7228
J. Phys. Chem. 1991, 95, 7228-7233
-
splitting in carbenes and SiF2can be calculated with an accuracy of 1 kcal/mol by the LDA/NL scheme. It is finally concluded that both electron correlation and nonlocal corrections are essential for an accurate (f0.25 e v ) theoretical estimate of electron affinities.
Acknowledgment. This investigation was supported by the Natural Science and Engineering Research Council of Canada (NSERC). We acknowledge an international collaboration grant from NSERC to G.L.G.We thank the University of Calgary
for access to their Cyber 205 facilities. Regism NO. H2, 1333-74-0; C, 7440-44-0; FI, 86-73-7; C12, 778250-5; Br2,7726-95-6; 12. 7553-56-2; CH, 3315-37-5; CF, 3889-75-6; CCI, 3889-76-7; CBr, 3889-77-8; CI, 3889-78-9; CH-, 28604-54-8; C F , 33412-11-2; CCI-, 117129-77-8; CBr-, 135226-14-1; CI-,60454-96-8; C H ~ 2465-56-7; , C F ~ 2154-59-8; , CCI,, 1605-72-7; CFCI, 1691-88-9; CBr,, 4371-77-1; 4371-79-3; SiF,, 13966.664 CH;, 50928-07.9; C F ~ 6621 , 2-40-6; cciy, I I 8364-73- I ; CFCI-, 69489-63-0; CBr;, 135226-15-2; CIy, 135226-16-3.
Theoretical Studies of the Low-Lying Excited States of Bicyclobutane: Photochemical Pathways to Butadiene and Cyclobutene Gary D. Bent Physics Department, University of Connecticut, Storrs, Connecticut 06269
and Angelo R. Rossi* T. J. Watson Research Laboratory, IBM Research Division, Yorktown Heights, New York 10598 (Received: January 22, 1991)
Both self-consistent field and configuration interaction calculations have been performed with several different basis sets to determine the low-lying excited states of bicyclobutane (C,H6).The only low-lying excited states found to exist below 7.0 eV contained substantial Rydberg character. Oscillator strengths calculated for those states with vertical excitation energies close to 6.7 eV indicate that three states are capable of forming C4Hsisomers when bicyclobutane is photolyzed at 6.7 eV. A detailed discussion of probable pathways for the photochemical decomposition of bicyclobutane to its isomeric partners, butadiene and cyclobutene, is given.
Introduction The energetics for thermal pathways involved in the interconversion of C4H6isomers (bicyclobutane, cyclobutene, and butadiene) has been extensively calculated.'-5 It was found that bicyclobutane converts to trans-butadiene while cyclobutene yields cis-butadiene. Both the thermal and photochemical conversion of cyclobutene to butadiene have also been studied theoretically." Although excited states of butadiene have been extensively investigated*I6 and the ground state of bicyclobutane has been the subject of several calculation^,'^-^^ only one calculation to date ( I ) Spellmeyer, D. C.; Houk, K. N. J . Am. Chem. Soc. 1988,110,3412. (2) Breulet, J.; Schaefer 111, H. F. J . Am. Chem. Soc. 1984, 106, 1221. (3) Hsu, K.; Buenker, R. J.; Peyerimhoff, S.D. J . Am. Chem. Soc. 1972, 94, 5639. (4) Hsu, K.; Buenker, R. J.; Peyerimhoff, S. D. J . Am. Chem. Soc. 1971, 91, 21 17. (5) Shevlin, P. B.; McKee, M.L. J . Am. Chrm. SOC.1988, 110, 1666. (6) Grimbert, D.; Segal, G.; Devaquet, A. J . Am. Chem. SOC.1975, 97, 6629. (7) Morihashi, K.; Kikuchi, 0.;Suzuki, K. Chrm. Phys. Lerr. 1982, 90, 346. (8) Breulet, J.; Schaefer 111, H. F. J . Am. Chem. Soc. 1984, 106, 1221. (9) Nascimento, M.A. C.:Galdard 111, W. A. Chem. Phys. 1979.36.147. (IO) Aoyagi, M.; Osamura, Y.;Iwata, S.J . Chem. Phys. 1985,83. 1140. (11) Cave, R. J.; Davidson, E. R. Chem. Phys. Leu. 1988, 148, 190. (12) Hosteny, R. P.; Dunning Jr., T. H.; Gilman, R. R.; Pipano, A,; Shavitt. I. J. Chem. Phys. 1975, 62, 4764. (13) Shih, S.;Buenker, R. J.; Peyerimhoff, S.D. Chcm. Phys. Leu. 1972, 16, 244. (14) Buenker, R. J.; Whitten, J. L. J . Chcm. Phys. 1968, 49, 538. (15) Dunning, Jr., T. H.; Hosteny, R. P.; Shavitt, 1. J . Am. Chem. Soc. 1973, 95, 5067. (16) Nascimento, M . A. C.; Goddard 111, W. A. Chem. Phys. 1980, 53, 251. (17) Newton, M . D.; Schulman, J. M.J. Am. Chcm. SOC.1972,94,767. (18) Hehre, W. J.; Pople, J. A. J . Am. Chcm. SOC.1975, 97, 6941. (19) Pomerantz, M.; Abrahamson, E. W. J . Am. Chem. Soc. 1%6, 88, 3970. (20) Bader, R. F.W.; Tang, T. H.; Tal, Y.; Biegler-Konig, F. W. J . Am. Chcm. SOC.1982, 104,946.
