16877
J. Phys. Chem. 1995,99, 16877-16882
Potential Surfaces of Gibbs Free Energies of Gas-Phase NH2Reactions
+ N20 and NH2- + C02
Satoshi Okada* and Yasuo Abe Research Institute for Advanced Science and Technology, University of Osaka Prefecture, Gakuen-cho 1-2, S a k i 593, Japan
Shinichi Yamabe Department of Chemistry, Nara University of Education, Takabatake-cho, Nara 630, Japan Received: November 30, 1994; In Final Form: July IO, 1 9 9 9
Ab initio calculations of the two title reactions have been made to compare reactivities of N20 and CO2 toward a nucleophile, NHz-. MP2/6-3 1+G* geometry optimizations have demonstrated that respective dual channels start from key intermediates and have revealed that multistep paths give the following products: (1) NH2NzO N3H20; (2) NH2- N20 OHN3H; (3) NH2C02 NCOH20; (4)NH2C02 HOHNCO. Three intermediates are generated via intramolecular proton transfers from the first adducts, H2N-N20- and HZN-COZ-. Reaction channels are guided by specific low-frequency vibrational modes in transition states and intermediates. Mp4/6-3 l+G*//MP2/6-3 1+G* reaction enthalpies are found to be in good agreement with observed ones. Among the four channels, only (2) has a barrier of the free energy at an isomerization (TS5) of the key intermediate. The barrier is related to the kinetic energy dependence on the rate of OH- production. The experimental “reversal” of the larger exothermicity and the slower rate of N20 reactions than those of COZreactions may be explicable in terms of the obtained free-energy changes.
+
+
-
-.+
+
+
I. Introduction Dinitrogen monoxide (N20) and carbon dioxide (C02) are isoelectronic and linear molecules. These are important constituents of planetary atmospheres and earth’s troposphere.’ In gas-phase reactions between CO;? and various anions, adducts and fragment species with C-0 bond cleavage have been observed.2 Also, gas-phase reactions between N20 and various anions have been studied extensively with the ion cyclotron resonance (ICR) mass spectrometer3 and flowing afterglow (FA)-selected ion flow tube Through these reactions, products with cleaved N-0 and N-N bonds are observed. The specific reactions of N20 with anions have been used to examine structures of intermediate and adduct ions diagn~stically.~ One of the characteristics of the reactions is a slower rate than the collision rate in spite of their large exothermicity. That is, most known atmospheric anions do not react as efficiently with N20 as expected by likely exothermic channels.4b In the reactions between alkyl halides and various anions, there is a general correlation between exothermicities and reaction efficiencies.6 Namely, as the exothermicity increases, the efficiency becomes larger. This expectable correlation does not necessarily hold for the reaction of NzO with anions. For instance, a gas-phase reaction between H3Siand N20 has a larger exothermicity and a smaller rate constant than that between H3Si- and COze7 In fact, ab initio calculations have given 5.2 and 2.9 kcal/mol activation energies in the respective reaction^.^ However, reversal of the exothermicity and the reaction rate still remains a problem. The nucleophile NH2- reacts with N2O and COz in the gas phase. For this ion-molecule reaction, the data shown in Table 1 have been reported.8 There is a large difference in reactivities ~
~
@
~~
Abstract published in Advance ACS Abstracts, November 1, 1995.
0022-365419512099-16877$09.0010
-
+
+
-
+
between N20 and C02. The following t h e e questions arise in view of the table. (1) Why is the rate constant (kexp)of C02 larger than that of N20 in spite of the smaller exothermicity of C02? (2) How are the products OH- in reactions 2 and 4 (shown in Table 1) and H20 in reactions 1 and 3 generated? (3) As the kinetic energy of NH2- increases in the reaction between N2O and NHz-, the branching ratio of OH- increases and that of N3- decreases. What is the reason for this unclear correlation between the energy and the ratio? In this work, those simple reactions, N20 NH2- and C02 NH2-, are investigated in order to shed light on their reaction mechanisms. Theoretical calculations have been performed for all possible intermediates and transition states (TSs). It will be demonstrated that potential energy surfaces of N20 reactions are quite different from those of C02 reactions.
