J . Phys. Chem. 1993,97, 10694-10701
10694
Studies on the Structure and &Bond Scission Reactions of Primary Alkyl Radicals, CH~(CHZ),CH~, for n = 1-6 J. Pacansky,’ R. J. Waltman, and L. A. Barnes IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120-6099 Received: July 20, 1993”
HF/6-3 1G* optimized geometries are reported for n-alkyl radicals from n-propyl to n-octyl in two extended chain conformations, one where the radical carbon 2p orbital housing the unpaired electron is eclipsed to a j3-CH bond and another where the orbital is eclipsed to a j3-CC bond. In all cases, the j3-CH eclipsed conformer is =100-200 cal/mol lower in energy than the j3-CC eclipsed conformer. The geometry a t the radical center is nonplanar by approximately 14O, indicative of some “s” character in the carbon 2p orbital containing the unpaired electron. In the radicals studied here, the bond lengths of the eclipsed j3-CH and &CC bonds are longer than the corresponding noneclipsed @-bonds,attributed to a hyperconjugative interaction. Potential functions for internal rotation about the a , j3, and y bonds reveal the following: rotation about a - C C bonds is free but rotation about j3- and y-bonds have barriers of ==3kcal/mol. Bond scissioning and isomerization reactions for n-alkyl radicals are calculated and compared with experimental data. The AE values, the changes in total energies between products and reactants, including zero point energies, for C-H rupture are of the order of 33 kcal/mol, while for C - C scissioning, AE == 20 kcal/mol. 1,3-, 1,4- and 1,5-isomerization reactions have much lower AE values and, on a relative basis, appear to be the preferred reaction pathway for the radicals.
Introduction Alkyl radicals are perhaps the simplest yet some of the most reactive organic radicals. They play a central role in the petroleum industry1and are reactive intermediates in the production of many commercial polymers.* As reactive intermediates they also play essential roles in polymer degradation,3 thus determining the stability of many materials such as coatings and lubricants toward heat, light, and high-energy radiation. Previously, we reported a number of studies on small alkyl systems such as methyl, ethyl, isopropyl, and tert-butyl which aided structural, kinetic, and thermodynamic ~ t u d i e s .However, ~ in order for this work to be more pertinent, encompassing studies on larger systems should be conducted. Therefore, we have theoretically investigated the structures of primary alkyl radicals with chain lengths up to nine carbon atoms to obtain: (1) optimized geometry for a number of pertinent conformations; (2) barriers for internal rotations about a-CC, &CC, and 7-CC bonds; (3) energetics for the j3-CH and 8-CC bond scission reactions; (4) energetics for 1-3, 1-4, and 1-6 hydrogen atom migration; and (5) vibrational frequencies and intensities and force fields. Due to the length of this study only the first four parts will be presented herein. The force fields, vibrational frequencies, and intensities will be given in another report along with experimental spectra of primary alkyl radicals. In addition, similar reports on large secondary and tertiary radicals are forthcoming.
Computational Details Standard ab initio calculations were performed using the IBM/ AIX3 version of the Gaussian computer codes5 The calculations were performed using the unrestricted Hartree-Fock (UHF) wave functions using the 6-3 lG* basis set.6 Selected calculations using the correlated MP2 wavefunction were also performed and described in the text as necessary. In all cases, the geometry was gradient optimized with no symmetry constraints imposed on the alkyl molecules. The vibrational frequencies for all molecules were calculated by analytical differentiation of the H F or UHF energy gradient at the optimized geometries. For all MP2 0
Abstract published in Advance ACS Absrracrs, September IS, 1993.
0022-365419312097-10694$04.00/0
calculations, second derivatives were computed by numerical differentiation at the optimized geometries. All of the computations were performed on IBM RISC 6000 Model 530,540, and 560 work stations. As an illustrative example, the CPU times required for the analytical frequency calculation for the n-octyl radical was approximately 84 h while for n-propyl, 40 min at the SCF level of theory. In all cases, direct SCF calculations were performed. The z matrices for all of the alkyl radicals were facilitated by using the Alchemy 11molecular modeling software tool,’ run on an IBM PSI2 Model 80 personal computer. Alchemy I1 allows an initial minimization of the molecule using a built-in force field, a conjugate gradient procedure that computes all partial first derivatives in order to move all of the atoms simultaneously during each iteration. The minimized geometry is stored on the PSI2 as Cartesian coordinates, which can readily be converted to a z-matrix file and then transferred to a workstation over a LAN (local area network), ready for use in a program application such as Gaussian.
