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Assignment of the two lowest valence transitions of 1,1′-bicyclohexylidene: an ab initio MRD-CI investigation
CHEMICAL
30 August 1996
PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 259 (1996) 178-184
Assignment of the two lowest valence transitions of 1,1'-bicyclohexylidene: an ab initio MRD-CI investigation Frans J. Hoogesteger a, Joop H. van Lenthe b, Leonardus W. Jenneskens a, * a Debye Institute, Department of Physical Organic Chemistry, Utrecht University, Padualaan 8, 3584 CH Utrecht, The Netherlands b Debye Institute, Theoretical Chemistry Group, Utrecht University, Padualaan 8, 3584 CH Utrecht, The Netherlands Received 21 March 1996; in final form 1 July 1996
Abstract
In contrast to the vapor phase UV spectrum of tetramethylethene (2, broad band centered at 7.0 eV, f 0.3), 1,1'-bicyclohexylidene (1) possesses two absorption bands (5.95 eV, f 0.19 and 6.82 eV, f 0.26). For 1 MRD-CI (6-31G) calculations reveal that they have to be assigned to a "rr ~ rr * (9.28 eV, HOMO ~ LUMO, bu, f 0.849) and a ~r ~ cr * (10.49 eV, HOMO ~ L U M O + 1, b,, f 0.13) valence transition. Both transitions are perfectly polarized along the carbon-carbon double bond. In the case of 2 similar calculations reveal that the 7.0 eV band consists of two transitions (Tr ~ rr *, 9.75 eV, HOMO ~ LUMO, b2, f 0.900 and 7r ~ tr *, 10.16 eV, HOMO ~ LUMO + 1, b~, f 0.045). Whereas the rr ~ ~" * transition is perfectly polarized along the double bond, the "rr ~ tr * transition is polarized perpendicular to this bond.
1. I n t r o d u c t i o n
energy-loss spectroscopy the vapor phase spectrum
The UV absorption spectrum of 1,1'-bicyclohexylidene (1, IUPAC name Al't'-bicyclohexylidene)
of 1 has been interpreted. The 5.95 eV band was assigned to a 7r ~ -rr * transition, while the 6.82 eV band was attributed tentatively to a 'Tr(CH2)'--~ 7r * transition involving intramolecular charge transfer from the cyclohexyi moieties into the carbon-carbon
differs from that of tetramethylethene (2). Whereas for 2 both in the vapor phase and in solution only one broad band centered at 7.0 eV (oscillator strength f 0.3) is found, [1] two distinct transitions are ohserved in the case of 1 (vapor phase: 5.95 eV, f 0.19 and 6.82 eV, f 0.26, [2] and solution (solvent n-pentane) 6.01 eV and 6.85 eV, Fig. 1 [2,3]). Moreover, in the vapor phase spectrum of 1, both bands possess vibronic fine structure [2]. On the basis of photoelectron, multiphoton ionization and electron
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[email protected],
double bond. The presence of vibronic fine structure was rationalized by invoking Rydberg contributions [2,4,5]. However, solid-state polarized reflection UV spectroscopy of 1 (single crystal) also gave two distinct absorption bands positioned at 5.95 and 6.32 eV; both possessing vibronic fine structure! These transitions were shown to be perfectly polarized along the carbon-carbon double bond [6]. Since Rydberg contributions generally become undetectable in the condensed state, the solid state as well as the solution UV data of 1 strongly suggest that
0009-2614/96/$12.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S 0 0 0 9 - 2 6 1 4 ( 9 6 ) 0 0 7 4 9 - X
FJ. Hoogesteger et al./ Chemical Physics Letters 259 (1996) 178-184
12xl 03 -~
/ / ~
10a_.--Eo -~ 4 2
j ~
o 4.5
5.0
s.s
~
~
6.0
s.s
7.0
transition energy (eV)
Fig. 1. UV Absorption spectrum of 1. The UV absorption spectrum of 1 was recorded on a Cary 5 UV-Vis spectrophotometer in deaerated (three freeze-pump-thaw cycles) spectrophotometric grade n-pentane under a nitrogen atmosphere at 298 K.
