3257
J . Phys. Chem. 1993,97,3257-3265
Kinetics, Energetics, and Dynamics of the Reactions of CN with NH3 and ND3 Roger F. Meads, Robert G. A. R. Maclagan, and Leon F. Phillips' Department of Chemistry, University of Canterbury, Christchurch, New Zealand Received: August 24, 1992
The rates of reaction of C N with NH3 and ND3 at 296 K have been measured by excimer laser flash photolysis and diode laser absorption spectroscopy. The results are in excellent agreement with previous measurements; for ND3 the rate constant is found to be smaller than that for NH3 by a factor of 2. The only products found were H C N and NH2 (observed as ND2 from the reaction with ND3); however, H N C formed as an initial reaction product might have isomerized to H C N prior to product analysis. Quantum-chemical calculations for this system support a mechanism that involves capture over the centrifugal barrier in the predominantly dipoleaipole potential to form a bound H3NCN* species, with subsequent dissociation to reactants or rearrangement over several low potential barriers to form the final products. Theoretical rate constants based on this mechanism, with energies derived from calculations at the MP4SDQ level (geometries optimized at the MP2 level), give results in satisfactory agreement with experiment, except that the observed isotope effect is not predicted, which implies that tunneling contributes at least a factor of 2 to the observed reaction rate for NH3 at 296 K.
Introduction The reaction of C N with NH3 is an interesting example of a reaction between a radical and a stable, singlet-state molecule having a large rate constant (ca. 3 X lo-" cm3 molecule-I s-' at 300 K) that decreases with increasing temperature, properties which are usually regarded as characteristic of a radical-radical reaction. Results of previous kinetic studies of this reaction are summarized in Table I. Boden and Thrush' measured the rate constant at 687 K by using absorption spectroscopy of the visible B X bands of C N to monitor the C N concentration in the presence of NH3. C N for the kinetic studies was generated by reaction of C2N2 with oxygen atoms in a heated fast-flow system, and the source of CN emission was a microwave discharge in mixtures of Ar, Nz, and CHI. Bullock et ala2generated CN in the presence of excess NH3 by pulse radiolysis of dilute mixtures of C2N2and NH3 in argon and monitored the decay of C N in states with u" = 0, 2, and 4 at 300 and 375 K by absorption spectroscopy in the B X system, using a high-pressure xenon arc as the light source. Their measurements demonstrated both a negative dependence of the rate constant on temperature and a positive dependence on vibrational excitation of the CN. They also observed the appearance of NHz(000) at a rate that was consistent with NH2 being a product of the C N + NH3 reaction. More recently, de Juan et al.3 and Sims and Smith4 used laser flash photolysis to generate C N and laser-excited fluorescence in the B X system to monitor its concentration. The kinetic data of Sims and Smith, which are of relatively high precision and cover a fairly wide temperature range, confirm the dependences of the rate constant on temperature and CN vibrational excitation that were reported by Bullock et al. While the present paper was in preparation we received a preprint of a paper by Yang et al.5 giving the results of rate constant measurements for the reactions of CN with NH3 and ND3 and with CHI and CD4 by laser flash photolysis and laser-induced fluorescence, over the temperature range from 221 to 740K. Their results for NH3, which are given in the form kNH3 = 10(-11~02f.09) exp(254f19/03, are in excellent agreement with the results of Bullock et alS2and de Juan et al.3 and in fair agreement with those of Sims and Smith.4 ForND3 theygivekND3 = 10(-~1~3**~0*)exp(31 lf18/0. There have been many experimental studies of C N radical reactions but few theoretical studies. Results of ab initio calculations have been reported for the reactions of CN with H + and with HCl.' Rate coefficients for the reaction of C N with H2
-
-
-
TABLE I: Results of Previous Measurements of the Rate Constant kT for the Reaction of CN with Ammonia. (Data for NH3 Unless Otherwise Indicated) T IK u "( CN ) kr/cmj molecule-] S K I ref (8.8 f 5.0) X 10-l2 2.1 x IO-" 2.5 X IO-II 3.8 X IO-II 1.8 X IO-" 2.3 X 10-l' (2.5 f 0.5) X IO exp((1500 f 600)/(RT))X (1.52 f 0.23) X 10-l1 exp((254 f 19)/T) X
687 300 300 300 375 315 295 294-7 16 221-740
1
2 2 2 2 2 3 4 5
IO-(I I o2*009)
exp((311 f 18)/T)
221-740 (for ND3)
IO-(" 38*008)
X
5
havebeencalculated bycombiningabinitioresults with transitionstate theory.*-9Results of ab initio calculations for the CN + 02 system have been used in quasi-classical trajectory calculations of the rate constant.1° No theoretical studies have been reported for the reaction of CN with NH3. The implication of the fast reaction rate and negative temperature dependence is that the reaction of C N with NH3 goes through a bound intermediate species CNNH3*. This further implies, since the CN NH3 system is small enough to be treated with useful accuracy by ab initio methods, that it ought to be possible to calculate energies, geometries, and vibrational frequencies of likely intermediates and transition states, to use the results of these calculations as a basis for elucidating the detailed reaction mechanism, and to calculate the overall reaction rate as a function of temperature by the methods used previously in this laboratory to treat the reactions of NO with NH2 and BH.11-12 Also, it ought to be possible to account for the observed effects of vibrational excitation of CN and to predict the magnitude of the NHj/NDj isotope effect. The aims of the present study were as follows: (1) to measure the room-temperature rate constant for reaction of CN(u=O) with NH3 by a different experimental method, namely, laser flash photolysis plus infrared diode laser absorption spectroscopy; (2) to measure the rate of reaction of CN with ND3 at room temperature; (3) to establish the identity of the reaction products experimentally; (4) to elucidate the probable reaction mechanism on the basis of the energies of intermediate complexes and
+
0022-3654/93/2091-3251~04.00/0 0 1993 American Chemical Society
Meads et al.
