to the cyclic conformer of diazomethane P2, with relatively higher energy barriers. One starts from CR1 fi TS1 fi 2 fi TS2 fi 3 fi TS4 fi P2, and the other CR1 fi TS1 fi 2 fi TS2 fi 3 fi TS3 fi 4 fi TS6 fi P2. The highest barrier in the former pathway is 60.7 kcal/mol (TS4), while the latter is 57.7 kcal/mol (TS6). The cyclic conformer of diazomethane is about 7 kcal/mol less stable than the linear counterpart. Therefore, these two pathways are not favorable as compared to the pathway to form product P1. Our aim in studying this reaction was to find other possible reactants which can replace imine, CH2NH, to react with NO and obtain lower barriers, especially in the similar pathway leading to the formation of N2 gas. Therefore, our follow-up sections will be focused on this reaction pathway. According to the photoelectron spectroscopy of the observed ionization potentials of silanimines studied by Pfister-Guillouzo et al. [52], they concluded that the first ionization energy was originated from the ejection of an
3. Results and discussion The possible reaction pathways for imine + NO are schematically depicted in Fig. 1. The approach of the two reactants forms a complex, called CR1, in which the N atom of NO attacks the N atom of imine in a position to form an s-trans conformer, 2, via transition state TS1. The other complex, called CR2, in which the N atom of NO attacks the N atom of imine in a position to form an s-cis conformer, 7, via transition state TS10. We plotted the calculated potential energy surfaces in Fig. 2. These two separated complexes lead to completely different follow-up reaction mechanisms and different product formations. Obviously, the formation of the s-cis conformer (7) has lower energy barrier. It may further form a four-member ring intermediate, 8, via TS11. Then 8 may open the ring by breaking CAN bond (via TS12) to form intermediate9 and followed by quickly passing TS14 to break the NAO bond to form a weakly bonded complex of H2CO—N2H (C-10 + 11). Or, 8 may decompose (via TS13) directly to form C-10 + 11. The latter has lower energy barrier. This weakly bond complex, C-10 + 11, then further decomposes (via TS15) to a thermodynamically very stable products P3 (H2COH + N2), which contains the expected harmless N2 gas. All the calculated energetics of reactants, intermediates, and products are listed in Table 2, and that of transition states in Table 3. The zero-point
H
H TS3
C N
TS1
C N
H
H
C N
C N
H N
O
H
H
N O
TS6
5
P1
H
N O
TS8 TS4
3
2
CR1
H
CH2 N N + OH N O
H
H
TS2
TS7
N
N O 4
H
C H
TS5
H H
95
H
N C
+ OH
H
N
H
C
P2
C NH + NO
N N
H TS12 H C
1+NO
NH O
H
H TS10
H
C N
H
C N
H
H O CR2
C
NH
O
N
TS9
TS14 O
TS13
O 7
N 9
H H
N
N
TS11
8
H O
TS15 + N2H
C H
H
H
H
H C-10+11
+
C H
N2
H P3
Fig. 1. The schematic diagram of the calculated possible reaction pathways of HN@CH2 + NO reaction.
OH 6
96
H.-L. Chen, J.-J. Ho / Journal of Molecular Structure: THEOCHEM 772 (2006) 93–102 RE(kcal/mol) TS8
TS12
TS11
TS4
60
TS6
TS13 50 TS2
TS5
40
c-CH2N2+OH TS7
TS14
8
P2
l-CH2N2+OH
9 30
P1
TS1
20
TS3 2
TS10 7
3
5
4
10 0
1+NO
TS15 CR1 CR2
-10 C-10+11 -20
6
TS9
-30 -40 H2COH+N2 P3
Fig. 2. The calculated potential energy surfaces of the possible reaction pathways of the HN@CH2 + NO reaction at the QCISD(T)/6-311++G(d,p)// B3LYP/6-311++G(d,p) Level. The labels in the figure represent the same species as those in Fig. 1.
Table 2 The calculated total energies at the QCISD(T)/6-311++G(d,p)//B3LYP/6-311++G(d,p) level together with zero-point vibration energies (QTE+ZPE) (a.u.), and the relative energies calculated at the same level (QRE) (kcal/mol) of reactants, intermediates, and products in HN@XH2(X = C, Si) + NO reactions Species (X = C)
QTE+ZPE (a.u.)
QRE (kcal/mol)
Species (X = Si)
QTE+ZPE (a.u.)
QRE (kcal/mol)
1 + NO CR1 CR2 2 3 4 5 6 7 8 9 C-10 + 11 P1 P2 P3
224.017321 224.019157 224.018738 223.982910 223.994252 223.993264 223.989204 224.051683 223.985391 223.960964 223.964586 224.036657 223.966131 223.953686 224.090790
0.0 1.2 0.9 21.6 14.5 15.1 17.6 21.6 20.0 35.4 33.1 12.1 32.1 39.9 46.1
1s + NO CR1s CR2s 2s 3s 4s 5s – 7s 8s 9s C-10s + 11a P1s P2s P3s
475.030618 475.032918 475.032783 475.034292 475.026928 475.025842 475.029196 – 475.036380 475.050961 475.038149 475.070823 475.028135 474.995093 475.168050
0.0 1.4 1.3 2.3 2.3 3.0 0.9 – 3.6 12.8 4.7 25.2 1.6 22.3 86.2
a
The value is calculated at QCISD(T)/6-311++G(d,p)//HF/6-311++G(d,p) level.
electron from the nitrogen lone pair orbital, similarly to the homologous imines. Nevertheless, the position of this band, definitely lower than the corresponding imine, indicates the more pronounced p-character of the nitrogen lone pair in silanimines. In this consequence we chose silanimine (H2SiNH) and its substituted derivatives (R1R2SiNR3) to replace imine in reacting with NO. First of all, we used NBO calculation method [53] to calculate the p-character of lone pair orbital of N atom in both imine and silanimine.
We found out that the orbital coefficients of 2py, 3py, 4px and 4py, respectively, of silanimine were much larger than the corresponding imine, indicating the more pronounced p-character of nitrogen lone pair orbital in silanimine, in good agreement with Pfister-Guillouzo observation. The calculated energetic data of reactants, intermediates, and products of silanimine with NO reaction are also listed in Table 2 and that of transition states in Table 3, with the same label notation as the imine counterparts, except
H.-L. Chen, J.-J. Ho / Journal of Molecular Structure: THEOCHEM 772 (2006) 93–102
97
Table 3 The calculated total energies at the QCISD(T)/6-311++G(d,p)//B3LYP/6-311++G(d,p) level together with zero-point vibration energies (QTE+ZPE) (a.u.), and the relative energies calculated at the same level (QRE) (kcal/mol) of all the transition states obtained in HN@XH2(X = C, Si) + NO reactions Species (X = C)
QTE+ZPE (a.u.)
QRE (kcal/mol)
Species (X = Si)
QTE+ZPE (a.u.)
