J. Phys. Chem. 1996, 100, 10123-10130
10123
A Theoretical Study of Reactions on the ClHCN Surface Lawrence B. Harding Chemistry DiVision, Argonne National Laboratory, Argonne, Illinois 60439 ReceiVed: February 19, 1996X
RHF+1+2/cc-pvdz calculations are reported for 14 minima and 9 transition states on the ClHCN ground state potential surface. The calculations predict the lowest energy route for the reaction Cl + HCN f HCl + CN to be a simple, direct, collinear abstraction. A lower energy addition reaction leading to the HClCN adduct is predicted to exist, but no direct pathway from HClCN to HCl + CN could be found. For the reaction of H with ClCN the calculations predict three pathways. These are, in order of increasing barrier height, addition to the carbon, forming HClCN; addition to the nitrogen, forming cis-ClCNH, and abstraction via a slightly bent transition state, forming HCl + CN.
I. Introduction Several experimental studies of reactions on the ClHCN surface have recently been reported that raise interesting questions about the topology of this potential surface. The experiments to date have examined the surface from three different starting points. De Juan et al.1 have looked at the reaction of translationally hot H atoms with ClCN. Two studies, Sims and Smith2 and Frost et al.,3 have been recently reported on the reaction of HCl with CN, examining the effect of vibrationally exciting either reagent. Finally, Metz et al.4 and Kreher et al.5 have reported results of the reaction of chlorine atoms with highly vibrationally excited HCN. We now briefly summarize the results of these experimental studies. De Juan et al.1 focused on reaction 1, where the H atoms
H + ClCN f HCl + CN
(1)
were produced translationally “hot” by the 248 nm photolysis of H2S providing a center-of-mass collision energy of 21.6 kcal/ mol. They were able to analyze the energy distribution in the products and concluded that the CN bond is essentially a spectator in which very little energy is deposited, while fairly large amounts of energy are deposited into center-of-mass translation, 〈fT〉 ) 0.33, and HCl vibration. Sims and Smith2 and Frost et al.3 have reported studies on reaction 2. Sims and Smith2 concluded that there is a negligible
CN(VCN) + HCl(VHCl) f HCN + Cl
(2)
enhancement of the rate on exciting the CN stretch. Frost et al.3 found that HCl(VHCl)1) reacts with CN 160 ( 70 times faster than does HCl(VHCl)0). These results then are consistent with the CN stretch also being a spectator in this reaction. A third relevant set of experiments have been reported by both Metz et al.4 and Kreher et al.5 These studies have focused on the reaction of translationally hot Cl atoms with highly vibrationally excited HCN, (3).
Cl + HCN(V1,V2,V3) f HCl + CN
(3)
Metz et al.4 examined the reactivity of two vibrational states of HCN, the (004) state in which four quanta of CH stretch are excited and the (302 state in which two quanta of CH stretch and three quanta of CN stretch are excited. They found these two states to react at comparable rates and concluded that “The X
Abstract published in AdVance ACS Abstracts, May 15, 1996.
S0022-3654(96)00490-X CCC: $12.00
CN bond in the Cl+HCN (302), (004) f HCl + CN reaction is clearly not a spectator”. They were also able to show that only 14% of the available energy ends up as HCl vibration, a surprisingly small amount since it is the HCl bond that is being formed in this reaction. Drawing on ab initio calculations reported by de Juan et al.,1 which will be discussed in more detail below, they suggested, as a possible explanation for these surprising results, that the mechanism for this reaction is not a simple direct collinear abstraction but rather an additionelimination mechanism Cl Cl + HCN
C
N
HCl + CN
(4)
H
in which the HClCN adduct is sufficiently long-lived to allow vibrational energy to flow into and out of the CN bond. Kreher et al.5 have confirmed the experimental findings of Metz et al.4 and have examined the reactivity of several different vibrational states of HCN. They find that excitation of even the first CH stretch overtone of HCN leads to vibrationally excited CN product and conclude, as did Metz et al.,4 that a long-lived complex must be involved. However, Kreher et al.5 report that some memory of the reactant vibrational state is retained in the product. They find, for example, that there is more vibrational excitation in the CN product resulting from reaction of the (302) state of HCN than from the (004) state, even though these two states possess essentially the same total internal energy. As discussed above, a great deal of very detailed information about reactions on this potential surface is now available. To our knowledge, only one ab initio theoretical study of this surface has been reported; these are the calculations of de Juan et al.1 They report MP4/3-21G* calculations on this surface as an aid to interpreting their experimental studies of reaction 1. Interestingly, they do report an indirect, addition-elimination mechanism for reaction 3. However, there is reason to question this conclusion. First, due to the use of a fairly small basis set, the MP4/3-21G* relative energies do not agree well with experiment. For example, reaction 1 is predicted to be 11 kcal/ mol endothermic instead of 8 kcal/mol exothermic. Second, the transition state structure they report for the second step of reaction 4, the elimination of HCl from HClCN, is collinear. It is not clear that this transition state actually connects HClCN to HCl + CN. Intuitively, it seems more likely that this is the transition state for a simple direct abstraction, Cl + HCN f © 1996 American Chemical Society