+
+
11. Method of Calculations Ab initio calculations are performed with GAUSSIAN 9212 installed at CONVEX C-220 at the Information Processing Center of Nara University of Education. GAUSSIAN 8813 installed at HITAC M-680H at the Institute for Molecular Science is also used. Geometries of reactants, products, transition states (TSs), and intermediates are fully optimized with the second-order MflllerPlesset perturbation (MP2) wave function of the 6-31+G* basis set. For the anion systems, inclusion of diffuse orbitals (+) is indispensable to describe properly electronic structures of these systems.I4 Vibrational analyses are made to check whether the obtained geometries are those of TSs or of intermediates. Analytic gradients and second derivatives are used in MP2/63 l+G* calculations. Intrinsic reaction coordinate (IRC) analysesI5 implemented in GAUSSIAN 92 have been carried out to relate TSs to intermediates on potential energy surfaces. 0 1995 American Chemical Society
Okada et al.
16878 J. Phys. Chem., Vol. 99, No. 46, 1995 TABLE 1: Reactions between NH2- and NO2 and COz in the Gas Phase
AH, (kcaVmo1) reaction
branching ratio (%)
101oke,,(cm3 molecules-' s-')
kex,JkADOa
+ N2O N3- + H20 (1) -0H-fN3H (2) NH2- + CO2 NCO- + H20 (3) - HO- + HNCO (4)
72 28 100
2.9
0.24
9.3
0.84
NH2-
+
+
0
expb -69.99; -59.24' -9.05 -43.33 4.31
calcd' -65.53 -9.23 -46.02 4.28
a Reaction efficiency, where k ~ is~calculated o by the method of Su and Bowers from ref 9. Thermodynamic values from ref 11 were used. This work. AH'ANl-) = 34.42 kcaVmol from ref 10a was used. e AHoAN3-) = 45.17 kcaVmol from ref log was used.
Electronic energies are reevaluated with single-point calculations of the fourth-order Mgller-Plesset energy (MP4(SDTQ)) of the 6-31+G* basis set. Gibbs free energies are obtained by the sum of the MP4 electronic energies, MP2 thermal corrections, and MP2 entropies. Electronic charges in parentheses in Figures 1 and 2 are of RHF/6-31+G*. MP2 and MP4(SDTQ) calculations are carried out with frozen four-core orbitals.
111. Geometric Results and Discussion Figure 1 shows geometries of reactants, intermediates, transition states, and products optimized with MP2/6-3 1+G*. When NH2- encounters N20 in Figure lA, the first ion-dipole complex 1 is formed. An alternative intermediate, l', shown in square brackets, is 17.42 kcal/mol (AG) less stable than 1.16 In 1, the second frequency (v2 = 430.2 cm-I) corresponds to the in-plane distortion mode leading to an intramolecular proton transfer." This transfer is facilitated by the Hd.**06-Coulombic attraction. Thus, TS1 is brought about by the conversion of vl(1) v* (= 1260.8 icm-l, TS1). In TS1, the hydrogen bond angle (LNHO) is 159.7', which is not too bent from an ideal 180' angle and facilitates the proton transfer. After TS1, another intermediate, 2, is generated. In 2, two low-frequency (v2 = 408.5 cm-' and v3 = 726.4 cm-') modes are available for further isomerizations. Along the v2 = 726.4 cm-' mode, 2 proceeds to TS2 in Figure 1A. At TS2, the reaction coordinate vector seems to indicate the H20 formation, although the newly formed OH bond distance is quite large, 3.23 8, (H-N0s.H-0). By the IRC calculation, the change (TS2 3) has been found, where 3 is regarded as a weak complex between H20 and the azide ion. In TS2, long-range Coulombic 0.a-H attraction is the driving force of H20 formation. The ion-dipole complex 3 is decomposed into the products H20 and N3-. From 2, the other vibration v3 = 408.5 cm-' leads to TS3 in Figure 1B. In TS3, the N*..O bond is large, 1.93 A, relative to that of 2, 1.46 8,. However, by the IRC calculation, TS3 is found not to give the OH- dissociation. TS3 is for the counterclockwise rotation of the N-H axis. That is, TS3 proceeds to another intermediate, 4. 