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decreased as the sparingly soluble polymer is dissolved. This “disordering” of the nematic host has recently been studied both experimentally62and t h e ~ r e t i c a l l y . ~ ~ The self-consistent coupling between short- and longrange orientational ordering is of course not overwhelmed in the case of bulk polymer melts.64 Here each chain is “dissolved” not in a nematic of small molecules but in a sea of other long flexible polymers. Long-range orientational ordering-a nematic state-arises from the mutual (62) B. Kronbere. I. Bassienana. and D. Patterson. J. Chem. Phvs.. 82. 1714 (1978); A. Dibault, CrCas&rande, M. VeyssiC, and B. Deloche; Phys. Reu. Lett., 45, 1645 (1980). (63) F. Brochard-Wyart, C. R. Acad. Sci. (Paris), 289, 229 (1979). (64) See, for example, the following review discussions of the experimental situation: F. Cser, J. Phys. Colloq. (Orsay, Fr.), C3, Supplement No. 4, Tome 40, C3-459(1979); E. T. Samulski and D. B. DuPrB, Adu. Liq. Cryst., 4, 121 (1979). Also, many papers on the subject have been assembled in “Liquid Crystalline Order in Polymers”, A. Blumstein, Ed., Academic Press, New York, 1978.
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interaction of the closely packed anisotropic units (persistence lengths) of each chain. In turn these “particles” have their size enhanced by the nematic field and thereby stabilize further the long-range ordering.& Similar effects have recently been considered@as well in rubber elasticity contexts, where the flexible polymer chains are cross-linked to form a network.
Acknowledgment. Over the course of the past several years I have had the great pleasure of collaborating with Drs. Boris Barboy, Avinoam Ben-Shaul, and Yitzhak Rabin on the researches described in this review. I thank them heartily for making these efforts so scientifically fruitful and personally enjoyable. This work was supported in part by NSF Grant CHE80-24270. (65) P. Pincus and P. G. de Gennes, J . Polym. Sci.: Polym. Symp., 65, 85 (1978); Y. Kim and P. Pincus, ACS Symp. Ser. No. 74 (1978). (66)J. P. Jarry and L. Monnerie, Macromolecules, 12, 317 (1979).
ARTICLES Excited States and Photochemistry of Saturated Molecules. 11. Potential Energy Surfaces in Low-Lying States of Ethane James W. Caldwell and Mark S. Gordon’ Department of Chemistry, North Dakota State University, Fargo, North Dakota 58105 (Received: Februaty 1, 1982; I n Final Form: June 1, 1982)
Ab initio calculations at both the restricted Hartree-Fock (RHF) and singly excited configuration interaction (SECI)levels have been carried out on sections of the potential energy surfaces for a number of low-lying excited singlet electronic states of ethane. All vertical states below the first ionization potential are predominantly Rydberg in character, as are all minima detected on the potential energy surfaces. The lowest IE, state is predicted to have only a very small (- 1kcal/mol) barrier separating its minimum-energy structure from the 1A” ethylidene + IXg+ H2products. Since the vertical E, molecule has more than enough energy to surpass this barrier, the state is effectively dissociative. The fact that it is also electronically forbidden may explain why the UV spectrum of ethane exhibits vibrational structure.
Introduction The vacuum-UV photolyses of the light normal alkanes are dominated by molecular elimination1 of H2at threshold energies. The threshold absorption spectra2are generally broad and featureless, with the striking exception of ethane, which possesses a clearly resolvable vibrational fine str~cture.~ The lack of features in the methane spectrum is evidently due to an allowed absorption to a state which is directly diss~ciative.~ The lowest vertical singlet state is (1) P. Ausloos and S. G. Lias in “Chemical Spectroscopy and Photochemistry in the Vacuum UV”, C. Sandorfy, P. Ausloos, and M. Robin, Eds., Reidel, Dordrecht, Netherlands, 1974, p 465. (2) B. A. Lombos, P. Sauvageau, and C. Sandorfy, J.Mol. Spectrosc., 24, 253 (1967). (3) E. F. Peamon and K. K. Innes, J. Mol. Spectrosc., 30,232 (1969). (4) M. S. Gordon and J. W. Caldwell, J. Chem. Phys., 70,5503 (1979); M.S.Gordon, Chem. Phys. Lett., 52, 161 (1977). 0022-3654/82/2086-4307$01.25/0
11T2which distorts from Tdto C2”symmetry and dissociates with no barrier to methylene (CH,) and HP. For C3 and higher alkanes, the lack of vibrational structure may be due to excitation into dissociative states or to a high density of vibronically coupled allowed states. The case of ethane is intriguing since the threshold photolyses5*were performed with 8.4-eV radiation, whereas the presumed 0-0 peak in the (allowed) absorption spectrum occurs at 8.65 eV. This indicates that the predominant threshold reaction may arise from absorption to a formally dipole-forbidden state. Calculations on the vertical spectrum of ethane6,7 (5) (a) R. F. Hampson, J. R. McNesbey, H. Akimoto, and I. Tanaka, J . Chem. Phys., 40, 1099 (1964); (b) S. G. Lias, G. J. Collins, R. E. Rebbert, and P. J. Ausloos, ibid., 52, 1841 (1970).