3258 The Journal of Physical Chemistry, Vol. 97, No. 13, 1993 L
I
a
16200
t
16200
1
I
t
15800 0
1
400
200
1
1
1
,
15900
600
200
0
t I microreconds
3.5
'
I
1
I
0
100
200
300
1 600
400
I / mlcroreconds
1
1
I
I
400
500
600
700
t / us
Figure 1. (a) Transient absorption due to C N with [ND,] = 0.74 X 10l4 molecule cm- 3. (b) Corresponding first-order decay plot.
transition states, as derived from a b initio calculations; and ( 5 ) to use quasi-classical trajectory calculations and microcanonical RRKM theory to calculate reaction rates as a function of temperature, to predict isotope effects, and to account for the effects of C N vibrational excitation on the value of the rate constant. Experimental Section
15
repetitively pulsed 193-nm laser photolysis (Lumonics TE-861T ArF laser, pulse energy ca. 70 mJ) of flowing mixtures of C2N2 with NH3 or ND3 in helium or argon at total pressures near 2 Torr. The photolysis cell was basically a 1.2-m length of SO-mm glass tubing with a calcium fluoride window at each end. The mode-selected probe beam from a Laser Analytics tunable diode laser made four passes through the cell, approximately collinearly with the unfocused photolysis beam, before being focused on a liquid-N2-cooled Judson Hg/Cd/Te infrared detector. The amplified detector output was taken to a computer-controlled LeCroy 8837F transient digitizer. Positions of C N rotational lines were calculated using the spectroscopic constants of Cerny et a1.13 Absolute line frequencies determined by comparison with listed CO lines,14 using etalon fringes spaced by 0.01 cm-' for interpolation, were in excellent agreement with thevalues reported by Davies and Hamilton.15 The pseudo-first-order decay of C N concentration was monitored using the P(10) line of the fundamental absorption band at 2003.062 54 cm-I . Typically, the C N decay profiles from 500 photolysis flashes were averaged and stored for each NH, or ND, pressure. Exposure of the CaF2 cell windows to the 193-nm laser radiation soon resulted in formation ofcolor centers. Infrared emission by thesecolor centers and from the excimer laser discharge interfered with the C N observations at times shorter than about 50 ps after the flash, but
I
I
I
I
0
.
10-
Q
-n VI
I)
'0
For the kinetic studies, C N radicals were generated by
1
5 -
7
0 8
this was not a serious problem in the present study because the signals of interest normally persisted for 500 ps or longer. (The standard way of eliminating the problem entirely is to place the mode-selection monochromator between the photolysis cell and the detector.) For product determinations, C N radicals were generated by 248 nm KrF photolysis of ICN in mixtures of ICN, NH3 or ND3, and helium, to avoid formation of NH2 or ND2 by direct photolysis. Transient signals due to ND2 from the reaction of C N with ND3, or from direct photolysis of ND3 in a blank experiment, were observed with the diode laser in the usual way. In the searches for other products, the photolyses were carried out in the kinetics cell, either with continuous mass spectrometric analysis of a flowing gas mixture using a Spectramass Dataquad or with a static gas fill, the products of prolonged exposure to pulses of 248-nm radiation being transferred to a Scintrex White
Reactions of C N with NH3 and ND3
The Journal of Physical Chemistry, Vol. 97, No. 13, 1993 3259
TABLE II: Experimental Room-TemperatureRate Constants kr for the Reaction of CN with NHJ species o”(CN) T/K kr/cm3 molecule-I s. I ref 0 300 2.1 x 10 2 ~~
0 0 1 0 0 0 0
295 295 294 300 296 300 296
~
(2.5 f 0.5) X IO I I (2.9 f 0.1) X IO-II (4.5 f 0.3) X IO I I (2.38 0.25) X IO I I (2.91 0.27) X IO I I (1.16 f 0.03) X 10 I ’ ( 1 . 4 5 * 0 . 2 5 ) X IO
3 4 4 5
this work 5 this work
cell (75-m path length) for identification by infrared spectroscopy using the diode laser. Materials, gas handling, and flow and pressure measurements were as described previously. I 6 - l All experiments were carried out at room temperature (296 f 2 K).
/”’
CIS H2NCNH
I
1%
H2
trans H2NCNH
L 2
Results of Kinetic Measurements Typical raw data showing the time dependence of absorption by CN, a t low and high values of [ND,], together with the corresponding first-order decay plots, are shown in Figures 1 and 2. Figure 3 shows the slopes of first-order decay plots, measured relative to the slope with no ammonia present, plotted against [NH,] or [ND,], as appropriate. The nonzero intercept on the [NHj] axis in Figure 3, and to a lesser extent on the [ND,] axis, is believed to result from the destruction of a fixed amount of NH3 or ND, by that part of the laser output that coincides with a strong absorption feature of the gas; once this part of the laser output has been absorbed, further destruction of the reagent is not significant. This belief is supported by the agreement between the present result for NH, and results obtained by previous workers. The slopes of the lines in Figure 3 lead to the roomtemperature rate constants that are given, together with their 95% confidence limits, Table 11. This table also summarizes previous room-temperature results for the reaction with NH3. Our results for NH, are seen to be in good agreement with those obtained previously. The H / D isotope effect, amounting to a factor of 2, is unexpectedly large.
Details of Quantum-Chemical Calculations The geometries of species that might be involved in the reaction of C N with NH, were optimized using a 6-31G* basis set at the H F and, in certain cases, MP2 levels of theory. Harmonic vibrational frequencies, MP4SDQ energies, and QCISD(T) energies were calculated for these geometries. For some species calculations were also performed following Pople’s G 1 procedure. Thecalculations employed either the Gaussian 82 or the Gaussian 90 program^.^^,^^
Calculation of Reaction Pathway The structures of species that might be involved in the reaction of C N with NH, are drawn to scale in Figure 4. Important geometric parameters obtained by optimizing the structures at the HF/6-31G* level are given in Table 111. Transition-state species are labeled TS,, while intermediates, reactants, and products are labeled according to their connectivity of atoms. TSg and TSlo appear to be torsional transition states of the intermediate species. As can be seen from Table 111, a number of the calculated geometries involved stretched bonds. Fourth-order unrestricted Moller-Plesset energies that include contributions from triple substitutions give poor results for geometries of this sort due to slow convergence of the unrestricted Moller-Plesset series.? Overestimation of the effects of triple substitutions in the MP4 energy has also been noted to occur for unsaturated radicals, such as cyano, and in some molecules that contain multiple
\ -c H2
TS,
7 ”\
v\
‘
Nl
H2NHCN
n2
TS,
Figure 4. Structures of CH3N2 species involved in the reaction of CN with NH3.
bonds.22~23Consequently, we have calculated MP4 energies at the MP4SDQ level rather than the MP4SDTQ level. For species that appeared to warrant higher level calculations, QCISD(T)//MP2 energies were determined. The QCISD(T) method24 is known to give energies close to full CI results, particularly for geometries close to equilibrium. However, because thecomputation time for a QCISD(T) energy calculation isseveral days, compared with several hours for an MP4SDQ energy calculation, QCISD(T) energies were calculated only for species corresponding to important features of the potential energy surface. Energies at other than the MP4SDQ/HF level will be referred to specifically in the text. Energies are uncorrected for zero-point vibrational energy unless otherwise stated. TheHF/6-31G*//HF/6-31G* and MP4SDQ/6-31GS//HF/ 6-3 1G* energies and calculated zero-point vibrational energies are given in Table IV together with MP4SDQ/6-3 1G*//MP2/ 6-31G* and QCISD(T)/6-31G*//MP2/6-31G* energies for those species for which they were obtained. Important points to notice in this table are that the MP4SDQ//HF energy of C N is lower than the MP4SDQ//MP2 energy and that the transitionstate species TS3 lies above the energy of the reactants at the H F / / H F level but below the energy of the reactants at the MP4SDQ//HFlevel. Thelackofimprovement in theCNenergy on going from the Hartree-Fock to the MP2 level suggests that the partial inclusion of correlation energy in the optimization at the MP2 level does not represent correlation effects in this species very well and implies that the tabulated energies relative to reactants at the MP4SDQ//MP2 level probably overestimate the true energy differences. However, the MP4SDQ//MP4SDQ energy of CN is only ca. 1 kJ mol-’ below the MP4SDQ//HF energy, so the extent of overestimation of the energy differences at the MP4SDQ//MP2 level must be fairly small. The thermochemistry of the four possible exothermic product channels is summarized in Table V. These MP4SDQ//HF
Meads et al.
