J . Phys. Chem. 1985,89, 2286-2291
2286
Thermal Decomposition of Formamide: Shock Tube Experiments and ab Initio CalculatIons Terumitsu Kskumoto, KO Saito,* and Akira Imamura Department of Chemistry, Faculty of Science, Hiroshima University, Higashi-senda-machi, Naka- ku, Hiroshima 730, Japan (Received: August 20, 1984)
The thermal decomposition of formamide diluted in Ar has been studied behind shock waves over the temperature range between 1690 and 2180 K and the total density range of 4.8 X lO”2.0 X IF5mol cm-,. The decomposition rate was monitored by means of the IR emission of the carbon monoxide produced. It was found that the decomposition proceeded in channel 1, HCONH2 CO + NH,, and the process proceeded in the falloff region under the present experimental conditions. Ab initio calculations have also been performed for the formamide decomposition. From falloff data and the results of the ab exp(-75.5 kcal mol-’/RT) s-I in the initio calculations, the rate constants for channel 1 were determined as k , = high-pressure limit and ko/[Ar] = 1014.92 exp(-49.1 kcal mol-l/RT) cm3 mol-’ s-l in the low-pressure limit. Relative rates between the competing channels were discussed in terms of the theory of unimolecular reactions. -+
Introduction The photolysis of formamide vapor has only been reported by Boden and Back.’ They studied the photolysis of formamide vapor at temperatures from 115 to 400 O C and at pressures from 8 to 50 torr, with 206.2-nm radiation. They deduced that there were three major primary processes: (@ = 0.45) HCONHz hv C O NH, (a) CHONH H (@ = 0.22) (b) CO NH2 H (@ = 0.35)
+ -- + ++ +
According to their experimental conditions and results of the quantum yields @, the threshold energy of channel a seems to be the lowest. Although the pyrolysis of formamide vapor apparently has not h e n studied previously, several competing channels could also be expected in the thermal system. There are several reports which have treated the problem of competitive reactions in thermal systems.24 However, since there are still unknown parameters in the descriptions, this problem has not been entirely settled. Especially for complex bond-breaking reactions, the direct experimental determination of the threshold energy is almost impossible. Recently a b initio molecular orbital methods have developed rapidly and have provided heats of reaction, potential barriers, molecular geometries, and also the vibrational frequencies of several intermediates and transition states. This valuable information can shed light on reaction mechanisms, and ab initio calculations have been applied to several unimolecular reactions.s In particular, for complex bond-breaking reactions, information about the transition states is required to test the experimental results. In this work, we have studied the pyrolysis of formamide in Ar behind shock waves. Also, we have tried to evaluate the geometry, the potential energy, and the vibrational frequencies of the probable transition state by ab initio M O methods.
Experimental Section The experiments have been performed in a shock tube of internal diameter 9.4 cm. A detailed description of the equipment was given in a previous papers6 All experiments were performed behind reflected shock waves. The conditions behind the reflected shock front were determined by using the ideal shock relations neglecting the effects of the heats of reactions. Because of larger diameter tube was used, the boundary layer effects were assumed ( I ) J. C. Boden and R. A. Back, Trans. Faraday Soc., 66,175 (1970). (2) E. V. Waage and B. S. Rabinovitch, Chem. Reu., 70, 377 (1970).
(3) I. E. Klein, B. S. Rabinovitch,and K. H. Jung, J. Chem. Phys. 67, 3833 (1977). (4) T. Just and J. Troe, J . Phys. Chem., 84, 3066 (1980). (5) For example, D. G. Truhlar, Ed.,“Potential Energy Surfaces and Dynamics Calculations”, Plenum Publishing Corp., New York, 1981. (6) K. Saito, Y. Yokubo, T. Fuse, H. Tahara, 0. Kondo, T. Higashihara, and I . Murakami, Bull. Chem. SOC.Jpn., 52, 3507 (1979).
0022-3654/85/2089-2286$01.50/0
to be negligible. These assumptions were verified to be reasonable in studies of the thermal decomposition of several small molec u l e ~ . ’ ~The thermal decomposition of formamide was monitored by observing the I R emission corresponding to the fundamental band of the CO produced. The radiation from the shock heated gas was taken out through a CaF2 window mounted on the shock tube wall, was passed through a slit (2 mm wide) and an interference filter (4.63 f 0.05 pm), and then was collimated on an InSb element maintained at 77 K. The output signal was fed into a digital wave memory and analyzed to obtain kinetic data. The time constant of the electrical and the optical system was about 10 ps. Mixtures used for the experiment were prepared by diluting the saturated vapor of formamide at room temperature (-4.0 X torr) with high-purity argon gas (>99.999%). The concentrations of formamide in these mixtures were about 50 ppm. Prepared gas mixtures were stored in glass flasks for more than 12 h before use to ensure the complete mixing. Since the concentration of formamide was very low, the adsorption of formamide on the shock tube walls was considered significant in the overall concentration. Therefore, after the gas mixture was introduced into the shock tube, it was evacuated roughly by a rotary pump and then the mixture was introduced again. After each run the residues in the shock tube were subjected to high-temperature combustion with O2 initiated by a shock wave. By use of this procedure, IR emission from unknown species (reactant and products adsorbed on the walls) was perfectly removed. The experimental conditions behind reflected shock waves were as follows: temperature 1690-2180 K; total density (4.80-20.4) x mol ern-,.
