J . Phys. Chem. 1991,95.8619-8625 transition the CIS and the RPA transition energies converge to the same value as the chain length is increased.
Conclusions The utility of the random phase approximation in conjunction with the INDO/S model Hamiltonian has been demonstrated. The INDO/S-CIS method has been very successful in the prediction of transition energies but has not been as satisfactory in the prediction of absorption probabilities. The RPA method maintains the ability to predict accurate transition energies but also provides considerable improvement in predicting experimental transition moments as well as providing a more consistent value when the transition moment is calculated by using dipole length or dipole velocity formalisms.11J5 With the INDO/S Hamiltonian (35) Oddershede, J.; Jsrgensen, P.; Becbe, N. H. F. J . Phys. B 1978, 11, 1.
(36) Rabalais, J. W. Principles of Ultraviolet Photoelectron Spectroscopy; Wiley: New York, 1977. (37) Brundle, C. R.; Robin, M. B.; Kuebler J. Am. Chem. SOC.1972,94,
1466.
(38) Parkin, J. E.; Innes, K. K. J . Mol. Spectrosc. 1965, IS,407. (39) Innes, K. K.; Byrne, J. P.; Roos, I. G. J . Mol. Specrrosc. 1967, 22,
125.
8619
both methods require careful consideration in the selection of the active orbitals in the calculation. This is a consequence of utilizing a model Hamiltonian and not a function of the methods themselves. It is encouraging, however, that a truncated active space is adequate to obtain predictive results. If it were not, some interesting systems would not be possible to study. The INDO/S-RPA method therefore meets the criteria set forth of being computational feasible for large systems. No degradation in predictability versus size was found to exist for the systems studied.
Acknowledgment. J.D.B.acknowledges support through a Tennessee Eastman Postgraduate Fellowship. This work was supported in part through grants from Eastman Kodak Co. and the Office of Naval Research. This work has benefited greatly from conversations with Jens Oddershede (Florida and Odense). Registry No. Naphthalene, 91-20-3; quinoline, 91-22-5; 1,2-diazine, 289-80-5; 1,3-diazine, 289-95-2; 1,4-diazine, 290-37-9; anthracene, 12012-7; benzene, 71-43-2; pyridine, 110-86-1;naphthacene, 92-24-0; pcntacene, 135-48-8; hexacene, 258-31-1;decacene, 24540-30-5;dodecacene, 24862-63-3. (40) Georgia, G. A.; Morris, G. C. J . Mol. Spectrosc. 1968, 26, 67. (41) Baba, H.; Yamazaki, I. J . Mol. Spectrosc. 1972. 44, 118.
Ab Initio Study of the Grignard Reactlon between Magnesium Atoms and Fluoroethylene and Chloroethylene Li Liu and Steven R. Davis* Department of Chemistry, University of Mississippi, University, Mississippi 38677 (Received: February 22, 1991)
-
Theoretical calculations using self-consistent field and Maller-Plesset perturbation theory through second order (MP2) have been carried out on the gas-phase Mg + C2H3X C2H3MgXreaction for X = F, C1. Optimized geometries for the reactants, transition states (TSs), and products have been determined along with relative energies and vibrational frequencies. The intrinsic reaction coordinate has been followed from the TS to reactants and products, confirming that the located structures all lie on the reaction potential surface. The transition states are found to possess C, symmetry, while the products belong to point group C,. The activation energies are calculated to be 22.8 kcal-mol-' for the Mg + C2H3F reaction, while that for the Mg + C2H3CIreaction is 29.7 kcal-mol-I. The overall exothermicity for both reactions is 54.3 kcalmol-' at the MP2/6-31G** level.