0022-3654/9 1 /2095-7228$02.50/0
TABLE I: Calclrlrted and Experimental Geometries of the C d State of Bicyclabutrneo parameted 4 - 3 1 G ( s ~ ) ~ 4-31GC 6-3 lGSe exDtd 1.479 1.485 1.463 1.497 1.063 1.069 1.076 1.071 1.503 1S O 1 1.488 1.498 1.074 1.080 1.084 1.093 1.076 1.083 I .088 1.093 133.4 132.5 131.7 119.6 120.0 120.7 121.7 121.7 121.6 121.2 122.9 124.2 124.6 124.8 121.5 1.2 0.5 1.8 -0.7 -1 54.62656 -1 54.62451 -1 54.87 1 14
All calculated geometries were optimized at the Hartree-Fock level. *This work. 'Reference 27. dReference 36. eHartree-Fock energies are given in atomic units. /Distances are given in A, and angles are given in degrees. A complete description of parameters is shown in Figure I.
has obtained excited-state energies for bicyclobutane.28 The excited states of bicyclobutane have been investigated spectroscopically by Wiberg et al.29930who discovered a weak (21) Gassman, P. G.; Greenlee, M. L.; Dixon, D. A,; Richtsmeier, S.; Gougoutas, J. Z. J . Am. Chem. Soc. 1983, 105, 5865. (22) Paddon-Row, M. N.; Houk, K.N.; Dowd, P. Tetrahedron Leo. 1981,
22, 4799. (23) Wiberg, K. B.; Bader, R. F. W.; Lau, C. D. H. J . Am. Chcm. Soc. 1987, 109, 1001. (24) Wiberg, K. B. J. Am. Chem. Soc. 1983, 105, 1227. (25) Wiberg, K. B.; Bonneville, 0.;Dempsey, R. lsr. J . Chcm. 1983,23, 85. (26) Goldberg, A. H.; Doherty, D. H. J. Am. Chcm. Soc. 1983, 105, 284. (27) Skancke, P. N. J . Mol. Srrucr. ( T H E W H E M ) 1982,86, 255. (28) Walters, V. A.; Haddad. C. M.; Thiel, Y.;Colson, S.D.; Wiberg, K. B.;Johnson, P. M.;Forcsman, B. J . Am. Chrm. Soc. 1991, 113, 4782. (29) Wiberg, K. B.; Ellison, W. B.; Peters, K. S.J . Am. Chem. Soc. 3977, 99, 3941.
0 199 1 American Chemical Society
The Journal of Physical Chemistry, Vol. 95, No. 19, 1991 1229
Excited States of Bicyclobutane
TABLE 11: Vertical Excitation Energies (eV) for the Rydberg States of Bicyelobutrne from HartreeFock CalculsHom state 4;31G(~p)~b 4-3 1 G(p)”sb 4-3 1G’(p P b 4-31G(3~p)” 1 ‘Al 2’Al(7a,-8a,) I ’Bz(7a,-4bz) 3’A,(7a ,--sa,) I I B, (7a ,-5b,) ’A2(7a,-+2a2) IB, (7a,+6b,) lB2(7a,-5bz) lAz(7a,-3az) ‘Az(laz+8a,) 2Al(7al-“)
0.0 6.04 6.44
0.0 6.36 6.46
0.0 6.25 6.32
6.54 7.37
6.58 7.36 8.15 8.18 8.21 8.35 8.59
6.45
0.0 6.04 6.43 6.44 6.60 7.49
(lv 2.6 20.4 27.5 30.2 33.5 25.5
8.61
Osee explanation of basis set notation given in the text. bCalculated at the 4-31G optimized geometry. CCalculatedat the 4-31G(3sp) optimized geometry. dThe average spatial extent of the highest occupied molecular orbital, (r2), in A2,calculated at the 4-31G(3sp) optimized geometry.
absorption at 5.7 eV and a stronger peak at 6.6 eV as well as several other peaks. Robin” measured a similar spectrum to that of Wiberg et al.; Walters et measured the two-photon spectrum of bicyclobutane and calculated several transition energies for the excited states. Those calculations are in good agreement with the values presented here and provide an excellent complementary study to this work. Recently, the photochemistry of bicyclobutane has been examined by Becknell et aL3* who irradiated bicyclobutane with 185-”wavelength radiation and obtained butadiene and cyclobutene as the primary photoproducts. Adam et al.33irradiated both cyclobutene and bicyclobutane with 185-nm radiation. The main products from the photolysis of bicyclobutane were the same as those seen by Becknell et al., although the percentages were different. The calculations described in this paper were undertaken to discover which excited states of bicyclobutane could be responsible for the photochemistry seen by these investigators.