10124 J. Phys. Chem., Vol. 100, No. 24, 1996
Harding
TABLE 1: Relative Energies and Zero-Point Energies (kcal/mol) of Minima and Transition States zero-point energy minima HCl + CN(2Σ+) HCl + CN(2Π) H + ClCN Cl + HCN Cl + HNC HClCN ClCNH (cis) ClCNH (trans) HCNCl (trans) complexes CN--HCl(2Σ+) Cl--HCN(2Π) HCN--Cl(2Σ+) Cl--HNC(2Π) HNC--Cl(2Σ+) transition statesc HCl + CN f Cl + HCN(2Σ+) HCl + CN f Cl + HCN(2Π) HCl + CN f H + ClCN H + ClCN f HClCN H + ClCN f ClCNH (cis) Cl + HCN f HClCN Cl + HNC f ClCNH (cis) HClCN f ClCNH (trans) ClCNH (cis) f ClCNH (trans)
relative energies RHF+1+2
RHF+1+2+QCa
expt
7.6 7.2 5.7 10.5 10.0 11.8 11.7 12.0
0.0b 15.9 0.8 -33.9 -19.6 -36.3 -26.0 -28.9 1.9
0.0b (0.0) 21.5 (21.2) 4.8 (2.9) -28.8 (-25.9) -13.3 (-11.4) -32.3 (-28.1) -22.7 (-18.6) -25.9 (-21.5)
0.0 26.1 -1.8 -22.6 -7.7
8.7 10.8 10.7 10.5 10.4
-3.1 -35.0 -35.6 -21.2 -21.6
-2.8 (-1.7) -30.0 (-26.8) -30.6 (-27.5) -15.0 (-12.1) -15.8 (-13.0)
5.8
8.1 27.8 28.5 13.4 15.7 -19.5 -17.8 12.8 -17.8
5.8 (4.0)
6.1 6.9 6.3 9.8 10.4 8.2 9.9
26.5 (25.0) 14.3 (13.6) 15.8 (14.5) -19.9 (-17.7) -15.0 (-12.2) 13.1 (13.7) -15.5 (-13.2)
a Numbers in parentheses include zero point. b Total energies for HCl+CN are -552.673 512 and -552.733 027 hartrees for RHF+1+2/ccpvdz and RHF+1+2+QC/cc-pvdz calculations, respectively. c Note that the transition state relative energies reported here are not barrier heights for the reactions shown but rather the energy of the transition state structures relative to HCl + CN.
HCl + CN. This would still leave open the question of whether or not a transition state for elimination of HCl from HClCN exists. The questions raised both by the experimental studies of Metz et al.4 and Kreher et al.5 and by the theoretical study of de Juan et al.1 are of great interest. Similar molecular elimination pathways from related free radicals, for example H2CN f H2 + CN and H3CO f H2 + HCO, have been occasionally postulated6 but generally ab initio calculations7,8 have not supported the existence of these pathways. The goal of the calculations reported here is a qualitative examination of the global topology of the HClCN surface focusing on the mechanisms of the reactions on this surface. In the next section the details of the calculational methods employed are described. The results are presented in section III and discussed in section IV and finally in section IV conclusions are drawn. II. Calculational Method The electronic structure calculations reported here are single reference, singles and doubles configuration interaction calculations using restricted Hartree-Fock orbitals, employing the Dunning,9,10 correlation consistent, polarized valence double zeta basis set (RHF+1+2/cc-pvdz). For points of C1 symmetry, these CI calculations include 107 704 configurations. The effects of higher-order excitations are estimated using a normalized Davidson11,12 correction (RHF+1+2+QC/cc-pvdz). The calculations were carried out on an 8 processor, IBM-SP1 computer using the COLUMBUS program package.13 It must be emphasized that due to limitations in both the size of the one-electron basis set and the use of an RHF reference wave function, these calculations are more qualitative in nature than quantitative. These limitations are made necessary by the need to do calculations at a large number of geometries in order to thoroughly search for alternative reaction pathways.
Figure 1. Schematic of the relative energies of the minima and transition states on the HClCN surface. All energies are relative to HCl + CN.
III. Results Altogether, 14 minima and 9 transition states have been located on this potential surface. The relative energies of these stationary points are summarized in Table 1 and depicted schematically in Figure 1. The relative energies of the first five minima in Table 1 are known from experiment and the experimental values are included in Table 1 for comparison. It can been seen from these results that the agreement between theory and experiment is reasonably good. The errors are in the range of 3-5 kcal/mol. One point to note here is that the Davidson correction has a fairly large effect on the calculated relative energies. This suggests that significant improvement
Reactions on the ClHCN Surface
J. Phys. Chem., Vol. 100, No. 24, 1996 10125
TABLE 2: Geometries and Harmonic Vibrational Frequencies for the Diatomic Species HCl and CN
TABLE 4: RHF+1+2 Geometries and Harmonic Vibrational Frequencies for the Planar Tetraatomic Species HClCN, ClCNH, and HCNCl (Numbers in Parentheses Include the Quadruples Correction)
ωe (cm-1)
Re (au) species
RHF+1+2(+QC)
expt
RHF+1+2(+QC)
expt
HCl CN(2Σ+) CN(2Π)
2.424(2.434) 2.221(2.243) 2.336(2.361)
2.408 2.215 2.324
3100(3040) 2215(2090) 1930(1830)
2991 2069 1814
TABLE 3: RHF+1+2 Geometries and Harmonic Vibrational Frequencies for the Triatomic Species HCN, ClCN, and HNC (Numbers in Parentheses Include the Quadruples Correction a
Rx RCN ω1 (cm-1)b ω2 (cm-1)c ω3 (cm-1)d b
HCN
ClCN
HNC
2.032(2.042) 2.187(2.210) 2255(2155) 780(725) 3550(3480)
3.117(3.133) 2.193(2.217) 2400(2290) 400(370) 770(740)
1.889(1.899) 2.221(2.241) 2165(2080) 455(445) 3910(3830)
a Rx ) RCH, RCCl, and RNH for HCN, ClCN, and HNC, respectively. CN stretch. c Degenerate bend mode. d CH, CCl, and NH stretches.
