J . Phys. Chem. 1986, 90, 6446-6451
6446
figure, we may regard the information obtained on the pyridine ring in the complex studied in the present work as pertaining equally well to pure pyridine. That is, we regard the chloroform as a label which facilitates the examination of the pyridine ring positions by simplifying the crystal structure and increasing the proton relaxation rate, as explained in the Experimental Section. This allows direct comparison to the earlier work of Ha and O'Konski. For nitrogen and chlorine, it is much more difficult to make contact between experimental and theoretical field gradient data, since neither nuclear quadrupole moment is known with notable precision. Since the corresponding field gradients arise mainly from charge in the immediate neighborhood of these nuclei, a prior knowledge of the geometry plays a less important role here than in the deuterium case. The calculated values of the shifts in field gradient agree with the experimental result that the semimajor tensor axis length decreases at both the chlorine' and nitrogen sites. This parallels the slight increase in calculated total atomic charge. As discussed above, the asymmetry parameter at nitrogen is predicted to increase substantially, in disagreement M ith the
experimental observation. Our experience is that nitrogen field gradients and the directions and relative magnitudes of the semiminor axes are very basis dependent for calculations done with such limited bases and in which symmetry does not fix the tensor directions, and although we report the computed values, we do so only for completeness. Values for the asymmetry parameters at the chlorine sites are not known experimentally, and the dubious nature of the theoretical results for nitrogen indicates that some mistrust of the very small computed asymmetry parameters for chlorine is justified.
Acknowledgment. We would like to thank Prof. Del Bene for her interest in this work, for several lively discussions, and for undertaking the calculations mentioned in the text. Thanks are also due to Evan Miller for undertaking field gradient calculations at nitrogen in several nitrogen heterocycles with a variety of Gaussian bases.23 (23) Evan D. Miller, unpublished Undergraduate Honors Thesis, University of Massachusetts, Amherst, MA, 1986.
Ab Initio Studies of Hydrocarbon Peroxyl Radicals Brent H. Besler, Michael D. Sevilla,* Department of Chemistry, Oakland Unicersity, Rochester, Michigan 48063
and Perry MacNeille Ford Motor Scientific Research Laboratory, Dearborn, Michigan 481 21 (Received: June IO, 1986; In Final Form: July 29, 1986)
Extensive ab initio molecular orbital calculations have been performed for the important series of peroxyl radicals (02'7, H02', CH302*,(CH3)2CH02',and (CH3CH2),CH02'. Parameters calculated include equilibrium geometries, harmonic vibrational frequencies, dipole moments, and isotropic and anisotropic hyperfine couplings. Equilibrium geometries were of primary interest. In the two large hydrocarbon peroxyl radicals the carbon atoms and appropriate hydrogen atoms were constrained to be coplanar and the 0-0 group was forced to be perpendicular to the carbon chain in order to stimulate the presence of a peroxyl radical site in a polyethylene chain. Calculations were performed with large Gaussian basis sets (up to 6-3 1 l++G(d,p)). Calculations for HO: including electron correlation utilizing Moeller-Plesset perturbation theory were performed at the following levels: MP2(6-31G(d)) and 6-31 lG(d,p), MP3(6-31 lG(d,p)) and MP4SDTQ(6-31 l(d,p)). Calculated values are compared against the highly accurate experimental data for HO,' known from microwave, laser magnetic resonance, and diode laser studies in order to determine the level of calculation necessary for accurate predictions. Comparison of the various calculations shows that MP2(6-3 1 G(d)) compares favorably with MP4SDTQ(6-31 lG(d,p)) at a considerable savings in computation time. Corrections to the H F bond distances and bond angles for the largest structures due to electron correlation are estimated from correlated calculations on the smaller peroxyl structures. Semiempirical calculations were also performed but were found to give poor agreement w>ithexperiment.
Introduction Peroxyl radicals play an important role in the chemistry of a variety of systems. Among these are the oxidation of hydrocarbons,' the chemistry of the upper atmosphere,* and the oxidative degradation of polymers and lipid^.^,^ The small peroxyl radicals H02' and CH302' appear in hydrocarbon oxidation as well as atmospheric chemistry, while those involved in polymer degradation involve large alkyl chains. The closely related 02'-radical ( I ) Benson, S. W.; Nangia, P.S. Arc. Chem. Res. 1979. 12, 223. (2) Heicklen, J. Atmospheric Chemisrry; Academic: New York, 1976. (3) Carlsson, D. J.: Dobbin, C. J . 8.: Wiles, D. M. Macromolecules 1985, 18, 2092. (4) (a) Sevilla, C. L.; Becker, D.; Sevilla, M . D. J . Phys. Chem. 1986, 90, 2963. (b) Yanez, J.: Sevilla, C. L.; Becker, D.: Sevilla, M. D. J . Phys. Chem., in press. (c) Becker, D.; Janez, J.: Sevilla, M. D.: Schlick, S.; Alonso-Amigo, M. G . J . Phys. Chem., in press. (d) Bors, W., Saran, M.. Tait, D., Eds.; Oxygen Radicals in Chemistry and Biology, Proceedings Third International Conference; Waltern De Grupter: Berlin, 1983.