Experimental Results Figure 1 shows a typical emission profile behind reflected shock waves. At the observed wavelength there is no fundamental vibrational frequency of the reactant. And in fact, the IR profile does not show a peak at the shock front, and this indicates that the contribution of the reactant to the emission profile is negligible. It was also ascertained that no emission signal from the sample gas without formamide could be detected. Therefore, the contributions of the impurities in Ar and the residues in the shock tube were negligible. The emission intensity begins to increase just behind the reflected shock front and seems to approach a constant value I, as the reaction proceeds. From auxiliary experiments on the IR emission of various diluted CO mixtures, this constant value, I,, was found to correspond to the CO concen(7) K. Saito, T. Kakumoto, and I. Murakami, J . Phys. Chem., 88, 1182 (1984). ( 8 ) K. Saito, T. Kakumoto, H. Kuroda, S. Torii, and A. Imamura, J . Chem. Phys., 80, 4989 (1984). (9) K. Saito, T. Kakumoto, H. Nakanishi, and A . Imamura, J . Phys. Chem., in press.
0 1985 American Chemical Society
The Journal of Physical Chemistry, Vol. 89, No. 11, 1985 2287
Thermal Decomposition of Formamide
T/ K
2200
2000
1
I
1800 I
1600
[Arlxl O6 /mol
400
0
800
1200
time/us
-. I
Figure 1. Typical emission profile at 4.63 pm. Conditions: T = 1870 K,total density 9.78 X 10" mol ~ m - -50 ~ , ppm HCONH2 in Ar.
A
4.80
-
0
9.58
-
5.31
10.2
1o4
v1
Y
m
TABLE I: Arrhenius Parameters of the Apparent Rate Constant, k,, for Various Total Densities
lArl /mol cm-3
(4.80-5.31)X 10" (9.58-10.2)X 10" (1.26-1.35)X (1.90-2.04)X
TIK 1813-2182 1793-2044 1690-2000 1721-2000
Als-'
E.lkca1 mol-'
109.'6*0.50 48.1 f 4.6 10'0.36*0.38 57.0 f 3.5 1010.62*0.78 58.5 f 6.4 10'0~96*0~" 60.4 f 2.6
tration of completely decomposed reactant. Also, it was verified in our previous studies that the increase of the IR emission with time corresponds to the CO concentration and that the vibrational relaxation is short compared with the rise time. This profile fits , thus the apparent rate constant the relation Z = I,( 1 - d k J )and k, (first order with respect to the reactant) for the increase of carbon monoxide was determined by linear least-squares analysis of the In [Z,/(Z, - Z)] vs. time plot from the profile for each run. Figure 2 shows an Arrhenius plot of k, against T1for different total densities. This figure shows that k, increases with increasing total density. In Table I values of the Arrhenius parameters of k,, that is, the preexponential factor A and the activation energy E,, evaluated by least-squares analysis, are listed for each total density. From Figure 2 and Table I, it is evident that the apparent first-order rate constants for CO production are in the falloff region under the present experimental conditions, because both the preexponential factor and the activation energy increase with increasing total density.
1o3
lo4 T - ~ / K " Figure 2. Arrhenius plot of k, for various total densities. Vertical lines indicate experimental errors. Ha
HCONHZ
--- + H
CONHz
(3)
The determination of the structures was performed by using the energy gradient method. The program used for calculations was (10) S. Glasstone, K. J. Laidler, and H. Eyring, 'The Theory of Rate Processes", McGraw-Hill, New York, 1941.
Ha
0
1 .083& 125.3'
HC Exp.a'
Ab Initio Calculations A theoretical prediction of the rate constant for the highpressure limit may be given by the transition-state formulalo where Q and Q*are the partition functions of the reactant and the activated complex, respectively, and Eo is the difference between the zero-point energy per mole of the reactant and that of the activated complex. It is difficult to predict the values of QI and Eo experimentally, but ab initio molecular orbital calculations facilitate the application of transition-state theory. In this paper, therefore, we tried to determine the structures and the vibrational frequencies of the molecules in the initial stable state and in the transition state and the potential energy differences between the reactant and the transition state. Ab initio calculations were carried out for the following three channels: HCONHZ CO + NH3 (1) HCONHZ CHO + NH2 (2)
6.0
5.0
Ha
\.