might result from the use of a multireference CI wave function rather than a RHF reference. As noted above, the primary questions being addressed here are qualitative ones and for this purpose it was decided that the ability to do calculations at a larger number of geometries was more important than improving the accuracy of the calculations by increasing the CI reference space. The calculated bond lengths and harmonic frequencies of the diatomic species, HCl and CN, are given in Table 2 along with the experimentally derived quantities. Note that the calculated quantities in this table come from supermolecule calculations in which the HCl and CN are fixed at a large separation. This is done to minimize the differential size consistency error when comparing to other points on the potential surface. From these results it can been seen that the RHF+1+2 bond lengths are typically too long by ∼0.01-0.015 au and the RHF+1+2 frequencies are too high by ∼100 cm-1. Inclusion of the Davidson correction for higher order excitations worsens the agreement between the calculated and observed bond lengths (errors of ∼0.025-0.035 au) but improves the agreement for the frequencies (errors of ∼20-50 cm-1). The calculated geometries and frequencies of the triatomic species HCN, HNC, and ClCN are given in Table 3. The HCN and HNC isomers are predicted to be separated by 14.3 kcal/ mol, in good agreement with the more accurate calculations of Lee and Bowman14,15 (14.6 kcal/mol). The calculated harmonic frequencies for HCN (3480, 725, and 2155 cm-1) agree quite well with those derived from experiment (3442, 727, and 2129 cm-1),16 the maximum error being 40 cm-1. Comparable agreement is found for the frequencies of HNC: calculated, 3830, 445, and 2080 cm-1; observed,17 3842, 490, and 2067 cm-1. Harmonic frequencies for ClCN have recently been extracted from experimental data18 and from high-level ab initio calculations.19 Again the agreement between the harmonic frequencies from the present calculations (2290, 370, 740 cm-1) and those derived from experiment (2216, 378, 741 cm-1) is quite good. The calculated properties of the covalently bound adducts, HClCN, ClCNH, and HCNCl are given in Table 4. To our knowledge there is no experimental information on any of these species. The calculations predict HClCN to be the most stable adduct followed by trans- and then cis-ClCNH. The predicted binding energies relative to H + ClCN are 37.1, 30.7, and 27.5 kcal/mol, respectively (neglecting zero point). These binding energies are 10-15 kcal/mol higher than those reported by de
ClCNH RCN (au) RHa (au) RClb (au) θHc (deg) θCld (deg) ω1 (cm-1) ω2 (cm-1) ω3 (cm-1) ω4 (cm-1) ω5 (cm-1) ω6 (cm-1)e
HClCN
cis
trans
2.361(2.379) 2.070(2.081) 3.303(3.330) 114.3(114.0) 122.6(122.6) 3235(3165) 1765(1675) 1230(1190) 770(725) 425(405) 850(805)
2.317(2.334) 1.933(1.945) 3.301(3.330) 117.6(118.2) 134.8(134.8) 3565(3470) 1890(1825) 925(875) 685(650) 425(405) 700(665)
2.337(2.359) 1.929(1.941) 3.270(3.294) 113.8(113.5) 127.5(126.6) 3620(3540) 1840(1755) 1080(1060) 685(660) 460(445) 710(690)
transHCNCl 2.337 2.068 3.349 116.5 126.0 3260 1760 1035 540 390
a RH ) RCH, RNH, and RCH for HClCN, ClCNH, and HCNCl, respectively. b RCl ) RCCl, RCCl, and RNCl for HClCN, ClCNH, and HCNCl, respectively. c θH ) θHCN, θHNC, and θHCN for HClCN, ClCNH, and HCNCl, respectively. d θCl ) θClCN, θClCN, and θClNC for HClCN, ClCNH, and HCNCl, respectively. e Out-of-plane modes.
