J. Phys. Chem. 1981, 85,3826-3828
3828
TABLE VII: Ionization Potentials (in e V )
H*O LiOH, H,O adsorbed o n Lia
“3
LiNH,
Ib, 17.83 18.53 12.4
3a1 13.05 14.97 8.3
Ibl 10.94 12.08 6.3
le
3a
15.40 16.43
9.30 11.34
a Experimental results from ref 32, relative t o Fermi level.
the present work might be of interest to students of molecule-surface interactions. For the sake of completeness, we report in Table VI1 ionization potentials for the systems LiOHz and LiNH3, calculated as differences of SCF energies using the Dunning basis set. The important features are the orbital energies relative to a strongly bound orbital, such as l b z of water or l e of ammonia. Table VI1 suggests that HzO 3al is stabilized by 1.2 eV by complex formation, and NH3 3a by 1.1 eV, due to their interaction with Li 2s. No such stabilization is observed in the ultraviolet photoelectron spectra of HzOadsorbed on Li surfaces.32 Taken together with the calculations of Schultz et al., this suggests that the favored adsorption site of H 2 0 on Li is in a bridging position rather than directly over an atom. (31) Schultz, J. A.; McLean, W.; Pedersen, L.; Jarnagin, R. C. Chem. Phys. Lett. 1979, 64,230. (32) McLean, W.; Schultz, J. A.; Pedersen, L. G.; Jarnagin, R. C. Surf. Sei.1979,83, 354.
Conclusions The calculations reported here, in particular the spin densities, strongly suggest that the complexes observed by Meier, Hauge, and Margrave and predicted by Trenary et al. and Nicely and Dye are indeed the same. UHF calculations with a good basis set are capable of quantitative predictions of spin densities for the types of systems considered here, namely, open-shell atoms forming donor-acceptor complexes with closed-shell molecules. Even the effects of rare-gas matrices can be qualitatively described, permitting speculation on the nature of the matrix sites occupied by the radical complexes. While we were not able to reproduce the small (-1%) vibrational frequency shifts reported by Hauge et al. for LiOHz vs. HzO, we have predicted vibrational frequencies for the as yet unobserved modes involving lithium. The popular 6-31G basis set of Pople et al. did not perform well in the present study. It exhibited a considerable ghost orbital effect, indicating that the function counterpoise correction should be applied whenever it is used for studies of intermolecular interactions. In addition, it could not account for the changes in spin density at lithium due to different environments. The similarity between UHF and PUHF spin densities for lithium with the 6-31G basis set indicates that spin polarization is practically nil. This in turn indicates that the basis set is very inflexible in the region near the nucleus.
Acknowledgment. We appreciate the assistance of Dr. Daniel M. Chipman regarding aspects of the spin-density calculations.
Calculation of Activation Energies for Hydrogen-Atom Abstractions by Radicals Containing Carbon Triple Bonds Robert L. Brown and Allan H. Laufer* National Bureau of Standards, Center for Chemical Physics, Chemical Kinetics Division, Washington, D.C. 20234 (Received: May 5, 1981; In Final Form: August 21, 1981)
Activation energies are calculated by the bond-energy-bond-order (BEBO) and the bond-strength-bond-length (BSBL) methods for the reactions of C2Hradicals with Hz, CH4,and C2Hsand for the reactions of CN radicals with H2 and CH4. The BSBI, technique accurately predicts the activation energies for these reactions while the BEBO method yields energies averaging 9 kcal higher than those observed. A possible reason for the disagreement is considered.
There are a number of semiempirical schemes which have been used to correlate and predict activation energies of hydrogen transfer reactions. One of the most popular is the bond-energy-bond-order (BEBO) method developed by Johnston and Parr.l It is based on the concept of conservation of bond order during the reaction. The input data are entirely empirical and consist of such nonkinetic quantities as bond lengths, bond dissociation energies, vibrational frequencies, etc. The BEBO method has been applied to a large number of reactions for which experimental data are available and is usually able to calculate (1) (a) H. S. Johnston and C. Parr, J.Am. Chem. SOC.,85,2544 (1963); (b) H. S. Johnston, “Gas Phase Reaction Rate Theory”, Ronald Press, New York, 1966.
activation energies to within 1or 2 kcal/mol. There are, however, several classes of reactions where the BEBO method fails. Abstractions by halogen atoms are generally predicted to have activation energies higher than those observed, often by 5-7 kcal/mol. BEBO also yields excessive activation energies for abstractions by the CF3 radical. A similar situation is found when the hydrogen atom is attached, either before or after reaction, to an unsaturated carbon. Experimental activation energies for reactions in this latter class are not numerous and rarely involve radicals having triple-bonded carbon. Some recent measurement^^-^ of the reactions of the ethynyl radical, (2) W. Lange and H. Gg. Wagner, Ber. Bunsenges. Phys. Chem., 79, 165 (1975).