Results and Discussion Geometry. Saturated hydrocarbons have a 3-fold barrier for internal rotation about each C-C bond; hence, in principle 3N conformers are possible. Although the total number of conformers which are possible for alkyl radicals will differ slightly from their parent closed shell hydrocarbon, still a large number will exist. A tractable study on primary alkyl radicals with carbon chains up to eight atoms long is only possible if we limit the scope of our calculations to the extended geometry of the chain. In this conformation, a local minimum exists when each carbon atom lies in a plane arranged in a zig-zag configuration. A primary alkyl radical, with a carbon skelton in an extended geometry, will thus have two conformers; one when the radical carbon 2p, orbital housing the unpaired electron is eclipsed with a 8-CH bond and another when the C 2p, is eclipsed with a 8-CC bond; for example, corresponding to H1 l-Cl-C2-H21 dihedral angles of 159O and 41°, respectively, for n-propyl. The major part of this report is an investigation into these conformers, and henceforth they are referred to as the 8-CH and 8-CC conformers. Computer drawings are shown for the 8-CH and 8-CC conformers of the 0 1993 American Chemical Society
Scission Reaction of Primary Alkyl Radicals
The Journal of Physical Chemistry, Vol. 97, No. 41, 1993 10695 H33
+ H32
HI2
U
H22
HU3
n22
+ HI2 H32 nu2
H22
H53
HI2
H52 HY2
H2Z
H32 HU2
HI2
H22
H31
HI2
n3 I
H5 I
H71
HI1
HI2 HI2
ti71
H51
HI I
H31
HI2 H82
n42
HI2
VH22 H82
Figure 1. UHF/6-3 1G* optimized geometries for n-alkyl radicals where a 8-CH bond is eclipsed with the half-filled p orbital at the radical center.
n-alkyl radicals in Figures 1 and 2. The total electronic and zero-point energies of the respective geometries are tabulated in Table I. For all of the unrestricted calculations performed, spin contamination of the UHF wavefunction was negligible. The expectation value for the spin eigenfunction when rounded off to two significant figures was equal to 0.76 (Table I). This is consistent with past studies which have shown that UHF calculations are very reliable for alkyl radicals.8 Table I lists the total energies for the radical systems studied. Regardless of the radical under consideration,the difference in total energy between the j3-CH and j3-CC conformers is about 100-200 cal/mol; the j3-CH conformer always has the lower energy. While the alkyl series from n-propyl through n-octyl is reported here, the methyl and ethyl free radicals have been discussed in detail in a previous publication: where it was established that the methyl radical had a planar radical center while the ethyl radical site was nonplanar. The series n-propyl through n-octyl are likewise nonplanar at the radical center. The nonplanar geometry about the radical center introduces some s character into the carbon p orbital containing the unpaired electron so that the geometry acquires a pyramidal structure resembling ammonia. The degree of nonplanarity or the pyramidal angle 6, as defined in Figure 3, is the angle that the C l - C 2 bond makes with the
n22
H62
Figure 2. UHF/6-3 1G* optimized geometries for n-alkyl radicals where a 8-CC bond is eclipsed with the half-filled p orbital at the radical center.
9
9 dsv
W
Figure 3. Definition of the pyramidal angle 6.
Hll-Cl-Hl2 plane (Figure 1). The 6 values are summarized in Tables I11 and V for all of the alkyl radicals and are about 14O in every case, consistent with previous results for the ethyl radical (6 = 129.4 Closer inspection of the optimized geometries for both the B-CH and j3-CC eclipsed alkyl radicals indicate that each system
TABLE I: UHF/631G* Total Energies for Optimized RAlkyl Radicals ( E Is Total Energy and ZE is Zero-Point Energy) parameter E 8-CH (hartrees) ZE BCH (kcal/mol) S2 E 8-CC (hartree)
ZE &CC (kcal/mol) S2
n-propyl -117.631 717 59.22 0.762 -117.631 434 59.27 0.762
n-butyl -156.666 560 78.41 0.762 -156.666 381 78.41 0.763
n-pentyl -195.701 246 97.58 0.762 -195.701 062 91.65 0.762
n-hexyl -234.735 945 116.73 0.762 -234.735 760 116.80 0.763
n-heptyl -273.770 641 135.87 0.762 -273.770 457 135.94 0.762
n-octyl -3 12.805 336 155.01 0.762 -312.805 151 155.07 0.762
Pacansky et al.
10696 The Journal of Physical Chemistry, Vol. 97, No. 41, 1993
TABLE 11: UHF/6-31C* Optimized Bond Lengths (A) for Alkyl Radicals (B-CH Eclipsed to Radical Center) bond n-propyl n-butyl n-pentyl n-hexyl n-heptyl n-octyl bond n-propyl n-butyl n-pentyl n-hexyl
n-heptyl n-octyl
~
c1c2 ClHll ClHl2 C2C3 C2H21 C2H22 c3c4 C3H31 C3H32 C3H33 c4c5 C4H41 C4H42 C4H43 C5C6
1.501 1.076 1.076 1.530 1.092 1.087 1.085 1.085 1.086
1.500 1.075 1.076 1.532 1.093 1.088 1.528 1.088 1.087 1.086 1.086 1.086
1.500 1.076 1.076 1.532 1.093 1.088 1.529 1.088 1.089
1.500 1.076 1.076 1.532 1.093 1.088 1.529 1.089 1.088
1.500 1.076 1.076 1.532 1.093 1.088 1.529 1.089 1.089
1.500 1.076 1.076 1.532 1.093 1.088 1.529 1.089 1.089
