J . Phys. Chem. 1989, 93, 3474-3479
3474
valve. A tunable pulsed dye laser, pumped by the doubled output of a pulsed Nd:YAG laser, is frequency doubled and focused into the interaction region of the chamber. The same laser beam, in these one-color TOFMS (mass-resolved excitation) experiments, is used to excite the molecules to SI and to photoionize them. Ions are accelerated into a flight tube and detected by a microchannel plate. The laser line width is measured to be 0.2 cm-I: transitions can be measured to 0.1 an-]. Styrene, trans-j3-methylstyrene, 3-methylstyrene, and anethole were all purchased from Aldrich, and 4-ethylstyrene was purchased from Karl Industries; all were used without further purification. The specificaly labeled compound, 3-methyl-d3-styrene, was synthesized as described below. All of the chemicals used were inhibited with a trace of 4-tert-butylcatechol and stored in the dark at 4 'C. The neat samples of these molecules were clear and viscous prior to use (except for anethole, which is a solid at 25 "C). Synthesis of 3-Methyl-d3-styrene (&).I5 To a solution of 3-bromostyrene (5.0 g, 27.3 mmol) and [bis(diphenyl( 1 5 ) Nugent, W. A,; McKinney, R. J. J . Org. Chem. 1985, 50, 5370.
phosphino)propane]nickel(II) chloride (90 mg,0.1 75 mmol) in ether (85 mL) was added dropwise methyl-d3-magnesium iodide in ether (33 mL of a 1.0 M solution, 33 mmol). The mixture was heated under reflux overnight and was quenched with half-saturated NH4CI. Extraction with ether and removal of solvent afforded the crude product which was taken up in methylene chloride, treated with 4-tert-butylcatechol (trace), filtered, concentrated, and distilled into a receiver containing trace amounts of 4-tert-butylcatechol, giving 3-methyl-d3-styrene (2.7 g, 8 1.7% yield) as a colorless liquid. bp C rt (0.05 mm);IH NMR (CDC13) 6 5.18 (d, 1 H, J = 10.9 Hz), 5.70 (d, 1 H, J = 17.5 Hz), 6.66 (dd, 1 H, J = 10.9, 17.5 Hz), 7.01-7.08 (m,1 H), 7.15-7.19 (m, 3 H); I3C NMR (CDC13) 6 20.52 (septet, J = 19.3 Hz), 113.51, 123.35, 126.95, 128.40, 128.58, 136.97, 137.50, and 137.89. Acknowledgment. We thank R. Ferguson, B. LaRoy, and A. C. Lilly for their support and discussion and J. Campbell for obtaining the N M R data. Registry No. 1, 100-42-5; 3, 873-66-5; 4a, 100-80-1; 5, 3454-07-7; 6, 104-46-1; D,, 7782-39-0.
Ab Inltio Calculations of the Electronic Structure and Vibrational Frequencies of the Dichloromethyl Radical and Cation Sherif A. Kafafi* and Jeffrey W. Hudgens* Chemical Kinetics Division, Center for Chemical Technology, National Institute of Standards and Technology, Gaithersburg, Maryland 20899 (Received: August 5, 1988; I n Final Form: November 1 , 1988)
Ab initio molecula_r orbital calculations on the % 'Al (C,) state of the CHC12cation and on the % 2Bl (C,), % ,A' (Q, A 2AI (C,), and C 2B2 (C,) valence states of the CHCI, radical are reported. The qualitative features of the molecular orbital interactions are presented. Using the 6-31G* basis set, we computed optimized structures with the Hartree-Fock , structure. The optimized and second-order Merller-Plesset levels of theory. The optimized structure of the CHC12cation is a C structure of the ground-state radical predicts that the C-H bond lies 15.5' out of the C1-C-CI plane. Frozen core single-point calculations using fourth-order Merller-Plesset theory and the 6-31G* basis set predict that the barrier to inversion in the % ,A' (C,)state of the CHC12 radical is 220 cm-l. Vibrational frequencies for each CHCl, species were computed from the HF/6-3 1G* optimized structures. These calculated frequencies compare favorably with previously reported experimental frequencies.
Introduction In recent years multiphoton ionization, photoelectron, and infrared spectroscopies have furnished an extensive list of vibrational frequencies for dichloromethyl (CHCI,) cations and radicals.'-* In contrast, there are no published theoretical calculations of the CHCl, cation and few calculations of the CHC1, radical,9-ll The ( 1 ) Long, G. R.; Hudgens, J. W. J. Phys. Chem. 1987, 91, 5870. (2) Andrews, L.; Dyke, J. M.; Jonathan, N.; Keddar, N.; Morris, A. J. Am. Chem. SOC.1984, 106, 299. (3) Carver, T. G.; Andrews, L. J. Chem. Phys. 1969, 50, 4235. (4) Rogers, E. E.; Abramowitz, S.; Jacox, M. E.; Milligan, D. E. J . Chem. Phvs. 1970. 52. 2198. (5)Jacox, M. E.; Milligan, D. E. J . Chem. Phys. 1971, 54, 3935. (6) Jacox, M. E. Chem. Phys. 1976, 12, 51. (7) Kelsall, B. J.; Andrews, L. J . Mol. Spectrosc. 1983, 97, 362. (8) Andrews, L.; Dyke, J. M.; Jonathan, N.; Keddar, N.; Morris, A. J . Chem. Phys. 1983, 79,4650. (9) Biddles, I.; Hudson, A. Mol. Phys. 1973, 25, 707. ( I O ) Molino, L. M.; Poblet, J. M.; Canadell, E. J . Chem. SOC.,Perkin Trans. 2 1982, 1217-1221.
