Faraday Discuss. Chem. SOC., 1984, 78, 35-47 Equilibrium Geometries and Hyperfine Interactions in Propane and Cyclopropane Cations BY STEN LUNELL" AND MING BAO HUANG Department of Quantum Chemistry, Uppsala University, Box 5 18, S-75 1 20 Uppsala, Sweden AND ANDERS LUND The Studsvik Science Research Laboratory, S-6 1 1 82 Nykoping, Sweden Received 26th March, 1984 The equilibrium geometries of the propane cation in its three lowest electronic states, ' B , , 'B2 and ' A , (C2u symmetry assumed), have been calculated by the UHF method within the ab initio MO-LCAO-SCF approximation. The 2 B , state is predicted to be lowest in energy and the 2B2 and 2A, states to be of almost the same energy, 12 kcal mol-' above the ' B , state. The isotropic hyperfine coupling constants have been calculated and compared with experi- mental data.The calculations confirm the e.s.r. identification of the 2B, state, obtained in an SF, matrix. The previous experimental assignment, 2B2, for the state obtained in Freon matrices was found to be ambiguous and an assignment to the ' A , state can not be ruled out. Dipolar hyperfine coupling constants have been calculated for the ' B , , 2B2 and ' A , states of the propane cation and for the 2A, ground state of the cyclopropane cation. In the latter case, comparison with experimental data has been made with reasonable agreement. The equilibrium geometry agrees well with previous calculations. Complementary experi- mental data for the propane and cyclopropane cations are reported. Positive ions of saturated hydrocarbons have recently been observed and charac- terized by electron spin resonance (e.s.r.) spectroscopy.14 In these studies the cations were generated by ionizing irradiation at low temperature of the hydrocarbon contained in a halogenated matrix.Under these conditions the cations are stably trapped, permitting their e.s.r. spectra to be recorded. These studies have shed new light on the electronic structure of the cations of hydrocarbons and particularly detailed results have been obtained for the cations of ethane and ~ r o p a n e . " ~ The assignments of the spectra have been based on intuitive arguments or, more recently, on semi-empirical molecular-orbital calculations. Ab initio results are available for the ethane ~ a t i o n , ~ but such calculations on the larger ions in the n-alkane series seem to be missing.Very recently, e.s.r. data for some cycloalkane cations were reported and com- pared with the results of ab initio calculation^.^-^ It was found that ab initio MO-LCAO calculations are able to confirm and refine the experimentally obtained geometry and spin distribution of these systems. A similar study of the cations of normal hydrocarbons therefore seems to be necessary. 23 years ago the equilibrium geometry of propane was successfully studied by means of its microwave spectrum," which indicated that it has C2v symmetry with the CH3 groups staggered with respect to the CH2 group. As with both methane and ethane, the three highest-lying occupied molecular orbitals (46,, 2b2 and 6a,) are energetically very close to one a n ~ t h e r .~ This makes it non-trivial to predict the symmetry of the ground state of the cation. Ionization of the highest occupied 3536 PROPANE AND CYCLOPROPANE CATIONS orbital will not necessarily give the most stable doublet state, especially in view of the rather large geometry changes that can occur upon ionization. In the e.s.r. experiments on the n-propane cation reported by Toriyama et a2.: two different spectra were obtained, depending on the matrix, which were assigned to two different states, 2Bl and 2B2. Their theoretical analysis is, however, simplified and based only on INDO calculations. Toriyama et aL4 observed that a change of ground state