This article not subject to US. Copyright. Published 1981 by the American Chemical Society
The Journal of Physical Chemistry, Vol. 85,No. 25, 198 1 3827
Activation Energies for Hydrogen-Atom Abstractions
TABLE I: Observed and Calculated Activation Energies activation energy, kcal/mol reaction C,H + H-H C , H + H-CH, C,H + H-CH,CH, CN + H-H CN + H-CH,
ln k e x p t l - 29.5a -27.4‘ -25.7a
In A B E B O - 24.7 -26.5 - 25.9
Ederived
2.9 0.5 -0 5.3b.e
1.7c*”
EBEBO 8.0 ( 8 . 3 ) 1 3 . 8 (12.6) 11.6 (11.1) 8.1 (8.4) 14.1 (12.9)
EBSBL 3.5 1.0 0.6 3.6d 0.9
a Experimental rate constants are in units of c m 3 molecule-’ s - l ; ref 3 and 4. E. A. Albers, K. Hoyermann, H. Schake, H. Schake, H. Gg. K. J. Schmatjko, H. Gg. Wagner, and J. Wolfrum, Symp. (Znt.)Combust.[Proc. 1, 15, 7 6 5 (1974). Wagner, and J. Wolfrum, Ber. Bunsenges. Phys. Chem., 81, 670 (1977). This value does not agree with that calculated in ref 6 by Berces and Dombi. Although we coded our own version of the energy part of the BSBL calculation, we possessed a copy of their BSBL program which included output for two sample reactions, H + H, and CH, + C,H,. For these two cases, our version gave the same numbers for the total energy and its substituent parts as a function of reaction path as did the Berces and Dombi version. In addition, the activation energies for several other reactions studied in ref 6 were calculated with our program and found t o be in agreement with the Berces and Dombi values. Because of this agreement between the two programs for these selected cases, we think it likely that the BSBL value shown in ref 6 for CN + H, is in error. e As measured in ref b and c. Evaluated in D. L. Baulch, J. Duxbury, S. J. Grant, and D. C. Montague, J. Phys. Chem. R e f . Data, 10,Suppl. l ( 1 9 8 1 ) .
TABLE I1 bond type (X-Y)
H-H H-CH, H-CH,CH, H-C,H H,C-C,H H,CH,C-C,H H-CN H,C-CN
___
%yo,’
a
0.74148 1.094f 1.091f 1.060f 1.45gh 1.459h 1.064f 1.45fjh
Vxyo,b
kcal 109.4 107.3 102.2 129.6 117.2 113.8 128.5 117.6
Mx, My,C amu 1.1 1,12 1,12 1,12 12,12 12,12 1,12 12,12
“cmx;Y
d
4405‘ 2916f 2953f 3300 900 900 3311f 900
a,,-a y , “ ev
0.75,’ 0 . 7 5 0.75, 0.08’ 0.75, 0 . 3 L, 0.75, 3.735 0.08, 3.73 0 . 3 , 3.73 0.75, 3.82’ 0.08, 3.82
a Bond Length. Bond energy. The bond energy is the potential energy of bond dissociation and was approximated by adding the zero-point energy of the bond stretching vibration t o t h e bond strength as calculated from heats of formation. For a discussion of this approximation, see T. Berces, Acta Chim. Acad. Sci. Hung., 92, 3 1 (1977). Thermochemical data were obtained from the following sources: D. D. Wagman, W. H. Evans, V. B. Parker, I. Halow, S. M. Bailey, and R. H. Schumm, Natl. Bur. Stan,d. (U.S.), Tech. N o t e , 270-3 (1968); D. R. Stull, E. F. Westrum, Jr., and G. C. Sinke, “The Chemical Thermodynamics of Organic Compounds”, Wiley, New York, 1 9 6 9 ; D. R. Stull and H. Prophet, Natl. Stand. R e f . DataSer., (U.S., Natl. Bur. Stand.), N o , 37 (1971); H. Okabe and V. H. Dibeler, J. Chem. Phys., 59, 2430 (1973). ‘ Atom masses. Stretching frequency. e Electron affinities, f G. Herzberg, “Electronic Spectra and Electronic Structure of Polyatomic Molecules”, Van Nostrand, Princeton, NJ, 1967. g K. P. Huber and G. Herzberg, “Constants of Diatomic Molecules”, Van Nostrand-Reinhold, New York, 1979. D. R. Lide, Jr., Tetrahedron, 1 7 , 1 2 5 (1962). Reference 6. J H. M. Rosenstock, K. Draxl, B. W. Steiner, and J. T. Herron, J. Phys. Chem. R e f . Data, 6, Suppl. 1 (1977).