~.
~1
~~I
~~
objective of this work is to provide the theoretical framework that can support discussions of vibrational spectroscopy of the dichloromethyl cation and radical. We construct this framework by presenting qualitative molecular orbital theory (QMOT) argument~'*-'~ and ab initio calculations of dichloromethyl cations and radicals. The QMOT arguments outline the principal interactions that cause differences of geometry and normal-mode frequencies among CHCI, species. - The ab initio calculations predict vibrational frequencies for the ground states of CHCI,' and CHC12 radical. In addition, we present calculations for the two lowest excited doublet valence states of planar CHC12radical. Calculations were performed at several levels of theory and basis set size,
~
( 1 1) Luke, B. T.; Loew, G. H.; McLean, A. D. J. A m . Chem. SOC.1987, 109, 1307. ( 1 2 ) Hoffmann, R. Acc. Chem. Res. 1971, 4 , I . ( 1 3) Gimarc, B. M. Molecular Structure and Bonding Academic Press: New York, 1979. (14) Lowe, J. P. Quantum Chemistry; Academic Press: New York, 1978; pp 347-380.
This article not subject to U S . Copyright. Published 1989 by the American Chemical Society
Structure of Dichloromethyl Radical and Cation
The Journal of Physical Chemistry, Vol. 93, No. 9,1989 3475
Computational Details In this study all calculations were performed using the GAUSSIAN 82 program of Pople et al.I5 The electronic properties of CHC1,’ were calculated by using 6-3 1G and 6-3 lG* standard basis setsI5 and the restricted HartreeFock (HF) method. The corresponding unrestricted H F treatments, UHF/6-31G and UHF/6-31G*, were applied to the open shell doublet states of CHC12 radical. The 6-3 1G* bases included a set of d polarization functions on the non-hydrogen atoms. Because U H F wave functions are not eigenfunctions of the total spin operator S2, they are normally contaminated by higher spin states. Spin contamination can be eliminated by using spin projection methodsI6 or performing restricted H F calculations on open shell systems.I7 In U H F calculations that used the 6-31G and 6-3 lG* bases reported in this work, the largest Szvalue for the doublet states studied was less than 0.81. (S2should be 0.75 for a pure doublet.) In view of this small spin contamination, no corrections to the U H F wave functions and energies were performed. Full geometry optimizations were performed on the CHCl, cation and radical to locate their equilibrium ground-state geometries. Minima in the potential surfaces of the various radicals were located by using analytical gradients.I5 Throughout these computations the C-CI bond lengths were assumed to be equal. Symmetry-constrained, C , optimizations on the ground and lowest two excited doublet states of CHC12 radical were also carried out. In this report the reference plane is defined by the carbon and two chlorine atoms. e(C1-C-Cl) is the in-plane angle between the two C-CI bonds, and @ is the dihedral angle between the plane formed by the chlorine and carbon atoms and the axis of the C-H bond. Harmonic vibrational frequencies (HVF) were calculated at the HF/6-31G* level for CHC12+and UHF/6-31G* for CHC12 radical by using analytical second-derivative techniques.I5 HVF‘s are useful in distinguishing minima (all vibrational frequencies are real) and saddle points (one complex frequency) in the potential energy surface. As noted elsewhere,18 harmonic mode frequencies calculated by this procedure are systematically overestimated by 9-13%. In this work the reported theoretical harmonic frequencies have been reduced by 10% to obtain more reasonable agreement with known experimental values. Since the CHCI, radical is nonplanar, it possesses two potential energy minima along the u4 (b,) out-of-plane (OPLA) bending coordinate. Thus, estimates of the frequency of the OPLA vibrational mode based upon the harmonic approximation are inappropriate. To find the energy levels of this double-well potential, we have solved the Hamiltonian for a quartic oscillator with the potential, V = (a@ - bp),after the method described by Laane.Ig The coefficients, a and b, are functions of (1) a,,.,,the equilibrium dihedral angle, (2) re, the C-H bond length, and (3) Bin,, the inversion barrier. The OPLA coordinate is 9 = re sin a, The reduced mass of the u4 (b,) mode for the X ZA’ (C,) CHC12 structure was calculated to be 1.59 amu.,O Because the magnitude of the reduced mass along the u4 normal coordinate changes very little as the geometry becomes nonplanar, this value was adopted for nonplanar structures. Electron correlation was partially accounted for by using second-order Merller-Plesset (MP2) perturbation theory.21 The geometry of CHC12+was reoptimized at the MP2/6-31G* level, and the geometries of the CHCI, radical species were reoptimized at the UMP2/6-31G* level of theory. The symmetry constraints (15) Binkley, J. S.; Frisch, M. J.: DeFrees, D. J.; Raghavachari, K.; Whiteside, R. A.; Schlegel, H. B.; Fluder, E. M.; Pople, J. A. Carnegie-Mellon University, Pittsburgh, PA, 1982. (16) Hameka, H. F.; Turner, A. G. J . Magn. Reson. 1985, 64, 66. (17) Rothaan, C. C. J. Rev. Mod. Phys. 1960, 179, 32. (18) Hehre, W.; Radom, L.; Schleyer, P. R.; Pople, J. A. Ab initio Molecular Orbital Theory; Wiley-Interscience: New York, 1986. (19) Laane, J. Appl. Specfrosr. 1970, 24, 73. (20) Binkley, J. S.; Frisch, M. J.; DeFrees, D. J.; Raghavachari, K.; Whiteside, R. A.; Schlegel, H. B.; Fluder, E. M.; Pople, J. A. Carnegie-Mellon University, Pittsburgh, PA, 1986. (21) Maller, C.; Plesset, M. S . Phys. Reo. 1934, 46, 618.