0022-365418612090-6446$01.5010
also appears in many oxidation p r o ~ e s s e s . ~Peroxyl ,~ radicals may also be used as electron spin resonance (ESR) probes in polymer chains and on metallic surfaces.6 Over the past decade a large amount of experimental data and a b initio calculations have appeared for the H02' radical.'-I4 In the cases of 02'-,CH302*, and the larger alkyl peroxy radicals data have been scarce and widely scattered among different areas of research. In this work ( 5 ) Bielski, B. H. J.; Richter, H. W. J . A m . Chem. SOC.1977, 99, 3019. (6) Kevan, L.; Schlick, S. J . Phys. Chem. 1986, 90, 1998. ( 7 ) Bair, R. A.; Goddard, W. A. J , A m . Chem. SOC.1982, 104, 2720. ( 8 ) Jackels, C. F.; Phillips, D. H. J . Chem. Phys. 1986, 84, 5013. (9) Cohen, D.; Basch, H.; Osman, R. J . Chem. Phys. 1984, 80, 5684. ( I O ) Beers, Y . ; Howard, C. J. J . Chem. Phys. 1976, 64, 1541. ( I I ) Lubic, K. G.; Amano, T.: Lehara, H.; Kawaguchi, K.; Hirota. E. J . Chem. Phys. 1984, 81, 4826. (12) Barnes, C. E.: Brown, J. M.; Radford, H. E. J . Mol. Spectrosc. 1980. 84. 119.
( 1 3 ) Saito, S. J . Mol. Spectrosc. 1977, 65, 229. (14) Adrian, F. J.; Cochran, E. L.; Bowers, V. A . J . C h e m Phys. 1967. 17. 5441
0 1986 American Chemical Society
Hydrocarbon Peroxyl Radicals
The Journal of Physical Chemistry, Vol. 90, No. 24, 1986 6447
we present a series of high-level a b initio calculations of various parameters of interest of the H02', CH302', and 02*radicals. These calculations are done with large polarized basis sets at the Hartree-Fock level. Correlated calculations were performed with Moeller-Plesset perturbation theory for 0:-, HO,', and CH302'. Also a Hartree-Fock level calculation is done for (CH3),CHOZ' and (CH3CH2)2CH02'in an attempt to serve as models for the peroxyl radicals sites formed in the y irradiation of polymers. Structural parameters, isotropic and anisotropic hyperfine couplings, and harmonic vibrational frequencies are all reported for the smaller structures. Finally, the internal rotation barrier of the 0-0 group about the C-0 axis in the five-carbon radical is calculated and used to predict the same for a peroxyl radical site in isotactic polyethylene. A thorough summary is presented of all experimental data and previous calculations related to these molecules. Comparison to experimental data provides a guide to the accuracy of the quantum mechanical predictions for different properties and allows us to predict corrections to the quantum mechanical calculations where no experimental data exist. This work should provide a guide for the direction of certain future experiments.
TABLE I: Ab Initio Optimized Geometries and Total Energies for Oz'-
Calculation Details All of the calculations performed in this study were performed by utilizing the unrestricted Hartree-Fock (UHF) methodI5 with the 6-31G(d), 6-31 lG(d,p), and 6-31 l++G(d,p) triple-split valence basis sets of Pople and c o - w ~ r k e r s . ~The ~ , ~6-31G(d) ~ basis includes a set of polarization functions on the non-hydrogen atoms, while the 6-311G(d,p) basis also includes a set of polarization functions on the hydrogens. The 6-31 l++G(d,p) basis is identical with the 6-31 lG(d,p) but also includes a set of diffuse functions on each atom. For the O,'-, HO,', and CH3O2' radicals, the effect of electron correlation was taken into account by the use of unrestricted Moeller-Plesset perturbation complete to second order (MP2), and to third (MP3) and fourth order (MP4) for the two smallest radicals. Most calculations done at the MP4 level neglect the effect of triple substitutions of virtual orbitals into the wavefunctions (MP4SDQ); however, the practice of incorporation of triples (MP4SDTQ) is becoming more common in recent years. The effect of the triples is discussed in detail by Krishnan et a1.22 All of our fourth-order calculations are done at the MP4SDTQ level. Generally only the correlation of the valence electrons is taken into account, the "frozen-core" app r ~ x i m a t i o n . For ~ ~ AH,, systems this approximation was shown to have the effect of raising the total energy by several millihartrees but had a negligibly small effect on the calculated equilibrium g e ~ m e t r i e s . ~The ~ . ~preceding ~ conclusions were also found to a m l v in test calculations done for us for 0,'- and HO,' at the M b i and MP4SDTQ levels.25 U H F wavefunctions have the unfortunate characteristic of not being eigenfunctions of the S 2 operator, being contaminated by higher spin states.26 Various methods are normally used to alleviate this problem. Among these are the use of spin projection26 and restricted open-shell Hartree-Fock theory.27 In this study