1.528 1.088 1.088
1.530 1.089 1.089
1.530 1.089 1.089
1.530 1.089 1.089
1.528
1.530
1.530
has shorter than normal bonds a to the radical center (Le., ClC2, ClH11, and ClH12). In the methylene unit /3 to the radical center, labeled C2, the C H bond in the P-CH eclipsed conformer, and the CC bond in the 6-CC eclipsed structure, have longer bond lengths when they are trans to the half-filled p orbital than in the other positions. The effect diminishes rapidly and is not observed strongly including and beyond the y methylene moiety. The a-CH bond lengths, in both the 0-CH and @-CC conformers, are between 1.075 and 1.076A, which is much shorter than those for (experimental) sp3 bond lengths, e&, rCH = 1.1 1 A for n-propane, n-butane, n-pentane, e t c 9 The a-CC bond lengths in both the 0-CH and 0-CC conformers are between 1.500 and 1.501 A, and like the a-CH bond lengths, are shorter than normal CC single bond lengths, for example, rcc = 1.53 A (experimental) for n-propane, n-butane, n-pentane, etc.? but considerably longer than C=C bond lengths, e&, for ethylene r c e = 1.34 A. The &CH bond lengths in the methylene groups are between 1.087 and 1.093 A, depending upon the conformer and whether or not the CH bond is trans to the half-filled p orbital and are closer to experimental bond lengths as those found in n-alkanes, where rCH = 1.11 A. Those trans to the unpaired electron are longer than those in the other positions. The 8-CC bond lengths in the methylene groups are between 1S30 and 1.539 A, depending upon the conformer and whether or not the CC bond is trans to the half-filled p orbital, and have about the same length as those found in propane where rcc = 1.527 A. All the bond lengths beyond the /3 position to the radical center, Le., y, 6, etc., are of similar lengths: the CC bonds are between 1.528 and 1.530 A, while the C H bonds are between 1.086 and 1.088 A, respectively. In fact, the optimized geometries for all of the primary alkyl radicals are almost identical regardless of the length of the carbon chain. This leads to the conclusion that the geometry of a primary alkyl radical may be viewed as two independent parts regardless of size; a saturated hydrocarbon chain attached to a -CH2-CH2-CHz0 containing the salient features of the primary radical site. Orbital plots for some alkyl radicals have previously been p ~ b l i s h e d . ~For example, the HOMO for the 8-CC eclipsed comformer of the n-propyl radical contains the unpaired electron on the radical center and the HOMO eclipses the P-CC bond. All of the other radicals investigated here have the same HOMO orbital plots with the only differences being the length of the chain, and whether or not the orbital containing the unpaired electron eclipses the 8-CC or P-CH bonds. In addition to the C 2p orbital, the HOMO also contains a large contribution from a 0-CH bond or the 0-CC bond that is eclipsed with the C 2p orbital and geometrically located in a trans position. The nonequivalent @-CHand @-CCbonds as well as the shortening of the a-CC bonds (Tables I1 and IV) compared to regular CC single bonds appear to be a consequence of hyperconjugative interaction between the formally singly occupied p-orbital at the
1.086 1.086 1.086
C5H51 C5H52 C5H53 C6C7 C6H61 C6H62 C6H63 C7C8 C7H7 1 C7H72 C7H73 C8H81 C8H82 C8H83
1.088 1.088 1.086 1.086 1.086
1.089 1.089
1.089 1.089
1.528 1.088 1.088
1.530 1.089 1.089 1.528 1.088 1.088
1.086 1.086 1.086
1.086 1.086 1.086
-20
' (0)
(b)
(C)
(d)
(4
(1)
Figure 4. Molecular orbital energies for n-alkyl radicals. Top: j3-CH. Bottom: 6-CC eclipsed conformers. (a) n-Propyl; (b) n-butyl;(c) n-pentyl; (d) n-hexyl; (e) n-heptyl; (f) n-octyl.
radical center and the molecular orbital for the eclipsed 8-CH and P-CC bonds. This has beendiscussed in a previous publication in detail.4 For example, in the &CC eclipsed conformer of the n-propyl radical, the a-CC bond adopts a partial double-bond character (see Tables I1 and IV) while the electron density in the 0-CC bond eclipsed to the aC 2p orbital is decreased, thus weakening, i.e., lengthening, these bonds. Molecular Orbital Energies. The spin-restricted open-shell ROHF/6-3 1G*energy levels for all of the molecular orbitals are shown in Figure 4. These were obtained by single-point ROHF energy calculations on the UHF/6-3 lG* optimized structures. The highest occupied molecular orbital, or HOMO, has the lowest energy for the n-propyl radical but increases modestly with methylene substitution, for both the 8-CH and 8-CC eclipsed conformers. Thus, in the order from the n-propyl to the n-octyl radical, the HOMO energies increase from -1 S O to -1.49 eV for the P-CH eclipsed n-alkyl radicals, and from -1.53 to -1.51 eV for the 6-CC eclipsed radicals. With increasing methylene substitution, the HOMO-LUMO gap decreases and appears to reach an asymptotic value, 7.7 eV for both the j3-CH and j3-CC eclipsed radical conformers.