Calculational Methods Basis Sts. The starting point for all calculations is the 4-3 1G basis” augmented with diffuse s and p functions. Several different sets of diffuse functions were added to the 4-31G basis to determine their effect on bicyclobutane geometry and on the nature of the low-lying excited states. One of the major focal points of the present work involves obtaining information on whether the excited states of bicyclobutane are predominately Rydberg. The notation 4-31G(p) defines a 4-31G basis set with diffuse p functions (ap= 0.02) while 4-31G(sp) denotes both diffuse s and p functions (as, a p = 0.02) added to all carbons atoms. The 4-31G*(p) denotes diffuse p functions ( a p= 0.02) plus an additional set of d polarization functions (ad = 0.80) on all carbon atoms. Finally, the 4-31G(3sp) basis denotes a diffuse set of three contracted s and p Gaussian functions selected to fit a Slater-type orbital with exponent ({3s = 0.483) added only to the bridgehead carbon atoms (C, and &). Optimized Ground-State Geometries. A view of the bicyclobutane molecule, the coordinate system used, and the structural parameters optimized in the SCF calculations, are given in Figure 1. The geometry of the ground state was optimized with a 4-31G(sp) basis (a,,a = 0.02) on the bridgehead carbons. The optimized geometricaf parameters calculated with this basis set are given in Table 1 and are compared to the optimized geometries of S k a n ~ k calculated e~~ using a 4-31G basis and a 6-31G* basid5 as well as the experimental geometry.36 The work of Skancke (30) Wiberg. K. B.; Peters, K. S.; Ellison, 0. B.; Aberti, F. J. Am. Chem. 1 9 n , 99,3947. (31) Robin, M. B. Higher Excited States of Polyatomic Molecules; Academic Press: New York. 1974; p 152. (32) Becknell, A.; Bcrson, J. A.; Srinivasan. R. J . Am. Chem. Soc. 1985. 107, 1076. (33) Adam, W.; Oppenlander, T.; Zang, G. J . Am. Chem. Soc. 1985,107, 3n.I I
SOC.
J7L I.
(34) Ditchfield, R.; Hehre, W. H.; Pople, J. A. J . Chem. Phys. 1971, 54. 724. (35) Hehre, W. H.; Ditchfield, R.; Pople, J. A. J . Chem. Phys. 1972, 56, 2257.
10
Figure 1. View of the bicyclobutane molecule showing the coordinate system, the atom labeling, and the structural parameters used in the calculations.
shows that adding a polarization function to the carbons results in a shortening of the carbon-carbon bonds compared to the experimental values. The 4-31G basis set with diffuse functions produced carbon-carbon bonds much closer to that of experiment. Ishida and O h n ~ have ) ~ shown that adding single polarization functions to double-h basis sets concentrates too much of the electronic charge density in the bonding regions between atoms. On the other hand, the carbon-hydrogen bonds determined with the 6-31G* basis are in better agreement with the experimental values. Excited States: SCF Calculations. The ground state of bicyclobutane (X’A,) has the following configuration: Ib: la: 2a: Ib: 3a: 2b: 4a: 2b: 5a: 6a: 3b: 4b: 3b: la: 7a: Calculations were initially performed with only the 4-3 1G basis set for all reasonable low-lying excited singlet states using the orthogonalized constrained basis set expansion (OCBSE) methodB from the GAMES system of programs.39 The excitation energies were found to be above the experimental ionization energy of 9.12 eV.3’ The OCBSE method, along with the various basis sets with diffuse functions which are described above, was then used to determine whether or not the low-lying excited states of bicyclobutane are Rydberg in character, similar to the situation with butadiene and cyclobutene. The vertical excitation energies for low-lying excited states of bicyclobutane, calculated by the ASCF method using the various basis sets with diffuse functions, are given in Table 11. It becomes clear from studying Table I1 that diffuse (36) Cox, K. W.; Harmony, M. D.; Nelson, G.; Wiberg, K. B. J . Chem. Phys. 1969, 50, 1976. (37) Ishida, T.; Ohno, K. Int. J . Quant. Chem. 1989, 35, 257. (38) Hurley, A. C. Introduction to the Electron Theory of Small Molecules; Academic Press: New York, 1976; p 262. (39) Dupuis, M.; Spangler, D.; Wendoloski, J. 1. GAMS (General Atomic and Molecular Electronic Structure System) 1980; Program Q G O l , Software Catalog, University of California, Berkeley.