Juan et al.1 The ordering of cis- and trans-ClCNH is also reversed relative to these earlier calculations, although the difference is well within the error bars of both calculations. At the RHF+1+2 level, the HCNCl adduct is predict to lie 36 kcal/ mol above HCN + Cl with at most only a small barrier to dissociation. Addition of the Davidson correction appears to eliminate this small minimum in the potential surface. In addition to the covalently bound adducts above, a number of long-range, noncovalent adducts were also found. The properties of these minima are given in Tables 5 and 6. The two most strongly bound complexes are predicted to be the CNHCl and Cl-CNH complexes. The former is bound by 2.8 kcal/ mol relative to HCl + CN and the latter by 2.5 kcal/mol relative to Cl + HNC. The binding energies and other properties of these complexes may be sensitive both to the long-range parts of the basis set and basis set superposition effects. Larger basis set calculations may be required to reliably predict the energies of these species. However, several qualitative conclusions can be drawn. The calculations predict the existence of two complexes of Cl with HCN and two with HNC. Two of these are hydrogen-bonded complexes in which a doubly-occupied chlorine orbital interacts with the CH or NH bond resulting in states of 2Π symmetry. The other two are complexes in which the singly-occupied chlorine orbital interacts with the 2s lone pair orbital of HCN or CNH. The binding energies of these complexes are quite similar, ranging from 1 to 2.5 kcal/mol, with the 2Σ+ complexes predicted to be slightly more stable than the 2Π hydrogen-bonded complexes. In principle, there could be as many as four linear complexes of HCl with CN, HCl-CN, HCl-NC, CN-HCl, and NCHCL. The calculations predict only one of these, CN-HCl, to be significantly bound. Of the four possible collinear orientations this is the only one in which hydrogen bonding and electrostatic (dipole-dipole) forces can both contribute to the binding. Two transition states20 for the reaction of Cl with HCN were located and their properties are given in Table 7. The lowest energy transition state is found to be for addition forming HClCN. This reaction is predicted to be 3.5 kcal/mol exothermic and has a barrier of 8.9 kcal/mol. The transition state occurs relatively early with a C-Cl distance ∼0.7 au longer than that of HClCN. The second transition state is the collinear abstraction process leading to HCl + CN. This reaction is 28.8 kcal/ mol endothermic and is predicted to have a barrier of 34.6 kcal/
10126 J. Phys. Chem., Vol. 100, No. 24, 1996
Harding
TABLE 5: RHF+1+2 Geometries, Harmonic Vibrational Frequencies and binding Energies for the Collinear Complexes of Atomic Chlorine with HCN and HNC (Numbers in Parentheses Include the Quadruples Correction) HCN--Cl(2Σ+)
Cl--HCN(2Π)
Cl--HNC(2Π)
HNC-Cl(2Σ+)
RCN (au) RHa (au) RClb (au) ω1 (cm-1) ω2 (cm-1) ω3 (cm-1)
2.186(2.208) 2.032(2.043) 5.77(5.66) 3550(3470) 2255(2160) 75(80)
2.221(2.240) 1.893(1.904) 5.08(5.04) 3890(3815) 2170(2090) 70(75) 550(525)
2.217(2.235) 1.890(1.901) 5.68(5.40) 3905(3825) 2180(2105) 75(80)
ω4 (cm-1)c
2.187(2.210) 2.034(2.044) 5.52(5.45) 3530(3460) 2250(2155) 55(60) 800(750)
780(725) 800(750) 55(55)
555(530) 65(65)
60(60) 1.1(1.2)
70(70) 1.5(1.7)
ω5 (cm-1)c
510(480)
40(45)
De (kcal/mol)
45(40)
1.7(1.8)
2.0(2.5)
RH ) RCH for the HCN complexes and RH ) RNH for the HNC complexes. RCl ) RHCl or RNCl depending on whether the chlorine is complexed to the H or the N end. c Bend modes. For the 2Σ+ states the bend modes consist of two degenerate pairs. For the 2Π states this degeneracy is lifted through interaction with the electronic wave function. a
b
TABLE 6: RHF+1+2 Geometry, Harmonic Vibrational Frequencies, and Binding Energy for the Collinear CN-HCl Complex (Numbers in Parentheses Include the Quadruples Correction) RCN (au) RHCl (au) RNH (au) ω1 (cm-1) ω2 (cm-1) ω3 (cm-1) ω4 (cm-1)a ω5 (cm-1)a De (kcal/mol) a
2.205(2.237) 2.430(2.439) 4.261(4.295) 3065(3015) 2240(2115) 95(90) 300(275) 50(45) 3.1(2.8)
Degenerate bend modes.
TABLE 7: RHF+1+2 Geometries, Harmonic Vibrational Frequencies, and Barrier Heights of the Transition States for the Reactions of Cl with HCN (Numbers in Parentheses Include the Quadruples Correction) Cl + HCN RCN (au) RCH (au) RCla (au) θHCN (deg) θClCN (deg) ω1 (cm-1) ω2 (cm-1) ω3 (cm-1) ω4 (cm-1) ω5 (cm-1) ω6 (cm-1) Eb (kcal/mol)
f HCl + CN(2Σ+) HCl + CN(2Π) 2.206(2.237) 2.934(2.987) 2.541(2.549) 180.0(180.0) 180.0(180.0) 2265(2140) 1045(1385) 790i(465i) 275(265)c 100(100)c
2.282 2.876 2.716 180.0b 180.0b 2400 435 6645i
42.0(34.6)
61.6
HClCN 2.229(2.257) 2.042(2.055) 3.989(4.036) 99.8(102.4) 107.3(107.3) 3255(3270) 1735(1765) 795(625) 285(215) 1525i(1095i) 775(710)d 14.3(8.9)
RCl ) RHCl for the two abstraction transition states and RCl ) RCCl for the addition transition state. b Assumed linear. c Degenerate bend modes. d Out-of-plane mode. a
mol. The calculated barrier for the reverse reaction, HCl + CN f Cl + HCN, is 4.0 kcal/mol (including zero point), in reasonable agreement with the observed activation energy of 4.3 kcal/mol (Sims and Smith2). At the transition state the HCl bond is extended by 0.11 au (5%) relative to that of the product HCl while the CH bond is extended by 0.94 au (46%) relative to that of the reactant HCN. The calculations predict that abstraction can also occur on an excited, 2Π, electronic surface. Reaction on this surface leads to CN in its lowest excited electronic state. However, the collinear barrier on this surface is predicted to be ∼20 kcal/mol above that on the ground state surface and consequently this surface is not expected to be important for thermal reactions. Two-dimensional plots of the 2Σ+ and 2Π potential surface are shown in Figure 2. Also shown on this plot is the line along which these two surfaces intersect.