from ,B2 to *B1 could be produced in their calculations by a slight tilting of the C3 axes of the CH3 groups.It is likely that this result is more or less a coincidence, since more relevant parameters such as C-C bond lengths and the C-C-C angle were left unchanged. A detailed theoretical study is therefore required. The main purpose of this work is to investigate the three lowest states of the propane cation, ’ B I , ,B, and * A , , using a6 initio MO-LCAO UHF calculations with reasonably large basis sets, in particular with respect to equilibrium geometries, relative energies and spin properties. These data are discussed together with avail- able e.s.r. spectra4 and some new e.s.r. data which are briefly reported. In addition, we report some theoretical and experimental results for the cyclopropane cation which supplement previous work by Ohta et aL7 and by Iwasaki et aL9 THEORY Energies and wavefunctions were calculated by the unrestricted Hartree-Fock (UHF) method within the a6 initio MO-LCAO-SCF approximation.Two different basis sets were used in the calculations, a 4-31G basis*’ and a larger basis of double-zeta quality, namely Dunning’sI2 (9s5p/4s) basis contracted to (4s2p/2s), with a scale factor of 1.25 for the hydrogen exponents. The 4-31G basis was used in the geometry optimizations of the 2Bl, 2B2 and ,A, states of C3Hl and the ,A, and 2B1 states of C3HL using the program MONSTER- GAUSS.I3 We have assumed that the cations have C,, symmetry, and that C3Hl has both CH3 groups staggered with respect to the CH, group. In all five cases the independent parameters were optimized and the notation used is shown in fig.l ( a ) and ( b ) . The optimized geometries, obtained in the 4-31G basis, were then used in the final calculations of wavefunctions and energies in the larger basis, for which the program MOLECULE'^ was used. Isotropic and anisotropic hyperfine coupling constants for the hydrogen atoms were calculated only in the double-zeta basis. The isotropic coupling constants were calculated both with and without previous annihilation of the quartet contamination in the total wavefunctions. In the former case, a program based on the theory of Amos and Snyder” was used. The anisotropic constants were calculated directly from the UHF function only, since previous experience with systems similar to the present ones, e.g. the methyl and ethyl radicals,I6 has shown that the proton dipolar couplings are normally relatively little affected by quartet annihilation.EXPERIMENTAL In earlier work^^,',^ cation radicals of propane and cyclopropane were produced by y- or X-irradiation of the solutes contained in a frozen matrix of SF6, CFC1, or CFC12CF2CI and the e.s.r. spectra were recorded at 4 and 77 K. In the present work, the cations were observed after X-irradiation at 77 K of propane and cyclopropane in a CF,CCI3 matrix. The temperature dependence of the e.s.r. spectra was investigated between 4 and 77 K using a liquid-helium flow cryostat manufactured by Oxford Instruments. The temperature depen- dence between 77 and 140 K was studied using a variable-temperature Dewar manufacturedS. LUNELL, M. B.HUANG AND A. LUND 37 " 2 Fig. 1. ( a ) Geometry and labelling used for the C3H6+ ion (C2v symmetry assumed). ( b ) Geometry and labelling used for the C3Hl ion (C2v symmetry assumed; the H,-C-H3 and H , -C-H, planes are perpendicular to the H2-C-C-C-H2 plane). by Varian. The spectra were recorded at X-band frequencies (9.3 GHz) on a Varian E9 spectrometer using 100 kHz magnetic field modulation. EXPERIMENTAL RESULTS CYCLOPROPANE CATION Experimental data have previously been reported by Shida et aL7 for a CFCl, matrix at 77 K and by Iwasaki et aL9 for a CFC12CF,C1 matrix at 4 K. At 4 K a spectrum 100 G wide with partially resolved