The Journal of Physical Chemistry, Vol. 97. No. 41, 1993 10697
Scission Reaction of Primary Alkyl Radicals
TABLE 111: UHF/6-31C* Optimized Bond Angles (degree) for Alkyl Radicals (8-CH Eclipsed to Radical Center) bond n-propyl n-butyl n-pentyl n-hexyl n-heptyl n-octyl bond n-propyl n-butyl n-pentyl n-hexyl n-heptyl n-octyl ClC2C3 C2ClHll C2ClH12 C2C3H31 C2C3H32 C2C3H33 c2c3c4 C3C2H21 C3C2H22 C3C4H41 C3C4H42 C3C4H43 c3c4c5 C4C3H31 C4C3H32 C4C5H51 C4C5H52 C4C5H53 C4C5C6 C5C4H41 C5C4H42 C5C6H61 C5C6H62 C5C6H63 C5C6C7 C6C5H51 C6C5H52 C6C7H71 C6C7H72 C6C7H73
113.00 120.19 120.48 111.02 111.18 110.98 108.95 109.62
113.22 120.51 120.22 109.14 109.16 112.91 108.82 109.49 1 1 1.19 111.16 111.22 109.44 109.60
113.18 120.48 120.24 109.16 109.15
113.18 120.51 120.24 109.11 109.11
113.18 120.49 120.23 109.10 109.12
113.18 120.48 120.23 109.11 109.12
C6C7C8 C7C6H61 C7C6H62 C7C8H81 C7C8H82
113.04 109.21 109.21 111.16 111.15 C7C8H83 111.28 113.23 113.19 113.19 113.19 C8C7H71 109.36 108.89 108.88 108.89 108.89 C8C7H72 109.35 109.55 109.56 109.56 109.55 HllClC2C3 -160.74 -159.78 -160.15 -159.80 -160.01 -160.04 109.34 109.34 109.30 109.30 ClC2C3H32 -179.30 109.32 109.33 109.28 109.28 ClC2C3C4 -179.29 -179.26 -179.30 -179.30 -179.29 H21C2C3H33 -56.87 112.98 113.30 113.26 113.26 H21C2C3C4 -56.77 -56.78 -56.83 -56.82 -56.81 109.48 109.36 109.36 109.36 ClC2C3H31 -59.38 -57.34 -57.27 -57.29 -57.30 -57.29 109.30 109.54 109.54 109.54 C2C3C4H43 179.97 111.27 109.31 109.31 109.26 C2C3C4C5 180.01 179.99 179.97 180.04 111.15 109.31 109.31 109.27 C2C3C4H41 59.91 57.96 57.91 57.88 57.94 111.15 C3C4C5H53 180.00 113.03 113.34 113.30 C3C4C5C6 179.97 179.97 179.96 109.37 109.22 109.28 109.28 C3C4C5H51 -59.94 -57.98 -57.95 -57.96 109.35 109.20 109.26 109.26 C4C5C6H63 180.00 111.16 109.32 109.32 C4C5C6C7 179.98 180.02 111.16 109.31 109.31 C4C5C6H61 59.94 57.94 57.93 111.27 C5C6C7H73 180.0 113.03 113.35 C5C6C7C8 179.98 109.35 109.21 109.27 C5C6C7H71 -59.94 -57.97 109.36 109.22 109.28 C6C7C8H83 179.99 111.28 109.31 C6C7C8H81 59.92 111.15 109.31 6 14.15 13.94 14.04 14.00 14.05 14.02 111.15 109.35 109.35
TABLE I V UHF/6-31C* Optimized Bond Lengths (A) for Alkyl Radicals (B-CC Eclipsed to Radical Center) bond n-propyl n-butyl n-pentyl n-hexyl n-heptyl n-octyl bond n-propyl n-butyl n-pentyl n-hexyl n-heptyl n-octyl 1.086 1.088 1.089 C1C2 1.501 1.501 1.501 1.501 1.501 1.501 C5H51 1 .oT9 1.086 1.088 1.089 ClHll 1.076 1.076 1.076 1.076 1.076 1.076 C5H52 1.089 1.086 ClH12 1.076 1.076 1.076 1.076 1.076 1.076 C5H53 C2C3 C2H2l C2H22 c3c4
1.537 1.087 1.087
C3H31
1.086 1.086 1.086
C3H32
C3H33 c4c5 C4H41 C4H42 C4H43 C5C6
1.539 1.088
1.088 1.528 1.088 1.088 1.086 1.086 1.086
1.539 1.088 1.088 1.530 1.088 1.088
1.539 1.088 1.088 1.530 1.088 1.088
1.539 1.088 1.088 1.530 1.088 1.088
1.539 1.088 1.088 1.530 1.088 1.088
1.528 1.088 1.088
1.530 1.089 1.089
1.530 1.089 1.089
1.530 1.089 1.089
1.528
1.530
1.530
C6C7 C6H6 1 C6H62 C6H63 C7C8
C7H71 C7H72 C7H73 C8H8 1 C8H82
C8H83
Barriers for Internal Rotation. The barriers for internal rotation about the a-, @-, and 7-C-C bonds for the n-alkyl radicals were investigated using the 8-CH eclipsed conformer of the n-hexyl radical as an illustrative example. These studies are important because an ultimate goal is to extend these studies to long chain molecules, i.e., polymers, consequently an understanding of rotational barriers in model systems such as the n-alkyl radicals studied here will provide a framework for subsequent studies. In this report, rotational barriers for the @-CHeclipsed conformer of the n-hexyl radical is considered as an illustrative example, and rotations about the a-, @-, and 7-C-C bonds are discussed, and these results are summarized in Figures 5-7. In Figure 5 the barrier for rotation about the a-CC bond is shown for the n-hexyl radical for various angles of a. To generate the rotational potential function, the geometry of the radical was reoptimized at the various angles of a. No imaginary frequencies were calculated a t all minima, while for structures at the top of the barriers, one imaginary frequency was obtained for each. The optimized configuration with the lowest relative total energy has the C 2p orbital containing the unpaired electron eclipsed to a 8-C-H bond and is assigned the relative angle of 0'. A complete 360° rotation about C1-C2 results in a 6-fold barrier but is completely described from 0 to 1 80°, as shown in Figure 5 . There are two relatively low minima at 0' (or 180') and 120'
1.086 1.086 1.086
1.528 1.088 1.088 1.086 1.086 1.086
1.530 1.089 1.089 1.528 1.088 1.088 1.086 1.086 1.086
corresponding to two @-CHeclipsed conformers, and one higher minimum corresponding to the @-CCeclipsed conformer. Thus, interconversion between any of the conformers takes place readily. We note that in the closed shell analogs of some of the radicals reported here, Le., up to n-pentane, correlation has played a significant role in determining the conformational potential surface.'O We have therefore additionally investigated the barrier for rotation about the a-CC bond at the MP2 level of theory using the 6-3 1G*basis set. The torsional potential generated at MP2 is qualitatively identical to theSCF torsional potential shown in Figure 5. At MP2, the @CHeclipsed conformer is 114 cal/ mol lower in energy than the @CCeclipsed conformer, compared to 1 16 cal/mol at SCF. The two lower lying minima are separated by a barrier of 176 cal/mol and are bracketed by two slightly higher barriers, 2 18 cal/mol. The conformational surface generated at MP2 is therefore quite similar to SCF, a t least for a rotations, and on this basis the remainder of the torsional potentials discussed here for the n-alkyl radicals will be at the SCF level of theory. In Figure 6 the barrier for internal rotation about C2-C3, the 8-CC bond, is shown for various angles of j3. For these studies, the molecule was partially reoptimized as a function of torsional potential. Thus thedihedralangle H21-C2-C3-H31 (see Figure 1, n-hexyl) was varied to impose the &rotation, and two dihedral
10698
Pacansky et al.
The Journal of Physical Chemistry, Vol. 97, No. 41, 1993
UHF/6-31C* ODtimized Bond Angles (degree) for Alkyl Radicals (8-CC EcliDsed to Radical Center)
TABLE V
~
bond
n-propyl n-butyl
ClC2C3 C2ClHll C2C1 H 12 C2C3H3 1 C2C3H32 C2C3H33 c2c3c4 C3C2H21 C3C2H22 C3C4H41 C3C4H42 C3C4H43 c3c4c5 C4C3H31 C4C3H32 C4C5H51 C4C5H52 C4C5H53 C4C5C6 C5C4H41 C5C4H42 C5C6H61 C5C6H62 C5C6H63 C5C6C7 C6C5H51 C6C5H52 C6C7H7 1 C6C7H72 C6C7H73
113.15 120.32 120.35 111.03 110.93 111.03 108.94 108.92
n-pentyl n-hexyl n-heptyl n-octyl
113.43 120.45 120.41 109.18 109.19
113.37 120.40 120.40 109.18 109.19
113.37 120.40 120.42 109.15 109.14
113.38 120.45 120.42 109.14 109.15
113.37 120.41 120.43 109.13 109.15
112.71 108.80 108.77 111.17 111.16 111.23
113.02 108.85 108.85 109.32 109.32
113.00 108.85 108.86 109.32 109.32
112.98 108.88 108.84 109.27 109.28
112.98 108.85 108.86 109.28 109.28
109.60 109.60
112.99 109.46 109.46 111.26 111.15 111.15 109.36 109.37
bond C6C7C8 C7C6H61 C7C6H62 C7C8H81 C7C8H82 C7C8H83 C8C7H71 C8C7H72 HllClC2C3 ClC2C3H33 ClC2C3C4 H21C2C3H33 H21C2C3C4 ClC2C3H31 C2C3C4H43 c2c3c4c5 C2C3C4H41 C3C4C5H53 C3C4C5C6 C3C4C5H51 C4C5C6H63 C4C5C6C7 C4C5C6H61 CSC6C7H73 C5C6C7C8 C5C6C7H71 C6C7C8H83 C6C7C8H8 1
113.30 109.53 109.51 109.31 109.31
113.27 109.52 109.52 109.33 109.31
113.26 109.53 109.53 109.27 109.27
113.03 109.22 109.22 111.16 111.16 111.27
113.34 109.28 109.29 109.31 109.32
113.30 109.29 109.29 109.32 109.32
113.03 109.22 109.21 111.28 111.16 111.16
113.35 109.27 109.27 109.31 109.32 6
109.35 109.31
n-propyl n-butyl
n-pentyl n-hexyl n-heptyl
n-octyl
82.15
81.52
8 1.09
82.07
113.04 109.21 109.21 111.15 111.15 111.28 109.35 109.35 8 1.30
180.01
180.00
180.08
179.99
180.02
-57.77 -57.95 180.00
-57.84 -57.92
-57.75 -57.81
-57.83 -57.92
-57.81 -57.89
59.96
179.99 57.95 179.99
179.99 57.92
180.03 57.95
180.01 57.90
-59.95
179.98 -57.98 180.00
180.03 -57.88
180.00 -57.9 1
180.02 57.98 180.01
180.00 57.92
~ ~ . . .
109.35 109.36
81.61 179.99 -57.91 -59.95
59.94
-59.93 14.56
13.82
14.07
120
180
14.13
13.95
180.0 1 -57.94 180.00 59.94 13.97
0.40
I
0 00 30
0
60
t H7I
*21
120
90
Angle, degrees HI)
H2I
H12
"21
"22
Hll
1122
150
180
t *I)
Figure 5. UHF/6-31G* torsional potential for a rotation of the 8-CH eclipsed conformer of the n-hexyl radical. The molecule is reoptimized at each point.
angles C2-C3-H31-C4 and H32-C3-H31-C4were frozen to prevent re-optimization to the lowest energy conformer, i.e., the n-hexyl radical shown in Figure 1. All other parameters were free to reoptimize. The calculations predict a 3-fold barrier that is relatively steep in energy. The relative low minimum, labeled A in the figure, corresponds to the optimized geometry of the n-hexyl radical with the radical center eclipsing a P-CHbond. In this conformation, the carbon atoms labeled C1 and C4 are trans to the rotation axis C2C3. There are two other relatively low minima
0
60
240
300
360
Angle, degrees
Figure6. UHF/6-31G* torsional potential for the@rotationofthe&CH eclipsed conformer of the n-hexyl radical. The molecule is partially reoptimized at each point, as described in the text.
a t 120and 240°,labeled C and E in the figure, and these structures correspond to gauche conformations of C1 with C4. The conformational interconversion between trans and gauche are separated by a relatively steep barrier of 2.5 kcal/mol, labeled B and F in Figure 6 . The interconversion between the two gauche conformers are separated by a barrier of 5.5 kcal/mol, labeled D in Figure 6 . The conformer at D has C1 and C4 cis to each other across the C2C3 bond and, consequently, the steric interactions due to a semirigid rotation causes the barriers to be
The Journal of Physical Chemistry, Vol. 97, No. 41, 1993 10699
Scission Reaction of Primary Alkyl Radicals
10
t
D
2
0
0
60
120
180
240
300
360
Angle, degrees
Figure 7. UHF/6-3 1G*rigid torsional potential for they rotation of the
b-CH eclipsed conformer of the n-hexyl radical. rather steep. In these structures, interconversion is predicted to be negligible under these conditions. In Figure 7 the barrier for internal rotation about the -/-CC bond, C3C4, is shown as a function of angle. The potential function generated here is completely rigid as the molecule was not re-optimized at each angle. As with 0 rotation, the calculations predict a 3-fold barrier that is relatively steep in energy. The relative low energy minimum, labeled A in the figure, corresponds to the optimized geometry. In this conformation, the carbon atoms labeled C2 and C5 are trans to the rotation axis C3C4. There are twoother relatively low minima at 120and 240°, labeled C and E in the figure, and these structures correspond to gauche conformations of C2 with C5. Theconformationalinterconversion between trans and gauche are separated by a relatively steep barrier of 1.7 kcal/mol, labeled B and F in Figure 7. The interconversion between the two gauche conformers are separated by a barrier of 7.7 kcal/mol, labeled D in Figure 7. The conformer at D has C 2 and C5 cis to each other across the C3C4 bond, and consequently, the steric interactions due to a rigid rotation causes the barriers to be rather steep. In these structures, interconversion is predicted to be negligible under these conditions. In summary, the a-, 0-, and y-rotation barriers teach us that (1) rotation about the a-CC bond has a very small barrier and (2) rotations about the 0-CC and y-CC bonds are similar to barriers observed in alkanes, -3 kcal/mol, but do get large from the nonbonded interactions between groups further down the chain, a consequence of the rigid rotation. B-CH and 6-CC Bond Scission Reactions. 0-CH and 8-CC scission reactions are central in polymer chain degradation, and their energetics merit further attention. To investigate these aspects, geometry optimizations and second derivatives were obtained on the molecules summarized in Table VI. Their total and zero-point energies are tabulated in Table VI, and some of the optimized structures are shown in Figure 8. The AE, defined below, for some 0-CH and 0-CC scission reactions are summarized in Table VII. These, of course, correspond to the AH for the reaction at T = 0 K.
Figure 8. HF/6-31G* optimized geometries for (a) ethene; (b) 1-butene; (c) 1-propene;(d) 3-pentylradical; (e) 4-heptylradical;(f) n-heptyl radical where the central methylene unit is oriented near the radical center; (9) n-undecyl radical where the central methylene unit is oriented near the radical center. All open-shell structureswereoptimized using unrestricted wave functions, and the spin contamination S2was 0.76 for all cases. For
all molecules, analytical frequency calculations were performed and no imaginary frequencies were calculated.
TABLE VI: RHF and UHF/6-31G+ Total Energies for Optimized Alkyl Molecules and Radicals total zero-point energy energy molecule (hartrees) (kcal/mol) H' -0.498 233 0 -78.031 72 34.3720 cH24.H~ -117.071 47 53.6236 CH3CH=CH2 72.96443 -156.106 08 CH,CH2CH=CH2 -195.705 17 97.9219 [CH3CH212CH2' -273.774 15 [CH&H2CH2]2CH2' 136.2007 -429.9 13 52 212.7318 [CHa(CHz)412CH2' -273.767 00 n-heptyl (Figure 8f) 136.3113 -429.900 50 n-undecyl (Figure 8g) 212.7964 For the 0-CH scission reactions, the conformers chosen for the ethyl, propyl, and butyl radicals have their respective carbon 2p orbitals containing the unpaired electron eclipsed with the hydrogen atom on the adjacent or Bcarbon atom, to facilitate the reaction. For the 8-CH scissions of the ethyl radical to ethene and a hydrogen atom, the propyl radical to propene plus hydrogen atom and the butyl radical to butene plus hydrogen atom, respectively, the AE (UHF) are 36.8, 33.3, and 33.6 kcal/mol, respectively. The decomposition of propyl to propene plus hydrogen was additionally computed a t MP2, giving a AE of 31.9 kcal/mol, similar to the S C F result. These values are the differences in total energies between product and reactant, corrected for zero-point energies. Kerr1* has measured the decomposition reactions of C-H rupture of alkanes and have reported activation energies of 40.9 and 37.0 kcal/mol for the 0-CH scission of the ethyl and propyl radicals to ethene and propene, respectively. Their respective back reactions, Le., ethene plus hydrogen atom and propene plus hydrogen atom to yield the ethyl and n-propyl radicals are 3.0 kcal/mol, respectively, thus the AE (UHF) values from experiment are 37.9 and 34.0 kcal/ mol, respectively. These values compare favorably with the calculated values presented above for the same reactions. In 0-CC scission reactions, the conformers chosen for the radicals which split toanother alkyl radical and ethenecorrespond
10700 The Journal of Physical Chemistry, Vol. 97, No. 41, 1993
TABLE VII: HF/6-31G* Difference in Total Energies with Zero-Point Correction reactant product AE(ca1c) (kcal/mol) 36.78 CH3CH2 33.32, 31.94 (MP2) CH3CH2CH2B-CH 33.62 CH3CH2CH2CH2&CH 20.09 CH3CH2CH2 8-CC 19.19 CH3CH2CH2CH2j3-CC 19.78 CH3[CH2]2CH2CH28-CC 19.68 C H ~ [ C H Z ] ~ C H 8-CC ~CH~ 19.73, 19.27 (MP2) CH,[CH2]4CH2CH2 &CC 19.73 C H ~ [ C H ~ ] J C H ~B-CC CH~ -2.12, -2.22 (MP2) CH~[CHZI~CH~CH~ -4.98 n-heptyl (Figure 8f) -8.24 n-undecyl (Figure 8g)
Pacansky et al.
AE(exptl1) (kcal/mol) 37.9 34.0 23.5 20.1
mittantly, with the latter eclipsing the adjacent C-H bond, is 2.3 to the ones which have their carbon 2p orbitals containing the kcal/mol higher in energy relative to the straight chain n-heptyl unpaired electron eclipsed to the adjacent or j3 C C bond. For the radical encountered in Figures 1 and 2. The difference in the j3-CC scission reactions listed in Table VII, the difference in total total energies, AE,for the hydrogen shift reactions are summarized energies (corrected for zero-point contributions) AE are =19-20 in Table VII, and we note that they are negative. kcal/mol and appears to reach an asymptotic value after n = 1, Let us consider the isomerization and C-C rupture of the under these conditions. K e d 1 has measured the activation energy n-pentyl radical, summarized in Table VII. Among the two for C-C rupture of the n-propyl and n-butyl radicals to ethene processes possible, the AE for isomerization, Le., a 1,3-hydrogen and methyl, and ethene and ethyl, as 31.4 and 28.7 kcal/mol, shift, is negative, while the AE for bond rupture of the n-pentyl respectively, while the reverse reactions are 7.9 and 8.6 kcal/mol, radical is positive. Thus, isomerization proceeds to lower energy respectively. Thus the experimental AE (UHF) values are 23.5 state along the reaction path seperated by an activation energy and 20.1 kcal/mol, consistent with values calculated from theory barrier, while bond scissioning and alkyl elimination proceeds to (Table VI). The energy penalty associated with losing an alkyl a higher energy state. At the SCF and MP2 level of theory, the fragment is much less than losing a hydrogen atom and reflects 1,3-hydrogen shift in n-pentyl is predicted to have a A E of -2 the difference between the C-H and C-C bond dissociation kcal/mol, much smaller than the 20 kcal/mol required for alkyl energies. elimination. The 1,Chydrogen shift in n-heptyl, Figure 8f, has Isomerization Reactions. Kossiakoff and Rice12have proposed a calculated (SCF) A E of -5 kcal/mol, and a 1,5-hydrogen shift that the activation energy for isomerization of long-chain alkyl in the n-undecyl radical, Figure 8g, has a A E of -8 kcal/mol radicals may be much less than the activation energy for their (Table VII). Thus, as the radical becomes larger and more decomposition. Subsequently this was experimentally confirmed flexible, the AE values decrease. The calculated AE values can by isolating both isomerization and decomposition products of alkyl radicals and looking at their product d i s t r i b ~ t i o n s . l ~ - ~ ~ serve to illustrate the important effect conformations of a Activation energies for isomerization of alkyl radicals can vary particular chain has on AE. For example, a 1,4-hydrogen shift in the n-heptyl radical having the straight-chain conformation, greatly, from =6 to 35 kcal/mol, depending upon the system." Figure 1, has a A E of +2.7 kcal/mol compared to -2 kcal/mol It has been found experimentally that isomerization does proceed for the corresponding 1,4-hydrogen shift in the n-heptyl conformer with n-pentyl and also alkyl radicals larger than n-pentyl but not shown in Figure 8f. with n-butyl.14 For example, a 1,2-hydrogen shift in the n-propyl radical has a gas phase activation energy of 35 kcal/mol,Il Conclusions rendering the competing methyl elimination a more favorable reaction. Conversely, 1,4- and 1,5-hydrogen isomerization of HF/6-3 lG* optimized geometries were reported for n-alkyl alkyl radicals are considered to be common reactions in many radicals from n-propyl to n-octyl in two conformations, one where chemical systems, and proceed with activation energies of = l o the radical carbon 2p orbital housing the unpaired electron was kcal/mol, making isomerization the more favorable competing eclipsed to a j3-CH bond, and another where the orbital was reaction with alkyl elimination.11 The lowering in the activation eclipsed to a 8-CC bond. In all cases, the8-CH eclipsed conformer energies of the larger hydrogen shifts is attributed to less strain was =loo-200 cal/mole lower in energy than the 8-CC eclipsed of the ring formed in the transition states. conformer. The geometry about the radical center was nonAs stated in the Introduction, alkyl radicals play essential roles planar by approximately 14O, indicative of some s character in in polymer formation, stability, and degradation, and thus we the carbon p orbital containing the unpaired electron. In all have investigated structural models here of suitable length, up cases, the eclipsed j3-CH and j3-CC bond lengths were longer to 11 carbon atoms (Figure 8g), using suitably flexible basis sets than the corresponding noneclipsed @-bonds, attributed to a (6-31G*) to obtain reliable data. We now investigate some hyperconjugative interaction. Potential functions for internal isomerization reactions of long-chain radicals to obtain inforrotation about the a-,8-, and y-bonds revealed the following: mation on their energetics and how conformation may effect AE. rotation about a-CC bonds was almost free but rotation about Thus the difference in total energies for some isomerization j3- and y-bonds had barriers of -3 kcal/mol and did get large reactions were investigated theoretically for the following: 1,3from the nonbonded interactions between groups further down hydrogen shift for the n-pentyl radical, a 1,4 shift for the n-heptyl the chain as a result of rigid rotation. Scissioning of 8-CH and radical and a 1,6 shift for the n-undecyl radical. For the latter j3-CC bonds and isomerization reactions for n-alkyl radicals were two, the central methylene unit was oriented such that it was in calculated and compared with experimental data. The AEvalues close proximity to the radical site at the end of the chain, thus for C-H rupture were of the order of 33 kcal/mol, while for C-C these two structures were additionally optimized and their scissioning, AE = 20 kcal/mol. For 1,3- and 1,4-, and 1,5structures are shown in Figure 9f,g. Note that the hydrogen hydrogen isomerization reactions of some n-alkyl radicals, the atom attached to the central methylene unit is in close proximity AE values became increasingly negative as flexibility was to the half-filled p-orbital at the end of the chain. The total introduced into the straight chains. energy for the n-heptyl radical optimized at such a geometry, References and Notes where the central methylene unit is in close proximity to the carbon 2p orbital containing the unpaired electron and, conco( 1 ) Leathard, D. A.; Purnell, J. H. Ann. Reu. Phys. Chem. 1970, 197.
Scission Reaction of Primary Alkyl Radicals (2) Hoyle, C. E.; Kinstle, J. F. Radiation Curingof Polymeric Materials; ACSSymposiumScrits;American ChemicalSociety: Washington, DC, 1989; p 417. (3) Schnabel, W. Polymer Degradation: Principles and Practical Applications; Macmillan Publishing: New York, 1981. (4) Pacansky. J.; Koch, W.; Miller, M. D. J . Am. Chem. Soc. 1991,113, 317. ( 5 ) Gaussian 88; Frisch, M. J.; Head-Gordon, M.; Schlegel, H. B.; Raghavachari, K.; Binkley, J. S.;Gonzalez, C.; Defrccs, D. J.; Fox, D. J.;
Whiteside, R. A.; Seeger, R.; Melius, C. F.;Baker, J.; Kahn, L. R.; Stewart, J. J. P.; Fluder, E. M.; Topiol, S.; Pople, J. A.; Gaussian, Inc.: Pittsburgh, PA. (6) Hariharan, P. C.; Pople, J. A. Chem. Phys. Letr. 1972, 66, 217. (7) Alchemy 11, Tripos Associates, Inc., 1988. (8) Pacansky, J.; Yoshimine, M. J . Phys. Chem. 1985, 89. 1880. Pacansky, J.; Liu, B.; Defrees, D. J . Org. Chem. 1986,51,3720. Honjou, N.;
The Journal of Physical Chemistry, Vol. 97, No. 41, 1993 10701 Yoshinime, M.; Pacansky, J. J . Phys. Chem. 1987,91,4455. Schubert, W.; Yoshimine, M.; Pacansky, J. J . Phys. Chem. 1981,85, 1340. (9) Scarsdale, J. N.; Van Alsenoy, C.; Schafer, L. J . Mol. Struct. 1982, 86, 277. (10) Aljibury, A. L.; Snyder, R. G.; Straws, H. L.; Raghavachari, K. J. Chem. Phys. 1986,84,6872. (11) (a) Kerr, J. A.; Lloyd, A. C. Q.Rev. 1968,22, 549. (b) Kerr, J. A. in Free Radicals, Kochi, J. K., Ed., John Wiley t Sons: New York, 1973; Vol. 1, pp 1-36. (12) Kossiakoff, A.; Rice, F. 0. J . Am. Chem. SOC.1943,65, 590. (13) Hardwidge, E. A.; Larson, C. W.; Rabinovitch, B. S.J. Am. Chem. SOC.1970, 92, 3278. (14) Endrenyi, L.; LeRoy, D. J. J . Phys. Chem. 1966, 70, 4081. (15) Watkins, K. W.; Ostreko, L. A. J . Phys. Chem. 1969, 73, 2080.