Figure 2. Contour plots of the 2Π and 2Σ+ collinear potential surfaces for the reaction Cl + HCN f HCl + CN. The contour increment is 2 kcal/mol. The dotted line crossing the contours is the seam of intersection between the two surfaces. Above this line the 2Π surface is lower, below this line the 2Σ+ surface is lower. The heavy solid contour corresponds to the energy of HCl + CN; lighter solid contours correspond to higher energy regions; dashed contours denote lower energy regions.
As noted above, in the vicinity of the transition states the 2Σ+ surface is well below the 2Π surface; however, on the Cl + HCN side, the 2Π surface drops below the 2Σ+ surface due to a hydrogen-bonding interaction between the chlorine lone pair and the CH bond of HCN. Three transition states for reaction of H with ClCN were located and their properties are listed in Table 8. These reactions are, in order of increasing barrier height, addition to the carbon forming HClCN, addition to the nitrogen, forming cis-ClCNH, and abstraction, forming HCl + CN. The barriers to the two addition reactions are predicted to be quite close while the
Reactions on the ClHCN Surface
J. Phys. Chem., Vol. 100, No. 24, 1996 10127
TABLE 8: RHF+1+2 Geometries, Harmonic Vibrational Frequencies, and Barrier Heights of the Transition States for the Reactions of H with ClCN (Numbers in Parentheses Include the Quadruples Correction) H + ClCN RCN (au) RCCl (au) RHa (au) θClCN (deg) θHb (deg) ω1 (cm-1) ω2 (cm-1) ω3 (cm-1) ω4 (cm-1) ω5 (cm-1) ω6 (cm-1)c Eb (kcal/mol)
f
HCl + CN(2Σ+)
HClCN
ClCNH (cis)
2.197(2.221) 3.485(3.477) 2.885(2.963) 175.0(175.7) 158.1(160.0) 2340(2230) 875(875) 525(475) 235(230) 1375i(1075i) 305(290) 27.7(21.6)
2.217(2.240) 3.161(3.172) 3.227(3.371) 158.2(159.1) 98.9(99.1) 2270(2165) 860(750) 725(590) 500(455) 1675i(1220i) 465(425) 12.6(9.4)
2.224(2.246) 3.126(3.144) 2.864(2.993) 163.3(163.8) 116.7(116.3) 2230(2145) 760(735) 645(610) 315(300) 1945i(1440i) 470(440) 14.9(11.0)
a RCl ) RHCl for the two abstraction transition states and RCl ) RCCl for the addition transition state. b θH ) θHClC, θHCN, and θHNC for columns 1, 2, and 3 respectively. c Out-of-plane mode.
abstraction barrier is predicted to be ∼10 kcal/mol higher. Interestingly, one might have expected two transition states for addition to the nitrogen one leading to cis product and a second leading to trans product. Only a cis transition state was found, this in spite of the fact that the cis product is the less stable product. A similar situation is found for the addition of Cl to HNC (see below). The transition state for H + ClCN abstraction is predicted to be planar, but not linear, having a ClCN angle of 175° and a HClC angle of 160°. The hydrogen and nitrogen are cis with respect to the ClC axis. This is in qualitative agreement with the calculations of de Juan et al.1 Although the fully optimized transition state structure is nonlinear, the difference in energy between a collinearly constrained barrier and the true transition state is quite small, ∼0.5 kcal/mol. The barrier height for H + ClCN abstraction is predicted to be 22.1 kcal/mol (including zero-point effects), slightly above the collision energy used in the experiments of de Juan et al.1 (21.6 kcal/mol). This difference, however, is well within the expected uncertainty of the calculations. Thus, the present calculations are consistent with the conclusion that the CN product observed in the H + ClCN reaction results from a simple direct abstraction reaction. A two-dimensional contour plot of the potential surface in the vicinity of this transition state is shown in Figure 3. The lowest barrier to decomposition of cis-ClCNH is predicted to be loss of atomic chlorine forming HNC. HNC has in fact been observed by Macdonald et al.21 as a product of the reaction of H with ClCN. The properties of this transition state are listed in Table 9. Note that the RHF+1+2+QC barrier for Cl-C bond cleavage, 7.7 kcal/mol, is less than the ClCNH bond energy, 9.4 kcal/mol. The reason for this is that the transition state for bond cleavage does not lead directly to Cl + HNC but rather to the Cl-CNH complex which is bound by 2.5 kcal/mol relative to Cl + HNC. There is no barrier to complex formation from Cl + HNC and there is a 0.8 kcal/mol barrier between the complex and cis-ClCNH (see Figure 1). Three isomerization pathways are found starting from transClCNH, two lead to cis-ClCNH and one leads to HClCN. The properties of these transition states are given in Table 10. The highest isomerization barrier for trans-ClCNH is predicted to be the (1,2)-hydrogen migration leading to HClCN. Although this barrier is quite high, it lies slightly below the barrier to the direct addition process, H + ClCN f HClCN. From HClCN, isomerization via (1,2)-hydrogen migration and CH bond cleavage are predicted to be competitive, although both of these pathways are much higher than C-Cl bond cleavage.