both bands correspond to valence transitions. This is supported by their oscillator strengths f (-rr ~ ~r * transition; oscillator strength for Rydberg vs. valence transition f 0.08 vs. 0.2-0.3) [4,5]. Here we report the results of MRD-CI [7,8] calculations on both 1 and 2 to aid the interpretation of their experimental UV absorption spectra. It is shown that as a consequence of the incorporation of cyclehexyl moieties, i.e. in going from 2 to 1, the transition energies and oscillator strengths of especially the second and third vertical transitions are affected.
179
tively. Transition energies and oscillator strengths f, were calculated for the lowest two transitions per symmetry. Since the current MRD-CI program allows no more than 100 orbitals in the active configuration interaction (CI) space, low-lying MOs were frozen and high-lying MOs were discarded. In the case of 1 from the total of 148 MOs, the lowest 36 MOs (energy < - 0 . 5 1 Eh), were frozen and the 14 highest MOs (energy > 1.53 E h) were discarded. Thus, the active CI space consisted of 10 occupied MOs (20 active electrons) and 88 virtual MOs. A total of 15688 configuration state functions (CSFs) was selected. For 2 from a total of 78 MOs, the lowest 15 MOs (energy < - 0 . 5 7 E h) were frozen; no MOs were discarded. The active CI space contained 9 occupied MOs (18 active electrons) and 54 virtual MOs. A total of 34964 CSFs was selected. T o assess basis set effects on the calculated vertical transition energies, MRD-CI calculations on 3 (RHF/6-31G optimized geometry) were performed using the 6-31G and 6-31G* [11] basis sets, respectively, and on either its RHF/6-31G or R H F / T Z V P optimized geometry with the TZVP basis set (triplezeta valence basis set augmented with d-functions on the heavy atoms and p-functions on hydrogen) [12], respectively. In the case of 3 the two lowest MOs were frozen. Ground state and excited state charge distributions were calculated by a Mulliken population analysis [13].
3. Results and discussion
3.1. 1,1'-bicyclohexylidene (1): ground state
2. Computational All calculations were run on either a Silicon Graphics Power Challenge 75 MHz or a Cray YMP computer using the quantum chemical program system GAMESS-UK [9,10]. Geometries were optimized [ 1,1'-bicyclohexylidene (1, C 2h symmetry); tetramethylethene (2, D 2 symmetry) and ethene (3, D2h symmetry)] at the RHF/6-31G level (convergence criterion 0.001 hartree/bohr) and characterized as real minima by performing a Hessian calculation. MRD-CI calculations [7,8] were performed using the RHF/6-31G optimized geometries and molecular orbitals (MOs) of 1, 2 and 3, respec-
The geometry of 1 was optimized at the R H F / 6 31G level (C2h symmetry, Fig. 2). Selected bond lengths, valence and dihedral angles are presented in ~:~,~,, ~ ~ ~ ~ ~,~{,~ ~ - ~ ' ~ ~ " :~ . ~ ~ "L~ [12 ~,~,-~,,-~{~,~,~, ~
~.~ ~ ~ , 9 ~ - ~ \ ~ - ~ . / / 7~ : ~ " ' =~'f/' , ~,,s~-,,s
~ ~.~ Fig. 2. RHF/6-31G optimized geometryof 1.
~
180
F.J. Hoogesteger et al. / Chemical Physics Letters 259 (1996) 178-184
Table 1 R H F / 6 - 3 1 G bond lengths (A), valence angles (°) and dihedral angles ( ° ) f o r l,l'-bicyclohexylidene 1 (C2h symmetry) a
lengths (2(1)- c(2) c(2)-c(3)
1.34 [1.339] 1.52 [1.511; 1.514]
C(7)-C(11)
1.53 [1.523; 1.519]
Bond
C(3)-C(7)
Valence angles C(1)-C(2)-C(3) C(2)-C(3)-C(7) c(3)-c(7)-c(11) C(7)-C(11)-C(9) Dihedral angles C(4)-C(1)-C(2)-C(3) c(4)-c(1)-c(2)-c(5)
1.54 [1.529; 1.531]
124.9 [124.40; 124.55]
111.3 [112.27; 111.88] 111.5 [111.08; 111.17] 111.I [110.42] 180.01180.01 1.0[0.7]
a Single-crystal X-ray (C i symmetry) data between square brackets [14].