3260 The Journal of Physical Chemistry, Vol. 97, No. 13, 1993 TABLE 111: Optimized Geometric
Parameters
for Species Involved in the NH3 + CN Reaction geometric parameterso
species NH N2 NH? N2H HzCN cis-HCNH frans-HCNH ‘BI CHz ‘ A ICH2 NH3 CH3 CN HNC HCN HzNCN CHjNz HNCHNH HNzCHz HCNzH2 HzNHNC H’NCN HHNHNC cis-H zNCN H HHNHCN HzNHCN rrans-HzNCNH
TS I TS2 TS3 TS.I
TS5 TSh TS7 TSx
TSY TSio
NH 1.024 N N 1.078 N H 1.013 N N 1.179 CH 1.082 HC 1.084 HC 1.08 1 HC 1.071 HC 1.097 NH 1.000 HC 1.073 CN 1.162 H N 0.985 HC 1.059 N I H 0.998 CH 1.08 1 N I H I 1.007 NiCN2 121.6 N I C 1.427 CNlN2 60.4 wN2NlCHl 112.1 NjC 1.315 CNlN2 62.5 wCNlN2Hl 107.2 NlHl 1.001 H3N2NI 11 1.6 N I H 1.001 NlHl 1.011 NlHlO.995 HlNlC 116.6 w H I N I C N 16.0 ? N H I 1.011 NlHl 0.997 HlNlC 114.9 ~ H I N I C H-33.7 , N I H 1 0.994 H I N I C117.2 w H I N I C N22.1 ~ N I H I 1.006 H ~ N I C129.5 N I H I 1.005 NlHiNz 129.5 NlHl 1.007 NlH’C 137.5 NlHl 1.000 H I N I C115.9 wHiNlCNz 23.3 N I H I 1.010 H~NIC 99.4 u H I N ~ C N -55.0 : NlHl 0.999 HzNlC 121.6 NlHl 0.996 N i H l C 115.7 u N ~ C N I H200.7 I N H I 1.010 N I C N ? 1 1 1.8 H N I 1.008 CNzNl 171.9 H N I 1.004 NIN~C 119.5
H N H 104.3 N H 1.029 CN 1.260 CN 1.234 C N 1.234 HCH 130.8 HCH 103.0 H N H 107.2 N C 1.154 C N 1.133 N I C 1.344 C N I 1.485 C N I 1.324 N2CH 116.4 NlN2 1.393 N I C H I 118.7 w N ~ N I C -104.2 H~ N I N Z1.508 NiNiHl 117.0 wCNIN~H -1 ~14.3 N I N 1.419 ~ NlNlC 125.7 N I C 2.352 N I H 2.001 ~ N I H2 1.000 H~NIC 117.4 U H Z N I C N156.7 Z N I H 2.209 ~ N I H 0.998 ~ H ~ N I 114.6 C wHlNlCH3 193.6 N I HI 1.000 H~NIC 116.6 wH2NlCN2 164.6 N l H l 1.303 NlCNz 142.6 NlH3 1.068 H ~ N I C118.2 N I H 1.091 ~ H3CNz 173.5 NlH20.996 HzNlC 116.8 u H I N I C N -196.9 ~ N I C 1.913 NlCNz 123.2
N I C 1.309 N I C N ? 177.8 N I H2 0.999 NlHzC 114.0 U N ~ C N I -24.8 H~ N I C 1.956 NzCHi 147.3 N I N ? 1.278 NzCH 121.5 NlNz 1.437 N2CH 126.5
N N H 113.0 HCN 120.8 N H 1.012 N H 1.008
CN2 1.138 NlN2 1.175 CN2 1.329 CN2H 108.1 C H I 1.078 NlCH2 115.4 wCNIN~H -109.1
HCN 133.8 HCN 126.9
C N H 115.2 C N H 114.5
H N l C 114.5 HCNl 108.9 N2H 1.010
CNlN2 118.4 C N l H 110.7
CH2 1.075 NIN~H 110.5
N2H 1.004
N2H2 0.999 NlCH 126.9
CH 1.085
NzHl0.998 N I N z H113.7 ~ wN2NlCH -109.1 N l H j 1.001 w H I N I N ~121.9 H~ CN2 1.160 H3N2 1.OOO N I C 1.360 N I C N 137.1 ~
N2C 1.287
H I N I N107.9 ~
HNlC 109.8 N2C 1.153 CN2 1.231 CN2H3 116.4
H l N l H j 127.0 N2H3 1.01 1
H3C 1.068 N I C 1.383 NlCN2 125.5
CN2 1.134 CH3 1.082 N2CH3 119.0
H I N I H 127.4 ~ CN2 1.259
NiC 1.352 N I C N 129.9 ~
CN2 1.237 CN2Hj 115.1
N2Hj 1.002
N I C 1.455 u H I N I C H122.0 ~ HiN2 1.556 u H I N I H ~ 110.4 N~ H3C 1.542 w H I N I H ~121.8 C N I C 1.338 NlCN2 157.5
CN2 1.165
HlNlC 108.1
N2C 1.170
H I N I H 115.9 ~
CN2 1.153
H I N I H 107.5 ~
CH3 2.268 N2CH3 40.4
CN2 1.177
CN2 1.185 CN2Hl 130.5
NlH, 0.997 wHlNlCN2 51.6
HlNlC 99.5
CN2 1.237 CNlH3 115.4 N I C 1.351 N I C N 158.1 ~
N2H3 1.070
HlNlC 122.2
CH3 1.834 NzCH, 102.9
CN2 1.165
CN2 1.182
HlNlC 98.9
CH 1.084
HNlN2 107.5
C H 1.077
H N I N 107.5 ~
CH3 1.064 U H I N ~ C H126.8 I N2C 1.239 U H I N I C H 90.7 J N2C 1.239 u C N ~ N I H122.8
Distances in angstroms, angles in degrees.