Figure 3. Contour plot of the collinear potential surface for the reaction H + ClCN f HCl + CN. The contour increment is 2 kcal/mol. The heavy solid contour corresponds to the energy of H + ClCN; lighter solid contours are higher energy regions; dashed contours are lower energy regions.
TABLE 9: RHF+1+2 Geometry, Harmonic Vibrational Frequencies, and Barrier Height of the Transition States for the Reaction Cl + HNC f cis-ClCNH (Numbers in Parentheses Include the Quadruples Correction) RCN (au) RCCl (au) RHN (au) θClCN (deg) θHNC (deg) ω1 (cm-1) ω2 (cm-1) ω3 (cm-1) ω4 (cm-1) ω5 (cm-1) ω6 (cm-1)a Eb (kcal/mol) a
2.215(2.230) 4.021(4.300) 1.891(1.901) 133.9(135.8) 171.1(177.7) 3895(3820) 2150(2100) 340(380) 320(255) 270i(110i) 540(460) 1.8(-1.7)
Out-of-plane mode.
TABLE 10: RHF+1+2 Geometries, Harmonic Vibrational Frequencies, and Barrier Heights of the Transition States for Isomerization of trans-ClCNH (Numbers in Parentheses Include the Quadruples Correction) trans-ClCNH
RCN (au) RCCl (au) RNH (au) θClCN (deg) θHNC (deg) ω1 (cm-1) ω2 (cm-1) ω3 (cm-1) ω4 (cm-1) ω5 (cm-1) ω6 (cm-1)a Eb (kcal/mol) a
cis-ClCNH nitrogen inversion
cis-ClCNH carbon inversion
HClCN (1,2)migration
2.228(2.247) 3.750(3.812) 1.887(1.897) 129.7(129.4) 171.6(172.2) 3965(3810) 2115(2020) 470(420) 250(255) 535i(510i) 110(80) 8.3(7.2)
2.352(2.375) 3.110(3.128) 1.963(1.980) 176.6(176.1) 113.4(112.9) 3285(3165) 1905(1850) 1120(1095) 725(700) 940i(915i) 450(370) 29.1(28.3)
2.331(2.354) 3.363(3.405) 2.475(2.493) 135.4(135.2) 57.0(57.1) 2650(2580) 1835(1750) 600(550) 410(385) 2100i(1945i) 275(280) 38.9(35.8)
f
Out-of-plane mode.
Cis-trans isomerization of ClCNH can occur by either inverting about the carbon atom or the nitrogen atom (rotation about the CN bond requires breaking the CN π bond and for this reason is higher in energy than the planar inversion
10128 J. Phys. Chem., Vol. 100, No. 24, 1996
Figure 4. Contour plot of the RHF+1+2+QC energy in the vicinity of the transition states for cis-ClCNH f trans-ClCNH and cis-ClCNH f Cl + HNC. The contour increment is 0.25 kcal/mol. Solid contours denote energies above that of the ClCNH f Cl + HNC transition state; dashed contours denote energies below this transition state. RCN and θClCN are optimized. RNH is kept fixed at 1.9 au. All geometries are planar.
Harding
Figure 5. Contour plot of the potential surface for the reactions H + ClCN f HClCN f Cl + CN f HCl + CN. Plotting conventions are the same as in Figure 2.
HCCH,22 O + HCCH,23 H + H2CO,24 H + HCN,25,26 and H + H2CCH2.22 IV. Discussion
pathways). Inversion about the nitrogen is predicted to be much lower energy than inversion about the carbon. The transition state for nitrogen inversion is very similar in both structure and energy to the transition state for C-Cl bond cleavage in cisClCNH (see Table 9). Similarly, the transition state for carbon inversion is similar in both structure and energy to the transition state for NH bond cleavage (Table 8). To better understand why these apparently unrelated transition states are so similar in structure and energy, we show in Figure 4 a contour plot of the potential surface in the vicinity of the transition states for C-Cl bond cleavage and nitrogen inversion (the lower of the two cis-trans isomerization paths). From this plot it is clear that the pathway for C-Cl bond cleavage starting from cisClCNH initially involves primarily increasing the CNH angle. Increasing this angle toward linear simultaneously raises the energy of HClCN and lowers the energy of the Cl + HNC asymptote. Thus, the two pathways, cis-trans isomerization and C-Cl bond cleavage, differ only in what happens after the CNH angle becomes close to linear. For cis-trans isomerization, the pathway involves primarily motion along the HNC angle coordinate throughout. For C-Cl bond cleavage, the path bends slightly before the CNH angle reaches 180° and becomes dominantly C-Cl stretch. Thus, although the structures and energies of the two transition states are quite similar, the reaction coordinates are quite different. For cis-trans isomerization, the reaction coordinate at the transition state is dominantly CNH bend while for C-Cl bond cleavage the transition state reaction coordinate is dominantly C-Cl stretch. In Figure 4 one can also see that the only Cl + CNH addition saddle point connects to the cis isomer of ClCNH, the less stable isomer. The same situation was noted above for the addition of H to ClCN. This is a very common feature of free-radical additions to multiple bonds. That is, the β substituent (the substituent on the side of the multiple bond not being attacked) tends to bend toward the approaching radical, resulting in a configuration in which the β substituent(s) is(are) cis to the new bond. This is seen, for example, in the addition of H +