4 (trans) is a geometrical isomer of 2 (cis) with respect to the N-N-N-0 axis. In 4, the second lowest frequency v2 = 397.6 cm-' is found to have the mode along the reaction coordinate. The hydroxyl group rotates around the N-0 bond, leading to TS4. After TS4, when the N-0 bond of 5 is elongated along the v3 = 397.5 cm-' vibration, TS5 is reached (Figure 1B). By the IRC calculation, the change (TS5 6) has been found. The ion-dipole complex OH--..N3H is decomposed into the products OH- and N3H in reaction 2. In Figure 2, geometries of reactants, intermediates, and transition states in the reaction between NH2- and C02 are shown. When NH2- encounters C02 in Figure 2A, the first intermediate 7 is formed. 7 is formed by the central attack of C02 by NH2-, while 1 is formed by the thermal attack of N20. In 7, the second-frequency vibrational mode has the component of intramolecular proton transfer. Along the vibrational mode, TS7 is attained from 7. In TS7, the hydrogen bond angle is
-
-
-
138.2'. This small angle would be related to a larger energy destabilization relative to that of 7 (shown later in Figure 4). After TS7, the second intermediate 8 is obtained. Similar to 2 in Figure lB, 8 has two important frequencies for the reaction progress. Along the v3 = 586.9 cm-' mode, the hydroxyl group rotates around the C-0 bond in Figure 2A. A resultant intermediate is 9 via TS8. 9 is a deprotonated anion of aminoformic acid. Along the v:!= 536.6 cm-' mode, HNCO and OH-, Le., products in reaction 4, are given. It is noticeable that these products are obtained without a weakly bound iondipole complex (directly from 9). Along the other vibrational mode (v2 = 543.7 cm-') of 8, the NH bond rotates around the C-N bond to give TS9 in Figure 2B. After TS9, the third intermediate 10 is formed. The hydroxyl bond rotates around the C - 0 bond in 10 to give TS10. After TSlO, the fourth intermediate 11 is obtained. The conversion from 8 to 11 is accomplished by NH and OH bond rotations. In 11, the hydroxyl group may move to the proton attached to the nitrogen atom. This movement gives rise to TS11. After TS11, an ion-dipole complex (12) is formed between the cyanate ion and the water molecule. When these molecules are separated, the products in reaction 3 are obtained. Geometric results can be summarized as follows. The first intermediate in the NH2- and N20 system is yielded by the terminal attack of N20 by NH2-. The first one in the NH2and C02 system is produced by the central attack. From the first intermediates, intramolecular proton transfers give rise to the second (and key) intermediates 2 and 8, respectively. In both systems, OH- is generated via intermediates (5 and 9) of N-H and 0-H bonds that are cis. When two bonds are not cis (in TS2 and ll),thermochemically stable H20 and N3- are readily formed. Low-frequency modes of intervening species can be guides to reaction progress.
IV. Energetic Results and Discussion Potential surfaces of Gibbs free energies are drawn in Figures 3 and 4. All species constituting these energy diagrams have been already shown in Figures 1 and 2. The stabilities of the first intermediates, 1 and 7, are examined in Figures 3 and 4. 7 is found to be overwhelmingly more stable than 1. The remarkable stability of 7 can be a driving force for the reaction progress.8 An energy level of the proton transfer TS1 in Figure 3 is only -0.62 kcal/mol (= -5.71 - (-5.09)) more stable than that of TS7 in Figure 4. Both levels are below those of the reactants. An energy level (-10.43 kcal/mol) of the key intermediate 2 is much higher than that of 8 (-30.32 kcal/mol). Starting from the intermediate 2, we have found the three energy barriers 12.79 kcal/mol of TS3, 2.16 kcal/mol of TS4, and 12.87 kcal/mol of TS5. The last activation free energy corresponds well to the observed one, 9.3 kcal/mol.lX In reaction 2, as the kinetic energy of NH2- increases, the branching ratio of OHhas increased.8 This correlation already put forth as question 3 in the Introduction can be interpreted in terms of the computed activation barrier. On the other hand, starting from the intermediate 7, we have found no endoergic energy levels in Figure 4.