QRE (kcal/mol)
TS1 TS2 TS3 TS4 TS5 TS6 TS7 TS8 TS9 TS10 TS11 TS12 TS13 TS14 TS15
223.974315 223.947069 223.979095 223.920525 223.953248 223.925325 223.957807 223.909658 224.050893 223.980740 223.919203 223.913857 223.922811 223.958819 224.021208
27.0 44.1 24.0 60.7 40.2 57.7 37.3 67.6 21.1 23.0 61.6 64.9 59.3 36.7 2.4
TS1s TS2s TS3as TS3s TS4s TS4as TS5s TS6s TS9s TS10s TS11s TS12s TS13s TS14s TS15sa
474.996855 474.983987 475.001371 475.012559 474.984922 475.006351 475.011118 474.984664 475.024125 475.000540 475.025832 475.026488 475.025225 475.017130 475.067761
21.2 29.3 18.3 11.3 28.7 15.2 12.2 28.8 4.1 18.9 3.0 2.6 3.4 8.5 23.3
a
The value is calculated at QCISD(T)/6-311++G(d,p)//HF/6-311++G(d,p) level.
suffixed with an s to represent silanimine analogues. The schematic diagram of possible reaction pathways of silanimine with NO is drawn in Fig. 3, and that of the calculated potential energy surfaces at QCISD(T)/6-311++G(d,p)// B3LYP/6-311++G(d,p) is plotted in Fig. 4. There are six reaction pathways to form three possible products similar to that of imine counterparts: (1) P1s (SiH2N2 + OH), (2) P2s (cyclic-SiH2N2OH), (3) P3s (H2SiOH + N2), respectively. However, the P2s is different from P2 in that the OH group is still bound to the cyclic-SiH2N2, while that in P2 the OH is completely detached from cyclic-CH2N2. This may attribute to the empty d-orbital of Si atom which provides more bonding character to lower the energy.
In most of the reaction pathways the calculated potential energy profiles of silanimine are similar to those of imine’s, but with much lower profiles, so do the energy barriers (about 30–40 kcal/mol lower in average). Therefore, silanimine is energetically more reactive, in good agreement with the observation by Pfister-Guillouzo et al. [52]. In addition, the most probable pathway of the reaction shifted to the formation of P3s (HOSiH2 + N2) (the barrier of rate-determining step is only 18.90 kcal/mol, the smallest among all the reaction pathways), CR2s fi TS10s fi 7s fi Ts11s fi 8s fi TS13s fi C-10s + 11 fi TS15s fi P3s, which was very different from the imine’s one, in which it lead to product P1 (CH2N2 + OH)
SiH2 N
N + OH P1s
TS3as
TS4as H
H
Si N
TS3s
N
H 4s H
TS1s
H
H
Si N H H
H
TS2s
H
Si N
Si N
N CR1s
N
H
O
N
N
O
N
H
O H 5s
TS6s
H
H
O
O TS4s
3s
2s
Si H
TS5s
H
N Si
H
H Si N H + NO
N P2s
OH TS9s
H TS12s
1s+NO
NH
H Si O
H
H
TS10s
H
Si N
H
Si N
H
H O CR2s
H N
N
TS11s
Si
NH
O
N
O 7s
N 9s
H
TS14s O
TS13s
8s
+ N2H
Si H
H O
TS15 H
+
Si H
C-10s+11
Fig. 3. The schematic diagram of the calculated possible reaction pathways of HN@SiH2 + NO reactions.
H P3s
N2
98
H.-L. Chen, J.-J. Ho / Journal of Molecular Structure: THEOCHEM 772 (2006) 93–102 RE(kcal/mol) TS2s
30 TS1s
20
TS4s
TS6s
H H
TS10s
TS3as
Si
N N OH
P2s
TS4as TS5s
TS3s 10 TS11s 0
CR1s -10
3s
1s+NO CR2s
2s
TS12s TS13s
4s
TS14s
5s
SiH2N2+OH TS9s
9s
P1s
7s 8s
TS15s
-20 C-10s+11 -30 -40 -50 -60 -70 -80
H2SiOH+N2 P3s
Fig. 4. The calculated potential energy surfaces of the possible reaction pathways of the HN@SiH2 + NO reaction at the QCISD(T)/6-311++G(d,p)// B3LYP/6-311++G(d,p) Level. The labels in the figure represent the same species as those in Fig. 3.
(the barrier of rate-determining step is 44.41 kcal/mol, the smallest among all the possible reaction pathways in the imine’s case). While in the process to form P3s there is a four-member ring intermediate 8s, much more stable (about 48 kcal/mol lower) than the corresponding similar structure 8. Also the energy barrier of TS11s (leading to the formation of 8s) decreases a great amount (only 3.0 kcal/mol as compared to TS11 of 61.6 kcal/mol in forming 8) due to the great instability of the double bond between Si and N atoms in silanimine. This result is also in good accord with the calculation done by Becerra et al. [54], in which they found a similar stable four-member ring structure (formoxysilylene-cyclic). Therefore, if we replace imine with silanimine to perform the reaction with NO the most probable reaction pathway will lead to the formation of P3s, transferring the reactive NO into stable and nontoxic N2 molecule. It sounds like a very valuable application. Now we try to find some substituted derivatives of silanimine to possibly further decrease the barrier of rate-determining step in this most preferable process. The rate-determining step in this process is the formation of intermediate 7s from CR2s via transition state TS10s. We substituted the hydrogens of silanimine with some electron-withdrawing, or, -donating group and calculated the energy barrier of TS10s. The result is shown in Table 4. In order to analyze the calculated result we followed the Mulliken DA (donor-acceptor) model [55,56]. The calculated ionization energies (IE), electron affinities (EA) and charge-transfer energies corresponding to the
Table 4 The energy differences (a.u.) between HOMOa(YN@SiZ2) and LUMOa(NO) with respect to the transition state energies of TS10s (kcal/mol) of various substituted silanimines calculated at QCISD(T)/6-311++G(d,p)// B3LYP/6-311++G (d,p) level Structure
DE[HOMO(YN@SiZ2) LUMO(NO)]
TS10s
HN@SiH2 (CH3)N@SiH2 HN@SiH(CH3) HN@Si(CH3)2 (CH3)N@SiH(CH3) (CH3)N@Si(CH3)2 (F)N@SiH2 HN@SiH(F) HN@Si(F)2 (F)N@SiH(F) (Cl)N@SiH2 HN@SiH(Cl) HN@Si(Cl)2 (Cl)N@SiH(Cl) (CH3)N@Si(Cl)2 (CH3)N@Si(F)2
0.44485 0.40230 0.43701 0.44769 0.41102 0.42024 0.47516 0.47164 0.49050 0.45378 0.43253 0.46593 0.47347 0.42308 0.43230 0.45900
18.90 14.42 18.84 20.87 15.09 15.70 20.06 21.93 20.96 18.63 17.26 20.73 19.19 15.80 17.64 20.56
a Frontier orbital energies are calculated at QCISD(T)/6-311++G(d,p)// B3LYP/ 6-311++G(d,p) level.