hyperfine structure was obtained. The spectrum has been interpreted using an anisotropic g-factor, anisotropic hyperfine couplings to four a-hydrogen atoms and nearly isotropic couplings to two p- hydrogen atoms.The hyperfine data of ref. (9) are included in tables 2 and 3 (uide infra). In the present work, e.s.r. spectra of the cyclopropane cation were obtained in a CF3CC13 matrix over the temperature range 4-77 K. The spectrum recorded at 10 K, fig. 2(a), has the same general shape as that obtained at 4 K by Iwasaki et ~ 1 . ~ We find for the isotropic part of the couplings a , = 22 G (2H) and a2 = - 1 1.5 G (4H), in close agreement with the values reported previously. Thus the matrix does38 PROPANE AND CYCLOPROPANE CATIONS Fig. 2. E.s.r. spectra of the cyclopropane cation in a CF3CC13 matrix recorded at ( a ) 1 1 , ( b ) 41 and ( c ) 60K. not significantly affect the magnitudes of the hyperfine couplings of the cyclopropane cation.As the temperature was raised the e.s.r. spectrum changed reversibly, fig. 2( 6) and (c), and at 60 K a single line 4 G wide became prominent. A spectrum resembling that in fig. 2(c) was also observed by Shida et u1.’ at 77 K. PROPANE CATION Experimental data at low temperatures (4 and 77 K) have been reported by Toriyama et aL4 In this case the isotropic hyperfine coupling constants depend on the matrix used. In the SF6 matrix the resolved hyperfine structure is due to the atoms labelled H2 on each methyl group [fig. l(b)] with u2 = 98.0 G (2H) at 4 K. In the CFC12CF2C1 matrix the hyperfine couplings are a , = 105.5 G (2H) and u3 = 52.5 G (4H). The assignments were made with the help of deuterium-labelled compounds. The results show quite unambiguously that the cation is in the 2BI state in the SF, matrix.The spectrum observed in the CFC12CF2C1 matrix was assigned to the 2B2S . LUNELL, M. B. HUANG AND A. LUND 39 state by Iwasaki and coworker^,^ who used INDO calculations. Although this assignment may be correct, it is by no means obvious that it is the only possible one, since it is known that the INDO method sometimes gives the wrong symmetry for the ground state of radi~a1s.l~ In fact, the assignment 2A1 can not be excluded on the basis of available experimental and theoretical data, as will be discussed below. In the present work, experimental e.s.r. data have been obtained for the propane cation in the CF,CC13 matrix at temperatures between 77 and 140 K. At 77 K the hyperfine couplings are similar to those reported in ref.(4) for the CFCl2CF2C1 matrix, namely a, = 110 G (2H) and a3 = 50 G (4H). Thus the cation is in the 2B2 or 2A, state in the CF3CC13 matrix. At 140 K the spectrum consists of a triplet with a, = 100 G (2H) and an additional septet splitting of 23 G (6 H). The spectral change between 77 and 140 K is reversible. This suggests the onset of rotation about the CI-C2 and C2-C3 bonds at 140K making the H, and H3 atoms magnetically equivalent. THEORETICAL RESULTS CYCLOPROPANE CATION EQUI LI BRI UM GEOMETRY AND ISOTROPIC HY PERF1 NE COUPLING CONSTANTS A careful theoretical study of the cyclopropane cation was recently published by Nakatsuji and coworker^.^ In particular, the geometric stability of the cation was thoroughly analysed using the Jahn-Teller theorem, as were the isotropic hyperfine coupling constants for the state of lowest energy, i.e.the *A, state. We will therefore limit the present discussion primarily to the anisotropic coupling constants, which were not considered by Nakatsuji and coworkers. Since certain differences exist with respect to both the geometry determination (different basis sets) and the calculation of the isotropic coupling constants (basis sets as well as theoretical model), we compare our present results with those of ref. (7) in tables 1 and 2 for the two lowest states, 2A1 and ,B2.