Table 1. The RHF/6-31G results are in line with those derived from the single-crystal X-ray structure [14]. Note, however, that in the solid state 1 possesses C i symmetry. Only approximate C2h symmetry is found upon taking into account the presence of a non-crystallographic mirror plane. The lowest RHF/6-31G Koopmans [15] ionization potential (IP) of 1 [8.48 eV (14b u, HOMO w-type)] is well separated from the next IPs [10.89 eV (9bg, HOMO-1 ~-type) and 11.90 eV (14ag, HOMO-2 (r-type)] and are in satisfactory agreement with available photoelectron spectroscopy data of 1, 8.16, 9.8 and 1 1 . 1 eV) [2,16].
3.2. Influence o f basis sets on the 7r ~ 7r * transition energy o f ethene (3)
Although it is well established that accurate excitation energies can only be obtained using extended basis sets, [17] it should be stipulated that the inclusion of diffuse orbitals may lead to an admixture of Rydberg contributions, thus, complicating the identification of valence transitions. To circumvent this problem the 6-31G basis set was used. As shown by MRD-CI calculations for the w ~ w* transition of ethene (3, D2h symmetry, RHF/6-31G geometry, exp. w ~ w* transition energy 7.60 eV [18]) with various basis sets (6-31G, 6-31G* [11] and TZVP [12]), this will affect the values of the calculated transition energies (Table 2). Note that MRD-CI calculations on 3 using its RHF/TZVP, instead of RHF/6-31G, geometry and the TZVP basis set gave nearly identical w ~ w * transition energies (Table 2). 3.3. M R D - C I calculations on 1,1'-bicyclohexylidene (1)
The lowest vertical electronic excitations of 1 were calculated by performing MRD-CI calculations on its optimized RHF/6-31G ground state structure and MOs (see Section 2). A total of 21 reference configurations was defined from which the most important single and double excitations were selected by applying the method of Buenker and Peyerimhoff [19], leading to a total of 5431 CSFs of ag symmetry, 3409 of a, symmetry, 3413 of bu symmetry and 3435 of bg symmetry. Reference configura-
Table 2 MRD-CI energies ( E h) for the ground state and ~ ~ ~ * excited state of ethene (3) and vertical transition energies (eV) calculated using different basis sets a Basis set
Ground state 1A g b Excited state 1B ~, ('rr ,n" * ) ~r ~ ir * Transition energy c
6-31G
6-31G *
TZVP
- 78.194592 - 77.841886 9.60
- 78.290353 - 77.947848 9.32
- 78.347788 [ - 78.347729] d - 78.024005 [ - 78.022172] d 8.81 [8.85] d
a Geometry optimized at R H F / 6 - 3 1 G [ R H F / T Z V P ] level; D2h symmetry ( C = C 1.32 [1.32] ,~, C - H 1.07 [1.08] .& and H - C - C 121.9 [121.7]°). b RHF ground state energies (Eh): 6-31G -78.004456, 6-31G * -78.031666 and TZVP -78.061448 [-78.061515], respectively. c Experimental: 7.60 eV. [18] a MRD-C1 on R H F / T Z V P geometry.