states (D+A and DA+) of HN@XH2 (X = C, Si) and NO molecules are listed in Table 5. These data are quite convincing since the calculated ionization potential of NO (9.23 kcal/mol) is in good agreement with the experimental observation [57,58] (9.26 kcal/mol). From the calculated charge transfer energies of either D+A or DA+
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99
Table 5 The calculated ionization energies (IE)a, electron affinities (EA)a, and charge-transfer energies corresponding to the states (D+A and DA+)b and the differences (in a.u.) between HOMO and LUMO energies in HN@XH2 (X = C, Si) + NO reactions Structure
D+A
DA+
1.42 0.96 0.46
8.27 8.77
8.37 7.56
HOMOd
LUMOd
DE[HOMO(HN@XH2) LUMO(NO)]
DE[HOMO(NO) LUMO(HN@XH2)]
0.42806 0.43162 0.37651
0.07201 0.06985 0.03652
0.50363 0.44485
0.49791 0.46458
IE
EA
QCISD(T)/ 6-311++G(d,p)//B3LYP/ 6-311++G(d,p) NO HN@CH2 HN@SiH2 e
NO HN@CH2 HN@SiH2
9.23(9.26)c 9.79 8.98
a
Adiabatic ionization energies (IE) and electron affinities(EA) of NO, HN@CH2 and HN@SiH2 (in eV). Charge-transfer energies (eV) of D+A and DA+ states, calculated according to the following formulas: D+A = IENO EAHN@XH2, + D A = IEHN@XH2 EANO. c The experimental ionization energy of NO, from Ref. [57,58]. d Frontier orbital energies are calculated at QCISD(T)/6-311++G(d,p)//B3LYP/ 6-311++G(d,p) level. e The values of HOMO and LUMO are alpha (a) orbitals.The HOMO is p character and the LUMO is r character. b
in the reaction system of HN@XH2 (X = C, Si) + NO we are able to predict the role of NO of being an electrophile or nucleophile. It is not that clear in the imine system, since the values of D+A and DA+ are quite close to each other. However, it is obvious that NO exhibits electrophilically towards silanimine since DA+ is much smaller than D+A, which indicates that the donation of an electron from silanimine is more preferable. We further employed the frontier orbital theory [59,60] to check the orbital interaction between these two reactants. The calculated HOMO and LUMO energies and their differences (DE) of NO and HN@XH2 (X = C, Si) at the QCISD(T) level are listed in the lower part of Table 5. It points out that the HOMO of silanimine and LUMO of NO are closer to each other, implying the electrophilic character of NO towards silanimine. In our attempts to find the substituted silanimine derivatives which might further decrease the barrier of rate-determining step (TS10s) in the process to form P3s (converting the NO into N2), we replaced the hydrogens of silanimine with methyl group, F, and Cl atoms (YN@SiZ2, where Y, Z = H, CH3, F, Cl). As shown in Table 4, the calculated barrier of TS10s could be further reduced to 14.42 kcal/mol for (CH3)N@SiH2, the smallest, as compared to other substituted counterparts, while the unsubstituted silanimine is 18.90 kcal/mol. In addition, among other substituted silanimines (CH3)N@SiH(CH3), (CH3)N@Si(CH3)2, and (Cl)N@SiH(Cl) also decrease the TS10s barrier to 15.09, 15.70, and 15.80 kcal/mol, respectively. While (Cl)N@SiH2, and (CH3)N@Si(Cl)2 decrease only a small amount, 17.26, and 17.64 kcal/mol, respectively. In contrast, the fluorine-substituted derivatives (F)N@SiH2, HN@SiH(F), and HN@Si(F)2 all increase the barrier around 2–3 kcal/mol (20 22 kcal/mol). An attempt was made to find the explanation. At first, the frontier orbital calculation showed that the difference between HOMO of YN@SiZ2 and LUMO of NO, DE[HOMO(YN@SiZ2) LUMO(NO)], decreases for most of the Nmethyl substituted compounds, which would enhance the
interaction and lower the energy barrier of TS10s. In addition, Pfister-Guillouzo et al. [52] pointed out that the N-methylation of silanimine induced the destabilization of the pSi@N orbital and the nitrogen nonbonding orbital, which would increase the energy of the nitrogen lone pair due to the donor inductive effect of the methyl group. However, the p system is less sensitive to the inductive effect than the lone pair (because of its delocalization in the p system). This explanation is in good agreement with our calculation in which the N-methylation of silanimine is the most reactive species among all in reducing the NO to N2 molecule, while the Si-methylation analogues do not show similar effect. For the electron-withdrawing substitution groups, most of the F-atom substituted silanimines increase the barrier (TS10s), due to the fact that the lone pair electrons of N-atom become less donorable to the NO molecule. As for the Cl-substituted analogues the energy barrier of TS10s are surprisingly smaller than the unsubstituted silanimine, especially for (Cl)N@SiH(Cl), only 15.80 kcal/mol. To understand this fact we performed an NBO calculation to the TS10s transition structure and found out that there was an interaction between the lone pair electrons of N atom of silanimine and the antibonding of rNO orbital in these substituted transition structures. The order of this calculated interaction energy from large to small is (CH3)N@SiH2. . .NO > (Cl)N@SiH2. . .NO > HN@SiH2. . .NO > (F)N@SiH2. . .NO, exactly the opposite order of the barriers of TS10s in these systems. The extent of this orbital interaction correlates oppositely to the TS10s barrier. Some of these transition structures are plotted in Fig. 5. The larger is the interaction energy the more stable the transition structure and therefore the smaller the barrier of TS10s. In addition, the bond length of NO in the TS10s of these systems becomes longer as the interaction energy increases, indicating the stronger lone pair interaction with the antibonding orbital of rNO , which increases the instability of the NO bond.
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H[6]
H
H
1.481
H[7]
124.82
Si[1]
C[7]
H[6]
1.013
1.479
133.10
N[2]
1.651
116.45
Si[1]
1.844
115.19
1.096 H
1.446
N[2]
1.645 1.845
118.09 115.98
H[5]
N[3]
H[5]
N[3]
1.165
TS10s
1.173 O[4]
O[4]
TS10s_CH3-N
F[7]
Cl[7] H[6]
H[6]
1.483
1.480 121.99 Si[1]
118.05
N[2]
Si[1]
N[2]
1.684
1.407
113.07
1.719
1.706
117.91
1.944
1.894
108.42
111.07
N[3]
H[5]
H[5]
N[3]
1.148 1.156
TS10s_Cl-N
O[4]
TS10s_F-N
O[4]
Fig. 5. The calculated transition structures of TS10s and its N-substituted analogues, YN@SiH2. . .NO (Y, @CH3, Cl, F), represented as TS10s_CH3–N, S10s_Cl–N, and TS10s_F–N, respectively. All are calculated at B3LYP/6-311++G** level.
4. Conclusions In considering the simple dissociation reaction, loss of OH from adduct 5 to form CH2N2, but not directly from adduct 3 or 4 could be explained as follow. From our calculated relative energies, the order of relative stability was 3 (14.5 kcal/mol) > 4 (15.1 kcal/mol) > 5 (17.6 kcal/mol), with adduct 5 the most unstable. It was due to the larger electron repulsion force existing between the lone pair electron of O atom and the facing C@N double bond (electron rich) in the construction of 5, which was not yet present in the structure of 3 and 4. Also, structure 3 might exist weak hydrogen bonding between the terminal H atom and the N ˚ ) of the C@N bond, which accounted for atom (2.09 A slighter more stable than adduct 4. Therefore, adducts 3 and 4 were stable enough not to proceed the dissociation process of losing OH to form CH2N2, as compared to adduct 5. In contrast to the silanimine counterparts, the calculated relative stability order was 5s (0.9 kcal/mol) > 3s (2.3 kcal/mol) > 4s (3.0 kcal/mol), with 4s the most unstable. Similar argument of existing weak hydrogen bonding ˚ ) could explain why 3s was slighter more stable in 3s (2.13 A than 4s, however, these two adducts could undergo dissociation process of losing OH and form linear SiH2N2 with some barriers. On the contrary, the 5s adduct appears to