MO Z
tY
SYMMETRY
23
ab2
22
loa,
e1
3 b , (LL‘MO)
18 17
.
9% 2b,
Figure 1. Seven highest occupied MO’s and three lowest empty MO’s of CHC12+ obtained from a b initio HF/STO-3G calculations.
mentioned above were also applied to these correlation calculations. These optimizations were followed by single-point calculations at the UMP4/6-31G*//UMP2/6-31G* level of theory. The Merller-Plesset calculations to fourth order (MP4) reported in this study have contributions from single, double, and quadruple substitutions from the starting HF determinant. The triple substitutions were excluded from the calculations to reduce the computation time. The core molecular orbitals were not included in all MP4 computations, Le., frozen core (FC) calculations. Hence, the previous notation will be represented by UMP4= FC/6-3 1G*//UMP2/6-3 lG* for open shell species and MP4= FC/6-31G*//MP2/6-31G* for closed shell ones. All computations in this study were performed on a VAX11/785 computer at the National Institute of Standards and Technology Scientific Computing Facility.
The Qualitative Molecular Orbital Description of C H Q Species Qualitative molecular orbital theory (QMOT) arguments have proved useful and successful for predicting the broad outlines of calculation^.^^-'^ They enhance understanding of the relationship between the approximate orbitals we visualize and the detailed results produced by the ab initio calculations. Therefore, in this section we apply QMOT to illustrate the major orbital differences between the CHC12cation and CHC12radicals that influence their geometries and vibrational potential energy surface. First, we will show the valence MO’s of the cation and discuss why CHC12+ favors a planar, C2, structure. Then we use the empty MO’s of the cation to make predictions about the ground-electronic-state geometry of the C2, CHCl, radical and how it differs from that of the C,, ground-state cation. We illustrate why the ground electronic state of the CHCl, radical favors a nonplanar, C, geometry over its planar, C , one. Last, the factors that determine the geometries of the lowest two excited valence states of the C,, CHClz radical are also discussed. The QMOT Description of the CHC12 Cation. Figure 1 illustrates the 10 higher energy molecular orbitals (MO’s 14-23) of the CHC12cation that greatly influence the molecular bonding and overall geometry. These orbitals are constructed from the results of a HF/STO-3G single-point calculation on CHCI,’ constrained to C , symmetry. (The first 13 occupied, u-bonding orbitals, MOs 1-13, which lie at very low energies, are not shown.) For CHC12+MO’s 14-20 are doubly occupied orbitals and MO’s 21-23 are unoccupied. As shown in Figure 1, there are three P MO’s: 17,20, and 21. MO 17 is bonding, M O 20 (HOMO) is
3476 The Journal of Physical Chemistry, Vol. 93, No. 9, 1989 nonbonding, and MO 21 (LUMO) is antibonding. The remaining molecular orbitals are of the u type. MO's 14-16,18, and 19 are aC+, and uczI bonding M O s . The unoccupied MO 22 and M O 23 are antibonding ac-cI MO's. The energy minimum of the CHCI2 cation lies at the planar C2"geometry. This preference for the planar structure is seen by examining the first-order energy change of each occupied molecular orbital in Figure 1 as the C-H bond is rotated slightly above the CI-C-CI plane. As the C-H bond rotates out of the CI-C-CI plane, the bonding overlap of the hydrogen s-orbital with the carbon p,-orbital decreases in the P M O S 14, 15, and 18; and thus, their bonding energies diminish. The orbital energies of a-MO's 16,19, and 20 are unaffected, to first order, by small C-H out-of-plane rotations because a node lies at the C-H bond. The n-bonding orbital, M O 17, is slightly stabilized by out-of-plane rotations as the hydrogen s-orbital increases its bonding overlap with the carbon pr atomic orbital. This stabilization is due mainly to higher order effects. In summary, the bonding of three occupied orbitals decreases, three remain unchanged, and one occupied orbital increases its bonding slightly. Thus, out-of-plane rotation of the C-H bond above or below the CI-C-Cl plane in CHC12+ is destabilizing and CHC12+ should prefer a planar geometry. Additional simple analyses show that all bond stretching and in-plane bending away from the C2, equilibrium structure also increases the total energy. Thus, the potential energy surface along each normal mode possesses a single minimum and each vibrational mode of CHCl2+ can be modeled by a nearly harmonic potential. The QMOT Description of CHC12 Radicals. Adding an electron to CHCI2+yields the CHCI2 radical. This extra electron may occupy any one of the empty, higher energy MO's. Restricting ourselves to the three antibonding levels shown in Figure 1 (MOs 21,22,23) and assuming, for now, a planar C, symmetry for the CHCI, radical, its ground state can be either 2Bl,'A,, or ,Bz Which one of those three doublet states is the lowest in energy for the planar CHCI2 radical? Inspection of Figure 1 reveals that the three empty