HC 3-21G
Ha
993
HC 4-31Gb'
y.993
HC 6-31G
Figure 3. Experimental and optimized geometries of formamide: (a) ref 12,(b) 13. Bond lengths are in angstroms and angles in degrees. All structures are planar.
with various basis sets (3-21G,4-31G,and 6-31G). In Figure 3 the calculated geometries of the reactant are shown as being in good agreement with the observed values.12 The differences are within 0.044 8,in bond distance and 2.3" in bond angle. The calculated geometry was found to depend slightly upon the choice of basis set. Figure 4 and Table I1 show optimized geometries of the three-center transition state corresponding to GAUSSIAN 80"
(11) J. S.Binkley, R. A. Whiteside, R. Krishnam, R. Seeger, D. J. DeFrees, H. B. Schlegel, S. Topil, L. R. Kahn, and J. A. Pople, QCPE, 102,939 (1980). (12) See G. Fagarosi, P. Pulay, and T.Torok, J . Mol. Struct. 57, 259 (1979). (1 3) L. Radom and N. V. Riggs, Ausr. J . Chem., 33, 249 (1980).
2288
The Journal of Physical Chemistry, Vol. 89, No. 11, 1985
Kakumoto et al.
(86.3 kcal mol-') for channel 1 cannot be regarded to be the actual barrier height because this energy may be lowered again by the 3-21G 4-31G 6-31G use of polarization functions and more sophisticated CI calcula1.821 1.790 1.829 r(C-N) tions. Recently we stuudied the unimolecular decomposition of 1.161 1.161 1.157 r(C=O) formic acid experimentally and theoretically.s In that work, we 1.190 1.193 r(C-Ha) 1.203 found the total energy difference calculated at the MP2 level to 1.004 1.004 r(N-H,) 1.012 overestimate the experimental value by about 20%. According 1.004 1.012 1.004 rW-H,) to this empirical knowledge, we can expect that the probable total 1.401 1.384 1.405 r(N-Ha) energy difference is lower than 86.3 kcal mol-'. 123.3 123.6 123.5 LNCO Fundamental vibrational frequencies for the reactant and the 50.1 50.3 fNCHa 50.6 168.6 169.9 169.3 fHaNX transition state are necessary to evaluate the zero-point energies 123.3 123.7 123.4 LH,NH, and the vibrational partition functions. We have calculated the 123.4 123.3 LH,NH, 123.7 vibrational frequencies of the reactant and the three-center 180.0 180.0 LH,NCO 180.0 transition state by the use of the IMSPAK program19 with 3-21G 71.6 70.1 71.4 LH,NCO and 4-31G basis sets. Table IV shows calculated vibrational -71.6 -70.1 -71.4 LH,NCO frequencies of the reactant together with the observed values.20,21 Bond lengths in A, angles in deg; dihedral angles defined as positive . In this table the values in parentheses indicate O , ~ ~ / V , ~Except clockwise. for the N H 2 wagging mode, calculated normal frequencies were greater than the observed fundamental frequencies by 9-1 9% and 1&16% for 3-21G and 4-31G basis sets, respectively. On the other Ha / hand, with respect to the NH2 wagging mode, the calculated value with 3-21G overestimates by 89%, whereas the value with 4-31G underestimates by 32% relative to the experimental value. It is assumed that this large discrepancy in the calculated results for the wagging mode can be accounted for by the introduction of polarization functions.23 However, in this paper for simplicity for reasons that follow, scalings of 0.842 for 3-21G and 0.921 for 4-31G have been applied to all calculated frequencies. The scaled values are given in Table V. Since a similar tendency is probably expected for the transition state, the same scalings have been applied for the transition state as well. Our main concern is not X Figure 4. Three-center transition state. X lies on the bisector of I-&",. each vibrational frequency but the zero-point correction and the ratio of the vibrational partition functions for the reactant and the transition state. For formamide the zero-point vibrational channel 1. In the process of formamide decomposing to carbon energies determined from the 12 calculated vibrational frequencies monoxide and ammonia, the CH, bond length becomes longer are 26.2 kcal mol-' for 3-21G and 28.4 kcal mol-' for 4-31G which than that of the reactant by ca. lo%, while the C N bond increases compare well with the experimental value of 27.6 kcal mol-'. by ca. 35%. The Ha atom approaches the N atom, and two H Corresponding zero-point vibrational energies of the 11 vibrational