energies include a scaling correction in the zero-point vibrational energy.27 The relative energies of species on pathways to exoergic products, with the exception of N2 + CH3, are plotted in Figure 5 ; these energies do not include the zero-point vibrational energy. Additional calculations were made for the reactants N H j and CN and the products NH2, HNC, and HCN following the G1 procedure.I8 These calculations show some important results. The first is that at this level of theory, which has been shown to give energies close to experimentally determined ones, the exoergicities of reaction to form NH2 + HNC and NH2 + HCN are reduced to 26.4 and 88.0 kJ mol-’, respectively. Second, a significant contribution to the G1 energy (ca. 0.05 hartree) arises
from the inclusion of higher polarization functions 2df in the basis set. This suggests that a larger basis set, which includes higher polarization functions on the non-hydrogen atoms, would improve the accuracy of the results obtained for all species. Such a basis set would stabilize species with stretched bonds more than other species. Higher level optimizations for all species would also increase accuracy, however higher level calculations using bigger basis sets for such a system as this, would have placed impractical demands on both the CPU time and the disk space available to us. The harmonic vibrational frequencies calculated for all species are given in Table VI. The zero-point vibrational energies and
Reactions of CN with NH, and ND3
The Journal of Physical Chemistry, Vol. 97, No. 13, 1993 3261
TABLE I V Calculated HF//HF, MP&DQ//HF, MP4SDQ//MP2, and QCISD(T)//MP2 Energies and Unscaled Zero-Point Vibrational Enemies. (Wbere Available. OCISD(T)//MPZ Enernies Are Given in Parentheses) energy/ hartrees species H
'x NH 'EN2
'91NH2 'A' N2 2 9 2 H2CN 'A' cis-HCNH 'A' rrans-HCNH '91CH2 ' A I CHI NHi CHJ CN HNC HCN NH] CN HlNCN CHiN2 HNCHNH HN2CH2 HCN2H2 H2NHNC HiNCN HHNHNC cis-HlNCNH HHNHCN H2NHCN c trans-H2NCN H
2x
+
TS I TS2 TSi TS4 TSs TSo TSi !A' TSx
TSU TSio
M P4SDQ/ H F
HF/HF -0.498 -54.959 -108.943 -55.557 -109.425 -93.432 -93.392 -93.398 -38.921 -38.872 -56.184 -39.558 -92.204 -92.855 -92.875 -148.389 -147.908 -148.462 -148.464 -148.402 -148.336 -148.368 -148.399 -148.426 -148.435 -148.442 -148.467 -148.444 -148.332 -148.363 -148.372 -148.382 -148.388 -148.402 -148.390 -148.413 -148.382 -148.377
23 43 95 70 40 31 96 75 50 37 36 99 83 33 20 19 66 01 52 03 30 43 70 81 37 80 26 12 74 19 65 40 25 29 37 44 04 86
-0.498 -55.076 -109.253 -55.708 -109.728 -93.696 -93.669 -93.679 -39.019 -38.991 -56.368 -39.687 -92.451 -93.137 -93.159 -148.819 -148.360 -148.905 -148.893 -148.836 -148.793 -148.809 -148.840 -148.861 -148.882 -148.882 -148.903 -148.894 -148.805 -148.813 -148.827 -148.832 -148.835 -148.854 -148.838 -148.851 -148.833 -148.825
23 68 23 01 14 58 92 26 90 99 28 59 65
products N2H + CH' ( ' A i ) N2H + C H 2 (lBI) NH cis-HCNH NH + ~ ~ u w - H C N H N H + H'CN NH2 + H N C HlNCN H NH2 HCN Nz C H j
+
+
+
+
MP4SDQ//HF 239.9 167.7 177.2 154.3 106.6 -75.4 -125.3 -162.4 -327.5
GI
ZPVE/kJ mol-' 21.1 16.5 54.0 37.0 70.1 70.8 72.6 48.4 47.2 97.2 81.3 11.9 44.8 47.2 109.1 97.2 121.8 124.1 128.2 127.1 128.1 115.8 108.1 123.8 108.3 125.9 125.8 104.8 107.1 101.6 99.1 112.0 117.8 100.3 1 10.0 115.6 121.2
-56.368 94 (-56.372 IO) -92.451 54 (-92.481 00)
11
73 93 89 81 29 25 98 55 83 05 53 63 07 16 57 72 43 49 93 36 78 92 54 71
TABLE V Exothermicities of the Possible Product Channels for Reaction of CN with NHI exothermicity
M P4SDQ/ MP2 -0,498 23
-148.820 48 (-148.853 09)
-148.843 67 (-148.869 40)
-148.834 62 (-148.856 65) -148.836 60 -148.839 28
Enorgy (kJlmol)
TS1
expt"
273.6 247.6 196.8 -26.4 -75.3 -88.0 . -257.6
TS8
I .
-2* 18 -49f40 -68 11 -245 f 1 I
The exothermicities quoted are experimental values in kJ mol-' for 298 K,based on enthalpies of formation given in the compilation of Lias etal.,?$with thecxceptionof theerror limits for the processgiving H2NCN as a product, which had to be guessed, and the heat of formation of CN, which was adjusted slightly to 438 kJ mol-' from the listed value of 435 kJ mol
vibrational frequencies given in Tables IV and VI are unscaled. Collision of C N with NH3 can lead in principle to formation of four possible complexes, depending on the relativeorientations of the reactants. We were able to optimize structures for complexes with orientation of either the C or N of CN toward H (HJ or NH3 (H2NHCN and H2NHNC, respectively) and with orientation of the C of C N toward the N of NH3 (H3NCN). Formation of HINCN and HzNHNC would be assisted by attractive dipole-dipole forces. We were unable to optimize a structure resulting fromcollision with the N of CN oriented toward the N of NH3. Our closest approximation to this structure has an energy 4 kJ mol-' below the energy of the reactants, with no
trans H ~ N C N H
___
HzNHNC
Figure 5. Relative energies of species on pathways to exoergic products (with the exception of N2 + C H I ) for the reaction of C N with NH,.
zero-point energy, and 4.5 kJ mol-' above the reactants, with zero-point vibrational energies included. A normal coordinate analysis of this structure shows that it possesses two imaginary vibrations and therefore is neither an intermediate nor a transitionstate species. The other three collision complexes are of lower energy than the reactants. Formation of the H2NHNC complex involves crossing a barrier that lies 16 kJ mol-' above the energy of the reactants. Reaction over this barrier would lead to a rate constant with a positive temperature dependence, which in practice is not observed. The H2NHNC complex consists essentially of an NH2 and an HNC
Meads et al.
3262 The Journal of Physical Chemistry, Yol. 97, No. 13, 1993
TABLE VI: Calculated Hartree-Fock Harmonic Vibrational Frequencies. (Calculated Values Are Unrcaled, Experimental Values in Parentheses) species CN NH N2 CH2 ‘BI CH? ‘AI NH2 N2H HCN HNC CH’ NH3 HzCN cis-H C N H
trans-HCNH HjNCN trans-HzNCNH HHNHNC HHNHCN HzNCN cis-H 2NCN H HzNHCN HCNzHz HlNHNC CHIN? HNCHNH HNzCHz
TS I TS?