1230 The Journal of Physical Chemistry, Vol. 95, No. 19, 1991
Bent and Rossi
TABLE 111: Vertical Excitation Emergies (eV) for the Rydberg States of Bicyclobutane from SCF a d CI C a l ~ u l a t i oUsing ~ the 4-31C(3sp) Basid state SCF CISDTQb CISD-le CISD-2" 2'Al 6.04 (6.55) 5.92 (6.58) 6.31 (6.42) 1'B2 6.43 (6.94) 6.41 (6.97) 6.29 (6.95) 6.77 (6.89) 3'A, 6.44 (6.95) 6.37 (7.03) 6.79 (6.91) I'B, 6.60 (7.1 1) 6.32 (6.98) 6.90 (7.02) 1'A2 7.49 (8.00) 7.32 (7.98) 7.83 (7.95) 2Al 8.61 (9.12) 8.46 (9.12) 9.00 (9.12)
TABLE IV: Corrected Vertical Excitation k r g i e s (eV) a d Oscillator Strengths, f(r), for the Rydberg States of Bicyclobutane" state AE % full Clb (r2) I'A, 0.00 99.6 2.3 99.1 23.5 2'A, 6.42 3.9 X IO4 1'B2 6.89 3.1 X 98.4 22.7 3'A, 6.91 1.7 X IO-* 96.5 19.9 I'B, 7.02 3.5 x 10-3 98.9 1'A2 7.95 98.8 22.0 2Al 9.12 99.1
a The values in parentheses are corrected by the difference between the calculated and the experimental ionization energies. bCISDTQ using the GAMESS program with excitation into an active space consisting of 5 HOMOs and IO LUMOs. 'CISD using the GAMESS program with excitation into an active space consisting of 9 HOMOs and 12 LUMOs. dMultireference ClSD using the MELD program.
'Also given is the average spatial extent, (G),in A2, of the total C1 wave function for each excited state. All quantities are from a CISD calculation with the 4-31G(3sp) basis. bEquation 1 in text is used as a measure of how close the calculations are to the full CI limit.
functions are needed to describe the excited states of neutral bicyclobutane. The results for the 431G*(p) yield lower excitation energies than the same basis without the d functions by approximately 0.1 eV. The spatial extent, (r2), of the excited orbitals for each of the low-lying states was calculated with the 4-31G(3sp) basis. The large values of (rZ) are consistent with the diffuse nature of Rydberg orbitals confirming that the 2IAI, I1Bz,3IAI, 1'B,,and 1!AZstates are essentially all Rydberg in character. Excited States: CI Calculations. To determine more accurate values of the low-lying Rydberg states of bicyclobutane, a series of configuration interaction (CI) calculations were undertaken with the GAMESS system of programs. The 4-31G(3sp) basis set was used for the CI calculations on bicyclobutane, and the geometry corresponded to the Hartree-Fock-optimized ground state for each state under consideration. Polarization functions are not used in the basis set since they were shown to be unimportant for similar calculations on Rydberg states of molecule^.'^,^ In a limited CI it is important to start with the set of orbitals that best describes the state being ~ a l c u l a t e d . ~ ,For ~ ' each excited state of bicyclobutane the eigenvectors for the CI calculation were obtained from the corresponding parent configuration of the SCF calculation. The results of a C1 calculation involving single, double, triple, and quadruple excitations (CISDTQ) for the I'B, state are shown in the third column of Table 111 and were derived from an active space consisting of the five highest occupied molecular orbitals (HOMO's) and the IO lowest unoccupied molecular orbitals (LUMO's) of bicyclobutane. The ground-state CI calculation was similar to the CI calculation for the excited state except that the active space consisted of the 4 occupied HOMO's and 11 LUMO's. For the singles and doubles CI calculations (CISD) shown in the fourth column of Table 111 (CISD-I), a larger active space was used consisting of the 9 HOMO's and 12 L U M O s of bicyclobutane. The active virtual orbital space must be selected with great care since this space is particularly ill-defined for configuration interaction calculations when diffuse functions are included in the basis.''*42 Thus a series of rotations were performed in which natural orbitals which had low occupation numbers after the CI calculation were replaced with virtual orbitals that were previously frozen. These rotations were continued until very little change in the energy resulted from changing orbitals as shown by the CISD-I results given in Table 111. The energies of CISD-1 also have an estimate of the quadruples contribution to the CI included. Experimental information on the excited states of bicyclobutane is scarce, making it difficult for comparison with the present theoretical calculations. However, the ionization energy is well known3! and comparison with the calculated values of the ionization energy are too low for both the CISD-I as well as the (40) Guest, M. F.; Rodwell, W.R. Mol. Phys. 1976, 32, 1075. (41) Buenker, R. J.; Peyerimhoff,S. D.;Kammer, W. E. J . Chem. Phys. 1971, 55, 814. (42) Shavitt, I. In Modern Theoretical Chemistry: Merhods of Electronic Strucrure Theory; Schaefer 111, H. F., Ed. Plenum: New York, 1977; Vol. 3, p 247.