* As is seen in table 1, the differences between the 4-3 1G and STO-4G geometries are rather small. Both basis sets predict a flattening 2f the equilateral triangle in the 2A1 state, accompanied by a slight shortening (0.02 A) of the C, -C2 and CI -C3 bonds, and a narrowing of the base of the triangle in the 2B2 state, accompanied by an elongation of the C,-C, and C,-C, bonds.The actual bond lengths differ between the two basis sets (0.02-0.04 A), whereas most bond angles are similar. For the isotropic hyperfine coupling constants (table 2) there is acceptable qualitative agreement between the present results after quartet annihilation (a UHFAA) and the results of the so called pseudo-orbital (PO) theory of ref. (7), and, in the case of the 2A, state, with experiment. Note, however, that significantly better quantitative agreement is obtained by following the suggestion by Snyder and Amos" to estimate the isotropic coupling constant from the quantity a(3a + aUHF).This gives the values a, = 17.8 G and a2 = - 12.3 G for the 2A1 state, and a, = - 19.3 G and a2=6.3 G for the 'B2 state, in excellent agreement with ref. (7) and (9). DIPOLAR COUPLING CONSTANTS The calculated (UHF) dipolar coupling constants for the cyclopropane cation are given in table 3 for the four equivalent a-hydrogen atoms [H2 in fig. l(a)] and * T h e symmetry designations in C,, symmetry are to some extent a matter of choice. We here follow ref. (7); in ref. (9), this state is labelled ' B , .40 PROPANE AND CYCLOPROPANE CATIONS Table 1. Optimiztd geometries and total energies for the ' A , and 'B2 states of C3Hl (distances in A, angles in degrees and energies in a.u.; for notation see fig. 1) 2A, 2B2 c3 H6 4-3 1 G" STO-4Gh 4-3 1 G" STO-4Gb 4-3 1 G" exptl' W C , -Cd 1.483 1 SO4 40 81.7 75.6 R(C,-H,) 1.075 1.088 R (C2 - H2) 1.072 1.092 Q 113.7 116.5 Y 109.7 P 120.9 121.0 4-3 1G energy double-zeta energy -1 16.573 59 - 1 16.705 43 ~ ~ ~~~~ 1.721 1.683 1 SO3 I .524 1.069 1.090 1.072 1.07 1.072 1.094 48 .O 50.1 60.0 60.0 120.6 119.6 113.7 120 108.1 108.5 120.6 -1 16.563 76 - 1 16.695 02 a This work.Ref. (7). Ref. (18). Table 2. Isotropic hyperfine coupling constants aH (in G) for the different hydrogen atoms of C3Hl S ( S + 1) isotropic coupling constants before after state annihilation annihilation HI H2 2A, 0.781 53 0.750 3 1 QUHF 24.9 -25.7 PO theory" 16.5 -12.3 ~ U H F A A 15.5 -7.9 exptl 21h 22' -12.5b -1 1.5' 2B2 0.756 28 0.750 03 QUHF -38.9 5.8 QUHFAA -12.8 6.5 PO theorya -19.9 7.1 a Pseudo-orbital theory, ref.(7). CF2C1CFCl2 matrix, ref. (9). CF3CC13 matrix, this work. the two P-hydrogen atoms (H,). The experimental data reported by Iwasaki et aZ.' are included for comparison. For the a-hydrogen atoms we note satisfactory agreement between theory and experiment, with respect to both the principal values and the directions of the principal axes of the dipolar tensor. For the P-hydrogen atoms, the agreement is at first sight considerably worse. There are, however, two possible reasons for the discrepancies. The first is that the anisotropy is very small, both in absolute terms and in comparison with the isotropic coupling constant (only ca. 15%). In the case of the a-hydrogen atoms, the dipolar coupling is much larger and ca.70% of the isotropic value. An accurate experimental determination is therefore much more difficult for the P-hydrogen atoms, especially of the direction cosines. The second reason is that the results of INDO calculations were used to extract the anisotropic component of the hyperfine coupling,' and this may have introduced errors which were not present in the raw data. In fact, we have simulated the experimentalS. LUNELL, M. B. HUANG AND A. LUND 41 Table 3. Calculated (UHF) dipolar coupling