Gibbs Free Energies of Gas-Phase Reactions
A
J. Phys. Chem., Vol. 99, No. 46, 1995 16879 v,=430,2 cm-'
10 441
10.25)
~'=1260.8icm"
10.35)
v2=408.5 cm''
+
(-)
(0.34)
v'-145.1 icm-'
+ (0.491
c
10.86)
(,
2.33 ',
c
.(
I
' 233
255
103 "4
'0 5 2 )
(0491
( - 1 08)
(0 34)
Q
3
TS2
&
v'=405.2 icm"
B
.v,=397.6
cm-'
v'=156.9 icm-' 10.45)
0.52)
(-0.971
II) ( - 1 03)
(-0 97)
TS4 (0 291
h.
4 hr
(-1 051
100li
~,=125.2cm-'
v'=407.5 icm"
v,=397.5 cm-' (-0.56) (0.44
10 651
(0.40)
+
10.401
c
(- 1 . 1 6)
,I'
2.39 (-0.151
10.281
(0.33)
6
(-1.22)
(0.28)
TS5 rc.
f
(-0.84)
l.33
117.2
(0.28)
5 'c.
Figure 1. Geometries of reactants (NHz- and NzO), intermediates (1, 2 , 3 , 4 , 5, and 6). transition states (TS1, TS2, TS3, TS4, and TS5), and products (H20 and N3- for (1) and HO- and N3H for (2)) optimized with MP2/6-31+G*. Bond distances are in angstroms, and angles are in degrees. Numbers in parentheses stand for electronic net charges (positive, cationic). For each transition state the reaction coordinate vector corresponding to the MP2/ 6-31+G* sole imaginary frequency ( Y * ) is sketched. For each intermediate, the low frequency ( V I . v2. or v3) leading to the reaction coordinate is shown. For the intermediate 2, two vibrational modes are shown and give two reaction channels, 1 and 2. Reactions 1 and 2 are also defined in Table 1.
& ,4;:
Okada et al.
16880 J. Phys. Chem., Vol. 99, No. 46, 1995 v,=522.7 cm-'
A (0 251
(- 1.49)1
v':1888.6
110.3
(-0.81)
(025)
(037)
127.4
136
0 (-0.80
(0.a~)
(-0.44)
2,'
(-)
If8
TS7 +
CCI
~ , = 5 3 66
v,=586.9 cm-'
(-0.85)
7
1-0.44)
~ , =(-)5 4 3 . 7cm-'
(-1.11)
138,2h,?(0,51)
(-0.79)
(0,851 27
N
1.25 10,90) 131.1 r116.1 '3g
114.8
130.4
+
icm-'
f-1.00)
cm-' ~'=550 5 icm"
(0451
10 30)
c
to (4)
0 841
(-0
1-1 33)
to (3)
10 33)
-
-
(4)
TS8
9
v'=804.5 icm"
B
(0.331
~ ' 3 2 8 7 . 2Icm-' v,=515.7 cm"
1-0 85)
(-0.82)
(0.571
(-0741
v,=206.0 cm-'
+
1-0 93)
10.45)
(0.50) 1-0 81)
(-0.98)
101 2
55
1-0.83) 10 47)
12 (049)
%
(3)
(040)
TS11 cc
11 %
Figure 2. Geometries of reactants (NH2- and COz), intermediates (7, 8, 10, 11, 12, and 9), transition states (TS7, TS9, TS10, TS11, and TSS), and products (OCNH and HO- for (3) and H20 and OCN- for (4))optimized with MP2/6-31+G*. Same notations as in Figure 1 are used.
The rate-determining step in Figure 3 is TS2 with AG* = -1.08 kcal/mol in reaction 1 or TS5 with AG* = 12.87 kcal/ mol in reaction 2. The step in Figure 4 is TS7 (except the
product of reaction 4) with AG* = -5.09 kcal/mol. Thus, question 1 put forth in the Introduction can be answered in terms of computed AG* values. The large exothermicity in the NH2-
Gibbs Free Energies of Gas-Phase Reactions
J. Phys. Chem., Vol. 99,No. 46, 1995 16881 A G= MP4I6-3 1+G'IIM P216-3 1 t G'
TS3 12.79
-5.71
=..