m
CISDTQ values presented in Table 111. There is very little correlation energy associated with a Rydberg orbital since it occupies a different region of space than the valence orbital^.^^,^ Thus, the error made in calculating the ionization energy of bicyclobutane should be approximately the same error that is made in calculating the excited Rydberg state. The values in parentheses in Table 111 are the energies which were corrected by adding the difference between the experimental and calculated ionization energies. As can be seen, the agreement for the corrected energies of a particular state is good among different calculations even if one is a CI and the other an SCF calculation. This agreement between different types of calculations lends credence to this method of correcting the calculated excited-state energies. Although a method of correcting the energies of the Rydberg states was employed, it is very difficult to determine whether or not the same level of configuration mixing is performed for each state. Thus, the energies of the Rydbexg states were also calculated with the MELD^^ program which uses a perturbation formula to keep configurations that are higher than a certain energy threshold. Using the formula M,(kept) (1) AE,(kept) + AE,(discarded) XlOO where AE,(kept) is the sum of the perturbative, approximate energies for the configurations included, and AE,(discarded) is the sum for the configurations discarded, it is possible to determine how close the calculation is to the full CI limit. The CISD-2 values given in Table I11 are results for Rydberg states that were derived from using the MELD program with three reference configurations for each state. Clearly, this method of doing CI comes much closer to obtaining the correct ionization energy and presumably the correct excitation energy for the Rydberg states. The 3'AI and l'BIstates are very close to being degenerate in these calculations. The CISD-2 results change the order of these states from that calculated by using the CISD-1 methodology. Walters et aLZ8 have calculated transition energies for several low-lying states of bicyclobutane, and their values agree quite well with the results given here. The transition density matrix from MELD was used to calculate the dipole length matrix elements, ( llAI(rI#f),where #frepresents particular excited state under consideration. The oscillator strengths were calculated according to the formula46 fir) = %I( 11AllrlW2AE (2) The calculated values of the oscillator strengths and the corrected vertical excitation energies from the CISD calculation from MELD using the 4-31G(3sp) basis are given in Table IV. Also shown is the percentage of a full CI calculated from eq 1 as well as the spatial extent of the total CI wave function for each excited state." (43) Winter, N. W.; Goddard 111, W. A,; Bobrowicz, F. W.J . Chem. Phys.
1975, 62, 4325.
(44) Schaefer 111, H. F. The Electronic Srrucrure of Atoms and Molecules; Addison-Wesley: Reading, MA, 1972. (45) Davidson, E. R. QCPE 1991, 23, Program No. 580. (46) Buenker, R.J.; Shih, S. K.; Peyerimhoff, S. D.Chem. Phys. 1979, 36, 97.
Excited States of Bicyclobutane
The Journal of Physical Chemistry, Vol. 95, No. 19, 1991 7231
TABLE V Equilibrium CeomeMes and Adiabatic Excitation Energies for Some Rydberg States of Bicyclobutane from Hartree-Fock Calculrtiom with a 4-31C(sp) Basis 1 'Al 2'Al l'B2 l'BI 1.728 I .758 1.479 1.739 1.063 1.503 1.074 1.076 133.4 119.6 121.7 124.2 1.3 -154.62656 0.0
Fz-H'o Y a
W
7
EHP AE,C eV
1.071 1.494 1.074 1.os 1 127.1 133.9 126.0 120.3 -2.9 -154.43872 5.62
1.071 1.497 1.074 1.083 131.0 133.8 128.1 119.1 -4.5 -1 54.42885 5.89
1.069 1.499 1.068 1.083 127.1 132.9 127.8 119.6 -4.1 -154.42109 6.10
'All distances are given in A, and all angles are given in degrees. See Figure I for a complete description of parameters. bHartree-Fock
energies are given in atomic units. 'The excitations energies are corrected by 9.12 - 8.61 = 0.51 eV which is the energy difference between the calculated and experimental ionization energies of bicyclobutane. Several equilibrium geometries for the Rydberg states were optimized a t the Hartree-Fock level by using the 4-31G(sp) basis and are given in Table V along with the corresponding adiabatic excitation energies.
Discussion Spectroscopic Comparisons. Wiberg et al.29*30obtained the electronic absorption spectrum of bicyclobutane and observed a broad, unresolved band from 5.96 to 7.17 eV which they labeled states A, B, C, and D in Table 111of their paper. At approximately 8.1 eV, they measured a sharp increase in absorption which was labeled state E. Wiberg et aL30 also noted a sudden broadening of the vibrational bands a t 6.0 eV suggesting that bicyclobutane undergoes a photochemical transformation beginning a t that energy. Robin3' also described the electronic absorption spectrum of bicyclobutane, and there is substantial agreement between his spectrum and that measured by Wiberg.29 The present study focused on the low-lying excited states which may participate in photochemical transformations. Thus, we did not calculate other higher excited states that may appear in the absorption spectrum. However, there does not appear to be any pure valence excited states in bicyclobutane, although there may be excited states which exhibit Rydberg-valence mixing, particularly when the bonds in the molecule begin to stretch during the incipient stages of photochemical dissociation. The energies of higher Rydberg states may be obtained from the equation" E, = IE [R/(n*)Z] (3)
-
where IE is the ionization energy from the ground state, R is the Rydberg constant, n* = n - 6, and 6 is the quantum defect for the Rydberg series being considered. The oscillator strengths (f,, can also be calculated and should remain constant for a particular set of Rydberg levels.Is The quantum defects calculated for bicyclobutane using eq 3 as well as the predicted oscillator strengths are given in Table VI. The values of the calculated quantum defects are very similar to those determined by Nascimento and GoddardI6 for trans-butadiene. A comparison of the calculated vertical excitation energies and oscillator strengths compared to the experimental peak positions and oscillator strengths is given in Table VII. The theoretical values for states C and D are predicted from quantum defect theory as given previously in Table V1. There is good agreement between the calculated values and the experimentally measured positions for states B and D, but the calculated oscillator strengths are too low by about 30% for both states. It can be seen from Table IV that the vertical excitation energy for the 1 'A2 state is close to the peak position for state D. The 1 'A2 state was calculated without diffuse d functions in the basis
-
(47) McMurchie, L. E.; Davidson, E. R. J . Chem. Phys. 1977, 66, 2959.