In the previous section, characteristics of the nine transition states located on the HClCN ground state surface are presented. In this section we start by considering more global aspects of the HClCN surface, focusing on the question of whether or not there is a direct pathway from HClCN to HCl + CN. Because this is a six-dimensional surface, an exhaustive search of the entire surface is not feasible and hence it is not possible to prove the nonexistence of a transition state for a given process. However, examination of aspects of the overall topology of this surface does suggest that the existence of a reaction path for the process, HClCN f HCl + CN, is unlikely. This point can be seen most clearly in the contour plot, Figure 5. The two explicit coordinates shown in this plot are the CH and CCl distances. At each point on this plot, the other planar degrees of freedom are optimized. Four minima can be seen in this plot, HCl + CN, Cl + HCN, H + ClCN, and HClCN. The minima are found to be separated by two intersecting ridges. The horizontal ridge corresponds to processes in which a CH bond is broken while the vertical ridge to processes in which a C-Cl bond is broken. The region in which these two ridges intersect is predicted to lie ∼28 kcal/mol above the energy of HCl + CN and appears to block any direct route from HClCN to HCl + CN. As noted above, the calculations of Figure 5 were all done under the constraint of planarity. Several tests were carried out to test the importance of this constraint. First, at each of the stationary points a full normal-mode analysis was done, including the nonplanar degree of freedom. For all nine stationary points (four minima, four transition states, and the second-order saddle point at RCCl ) 3.6 au and RCH ) 3.4 au) the out-ofplane coordinate was found to be bound. Second, at the secondorder saddle point, a full search of the out-of-plane coordinate was performed (keeping the other five coordinates fixed) to determine whether or not a second minimum exists at a nonplanar geometry. The energy was found to increase monotonically as the NCClH dihedral angle was varied from 180° to 0°.
Reactions on the ClHCN Surface
Figure 6. Normal-mode frequency correlations for the reaction Cl + HCN f HCl + CN.
Although the results depicted in Figure 5 suggest that the existence of a decomposition path leading directly from HClCN to HCl + CN is unlikely, this cannot be proven due to the high dimensionality of the surface. However, these calculations do place an added constraint on any explanation for the vibrationally excited CN produced in the reaction of Cl + HCN. This constraint is related to the experimental study of de Juan et al.1 on the reaction of H with ClCN. From Figure 1, it can be seen that the lowest energy pathway for the H + ClCN reaction is addition forming HClCN. The barrier for this addition is 11 kcal/mol less than the barrier for H + ClCN abstraction. Thus it is very likely that HClCN is being produced in both the Cl + HCN studies and the H + ClCN study. The fact the no vibrationally excited products are observed in the H + ClCN study then make it unlikely that HClCN is the source of this product in the Cl + HCN reaction. These calculations suggest that the only pathways to formation of CN from either Cl + HCN or H + ClCN reactants are the direct abstraction pathways. It remains then to be understood how the Cl + HCN abstraction reaction leads to vibrationally excited CN. The final answer to this question will have to await detailed modeling of the dynamics of this reaction on a realistic potential surface. The present calculations do, however, suggest two possible explanations for the observed products. First, the correlation of vibrational modes along the abstraction path is suggestive. Figures 6, 7, and 8 are plots of the normal-mode vibrational frequencies for the reactants, transition state, and products for the three reactions Cl + HCN f HCl + CN, H + ClCN f HCl + CN, and H + HCN f H2 + CN, respectively. Only the first of these reactions produces large amounts of vibrationally excited CN. In each of these plots it can be seen that the CN stretch frequency is largely unaffected by progress along the reaction coordinate. However, for the first two reactions the CN stretch mode is crossed by a second mode which is strongly coupled to the reaction coordinate; in the case of the Cl + HCN abstraction, two such crossings occur one on either side of the transition state, while for H + ClCN only one crossing occurs (on the product side of the transition state). The existence of these mode crossings does not guarantee that energy will flow between these modes during the course of these reactions. For example, in the H2 + OH reaction27 the OH bond is found to be a spectator in spite of the existence of a similar
J. Phys. Chem., Vol. 100, No. 24, 1996 10129
Figure 7. Normal-mode frequency correlations for the reaction H + ClCN f HCl + CN.