0
'
-1.28
-17.08
0
4 B r.
/
NH;
TS1
OH-
12.87 2.16
4
TS4
5
c
1.73
~,-2.40
, , , \
TS5
5
5
5.
,
6
.
+ N,H
-9.23
(2)
5
5
-50. N O:
-1 00
50
c
-68.24
! OH- + O C N H
TS8 5
= L z
o
8
NHi
5 4
t
Y
-50
-100
10
- CO,
(4)
/
(3)
TS7 c
7
8
5
5
TS10
TS9 5
,1
TSl 1 5
5 5
-46.02 -51.73
5
12
-
OCN-
t
HZO
5
-
V. Concluding Remarks
+
In this theoretical study, gas-phase reactions, N20 NH2and CO2 NHz-, have been investigated. The major concern is the reversal of exothermicities and reaction rates. The present MP4/6-3 1+G*//MP2/6-31 +G* calculations have clarified all the elementary processes and free-energy changes of N20 NH2- and COZ NHz- reactions. The following results have been obtained. (1) In Table 1, reaction energies AHr's computed with MP4/ 6-3 1+G*//MP2/6-3 l+G* are in good agreement with experimental values. (2) The first intermediate NHz--CO2,7, formed by the center attack has an overwhelmingly larger stabilizing energy, -45.67 kcal/mol, than that, - 17.08 kcdmol, of NHz--N20,1, formed by the terminal attack. The former larger energy is a driving force of the ready reaction of C02 (3). (3) Proton-transfer steps, TS1 in Nz0 and TS7 in COZ,from the first intermediates are -5 kcal/mol more stable than those from the reactants. That is, the proton transfer has no activation barriers. (4) From the second and key intermediates 2 and 8, reaction channels are found to be divided (branched). (5) In Figure 3, TS5 has a noticeable activation energy AG* = 12.87 kcal/mol. This energy barrier may be related to the center of mass kinetic energy dependence on the reaction rate of the OH- production in reaction 2. This energy barrier corresponds well to A b o b s = 9.3 kcal/mol.Is
+
__--
-45.67
and N20 system does not correspond to the small A@ values. The proton transfer, N3-**.H2O (3) N3H-*OH- (6), is unlikely due to the large energy difference (65.84 kcaymol) shown in Figure 3.
+
4.28
-5.09
+
(6) Specific low-frequency vibrational modes in transition states and transient intermediates are found to indicate reaction pathways.
Supporting Information Available: Infomation on the method of calculating Gibbs free energies and geometries in Z-matrices of the species in Figures 1 and 2 (26 pages). Ordering information is given on any current masthead page. References and Notes (1) (a) McElroy, M. Chem. Eng. News 1983,21,5-6. (b) Dickinson, R. E.; Cicerone, R. J. Nature 1986, 319, 109-115. (2) (a) McDonald, R. N.; Chowdhury, A. K. J . Am. Chem. SOC.1983, 105, 198-207. (b) McDonald, R. N.; Chowdhury, A. K. J . Am. Chem. SOC. 1983, 105, 7267-7271. (c) McDonald, R. N.; Gung, W. Y . J. Am. Chem. SOC.1987, 109, 7328-7334. (3) Wight, C. A.; Beauchamp, J. L. J . Phys. Chem. 1980, 84, 25032506. (4) (a) Fehsenfeld, F. C.; Ferguson, E. E. J . Chem. Phys. 1976, 64, 1853-1854. (b) Bierbaum, V. M.; DePuy, C. H.; Shapiro, R. H . J. Am. Chem. SOC.1977, 99, 5800-5802. (c) Dawson, J. H. J.; Nibberig, N. M. M. J . Am. Chem. SOC.1978, 100, 1928-1929. (5) Kass, S. R.; Filley, J.; Van Doren, J. M.; DePuy, C. H . J . Am. Chem. SOC. 1986, 108, 2849-2852. (6) DePuy, C. H.; Gronert, S.; Mullin, A,; Bierbaum, V. M. J . Am. Chem. SOC. 1990, 112, 8650-8655. (7) Sheldon, J. C.; Bowie, J. H.; DePuy, C. H.; Damrauer, R. J . Am. Chem. SOC.1986, 108, 6794-6800. (8) Bierbaum, V. M.; Grabowski, J. J.; DePuy, C. H . J . Phys. Chem. 1984, 88, 1389-1393. (9) Su, T.; Bowers, M. T. Int. J . Mass Spectrom. Ion Phys. 1973, 12, 347-356. (10) (a) Dixon, H. P.; Jenkins, H. D. B.; Wddington, T. C. Chem. Phys. Lett. 1971, I O , 600-604. (b) Benson, S. W. Thermochemical Kinetics, 2nd ed; Wiley: New York, 1976. (c) J. Phys. Chem. Ref. Data 1977, 6 (Suppl. l), 1-776. (d) J . Phys. Chem. Ref. Data 1977, 6 (Suppl. l), 1-777. ( e ) J . Phys. Chem. Ref. Data 1988, 17 (Suppl. l), P-783. (0J . Phys. Chem.