Introduction An understanding of the oxidation of magnesium by fluorine is an important subject in the area of combustion chemistry. The reaction of magnesium with fluorocarbons such as tetrafluoroethylene (TFE) has especially received attention due to its applications as both solid rocket motor igniters and high-energy output flares.'-s Formulations of magnesium dispersed in solid TFE burn readily, producing MgF, and carbon as final products. The combustion mechanism is not entirely clear$*' and both experimental and theoretical methods are being used to help (1) Kcllcr, R. B., Ed. Solid Rocket Motor Igniters; NASA SP. 8051; March 1971. (2) LoFiego, L. Paper 68-32, Western State Section/The Combustion Institute, 1968 Fall Meeting, Menlo Park, CA. (3) Robertson, W. E. Am. Inst. Astronaut. Aeronaut. 1972, Noc-Dec, Paper 72-1 195. (4) Crosby, R.;Mullenix, G. C.; Swenson, I. Am. Inst. Astronaut. Aeronaut. 1972, Paper 72-1 196. (5) Peretz, A. J. Spacecr. Rockets 1984, 21, 222. ( 6 ) Kubota, N.: Serizawa, C. Am. Imt. Astromut. Aeronauf. 1986, Paper 86-1592. (7) Kubota, N.; Serizawa, C. Propellants, Explos., Pyrotech. 1987, 12, 145.
0022-3654/91/2095-8619$02.50/0
understand the intermediate processes. Characterization of the reaction intermediates and mechanism can be used to help model the kinetics of the combustion reaction. One possible step in the mechanism for this reaction is the insertion of magnesium into a C-F bond to form a Grignard structure. A previous pap9 has examined the reaction of Mg atoms with fluoromethane by using ab initio calculations, while in the present paper we investigate the reaction of Mg atoms with fluoroethylene as a pioneer study for the reaction of Mg atoms with C2F4. The reaction of atomic Mg with alkyl halides to form a Grignard reagent under isolated conditions has received interest because the system is free from solvent perturbations. Skell and Girard9 reported the first observation of the reactivity of ground-state magnesium atoms with alkyl halides in 1972, and Auklo reported the results of matrix isolation studies for the insertion of a magnesium atom into the carbon-halogen bond of methyl halides. This latter study provided the first spectroscopic characterization of an unsolvated Grignard species. In the (8) Davis, S . R. J . Am. Chem. Soc. 1991, 113, 4145. (9) Skell, P. S.;Girard, J. E. J . Am. Chem. Soc. 1972, 94, 5518. (IO) Auk, B. S . J . Am. Chem. SOC.1980, 102, 3480.
0 1991 American Chemical Society
8620 The Journal of Physical Chemistry, Vol. 95, No. 22, 1991
Liu and Davis
TABLE I: Calculated and Experimental Vibrational Frequencies (cm-I) for C2H3Fand C2H3CI CZH+2I MP2/6-31G** 407 645 759 913 1006 1075 1352 1455 1702 3262 3313 3372
C2H3F
SCF/6-3 1 G** 523 800 1024 1030 1091 I284 1450 I549 I892 3341 3402 3438 a Reference
20.
MP2/6-3 1G** 474 743 863 955 988 1172 1366 1466 1755 3279 3310 3393
irrep a’ a” a” a’ a’’ a’ a’ a’ a’ a’ a’ a’
expt‘ 490 713 923 863 929 1 I57 1305 1380 1656 3052 3080 3115
irrep a’ a’’ a’
exptb 395 620 724 896 943 1030 1280 1370 1610 3030 3080 3130
a’‘
a” a’ a’ a‘ a‘ a’ a’ a’
Reference 2 1.
meantime, theoretical calculations have been carried out for the methylmagnesium halides CH3MgX (X = F, CI) to obtain equilibrium and transition-state geometries, overall reaction energies and activation barriers, and vibrational frequencies.*J1-13 However, theoretical studies have not been reported on the reaction system of atomic Mg with haloethenes, C2H3X(X = halogen). The calculations reported here characterize the transition state (TS) geometries for the Mg insertion reaction into the C-X bond of C2H3.Xto form the Grignard products C2H3MgX(X = F, Cl). The activation energies and potential energy surface (PES) along the intrinsic reaction coordinate are determined, as well as the equilibrium geometries and vibrational frequencies of the Grignard products.