TS, TSJ
TS3 TSb
TS7 TSn TSr
harmonic vibrational frequencies/cm
I
1982 (2069) 3528 (3282) u 2758 (2360) a1 1238 (963), a l 3327, bl3527 a l 1567, a l 3151, b2 3177 a l 1710 (1497), a l 3606 (2961), bz 3707 a’ 1264, a‘ 166 I , a‘ 3276 7r 889 (713), u 2438 (2097), u 3679 (331 1) 7r 541 (463). u 2309 (2024), u 4094 (3653) a”307 (606),e’ 1540(1388),a’3285e’3461 a l 1208 (950), e 1849 (1627), a1 3690 (3337), e 3823 (3444) bl 1033, b2 1073, a1 1436, a1 1639, a1 3234, bz 3319 a’ 1013, a” 1063, a’ 1267, a’ 1664, a’ 3250, a’ 3582 a’ 1033, a” 1100, a’ 1332, a’ 1701, a‘3295, a’ 3678 e66, 182,e369, 1170,e 1827,2056,3709, e 3857 375,495,540,755, 1092, 1185, 1397, 1788, 1933,3771,3776,3922 120, 131, 197,275,390,867,871,1706, 2314,3643, 3744,3818 107, 120, 155,252,365, 1021, 1022, 1708, 2422,3560,3634,3734 461,532,691, 1159, 1324, 1805,2603, 3788, 3891 334,480,534,780, 1044, 1153, 1344, 1801, 1965,3598,3764,3904 376, 555,694,977, 1154, 1298, 1416, 1766, 18253293,3789,3898 667,841,948, 1016, 1106, 1141, 1255, 1589, 1826,3200,3764,3888 154,560,701, 1010, 1232, 1440, 1509, 1624, 1849,3734,3768,3830 180,505,912, 1147, 1243,1543, 1622, 1628, 1690,3235,3328,3330 611,656,848, 1077, 1197,1234, 1299, 1510, 1592,3329,3685,3715 866,982, 1055, 1101, 1242, 1298, 1365, 1430, 1669,3299,3394,3736 3051i, 300,327,679, 1010, 1011, 1441, 1466, l754,2010,37I6,38lO 651i, 155,208,401, 448,851, 1657, 1707, 2242,2630,3736,3866 1904i. 163, 179, 329, 594,983, 1630, 1632, 1822,2147,3702,3809 1336i,307,331,509,633,718, 1144, 1288, 1801,2168,3774,3899 64% 172, 339,619, 663,886,941, 1726,2102, 3649, 3750, 3884 856i, 194,525,670, 1111, 1130, 1210, 1816, 2077,3407,3727,3822 1048i, 279,528,535,617,667, 1 130, 1297, 1808, 2206,3793, 3906 6971, 132, 333, 727, 867, 902, 975, 1723, 1798, 3540,3651, 3754 5761,371,406, 1073, 1116, 1247, 1339, 1662, u
(I
1899,3206,3282,3681
TSio
4461,462,809,965, 1189, 1241, 1408, 1573, 1796,3355,3685,3787
molecule connected by a long bond, which implies that this pathway corresponds to a direct H-abstraction mechanism. Similarly, at least at the Hartree-Fock level of theory, formation of the H2NHCN complex proceeds over a barrier lying 43.4 kJ mol-’ higher in energy than the reactants and this complex has astructureconsistingof an NH2 andan H C N moleculeconnected by a long bond, which again suggests an H-abstraction channel. Inclusion of correlation energy appears to remove the barrier; however, our attempts to optimize this structure a t the MP2 level failed. The reason appears to be that the best MP2 geometry would be significantly different from the H F geometry. Therefore
the relevance of the MP4SDQ//HF energies is doubtful, and we still believe that formation of the H2NHCN complex involves passage over a significant barrier. Both of these complexes have barrierless pathways to products H N C + NH2 or HCN + NH2. The H3NCN intermediate has no barriers to formation. Possible pathways for subsequent reaction include loss of an H atom and 1,3 migration of H. Our calculations show that the barrier to formation of HzNCN + H lies 37.7 kJ mol-’ above the energy of the reactants, which enables this reaction path to be ruled out. At the MP4SDQ//HF level, migration of H from N to N’ involves passage over a barrier lying 21.9 kJ mol-’ above the energy of the H3NCN intermediate and 33.0 kJ mol-’ below theenergyofthe reactants. At the MP4SDQ//MPZandQCISD(T)//MPZ levels of theory, this barrier lies 23.7 and 33.5 kJ mol-’ above the energy of the H3NCN intermediate and 37.7 and 9.3 kJ mol-1 1 below the energy of the reactants. Following H-migration, the cis form of the H2NCNH intermediate can undergo isomerization to the trans form or dissociation to products NH2 + HNC. The intermediate is very asymmetric, which implies that considerable contortion of the molecular skeleton occurs during the H-atom transfer. From the transHzNCNH intermediate, further rearrangement, involving migration of the same H atom from N’ to C, leads to the products N H 2 HCN. The G1 calculations mentioned earlier showed the exoergicities of the reactions to form NH2 + H C N or N H 2 + H N C to be considerably less than those calculated at the MP4SDQ//HF level, which suggests that more extensive calculations, at higher levels of theory and with arger basis sets, may show the pathway to formation of NH2 + N C to be much less favored than the pathway to formation of N H 2 HCN. On the basis of the foregoing discussion, we conclude that the reaction proceeds, from the HJN-CN complex formed initially, by rearrangement over the most important secondary barrier to form cis-HzN-CNH, followed by further rearrangement over lower barriers to give the final products N H 2 and HCN.