1
-'
2
Figure 2. Possible reaction pathways for the photochemical transformation of bicyclobutane to (a) cis-butadiene, (b) cyclobutene, and (c)
trans-butadiene.
which are most likely needed to describe this state. The 1!A2state is not included in Table VI because it is a forbidden transition from the ground state, and its oscillator strength is probably much smaller than values predicted for the Rydberg 4 P states. Walters et a1.28 calculated the oscillator strength for the 1'A2 state to be less than 5 X The agreement between the calculated excitation energies and states A and C is poorer, but it is difficult to exactly locate these peak positions since they involve weak excitations forming a shoulder on much stronger transitions. Walters et ala2*locates the band origin for state A at 5.70 eV which agrees well with the calculated excitation energy of 5.62 eV shown in Table V for the relaxed 2'A1 state. The oscillator strength is about 30% lower than the observed value which is consistent with the differences observed for states B and D. These results give us some degree of confidence in assigning state A as the calculated 2'AI state. The evidence is not as strong for assigning the calculated 'A1(4s) state as state C in the experimental spectrum; however, the experimental peak assignment and calculated excitation energy are close and the oscillator strengths are the same order of magnitude. Robin" assigns state A to 3s Rydberg transition, state B to a 3p Rydberg transition, and states C and D to higher Rydberg transitions. The calculated excited Rydberg states are consistent with these assignments. The sharp increase in absorption beginning at 8.1 eV, labeled E by Wiberg, is attributed by Robin to u* transitions which may be a mixture of Rydberg and valence character. Photochemical Comparisom In the work of Becknell et. al.,32 the irradiation of bicyclobutane a t 185 nm produces butadiene and cyclobutene in the ratio 1O:l which was later revised to a 13:l ratio.48 Adam et using the same solvent and wavelength, produced butadiene and cyclobutene as primary products but essentially in the ratio 1:l. Becknell" suggested that these workers may have used a bicyclobutane sample contaminated with cyclobutene. Both sets of investigators postulated the sequence of reactions shown in Figure 2a as the pathway by which butadiene was formed while Adam et aLs3 favored the pathway shown in Figure 2b for the formation of cyclobutene. In addition, Becknell et ai. postulated the pathway shown in Figure 2c as an alternative possibility for the formation of butadiene. By performing deuterium (2H) and carbon-13 (I3C)labeling studies on bicyclobutane, they were able to show that butadiene formation, in a of ratio 2:1, is possible from both pathways shown in Figure 2, a and c. Becknell et mentioned the possibility for more than one excited state participating in these reactions, and this will be discussed below in more detail. As can be seen in Table IV, there are four possible excited states in the range of irradiation at 185 nm (6.7 eV) and include the 2'AI, 1'B2, 3'A1, and l'BI states. It is not surprising that these states are clustered close together since the 2'AI state is essentially a Rydberg state of S symmetry derived from excitation to the 3s
-
(48) Becknell, A. Diss. Absrr. h i . 1988, 848, 2971. Available from University Micofilms, Int. order number DA8728 107.
7232 The Journal of Physical Chemistry, Vol. 95, No. 19, 1991
Bent and Rossi
TABLE VI: Oscillator Strength0 and Excitation Energies (eV) of Rydberg Series for the Bicyclobutane MdeculeO
np,('BJ
AI)
6 = 0.75 n
En
3
6.42 7.83 8.37 8.63 8.77 8.86
4 5
6 7
8
np,('B2)
6 = 0.45
fn 3.9 x 1.3 X 5.8 X 3.1 x 1.8 X 1.2 x
fn
En
7.02 8.04 8.46 8.68 8.80 8.88
10-4
IO4 IO" 10-5
10-5
3.5 x 1.3 x 6.2 X 3.4 x 2.1 x 1.3
nPz('Al)
8 = 0.53
X
fn
En
lo-'
10-3
IO4 IO4 10-4
IO4
6 = 0.52
6.89 7.99 8.44 8.67 8.79 8.88
3.1 X 1.1 x 5.2 X 2.9 x 1.7 x
fn
E"
6.91 8.00 8.44 8.67 8.80 8.88
10-2
IO-' 10-3
10-3 1.1 x 10-3
1.7
X
6.2 x 2.9 x 1.6 X 9.5 x 6.2 X
10-3
10-3 IO-' 10-4
IO4
'The series n = 3 corresponds to calculated values while the higher series, n L 4, are predicted values based on quantum defects. TABLE VII: Comparison of Experimental Peak Positions for Bicyclobutane with Cakulrted Vertical Excitatiom Eaergies and Comparison of Experimental rad Theoretical M i t o r Sh.eantbs
experimental stateb peak, eV f, A 5.8.' 5.7bL 5.3 X IO-'
state 2'Al(3s)
theoretical E, eV f/ 6.42 3.9 X 10-4
B
6.6H
7.4 X
I'B2(3py) 3'Al(3p,) 1'Bl(3p,)
6.89 6.91 7.02
5.2 X IOb2
c
7.4a-C
6.6 X lo-'
lA,(4s)
7.83
1.3 X IO4
'B2(4Py) 'Al(4p,) IBI(4p,)
7.99 8.00 8.04
1.9 X
D
8.0: 7.9b.c 2.8 X
- - - - _'.