be more stable as compare to the imine counterpart, partly because that the Si atom has the empty d-orbital which may accommodate the lone pair electron of the O atom in the 5s construction, and hence lower the energy. This argument could also be supported by the fact that the OH group could be easily migrated to the Si atom with the very low barrier (TS9s, 3.2 kcal/mol relative to 5s). Also from our NBO calculation there was a strong interaction between the lone pair electron of oxygen atom to the antibonding of N@N, which was not seen in its counterpart of 5. All these probably make 5s to be less feasible to perform the dissociation of losing OH, instead, it turns out to form products P3s directly. In the replacement of imine with silanimine toward the reaction with NO the barriers of rate-determining step of all reaction pathways were greatly reduced (ca. 30– 40 kcal/mol smaller), and the most probable reaction pathway became the one that reduced NO to N2 molecule via a SiANANAO four-member ring structure mechanism. The barrier of rate-determining step (TS10s) of this pathway was calculated to be 18.90 kcal/mol at QCISD(T)/6311++G(d,p)//B3LYP/6-311++G(d,p) level for unsubstituted silanimine, and further decreased to 14.42 kcal/mol for N-methyl silanimine. The result of this study will be of great value in searching for the effective reagents of
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converting the industrial pollutants containing toxic NO into stable and harmless nitrogen gases. Acknowledgements Support for this research from the National Science Council of the Republic of China (NSC 94-2113-M-003005) is gratefully acknowledged. We are also grateful to the National Center for High-Performance Computing where the Gaussian package and the computer time were provided. Appendix A. Supporting Information Figures showing the optimized geometries of the possible adducts and transition states on the potential surfaces of both imine and silanimine plus NO reactions calculated at the B3LYP/6-311++G** level are available free of charge in this publication. Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.theochem.2006.06.022. References [1] R.K. Lyon, US Patent 3, 900 (1975) 559. [2] R.K. Lyon, Int. J. Chem. Kinet. 8 (1976) 315. [3] R.K. Lyon, J.P. Longwell, in: S. Kasuga et al. (Eds.), Proceedings of the 4th International Clean Air Congress, Industrial Pollution Control Association of Japan, Tokyo, 1977, p. 691. [4] R.K. Lyon, J.P. Longwell, in: Proceedings of the NOx Control Technology Seminar, Electric Power Research Institute, Palo Alto, CA, 1976, p. 22. [5] R.K. Lyon, D. Benn, in: Proceedings of the 17th Symposium (International) on Combustion, Combustion Institute, Pittsburgh, 1979, p. 601. [6] R.K. Lyon, Hydrocarb. Process 58 (1979) 109. [7] R.K. Lyon, A. Tenner, Paper 78–81. Presented at the 71st Meeting of the Air Pollution Control Association, June 1978. [8] A.M. Dean, J.D. Hardy, R.K. Lyon, Presented at the 15th International Symposium on Free Radicals, Nova Scotia, Canada, June 1981. [9] B.E. Hurst, Glass Technol. 24 (1983) 97. [10] B.E. Hurst, Stud. Environ. Sci. 21 (1982) 725. [11] J.A. Miller, M.C. Branch, R.J. Kee, Combust. Flame 44 (1981) 81. [12] A.M. Dean et al., US Patent 4, 507 (1985) 269. [13] R.K. Lyon, Environ. Sci. Technol. 21 (1987) 231. [14] J.A. Miller, S.J. Klippenstein, J. Phys. Chem. A 104 (2000) 2061. [15] M. Misono, Y. Hirao, C. Yokoyama, Catal. Today 38 (1997) 157. [16] A.N. Hayhurst, A.D. Lawrence, Combust. Flame 110 (1997) 351. [17] K. Honkala, P. Pirila, K. Laasonen, Surf. Sci. 489 (2001) 72. [18] R. Smits, Y. Iwasawa, Appl. Catal. B-Environ. 6 (1995) 201. [19] S. Suzuki, H. Moriyama, K. Murata, Energ. Fuel. 16 (2002) 1173. [20] C. Schmidt, T. Sowade, E. Loffler, A. Birkner, W. Grunert, J. Phys. Chem. B 106 (2002) 4085. [21] V.I. Parvulescu, P. Grange, B. Delmon, Catal. Today 46 (1998) 233. [22] Y. Traa, B. Burger, J. Weitkamp, Microporous Mesopor. Mater. 30 (1999) 3. [23] S. Bennici, A. Gervasini, N. Ravasio, F. Zaccheria, J. Phys. Chem. B 107 (2003) 5168. [24] Y.H. Yeom, B. Wen, W.M.H. Sachtler, E. Weitz, J. Phys. Chem. B 108 (2004) 5386. [25] W.F. Cooper, J. Park, J.F. Hershberger, J. Phys. Chem. 109 (1993) 3283.
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Computational investigation of the reaction of NO with imine, silanimine, and its substituted derivatives Hui-Lung Chen, Jia-Jen Ho
*
Department of Chemistry, National Taiwan Normal University, 88, Section 4, Tingchow Road, Taipei 116, Taiwan Received 7 April 2006; received in revised form 15 June 2006; accepted 21 June 2006 Available online 27 June 2006
Abstract The reaction mechanisms of HN@XH2 (X = C, Si) + NO were studied at the QCISD(T)/6-311++G(d,p)//B3LYP/6-311++G(d,p) level. The result indicated that the most favorable pathway of HN@CH2 + NO would lead to the formation of CH2N2 + OH with the calculated barrier of 44.41 kcal/mol, while in the reaction of HN@SiH2 + NO the most preferable pathway shifted to the production of H2SiOH + N2, a direct reduction of NO into a stable and nontoxic nitrogen molecule. The barrier of rate-determining step was calculated to be 18.90 kcal/mol, and it could be further decreased to 14.42 kcal/mol in the N-methyl substituted silanimine (CH3N@SiH2). It could be advantageous if it would act as a reactant in converting the reactive and toxic NO into a harmless N2 gas in several NO-producing combustion systems. The possible explanation to the differences between imine and silanimine toward the reaction with NO was provided. 2006 Elsevier B.V. All rights reserved. Keywords: Ab initio; NO; Imine; Silanimine; Donor–acceptor
Mechanism of the Thermal DeNOx reaction
1. Introduction The production of nitrogen oxides via the combustion of fossil fuels attracts great interest because they are considered as toxic pollutants to the atmosphere. In 1970s it was first reported by Richard Lyon that ammonium could rapidly and nearly quantitatively reduce NO to N2 and H2O if used in the presence of O2 at temperatures of 900–1100 C [1,2]. This new chemical reaction was quickly developed into what is called the Thermal DeNOx process and its development has been reported in a series of papers [3–11]. The model developed by Dean, DeGregoria, Hardy, and Lyon (the so called DDHL model [12]) consists of a set of reactions involving the nitrogenous species shown in the following scheme:
N2 + H2O NO
NH2
NH3
OH O
M
0166-1280/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2006.06.022
N2 + H
NH2 O2 OH O
NH3 + NO
NH2 M
HNO
NH O2
OH
H + NO
NO pathway
H2 O + NO
The key reaction in thermal DeNOx is the reaction between NH2 and NO, which has two major product channels:
NH2 + NO $ N2 + H2 O Corresponding author. Tel.: +886 2 29309085; fax: +886 2 29324249. E-mail address: [email protected] (J.-J. Ho).