all calculations involve no spin projection. For most ground-state calculations on free radicals this does not present a problem, as the S2 expectation value (denoted ( S 2 ) )for the zeroth-order wavefunction ((SZ),) is normally quite close to that of a pure doublet or triplet wavefunction. The ground states of all radicals involved in this study are doublets and therefore should have an ( S 2 ) ,value of 0.75. Fortunately the largest ( S 2 ) ,in this study was no larger than 0.784, indicating that the effects due to spin contamination are very low. Schlegelz8has recently shown that (Sz) correct to first order ((SZ),) is appropriate for MP2 calculations and that ( S 2 )correct to second order ( ( S 2 ) 2is) appropriate for MP3 and MP4 calculations. In the tables, the ( S 2 ) , values are listed for U H F calculations and ( S 2 ) for , the remainder. The results of Schlegel show that both the first- and second-order corrections to ( S 2 )result in a value that is closer to that of an uncontaminated wavefunction. Equilibrium geometries at the U H F and MP2 level were calculated by utilizing analytic gradients.z1 At the MP3 and MP4 level, a Fletcher-Powell algorithmz9 was used. Harmonic vibrational frequencies were calculated with analytic second derivatives at the U H F leve130 and numerically at the MP2 level.31 HO,', Complete geometry optimizations were performed for 02*-, and CH,O,'. For the two larger peroxyl radicals, some geometrical parameters were fixed. These are detailed in Results. Finally calculations were attempted with Dewar's AM1 and MNDO semiempirical methods,3zbut they were found to give poor results for the radicals. All computations in this study were done with the Gaussian 82 system of programs33on the VAX-I 11780, VAX 8600, and Microvax I1 systems of the Ford Motor Co. Scientific Research Labs in Dearborn, MI, the Oakland University Department of Engineering's Microvax 11, and the Cray-XMP at the Naval Research Lab in Washington, DC.
( 1 5 ) Pople, J . A,; Nesbet, R. K. J . Chem. Phys. 1954, 22, 541. (16) Hariharan. P. C.: Pode. J. A. Theor. Chim. Acta 1973. 28. 213. (17) Krishnan, R.; Binklei, J. S.; Seger, R.; Pople, J. A. J . Chem. Phys. 1980, 72, 650. (18) Pople, J. A.; Binkley, J. S.; Seger, R. Inr. J . Quantum Chem. 1976,
Results Our results are presented in Tables I-V and are described for the individual structures below. O;-. There have been few theoretical experimental or theoretical studies of the 02'-anion. The most comprehensive theoretical study to date is that of Das et al.34 They performed a
SIO,1. (19) Binkley, J. S.; Pople, J. A. Int. J . Quantum Chem. 1975, 9, 229. (20) Krishnan. R.: Pode. J. A. I n f . J . Ouantum Chem. 1978. 14. 91. (21j Pople, J. A,; Schlegel, H . B.; BinklG, J. S . Int. J . Quantum Chem.
total energies, harteees (AUl UHF/6-31G(d) UHF/6-3 1 1++G(d,p) MP2/6-31G(d) MP2/6-31 IG(d,p) MP3/6-311G(d,p) MP4SDTQ/6-31 IG(d,p) AM1 exp3* expt3'
SCF34 M C S C F [4]u34 M C S C F [76]34 MCSCF34
This Work 1.2964 (SZ), = 0.7650 1.2895 (S'), = 0.7840 1.3798 ( S ' ) , = 0.7513 1.3626 (Sz) = 0.7530 1.3300 (S') = 0.7527 1.3717 (Sz) = 0.7531 1.1740 Previous Work 1.341 1.377 1.279 1.360 1.356 1.347
-149.56398 -149.634 50 -149,92022 -1 50.028 42 -149.985 75 -150.010 16
-149.6399 -149.705 4 -149.763 7 -149.833 43
Number in brackets denotes the number of configurations in the M C S C F wavefunction. See ref 34 for full details.
1979. S I 3 . 225.
(22) Kkhnan, R.; Frisch, M. J.; Pople J . A. J . Chem. Phys. 1980, 72, 4244. (23) DeFrees, D. J.; Levi, B. A,; Pollak, S. K.; Hehre, W. J.; Binkley, J . S., Pople, J . A. J . A m . Chem. SOC.1979, 101, 4085. (24) Ditchfield, R.; Seidman, K. Chem. Phys. Lett. 1978, 54, 57 (25) The MP2 analytic gradients algorithm in Gaussian 82 does not allow for "frozen-core" calculations for open-shell systems, so all MP2 calculations were done with all electrons included. To test the effect on calculated geometry, a "frozen-core" MP2 calculation was performed on H 0 2 with Fletcher-Powell optimization and no change was found in the predicted geometry. (26) Hameka, H. F.; Turner, A. G. J . Magn. Reson. 1985, 64, 66.