'Robin (ref 31). bWiberg et al. (ref 29). (Peak positions were determined as one-half the bandwidth given in ref 29. "The calculated oscillator strengths corresponding to states B and D are evaluated by summing the oscillator strengths given in Table VI for the 3P and 4P Rydberg states, respectively. TABLE VIII: Mulllken Population Analysis for tbe Ground State and Several Excited States1
overlap populationb state I'A, 2A, 2'Al 3'Al I'B2
I'B,
CI-C3 -0.051 -0.579 -0.189 0.079 -5.778 0.027
Cl-C2
C3-H6
C2-Hs
C2-Hlo
0.314 0.303 0.309 0.201 0.312 0.21 1
0.808 0.749 0.737 0.731 0.807 0.756
0.795 0.764 0.749 0.780 0.767 0.804
0.738 0.744 0.753 0.765 0.747 0.754
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
I'
'
" ""
'
" "
'
I
.
'
'
~
" " "
I' '
""
'
~
~
'
" ""
'
"The wave functions are derived from SCF calculations. bSee description of structural parameters given in Figure l . orbital while the IiB2, 3'AI, and l l B 1states all have symmetry of P Rydberg states involving excitation to 3p,, 3p,, and 3p, orbitals, respectively. In an atom, all these states would be degenerate, and, in bicyclobutane, the states derived from P symmetry are nearly degenerate. Orbital plots of the 7al orbital (1 IA, state), the 8al orbital (3IAl and the 4b2 orbital ( 1'B2 state), are given in Figure 3 to illustrate several features of bond fragmentation in bicyclobutane. A Mulliken population analysis for the ground state and several excited states of bicyclobutane calculated at the SCF level is given in Table VIII. Any attempt to quantify the relationship between population analysis and electron density is risky but nonetheless may provide qualitative guidance in understanding the origin of photochemical transformations. Furthermore, the population analysis given in Table VI11 was computed with the 4-31G(3sp) basis which contains diffuse functions and may produce unreliable results. However, the results for the population analysis will be used to show trends by comparing population changes of the ground state with the excited states. (49) The initial configuration for the 3'A, excited state is formed by removing an electron from the doubly occupied 7al orbital and placing it in the 9al orbital of the ground state. However. the SCF calculation on the 3'A, excited state lowers the energy of the highest singly occupied orbital so that it becomes the 8al orbital.
Figure 3. Plots of the 7al orbital for the ground state (top), 8al orbital for the 3'Al state (middle), and 4b2orbital for the 1'B2 state (bottom) in the plane of the bicyclobutane molecule which contains atoms CI,C3, H5, and H6 bz plane). The dimensions of the 7al orbital are 4.5 au X 4.5 au and have contour values 0.05e/au3 while the 8a, and 4b2orbitals have a spatial extent of 13 au X 13 au and have contour values of values 0.004e/au3.
The overlap population analysis, in going from neutral bicyclobutane to the radical cation, yields a substantial weakening of the CI-C3 bridgehead bond. One might then be tempted to speculate that excitation from the 7al orbital to any diffuse Rydberg orbital, having minimal bonding capability and little interaction with the molecular core, would produce weakening of the bridgehead bond with little change in the other C-C bonds. The actual situation is graphically depicted in Figure 3 where 2s and 2p orbitals from the molecular core mix with diffuse Rydberg orbitals to produce bonding or antibonding regions. For the 8al orbital in the 3'Al state the molecular core orbitals mix to
7233
J. Phys. Chem. 1991, 95, 7233-7239 strengthen the CI-C3 bond, while for the 4b2 orbital in the 11B2 state, the 2py orbitals mix to produce an antibonding region across the CI-C3 bond. The oscillator strength of the 2lA1 state Cf(r) in Table IV) is relatively small and further off-resonance than the other states eliminating it from consideration as one of the states leading to the products in Figure 2. An examination of the 8al orbital in Figure 3 reveals that the bridgehead bond should be strengthened; a population analysis confirms this result but also suggests weakened C-C side bonds, indicating a tendency for the 3'AI state to produce a trans-butadiene product according to the concerted pathway given in Figure 2c. It is also interesting to attempt to predict how the intermediate (2)in Figure 2, a or b, will evolve from examination of the 4b2 orbital derived from the 1 IB2 state and shown in Figure 3. The 4b2 orbital mixes in a substantial 2p, antibonding character which leads to a very weakened bridgehead bond. This result is confirmed in the population analysis given in Table VI11 showing a very negative value for the C-C bridgehead bond while the C-C side-bond populations show no significant change. Becknel14' cites the 1'B2 state as being the most likely state for forming cis-butadiene by the mechanism given in Figure 2a. It is possible that 2 would open to give a carbene (3)in Figure 2a, and subsequently produce cis-butadiene or cyclobutene (3)in Figure 2b by hydrogen migration. The population analysis of the l'BI state given in Table VI11 shows a strengthened bridgehead C-C bond and weakened C-C side bonds yielding a trend similar to the 3'AI state. Thus, the l'BI state may also participate in the formation of trans-butadiene as shown in Figure 2c. Some of the structural changes prediced by the Mulliken population analysis are partially supported by an examination of Table V. In the relaxed 1'B2 and l'BI states, the bond distance across the bridge is greatly increased over that of the ground state, reflecting the weakened nature of this bond. The flap angle y is markedly increased from ground-state value, leading to a more planar structure. The assignment of the three Rydberg states of bicyclobutane, nearly degenerate at 6.9 eV, to photochemical products is suggested by the shape of the Rydberg orbitals obtained from orbital plots and a Mulliken population analysis. However, the key word is suggested. Much more must be known about the complete
potential energy surfaces of each of the excited states before these suggestions can be taken as a definite possibility. For example, the potential energy surfaces for the excited states may cross or mix by vibrational coupling allowing each state to contribute to more than one product.
Conclusions The calculated excitation energies of three low-lying states in bicyclobutane are nearly degenerate at 6.9 eV and have essentially 3P Rydberg character. The calculated 3P Rydberg states correspond to a broad absorption band which peaks at 6.6 eV. The sum of the calculated oscillator strengths for these states agrees well with the measured oscillator strength. The predicted 4P Rydberg states correspond to a broad absorption band with a peak at 7.8 eV. The sum of these predicted oscillator strengths agrees well with the measured oscillator strength. The calculated 2'AI state, with 3 s Rydberg character, and the 'Al state with 4 s Rydberg character, correspond to weak transitions which experiment locates at 5.8 and 7.4 eV, respectively. The calculated and predicted oscillator strengths are both in good agreement with measured values for these S Rydberg states, The calculated oscillator strengths indicate that all three 3P Rydberg states are capable of participating in photochemical isomerizations that occur upon irradiating at 6.7 eV. Based upon the bonding characteristics of the excited Rydberg orbitals and population analyses, the present calculations point to mechanisms in which photochemical decomposition from the 11B2state leads cis-butadiene and/or cyclobutene while the l'BI and 3'AI excited states produce trans-butadiene via a synchronous pathway. Acknowledgment. We thank Professor Ernest Davidson for supplying us with the MELD program and for many helpful discussions. Professor Kenneth Wiberg was extremely helpful in providing us with an interpretation of the absorption spectrum of bicyclobutane. We are also grateful to Professor Jerry Berson and Dr.R. Srinivasan for their help with the experimental photochemical results. Finally, G.D.B. thanks his colleagues, Professors J. Javanainen, G. Epling, and H. Frank, for their assistance in understanding the photochemical equations, and Dr.Stephen Blechner who interfaced the output from GAMES to the POLYATOM properties package.
Nature of 2a/l a* Three-Electron-Bonded Chlorlne Adducts to Sulfoxldes Kamal Kisbore and Klaus-Dieter Asmus* Hahn- Meitner-Institut Berlin, Bereich S,Abteilung Strahlenchemie, Postfach
39 01 28,
D-1000 Berlin 39,
Germany (Received: February 12, 1991; In Final Form: April 10, 1991) Reaction of sulfoxide radical cations, R2S0.+,with chloride ions in acidic aqueous solutions (pH 5 6) leads to optically absorbing transient RsO:.Cl radicals, which are characterized by a sulfurchlorine threeelectron bond containing two bonding a-electrons and one antibonding u* electron. The same species is formed upon oxidation of sulfoxides by C12*-,although only with relatively low rate constants. The measured A, are 390, 400, and 410 nm for the R2SO:.Cl species with R = Me, Et, and n-Pr, respectively. Equilibrium constants for R2SO'+ + C1- s R2SO:.CI have been determined to be 560,600, and 575 M-I, for the same respective series of species (error limit f20%). It is considered that our three-electron-bonded species is identical with an electronically not further specified chlorine-atom adduct to sulfoxide, R2SO(CI)', observed earlier in sulfoxide-containing solutions of carbon tetrachloride and dichloromethane. The R2SO:.CI exhibit oxidizing properties and are shown to oxidize, for example, organic sulfides and disulfides (rate constants on the order of lo* M-l S-') or SCN(rate constants on the order of IO9 M-'s-l). The optical and kinetic results are discussed in light of the electronic properties of the radical species.
Introduction The direct identification and characterization of transients generated upon oxidation of organic sulfoxides has been the subject of several but not too many investigations. Detailed information exists on the neutral intermediates generated in oxidation of 0022-3654/9 1/2095-7233$02.50/0
sulfoxides by 'OH radicals as studied by pulse radiolysis' or ESR flow photoW.24 This Process Proceeds via addition of the (1) Veltwisch, D.;Janata. E.;Asmus, K.-D. J . Chcm. Soc., Perkin Trans. 2 1980, 146.
Q 1991 American Chemical Society