N2 pathway
OH + NNH
NH2 + NO $ NNH + OH
*
NH3 + N2
a radical-producing channel a chain-terminating channel
Although the model proves to be successful at predicting actual field performance [13] the details of the reaction
94
H.-L. Chen, J.-J. Ho / Journal of Molecular Structure: THEOCHEM 772 (2006) 93–102
mechanism remain controversial. Several other studies [14–24] also have been conducted by using catalysts to eliminate the production of NOx, however, the diversity and complexity of these reaction mechanisms were still unknown. There were other important reaction mechanisms studied to reduce the emission of nitrogen oxides from internal-combustion engine, such as NCO + NO by Hershberger [25], and Lin et al. [26], and NCN + NO by Hershberger [27], and Chen et al. [28]. Theoretical studies on the mechanism of halogenated carbenes with NO, and methylidyne radical with NO2 were also performed by Liu [29], and Tao et al. [30]. Recently, several experimental studies about the reaction of nitric oxide (NO) with a series of organic compounds (such as amines, imines, enamines, and amidines) was also reported widely by Hrabie and Keefer et al. [31–36]. Our purpose of this study is to find the possible reactants which may react with NO to form the stable product such as N2 which is not harmful to our environment and possibly with lower energy barriers. The first portion of this paper focuses on imine to react with NO. We calculate most of the probable reaction pathways and plot the potential energy surfaces, find the possible pathway leading to stable N2, and perform transition barrier calculations. In the second portion we replace imine with silanimine and emphasizing on this N2 formation pathway, and find the barrier of rate-determining step is greatly reduced. We further replace the silanimine with substituted derivatives to compare the energy barriers, and the results are discussed. 2. Computational methods Ab initio molecular orbital calculations were carried out using the Gaussian 03 suite of programs [37]. The geomet-
rical structures of all the reactants, intermediates, transition states, and the products were optimized by using hybrid density functional, B3LYP, method [38,39] with 6311++G(d,p) basis set. The calculated equilibrium structures (local minima and saddle points) were characterized by harmonic vibrational frequency calculations at the same level of theory. Zero-point energy (ZPE) correction was also considered at B3LYP/6-311++G(d,p) level. Intrinsic reaction coordinates (IRC) [40] calculations were performed at the same level of theory to actually establish the link between transition state and the intermediates. To further correct for electron correlation, single point calculations were carried out at the QCISD(T)/6311++G(d,p)//B3LYP/6-311++G(d,p) level of theory [41–44]. We referred to the work of Liu et al. [29] in which they used similar method of calculation QCISD(T)/6311G(df,p)//B3LYP/6-311G(d,p) and found that the spin contamination for NO radical was not severe (ÆS2æ = 0.76). We expanded the basis set by adding the diffuse functions for both heavy and light atoms. Also we tried several other methods to calculate the geometrical parameters and proton affinity of CH2NH molecule, as well as the dissociation energy of CH2N2 fi CH2 + N2 (where CH2N2 is among the important product in the titled reaction), which were all compared with the known observed values and the result was listed in Table 1. The best fit of various calculation methods to the observed values [45–51] was QCISD(T)/6-311++G(d,p)//B3LYP/6311++G (d,p). In addition, we also carried out the same method to calculate the reaction energy of the (1/2) C2H4 + (1/2) trans-N2H2 fi CH2@NH, and the result, DE = 8.91 kcal/mol, was in good agreement with the calculated value obtained by Oliveira et al. [47] (ca. 9.1 kcal/ mol, by W2 method). Consequently, QCISD(T)/
Table 1 The geometries (bond lengths and angles), proton affinities (PA) of the CH2@NH molecule and the dissociation energy of CH2N2 fi CH2 + N2 calculated at various levels of theory and some experimental and other calculated data available from the literature ˚) ˚) ˚) ˚) Level of theory C–N (A N–H (A Cis-C–H (A Trans-C–H (A \HNC Proton affinities Dissociation energies MP2/6-31G MP2/6-31+G* MP2/6-311++G** B3LYP/6-31G B3LYP/6-31+G* B3LYP/6-311++G** QCISD(T)/6-311+ +G**//B3LYP/6-311++G** Data from literature a b c d e f g h i
(kcal/mol)a
(kcal/mol)b
1.28 1.28 1.28 1.28 1.27 1.27
1.03 1.03 1.02 1.03 1.03 1.02
1.10 1.10 1.10 1.10 1.10 1.10
1.09 1.09 1.09 1.09 1.09 1.09
109.7 110.1 109.2 113.7 110.9 110.9
131.70 203.25 205.56 215.08 204.90 206.21 207.42
31.66 38.92 36.76 55.63 45.78 43.75 30.16
1.27c
1.02c
1.09c
1.09c
110.4c
206.2 ± 1.5d, 207.5(calcd.)e
<35f, <44g <41.7h, 25i
The energy difference between the cation CH2NH+ and the neutral CH2NH molecule. The energy difference between the CH2N2 and the CH2(a˜1A1) + N2 molecule. References [45]. References [46,47]. References [46,47]. References [48–51]. References [48–51]. References [48–51]. References [48–51].
H.-L. Chen, J.-J. Ho / Journal of Molecular Structure: THEOCHEM 772 (2006) 93–102
6-311++G(d,p)//B3LYP/6-311++G (d,p) accounts for our choice of calculation method in this study. Unless otherwise specified, the QCISD(T) single-point energies are used in the following discussions.
vibration energy (ZPE) correction is considered, and the energies relative to the reactants calculated at QCISD(T) levels are denoted as QRE. The highest transition barrier in the whole pathway from CR2 to product P3 will be 61.6 kcal/mol (TS11,QCISD(T)). There is another pathway leading to the same product from CR1 (CR1 fi TS1 fi 2 fi TS2 fi 3 fi TS3 fi 4 fi TS5 fi 5 fi TS8 fi 6 fi TS9 fi P3), with much higher energy barrier, 67.6 kcal/mol (TS8). Diazomethane, P1 products (CH2N2 + OH), could also be formed via the pathway of CR1 fi TS1 fi 2 fi TS2 fi 3 fi TS3 fi 4 fi TS5 fi 5 fi TS7 fi P1 with much smaller energy barriers, the highest one in the whole pathway is 44.41 kcal/mol (TS2). During our calculation we found two possible pathways leading to the cyclic conformer of diazomethane P2, with relatively higher energy barriers. One starts from CR1 fi TS1 fi 2 fi TS2 fi 3 fi TS4 fi P2, and the other CR1 fi TS1 fi 2 fi TS2 fi 3 fi TS3 fi 4 fi TS6 fi P2. The highest barrier in the former pathway is 60.7 kcal/mol (TS4), while the latter is 57.7 kcal/mol (TS6). The cyclic conformer of diazomethane is about 7 kcal/mol less stable than the linear counterpart. Therefore, these two pathways are not favorable as compared to the pathway to form product P1. Our aim in studying this reaction was to find other possible reactants which can replace imine, CH2NH, to react with NO and obtain lower barriers, especially in the similar pathway leading to the formation of N2 gas. Therefore, our follow-up sections will be focused on this reaction pathway. According to the photoelectron spectroscopy of the observed ionization potentials of silanimines studied by Pfister-Guillouzo et al. [52], they concluded that the first ionization energy was originated from the ejection of an
3. Results and discussion The possible reaction pathways for imine + NO are schematically depicted in Fig. 1. The approach of the two reactants forms a complex, called CR1, in which the N atom of NO attacks the N atom of imine in a position to form an s-trans conformer, 2, via transition state TS1. The other complex, called CR2, in which the N atom of NO attacks the N atom of imine in a position to form an s-cis conformer, 7, via transition state TS10. We plotted the calculated potential energy surfaces in Fig. 2. These two separated complexes lead to completely different follow-up reaction mechanisms and different product formations. Obviously, the formation of the s-cis conformer (7) has lower energy barrier. It may further form a four-member ring intermediate, 8, via TS11. Then 8 may open the ring by breaking CAN bond (via TS12) to form intermediate9 and followed by quickly passing TS14 to break the NAO bond to form a weakly bonded complex of H2CO—N2H (C-10 + 11). Or, 8 may decompose (via TS13) directly to form C-10 + 11. The latter has lower energy barrier. This weakly bond complex, C-10 + 11, then further decomposes (via TS15) to a thermodynamically very stable products P3 (H2COH + N2), which contains the expected harmless N2 gas. All the calculated energetics of reactants, intermediates, and products are listed in Table 2, and that of transition states in Table 3. The zero-point
H
H TS3
C N
TS1
C N
H
H
C N
C N
H N
O
H
H
N O
TS6
5
P1
H
N O
TS8 TS4
3
2
CR1
H
CH2 N N + OH N O
H
H
TS2
TS7
N
N O 4
H
C H
TS5
H H
95
H
N C
+ OH
H
N
H
C
P2
C NH + NO
N N
H TS12 H C
1+NO
NH O
H
H TS10
H
C N
H
C N
H
H O CR2
C
NH
O
N
TS9
TS14 O
TS13
O 7
N 9
H H
N
N
TS11
8
H O
TS15 + N2H
C H
H
H
H
H C-10+11
+
C H
N2
H P3
Fig. 1. The schematic diagram of the calculated possible reaction pathways of HN@CH2 + NO reaction.