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suggest that there are two dipole-forbidden singlet states (2Ab and lEg in D3dsymmetry) below the first allowed state. So, the threshold photochemistry and the absorption spectrum may be due to different electronic states. In addition to reaction 1,the other photoprocesses which are observed for ethane are
+ H~ C2H6 A CH, + CH2 C2H6 A ~
CzH6
2
2CH3
5
(2)
(3) (4)
Reaction 2 steadily increases in importance as the photolysis energy is increased5b and becomes the dominant process near the ionization potential. Reaction 3 is only important5bin the 10.0-eV photolysis, and reaction 4 makes only a small contribution at all energies. In this paper, we report the results of investigations of potential energy surfaces in singlet excited states of ethane, with particular emphasis on low-energy photochemical processes. An analysis of the vibrational structure of the electronic absorption spectrum will appear in a subsequent paper.s
Computational Details Most of the calculations were carried out with the previously described’ STO-4G+ basis set: the minimal STO-4G basis setg augmented by a set of diffuse s and p orbitals (with exponent { = 0.0178) centered at the midpoint of the C-C bond. Limited use was made of the analogous split valence 4-31G+ basis set, using the same exponent as STO-4G+ for the diffuse functions. The excited-state wave functions were generated by using singly excited configuration interaction (SECI) with the carbon 1s orbitals excluded. An open-shell restricted Hartree-Fock method” was also used to study certain features of the potential energy surfaces. Geometry optimizations were performed initially by using an adaptation of the conjugate directions method12and, at later stages, with the numerical Fletcher-Powell method described by Pople and co-~orkers.’~ The strategy employed for the geometry searches was to optimize the geometry of a particular state subject to the symmetry restrictions of the parent point group. At the optimal geometry within that point group, the molecular framework was displaced along all nontotally symmetric internal symmetry coordinates. If an energy lowering was detected by this procedure, the geometry was reoptimized subject to the symmetry restrictions of the subgroup. This procedure was followed until an apparent minimum was found. In some cases, such minima were verified with numerically generated harmonic force fields. Results and Discussion The results of the procedure described in the previous paragraph are summarized in the schematic diagram (6)R.J. Buenker and S. D. Peyerimhoff, Chem. Phys., 8, 56 (1975). (7)J. W.Caldwell and M. S. Gordon, Chem. Phys. Lett., 59, 403 (1978). (8) J. W.Caldwell and M. S. Gordon, J. Mol. Spectrosc., in press. (9)W.J. Hehre, R. Ditchfield, R. F. Stewart, and J. A. Pople, J. Chem. Phys., 52, 2769 (1970). (10)R. Ditchfield, W.J. Hehre, and J. A. Pople, J. Chem. Phys., 54, 724 (1971). (11)J. W.Caldwell and M. S. Gordon, Chem. Phys. Lett., 43, 493 (1976). ~ - .-_,. (12)M.J. D.Powell, Comput. J.,1, 155 (1964). (13)J. B. Collins, P. R. vR. Schleyer, J. S. Binkley, and J. A. Pople, J . Chem. Phys., 64,5142 (1976).
‘fI.3
0.0
Flgure 1. Energy-level diagram resulting from geometry distortions. Energles are from STO-40+. A superscript means the state is apparently s t a k to further distortions. A superscript indicates states whose geometries are similar to that of 2A, Positive definite force constant matrices have been verified for lb,, lA,, and 28, in CPh symmetry.
+
TABLE I: Vertical Singlet States o f E t h a n e A E , eV
state
STO-4Gt
B P
P,b 0.017 0.970 0.967 0.990 0.984 0.994 0.991
0.0
0.0
ZA,, 1% lA,, 2% lAlu 2A2u 3Eu
9.61 10.11 10.16 10.40 10.48 10.50 10.69 10.69
9.16 9.21 9.91 9.86 9.99 10.04 9.99 10.00
IP(2E,)
12.86
12.25
1AI,
1%
dominant configuration
0.991 0.981
Buenker a n d Peyerimhoff, ref 6 of t e x t . Net Mulliken population in Rydberg basis functions. Ground G r o u n d s t a t e = ( c o r e ) 4 2aYg 2atU le: 3a:, l e i 2a2,(3p)2eu(3pn)4alg(3s). . .
shown in Figure 1, in which all energies are given relative to the ground state in its equilibrium geometry. The column labeled “VERTICAL” represents the vertical excitation energies predicted with STO-4G+. The leftmost column illustrates the energy lowering obtained for each vertical state upon geometry relaxation within D3dsymmetry. The four rightmost columns, on the other hand, depict the further lowering due to relaxation of symmetry from D3d into the indicated point group. A superscript asterisk indicates that the structure has been verified to be stable against further distortions. Thus, for example, the lAl, state in D M symmetry becomes an A, state upon distortion to C2h. Since there are two lower A, states ut this geometry, we have 1Al,(D3d) 3A,(C2h). Furthermore, this state becomes 4A in C2 symmetry. Only those states whose geometries were investigated are listed in Figure 1, and the four rightmost columns only contain states which are unstable to distortion from D3d.
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Low-Lying States of Ethane 1.09 I O 0.1 7
a 2A
19
111.11
d. IA2,
1.90
1.46
H 1.12 113.33
b. IEP
e. 2E,
1,46
1.46
Flgure 2. Optimal S T W G + D, ethane structures. Bond lengths are given in angstroms and angles in degrees. Only the unique atom parameters are shown.
H
O)
2 *IO
H
yl
\
12
H
P = I O
('2h)
c) 2A*
120 HM
&kc ('2h)
H Flgure 3. Ethane ion (C2He+)structures, from ref 14 of text. Assumed symmetries are given in parentheses. Bond lengths are in angstroms and angles in degrees.
The STO-4G+ vertical excitation energies' (calculated at the STO-3G ground-state geometry) for the singlet states below the first Koopman's theorem ionization potential are compared with the large-scale CI results of Buenker and PeyerimhofP in Table I. The column labeled contains the STO-4G+ Mulliken populations for the diffuse functions (Rydberg orbitals). Both calculations predict the two lowest states to be dipole forbidden and find the next three states to be allowed and very closely spaced. As noted in previous the STO-4G+ with SECI calculations tend to overestimate vertical excitation energies.
P =IO
Figure 4. Structures and Rydberg populations (PA)for Rydberg excited states in D,, subgroups. Bond lengths are in angstroms and angles in degrees. Point groups given In parentheses.
Geometry optimization in DSdsymmetry leads to the structures shown in Figure 2 and the energy changes shown in Figure 1. In the following paragraphs each of the five lowest-lying vertical excited states is considered and their behavior upon distortion from the vertical geometry is discussed. 2A,. The 2Alg state undergoes the largest shift in energy and structure due to the DU geometry optimizations, becoming the lowest excited state. The long C-C bond length and nearly planar methyl groups (Figure 2a) are also found for the 2A1gethane ion (C2H6+)in the theoretical studies of Richartz, Buenker, Bruna, and Peyerimh~ff'~ (Figure 3a). This similarity in structure is not surprising since 21A1, ethane corresponds to a 3alg 3s Rydberg state (PR= 0.97) and 2Al Cz&+ corresponds to removal of an electron from the 6 C bonding 3alg orbital. The latter accounts for the long C-C bond length. The 2'Alg state is apparently stable in D3d symmetry since all internal symmetry coordinate distortions raise the energy relative to the DSdminimum. IE,. The lEg state becomes the second lowest state after DSdgeometry optimization, with the structure shown in Figure 2b. However, since lEg is doubly degenerate, it is
-
(14) A. Richartz, R . J. Buenker, P. J. Bruna, and S. D. Peyerimhoff, Mol. Phys., 33, 1345 (1977).
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Caldwell and Gordon
k
-35-
L 39
‘0
I
, I3
I2
m
14
-
Rii) 2
3
4
I5
I6
17
e
-
+---..-
Flgure 6. Relative energies (eV) for the reaction 1A” C,H, 1A” CH,CH lBgf H, along the minimum-energy path. See text for definition of R .
+
Flgure 5. STO-4G+ SECI energy of 1 ‘A” and 1 ’A‘ ethane as a function of CH,, the molecular elimination of H,.
expected to distort to a lower symmetry. This is indeed the case, with distortions to both C2hand C3symmetries yielding energy lowerings. In C2hsymmetry, 1E splits into an A, and a B, state. Since 1E is the lowest b3dstate at its optimal geometry, the two states are 2 4 and 1B , and the C3 state is 1E. The lB, state is unstable to furtier distortion to C, 1A”. The optimal geometry of lA”, shown in Figure 4a, exhibits one pair of long C-H bonds (hereafter referred to as CHL), while the opposite end of the molecule has a structure similar to that of a typical methyl group. Further reduction of symmetry to C1 results in a very small (