C2H,with H2, CH4, and C2H6have made additional tests of BERO possible for reactions involving highly unsaturated bonds. Further, the experimental results for the C2H abstraction reactions were obtained at room temperature. Since the Arrhenius parameters are not experimentally available, the BEBO method offers an estimate of the activation energy and frequency factors which permit extrapolation to other temperature regimes. As we shall show later, BEBO could not accurately predict the activation energies for these reactions. We have also examined a recently published prediction scheme developed by Berces and D ~ m b i , called ~ , ~ the bond-strength-bond-length (BSBL) method. They find that it gives far more satisfactory results for those cases where BEBO breaks down. Both BEBO and BSBL assume that the transfer of hydrogen from a donor molecule AH to an acceptor radical B takes place by way of a linear transition state. This is in accord with quantum-mechanical calculations for simple transfer reactions like H + Hz. A reaction path is defined by the equation exp(-aAHXAH) + exp(-aHBXHB) = 1 Here
Xij
= Rij - Ri{’, where Rij is the length of the bond
(3) A. H. Laufer and A. M. Bass, J. Phys. Chem., 83, 310 (1979). (4) A. H. Laufer, J. Phys. Chem., following paper in this issue. (5) T. Berces and J. Dombi, Int. J . Chern. Kinet., 12, 123 (1980). (6) T. Berces and J. Dombi, Int. J. Chem. Kinet., 12, 183 (1980).
between atoms i and j, and Ri; is its equilibrium length. The constants uAH and uHB are different for the two methods. BEBO uses am = am = 1/0.26, thus giving the same path for all reactions. (This number, 0.26, is the constant in the Pauling bond-distance-bond-order relationship used by BEBO.lb) BSBL allows for changes in the shape of the reaction path by using a aij = 2& where pij is the Morse constant for the particular bond. /3- is calculated7 from the bond’s stretching frequency, its Aissociation energy, and the reduced mass obtained from the masses of the two atoms making up the bond. To estimate the energy of stretched bonds, BEBO relates the bond energy to the bond distance through an empirical expressionlb analogous to Badger’s rule for force constants. BSBL uses Morse functions7 to calculate these energies. To have simultaneous bonding of A and B to H, the electrons on these atoms must have parallel spins. BEBO uses the Sate* anti-Morse function to calculate the replusion between A and B caused by the antibonding character of the parallel spins (the triplet repulsion energy). BSBL, on the other hand, does not attempt to calculate the repulsion directly but instead combines it with a stabilization contribution resulting from delocalization of the unpaired electron over the atoms of the complex. Berces (7) G. Herzberg, “Spectra of Diatomic Molecules”, 2nd ed., Van Nostrand, New York, 1950. (8) S. Sato, J. Chem. Phys., 23, 392 (1955).