+
k
+
Experimental Identification of the Reaction Products The identification by Bullocket al.2of NH2as a reaction product was confirmed in the present work for the reaction of C N with ND3. From the data of Meunchausen et al.,2Babsorption lines of ND2 were expected in the vicinity of 1179.7 cm-I, a frequency that was within the range covered by one of our laser diodes. Several transient absorptions in this region were found when ND3 alone was photolyzed at 193 nm, and these absorptions appeared with much greater intensity when C2N2 was photolyzed at 193 nm or ICN was photolyzed at 248 nm in the presence of ND3. Unfortunately, the absorptions were all too weak to be used for kinetic measurements. Nevertheless there seems to be no reason to doubt the identification of NH2/ND2 as a major reaction product. Mass analysis of samples withdrawn continuously from a flowing mixture of ICN, NH3, and He that was being irradiated at 248 nm showed a 15-20% increase in signal at m/e = 27 over the background signal obtained with the photolysis laser turned off, showing that either H C N or H N C was being produced by the reaction. No change was detectable at m/e = 28 (N2+), 42 (H2NCN+), or 43 (H+.H2NCN) or at any other peak below mass 43. Spectroscopic observations in the region of the C N stretch at 2250 cm-I also showed no evidence of the presence of CNNH2 in samples that had undergone prolonged photolysis. Thus it would appear that we can rule out processes that give HzNCN + H and N 2 + CH3 as products as important reaction channels, and it only remains todiscriminate between the processes that give N H 2 + H N C and NH2 + H C N as products. Attempts were made to observe kinetic buildup of the P(9)(001 000) absorption line29of HCN at 2069.520 08 cm-l and the R(8)(001 000) absorption line30 of H N C at 2050.061 22 cm I , but the absorptions were too weak. Instead, static mixtures
- -
Reactions of C N with NH3 and ND3 of ICN and NH3 were irradiated for 30-45 min and then transferred to a White cell providing a 75-m path length for absorption. The resulting spectra contained the P(9) and P( 15) lines of H C N at 2069.52008 cm-I and 2050.421 12 cm.1, respectively, with absorptions a t least 20 times greater than the background noise. No evidence for the presence of H N C was found in the region of the R(8) and R( 15) lines at 2050.06 1 22 cm-I and 2069.150 57 cm-I, respectively. Thus, a t least at long times, H C N is a major product. It remains to consider whether H N C formed as an immediate product might be capable of isomerizing completely to H C N in a time of the order of 45 min. The answer to this question is dependent on two factors, one of which is the magnitude of the activation energy for the isomerization process. As yet, no direct measurement of this quantity has been made. Murrell et aL3I obtained values for the energy difference between the two isomers and the activation energy for isomerization by adjusting a potential surface for the HCN/HNC system in order to fit their calculated frequencies to experimental spectroscopic transitions. On the basis of their conclusion that the potential maximum between H C N and H N C lies 98 kJ mol-l above the lowest level of HNC, and assuming a value of 1012s-I for the pre-exponential factor, the rate constant for isomerization ofHNCatroom temperaturebecomes 1.3 X IWS-~. Thiswould suggest that the interconversion rate is negligible. However, if the maximum exothermicity of the process giving the products N H 2 HNC, namely, 20 kJ mol-’, were to appear as internal excitation of the H N C product, and thermal activation were assumed to begin at the 18 kJ mol-’ level, in the worst case the isomerization rate would be around I t 2 s-I and the main product observed after 45 min might well be HCN, even if the initial product was HNC. Ab initio calculations of the activation barrier for isomerization give uniformly higher values than that found by Murrell et al. Recently Lee and Rendle32 reported the results of an extensive ab initio study of the HCN/HNC system. Their results, obtained by a coupled cluster method with very large basis sets, show the transition state to lie 186.6 f 4 kJ mol-1 above HCN, or 124.7 kJ mol-’ above HNC, using Pau and Hehre’s value3) of 6 1.9 f 8 kJ mol-’ for the HCN/HNC energy difference. Our G1 calculations gave a value of 61.6 kJ mol-’ for the H C N / H N C energy difference and 186.1 kJ mol-’ for the energy of the transition state relative to HCN, in excellent agreement with values obtained by other methods. Taking the activation barrier relative to H N C to be 124.7 kJ mol-’ and assuming thermal activation to commence at the 18 kJ mol-l level, we find a worst case isomerization rate of 2 x 10-7s-I, which is entirely negligible. Thesecalculations seem likely to be more accurate than the fitting procedure of Murrell et al. Therefore, consideration of the first factor, the height of the activation barrier, leads to the conclusion that H N C formed as a product of the reaction should not have isomerized to H C N prior to observation of its spectrum in the White cell. The second factor to be considered is possible catalytic activity of the walls of the photolysis cell, transfer line, and White cell toward the isomerization reaction. The body of the White cell was a teflon-coated glass cylinder ca. 25 cm in diameter and should have been inactive. The anodized aluminum end plates and the gold-plated mirrors might have catalyzed the reaction; however, the search for H N C was carried out by monitoring the infrared transmission while the gases were being admitted to the cell, so that there would have been insufficient time for more than a small fraction of the H N C to have contacted these surfaces. The photolysis cell and transfer line were made of glass, with glass-key and teflon-key stopcocks, which should have been inactive, but the walls of the photolysis cell became coated with C N polymer during the course of the experiments and this could have increased their catalytic activity toward H C N / H N C
+
The Journal of Physical Chemistry, Vol. 97, No. 13, 1993 3263
TABLE VII: Calculated Rate Constants, Using MPBDQ// MP2 Enernies T IK 10”kl IO-”k.l 1 0.‘ I k? IO”kT
+
200 250 300 350 400 450 500
2.930 2.900 2.895 2.893 2.895 2.904 2.907
200 250 300 350 400 450
2.761 2.730 2.726 2.726 2.734 2.745 2.752
(a) N H J CN 3.305 5.935 9.198
10.50 12.48 16.20 20.68
1.042 I .068 1.091 1.115 1.139 1.161 1.185
6.94 4.41 3.07 2.55 2.42 I .94 1.58
0.5142 0.5345 0.5535 0.5729 0.5916 0.6090 0.6277
7.1 1 4.61 3.23 2.49 1.81 1.45 1.18
(b) N W C N
500
1.480 2.632 4.114 6.054 8.294 10.84 13.97
isomerization. It seems significant that H N C apparently has never been observed in the laboratory a t room temperature. Thus, we cannot entirely rule out the possibility that the reaction occurred by the channel leading to NH2 + H N C and that the H N C was converted to H C N between production and analysis, but the available evidence favors the process giving NH2 + H C N as products.