Computational Methods The ab initio calculations were performed with the GAUSSIAN a6I4 and GAUSSIAN galS series of programs on either a Cyber 205 or MicroVax I1 computer. The equilibrium and transition-state geometries were determined at the self-consistent field (SCF) and correlated levels of theory using the 3-21G*,I6 6-31G*,I7 and 6-3 IG**I* basis sets. Electron correlation effects were included by using Moller-Plesset perturbation theory through second order (MP2) with all orbitals active.I9 The optimized geometries were determined by using analytic gradient techniques in conjunction with the Berny algorithm.20-21 Stationary points were characterized as either a minimum or transition state (one imaginary frequency) by determination of harmonic vibrational frequencies. For SCF calculations, analytic second derivatives22were used, while for the MP2 calculations numerical differentiation of analytic first derivative^^^ was performed. The reaction paths down from the transition state along the intrinsic reaction coordinate were examined by using the method of Gonzalez and S ~ h l e g e l . ~ ~ (11) Sakai, S.;Jordan, K. D. J . Am. Chem. Soc. 1982, 104,4019. (12) Jasien, P. G.; Dykstra, C. E. J. Am. Chem. Soe. 1983, 105. 2089. (13) Jasien, P. G.; Dykstra, C. E. J . Am. Chem. Soe. 1985, 107. 1891. (14) Frisch, M. J.; Binkley, J. S.;Schlegel, H. B.; Raghavachari, K.; Melius, C. F.; Martin, R. L.; Stewart, J. J. P.; Bobrowicz, F. W.; Rohlfing, C. M.; Kahn, L. R.; Defrees, D.J.; Seeger, R.; Whiteside, R. A.; Fox, D. J.; Fluder, E. M.;Pople, J. A. Gaussian 86; Carnegie-Mellon Quantum Chemistry Publishing Unit: Pittsburgh, PA, 1984. ( 1 5) Frisch, M.J.; Head-Gordon, M.; Schlegel, H. B.; Raghavachari, K.; Binkley, J. S.;Gonzales, C.; Defrees, D. J.; Fox, D. J.; Whiteside, R. A,; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Stewart, J. J. P.; Fluder, E. M.;Topiol, S.;Pople, J. A. Gaussian 88; Gaussian, Inc.: Pittsburgh, PA, 1988. (16) Pietro, W.J.; Francl, M.M.; Hehre, W.J.; DeFrees, D. J.; Pople, J. A.; Binkley, J. S.J. Am. Chem. Soc. 1984, 104, 5039. (17) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acra 1973, 28, 213. (18) Francl. M.M.;Pietro, W. J.; Hehre, W.J.; Binkley, J. S.;Gordon, M. S.;DeFrees. D. J.; Pode. J. A. J. Chem. Phvs. 1982. 77. 3654. (19) Krishnan. R.; Pople,’ J. A. Inr. J . Quahum Chem.’1978, 14, 91. (20) Schlegel, H. B. J . Compur. Chem. 1982, 3, 214. (21) Pople, J. A.; Krishnan, R.; Schlegel, H. B.; Binkley, J. S. Inr. J . Ouantum Chem. 1979. S13. 325. (22) Pople, J. A.; Krishnan, R.; Schlegel, H. B.; Binkley, J. S. Inr. J . Quanrum. Chem. 1979. S13, 325. (23) Krishnan. R.;Schlegel, H.B.;Pople, J. A. J. Chem. Phys. 1980, 72, 4654.
-
SCF/6-3lG** 43 1 697 773 1077 1090 1139 1423 1532 1840 3329 3403 3424
F\ (1.342)
;::J:;)3‘4.::l(,,, (1.082)
H
c‘\
H’
123.0” 122.1’
121.5” 121.2.
1.326. 1.33 1” 125.7’ (1.329) 119.4’
1.082” 1.076.
( 1.087) ‘H
H
\
H
Figure 1. Optimized a b initio and experimental geometries for fluoroethylene and chloroethylene. Units are in angstroms and degrees. Symbols are defined as ’ = SCF/6-31G*, ” = MP2/3-21G*, * = MP2/6-31G**, ( ) = experimental.