constants in the cyclopropane cation (*A ,) direction cosines" principal nucleus value/G X Y z H2 +9.5 -0.9 -8.6 exptl +8.2 -1.3 -6.9 H , -1.7 + 0.3 +1.4 exptlb +3.2 -1.0 -2.2 0.337 -0.75 1 0.567 0.578 -0.478 0.66 1 0.0 1 .o 0.0 0.0 0.0 1 .o 0.846 -0.022 -0.533 0.794 0.142 -0.592 -0.999 0.0 0.038 0.686 0.728 0.0 - 0.413 0.660 0.628 0.188 0.868 0.46 1 0.038 0.0 0.999 -0.728 0.686 0.0 " The direction cosines are given for one of the equivalent protons and those for the others can be obtained by symmetry operations; coordinate system as in fig.l(a). Ref. (9), CFC13 matrix. spectrum obtained by Iwasaki et u Z . , ~ using our theoretical data from table 3, with a fit which is about as good as with the data of ref. (9). The theoretical results must therefore be considered to be satisfactory. PROPANE CATION EQUILIBRIUM GEOMETRIES AND ENERGIES OF THE 2 B ~ , 2B2 AND 2 A ~ STATES The 4-31G optimized geometry parameters of the 2 B I , 2B, and 2A1 states are given in table 4 [for notation see fig. l(b)], together with the 4-31G optimized parameters of neutral propane.Also included in table 4 are the total energies obtained at the optimized geometries using the 4-31G and double-zeta bases. Table 4 shows that in both the 4-31G and the double-zeta bases the state of lowest energy is the 2Bl state. In the 4-31G basis the minima of the 2B2 and *Al energy surfaces lie 11.5 and 12.0 kcal mol-I respectively, higher than the 2B1 energy minimum, and in the double-zeta basis the corresponding values are almost the same (12.0 and 1 1.7 kcal mol-I). The 2B2 and 2AI states are hence placed at almost exactly the same energy above the 2Bl state, even though they have very different equilibrium geometries, especially for the carbon framework ( cJ: table 4). A complete calculation of the full potential-energy surfaces for all three states would be both tedious and not very useful.In fig. 3 we show the relative energies of the 2B,, 2B2 and 2A1 states at the three different optimized geometries of table 4. Note that at the optimum geometry for one state the other two states lie rather far (240 kcal mol-') above this lowest state. In addition to the relative energies of the three states, fig. 3 also shows the slopes of the different energy surfaces at the considered geometries. Table 4 and fig. 3 show that the equilibrium geometry of the propane cation is shifted from that of neutral propane in different ways for the different states. These geometry changes can be understood from the shapes of the singly occupied42 PROPANE AND CYCLOPROPANE CATIONS Table 4.4-31G optimizaed geometries and total energies for the 2 B , , 'B2 and * A , states of C3Hg (distances in A, angles in degrees and energies in a.u.; for notation see fig. 1) 4-3 1 G energy" +117.0 double-zeta energy" + I 17.0 1.646 1.075 1.095 I .073 96.1 112.5 93.9 112.2 1 1 1.8 -0.7 17 97 (0) (0) -0.849 95 I .480 1.177 1.077 I .088 121.5 70.3 113.5 109.0 109.7 -0.699 65 (48. I ) -0.830 75 (50.2) 1.600 1.092 1.078 1.080 130.5 129.2 1 1 1.8 109.9 105.8 -0.698 89 - (50.2) (49.0) -0.831 29 1.530 1.085 1.083 1.084 112.6 106.4 I 1 1.3 107.8 11 1.0 1.093 81 " The values within parentheses give the energies relative to the energy of the ' B , state in the same basis (in kJ mol-'). -116.5500 - 1 1 6.6000 c : v q-116.6500 -116.7000 90.0 2 B2 A , 2 B1 2 100.0 110.0 120.0 130.0 140.0 g P / O Fig.3. Relative energies of the 'B,, 'B, and ' A , states of C3Hl at the optimized geometries for each state (4-3 1G basis). The signs u , \ and / indicate that the energy derivatives with respect to q are zero, negative and positive, re2pectively. R = ( a ) 1.646, (b) 1.480 and (c) 1.600 A. molecular orbitals (SOMO), which can be clearly identified in all three states (fig. 4). As a general rule, single occupancy of a