Theoretical Calculation of the Rate Constant Rate constants klfor capture over the centrifugal barrier in the predominantly dipole-dipole long-range potential were calculated as previously described,34assuming the Morse well depth for complex formation to be as found in the last section and multiplying the raw dipole-dipole rate by a factor of 0.5 to allow for collisions occurring with the wrong orientation. The resulting values of kl are given in the second column of Table VI1 for the temperaturevalues that aregiven in the first column. Thecapture program also returned the distribution over E, the sum of translational and rotational energy for the reactants, for successful collisions, weighted by the product of effective cross section and collision velocity, and similarly weighted average values of frequencies for the vibrational motion of the reactants a t the top of the centrifugal barrier, where they exist momentarily in states similar to the “pendulum” states of Friedrich et al.35 For each value of reactant energy E, barrier-crossing rates were calculated by the basic RRKM formula where numbers w ( E ) and densities of energy levels p(E) for transition states and bound complexes were calculated by the Beyer-Swinehart a l g ~ r i t h m . ~ ~The . ’ ~third and fourth columns ofTableVII containvaluesof k-1,the rateconstant fordissociation back to reactants, and of k2, the rate constant for crossing the first potential barrier at the transition state TS4 of Figure 5 . For reasons that will become clear shortly, these barrier-crossing rates were calculated using the energy values from the MP4SDQ// MP2 calculations of the last section. For the transition state corresponding to dissociation of the CN.NH3* complex back to reactants, the vibrational frequencies comprised the experimental frequencies for the separated reactants, together with the average centrifugal barrier frequencies returned by the capture program. For other species the vibrational frequencies and zero-point energies were the Hartree-Fock values returned by Gaussian, multiplied by a factor 0.89.27 Because the overall reaction rate is not limited by the subsequent barriers on the reaction pathway of Figure 5 , the overall rate constant kT is given by the average value of
k , W = k , ( E ) k , ( E ) / k l ( E )+ k,(E)l (2) over the known distribution of E at each temperature T. The
The Journal of Physical Chemistry, Vol. 97, No. 13, 1993
3264 8
I
1
6 -
5 r
0 8 4 -
0 ' 100
1
I
I
1
1
200
300
400
500 T/K
600
700
1
i
800
900
Figure 6. Theoretical and experimental rate constants for reaction of CN with ammonia. Theoretical data: small circles, results from the present work for MP4SDQ//MP2 energies and zero-point energies (with (unfilled circles) and ND3 (filled circles); correction f a ~ t o r 0 . 8 9for ~ ~NH3 ) small squares, same as the small circles but using experimental zeropoint energiesof CN. NH3,snd ND3. Experimentaldata, for NH3 unless otherwise specified: large unfilled triangles, results of Sims and Smith;J large half-filled triangle, result of de Juan et aI.$ large unfilled squares, results of Bullock et al.;2 large half-filled square, result of Boden and Thrush;' large circles, experimental results from the present work for NHJ (unfilled circle) and ND3 (filled circle). Dotted curves, formulas of Yang et al.,5NH3 above and ND, below.
resulting values of kTforthe MP4SDQ//MP2 energies are given in the fifth column of Table VII. The calculated values of k j m are very sensitive to the well depth of the H3N.CN complex and to the height of the first potential barrier, so that the different theoretical treatments of the last section yield markedly different values for the overall rate constant. Thus, using the MP4SDQ//HF energies, we find values of 101lk3w equal to 1.80 or 1.09 for NHj and 1.82 or 1.18 for ND3, where the first figure results from using the calculated zero-point energies for the reactants and the second figure results from using the experimental zero-point energies for ammonia and CN. Similarly, using the MP4SDQ//MP2 energies we find values of l0lIkjw equal to 3.07 or 1.96 for NH3 and 3.23 or 1.94 for ND3. Using theQCISD(T)//MP2energiesweobtain 1011k3w values of 0.108 or 0.045 for NH3 and 0.069 or 0.034 for ND3. Both of the MP4SDQ calculations, that using Hartree-Fock geometries and that using MP2 geometries, give results that must be regarded as satisfactory at the present state of the theory, which implies that the errors in the calculated energy values are of similar magnitude for the reactants, the CNNH3 complex, and the transition stateat the topof the first barrier. TheQCISD(T)//MP2 calculation gives a markedly shallower potential well for the complex and an energy much closer to zero for the transition state TS4, and both of these differences lead to very low values for the calculated overall rate constant by comparison with experiment. Thus the improvement obtained by going toQCISD(T)//MP2 evidently is not an advantage for our present purpose, a t least when no allowance is made for tunneling through barriers. Unfortunately, energy values obtained by the G1 method24 take much longer to calculate and are not yet available for this system. Figure 6 shows experimental and calculated rate constant values as a function oftemperature. Thesmallcirclesshow thecalculated results using MP4SDQ//MP2 energies plus calculated zero-point energies for all species, open circles being for NH3 and filled circles for ND3. The small squares, also unfilled for NH3 and filled for ND3, are values calculated with the same energy values except that the listed experimental vibration frequencies were used to calculate the zero-point energies of the reactants. The experimental results of Sims and Smith4 are shown by large unfilled triangles, and the single large half-filled triangle is from de Juan et ale3The large unfilled squares are the results of Bullock
Meads et al. et ale,] and the single larged half-filled square is Boden and Thrush's value.! The two large circles (unfilled for NH3, filled for ND3) are the experimental values from the present work. The rate constant expressions given by Yang et ala5are plotted as dotted lines, with NH3 above and ND3 below. In general the agreement between different experimenters is good, and the agreement between theory and experiment is tolerable, with one major point of difference, namely, the magnitude of the deuterium isotope effect. The calculated (MP4SDQ//MP2) differences in zero-point energy between the undeuterated and deuterated reactants, CH3NCN complex, and transition state TS4 at the top of the first barrier are 23.3,27.3,and 19.7 kJ mol-',respectively. These values differ amongst themselves by much less than the ca. 40 kJ mol-' vibrational energy of an N-H bond, so no large deuterium isotope effect would be expected, and the detailed calculations reinforce this expectation. However, the experiments show that the reaction with ND3 is slower than the reaction with NH3 by a factor of 2 a t 296 K, so we are obliged to conclude that tunneling through the first barrier contributes at least a factor of 2 to the overall reaction rate. Inclusion of tunneling would reduce the discrepancy between the experimental rate constants and those calculated using the QCISD(T)//MP2 energies, but calculations with these energies in which the effect of tunneling is simulated by artificially reducing the height of the first barrier show that the effect is much too small to bring the two sets of values into agreement. When the first barrier is lowered from 16.75 to 8.75 kJ mol-' the effect is to increase k3w by a factor of 3, and a further reduction by 5 kJ mol-' contributesonly another factor of 2, whereas thediscrepancy between theory and experiment amounts to a factor of between 20 and 100. Calculations similar to those in ref 11 predict that there should be no significant deuterium isotope effect for the reaction of N H 2 with NO; evidently this needs to be tested experimentally. If the nature of the reaction products were determined entirely by statistics, the ratio of H N C to HCN, or of DNC to DCN, in the products at total energy E should be equal to the ratio of the numbers of states w(E) above the barriers TSs and TS,, respectively, in Figure 5. Unfortunately, the difference between these calculated barrier energies is of similar magnitude to the uncertainty in the energies themselves, so that the conclusions to be drawn are at best qualitative. Nevertheless, the results of the present calculations do favor the production of H C N over HNC, because the barrier to H C N formation is lower by 7.1 kJ mol-'. When the ratios of w(E) are averaged over the appropriate distributions of E, the predicted ratio of H C N to DCN in the products at 300 K is typically found to be about 3. Experimentally, there is no evidence for any production of HNC, a result that could be taken as implying that the accuracy of the energy values is not good enough and/or that the nature of the products is largely determined by the dynamics of the system, rather than by statistics, as it evolves on the potential surface which includes the important configurations whose relative energies are shown in Figure 5 . To account for the observed effect of C N vibrational excitation on the reaction rate in terms of the present model, it is necessary to assume that the C N vibrational energy contributes more to the value of kz(E) for crossing the first potential barrier than it does to k-l(E), in the channel for dissociation back to reactants, and so enhances the overall reaction rate. If the C N vibration merely contributed to the general pool of energy available to the collision complex, the effect of excitation should be the same as the effect of an increase in temperature, Le., to decrease the overall reaction rate. Thus, the observation that the reaction rate is enhanced by excitation of a reagent for a system with a negative temperature coefficient implies that the particular mode of excitation does not couple completely with other modes of the complex in the input
Reactions of CN with NH3 and ND3 channel. This is reasonable, since coupling would be expected to be greater in the tight transition state which we have labeled TS4 than in the loosely bound collision complex. The effect of vibrational excitation of C N is then to increase the amount of kinetic energy available for crossing the first barrier relative to the kineticenergy in thechannel for dissociation back to reactants. The difference between the average amounts of CN vibrational energy going into the transition states associated with k-,and k2 does not need to be very large to account for the observed effect, which amounts to a factor of 1.56 f 0.18 in the measured values of k295 for CN(u” = 1) relative to CN(U”=O).~The energy of a single vibrational quantum of C N is 24 kJ mol-’, and we can simulate theeffect ofexciting thisvibration by reducing theenergy of transition state TS4. With MP4SDQ f f MP2 energy values, a reduction of only 4 kJ mol-’ in the height of the first barrier increases k2 sufficiently to raise the calculated value of k295 by a factor of 1.44, without altering the value of kl.