MO's (21, 22, 23) are antibonding between the carbon and chlorine atoms. The presence of an electron in any of these levels will strongly affect the C-CI bond lengths and C1-C-Cl bond angles. Since x-antibonding interactions are weaker than a-antibonding ~ n e s , ' ~ - I ~ the odd electron will favor occupying the n-antibonding MO 21 over the u-antibonding M O s 22 or 23. Accordingly, planar CHCI, radical is predicted to have a X 2Bl (C2J ground state. QMOT arguments lead to the prediction that the out-of-plane rotations of the C-H bond in the CHCl, radical are less destabilizing compared to those in CHC12+. Therefore, the ground electronic state of the CHC12' radical could have a nonplanar, C, geometry. The behavior of the doubly occupied orbitals, MO's 14-20, is the same as in the cation. But in the CHC12 radical the polarizable frontier orbital, MO 21, will contribute a stabilization energy as the hydrogen atom rotates above the Cl-C-CI plane and the bonding overlap with the carbon px orbital increases. Similarly, M O 17 is also stabilized by the out-of-plane motion of the C-H bond. Because the energy contribution of the frontier orbital could dominate the total energy change for small C-H rotations along the dihedral angle, slightly nonplanar C, structures could lie at lower energy than planar ones. However, as the hydrogen atom rotates appreciably above the CI-C-CI plane, the three destabilizing interactions in u-MO's 14, 15, and 18 should overcome the stabilizing interactions of n-MO's 17 and 21. Therefore, the out-of-plane rotation of the C-H bond in CHCI, radical is less destabilizing than the corresponding ones in CHC1,'. MoLeover, the ground electronic state of CHCl, radical could be of X ,A' symmetry in the C, point group. The orbital energy changes as a function of the dihedral angle, 9, in CHCl, radical will produce a double-minimum potential energy surface with minima at +a, and -arn.In addition, the double-minimum potential energy surface along the out-of-plane bending coordinate of CHC12 radical will cause the v4 (b,) OPLA mode to exhibit irregular vibrational spacings that cannot be modeled with a harmonic potential.
Kafafi and Hudgens TABLE I: Total Energies (hartrees) of the Chloromethyl Cation and Radicals Obtained at Different Levels of Theoryo species
electronic state
CHCI2+ % 'A, (C,)
level of calculation
HF/6-31G HF/6-31G* MP2/6-31G* MP2=FC/6-31G*//MP2/ 6-31G* MP3=FC/6-31G*//MP2/ 6-31G* MP4=FC/6-3 lG*//MP2/ 6-31G* CHCI,' % 2A' (C,) UHF/6-31G UHF/6-3 1G* UMP2/6-31G* UMP2=FC/6-3 lG*//UMP2/631G* UMP3=FC/6-3 lG*//UMP2/631G* UMP4=FC/6-3 lG'//UMP2/631G* CHC12 i< 2B, (C2") UHF/6-31G UHF/6-31G* UMP2/6-3 1G* UMP2=FC/6-3 IG*//UMP2/631G* UMP3=FC/6-31G*//UMP2/631G* UMP4=FC/6-31G*//UMP2/631G* CHC12b A 2AI (C,) UHF/6-31G UHF/6-31G* UMP2/6-3 1G* UMP2=FC/6-3 lG*//UMP2/631G* UMP3=FC/6-3 IG*//UMP2/631G* UMP4=FC/6-3 lG*//UMP2/631G* CHC1,6 2B, (C2J UHF/6-31G UHF/6-31G* UMP2/6-31G* UMP2=FC/6-3 lG*//UMP2/631G* UMP3=FC/6-3 lG*//UMP2/631G* UMP4=FC/6-3 lG*//UMP2/631G*
e
total energy -956.958 -951.053 -957.463 -951.438
064 670 253 206
-951.461 936 -957.468943 -951.288941 -951.358049 -957.150 342 -951.125636 -951.155621 -951.160 092 -951.287 808 -957.356 541 -951.149 141 -951.124356 -951.154 588 -951.159094 -951.1 86 014 -951.231 360 -951.631 918 -951.601 913 -951.635 469 -951.644 121 -951.094434 -951.138 910 -951.549519 -951.525 184 -951.551 203 -951.559082
"All frozen core (FC) results are single-point calculations on optimum geometries obtained from second-order M~rller-Plesset (MP2) computations. *Transition structure.
When the structure of the ,A' radical is constrained to the C, point group, its bond lengths and angles can be compared directly with those in CHC12+. Out-of-phase repulsions between the carbon px and chlorine px atomic orbitals in MO 21 (Figure 1 ) wilJ cause the C-CI bonds to be longer than those in the cation. The X ,B, (C), CHC12 radical should possess a slightly smaller CI-C-CI bond angle because of through-space bonding interactions between the terminal chlorine px orbitals. But because M O 21 does not contribute to C-H bonding, the C-H bond lengths in the radical should be almost the same as in CHC12+. The structures of symmetry constrained, C, excited A 2A1and 'B2 states22 of CHC1, radical will differ also from those in CHC12+. Both excited radicals should have repulsive C-C1 interactions tha_t cause the C-CI bonds to be longer than in the cation. The A 2AI radical should favor a larger CI-C-CI angle because the bonding overlap in MO 22 between the chlorine p-orbitals and the 3 - H lobe increases as the Cl-C-Cl angle increases. But the C ,B2 radical should have a smaller Cl-C-C1 angle so that repulsions between the in-plane carbon p,-orbital with the chlorine p,-orbitals in M O 23 are minimized. As in the (22) The letter order used with the state symmetry assignments is based upon the expectation that the B 2AI (C,) 3s Rydberg state liss in energy between the two lowest valence states labeled in this report as A 2A, and C 2B2.