certain molecular orbital, instead of double, changes the bonding situation such that the bond length increases when the MO is bonding and decreases where it is antibonding ( i e . both bonding andS. LUNELL, M. B. HUANG AND A. LUND f 43 Fig. 4. Schematic representations of the three highest occupied MO in neutral C3Hs: ( a ) 2 bZ, ( b ) 4b, and ( c ) 6 ~ 1 .antibonding effects become weaker). Thus the antibonding character of the B2 orbital between tbe pT orbitals on the carbon atoms results in a shortened C-C bond ( R = 1.480 A) when it is singly occupied in the 2B2 state. The 46, orbital, on the other hand, displays bonding between the mid-carbon and the end-carbons and potential antibonding between the two end-carbons. m i n it is singly occupied in the 2B1 state, the C-C bonds are lengthened ( R = 1.646 A) and the C-C-C angle becomes smaller ( 4 = 96.1 "). The bonding situation is thus almost identical to that found in the cyclopentane ~ a t i o n . ~ ' ~ Finally, the 6 ~ 1 orbital is bonding between all three carbons for a bent geometry. Single occupancy weakens this bonding, leading to longer C-C bonds ( R = 1.601 A) and a larger C-C-C angle ( 4 = 130.5 "). A final point of interest is the changes in the C-H bond lengths.One can see from table 4 that the 2B1 state, on one hand, and the 2B2 and 2A, states, on the other, behave differently in this respect. In the 2B, state, the bonds to the in-plane end-hydrogens (H2) are lengthened, whereas the other C-H bonds become shorter. For both the 2B2 and 2A1 states, however, the bond lengthening occurs for the mid-carbon hydrogens (Hl). This difference, which can be seen to be consistent with the shape of the orbitals in fig. 4, is important in connection with the possible decomposition of the cations by deprotonation at higher temperatures (vide infru). ISOTROPIC COUPLING CONSTANTS The calculated isotropic hyperfine coupling constants at the different protons in C3Hl are given in table 5 for the three different states, under the headings uUHF44 PROPANE AND CYCLOPROPANE CATIONS Table 5.Isotropic hyperfine coupling constants aH (in G) for the different hydrogen atoms of C3HZ S ( S + 1) before after isotropic coupling constants state annihilation annihilation HI H2 H3 2B, 0.763 86 0.750 12 aUHF a u H FAA 2B2 0.757 48 0.750 04 ~ U H F 2A, 0.759 17 0.750 06 ~ U H F ~ U H F A A a u H FAA exptl SF6 matrixu CFC12CFzCl matrixU CFC13 matrix" CF3CC13 matrix' -16.3 -5.4 206.9 181.4 84.4 69.7 105.5 100 110 65.1 55.3 -0.1 -0.03 0.1 4.3 98.0 - 14.9 -4.9 40.2 26.6 18.1 16.6 52.5 52 50 Ref. (4). ' This work. (without quartet annihilation) and aUHFAA (after annihilation).Considering first the 'B1 state, one can see that the largest coupling is obtained for the two in-plane end-carbon hydrogens (H2), whereas the couplings for H I and H3 are one order of magnitude smaller. This is consistent with the form of the singly occupied molecular orbital in fig. 4. In the 2B2 and 2A, states, however, the in-plane hydrogens have practically vanishing coupling constants and instead the mid-carbon hydrogens (HI) show large isotropic couplings, with non-negligible values for the four out-of-plane hydrogens (H3). Again, this is in agreement with the SOMO in fig. 4, which shows that the delocalized unpaired spin is responsible for most of the isotropic coupling and that spin polarization is of minor importance. One can compare the calculated coupling constants with the experimental values obtained by Iwasaki and c o ~ o r k e r s , ~ which are also included in table 5.An interesting feature of the experiments is that two different types of spectra were obtained, one in the SF6 matrix and another, quite different, in the CFCl2CF2C1 and CFC13 matrices. In the first case a coupling constant of 98.0 G is obtained