Acknowledgment. We are grateful to Mr. Murray Salt for the preparation of ND3samples. One of us (R.F.M.) is grateful for the award of a New Zealand Universities Grants Committee Postgraduate Scholarship. We are grateful to Professor M. C. Lin for providing results from his group prior to publication. References and Notes ( I ) Boden, J. C.;Thrush, B. A. Proc. R. SOC.London, A 1968,305, 107. (2) Bullock, G.E.; Cooper, R.; Gordon, S.; Mulac, W. A. J . Phys. Chem. 1972, 76, 193 I . (3) de Juan, J.; Smith, 1. W. M.; Veyret, B. J . Phys. Chem. 1987, 91, 69. (4) Sims, I. R.; Smith, I. W. M. J . Chem. Soc., Faraday Trans. 2 1988, 84, 527. (5) Yang, D. L.; Yu, T.; Lin, M. C. Chem. Phys. Lett., submitted for
publication. (6) Bair, R. A.; Dunning, T. H. J. Chem. Phys. 1985,82, 2280. (7) de Juan, J.; Callister, S.; Reisler, H.; Segal, G. A,; Wittig, C. J . Chem. Phys. 1988,89, 1977. (8) Wagner, A. F.; Bair, R. A. Int. J. Chem. Kiner. 1986, 18, 473. (9) Sun, Q.;Wang, D. L.; Wang, N. S.; Bowman, J. M.; Lin, M. C. J . Chem. Phys. 1990, 93,4730. (IO) Phillips, L. F. Prog. Energy Combusr. Sci. 1992, 18, 75.
The Journal of Physical Chemistry, Vol. 97, No. 13, 1993 3265 ( I I ) Phillips, L. F. Chem. Phys. Lett. 1987, 135, 269. (12) Phillips, L. F. Chem. Phys. Leu. 1990, 168, 197. (13) Cerny. D.; Bacis. R.; Guelachvili. G.;Roux, F. J . Mol. Spectrosc. 1978, 73, 154. (14) Guelachvili, G.; Rao, K. N. Handbook of infrared standards; Academic Press: New York, 1986. (15) Davies, P. B.; Hamilton, P. A. J . Chem. Phys. 1982, 76, 2127. (16) Whyte. A. R.; Phillips, L. F. Chem. Phys. Leu. 1983, 98, 590. (17) Harrison, J. A.; Meads, R. F.; Phillips, L. F. Chem. Phys. Lert. 1988, 148, 125. (18) Pople. J. A.; Head-Gordon, M.; Fox, D. J.; Raghavachari, K.;Curtiss, L. A. J. Chem. Phys. 1989, 90, 5622. (19) Binkley, J. S.; Frisch, M. J.; DeFrees, D. J.; Raghavachari, K.;
Whiteside, R. A.; Schlegel, H. B.; Fluder, E. M.; Pople, J. A. Gaussian 82; Carnegie Mellon University: Pittsburgh, 1982. (20) Frisch, M. J.; Head-Gordon, M.; Trucks, G. W.; Foreman, J. B.; Schlegel, H. B.; Raghavachari, K.; Robb, M.; 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.; Topiol, S.; Pople, J. A. Gaussian 90, Revision F; Gaussian Inc.: Pittsburgh, 1990. (21) Handy, N. C.; Knowles, P. J.; Somasundaram,K. Theor. Chim. Acta 1985, 68, 87. (22) Raghavachari, K. J . Chem. Phys. 1985,82, 4607. (23) Nobes, R. H.; Pople, J. A.; Radom, L.; Handy, N. C.; Knowlcs, P. J . Chem. Phys. Lett. 1987, 138, 481. (24) Pople, J. A.; Head-Gordon, M.; Raghavachari, K. J . Chem. Phys. 1987, 87, 5968. (25) Lias, S. G.;Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin, R. D.; Mallard, W. G.Gas-phase ion and neutral thermochemistry. J . Phys. Chem. Ref. Data 1988, 17 (Suppl. I ) . (26) J. Berkowitz, private communication to E. E. Ferguson; see: Petrie,
S.;Freeman, C. G.;Meot-Ner, M.; McEwan, M. J.; Ferguson, E. E. J . A m . Chem. Soc. 1990, 112, 7121. (27) DeFrees, D. J.; McLean, A. D. J . Chem. Phys. 1985.82, 333. (28) Meunchausen, R. E.; Hills,G. W.; Merienne-LaFore, W. F.; Ramsay, D. A.; Vervloet, M.; Birss, F. W. J . Mol. Spectrosc. 1985, 112, 203. (29) Choe, J. L.; Kwak, D. K.; Kukulich, S. G. J . Mol. Specrrosc. 1987, 121, 75. (30) Burkholder, J. B.; Sinha, A.; Hammer, P. D.; Howard, C. J. J. Mol. Spectrosc. 1987, 126. 72. (31) Murrell, J. N.; Carter, S.; Halonen, L. 0. J . Mol. Spectrosc. 1982, 93, 307. (32) Lee, T. J.; Rendle, A. P. Chem. Phys. Lett. 1991, 177, 491. (33) Pau, C.; Hehre, W. J. J . Phys. Chem. 1982,86, 321. (34) Phillips, L. F. J . Phys. Chem. 1990, 94, 7482. (35) Friedrich, B.; Pullman, D. R.; Herschbach, D. R. J . Phys. Chem. 1991, 95, 81 18. (36) Stein, S. E.; Rabinovitch, B. S. J . Chem. Phys. 1973, 58, 2438. (37) Gilbert, R. G.QCPE 1983, 3, 64.