J. Phys. Chem. 1981, 85,3828-3831
3828
and Dombi call this combined repulsion and stabilization energy the end-group contribution. It consists of the energy of an unstretched bond between A and B which is weighted by a factor involving the Morse parameter for an A-B bond and by an additional factor containing the electron affinities of A and B. In cases where other atoms are bound to A or B, the electron affinity is considered to be that of the whole group of atoms. In both methods the maximum of the sum of these energies along the path is taken to be the energy of activation. The configuration of the A-H-B complex at this energy maximum is assumed to correspond to that of the transition state in the activated-complex theory. Both methods evaluate the structure of the transition state, determine force constants and vibrational frequencies, and through the activated-complex theory determine the Arrhenius parameters. As a test of these two methods, we have calculated activation energies for the following reactions: CzH + Hz, CH4, CzH6,and CN Hz and CHI. The CN radical has an electronic structureg very much like that of C2H so that similar behavior is to be expected. For the BEBO calculation, a simple transition state was assumed with the usual vibrational analysis leading to the evaluation of the partition functions required for the activated-complex theory. This allowed us to calculate Arrhenius frequency factors. The particular version of BEBO used incorporated the modifications proposed by Gilliom.lo The detailed computer code of the established BEBO procedure, which does not differ in substance from that of Gilliom, is being published elsewhere.ll All of the experimental results for the CzH reactions were measured at room temperature. Thus there are no direct measurements of the activation energies. These can, however, be estimated from the observed rate constants and the BEBO calculated frequency factors through use of the Arrhenius relation. This was
+
(9) J. Pacansky and G . Orr, J. Chem. Phys., 67, 5952 (1977). (10) (a) R. D. Gilliom, J. Chem. Phys., 65, 5027 (1976); (b) R. D. Gilliom, J.Am. Chem. Soc., 99,8399 (1977). In ref. 6, Berces and Dombi claim that Gilliom’s value of 0.45 for the anti-Morse constant in the BEBO triplet repulsion energy should be reduced by a factor of 2 in order t o reproduce his published results. We were able to obtain his results without any such reduction. (11) R. L. Brown, J. Res. Nutl. Bur. Stand. (U.S.), in press.
done for the C2H reactions shown in Table I, which lists the observed rate constants, the frequency factors calculated by the BEBO method, the derived experimental activation energies, and the activation energies calculated by the BEBO and BSBL techniques. For the BSBL method, only the potential energy of activation was calculated. This will differ somewhat from the Arrhenius energy parameter. Such a difference is shown for the BEBO energies. For these, the first energy listed is the potential energy of activation like that given for the BSBL calculations. The energy in parentheses was determined by differentiating the logarithm of the calculated rate constant with respect to 1/T and is a representation of the actual Arrhenius parameter. All of the data used for calculating the activation energies are shown in Table 11. We can see from Table I that, for the C2H abstraction reactions, the values of k derived from the BEBO preexponential factor and activation energy are from lo3 to lo9 slower than those experimentally measured, which is quite unsatisfactory. It should be noted that the value for the maximum activation energy may be derived by assuming a frequency factor equal to the collision rate. This leads, for example in the case of CzH + CH4,to a maximum E, = 3.3 kcal/mol or about 9 kcal/mol less than that calculated by the BEBO method. Alternatively, the BSBL method yields far more accurate estimates of activation energies for these reactions than does the BEBO technique. One possible explanation12 for the superiority of BSBL may lie in its method of handling the end-group interaction. BEBO is least satisfactory in cases where the end groups have large electron affinities; this is the case for the reactions considered here. If one considers the transition state to be made up of two one-electron bonds A-H.B and one additional antibonding electron shared by A and B, then the repulsion between A and B would be lowered if either or both had a strong tendency to attract this extra electron. BEBO takes no direct account of the electron affinity of these end groups. Acknowledgment. This work was supported in part by the Planetary Atmospheres program of the NASA. (12) Z. B. Alfassi and S. W. Benson, Int. J.Chem.Kinet., 5,879 (1973).
Reactions of Ethynyl Radicals. Rate Constants with CH4, C2ti6, and C2D6 Allan H. Laufer National Bureau of Standards, Chemical Kinetics Divisions, Center for Chemical Physics, Washington, D.C. 20234 (Received: May 5, 198 1; I n Final Form: August 2 1, 198 1)
The rate constants for the abstraction of H atoms from CHI, C2H6, and D atoms from C2D6 by C2H (ethynyl) radicals have been determined by using a flash photolysis-kinetic spectroscopic technique. The values obtained, cm3 molecule-l s-l, respectively. (6.5 f 0.4) X and (3.1 f 0.5) X at 297 K, are (1.2 f 0.2) X The rate constants are independent of added helium over the pressure range 20-700 torr. The kinetic parameters were determined by monitoring the acetylene product spectroscopically using CzH-CF3 as the source of ethynyl radicals.
lene-containing systems which may be as diverse as the planetary htmosphere of Jupiter and pyrolysis of hydrocarbon systems. However, there have been few direct
(1) W. Lange and H. Gg. Wagner, Ber. Bunsenges. Phys. Chem., 79, 165 (1975). (2) A. H. Laufer and A. M. Bass, J. Phys. Chem., 83, 310 (1979).
This article not subject to US. Copyright. Published 1981 by the American Chemical Society