Structure of Dichloromethyl Radical and Cation
The Journal of Physical Chemistry, Vol. 93, No. 9, 1989 3477
TABLE 11: Optimized Geometrical Parameters at Several Levels of Theory for CHCll Cation, Ground-State Radical, and Ground- and Excited-State C b Transition Structures theory level point group electronic state r(C-H), 8, r(C-Cl), 8, e(Cl-C-Cl), deg 9,, deg
a
CHCI2 Cation 1.0744 1.0784 1.0919
1.6740 1.6208 1.6207
124.10 124.12 124.22
0.0 0.0 0.0
CHC12 Radical 1.115 1.077 1.067 1.0669 1.0702 1.0809
1.72 1.715 1.800 1.7747 1.7124 1.7029
118.0 120.4 116.4 126.32 127.22 126.82
0.0 0.0 15.8 16.2 15.5
CHCI2 (Transition Structure) 1.0647 1.0675 ZBI 1.0771
1.7646 1.7025 1.6926
119.94 120.54 120.78
0.0 0.0 0.0
CHC12 (Transition Structure) 1.0851 1.0799 1.0946
2.01 18 1.9151 1.8520
155.30 155.50 152.00
0.0 0.0 0.0
CHC1, (Transition Structure) 1.0729 1.067 1 1.0746 2B2
1.9953 1.8948 1.8554
100.70 102.68 103.92
0.0 0.0 0.0
HF/6-31G HF/6-3 1G* MP2/6-31G*
c2d C2” c2d
% IA, % IA, % ‘Al
INDO*
CS
UHF/MNDOb UHF/3-21Gc UHF/6-3 1G UHF/6-31G* UMP2/6-31G*
CS
% 2A‘ % 2A‘ % 2Af % 2A‘
CS
% ZAf
UHF/6-3 1G UHF/6-3 1G* UMP2/6-31G*
C2” C2” C2”
2 2B1 2 2BI
UHF/6-3 1G UHF/6-3 1G* UMP2/6-31G*
c, C2” C2”
A 2Al A 2A1 A 2Al
UHF/6-31G UHF/6-3 1G* UMP2/6-31G*
C2” C2”
e 2B2 e 2B2
Reference 9.
CS CS
cs
2 2Af
%
c2d
Reference 10. Reference 11.
A
2B1state, the C-H bond lengths of the 2A, and states should be almost the same as in the cation.
2B2radical
Results and Discussion of the ab Initio Calculations Equilibrium Geometries. Table I lists the total energies, at several levels of theory, for the optimized geometry of each CHClz species. The electronic states of the radical lie in the energy order predicted with the QMOT arguments. Table I1 displays the optimized geometries for each species as the basis sets are increased in size and as electron correlation is added. The most extensive optimizations of the cation and radical structures which were performed with a UMP2/6-31G* calculation also conform to the QMOT predictizns. CHC12 cation possesses a planar, C2, geometry with-a X IA, ground state. The ground-state CHC12 radical is af_X2Afsymmetry in the C,point group. The geometry optimized X 2A’ CHCI2 radical has two degenerate equilibrium positions for the hydrogen atom located symmetrically above and below the C1-C-C1 plane (at +a,,, and -a,,,). As shown in Table 11, the predicted out-of-plane (dihedral) angle, a,,,, in the X 2A’ (C,) CHC12 radical varies as a function of basis set and computational complexity. Previous semiempirical I N D 0 9 and MNDO’O calculations based upon minimal orbital basis sets have predicted essentially planar structures. Ab initio calculations at several theory levels predict more radically nonplanar structures with a,,, = 13-16.2’. Our most extensive ab initio calculation which optimized the structure at the UMP2/ 6-31G* level predicts a dihedral angle of a,,, = 15.5’. Ab initio UHF/3-21G calculations predict nearly the same dihedral angle as the more extensive calculations. We note that ab initio calculations of radicals with 6-31G and 6-31G* bases generally give more reliable results than semiempirical procedure^.^^,^^ The nonplanar C, X 2Afstate of the CHC12 radical correlates with the planar C, X 2BI state. When harmonic frequencies for the planar C2, radical structure are evaluated, the out-of-plane bending mode is a complex number. A complex frequency indicates that the C2, structure is a saddle point in the potential energy surface between the two equilibrium nonplanar structures centered at +ap,and -a,,,. Thus, in the tables we have labeled the X 2BI state as a “transition structure”. (23) Clark, T.A Handbook of Computational Chemistry; Wiley-Interscience: New York, 1985.