(27) Rothaan, C. C . J. Rev. Mod. Phys. 1960, 179, 32. (28) Schlegel, H. B. J . Chem. Phys. 1986, 84, 4530. (29) Fletcher, R.; Powell, M. J. D. Comput. J . 1963, 6, 163. (30) Takada, T.; Dupuis, M.; King, H. F.J . Chem. Phys. 1981, 75, 332. ( 3 1 ) Hout, R. F.; Levi, B. A,; Hehre, W. J. J . Comput. Chem. 1982, 3(2), 234. (32) Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.; Stewart, J . J. P. J . A m . Chem. SOC.1985, 107, 3902. (33) Binkley, J. S.; Whiteside, R. A,; Raghavachari, K.; Seger, R.; DeFrees, D. J.; Schlegel, H. B.; Topiol, s.;Kahn, L. R.; Frisch, M. J.; Fuder, E. M.; Pople, J. A. Gaussian 82, Carnegie-Mellon University, Pittsburgh, PA.
6448
The Journal of Physical Chemistry, Vol. 90, No. 24, 1986
Besler et al.
TABLE 11: Ab Initio Optimized Geometries for HOz'
r(0-O), A
r(H-0), A iH-0-0,deg This Work
UHF/6-31G(d) UHF/6-311 ++G(d,p) MP2/6-3 l G ( d ) MP2/6-31 IG(d,p) MP3/6-31 lG(d,p) MP4SDTQ/6-311G(d,p) AM 1
1.3088 1.2987 1.3257 1.3078 1.3097 1.3241 1.1747
0.9534 0.9477 0.9830 0.9685 0.9647 0.9705 1.010
exptI0
1.335 1.3305 1.3339 1.313 1.314 1.367 1.334 1.342
0.977 0.9707 0.9774 0.950 0.951 0.983 0.975 0.972
total energies, AU
105.7 106.5 104.5 104.9 105.1 104.5 1 12.6
( S ' ) = 0.7594 ( S ' ) , = 0.7613 ( S ' ) , = 0.7516 ( S 2 ) ,= 0.7515 ( S ' ) , = 0.7516 ( S 2 ) ,= 0.7518
-150.170 53 -150.223 37 -150.502 36 -1 50.622 86 -150.591 90 -150.61237
Previous Work expt"
expt'! UHF/~-~IG(~,P)~~ ROHF/6-3IG(d)O5' GVB-CIS2 MCSCF9 GVB-CI'
104.1 104.29 104.15 105.8 105.8 103.3 104.7 104.2
-1 50.17664 -150.41288 -150.3982
isotropic hyperfine couplings, G -9.0938
H Olb 02 H 01 02
UHF/6-3 1 1 ++G(d,p) UHF/6-31 l++G(d,p) at MP4SDTQ/6-31 lG(d,p) geometry
H 01 02
exptI3 exptI4
H H
-9.0938 -15.8274 -39.9810 -9.5872 -17.2670 -43.7433 -8.5046 -16.4552 -42.4229 -9.84 -10.2
Anisotropic Hyperfine Couplings, G and Direction Cosines at UHF/6-31 lG++(d,p) Level Using the MP4SDTQ/6-31 lG(d,p) Geometry H X Y Z -5.008 -4.505 9.513
0.929 23 0.000 00 -0.369 51
0.000 00 I.000 00 0.000 00
0.369 51 0.000 00 0.929 23
01
X 0.000 00 -0.057 06 -0.998 37
Y
Z 0.000 00 -0.998 37 0.057 06 Z 0.00000 0.14801 0.988 99 6.95
-24.628 8.968 15.659 02 -97.338 47.787 49.55 1
exptI3
1.000 00 0.000 00
0.000 00
X
Y
0.000 00 0.988 99 -0. I48 01 H -4.07
1.00000 0.000 00 0.000 00 -2.89
" R O H F indicates restricted open Hartree-Fock. bO1 is the middle oxygen and 0 2 is the terminal.
series of multiconfiguration self-consistent field (MCSCF) calculations on the ground and first three excited states of 02'-.The results of our calculations for the equilibrium ground-state geometry and total energy for 02'-are summarized in Table I. Experimental data on the structure of 02'-has been obtained from low-energy elastic electron scattering (LEEES)35-37and molecular photodetachment ~ p e c t r o s c o p y .The ~ ~ experimental bond length is reported to be 1.377 and 1.341 A by the two methods, re~~ spectively. As is typical of Hartree-Fock c a l c u l a t i o n ~the calculated bond length at both the UHF/6-3 1G(d) and U H F / 6-3 11 ++G(d,p) level is too short. This is quite pronounced in the case of 02'-.The larger basis set result is shorter and is probably quite close to the Hartree-Fock limit. Incorporation of electron correlation results in a marked improvement in the equilibrium geometry. It is interesting to note that the MP2/631G(d) and MP4SDTQ/6-31 lG(d,p) results are quite close to (34) Das, G.; Wahl, A. C.: Zemke, W. T.: Stwalley, W. C. J . Chem. Phys. 1978, 68, 4252. (35) Linder, F.; Schmidt, H. Z . Narurforseh. A : Asrrophys., Phys. Phys. Chem. 1971. 26a, 1617. (36) Burrow, P. D. Chem. Phys. Lett. 1974, 26, 265. ( 3 7 ) Boness, M . J. W.: Schulz, G. J. Phys. Reo. A 1970, 2, 2182. (38) Celotta, R. J.; Bennet, R. A,; Hall, J. L.: Siegel, M. W.; Levine, J. Phys. Rec. A 1972, 6. 631.
each other and compare favorably to the experimental results. Our calculations would seem to favor the accuracy of the longer experimental bond length. The fundamental vibrational frequency of 02*has been determined by LEEES35-37and Raman s p e c t r o ~ c o p yto~ be ~ 1090 cm-' with an anharmonicity component of approximately 8 cm-' as shown in Table V. Typical of Hartree-Fock c a l c u l a t i ~ n s , ~ ~ ~ ~ ~ the frequency is predicted to be too high. In this case the overprediction is nearly 35%. A comparison of calculated frequencies at the HF/6-31G(d) level with experimental data shows a mean overestimation of 13%.27 The MP2/6-3 1 1G(d,p) calculation predicts the experimental frequency nearly exactly, confirming the low anharmonicity of the vibration. HO,'. There have been numerous theoretical and experimental studies on the structure and properties of HO,'. Among the best of the theoretical studies are those of Bair and G ~ o d a r dJackels ,~ and Phillips,8 and Cohen et aL9 High-quality experimental data obtained from microwave,I0 laser infrared," and laser magnetic resonance spectroscopyi2of DOz' and HO,' permit the structure (39) Holzer, W.; Murphy, W . F.; Bernstein, H. J.; Rolfe, J . J . Mol. Speetrose. 1968, 26, 543. (40) Pople, J. A,: Schlegel, H . B.; Krishnan, R.: DeFrees, D. J.: Binkley, J. S.: Frisch. M. J.: Whiteside, R. A. Int. J . Quantum Chem. 1981, S15, 269.
Hydrocarbon Peroxyl Radicals
The Journal of Physical Chemistry, Vol. 90, No. 24, 1986 6449 TABLE 111: Ab Initio Calculations for CH3O2'a,b parameter
LC-0-0 r(C-0) r(0-0) r(C-HA)
LHA-C-0 r(C-H,) LHB-C-0
Z
Figure 1. Structure and coordinate system used in calculations for the hydroperoxyl radical, HOz'. The molecule lies in the X Z plane with the z axis along the OH bond.
W2)0
TE
d
/
/
/
\
HA
0.
CIS
LC-0-0 r(C-0) r(0-0)
4C-W
HA
LHA-C-0 TRANS
Figure 2. Cis and trans forms of the methyl peroxyl radical. the COO plane.
r(C-H,) HA
LHB-C-0 (S2), TE
lies in
trans
cis
6-3 1G(d) 110.9 1.4166 1.301 1 1.0797 105.6 1.081 110.0 0.7598 -1 89.2023
112.4 1.4213 1.2979 1.0789 109.1 1.0811 108.3 0.7604 -1 89.2001 7
MP2/6-31G(d,p) 110.1 1.4505 1.3111 1.0884 105.4 1.0895 108.9 0.7515 -189.66799
111.5 1.4532 1.3102 1.0879 107.8 1.0900 107.5 0.7516 -189.66731
6-311++G(d,p) of H 0 2 ' to be precisely determined. The accuracy of theoretical LC-0-0 111.6 113.0 geometry predictions can thus be assessed. Our theoretical results, 1.4163 r(C-0) 1.4214 as well as those of other researchers, are presented along with the 1.2903 1.2871 r(0-0) experimental data in Tables I1 and V. The U H F calculations 1.0806 1.0805 r(C-H,) follow the pattern of underpredicting the experimental bond 105.6 109.1 LHA-C-0 lengths. Also the U H F calculations overpredict the experimental 1.0824 1.0818 r(C-H,) bond angles as is observed with most molecules.23The larger basis 109.9 108.3 LHB-C-0 0.7620 0.7629 set U H F calculation is farther from experiment than the (S2)0 -189.25774 TE -189.25984 UHF/6-31G(d), as was the case with 02*-. The UHF/6-31G(d) calculations predict the 0-0 distance too short by 0.02 A, the GVB-CI' 0 - H distance too short by 0.02 A, and the bond angle too large LC-0-0 110.2 by 1.5". The incorporation of electron correlation again markedly 1.442 r(C-0) improves the geometry prediction. Particularly, the MP2/61.339 r(0-0) -189,4090 TE 31G(d) and MP4SDTQ/6-31 lG(d,p) results agree very well with each other and experiment. bond distances in angstroms. Predicted internal rotational Harmonic vibrational frequencies which are presented in Table barrier: 6-31G(d), 1.3 kcal/mol; 6-31 l++G(d,p), 1.0 kcal/mol; V are computed at the U H F and MP2 levels. The U H F calcuMP2/6-31G(d), 0.43 kcal/mol. lations overpredict the frequencies by approximately 18% for the are two minima: with the C-0-0 arm either cis or trans to one 0 - H stretch and 16% for the remaining two. This is typical of of the hydrogens (see Figure 2). The trans structure is enerU H F calculation^.^^^^^ The MP2/6-3 1lG(d,p) are frequencies getically favored, but the barrier to C H 3 group rotation is quite much closer to experiment, except for the 0-H stretch, which is low (0.4 kcal/mol) and at room temperature it should behave expected since the 0-H stretch is quite anharmonic. It is difficult nearly as a free rotor. At the MP2/6-3 lG(d) level the C-0-0 to assess whether the discrepancy for the other two frequencies bond angle is predicted to be 110.1O in the trans structure. The is due to calculational error or anharmonicity in the vibrational 6-3 1G(d) calculation for the trans structure predicts the C-0-0 mode. bond angle to be 0.8" greater than the MP2/6-31G(d) calculation. Finally, a calculation of the ESR isotropic and anisotropic Also the 0-0 bond length is 0.01 A shorter, and the C - 0 bond hyperfine couplings for H 0 2 ' is presented in Table 11. The anlength 0.03 A shorter. This follows the pattern established by isotropic couplings are presented with their respective direction 02'-and HO,'. The two previous theoretical calculations on cosine matrices (see also Figure 1). These parameters are comCH3O2' were a U H F geometry optimization by Bagus et al.41942 puted by using UHF/6-311 ++G(d,p) calculation at the and a GVB-CI calculation by Bair and Goddard.' The results MP4SDTQ/6-31 lG(d,p) geometry. Also shown are the experimental results obtained by microwave and ESR s p e c t r o ~ c o p y . ' ~ ~ ~ ~of those calculations and the rest of the structural parameters are shown in Table 111. Our predicted geometry agrees quite well The agreement with experiment is good and indicates that the with that of Bair and Goddard. In all cases the trans geometry radical is a n-type with most of the unpaired spin located on the is predicted to be the global minimum. Vibronic spectral data terminal oxygen. A Mulliken population analysis predicts that obtained by Hunziker and Wendt43show internal rotation in the approximately 85% of the spin density lies on the terminal oxygen. CH302' in agreement with these calculations. The modification to Gaussian 82 which allows the calculation of Very recently the infrared spectra of CH302' and the CH302' anisotropic hyperfine couplings was provided by C h i ~ m a n . ~ ' dimer in an argon matrix have been observed by Ase, Bock, and CH302'. The CH3O2' radical is quite interesting, as it is the S n e l ~ o n . By ~ ~ the technique of isotopic substitution they were smallest of the hydrocarbon peroxyl radicals and is of the proper able t o observe and characterize 8 of t h e 12 infrared-active funsize to be accurately studied by current a b initio techniques. As damentals of CH3O2'. Their results and our calculated values of this date there are only two theoretical calculations known to at the UHF/6-31G(d) level for all 12 fundamentals are given in us and no experimental data on the structure of the C H , 0 2 ' Table V. The ab initio frequencies fit the overestimation mean it is radical. From the previous calculations on H 0 2 ' and 02'-, suggested that the MP2/6-31G(d) level of calculation is capable of accurately predicting the geometry of peroxyl radicals. The (42) (a) Bagus, P. S.; Lin, B.; McLean, A. D.; Yoshimine, M. In Computational Merhods in Chemistry; Bargon, J., Ed.; Plenum: New York, 1980; calculations at both the U H F and MP2 levels predict that there p 223. (b) Rakoczi, F. J.; Ha, T. K.; Gunthard, Hs. H. Chem. Phys. 1983,
~
(41) Daniel M . Chipman Radiation Laboratory, University of Notre Dame, Notre Dame, IN 46556
74, 273.
(43) Hunziker, H. E.; Wendt, H. R. J . Chem. Phys. 1976, 64, 3488. (44) Ase, P.; Bock, W.; Snelson, A. J . Phys. Chem. 1986, 90, 2099.
6450
The Journal of Physical Chemistry, Vol. 90, No. 24, 1986 H ,
,,H
Besler et al. TABLE V Ab Initio Calculations of Harmonic Vibrational Frequencies
02.frea. cm-'
0-0 stretch
Figure 3. Structure of the isopropyl peroxyl radical showing the cis and trans forms. The H A C O O atoms lie in the plane shown and this plane is perpendicular to the plane formed by the three carbon atoms. TABLE IV: Ab Initio Calculations for (CH&CH02' and (CH,CH,),CHO,' 6-3 1G(d)
ic-0-0 iHA-C-O r(C-0) r(0-0) r(C-C) 4c-H~)
(S2h TE
ic-0-0 LHA-C-0 (S2)0
TE e ~ p LCOO t ~ ~
trans
cis
(CHd2CH02' 112.3 103.4 1.4258 1.3014 1.5277 1.0821 0.7600 -267.27977 AU
112.8 108.8 1.4257 1.2982 1.5273 1.0805 0.7606 -267.27876 AU
(CH,CH2)2CH02' 112.4 103.5 0.7608 -345.34550 11 1 (+2, -1)
113.1 109.0 0.7610 -345.34532
of 13% reported by Hout et at.31and Pople et aL40 Larger Peroxyl Radicals. The major impetus for the calculations on (CHJ2CHO2*and (CH3CH2)2CH02'is to provide a model for a peroxyl radical site in isotactic polyethylene and lipids. It has been determined by Iwasaki et and Hori et al.46that the C - 0 - 0 group lies in a plane perpendicular to the main polymer chain axis. In our study it was therefore chosen that in our geometry optimization the carbon chain is constrained to be planar and the C-0-0 group constrained to be perpendicular to the chain axis. The UHF/6-3 1G(d) level of calculation was chosen due to its cost effectivenessand capability of producing predictable and slight underestimation of bond distances and slight overestimation of the C - 0 - 0 and H-0-0 bond angles in CH302' and H02', respectively, relative to the MP2/6-31G(d) level of calculation. It is recalled that at this level agreement with experimental geometry is excellent. For the (CH,),CHO,' structure the LC-C-C of the carbon chain was constrained to be 109.47O (see Figure 3). The terminal methyl groups were fixed in the appropriate geometry as shown in Figure 3. The C-H distances were fixed at 1.08 A and the appropriate angles constrained to be tetrahedral. Within these constraints, a total geometry optimization was performed on this structure with the 0-0 group at both the cis and trans conformations. The calculated geometric parameters are shown in Table IV. The C-0 and 0-0bond distances are predicted to be nearly the same as those in the CH302' radical, calculated at the UHF/6-31G(d) level. The LC-0-0 however is predicted to be 1.4' greater. Following the patterns established earlier, the LC(30 that would be predicted at the MP2/6-31G(d) for the trans structure, were it possible to perform the calculation, would be approximately 11 1 S 0 . For the (CH3CH,),CH0,' structure (see Figure 4), only the ~ C - 0 - 0 and LH-C-O parameters were optimized due to the high cost of the calculation. The same basis set and constraints as the previous structure were used. In addition we constrained the C - C distance in the chain, the C-H distance for the hydrogen trans to the C-0-0 group, the C-0 distance, and the 0-0distance to be those obtained from the geometry optimization of the (45) Iwasaki, M.; Sakai, J. J . Polymn. Sci. Part A-2 1968, 6, 265. (46) Hori, Y.; Aoyama, S.; Kashiwabara, H. J . Chem. Phys. 1981, 75, 1582.
UHF/6-3 1G(d) UHF/6-31 I++G(d,p) MP2/6-31 IG(d,p) AM 1
1468.1 1425.6 1087.5 1924.4 1089 1090 1458 1074 1099
expt3' SCF'4 M C S C F [4]34 MCSCF [76]34
HO,' freq, cm-l 0 - H stretch ( q ) 6-3 lG(d) 6-3 1 1 ++G(d,p) MP2/6-31 lG(d,p) AM 1 exptS3
4015.4 4064.5 3146.7 3183.0 3436.2
bend (v2) 6-31G(d) 6-3 1 1++G(d,p) MP2/6-31 lG(d,p) AMI expts4
1621.9 1603.6 1461.6 1772.7 1391.8
0-0 stretch (Y,) 6-3 1G(d) 6-31 l++G(d,p) MP2/6-3 1 lG(d,p) AM 1 exptS5
1251.0 1268.9 1250.4 1644.0 1097.6
CH,O,' freq, cm-I 6-31G(d) C H 3 int rot. C - 0 - 0 bend C - 0 str CH, rock C - 0 - 0 asym str CH, rock C-H bend C-H bend C-H bend C-H str C-H str C-H str
180.8 535.2 1063.9 1279.6 1280.7 1343.5 161 1.7 1631.0 1646.8 3243.1 3328.7 3346.1 H..J
e ~ p t ~ ~ 492 902 1112 1183 1414 1440 1453 2968
H
Figure 4. Structure of the 3-pentyl peroxyl radical showing the cis and trans forms. The plane shown contains the HACOO group and is perpendicular to the plane that contains the five carbon atoms.
previous structure. The terminal methyl groups were treated as above. Finally, HA was constrained to be perpendicular to the plane of the carbon chain. The C-H distance was set at 1.08 8, and the LH-C-H set to be tetrahedral. Optimization was performed for both the cis and trans conformers. No appreciable change was found for either of the two parameters being optimized
Hydrocarbon Peroxyl Radicals from those in CH3CH02' in the trans structure. However, in the cis structure, the ~ C - 0 - 0 was almost 1O greater and the LH-C-O was approximately 5 O greater. This same behavior was predicted above for CH302'. The two conformers of (CH3CH2)2CH02' were found to be nearly equal in energy. From this we conclude that the addition of further carbons to the chain will not noticeably affect the geometry of the peroxyl radical site and that the actual LC-0-0 is to a good approximation 111.So in the trans conformation and 112.5' in the cis conformation. The equality in energy indicates that neither conformation is favored above the other. For more than a decade the LC-0-0 bond in hydrocarbon peroxyl radicals has been taken by many researchers to be that determined experimentally for the '02CFCONH2 radical in the single-crystal ESR study of Toriyama and I ~ a s a k i , ~where ' the LC-0-0 angle was determined to be 104'. More recently the LC-0-0 at a peroxyl radical site formed in irradiated isotactic polypropylene has been determined by Shimada et a1.48349to be 11 1'. They report an experimental uncertainty of +2O and -lo. Our calculations clearly support the findings of Shimada et al. for hydrocarbon peroxyl radicals. C-0-0 Internal Rotation Barrier. A question of interest to many researchers in the field of ESR spectroscopy is the nature of the rotation of the 0-0 group at peroxyl radical sites formed in polymer chains at room temperature. The motion is thought to occur by one of two mechanisms: rotation about the C-0 axis or motion of the entire C-0-0 group about the chain axis. Experimental results usually favor the chain axis motion.6 From the structure of a peroxyl radical site in a polyethylene chain, it appears that the steric repulsion of the hydrogens attached to the carbons to step down the chain would provide the most hindrance to rotation about the C - 0 axis. In order to determine an approximate barrier to the internal rotation of the 0-0group about the C - 0 axis a series of calculations was performed at the UHF/6-3 1G(d) level using the rigid-rotor approximation with the trans (CH,CH,),CHO,' structure above. The entire geometry (47) Toriyama, K.; Iwasaki, M. J . Phys. Chem. 1969, 73, 2663. (48) Schimada, S.; Kotake, A.; Hori, Y.; Kashiwabara, H. Macromolecules 1984, 17, 1104. (49) Shimada, S.; Hori, Y., Kashiwabara, H. J . Am. Chem. Soc. 1985, 18, 170. (50) Komornicki, A,; Jaffe, R. L. J . Chem. Phys. 1979, 71, 2150. (51) Hehre, W. J.; Radom, L.; Schleyer, P.; Pople, J. A. A6 Initio Molecular Orbital Theory; Wiley Interscience: New York, 1986. (52) Oakes, J. M.; Harding, L. B.; Ellison, G. B. J . Chem. Phys. 1985, 83, 5400. (53) Yamada, C.; Endo, Y.; Hirota, E. J . Chem. Phys. 1983, 78, 4379. (54) Nagai, K.; Endo, Y.; Hirota, E. J . Mol. Spectrosc. 1981, 89,520. (55) Johns, J. W. C.; McKellar, A. R. W.; Riggin, M. J . Chem. Phys. 1978, 68, 3957.
The Journal of Physical Chemistry, Vol. 90, No. 24, 1986 6451 was held constant, while the 0-0group with LC-O-0 at 112.4O was rotated about the C-0 axis. Calculations were performed at 10 equally spaced points. Due to the symmetry of the barrier only half of a full rotation need be examined. Loss of the C, symmetry of the structure when the C-0-0 group is not perpendicular to the carbon chain results in great calculational difficulty. The barrier to internal rotation using this approximation is predicted to be 39 kcal/mol. Most likely this is higher than the actual barrier. Also the structure with the C-0-0 group cis to the attached hydrogen is predicted to be 1.2 kcal/mol higher in energy than the trans structure, when the rigid-rotor approximation (trans LC-0-0) is used. Within this approximation, the terminal oxygen on the 0-0 group approaches within 1.5 8, of one of the methylene hydrogens which is attached to the carbon two sites down the chain. This close approach accounts for the unusually high barrier.
Conclusions We have performed a series of high-level ab initio calculations on the series of radicals 02'-, HOz', and CH302'. The accuracy of the MP2/6-31G(d) model is verified for HO,'. This lends support to the predictions of the equilibrium structure of CH30,'. Also patterns established in the calculations of these three radicals allows us to predict correction to the UHF/6-31G(d) calculations on the two large peroxyl structures. These two large structures serve as models for a peroxyl radical site in isotactic polyethylene. It appears that the LC-0-0 bond angle is close to 11 1 S o ,which is verified by recent experimental results. The cis and trans conformations of the 0-0 group are isoenergetic, which suggests that in an extended system equal numbers of both would be present. Finally, the barrier to internal rotation of the 0-0group at a peroxyl radical site in polyethylene appears to be high enough that at room temperature this motion would be almost completely hindered. This work also has a bearing on saturated lipid peroxyl radicals which in the extended chain form should approximate that of a polyethylene peroxyl
Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, the Office of Health and Environmental Research of the U. S. Department of Energy, and the U. S. Army Natick Research and Development Laboratory for support of this research. We also thank P. P. Schmidt, L. Blum, and the O N R / N R L for computer time on the Cray XMP-12 at the Naval Research Laboratory in Washington, DC. Finally, we thank N. Loh for the use of the O U Department of Engineering Microvax 11. Registry No. 02'-, 11062-77-4; HO;, 3170-83-0; CH302', 2143-58-0; (CH3)f2H02', 4399-86-4; (CH,CH2),CH02', 42953-27-5; isotactic polyethylene, 67462-86-6.