Okada
16882 J. Phys. Chem., Vol. 99, No. 46, 1995 Ref. Data 1988, 17 (Suppl. l), P-781. (9) Donald, H.; Jenkins, B. J. Phys. Chem. 1993,97, 7876-1879. (11) AHDt(N3-) = 34.42 kcal/mol from ref loa, A.H0n98(HNCO) = -30.0 kcaYmol from ref lob, AH0Q98(H20)= -57.796 kcaYmol from ref IOc, AH"~98(C02)= -94.051 kcaymol from ref loc, AH0n98(N3H) = 70.3 kcaYmol from ref lOc, Aff0a98(N20) = 19.61 kcaYmol from ref 10d, AH0f298(CNO-) = -52.58 kcaYmo1 from ref 8, AWANH2-) = 27.0 kcaV mol from ref IOe, AH'AHO-) = -32.74 kcaYmol from ref lOf, and AH"AN3-) = 45.17 kcaVmol from ref log were used. (12) Frisch, M. J.; Trucks. G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; DeFrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian 92, Revision C: Gaussian Inc.: Pittsburgh, PA, 1992. (13) Frisch, M. J.; Head-Gordon, M.; Schlegel, H. B.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; DeFrees, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Stewart, J. J. P.; Fluder, E. M.; Topiol, S.; Pople, J. A. Gaussian 88; Gaussian, Inc.: Pittsburgh, PA, 1988. (14) Clark, T.; Chandrasekhar, J.; Spitznagel, G. W.; Schleyer, P. v. R. J . Comput. Chem. 1983,4, 294-301. (15) (a) Fukui, K. J . Phys. Chem. 1970, 74,4161-4163. (b) Gonzalez, C.; Sosa, C.; Schlegel, H. B. J . Phys. Chem. 1989, 93, 2435-2440. (16) Besides the instability of 1' relative to that of 1, the subsequent transition state of intramolecular proton transfer, TS4', has a quite large activation Gibbs free energy (vide infra). Thus, the central N attack of N20 by NH2- is ruled out.
A GzMP416-31 tG'// MP26-31+G'
-
et
al.
34.78
I
TS4' c
(-0.30) 6-
-100
1.25 0 (-0.37) (0.26)
1' 5
(17) In general, low-frequency vibrational modes are converted to reaction coordinates. This is because "fragile" modes correspond to ready and irreversible geometric distortions. (18) Glasstone, S.; Laidler, K. J.; Eyring, H. The Theory of Rate Processes; McGraw-Hill: New York, 1941. k = ( K T / ~(RT/P)exp(-AG*l ) RT), where k is the second-order rate constant; T is temperature; K is the Boltzmann constant; h is Planck's constant; R is the gas constant; P is the pressure; AG* is the free energy change. kexp = 0.812 x cm3 molecule-' s-I, T = 298.15 K, and P = 4.6 x atoms were used. The observed rate constant kexpis taken from ref 8. JP9431651