TABLE 111: Separation Energies (in cm-’) between the *A’ State and Higher Energy States of the CHCll Radical Computed at Different Levels of Theory
level of calculation UHF/6-31G
electronic state % 2A’ 2 2BI
A 2Al
UHF/6-3 1G*
e 2B2
% 2Af % 2B1
A 2A, UMP2/6-31G*
e
2B2
% 2Af % 2Bl
4 2Al C
UMP2=FC/6-3 lG*//UMP2/6-3 1G*
2B2
2 2A‘ 2 2B1
A 2A, UMP3=FC/6-3 lG*//UMP2/6-3 1G*
e 2B2
8 2A‘
X 2Bl A 2AI 2B2 UMP4=FC/6-3 lG*//UMP2/6-3 1G*
e
% 2A‘ % 2Bl
5 2A1 C 2B2
relative energy 0 248 22 576 42 687 0 308 27 802 48091 0 262 25 976 44058 0 280 25 836 43 929 0 227 26 368 44 859 0 220 25 318 44114
Harmonic frequency evaluations revealed that the A 2Al (C,) and C 2Bz (C,) radicals presented in this paper are also “transition structures”. These C2, structures should have stable states belonging to the C,point_group which correlate adiabatically to !a A ’A’ state and to a C ZA’f state, respectively. Because the A 2A’ state belongs to the_ same irreducible representation as the ground state and the C 2A’f state has adjacent states of 2A’’ symmetry, the minimum geometries and vibrational frequencies of these states could not be determined by the GAUSSIAN 8 2 program. In view of the similarity of the C2,-and C, geometrical structures c_alculated by this study for the X radical, we expect that stable A 2A’ and C 2Affnonplanar radicals also reside near the energies calculated for the planar structures. In agreement with our QMOT arguments presented earlier for symmetry-constrained C, radicals, all C-H bond lengths in the
3478 The Journal of Physical Chemistry, Vol. 93, No. 9, 1989
Kafafi and Hudgens
TABLE IV: Scaled Theoretical Vibrational Frequencies (in cm-I) Predicted for CHC12+and the CHClz Radicals Calculated from the HF/6-31G* and UHF/6-31G* Optimized Structures, Respectively (Experimental Frequencies in Parentheses) vibrational motion u , C-H sym stretch u2
u, u4 u5 u6
C-CI sym stretch CC12 scissors OPLA bend H-C-CI in-plane bend C-CI asym stretch
CHCI, radical
CHC12 cation .% ‘A,” 2937 (3033)c 818 (860)b 348 849 b2 1365 (1291)” b2 1013 (1044)*
a, a, a, b,
2Atb a’ 3086 a’ 726 a’ 292 a’ 203e (244)’ a” 1237 (1226)’ a” 969 (902)’
.% 2B,
A 2A,
e 2B2
a, 3114 a, 714 a, 297
a, 3035 a, 381 a, 230 g b2 1254 b2 916
a, 3155 a, 573 a, 264
g
b2 1225 b2 897
g
b2 1186 b2 778
‘ Z P V E = 10.6 kcal/mol. b Z P V E = 9.6 kcal/mol. CArgonmatrix results of ref 8. dGas-phase photoelectron spectrum of ref 2 and 7. ‘Frequency estimated from double-minimum potential. See text. ’Frequency derived by difference of theoretical cation and 41 band reported in ref 1 for Rydberg state. 8Imaginary frequency (this radical is a transition structure). “Argon matrix results of ref 4, 5 , and 6. ‘Argon matrix results of ref 3.
cation and ground- and excited-state radicals are comparable within 0.01 8, or less (Table 11). The C-CI bond lengths in the ground- and excited-state CHCl, radicals ar_elonger than those in CHCI,’. The C-CI bond length in ihe X ,BI CC,,) CHCl2 radical is -0.16 8, shorter than in the A ,A1 and C ,B2 states. The CI-C-CI bond angles also conform to the-QMOT predictions. The CI-C-CI bond angles in the X 2B and A ,Al (C,,) raiicals are wider than in the cation. The C1-C-CI angle in the C ,B2 (e,,) radical is smaller than in the cation. The difference between 6-31G and 6-31G* basis sets is that the latter contains a set of d-type polarization functions on the non-hydrogen atoms. This difference manifested itself in calculated C-CI bond lengths. As shown in Table 11, C-CI bond lengths obtained from 6-31G* basis set are shorter by about 0.05 8, for all radicals. All other bond lengths and angles obtained from both bases are comparable. The importance of including d-type polarization functions in the basis sets used in ab initio calculations have been stressed recently by several workers.’8%22 Table I1 also lists the geometrical parameters of the CHCl, cation and radicals obtained from Mdler-Plesset optimizations to second order using 6-31G* basis sets. By comparing the bond lengths and angles listed in Table 11, we find that electron correlation only slightly affected bond angjes. The largest bond angle change was the CI-C-CI angle in the A *Al CHCll radical which decreased by 3.5O compared to the angle obtained from the UHF/6-3 1G* calculation. Relative to UHF/6-3 1G* results, electron correlation increased the C-H bond length about 0.01 8, in all species. In the radicals the C-CI bond lengths species decreased by 0.01-0.06 8,. Relative Energies between Ground ana‘ Excited States of CHCI, Radicals. Table 111 lists the separ_ation energies computed at different levels of theory between the X ,A’ (C,) state of the CHC12 radical and higher energy states. -The difference in total energies between the geometry optimized X ,A’ (C,) radical structure and ,B1 (C2J “transition structure” is the inversion barrier that and -arn)equlibrium geometries. Our separates the two (+arn UHF/6-31G* inversion barrier of 308 cm-I agrees with the value of 315 cm-l previously reported by Luke et a1.I’ This inversion barrier diminishes by 80 cm-’ (30%) between UHF/6-31G* and the UMP4=FC/6-3 lG*//UMP2/6-3 lG* calculations to yield an improved inversion barrier of 220 cm-l. The other radical excited valence states, A 2Al and ,B2, were found by UMP4 computations t o lie 25 318 and 44 114 cm-’, respectively, above the X ,A’ state. Because the equilibrium structures of these states belong to the C, point group, the calculated energies based upon C,, structures should be viewed as upper limits. No published experimental spectrum of C H C b radicals _reported to date can be conclusively assigned to the A 2Al and C ,B2 states. Emmi et al.24have reported a solution-phase UV absorption spectrum of CHCI, radical between 220 and 330 nm (45, 450-30,300 cm-I) which may include features from these states. However, the data do not lend itself to any assignments. The gas-phase spectrum of CHCI, radical reported by Long and (24) Emmi, S . S . ; Beggiato, G.; Casalbore-Miceli, G.; Fuochi, P. G. J . Radioanal. Nucl. Chem. Lett. 1985, 93(4), 189.
Hudgens’ is unrelated to the A ,Al or ,B2 states. This REMPI spectrum originates from a two-photon resonance with a 3d Rydberg state that resides at 54 024 cm-I. Vibrational Analysis of the CHCI, Cation and R ,BI Radical. Table IV presents the calculated harmonic vibrational frequencies (scaled by 0.9) derived from the optimized HF/6-31G* and UHF/6-31G* structures of CHCI, cation and radicals using analytical second-derivativet ~ h n i q u e s . ’Since ~ the v4 OPLA bend of the X ,A’ radical is not harmonic, this frequency was calculated by solving the double-minimum quartic potential os~illator.’~ (The predicted OPLA frequency derived by this procedure requires no subsequent scaling.) During these calculations we adopted the UMP4=FC/6-3 lG*//UMP2/6-3 1G* inversion barrier of 220 cm-’ and the optimized UMP2/6-3 lG* structure. The vibrational frequency derived from this quartic oscillator calculation was v4 = 243 cm-I. Table IV also reports in parentheses experimentally observed frequencies of the CHCl, cation and ground-state radical. The in-plane vibrational frequencies were observed by infrared spectra of species trapped in an argon matrix or by photoelectron spectroscopy. The ab initio and experimentally observed frequencies agree within the uncertainties. The only experimental data regarding the v4 out-of-plane bending frequencies is derived from an observation of the 4; hot band in the two-photon resonant REMPI spectrum of the CHCl, radical. The position of this 4; hot band in the REMPI spectrum indicates that the v4 OPLA vibrational frequency in the 3d Rydberg is 605 cm-I greater than in the X *A’ state. Since a Rydberg orbital contributes little to the chemical bonding within a Rydberg state, the vibrational frequencies in a Rydberg state closely resemble those of the cation.2s For example, the 3d Rydberg state v2 C-C1 symmetric stretching frequency in CHCl, is 845 cm-l. An essentially identical CHCl, cation frequency of v 2 = 860 (iz30) cm-I was observed by gas-phase photoelectron spectroscopy. Thus, we have adopted the 4; band in the 3d Rydberg spectrum as the difference in v4 frequencies between the ground-state cation and radical. The ab initio calculations predict that the difference in v4 OPLA frequencies between the ground-state cation and radical (Le., the 4; hot band in a photoelectron spectrum) is 606 cm-’. This value agrees remarkably well with the observed 4; hot band in the REMPI spectrum. In Table IV we present the 4; experimental value in terms of t h e ground-state u4 OPLA frequency, u4 = 244 cm-l, which we derived from the difference between the ab initio v4 frequency of the cation and the 41 hot band observed in the REMPI spectrum. Since the v4 (OPLA) frequency of 244 cm-’ accounts for the intensity of 4; hot band in the ambient-temperature REMPI spectrum,’ the v4 frequencies presented here seem very reasonable. Conclusion
In conclusion, the agreement between the calculated ab initio vibrational frequencies with the experimentally observed fre(25) See for example: Aduances in Multiphoton Processes and Spectroscopy; Lin, s. H., Ed.; World Scientific Publishing Co.: Singapore, 1988; Vol. 4, pp 171-296
J. Phys. Chem. 1989, 93, 3479-3483 quencies causes us to believe that the theoretical treatment presented here accurately depicts the structure of the dichloromethyl cation and radicals. We note that the theoretical studies which compare the cation and ground-state structures are particularly useful during the interpretation of REMPI spectra. Such
3479
calculations can explain the vibrational bands observed in REMPI spectra and avoid the difficulties involved with explicit calculations of Rydberg states. Registry No. CHCI2, 3474-12-2; CHCI2+,56932-33-3.
Low-Frequency Raman Spectra of Even a,o-Disubstituted n-Alkanes Kyriakos Viras,+ Fotini Viras,* Carl Campbell, Terence A. King, and Colin Booth* Departments of Chemistry and Physics, University of Manchester, Manchester M13 9PL, UK (Received: August 9, 1988)
Low-frequency Raman spectra of even a,w-disubstituted n-alkanes have been recorded. The major features in the spectra arise from whole-chain longitudinal and bending vibrations. The effects of end group, chain length, and temperature on the frequencies of these vibrations are described, and the frequencies of the longitudinal vibrations are interpreted in terms of the chain model of Minoni and Zerbi
Introduction Bands in the low-frequency region (5-200 cm-l) of the Raman spectra of crystalline n-alkanes have been assigned to whole-chain vibrations.l,2 The most informative and widely studied of these bands is the single-node longitudinal acoustical (or accordion) mode (LAM-l), since its frequency is approximately proportional to the reciprocal of the ordered-chain (stem) length from which it originates irrespective of the chain packing in the crystal. Consequently LAM-1 has been used as a spectroscopic probe for stem lengths in lamellar crystals of polymer^,^ as well as in multilayer crystals of oligomers such as the n-alkanes. A wellrecognized difficulty (see, e.g., ref 3) is the perturbation of the vibration by end effects, Le., end groups (including chain folds) through their inertial masses or interlayer (or interlamellar) forces. The perturbation of the LAMs by end effects has been investigated theoretically by use of simple rod4 or chains models. Experimental observations on end-modified n-alkanes are most readily i n t e r ~ r e t e d . Here ~ ~ we report a new investigation of the perturbation of the LAMs of even a,o-disubstituted n-alkanes, i.e.
where n is in the range 6-16 and X = OH, C1, Br, and I, and also corresponding a,w-diesters, i.e. CH3OOC(CH2),2COOCH3 The results offer a systematic empirical view of the effects of end masses and forces in a simple system.
Experimental Section Materials. Except for the a,w-diiodo-n-alkanes, the disubstituted oligomers were obtained from commercial sources. The diesters were distilled before use; the others were used as received. The diiodoalkanes were prepared from the corresponding dihydroxy compounds by reactionlo with KI and H3P04. Raman Spectroscopy. Raman scattering at 90' to the incident beam was recorded by means of a Spex Ramalog spectrometer fitted with a 1403 double monochromator and a 1442U third monochromator in the scanning mode. The operation of the instrument was controlled by a DM 1B Spectroscopy Laboratory Coordinator Computer. The light source was a Coherent Innova 'Permanent address: Physical Chemistry Laboratory, University of Athens, 13A Navarinou Street, Athens 106 80, Greece. *Permanent address: Department of Physics, University of Athens, 104 Solonos Street, Athens 106 80, Greece.
0022-365418912093-3479$01.50/0
90 argon -ion laser operated at 514.5 nm and 500 mW. Typical operating conditions for low frequencies (5-300 cm-') were bandwidth, 1.5 cm-'; scanning increment, 0.1 cm-I; integration time, 2 s. On occasion, for very low frequencies, the conditions were bandwidth, 0.8 cm-'; scanning increment, 0.05; integration time, 5 s. The frequency scale was calibrated by reference to the spectra of L-cystine and n-hexacosane, the latter being used immediately before recording a spectrum. Samples were enclosed in a capillary and held at a constant temperature ( f l K) in the range 133-298 K by means of a Harney-Miller cell (available from Spex Industries Inc.). For lower temperatures, down to 77 K, the sample was held to A0.5 K within the vacuum chamber of a cryostat (Oxford Instruments Ltd., Model CF104 plus Model CF5244 temperature control unit). The intensity of a Raman band was observed over a period of time to ensure equilibration of the sample at a given temperature. Generally high-frequency spectra were recorded immediately after the low-frequency spectra, in order to confirm that samples were unchanged by exposure to the laser beam.
Results and Discussion Spectra were recorded over the frequency range 5-300 cm-' and at several temperatures within the range 293-133 K. Band frequencies are listed in Table I: the assignments of the bands denoted (1) and (2) are discussed later. Spectra obtained for a,w-dibromo- and a,w-dihydroxy-n-alkanes are shown in Figure 1. Although there are differences in detail within these two sets of spectra, for a given series the general features are reproduced from sample to sample and a general decrease in band frequency with increase in chain length is apparent. This was found to be the case for all series of a,w-disubstituted n-alkanes investigated, as for the n-alkanes themselves,'P2 as illustrated for selected bands in Figure 2. The effect of changing the temperature is illustrated in Figure 3 for a,w-diiodo-n-octane. The effect of lowering the temperature is to sharpen the bands and accentuate weak features. With the (1) Mizushima, S.;Shimanouchi, T. J. Am. Chem. SOC.1949, 71, 1320. (2) Olf, H. G.; Fanconi, B. J. Chem. Phys. 1973, 59, 534. (3) Rabolt, J. F. CRC Crit. Rev., Solid State Mater. Sci. 1977, 1 2 , 165. (4) Hsu,S. L.; Krimm, S. J. Polym. Sci., Polym. Phys. Ed. 1977, 15, 1769. (5) Minoni, G.; Zerbi, G. J . Phys. Chem. 1982, 86, 4791. (6) Fanconi, B.; Chissman, J. J. Polym. Sci., Polym. Lett. Ed. 1975, 13, 421. (7) Nomura, H.; Koda, S.; Kawalzumi, F.; Miyahara, Y. J . Phys. Chem. 1977, 81, 2261. (8) Rabolt, J. F. J . Polym. Sci., Polym. Phys. Ed. 1979, 17, 1457. (9) Minoni, G.; Zerbi, G.; Rabolt, J. F. J. Chem. Phys. 1984, 81, 4782. (10) Furniss, B. S.; Hannaford, A. J.; Rogers, V.;Smith, P. W. G.; Tatchell, A. R. Vogel's Textbook of Practical Organic Chemistry, 4th ed.; Longman: London, 1978.
0 1989 American Chemical Society