OH 6
96
H.-L. Chen, J.-J. Ho / Journal of Molecular Structure: THEOCHEM 772 (2006) 93–102 RE(kcal/mol) TS8
TS12
TS11
TS4
60
TS6
TS13 50 TS2
TS5
40
c-CH2N2+OH TS7
TS14
8
P2
l-CH2N2+OH
9 30
P1
TS1
20
TS3 2
TS10 7
3
5
4
10 0
1+NO
TS15 CR1 CR2
-10 C-10+11 -20
6
TS9
-30 -40 H2COH+N2 P3
Fig. 2. The calculated potential energy surfaces of the possible reaction pathways of the HN@CH2 + NO reaction at the QCISD(T)/6-311++G(d,p)// B3LYP/6-311++G(d,p) Level. The labels in the figure represent the same species as those in Fig. 1.
Table 2 The calculated total energies at the QCISD(T)/6-311++G(d,p)//B3LYP/6-311++G(d,p) level together with zero-point vibration energies (QTE+ZPE) (a.u.), and the relative energies calculated at the same level (QRE) (kcal/mol) of reactants, intermediates, and products in HN@XH2(X = C, Si) + NO reactions Species (X = C)
QTE+ZPE (a.u.)
QRE (kcal/mol)
Species (X = Si)
QTE+ZPE (a.u.)
QRE (kcal/mol)
1 + NO CR1 CR2 2 3 4 5 6 7 8 9 C-10 + 11 P1 P2 P3
224.017321 224.019157 224.018738 223.982910 223.994252 223.993264 223.989204 224.051683 223.985391 223.960964 223.964586 224.036657 223.966131 223.953686 224.090790
0.0 1.2 0.9 21.6 14.5 15.1 17.6 21.6 20.0 35.4 33.1 12.1 32.1 39.9 46.1
1s + NO CR1s CR2s 2s 3s 4s 5s – 7s 8s 9s C-10s + 11a P1s P2s P3s
475.030618 475.032918 475.032783 475.034292 475.026928 475.025842 475.029196 – 475.036380 475.050961 475.038149 475.070823 475.028135 474.995093 475.168050
0.0 1.4 1.3 2.3 2.3 3.0 0.9 – 3.6 12.8 4.7 25.2 1.6 22.3 86.2
a
The value is calculated at QCISD(T)/6-311++G(d,p)//HF/6-311++G(d,p) level.
electron from the nitrogen lone pair orbital, similarly to the homologous imines. Nevertheless, the position of this band, definitely lower than the corresponding imine, indicates the more pronounced p-character of the nitrogen lone pair in silanimines. In this consequence we chose silanimine (H2SiNH) and its substituted derivatives (R1R2SiNR3) to replace imine in reacting with NO. First of all, we used NBO calculation method [53] to calculate the p-character of lone pair orbital of N atom in both imine and silanimine.
We found out that the orbital coefficients of 2py, 3py, 4px and 4py, respectively, of silanimine were much larger than the corresponding imine, indicating the more pronounced p-character of nitrogen lone pair orbital in silanimine, in good agreement with Pfister-Guillouzo observation. The calculated energetic data of reactants, intermediates, and products of silanimine with NO reaction are also listed in Table 2 and that of transition states in Table 3, with the same label notation as the imine counterparts, except
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97
Table 3 The calculated total energies at the QCISD(T)/6-311++G(d,p)//B3LYP/6-311++G(d,p) level together with zero-point vibration energies (QTE+ZPE) (a.u.), and the relative energies calculated at the same level (QRE) (kcal/mol) of all the transition states obtained in HN@XH2(X = C, Si) + NO reactions Species (X = C)
QTE+ZPE (a.u.)
QRE (kcal/mol)
Species (X = Si)
QTE+ZPE (a.u.)
QRE (kcal/mol)
TS1 TS2 TS3 TS4 TS5 TS6 TS7 TS8 TS9 TS10 TS11 TS12 TS13 TS14 TS15
223.974315 223.947069 223.979095 223.920525 223.953248 223.925325 223.957807 223.909658 224.050893 223.980740 223.919203 223.913857 223.922811 223.958819 224.021208
27.0 44.1 24.0 60.7 40.2 57.7 37.3 67.6 21.1 23.0 61.6 64.9 59.3 36.7 2.4
TS1s TS2s TS3as TS3s TS4s TS4as TS5s TS6s TS9s TS10s TS11s TS12s TS13s TS14s TS15sa
474.996855 474.983987 475.001371 475.012559 474.984922 475.006351 475.011118 474.984664 475.024125 475.000540 475.025832 475.026488 475.025225 475.017130 475.067761
21.2 29.3 18.3 11.3 28.7 15.2 12.2 28.8 4.1 18.9 3.0 2.6 3.4 8.5 23.3
a
The value is calculated at QCISD(T)/6-311++G(d,p)//HF/6-311++G(d,p) level.
suffixed with an s to represent silanimine analogues. The schematic diagram of possible reaction pathways of silanimine with NO is drawn in Fig. 3, and that of the calculated potential energy surfaces at QCISD(T)/6-311++G(d,p)// B3LYP/6-311++G(d,p) is plotted in Fig. 4. There are six reaction pathways to form three possible products similar to that of imine counterparts: (1) P1s (SiH2N2 + OH), (2) P2s (cyclic-SiH2N2OH), (3) P3s (H2SiOH + N2), respectively. However, the P2s is different from P2 in that the OH group is still bound to the cyclic-SiH2N2, while that in P2 the OH is completely detached from cyclic-CH2N2. This may attribute to the empty d-orbital of Si atom which provides more bonding character to lower the energy.
In most of the reaction pathways the calculated potential energy profiles of silanimine are similar to those of imine’s, but with much lower profiles, so do the energy barriers (about 30–40 kcal/mol lower in average). Therefore, silanimine is energetically more reactive, in good agreement with the observation by Pfister-Guillouzo et al. [52]. In addition, the most probable pathway of the reaction shifted to the formation of P3s (HOSiH2 + N2) (the barrier of rate-determining step is only 18.90 kcal/mol, the smallest among all the reaction pathways), CR2s fi TS10s fi 7s fi Ts11s fi 8s fi TS13s fi C-10s + 11 fi TS15s fi P3s, which was very different from the imine’s one, in which it lead to product P1 (CH2N2 + OH)
SiH2 N
N + OH P1s
TS3as
TS4as H
H
Si N
TS3s
N
H 4s H
TS1s
H
H
Si N H H
H
TS2s
H
Si N
Si N
N CR1s
N
H
O
N
N
O
N
H
O H 5s
TS6s
H
H
O
O TS4s
3s
2s
Si H
TS5s
H
N Si
H
H Si N H + NO
N P2s
OH TS9s
H TS12s
1s+NO
NH
H Si O
H
H
TS10s
H
Si N
H
Si N
H
H O CR2s
H N
N
TS11s
Si
NH
O
N
O 7s
N 9s
H
TS14s O
TS13s
8s
+ N2H
Si H
H O
TS15 H
+
Si H
C-10s+11
Fig. 3. The schematic diagram of the calculated possible reaction pathways of HN@SiH2 + NO reactions.
H P3s
N2
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H.-L. Chen, J.-J. Ho / Journal of Molecular Structure: THEOCHEM 772 (2006) 93–102 RE(kcal/mol) TS2s
30 TS1s
20
TS4s
TS6s
H H
TS10s
TS3as
Si
N N OH
P2s
TS4as TS5s
TS3s 10 TS11s 0
CR1s -10
3s
1s+NO CR2s
2s
TS12s TS13s
4s
TS14s
5s
SiH2N2+OH TS9s
9s
P1s
7s 8s
TS15s
-20 C-10s+11 -30 -40 -50 -60 -70 -80
H2SiOH+N2 P3s
Fig. 4. The calculated potential energy surfaces of the possible reaction pathways of the HN@SiH2 + NO reaction at the QCISD(T)/6-311++G(d,p)// B3LYP/6-311++G(d,p) Level. The labels in the figure represent the same species as those in Fig. 3.