for the two in-plane end-carbon hydrogens ( H2), with the remaining couplings being too small to be resolved. A comparison with the theoretical results in table 5 shows that the cation must be in the 2 B , state, even though the quantitative agreement between theory and experiment clearly leaves room for improvement. In the CFCl2CF2C1 matrix, on the other hand, a coupling constant of 105.5 G was obtained for the mid-carbon hydrogens ( H , ) and 52.5 G for the four out-of-plane end-carbon hydrogens (H3).In this case the assignment is less obvious. Iwasaki and coworkers4 assigned this spectrum to the 2B2 state, guided by INDO calculations, and the possibility of a 2A1 assignment was not even considered. However, the observed hyperfine structure is consistent with both the 2bz and the 6 ~ 1 orbitals being SOMO (cf. fig-4). Table 5 shows that HI has the largest coupling constant and H3 the second largest in both the 2B2 and the 2A, states, in complete agreement withS. LUNELL, M. B. HUANG AND A. LUND 45 Table 6. Calculated (UHF) dipolar coupling constants in the states ' B , , ' B , and ' A , of the propane cation direction cosines' principal nucleus value/G X Y z 9.40 -7.67 - 1.73 7.60 -6.19 - 1.41 7.90 -6.22 - 1.68 12.9 1 -7.42 -5.49 2.43 -1.38 - 1.05 2.70 - 1.69 -1.01 12.25 -7.20 -5.05 7.43 -4.35 -3.08 4.5 1 -4.15 -0.36 0.0 0.0 1 .o 0.464 0.0 -0.886 0.190 0.170 0.967 0.0 1 .o 0.0 0.967 0.255 0.0 0.532 0.209 -0.82 1 0.0 1 .o 0.0 0.944 0.0 -0.33 1 0.087 0.496 0.864 0.78 1 0.624 0.0 0.0 1 .o 0.0 -0.755 -0.605 0.255 0.174 0.0 0.985 0.0 0.0 1 .o -0.297 0.954 0.050 1 .o 0.0 0.003 0.0 1 .o 0.0 -0.903 -0.328 0.279 -0.624 0.78 1 0.0 0.886 0.0 0.464 -0.628 0.778 -0.0 13 -0.985 0.0 0.174 -0.255 0.967 0.0 -0.793 -0.2 17 -0.569 -0.003 0.0 1 .o 0.33 1 0.0 0.944 -0.42 1 0.804 -0.41 9 The direction cosines are given for one of the equivalent protons and those for the others can be obtained by symmetry operations; coordinate system as in fig.l(b). experiment. We have also shown (vide supra) that there are no energetic reasons to prefer the 'B2 state over the *AI state (or vice versa). A quantitative comparison between the theoretical and experimental values for the H, coupling constants shows that the 'B2 value is 80% too large, while the ' A , value is 30% too small. The discrepancy between theory and experiment is thus considerable, but if any preference must be shown the values support assignment to 2Al rather than ' B 2 . As additional support for this choice one could consider the fact that the calculated coupling constant is too low by approximately the same factor as in the *BI state. However, there is no guarantee that basis-set effects and other errors are regular enough to allow safe extrapolation from one atom to another and from one electronic state to another.Calculations using more accurate methods and basis sets would therefore help in this assignment. Such calculations have been started.46 PROPANE AND CYCLOPROPANE CATIONS DIPOLAR COUPLING CONSTANTS No anisotropic hyperfine coupling constants were reported in ref. (4), nor were they possible to extract from the present measurements. We have nevertheless calculated the relevant proton dipolar couplings for the three states of interest (table 6). As can be seen the largest anisotropy is found for the HI atoms in all the states considered. Although the anisotropy of H, is almost identical in magnitude in the 2B2 and 2A1 states, its directions are different, which in principle should provide the possibility of distinguishing between these states.Presently available experi- mental spectra do not, however, allow a distinction on this ground. DISCUSSION Although the existence of matrix effects in e.s.r. spectra is well known and extensively studied, the case of propane is unusual