Figure 8. Normal-mode frequency correlations for the reaction H + HCN f H2 + CN (data taken from ref 8).
mode crossing. The mode crossings shown in Figure 6 do, however, suggest a possible explanation for the observations of Metz et al.4 and Kreher et al.5 that should be explored. The final determination of the effect these mode crossings have on the dynamics of this reaction will have to await a detailed modeling of the dynamics on a realistic potential surface. A second possible explanation for the observation of vibrational excited CN product involves the long-range complexes. As noted in the previous section, significantly bound Cl-HCN and CN-HCl complexes are predicted to exist, one on the reactant side of the abstraction transition state and the other on the product side. Either of these complexes, if formed in the abstraction reaction, may influence the final product state distribution. Formation of the latter complex requires a significant exit channel rearrangement, from Cl-H-CN to CNH-Cl. The possible role of the former, Cl-HCN, complex is complicated by the fact that it lies on a different electronic surface, 2Σ+, from that of the transition state, 2Π. It is perhaps easier to envision how the product-side complex might influence
10130 J. Phys. Chem., Vol. 100, No. 24, 1996 the final product state distribution; it is, however, more difficult to see how this complex might explain the similar reactivities of the (004) and (302) states. V. Conclusions The present calculations show that the potential surface for reaction 3 is qualitatively similar to that for H + HCN f H2 + CN. The transition state is collinear and the path does not directly involve the intermediacy of a covalently bound HClCN complex. The HClCN complex can be formed at energies well below that of the abstraction reaction; however, further reaction of HClCN requires the surmounting of barriers in excess of that for direct abstraction. No direct transition state connecting HClCN with HCl + CN could be located. The calculations also predict the existence of bound, long-range complexes on both sides of the abstraction transition state. The influence of these complexes on the dynamics has yet to be determined. The present calculations suggest then that the simplest explanation for the results of Metz et al.4 and Kreher et al.,5 namely the existence of a direct, accessible transition state for the reaction HClCN f HCl + CN, is incorrect. Determination of the correct explanation of these results will have to await a detailed, dynamical study on a realistic potential surface. Such a study is currently being planned.28 Acknowledgment. This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, under Contract W-31-109-ENG38. The author thanks Fleming Crim for bringing this problem to his attention and George Schatz for helpful discussions concerning this work. References and Notes (1) de Juan, J.; Callister, S.; Reisler, H.; Segal, G. A.; Wittig, C. J. Chem. Phys. 1988, 89, 1977. (2) Sims, I. R.; Smith, I. W. M. J. Chem. Soc., Faraday Trans. 2 1989, 85, 915.
Harding (3) Frost, M. J.; Smith, I. W. M.; Spencer-Smith, R. D. J. Chem. Soc., Faraday Trans. 2 1993, 89, 2355. (4) (a) Metz, R. B.; Pfeiffer, J. M.; Thoemke, J. D.; Crim, F. F. Chem. Phys. Lett. 1994, 221, 347. (b) Pfeiffer, J. M.; Metz, R. B.; Thoemke, J. D.; Woods, E., III; Crim, F. F. J. Chem. Phys. 1996, 104, 4490. (5) Krehr, C.; Theinl, R.; Gericke, K.-H. J. Chem. Phys. 1996, 104, 4481. (6) Seakins, P. W.; Leone, S. R. J. Phys. Chem. 1992, 96, 4478. (7) Slagle, I. R.; Kalinovski, I. J.; Gutman, D.; Harding, L. B. J. Phys. Chem., submitted for publication. (8) ter Horst, M. A.; Schatz, G. C.; Harding, L. B. J. Chem. Phys., submittted for publication. (9) Dunning, T. H., Jr. J. Chem. Phys. 1989, 90, 1007. (10) Woon, D. E.; Dunning, T. H., Jr. J. Chem. Phys. 1993, 98, 1358. (11) Langhoff, S. R.; Davidson, E. R. Int. J. Quantum Chem. 1974, 8, 61. (12) Silver, D. W.; Davidson, E. R. Chem. Phys. Lett. 1978, 52, 403. (13) Shepard, R.; Shavitt, I.; Pitzer, R. M.; Comeau, D. C.; Pepper, M.; Lischka, H.; Szalay, P. G.; Ahlrichs, R.; Brown, F. B.; Zhao, J.-G. Int. J. Quantum Chem. 1988, S22, 149. (14) Lee, T. J.; Dateo, C. E.; Gradzy, B.; Bowman, J. M. J. Phys. Chem. 1993, 97, 8937. (15) Bowman, J. M.; Gradzy, B.; Bentley, J. A.; Lee, T. J.; Dateo, C. E. J. Chem. Phys. 1993, 99, 308. (16) Strey, G.; Mills, I. M. Mol. Phys. 1973, 26, 129. (17) Creswell, R. A.; Robiette, A. G. Mol. Phys. 1978, 36, 869. (18) Meyer, F.; Dupre, J.; Meyer, C.; Koivussaari, M.; Blanquet, G. Mol. Phys. 1994, 83, 741. (19) Lee, T. J.; Martin, J. M. L.; Dateo, C.; Taylor, P. R. J. Phys. Chem. 1995, 99, 15858. (20) A third transition state, leading to HCNCl, may exist; however, the HCNCl minimum is so shallow that it was not possible to locate the transition state leading to it. (21) Macdonald, R. G., private communication. (22) Harding, L. B.; Wagner, A. F.; Bowman, J. M.; Schatz, G. C.; Cristoffel, K. J. Phys. Chem. 1982, 86, 4312. (23) Harding, L. B.; Wagner, A. F. J. Phys. Chem. 1986, 90, 2974. (24) Saebo, S.; Radom, L.; Schaefer, H. F., III J. Chem. Phys. 1983, 78, 845. (25) Bair, R. A.; Dunning, T. H., Jr. J. Chem. Phys. 1985, 82, 2280. (26) Wagner, A. F.; Bair, R. A. Int. J. Chem. Kinet. 1986, 18, 473. (27) Schatz, G. C. J. Phys. Chem. 1995, 99, 516. (28) Schatz, G. C., private communication.
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