(the barrier of rate-determining step is 44.41 kcal/mol, the smallest among all the possible reaction pathways in the imine’s case). While in the process to form P3s there is a four-member ring intermediate 8s, much more stable (about 48 kcal/mol lower) than the corresponding similar structure 8. Also the energy barrier of TS11s (leading to the formation of 8s) decreases a great amount (only 3.0 kcal/mol as compared to TS11 of 61.6 kcal/mol in forming 8) due to the great instability of the double bond between Si and N atoms in silanimine. This result is also in good accord with the calculation done by Becerra et al. [54], in which they found a similar stable four-member ring structure (formoxysilylene-cyclic). Therefore, if we replace imine with silanimine to perform the reaction with NO the most probable reaction pathway will lead to the formation of P3s, transferring the reactive NO into stable and nontoxic N2 molecule. It sounds like a very valuable application. Now we try to find some substituted derivatives of silanimine to possibly further decrease the barrier of rate-determining step in this most preferable process. The rate-determining step in this process is the formation of intermediate 7s from CR2s via transition state TS10s. We substituted the hydrogens of silanimine with some electron-withdrawing, or, -donating group and calculated the energy barrier of TS10s. The result is shown in Table 4. In order to analyze the calculated result we followed the Mulliken DA (donor-acceptor) model [55,56]. The calculated ionization energies (IE), electron affinities (EA) and charge-transfer energies corresponding to the
Table 4 The energy differences (a.u.) between HOMOa(YN@SiZ2) and LUMOa(NO) with respect to the transition state energies of TS10s (kcal/mol) of various substituted silanimines calculated at QCISD(T)/6-311++G(d,p)// B3LYP/6-311++G (d,p) level Structure
DE[HOMO(YN@SiZ2) LUMO(NO)]
TS10s
HN@SiH2 (CH3)N@SiH2 HN@SiH(CH3) HN@Si(CH3)2 (CH3)N@SiH(CH3) (CH3)N@Si(CH3)2 (F)N@SiH2 HN@SiH(F) HN@Si(F)2 (F)N@SiH(F) (Cl)N@SiH2 HN@SiH(Cl) HN@Si(Cl)2 (Cl)N@SiH(Cl) (CH3)N@Si(Cl)2 (CH3)N@Si(F)2
0.44485 0.40230 0.43701 0.44769 0.41102 0.42024 0.47516 0.47164 0.49050 0.45378 0.43253 0.46593 0.47347 0.42308 0.43230 0.45900
18.90 14.42 18.84 20.87 15.09 15.70 20.06 21.93 20.96 18.63 17.26 20.73 19.19 15.80 17.64 20.56
a Frontier orbital energies are calculated at QCISD(T)/6-311++G(d,p)// B3LYP/ 6-311++G(d,p) level.
states (D+A and DA+) of HN@XH2 (X = C, Si) and NO molecules are listed in Table 5. These data are quite convincing since the calculated ionization potential of NO (9.23 kcal/mol) is in good agreement with the experimental observation [57,58] (9.26 kcal/mol). From the calculated charge transfer energies of either D+A or DA+
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99
Table 5 The calculated ionization energies (IE)a, electron affinities (EA)a, and charge-transfer energies corresponding to the states (D+A and DA+)b and the differences (in a.u.) between HOMO and LUMO energies in HN@XH2 (X = C, Si) + NO reactions Structure
D+A
DA+
1.42 0.96 0.46
8.27 8.77
8.37 7.56
HOMOd
LUMOd
DE[HOMO(HN@XH2) LUMO(NO)]
DE[HOMO(NO) LUMO(HN@XH2)]
0.42806 0.43162 0.37651
0.07201 0.06985 0.03652
0.50363 0.44485
0.49791 0.46458
IE
EA
QCISD(T)/ 6-311++G(d,p)//B3LYP/ 6-311++G(d,p) NO HN@CH2 HN@SiH2 e
NO HN@CH2 HN@SiH2
9.23(9.26)c 9.79 8.98
a
Adiabatic ionization energies (IE) and electron affinities(EA) of NO, HN@CH2 and HN@SiH2 (in eV). Charge-transfer energies (eV) of D+A and DA+ states, calculated according to the following formulas: D+A = IENO EAHN@XH2, + D A = IEHN@XH2 EANO. c The experimental ionization energy of NO, from Ref. [57,58]. d Frontier orbital energies are calculated at QCISD(T)/6-311++G(d,p)//B3LYP/ 6-311++G(d,p) level. e The values of HOMO and LUMO are alpha (a) orbitals.The HOMO is p character and the LUMO is r character. b
in the reaction system of HN@XH2 (X = C, Si) + NO we are able to predict the role of NO of being an electrophile or nucleophile. It is not that clear in the imine system, since the values of D+A and DA+ are quite close to each other. However, it is obvious that NO exhibits electrophilically towards silanimine since DA+ is much smaller than D+A, which indicates that the donation of an electron from silanimine is more preferable. We further employed the frontier orbital theory [59,60] to check the orbital interaction between these two reactants. The calculated HOMO and LUMO energies and their differences (DE) of NO and HN@XH2 (X = C, Si) at the QCISD(T) level are listed in the lower part of Table 5. It points out that the HOMO of silanimine and LUMO of NO are closer to each other, implying the electrophilic character of NO towards silanimine. In our attempts to find the substituted silanimine derivatives which might further decrease the barrier of rate-determining step (TS10s) in the process to form P3s (converting the NO into N2), we replaced the hydrogens of silanimine with methyl group, F, and Cl atoms (YN@SiZ2, where Y, Z = H, CH3, F, Cl). As shown in Table 4, the calculated barrier of TS10s could be further reduced to 14.42 kcal/mol for (CH3)N@SiH2, the smallest, as compared to other substituted counterparts, while the unsubstituted silanimine is 18.90 kcal/mol. In addition, among other substituted silanimines (CH3)N@SiH(CH3), (CH3)N@Si(CH3)2, and (Cl)N@SiH(Cl) also decrease the TS10s barrier to 15.09, 15.70, and 15.80 kcal/mol, respectively. While (Cl)N@SiH2, and (CH3)N@Si(Cl)2 decrease only a small amount, 17.26, and 17.64 kcal/mol, respectively. In contrast, the fluorine-substituted derivatives (F)N@SiH2, HN@SiH(F), and HN@Si(F)2 all increase the barrier around 2–3 kcal/mol (20 22 kcal/mol). An attempt was made to find the explanation. At first, the frontier orbital calculation showed that the difference between HOMO of YN@SiZ2 and LUMO of NO, DE[HOMO(YN@SiZ2) LUMO(NO)], decreases for most of the Nmethyl substituted compounds, which would enhance the
interaction and lower the energy barrier of TS10s. In addition, Pfister-Guillouzo et al. [52] pointed out that the N-methylation of silanimine induced the destabilization of the pSi@N orbital and the nitrogen nonbonding orbital, which would increase the energy of the nitrogen lone pair due to the donor inductive effect of the methyl group. However, the p system is less sensitive to the inductive effect than the lone pair (because of its delocalization in the p system). This explanation is in good agreement with our calculation in which the N-methylation of silanimine is the most reactive species among all in reducing the NO to N2 molecule, while the Si-methylation analogues do not show similar effect. For the electron-withdrawing substitution groups, most of the F-atom substituted silanimines increase the barrier (TS10s), due to the fact that the lone pair electrons of N-atom become less donorable to the NO molecule. As for the Cl-substituted analogues the energy barrier of TS10s are surprisingly smaller than the unsubstituted silanimine, especially for (Cl)N@SiH(Cl), only 15.80 kcal/mol. To understand this fact we performed an NBO calculation to the TS10s transition structure and found out that there was an interaction between the lone pair electrons of N atom of silanimine and the antibonding of rNO orbital in these substituted transition structures. The order of this calculated interaction energy from large to small is (CH3)N@SiH2. . .NO > (Cl)N@SiH2. . .NO > HN@SiH2. . .NO > (F)N@SiH2. . .NO, exactly the opposite order of the barriers of TS10s in these systems. The extent of this orbital interaction correlates oppositely to the TS10s barrier. Some of these transition structures are plotted in Fig. 5. The larger is the interaction energy the more stable the transition structure and therefore the smaller the barrier of TS10s. In addition, the bond length of NO in the TS10s of these systems becomes longer as the interaction energy increases, indicating the stronger lone pair interaction with the antibonding orbital of rNO , which increases the instability of the NO bond.