F.J. Hoogesteger et al. / Chemical Physics Letters 259 (1996) 178-184
181
Table 3 MRD-CI energies(E h) and vertical transition energies (eV) of the two lowest excited states per symmetry for 1a
were calculated. The ground state energy (RHF -- 4 6 5 . 8 7 5 0 3 4 E h) moderately decreased to -- 4 6 5 . 9 3 8 3 7 8 E h u p o n C I . E x c i t e d s t a t e e n e r g i e s ,
State
Energy
symmetry
Transition
Osc. strength
Polari-
vertical transition energies,
energy
(f)
zati°nb
a n d p o l a r i z a t i o n s a r e p r e s e n t e d in T a b l e 3. W h e r e a s
oscillator strengths (f)
2Ag 1A u 2A u IB u 2Bu 1Bg
-465.410614 -465.500749 -465.488344 -465.597163 -465.552797 -465.560505
14.36 11.91 12.25 9.28 10.49 10.28
0.0000 0.1126 0.0086 0.8494 0.1282 0.0000
d_ .1_ II I[ -
t h e l o w e s t t r a n s i t i o n ( 9 . 2 8 e V , b u, f 0 . 8 4 9 4 ) c o r r e s p o n d s to a ~ r ~ " HOMO~LUMO transition
2Bg
-465.518276
11.43
0.0000
-
m e t r y f o r b i d d e n . T h e n e x t t r a n s i t i o n ( 1 0 . 4 9 e V , b u,
a n d is p e r f e c t l y p o l a r i z e d a l o n g t h e c a r b o n - c a r b o n double bond, the second lowest transition (10.28 eV, b g , cr ~ rr *, H O M O - 1 ~ L U M O , f 0 . 0 0 0 0 ) is s y m -
a MRD-CI ground state ( l A g ) energy: -465.938378 E h. b Notation used: II, polarized along C(1)-C(2) double bond; _1., polarized perpendicular to C(1)-C(2) double bond, in plane C(3)-
"iT ~ tr *, H O M O ~ L U M O + 1, f 0 . 1 2 8 2 ) is allowed and also perfectly polarized along the carbon-carbon double bond. For the assignment of
c ( 5 ) - c ( 4 ) - c ( 8 ) ; see Fig. 2.
the two experimentally
observed
bands
the calcu-
lated first and third excited state are of interest (vide t i o n s w e r e c h o s e n to b e a s c l o s e a s p o s s i b l e to t h e
s u p r a a n d R e f s [2,6]). T h e m o s t i m p o r t a n t c o n f i g u r a -
HOMO
~ LUMO
tions for the ground state and these excited states are
lowed.
The
two
transition as far as symmetry lowest
states for each
al-
symmetry
p r e s e n t e d i n T a b l e 4. S i n c e f o r t h e r e f e r e n c e c o n f i g u -
Table 4 Most important configurations of the ground state and excited states of 1a c 2b
MO 9a u
14ag
9bg
14b u
15ag
2 2 2 2 2
2 2 2 2 2
2 -
. 2 1 1 -
Lowest lr --* "rr" (1B u) excited state 0.9451 R 2 2 2 0.0045 2 2 2 0.0005 R 2 2 1 0.0004 R 2 1 2 0.0002 R 2 1 2
1 l 2 2 2
1 . . -
rr ~ tr * (2B u) excited state 2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 1 2 1 2 2 2 2 1 2 2 2 2 1 2 1 2 2
. . . . 1 -
Ground state ( l A g ) 0.9513 R 2 0.0096 R 2 0.0034 2 0.0022 2 0.0004 R 2
Second lowest 0.9113 R 0,0177 0.0081 0.0020
0.0007 0,0003 0.0003 0.0003
R R R R
16ag
15b u
.
. . 1 . 2
.
.
1
.
.
. -
.
.
.
-
.
-
1
. 1
a Only configurations with c 2 >_ 0.0002 are tabulated. b Reference configurations of MRD-CI calculation are labeled 'R'; see text. c Singly occupied 2lag orbital.
. .
.
.
-
-
-
.
-
. .
-
.
1 .
1
-
.
. .
.
. 1
.
.
.
.
1 -
.
.
.
.
-
.
.
.
.
.
.
.
. .
.
. -
. .
. 1
.
.
.
1 1 -
.
. 1
.
. .
1Sag
. .
.
.
-
.
. .
10b e
. .
.
. .
.
.
.
17ag
.
.
.
.
.
. .
.
. .
.
.
.
.
.
.
10a u
.
.
. .
16b u
. .
. .
c._
182
FJ. Hoogesteger et al./ Chemical Physics Letters 259 (1996) 178-184
rations the sum of the squares of the CI coefficients (c 2) are larger than 0.9, the set of reference configurations ( ' R ' ) taken into consideration was adequate. The results provide compelling evidence that the two absorption bands observed for 1 both in the vapor phase and in the condensed state have to be assigned to a ~r ~ "rr * (HOMO ~ LUMO) and -rr ~ tr * (HOMO ~ L U M O + 1) transition. In agreement with the solid-state (single crystal) polarized reflection UV spectral data [6] these transitions are symmetry allowed and perfectly polarized along the carb o n - c a r b o n double bond. Hence, the previous as•
signment of the second transition as '-rr(CH2)' --~ ,rr , which was based on the assumption that excitation occurs from a 'ribbon-type' MO [20,21] discernible in compounds containing cyclohexane moieties, has to be incorrect [2]. The 'ribbon-type' MO in the case of 1 is related to the highest-filled MOs in cyclohexane (4eg) and is composed of " r r ( C H 2 ) ' a n d o ' ( C C ) local orbitals. According to photoelectron spectroscopy [21], the 'ribbon-type' MO is separated from the other ~r and tr MOs by a considerable energy gap, i.e. for I it is observed at 9.8 eV (6-31G, 10.89 eV, 9bg, HOMO-1 a-type) [2]. A survey of the most important configurations reveals that the 'ribbon-type' MO does not contribute (Tables 4 and 5, vide infra). Note that our MRD-CI calculations reveal that the tr ~ ~r* (HOMO-1 ~ LUMO) transition involving excitation from the 'ribbon-type' MO to the ~ * L U M O is symmetry forbidden (Table 3). Although for both transitions the absolute value of the MRD-CI transition energies deviate from the experimental values, the difference between both transitions is described reasonably well (rr ~ tr * transition energy minus ~r ~ rr * transition energy: exp. 0.87 eV and MRD-CI 1.21 eV, Table 3 and Ref. [2]). To assess charge redistributions upon excitation, a Mulliken population analysis of the CI wavefunction was performed [13]. The results show that the 7r ~ • r * (HOMO ~ LUMO) transition induces only a minor redistribution of electron density (Table 5). This is not surprising since both the H O M O and L U M O are primarily localized on the olefinic carbon atoms. In contrast, considerable charge redistribution is found for the 7r ~ tr * (HOMO ~ L U M O + 1) transition. Note that the ~ * L U M O + 1 is delocalized over the entire molecular framework and pos-
Table 5 Mullikenpopulation analysis of the ground state and the lowest ~r ~ ~r* (IB u) and ~ ~ tr* (2B u) excited states of 1
C(l); c(2) c(3); c(4); c(5); c(6)
Population Ground (It, I t ' ) statea stateb 5.995 -0.052 6.336 -0.002
(ax, tr*) stateb -0.198 -0.018
C(7); C(8); C(9); C(10)
6.293
- 0.025
- 0.031
c(11); c(12) H(13); H(14); H(15); H(16) H(17); H(18); H(19); H(20) H(21);H(22); H(23); H(24)
6.303 0.843 0.834 0.847
-0.022 +0.021 +0.007 +0.009
+0.005 -0.019 +0.140 +0.020
H(25); H(26); H(27); H(28) H(29); H(30) H(31); H(32)
0.854 0.846
+ 0.022
-0.006
Atom
0.847
+0.016 -0.004
0.000 +0.021
a Mulliken population, b Difference with ground state Mulliken population ( - : decrease in electron population; +: increase in electron population).