in that these effects are large enough to produce cations in different electronic states in different matrices. The explanation of the difference between e.g. the SF6 and CFCl2CF2C1 matrices presents interesting problems, since in principle both steric and electronic explanations are possible. A steric explanation would be based on the fact, shown in fig. 3 , that the ground state of the cation is ' B , for some geometries, 2B2 for some geometries and 2AI for some geometries.It is also not unreasonable to assume that the geometry of the cation can be affected by the steric properties (molecular shape, packing etc.) of the matrix. An electronic explanation, on the other hand, assumes a direct dependence of the electronic state of the cation on the electronic properties (ioniz- ation potential, polarizability etc.) of the matrix. The geometry of the cation then becomes a consequence of its electronic state (cf: fig. 3). Whichever explanation one attempts, however, correct knowledge of the electronic state of the cation is a prerequisite for any meaningful discussion. Although this knowledge is satisfactory for the SF6 matrix, our present results show that the situation is less clear for the CFCl2CF2C1 matrix.Additional experimental evidence has been collected by means of deuteration and by considering the decomposition of the cations at higher temperature^.^ The deuteration experiments give definitive confirmation that the largest hyperfine coup- ings occur at the in-plane end-carbon hydrogens (H,) in the SF6 matrix and at the mid-carbon hydrogens (H,) in the other matrix. From the decomposition reaction one can see that the cations are deprotonated at an end carbon in the SF6 matrix and at the mid carbon in the CFCl2CF2C1 m a t r i ~ . ~ Both these experiments thus confirm the 2B, assignment for the SF6 matrix but, unfortunately, neither of them discriminates between the ,B2 and 2A, assignments in the other matrix. Deproton- ation, for instance, is expected to occur when the C-H bonds have been lengthened, but this singles out the C-Hi bonds in both the 2B2 and the *Ai states (cJ table 4).The experimental spectra of the cyclopropane cation at low temperatures [ref. (9) and fig. 21 seem to be affected by g-factor anisotropy in the CFC13, CFCl,CF,Cl and CF3CC13 matrices. The anisotropy (gl = 2.0023, g, = 2.0039 and g , = 2.0060)9 is larger than has previously been reported for hydrocarbon cation radicals.20321 Sevilla and coworkers22 recently observed that the e.s.r. spectrum of the methyl formate cation had marked g-factor anisotropy and showed chlorine hyperfine structure in the CFC13 matrix. Iwasaki et aL9 observed hyperfine lines caused by the CFC13 matrix in the cation spectrum of cyclopropane. These facts show that the cation and the matrix can interact.It is possible that the g-factor anisotropy of the cyclopropane cation noticed for the CFC13, CFC1,CF2C1 and CF3CC13 matrices is caused by an ion-matrix interaction.S. LUNELL, M. B. HUANG A N D A. LUND 47 According to Sevilla and coworkers, a strong interaction occurs when the differ- ence between the ionization potentials of the matrix and the solute molecules is small, which is indeed the case for both the cyclopropane and the propane cations in the CFC13, CFC12CF2C1 and CF3CC13 matrices. The difference is larger for the SF6 matrix, which implies that the propane cation is less affected by the matrix. This is consistent with the fact that the 2 B , ground state, predicted for an isolated ion, is obtained in the SF6 matrix and not in the other matrices.However, further work, both theoretical and experimental, is needed in order to understand the detailed mechanism of the matrix-solute interaction in these systems. 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