100
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H[6]
H
H
1.481
H[7]
124.82
Si[1]
C[7]
H[6]
1.013
1.479
133.10
N[2]
1.651
116.45
Si[1]
1.844
115.19
1.096 H
1.446
N[2]
1.645 1.845
118.09 115.98
H[5]
N[3]
H[5]
N[3]
1.165
TS10s
1.173 O[4]
O[4]
TS10s_CH3-N
F[7]
Cl[7] H[6]
H[6]
1.483
1.480 121.99 Si[1]
118.05
N[2]
Si[1]
N[2]
1.684
1.407
113.07
1.719
1.706
117.91
1.944
1.894
108.42
111.07
N[3]
H[5]
H[5]
N[3]
1.148 1.156
TS10s_Cl-N
O[4]
TS10s_F-N
O[4]
Fig. 5. The calculated transition structures of TS10s and its N-substituted analogues, YN@SiH2. . .NO (Y, @CH3, Cl, F), represented as TS10s_CH3–N, S10s_Cl–N, and TS10s_F–N, respectively. All are calculated at B3LYP/6-311++G** level.
4. Conclusions In considering the simple dissociation reaction, loss of OH from adduct 5 to form CH2N2, but not directly from adduct 3 or 4 could be explained as follow. From our calculated relative energies, the order of relative stability was 3 (14.5 kcal/mol) > 4 (15.1 kcal/mol) > 5 (17.6 kcal/mol), with adduct 5 the most unstable. It was due to the larger electron repulsion force existing between the lone pair electron of O atom and the facing C@N double bond (electron rich) in the construction of 5, which was not yet present in the structure of 3 and 4. Also, structure 3 might exist weak hydrogen bonding between the terminal H atom and the N ˚ ) of the C@N bond, which accounted for atom (2.09 A slighter more stable than adduct 4. Therefore, adducts 3 and 4 were stable enough not to proceed the dissociation process of losing OH to form CH2N2, as compared to adduct 5. In contrast to the silanimine counterparts, the calculated relative stability order was 5s (0.9 kcal/mol) > 3s (2.3 kcal/mol) > 4s (3.0 kcal/mol), with 4s the most unstable. Similar argument of existing weak hydrogen bonding ˚ ) could explain why 3s was slighter more stable in 3s (2.13 A than 4s, however, these two adducts could undergo dissociation process of losing OH and form linear SiH2N2 with some barriers. On the contrary, the 5s adduct appears to
be more stable as compare to the imine counterpart, partly because that the Si atom has the empty d-orbital which may accommodate the lone pair electron of the O atom in the 5s construction, and hence lower the energy. This argument could also be supported by the fact that the OH group could be easily migrated to the Si atom with the very low barrier (TS9s, 3.2 kcal/mol relative to 5s). Also from our NBO calculation there was a strong interaction between the lone pair electron of oxygen atom to the antibonding of N@N, which was not seen in its counterpart of 5. All these probably make 5s to be less feasible to perform the dissociation of losing OH, instead, it turns out to form products P3s directly. In the replacement of imine with silanimine toward the reaction with NO the barriers of rate-determining step of all reaction pathways were greatly reduced (ca. 30– 40 kcal/mol smaller), and the most probable reaction pathway became the one that reduced NO to N2 molecule via a SiANANAO four-member ring structure mechanism. The barrier of rate-determining step (TS10s) of this pathway was calculated to be 18.90 kcal/mol at QCISD(T)/6311++G(d,p)//B3LYP/6-311++G(d,p) level for unsubstituted silanimine, and further decreased to 14.42 kcal/mol for N-methyl silanimine. The result of this study will be of great value in searching for the effective reagents of
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converting the industrial pollutants containing toxic NO into stable and harmless nitrogen gases. Acknowledgements Support for this research from the National Science Council of the Republic of China (NSC 94-2113-M-003005) is gratefully acknowledged. We are also grateful to the National Center for High-Performance Computing where the Gaussian package and the computer time were provided. Appendix A. Supporting Information Figures showing the optimized geometries of the possible adducts and transition states on the potential surfaces of both imine and silanimine plus NO reactions calculated at the B3LYP/6-311++G** level are available free of charge in this publication. Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.theochem.2006.06.022. References [1] R.K. Lyon, US Patent 3, 900 (1975) 559. [2] R.K. Lyon, Int. J. Chem. Kinet. 8 (1976) 315. [3] R.K. Lyon, J.P. Longwell, in: S. Kasuga et al. (Eds.), Proceedings of the 4th International Clean Air Congress, Industrial Pollution Control Association of Japan, Tokyo, 1977, p. 691. [4] R.K. Lyon, J.P. Longwell, in: Proceedings of the NOx Control Technology Seminar, Electric Power Research Institute, Palo Alto, CA, 1976, p. 22. [5] R.K. Lyon, D. Benn, in: Proceedings of the 17th Symposium (International) on Combustion, Combustion Institute, Pittsburgh, 1979, p. 601. [6] R.K. Lyon, Hydrocarb. Process 58 (1979) 109. [7] R.K. Lyon, A. Tenner, Paper 78–81. Presented at the 71st Meeting of the Air Pollution Control Association, June 1978. [8] A.M. Dean, J.D. Hardy, R.K. Lyon, Presented at the 15th International Symposium on Free Radicals, Nova Scotia, Canada, June 1981. [9] B.E. Hurst, Glass Technol. 24 (1983) 97. [10] B.E. Hurst, Stud. Environ. Sci. 21 (1982) 725. [11] J.A. Miller, M.C. Branch, R.J. Kee, Combust. Flame 44 (1981) 81. [12] A.M. Dean et al., US Patent 4, 507 (1985) 269. [13] R.K. Lyon, Environ. Sci. Technol. 21 (1987) 231. [14] J.A. Miller, S.J. Klippenstein, J. Phys. Chem. A 104 (2000) 2061. [15] M. Misono, Y. Hirao, C. Yokoyama, Catal. Today 38 (1997) 157. [16] A.N. Hayhurst, A.D. Lawrence, Combust. Flame 110 (1997) 351. [17] K. Honkala, P. Pirila, K. Laasonen, Surf. Sci. 489 (2001) 72. [18] R. Smits, Y. Iwasawa, Appl. Catal. B-Environ. 6 (1995) 201. [19] S. Suzuki, H. Moriyama, K. Murata, Energ. Fuel. 16 (2002) 1173. [20] C. Schmidt, T. Sowade, E. Loffler, A. Birkner, W. Grunert, J. Phys. Chem. B 106 (2002) 4085. [21] V.I. Parvulescu, P. Grange, B. Delmon, Catal. Today 46 (1998) 233. [22] Y. Traa, B. Burger, J. Weitkamp, Microporous Mesopor. Mater. 30 (1999) 3. [23] S. Bennici, A. Gervasini, N. Ravasio, F. Zaccheria, J. Phys. Chem. B 107 (2003) 5168. [24] Y.H. Yeom, B. Wen, W.M.H. Sachtler, E. Weitz, J. Phys. Chem. B 108 (2004) 5386. [25] W.F. Cooper, J. Park, J.F. Hershberger, J. Phys. Chem. 109 (1993) 3283.
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