sesses both cr and 'rr'-type topology. A decrease in the electronic population of the two olefinic carbon atoms (C(1) and C(2) - 0 . 1 9 8 au) concomitant with an increase of the population on the four equatorial allylic hydrogen atoms (H(17)-H(20) + 0 . 1 4 0 au) is found. Thus, for the ~r -o tr * transition charge transfer occurs from the double bond into the cyclohexyl moieties [2]. The MRD-CI oscillator strength f for the rr ~ ~r * transition (0.8494) is larger than the experimental value ( f 0.19; vapor phase), while that of the ~r tr * transition ( f 0.1282) is smaller (exp. f 0.26) [1,2]. Since the quality of the 6-31G wavefunction is not sufficient for an accurate calculation of f , we refrain from further discussion. 3.4. A comparison between l,l'-bicyclohexylidene (1) and tetramethylethene (2) According to the MRD-CI results the two distinct valence transitions of 1 discernible in the UV region have to be assigned to a 7r--*-tr * and a 7r ~ tr * transition. The question arises whether these results are either unique to 1 or general to simple tetra-alkylated olefins. To gain insight the vertical transitions of tetramethylethene (2) were calculated foilowing the same approach as used for 1. The geometry of 2 was optimized in D a symmetry at the
FJ. Hoogesteger et al. / Chemical Physics Letters 259 (1996) 178-184
Table 6 MRD-CI energies ( E h) and vertical transition energies (eV) of the two lowest excited states per symmetry for 2 a State Energy symmetry
Transition energy
Osc. strength Polari(f) zation c
2AI IB t 2B~
-233.701057 -233.867100 -233.818473
14.68 10.16
0.0030 0.0450
3- L
IB2
-233.882086
2B 2 IB 3
-233.838799 - 233.833501
11.48 9.75 10.93
0.0554 0.9001 0.0031
3, ± II II
11.07
0.0073
3.
2B 3
-233.787136
12.34
0.0005
3,
a Geometry optimized at the RHF/6-31G level; D 2 symmetry (C = C 1.34/~, C - C 1.51 /~, 3 C - H 1.09 ,~,, 1.08 ,~ and 1.09 ,~, C H 3 - C - C 124.3 °, C H 3 - C - C H 3 111.4 °, 3 H - C H 2 - C 109.8 °, 114.0 ° and 110.7 °, 3 H - C - H 107.3 °, 106.8 o and 107.9°); ground state(1A l) energies(Eh): RHF/6-31G,-234.086330; MRD-C1,
-234.240456. b Experimental 7.0 eV [1], see text. c Notation used: II, polarized along C - C double bond; 3,, polarized perpendicular to C - C double bond, in plane formed by C-atoms; 3, 3_, polarized perpendicular to both the C - C double bond and the plane formed by the C-atoms.
R H F / 6 - 3 1 G level (Table 6). From a total of 24 reference configurations 8919 CSFs of al symmetry, 8661 of bl symmetry, 8544 of b E symmetry and 8840 of b 3 symmetry were selected. For the two lowest states of each symmetry, state energies, vertical transition energies and oscillator strengths were calculated (Table 6). In analogy to 1, the lowest vertical excitation is a ~r ~ 7r * transition (9.75 eV, H O M O -~ LUMO, bE, f 0.9001) which is perfectly polarized along the carbon-carbon double bond. The next transition can be described as a "rr ~ t r * transition (10.16 eV, H O M O ~ L U M O + 1, b I, f 0.0450) and is polarized perpendicular to the plane formed by the carbon atoms. The third transition (10.93 eV, H O M O - I ~ L U M O , b 2 , f 0.0001) is a t r ~ 7r * transition. A1though it is perfectly polarized along the carboncarbon double bond, its oscillator strength is very low. These results show that, although for both 1 and 2 the "rr ~ zr * transition represents the lowest excited state, the second (1, tr -~ ,r *, f 0.0000 and 2, ~ tr ~, f 0.0450) and third (1, ~r ~ cr *, f 0.1282 and 2, ~r ~ 7r * f 0.0001) transitions are inter'
changed. In addition, due to the reduction in symmetry in going from 2 (D 2) to 1 (C2h) both the oscilla-
183
tor strengths and the polarization of the second and third transition are affected.