Rmults and Discussion C2H3Fand C2H3CI. Equilibrium structures have been determined previously at the MP2/3-21G* level for C2H3FZS and the SCF/6-31G* level for C2H3C1.26 We have obtained the optimum geometries at the MP2/6-31G** level for both haloethenes, and these parameters along with those calculated previously are collected in Figure 1. The overall agreement among the various calculational methods is good, as is the agreement with experimental values.27 For fluoroethylene, increasing the basis from 3-21G* to 6-31G** in the MP2 calculations decreased the C-H and C-C bond lengths by an average of 0.005 A, while the C-F bond length decreased substantially by 0.054 A. All the in-plane angles are within 1 deg of the MP2/3-21G* results. Comparing the chloroethylene results at the SCF/6-31G* and the MP2/631G** levels shows that the C-H bond distances increase slightly and the C - C bond length increases by 0.02 A, while the bond angles are all very similar. The C-Cl bond distance decreases by 0.008 A, however, in contrast to the fluoroethylene molecule in the same basis sets in which the C-F bond increased in length by 0.023 A. A comparison of the experimental and theoretical geometries indicates that the results at the MP2/6-31G** level are closest on average to the experimental results. The calculated (24) Gonzalez, C.; Schlegel, H. B. J . Phys. Chem. 1989, 90,2154. (25) Schlegel, H. B. J . Phys. Chem. 1982,86,4882. (26) Schlegel, H.B.; %a, C. J. Phys. Chem. 1984.88, 1141. (27) Kivelson, D.; Wilson, E. B.; Lide, D. R. J. Chem. Phys. 1960,32,205.
The Journal of Physical Chemistry, Vol. 95, No. 22, 1991 8621
Ab Initio Study of the Grignard Reaction
TABLE 11: Calculated Vibrational Frequencies (en-’) for the Grignrnl Products CzH&lgF and CzH&lgCI C2H3MgF SCF/6-3 1G** 98 138 248 397 496 84 1 1082 1100 1 I70 1385 1554 1773 3228 3253 3312
SCF/3-21 G* 101 146 250 414 511 914 1119 1131 1189 I423 I576 1765 3212 3252 3306
1.707 1.732‘ 1.7520
CZHjMgCI MP2/6-3 1G** 93 133 236 359 485 814 978 1025 1090 1298 1470 1658 3176 3192 3264
irrep a‘ a” a’ a” a’ a’ a” a’ a” a’ a’ a’ a’ a‘ a’
SCF/3-21G* 84 124 232 393 419 660 1119 1135 1188 1422 1574 1764 3220 3255 3310
\
f::;:, \ 2*076*
/
level SCF/3-21G* SCF/6-3 1G* SCF/6-31GS* MP2/6-31G* MP2/6-3 1G**
H
121.9 122.8’ 121.6.
123.1 122.9’ 122.8.
1.078 1.081‘ 1.085s
a
\
\
/
H
M?
,:;::2.068*
121.3 122.7’ 121.0.
123.1 123.0’ 122.8*
i:tJs, 1.085*
Figure 2. Optimized geometries for the C2H3MgF and C2H3MgCI Grignard molecules. Units are in angstroms and degrees. Values from top to bottom are at the SCF/3-2IGS, SCF/6-3IGS*, and MP2/631G** levels, respectively.
normal mode vibrational frequencies are compared with the available experimental values28-29 in Table I. At the SCF/631G** level, the calculated harmonic frequencies tend to be 6 16% higher than the experimental frequencies for both C2H3F and C2H3CI. At the MP2/6-31G** level, this variation reduces to about 3 8% higher than the experimental values. C2H3MgFand C2H3MgCI. The fully optimized geometrical parameters for the Grignard structures C2H3MgFand C2H3MgCl have been obtained and are given in Figure 2. Both molecules are planar (C, symmetry) with a linear C-Mg-X arrangement. Extension of the basis set from 3-21G* to 6-31G** in the SCF calculations lengthens the C-H bonds by an average of 0.002 A and decreases the C=C bond by 0.001 A. The Mg-F bond lengthens by 0.025 A, while the Mg-CI bond remains unchanged. The C-Mg bond, however, is lengthened by 0.010 A in C2H3MgF and by 0.007 A in C2H3MgCI. The bond angles are relatively constant except those on the Mg side of the molecule, with the Mg-C( I)