atoms bonded to the N atom (H, and H,) move out of the momodes of the transition state are 21.3 kcal mol-' for 3-21G and lecular plane. As the reaction proceeds, the CH, and the C N 23.3 kcal mol-' for 4-31G. According to the 4-31G calculation, bonds break and the NH bond is formed. From these optimized the zero-point correction lowers the calculated barrier at the geometries, values of fi/Z are evaluated to be 1.77, 1.87, and 1.83 MP2/6-31G level for channel 1 from 86.3 to 81.2 kcal mol-'. for 3-21G, 4-31G, and 6-31G, respectively, where Z and fi are the Values of QtVib/Qvib evaluated from the scaled vibrational moments of inertia for the reactant and the transition state. These frequencies are 4.05 and 1.96 at 1900 K for 3-21G and 4-31G, values are in good agreement with each other. respectively. This difference only changes the preexponential In Table I11 total energies (in hartrees) and relative energies factor of the high-pressure limit rate constant by a factor of 2. (in parentheses in kcal mol-' relative to the reactant) are listed The temperature dependnece of Qtvib/Qvib is negligibly small. for the reactant, the three-center transition state, and radicals that determined above, we evaluated the From fill and Qtvib/Qvib were produced via channels 2 and 3. In the restricted Hartreepreexponential factor of the high-pressure limit rate constant as Fock (RHF) calculations, the total energy differences for channel follows 1 are 97-104 kcal mol-'. For the transition state of channel 1, the contribution of the electron correlation effect is expected to A = ( k T / h ) ( Q * / Q )= 10'4.02SKI at 1900 K be fairly large. Thus, we applied the Mdler-Plesset second-order In this evaluation the 6-31G result for $/Z and the 4-31G result perturbation (MP2) with the 6-31G basis set. The calculated were used. At high temperatures the tunneling effect of QtYib/QYib values are also indicated in Table 111. As expected, the total energy is unimportant. The tunneling is 9.8% at 1900 K with a Wigner difference decreased remarkably to a value of 86.3 kcal mol-'. model.24 The value of the preexponential factor evaluated above On the other hand, potential barriers for channels 2 and 3 are compares reasonably with other reactions of a similar type. 104.2 and 88.4 kcal mol-', respectively. These values are in agreement with experimental heats of reaction'"18 at 0 K for the Discussion corresponding channels (97.6 kcal mol-' for channel 2 and 89 kcal Evaluation of High- and Law-Pressure Limit Rate Constants. mol-' for channel 3). It appears that, even a t the level of In the falloff region, both the inter- and the intramolecular enMP2/6-31G calculations, the potential barrier for channel 1 is ergy-transfer processes are equally important. In order to evaluate lower than that for channels 2 and 3. The above calculated energy the high- and the low-pressure limit rate constants, reduced forms of the falloff curves in terms of the strong-collision assumption (14) "JANAF Thermochemical Tables", 2nd ed.,US.National Bureau of Standards,Washington, D.C., Natl. Stand. Ref:Data Ser. (US., Natl. Bur. (19) K. Morokuma, S. Kato, K. Kitaura, I. Ohmine, S. Sakai, and S . Stand.), NSRDs-NBS 37 (1971). (15) M. W. Chase, J. L. Curnutt, A. T. Hu, H. Prophet, A. N. Syverud, Obara, "Program Library of Institute for Molecular Science", No. 372, 1972. and L. C. Walker, J . Phys. Chem. Ref:Data, 3, 311 (1974). (20) J. C. Evance, J. Chem. Phys., 22, 1228 (1954); 31, 1435 (1959). TABLE 11: Optimized Geometries of Three-Center Transition State'
-,--c-o
(16) M. W. Chase, Jr., J. L. Curnutt, J. R. Downey, Jr., R. A. McDonald, A. N. Syverud, and E. A. Valenzuela, J. Phys. Chem. ReJ Data, 11, 695 (1982). (17) S . W. Benson, "Thermochemical Kinetics", 2nd ed.,Wiley, New York, 1976. (18) R. A. Back and J. C. Boden, Trans. Faraday SOC.,67, 88 (1971).
(21) S. T. King, J . Phys. Chem., 75, 405 (1971). (22) Y.Sugawara, Y. Hamada, A. Y. Hirakawa, M. Tsuboi, S. Kato, and K. Morokuma, Chem. Phys., 50, 105 (1980). (23) For example, N. Tanaka, Y. Hamada, Y. Sugawara, M. Tsuboi, S . Kato, and K. Morokuma, J . Mol. Spectrosc., 99, 245 (1983). (24) E. P. Wigner, Z.Phys. Chem., Abt. B, 19, 903 (1932).
The Journal of Physical Chemistry, Vol. 89, No. 11, 1985 2289
Thermal Decomposition of Formamide
TABLE 111: Total Energies (in hartrees) and Relative Energies (in parentheses in kcal mol-' Relative to Formamide) channel 1 channel 2 method HCONHz 3-center TS CHO N H
+
-167.984 899 (0.0) -168.681 58gb (0.0) -168.855073 (0.0) -169.175466 (0.0)
RHF/3-21G RHFj4-31G RHF/6-3 1G MP2/6-31GU
-167.830 955 -168.517647 -168.689654 -169.037871
(96.6) (102.9) (103.8) (86.3)
-169.009383 (104.2)
H
channel 3 + CONH2
-169.034639 (88.4)
"At 6-31G SCF optimized geometries. bReference 13. 8
TABLE I V Observed and Calculated Vibrational Frequencies (in cm-') of Formamide
I
I
I
I
I
WnIni"
no. V1 *2 *3 *4
*5 *6 *7
*0 y9
v10 "1 I
*I2
assignt NH2 asym str NH2 sym str CH str CO str NH2 scis CH bend CN str NH2 rock NCO bend CH deform NH2 twist NH2 wag
*owb
3545 345 1 2852 1734 1572 1378 1255 1059 565 1030 602 289
3-2 1G 3904 (1.10) 3775 (1.09) 3206 (1.12) 1913 (1.10) 1808 (1.15) 1573 (1.14) 1359 (1.08) 1155 (1.09) 620 (1.10) 1209 (1.17) 715 (1.19) 547 (1.89)
" Values in parentheses indicate W , , ~ / Y , ~ .
4-31G' 3964 (1.12) 3826 (1.11) 3249 (1.14) 1898 (1.10) 1822 (1.16) 1561 (1.13) 1391 (1.11) 1178 (1.11) 623 (1.10) 1190 (1.16) 677 (1.13) 196 (0.68)
References 20 and 21.
'Reference 22.
10
10 3 I (0
a'
TABLE V Vibrational Frequencies (in cm-I) of Formamide and Three-Center Transition State
HCONH2
3-center TS %Id
%Id UnM
"
3545 3451 2852 1734 1572 1378 1255 1059 1030 602 565 289
3-21B
4-31Gb
3-21G
10
4-31G
3904 (3289)' 3964 (3650)d 3707 (3123)' 3803 (3502)d 3572 (3009) 3661 (3371) 3775 (3180) 3826 (3523) 2493 (2100) 2526 (2326) 3206 (2701) 3249 (2992) 1915 (1763) 1917 (1615) 1913 (1612) 1898 (1748) 1692 (1425) 1680 (1547) 1808 (1523) 1822 (1678) 1392 (1173) 1346 (1239) 1573 (1325) 1561 (1437) 853 (785) 896 (755) 1359 (1145) 1391 (1281) 769 (648) 736 (678) 1178 (1085) 1155 (973) 602 (507) 582 (536) 1209 (1019) 1190 (1096) 677 (623) 388 (327) 345 (318) 715 (602) 254 (214) 256 (236) 623 (574) 620 (522) 196 (180) 547 (461) 22141' (18651') 22041' (20291')
" References
20 and 21. Reference 22. 'Calculated frequencies decreased by 15.8% are given in parentheses. dCalculated frequencies decreased by 7.9% are given in parentheses.
were constructed by using the method described in ref 25. Figure 5 shows the falloff curves of k, with the temperature as a parameter. For the Kassel parameters SKand BK the definitions suggested by Troe26have been adopted. The results are SK= 7.2, 7.4, 7.6, 7.7, and 7.9 and BK = 16, 15, 15, 14, and 14 at 1700, 1800, 1900, 2000, and 2100 K, respectively. The reduced falloff curves were obtained by use of the Kassel integral tables26and were fitted to the experimental data points in such a way as to meet the following requirements at the same time: (a) the calculated curves fit the experimental data points reasonably well, (b) the high- and the low-pressure limit rate constants give temperature-independent activation energies, E,, and EaO,in the experimental region, and (c) the difference between E,, and EaO values obtained agrees with the r e l l a t i ~ n ~ ~
where
is the vibrational partition function of the three-center
( 2 5 ) J. Troe and H . ( 1967).
Gg. Wagner, Ber. Bunsenges. Phys. Chem., 71, 937
(26) J. Troe, Ber. Bunsenges. Phys. Chem., 78, 478 (1974).
10-2
10-6
[Arl/mol
Figure 5. Falloff curves with temperature as a parameter.
transition state evaluated by the ab initio calculations as described above. The rate constants for the high-pressure limit k , and for the low-pressure limit ko/[Ar] were then determined at the five temperatures indicated in Figure 5 . Thus, Arrhenius expressions for these rate constants were obtained as k, = lOI4.O2 exp(-75.5 kcal mol-'/RT) s-l and ko/[Ar] = 1014.92exp(-49.1 kcal mol-'/RZ') cm3 mol-]
s-l
respectively. In this procedure the preexponential factor of the high-pressure limit rate constant, 1014.02s-I, was taken from the results of the ab initio calculations for the transition state. Since in general the extrapolation of the falloff curves causes some arbitrariness in the determination of the limiting rate constants, especially in an experiment with a small range of pressure, the use of ab initio calculations may eliminate this problem to some extent. Although recently Troe et al.27928published a method for obtaining a reduced falloff curve including the weak-collision effect, in this initial attempt the high-pressure rate constants here (27) J. Troe, Ber. Bunsenges. Phys. Chem., 87, 161 (1983). (28) R. G.Gilbert, K. Luther, and J. Troe, Ber. Bunsenges. Phys. Chem., 87, 169 (1983).
2290 The Journal of Physical Chemistry, Vol. 89, No. 11, 1985
Kakumoto et al.
TABLE VI: Calculated Parameters for Low-Pressure Limit Rate Constant of Channel 1"
T/K 1700 1800 1900 2000 2100
10-'4ZLJ/ cm3 mol-' s-'
FE
Fro,
F,,,
3.95 4.02 4.08 4.15 4.21
1.49 1.54 1.58 1.62 1.67
2.25 2.16 2.07 1.99 1.92
2.33 2.21 2.1 1 2.01 1.93
QYib
int
(koSC/[Arl)/ cm3 m o P s-'
91.4 125 170 229 307
2.80 6.76 1.45 2.81 5.03
X 10" X 10" X loi2 X lo1* X 1OI2
(ko0"/[ArI)/
cm3 m o P s-I 4.05 X 9.09 X 1.87 x 3.59 x 6.46 x
lo8 lo8 109 109 109
lo3& 1.45 1.34 1.29 1.27 1.29
-(AE)/ cal mol-' 7.59 7.67 7.99 8.53 9.30
"Eo= 72.0 kcal mol-'; E, = 27.6 kcal mol-'; uLJ(Ar) = 3.542 A; uLj(HCONH2) = 4.965 A; cLJ(Ar)= 93.3 K;~LJ(HCONH,)= 655.4 K; M(Ar) = 39.948 g mol-'; M(HCONH2) = 45.041 g mol-I; &+b,h = 3.40 X lo6 mol kcal-' (without torsion); a(Eo) = 0.936; Fanh= 1.29. uLJand tLJare from ref 31. TABLE VII: Low-Pressure Limit Rate Constants of Channels 2 and 3 channel 2'
T/K
-(AE)/ cal molv1
1700 1800 1900 2000 2100
7.59 7.67 7.99 8.53 9.30
FE 1.36 1.39 1.42 1.45 1.48
lo'& 1.59 1.49 1.44 1.43 1.45
(kOSC/[ A d ) / cm3 mol-' s-' 3.57 1.27 3.84 1.01 2.39
channel 3b
(ko"ld/[Arl)/ cm3 mol-' s-'
lo9 10"' 10" x 10" X 10"
5.67 X 1.88 x 5.52 x 1.45 X 3.47 x
X X X
lo6 107 107 lo8 10s
FE
io3&
1.40 1.43 1.46 1.49 1.53
1.55 1.44 1.40 1.38 1.40
(koSc/[Arl)/ cm3 mol-' s-' 1.64 X 10'O 5.07 X 1O'O 1.35 X 10" 3.20 X 10" 6.81 X 10"
( k ~ ~ l ~ / [I/A r l cm3 mol-' s-' 2.57 x 107 7.33 x 107 1.89 X lo8 4.43 x 108 9.56 X lo8
OEo = 97.6 kcal mol-I. * E o = 89 kcal mol-'. Chart I M ~ , / k c a lmol-'
(11 (2 ) (3 1 (4) (5 1
HCONH,
CO + NH, CHO + NH, + H + CONH, + HCONH + H -+ CH,O + NH
+
+
4.6 97.6 89 see text
104
are based on the a b initio calculations so this new method was not used. Therefore, our method may lead to a little underestimation in the low-pressure rate constants. Reaction Mechanism of Formamide Decomposition. For the initiation reaction the channels in Chart I are considered to be probable, where the heats of formation AHfoofor the species were cited from ref 14-18. Channels 1 and 5 are three-centered reactions having tight transition states. The threshold energy for channel 1 is evaluated from the activation energy of the highpressure limit rate constant by using the following relation25
where ZLJis the Lennard-Jones collision frequency, pvib,h(EO) the harmonic oscillator density of states at Eo, Eo the threshold energy the of the reaction, Qvibthe vibrational partition function, Fanh anharmonicity factor, FE the energy dependence of the density of states, F,, the rotational factor, and Frat int were calculated by using the approximate equations (9.9)-(9.16) appearing in ref 30. The above equation was evaluated at five different temperatures, and the results are listed in Table VI. The molecular constants used in the calculations are shown below Table VI. Actually, at high temperatures the strong-collision assumption is not supposed to hold; that is, the average energy ( A E ) that is transferred during collisions between the reactant and the diluent molecules is much lower than RT, the thermal energy of the system. This effect, the weak-collision effect, causes a reduction in the apparent reaction rate at high temperatures. The parameter expressing the weak-collision effect is defined as the collision efficiency p,
p, = koOb"d/kosC and
The value of the threshold energy for channel 1 is found to be 72.0 kcal mol-'. On the other hand, the calculated value was found to be 81.2 kcal mol-' at the MP2/6-31G level with the zero-point correction. However, we can expect that the actual threshold energy is lower than 8 1.2 kcal mol-' as mentioned above. From this point of view, the experimental value is not inconsistent with the results of the a b initio calculations. For channel 5 , the threshold energy is much larger than the heat of reaction of 104 kcal mol-'; therefore the contribution of channel 5 to the overall reaction seems to be negligibly small under the present experimental conditions. Channels 2-4, on the other hand, are single-bond fissions; therefore these channels have loose transition states. The threshold energies for these channels are equal to the respective heats of reaction if the potential barriers due to the centrifugal force are neglected. Although the heat of formation for the HCONH radical is not available, the heat of reaction for channel 4 is perhaps larger than 90 kcal mol-I. Thus, as the threshold energies for channels 2-4 are larger than that of channel 1 by more than ca. 17 kcal mol-', it may be concluded that the initial decay rate is mostly governed by channel 1 energetically. Low-Pressure Limit Rate Constants. The theoretical calculation of the low-pressure limit rate constant was performed by using the strong-collision formulation given by Troe29s30 koSC/[Ar] = ZLJPvib.h(EO)RTQvibexp(-EO/RT)FanhFEFrotFrot
int
where kOobsd is the low-pressure limit rate constant obtained experimentally. The values of & and -( AE) are also listed in Table VI. The magnitude of p, is in the range (1.27-1.45) X 10" over the temperature range studied, and the mean of the average energy transferred per collision -(AE)is about 8.2 cal mol-I. However, may be underestimated as stated above, our evaluation of kOobsd due to the use of classical falloff treatment. This may cause the values of 8, and - ( A E ) to be somewhat smaller than expected. There are several reports that have treated the problem of competitive reactions in thermal However, there are still unknown parameters in the descriptions that have to be evaluated from elaborate experiments. If for the competing channels the situation of the energy distribution near the threshold energy is assumed to be the same, an approximate estimate of the low-pressure limit rate constants for channels 2 and 3 is possible by using the ( AE) values obtained from data of channel 1. For this approximation much qualitative success has been obtained for the explanation of the relative rates between competing In Table VI1 the low-pressure limit rate constants for channels 2 and 3 calculated on the basis of this assumption (29) J. Troe, J . Chem. Phys., 66,4745 (1977). (30) J. Troe, J . Chem. Phys., 66, 4758 (1977). (31) R. C. Reid, J. M. Prausnitz, and T. K. Sherwood, 'The Properties of Gases and Liqiud", 3rd ed., McGraw-Hill, New York, 1980.
J. Phys. Chem. 1985,89, 2291-2293 are listed together with the weak-collision parameters. As a result, we have Arrhenius expressions KO(2)Q1Cd/ [Ar] = 10'6.13 exp(-73.0 kcal mol-'/RT) cm3 mo1-ls-l and ko(3)=Icd/[Arl = 10'5.66exp(-64.2 kcal mol-'/RT) cm3 mol-' s-l
for channels 2 and 3, respectively. In this experimental temperature range, the low-pressure limit rate constant for channel
2291
1 is larger than those for channels 2 and 3. These calculations are consistent with the experimental and ab initio calculated results that the formamide pyrolysis is governed mainly by channel 1. Acknowledgment. We thank Miss R. Ito for her experimental assistance and Prof. D. Munch for useful suggestions. We are also grateful to the Computer Center of the Institute for Molecular Science and the Information Processing Center of Hiroshima University for generous permission to use HITAC M-200H computers. Registry No. HCONH2, 75-12-7.
Polarlzablllty and Second Hyperpolarlzablllty of Some Molecular Cations. The Effect of Charge Variation on These Properties J. Waite* and M. G. Papadopoulos Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, GR-116 35 Athens, Greece (Received: October 26, 1984)
The polarizability, a,and second hyperpolarizability, y, of some molecular cations have been determined by employing the CHF-PT-EB-CNDO procedure. The effects of charge variation and isomerism on a and y are discussed.
Introduction Our interest in the static, electric polarizability, a,and hyperpolarizability,' y, of molecular cations has been initiated by the interesting study of Hinchliffe et a1.2 who found that the computed polarizability value of the naphthalene dication (6, Figure 1) is larger than the value of its neutral precursor determined by the same theoretical method. This rather unexpected finding, at least in comparison to what one observes in atoms,* stimulated our interest to investigate the polarizabilities and in particular the second hyperpolarizabilities of molecular cations, as the latter, being fourth-order properties, are known to be more sensitive probes to changes induced in the electronic structure. For this investigation a series of molecular cations has been chosen which show extensive delocalization similar to that in the naphthalene dication (6). The main objectives of this communication are to investigate the following. (a) The effect of charge variation on a and y. One may find few studies that deal with aspects of this q u e s t i ~ n , ~while - ~ no comprehensive treatment of this problem is currently available in the literature (that is considering a and y as well as positive and negative values of molecular charge). The present analysis relies on an internally consistent methodology by which variations of both a and y are considered. The reported results on a and y of cations are combined and correlated with the findings from our previous work on these properties of (1) (a) The average polarizability, a,and second hyperpolarizability, y, are given byIb a = (1 /3)(a,, Y = (1/5)(Yxm
+ a y y + a,)
+ Yyyyy + Y m z + 27,
+ 2Yxm + 2YYY,J
where x, y, and z define Cartesian components. Expressions for the relevant tensor components in terms of which a and y are given; SIX McWeeny et al.lC (b) Buckingham, A. D.; Orr, B. J. Q.Rev., Chem. SOC.1967, 21, 195. (c) McWeeny, R. Phys. Rev. 1962,126, 1028. Dierchen, G.; McWeeny, R. J. Chem. Phys. 1966, 44, 3554. Dodds, J. L.; McWeeny, R.; Raynes, W. T.; Riley, J. P. Mol. Phys. 1977, 33, 611. (2) Hinchliffe, A.; Munn, R. W.; Siebrand, W. J . Phys. Chem. 1983,87, 3887. (3) Marchese, F. T.; Jaffc, H. H. J . Mol. Sfrucf.1981, 86, 97. (4) Waite, J.; Papadopoulos, M. G. J. Compur. Chem. 1983, 4, 578. (5) Waite, J.; Papadopoulos, M. G. J. Mol. Srrucr. 1982, 108, 247.
0022-3654/8S/2089-2291$01.50/0
negative ions and their neutral p r e c ~ r s o r . ~ (b) The difference in property values, a and y, associated with the various positively charged isomers of naphthalene and anthracene. The answer to this problem, besides its own interest, contributes to the understanding of the differential effect that intramolecular changes have on the electronic properties of the molecule. N o estimates, experimental or theoretical, exist in the literature for the hyperpolarizability of molecular cations, although these species define one of the most extensively studied areas (topics) of organic ~hemistry.~.'Thus the errors in the reported results cannot be defined with certainty. Care has, however, been taken to ensure the validity of the observed trends and relationships.
Method The computations of a and y for the studied cations have been performed by employing the CHF-PT-EB-CNDO method, the reliability of which is well established.*-" This approach uses a C N D O wave function, incorporating both u and .rr electron contributions that are defined in terms of an extended basis set optimized with respect to available experimental property values (y and/or a) of species similar to those under s t ~ d y . ~The ,~ perturbation of this wave function, due to an applied static electric field, is effected by employing the theory of McWeeny et al.Ic The essential characteristics of the electronic charge distortion which occurs when the molecular cation is placed in a uniform electric field are correctly described by our model (CHF-PTEB-CNDO) since (a) it allows for correlation effects, to a considerable extent, via the calibration of the basis sets to experimental electric property value^,^^'^ and (b) it employs basis sets which (6) Tidwell, T. T. Angew. Chem., Inr. Ed. Engl. 1984, 23, 20. (7) Schleyer, P.v. R.; Kos, A. J.; Raghavachari, K.J. Chem. Soc., Chem. Commun. 1983,1296. Lammertsma, K.;Schleyer, P.v. R. J. Am. Chem. Soc. 1983,105,1049. Olah, G. A.; Staral, J. S. J. Am. Chem. Soc. 1976,98,6290. Lammertsma, K.;Olah, G. A.; Berke, C. M.; Streitwieser Jr., A. J . Am. Chem. SOC.1979, IOZ, 6658. Olah, G. A.; Singh, B. J. J . Org. Chem. 1983, 48,4830. Prakash, G. K.S.;Rawdah, T. N.; Olah, G. A. Angew. Chem., Int. Ed. Engl. 1983, 22, 390. (8) Nicolaides, C. A.; Papadopoulos, M. G.; Waite, J. Theor. Chim. Acro 1982, 61, 427. (9) Papadopoulos, M. G.; Waite, J.; Nicolaides, C. A. J. Chem. Phys. 1982, 77, 2527.
0 1985 American Chemical Society