4. Conclusions MRD-CI calculations reveal that the two distinct transitions found in the UV region for 1,1'-bicyclohexylidene (1) have to be assigned to a ~r --* 7r * (HOMO ~ LUMO) and a ~r ~ cr * (HOMO L U M O + 1) transition. In line with experiment [6] b o t h transitions are perfectly polarized along the carbon-carbon double bond. T h e rr ~ tr" transition possesses charge-transfer character; charge redistribution from the double bond into the cyclohexylidene rings occurs. A comparison with MRD-CI resuits obtained for tetramethylethene (2) reveals that t h e introduction of cyclohexyl moieties in going from 2 to 1 affects both the transition energy and o s c i l l a t o r strength of especially the s e c o n d a n d third valence transitions.
Acknowledgements This work was sponsored by the Stichting Nationale Computerfaciliteiten (National Computing Facilities Foundation, NCF) for the use of supercomputer facilities, with financial support from the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (Netherlands Organization for Scientific Research, NWO).
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[3] F.J. Hoogesteger, R.W.A. Havenith, J.W. Zwikker, L.W. Jelmeskens, H. Kooijman, N. Veldman and A.L. Spek, J. Org. Chem. 60 (1995) 4375. [4] M.B. Robin, Higher excited states of polyatomic molecules, Vol. III (Academic Press, New York, 1985). [51 M.B. Robin, Chemical spectroscopy and photochemistry in the vacuum-ultraviolet, Eds. C. Sandorfy, P.J. Ausloos and M.B. Robin (Reidel, Dordrecht, 1974).
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FJ. Hoogesteger et al./ Chemical Physics Letters 259 (1996) 178-184
[7] R.J. Buenker, S.D. Peyerimhoff and W Butscher, Molec. Phys. 35 (1978) 771. [8] R.J. Buenker, S.-K Shih and S.D. Peyerimhoff, Chem. Phys. 36 (1979) 97. [9] GAMESS-UK is a package of ab initio programs writl~n by M.F. Guest, J.H. van Lenthe, J. Kendrick, K. Schoffel, P. Sherwood and R.J. Harrison with contributions from R.D. Amos, R.J. Buenker, M. Dupuis, N.C. Handy, I.H. Hillier, P.J. Knowles, V. Bonacic-Koutecky, W. yon Niessen, V.R. Sannders and A.J. Stone. The package is derived from the original GAMESS code due to M. Dupuis, D. Spangler and J. Wendolowski, NRCC Software Catalog, Vol. 1, Program No. QG01 (GAMESS), 1980. [10] R.J. Buenker, Stud. Phys. Theoret. Chem. 21 (1982) 17. [ll] P.C. Hafiharan and J.A. Pople, Theor. Chim. Acta 28 (1973) 213. [12] T.H. Dunning, Jr., J. Chem. Phys. 55 (1971) 716.
[13] R.S. Mulliken, J. Chem. Phys. 23 (1955) 1833. [14] N. Veldman, A.L. Spek, F.J. Hoogesteger, J.W. Zwikker and L.W. Jenneskens, Acta Crystallogr. C50 (1994) 742. [15] T.A. Koopmans, Physical (1933) 104. [16] R.S. Brown, J.M. Buschek, K.R. Kopecky and A.J. Miller, J. Org. Chem. 48 (1983) 3692. [17] K.B. Wiberg, C.M. Hadad, J.B. Foresman and W.A. Chupka, J. Phys. Chem. 96 (1992) 10756 and references cited. [18] A. Gedanken, N.A. Kuebler and M.B. Robin, J. Chem. Phys. 76 (1982)46. [19] R.J. Buenker and S.D. Peyerimhoff, Theoret. Chim. Acta 35 (1974) 33. [20] R. Hoffman, P.D. Moll~re and E. Heilbronner, J. Am. Chem. Soc. 95 (1973) 4860. [21] E. Heilbronner, E. Honegger, W. