J. Phys. Chem. 1984,88, 4069-4073
4069
Calculation of the Frequencies and Intensities in the Infrared Spectra of Matrix-Isolated tert-Butyl Radical and Isobutane B. Schrader,? J. Pacansky,* IBM Research Laboratory, S a n Jose, California 95193
and U. Pfeiffer Institut fur Physikalische und Theoretische Chemie, Universitat Essen, D 4300 Essen, West Germany (Received: January 3, 1984; In Final Form: February 23, 1984)
The IR spectrum of the pyrolysis product of azoisobutane has been shown to yield the matrix-isolated tert-butyl radical. In support of this its spectrum has been simulated by a normal-coordinate calculation combined with a calculation of the infrared intensities of all vibrations by a modified INDO open-shell procedure. For comparison, the frequencies and infrared intensities of the isobutane7moleculehave been calculated by using the INDO closed-shelloption and the force field of Snyder and Schachtschneider. Both observed spectra are well reproduced, showing that the method of simulation is working satisfactorily for molecules with both closed and open shells. The pyramidal deformation vibration of the tert-butyl radical is calculated to have a low intensity and to have a band center at 158 cm-', below the limit of the observed matrix spectrum at 250 cm-I. This is in contrast to the same vibration in the ethyl radical which is calculated and observed to be the most intense vibration in the spectrum at 540 cm-', but'it is in accordance with the expectations concerning the properties of primary, secondary, and tertiary radicals.
Introduction The question of the structure of the radical center in alkyl radicals and especially in tert-butyl radical has been the subject of numerous experimental and theoretical papers. New ab initio as well as studies on the temperature dependence of 13Chyperfine splitting of the central atom3 for the tert-butyl radical were in favor of a nonplanar structure. Since vibrational spectra are a sensitive indicator of molecular structures, the infrared spectra of the matrix-isolated alkyl radicals have been inve~tigated.~,~ There are only a few investigations of vibrational frequencies of free radicals, even fewer calculations of force constants,6aand infrared intensities of free radicals.6b Therefore, in addition to an ab initio calculation of infrared frequencies,' a combined frequency and intensity calculations has been carried out for the ethyl radical, in order to make better use of the second dimension in the infrared spectrum, the intensity of the vibrations. This paper is intended to investigate further the applicability of this method both for stable molecules and for radicals by a normal-coordinate and intensity calculation of the two related molecules isobutane and the tert-butyl radical. The reason for taking these two molecules is that the force field of isobutane is well established9 so that a good basis is supplied for the transfer and adjustment of the force constants to the tert-butyl radical even-as is the case-when the number of reliable frequencies is smaller than the number of force constants used in the calculation. Our experience has shown10-12,16 that a combination of a normal-coordinate calculation with a CNDO calculation according to the Segal and Klein procedurel3 satisfactorily reproduced infrared intensities and, by a modified procedure, even the Raman intensities. In order to reproduce the infrared intensities of radicals properly we have combined the normal-coordinate calculation with the INDO procedure, since it was developed specially to improve the unpaired spin di~tribution.'~ The aim of the calculation was to support the view that the observed IR spectrum is due to the tert-butyl radical and that its structure is in accordance with the predictions of the ab initio calculation. A further proof of the calculated force field may be, of course, the comparison of the force constants typical for the ethyl radical with those of tert-butyl. Finally, the intensity calculation for both molecules, isobutane and tert-butyl radical, is intended to show On sabbatical leave from the Universitat Essen, Institut fur Physikalische and Theoretische Chemie, D 4300 Essen, West Germany. 0022-365418412088-4069$01.SO10
TABLE I: Force Constants Used for the Calculation of the Infrared Spectra of Isobutane and the tert-Butyl Radical" isobutane tert-butyl name no. no. ethvl 4.387 1 4.700 5.442 4.645 2 4.699 4.633 4.645 3 4.330 4.385 4.534 0.540 0.540 4 0.540 0.645 5 0.535 0.585 0.532 0.657 1 .OS4 6 1.084 0.024 0.024 7 0.024 0.101 8 0.101 0.043 0.060 9 0.043 0.416 0.382 10 0.328 FRB l2 FRt 13 0.079 1 0.417 0.417 FRc$ l4 Fss 15 -0.012 2 -0.012 0.000 16 0.012 Frr 17 -0.041 3 -0.041 18 -0.031 19 0.127 20 -0.005 21 0.002 22 0.009 23 0.049 14 0.049 -0.052 15 -0.052 q# 24
$
3
$
"Units of mdyn 8,-' (100 N m-I), mdyn rad-' mdyn 8, rad (10-l8 J rad-*).
N rad-'), and
if the calculated intensities may be of help during the process of the assignment of the observed to calculated vibrations and the (1) R. E. Overill and M. F. Guest, Mol. Phys., 41, 119 (1980). (2) M. Yoshimine and J. Pacansky, J. Chem. Phys., 74, 5168 (1981). (3) D. Griller, K. U. Ingold, P. J. Krusic, and H. Fischer, J . Am. Chem. SOC.,100, 6750 (1978).
(4) J. Pacansky, D. W. Brown, and J. S. Chang, J . Phys. Chem. 85, 2562 (1981). (5) J. Pacansky and J. S. Chang, J. Chem. Phys., 74, 5539 (1981). (6) (a) L. A. Kotorlenko and S.A. Samoilenko, Russ. Chem. Rev. (Engl. Traml.),46,337 (1977); (b) J. H. Newton and W. B. Person, J . Chem. Phys., 68, 277 (1978); A. Kormornicki and R. L. Jaffe, ibid.,71, 2150 (1979). (7) J. Pacansky and M. Dupuis, J . Am. Chem. SOC.,104, 415 (1982).
0 1984 American Chemical Society
4070 The Journal of Physical Chemistry, Vol. 88, No. 18, 1984 TABLE II: Observed and Calculated Frequencies, Potential Energy Distribution, and Calculated Intensities for the Isobutane Molecule calcd frequency, intensity, Cm-1 potential energy cm2 obsd" calcd species distribution mol-' s-l 2965 2956 0.85K, 0.15Kf 32.445 2958 2956 0.66K, + 0.33Kf 27.635 295 1 2953 0.49K, + 0.51Kf 34.693 2952 (0.123) 1.OOK, 2898 2904 29.789 0.97Kf, 2878 19.286 0.64K, 0.33Kf 2879 2877 2879 8.033 0.64K, 0.33Kf 1473 1475 1.277 0.11H.3 0.85H, 1469 1468 0.657 0.89Hu 0.10KB 1465 1459 0.031 0.93Hu 0.07Hp 1464 0.93Hu 0.07Hp 0.000 1380 1389 0.57Hp 0.042 0.48H, 1376 0.57Hp 0.48H, 1.654 1365 1334 0.22KR + O.O9H, + 1330 0.017 0.12H.3 + 0.63Ht 1189 1181 O.llKR O.lOH, 0.099 0.61Hg 1173 0.32KR 0.34HB 0.169 1170 0.17Hr 984 O.O7K, 0.91Kg 0.000 96 1 951 0.065 0.34KR + 0.53Hp 0.1OH{ 913 917 2.049 0.24Kn 0.71 Hn 0.1 5 H r 796 797 0.88KR 0.12Hp 0.005 415 433 0.211 0.21H.q 0.33Hr O.SSH@ 367 382 0.14Hg 0.91Hm 0.310 l.OOH, 117 0.057 1.OOH, 0.000 114
+
+ + + + + + + +
Schrader et al. TABLE 111: Geometrical Parameters for the tert -Butyl Radical, from Ref 2, for the Numbering of the Atoms" (1-2)R, (2-5)r, A (2-11)r', A (2-1-3)@, deg (1-2-5)Pl, deg (1-2-1 1)P2, deg (6-2-S)a1, deg (6-2-1 1)a2, deg pyramidal angle, deg
1.502 1.084 1.091 118.4 11 1.4 111.5 107.1 108.0 7.4
"See Figure 3.
TABLE I V Observed and Calculated Frequencies, Potential Energy Distribution, and Calculated Intensities for the tert-Butvl Radical calcd frequency, intensity, cm-I potential energy cmz obsd" calcd species distribution mol-' s-l 297 1 0.99K, 47.447 2966 O.99Kr 0.000 2931 2933 0.88K, 0.1 lKf 29.716 2931 2933 0.88K, + O.llK+ 14.416 2825 2833 17.316 O.lOK, + 0.88Kf 2825 2833 O.lOK, + 0.88Kf 17.631 1455 1458 0.08HP 0.89H, 0.963 1455 1458 O.93Hm+ O.06HB 0.312 1454 0.95H, + 0.05HP 0.069 1375 1453 0.06Hp 0.94H, 0.000 1371 1368 0.37H, 0.34HP + 3.441 0.1OKR 0.14FRR 1367 1330 0.046 0.58Hu + 0.52H.3 0.14FRR 1279 1261 0.69KR + 0.29H, + 0.084 0.34HB 0.17H+ 0.33F~~ " Reference 9. 992 1003 O.06Ha + 0.88Hg 0.025 0.25KR + 0.66Hp 925 0.307 adjustment of the force constants. 904 O.O6K, + 0.92Hp 0.000 811 904 0.1OKR O.O4H, + 0.086 Calculation of the Frequencies and Intensities 0.84Hg 733 751 0.99KR 0.000 The frequency calculations have been carried out by using the 541 422 0.343 0.21H.3 + 0.85H, modified programs of Shimano~chi.'~ The intensities have been 1.31Hm- 0.37FR+ 158 2.241 calculated by INDO calculations of the molecules distorted ac0.19KR cording to the quantum-mechanical amplitudes of the normal 119 0.99H, 0.270 vibrations. Details are given in the preceding papers.8~10-12~16 0.99H, 115 0.000
+ + +
+
+ + +
+ +
+
+ +
+
+
+ + + +
+
+
+
Zsobutane. In accordance with the calculations of Snyder and Schacht~chneider,~ the Cartesian coordinates of the isobutane molecule have been derived by the assumption that the C-C bond length is 1.540 A and that all C-H bonds are equal, namely 1.093 A, and all angles are tetrahedral with staggered conformation and symmetry C3u.The force field is defined by Figure 1, and the force constants are given in Table I; they are essentially the same as those used by Snyder and Schacht~chneider.~ Only the C-H stretching force constants needed to be modified. The calculated frequencies are compared to the observed frequencies (taken from ref 9) in Table 11. Also listed in Table I1 are the intensities calculated by the closed-shell option of the INDO program, and the potential energy distribution. The observed spectrum of
(8) J. Pacansky and B. Schrader, J . Chem. Phys., 78, 1033 (1982). (9) R. G . Snyder and J. H. Schachtschneider, Spectrochim. Acta, 21, 169 (1969). (10) M: Spiekermann, D. Bougeard, H. J. Oelichmann, and B. Schrader, Theor. Chim. Acta, 54, 301 (1980). (1 1) M. Spiekermann, B. Schrader, A. de Meijere, and W. Liittke, J . Mol. Struct, 77, 1 (1981). (12) B. Schrader, D. Bougeard, and W. Niggemann in "Computational Methods in Chemistry" J. Bargon, Ed., Plenum Press, New York, 1980. (13) G. A. Segal and M. C . Klein, J . Chem. Phys., 47, 4236 (1967). (14) J. A. Pople, D. L. Beveridge, and P. A. Dobosh, J. Chem. Phys., 47, 2026 (1967). (15) T. Shimanouchi, "Computer Programs for Normal Coordinate Treatment of Polyatomic Molecules", The University of Tokyo, Tokyo, Japan, 1968. (16) M. Spiekermann and D. Bougeard, J . Mol. Struct., in press.
"Other observed bands a t 1252, 1205, 1184, and 1129 cm-I.
matrix-isolated isobutane is given in Figure 2, together with the calculated infrared spectrum. Lorentz-type bands are drawn with a half-width of 2 cm-', the area of which is proportional to the calculated intensity. tert-Butyl Radical. The Cartesian coordinates of the tert-butyl radical were transferred from a HONDO calculation, reported by Yoshimine and Pacansky.* In this paper, the ab initio calculations suggest that the radical center is nonplanar with a pyramidal angle of 7.4', with staggered conformation and C,, symmetry. The structural parameted taken for our calculation are given in Table 111. The observed infrared frequencies are taken from the paper of Pacansky and Chang.5 The force field is defined by Figure 3. The force constants adjusted to represent the frequencies of the tert-butyl radical are given along with those for isobutane in Table I. The calculated and observed frequencies and the potential energy distribution are given in Table IV along with the infrared intensities which were calculated by using the open-shell option of the INDO procedure. The calculated intensities are also shown as a spectral diagram in Figure 4. Results and Discussion Zsobutane. As Table I1 and Figure 2 shown, the frequencies and the relative intensities of the calculated infrared spectrum for isobutane are a good simulation of the observed spectrum. The force constants used for this calculation are listed in Table I. They
The Journal of Physical Chemistry, Vol. 88, No. 18, 1984 4071
Matrix-Isolated tert-Butyl Radical and Isobutane ( 1 . 2) R ( 1 - 3) R ( 1 - 4) R
a a a a a
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
a
20
a
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
(2-5) r
( 2 -6) r ( 3 - 7) (3.8) (4-9) ( 4 - 10) 12-11) 13-12) ( 4 . 13) (1 - 14) 5-2-11 6-2-11 5.2-6 7-3-12 8-3.12 7-3-8 9-4.13 10-4-13 9-4-10 5-2-1 6.2-1 11.2-1 7-3-1 8.3-1 12-3-1 9.4.1 10.4-1 13-4.1 14-1.2 14-1.3 14-1-4 2-1-3 3-1-4 4-1.2 2-1 3-1 4-1
r
r r r r' r'
r'
r" a
a (3 3(
p
0 p p 0
r r
5 ,$ ,$ ,$
r r 7
Figure 1. Definition of the force field of isobutane (only the upper right of the matrix is shown).
a 100
%T
0 b
b
%T
3000
2000
1500
1000
500
cm-1 Figure 2. (a) Observed infrared spectrum of argon-matrix-isolated isobutane, after ref 5, mixing ratio: 1/500 at 10 K. (b) Calculated infrared spectrum. The calculated intensities are proportional to the Lorentz-type band area, drawn with a half-width of 2 cm-I.
are taken from Snyder and Schachtschneider's original papersg with the exception of the C-H stretching force constants which are adjusted during the calculation. The calculated infrared intensity for the four infrared-inactive vibrations of the species A2may be regarded as a check of the intensity calculation. Indeed,
three of the four A2 vibrations show an intensity value of 0.0002. The exception is the A2 vibration, v,(CH,), calculated to have a frequency of 2952 cm-' with an intensity of 0.123 cm2 mol-' s-'. This is small compared to the calculated intentsity of the other CH stretching vibrations, (8-34) X 10l6cmz mol-' s-l. The origin
4072
The Journal of Physical Chemistry, Vol, 88, No. 18, 1984
( 5 . 2 - 1 1 ) 01 ( 6 - 2 - 11) 01 ( 5 - 2 - 6 ) OL ( 7 - 3 - 1 2 ) CY ( 8 - 3 - 1 2 ) OL ( 7 - 3 - 8 ) OL ( 9 . 4 - 1 3 ) 01 ( 1 0 - 4 - 1 3 ) OL (9-4-10)a (5-2-1)B (6-2-1)b (11-2-1) (7-3-116 (8-3-1) (12-3-1)p (9-4-1)p (10-4-1)p ( 1 3 - 4 - 1 ) fl 2 - 1 - 3 q5 3 - 1 - 4 q5 4 - 1 - 2 q5 2-1 7 3-1 7 4-1 r
13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
Schrader et al.
4
14 15 15
*r
3
11
5 12 12
15 14 15
15 14
30 31 32
1
33 34 35 36
Figure 3. Definition of the force field of terr-butyl radical.
b
3000
2000
1500
1000
500
cm-1 Figure 4. (a) Observed infrared spectrum of argon-matrix-isolatedtert-butyl radical after ref 5. (b) Calculated infrared spectrum, drawn as in Figure 2.
of this artifact is not yet known. tert-Butyl Radical. A characteristic feature of the infrared spectrum of the ethyl radical is the IR band at 2840 cm-’. If the relatively free rotation about the a-CC bond is neglected, then
it can be showns to belong to the stretching vibration of a C-H bond in the trans position to the unpaired electron of the radical center which is weaker than the other C-H bonds in the gauche positions. This band is equivalent to the so-called Bohlmann band”
Matrix-Isolated tert-Butyl Radical and Isobutane
f
Figure 5. Representation of typical calculated vibrations of the ?err-butyl radical: (a and b) totally symmetric stretching vibration (A,) of the gauche CH bonds at 2933 and the trans bonds at 2833 cm-I, (c) totally symmetric CH, deformation (A,) at 1330 cm-’, (d) totally symmetric pyramidal deformation (A,) at 158 cm-I.
in amines1*or ethers with C-H bonds trans to nonbonded electron pairs. In the tert-butyl radical there are, in accordance with the ab initio calculation,2 three such C-H bonds and indeed the spectrum shows a strong band at 2825 cm-I. Therefore, the C-H bonds in the CH, groups in tert-butyl were represented by two different force constants, the starting values of which were taken from our calculations of the ethyl radical.* They were fitted to the best representation of the observed spectrum with an interaction force constant taken from isobutane, no. 2,3, and 9 in Table I and Figure 3. In principle, there is a danger of misinterpretation when single C-H frequencies of C H 3 groups are discussed, ignoring Fermi resonances. McKean has shown that this danger can be circumvented by using CDzH derivatives.20 Pacansky and Coufalzl have observed the band at 2846 cm-’ for the HCDlCD2 radical under conditions where Fermi resonance and couplings are absent, thus revealing that the new CH stretching frequency is not a manifestation of a resonance. Since this same spectral feature is characteristically observed in the spectra of alkyl radi c a l ~it, ~is reasonable to conclude that it is also free from reso(17) (18) (1977). (19) (20)
F. Bohlmann, Ber., 91, 2157 (1958). E. Flood, P. Pulay, and J. E. Boggs, J . Am. Chem. Sac., 99, 5570
J. Pacansky and H. Coufal, J . Chem. Phys., 72, 3298 (1980). D. C. McKean, Chem. Sac. Reu, 7,399 (1978); D. C. McKean Chem. Cammun., 1373 (1971). (21) J. Pacansky and H. Coufal, J . Chem. Phys., 72, 5285 (1980).
The Journal of Physical Chemistry, Vol. 88, No. 18, 1984 4013 nances or couplings in the tert-butyl radical. The potential energy distribution (Table IV) and Figure 5 reveal that there are indeed two different totally symmetric stretching vibrations of the methyl groups, that of the “gauche” C-H bonds at 2932 cm-I and the other of the “trans” C-H bonds at 2825 cm-’, both with about 85% of the vibration energy on these bonds. The force constant of the C-C bonds was taken as typical for C-C single bonds at sp3 centers, Le., 4.700 mdyn A-‘. The other force constants were transferred from isobutane. The most intense band in the calculated spectrum at 2971 cm-I does not appear to be observed; however, this cannot be decided upon at this time to any degree of certitude, because this region of the spectrum contains a large number of reaction product bands.s During the calculation the deformation force constant H p (no. 5 in Table I and Figure 3) was fitted for the best reproduction of the observed frequencies. As a result, H p developed a value of 0.535, smaller than the medium of the values in ethyl, 0.585 and 0.532, which were already smaller than for saturated hydrocarbons, 0.645. This may be due to the relatively small steric hindrance of C H deformations in tert-butyl. The values of other force constants may be in doubt, since the number of established observed frequencies was too small to make an adjustment possible. The analysis of the vibrational spectra of other isotope-substituted compounds would be helpful for further refinements, especially the Raman spectra of the matrix-isolated radical which are not yet known, unfortunately. We have tried to adjust several force constants describing forces about the radical center by leastsquares-fit procedures. Indeed, we found another set which reproduced the observed frequencies somewhat better than the set given in Table I. However, the calculated intensities in the region 1200-1500 cm-’ changed drastically away from the observed pattern. Therefore, we rejected this set of force constants as physically not acceptable. As is shown in Table IV, there are four bands in the radical spectrum at 1252, 1205, 1183, and 1129 cm-’ which could not be assigned to calculated bands. There remains a probability that these bands belong to other reaction products or may be due to overtones or combinations. This will be a matter of further work. In comparison with the spectra calculated for the ethyl radical, it is surprising that the pyramidal deformation vibration is calculated to have a very low frequency, 158 cm-l, and a weak intensity (2.241 X 1OI6cm2 mol-’ s-’) compared to ethyl for which it is the most intense band at a much higher frequency (26.76 X 10l6 cm2 mol-0’ s-I at 541 cm-I for CH3CHz). However, this dramatic change in intensity is expected because the observed intensity of the pyramidal bending mode decreases from CH,, CH3CH2,to (CH3)2CH.19Thus, the substitution of more methyl groups for hydrogen decreases the intensity of the absorption. The decrease in frequency is mainly due to the increase of the vibrating masses. The calculated frequency of tert-butyl, 158 cm-’, is in very good agreement with the value concluded from ESR result^,^ Le., 150 cm-I (as upper limit); however, it is not yet observed.
Conclusion The calculation of the IR spectrum of tert-butyl radical leads to the following conclusions: The main features of the observed spectrum are reproduced by the calculation which was performed on the basis of the geometry calculated by the HONDO ab initio method and force constants transferred from isobutane and the ethyl radical. Therefore, this supports the observed spectrum and indicates that the HONDO geometry is very probable. Furthermore, it shows that the procedure for the simulation of IR spectra is also suitable for radical spectra. The combination of frequency and intensity calculations seems to be a way of finding physically meaningful sets of force constants from the large number of mathematically acceptable sets. Registry No. Azisobutane, 3896-19-3; tert-butyl radical, 1605-73-8; isobutane, 75-28-5; ethyl radical, 2025-56- 1.
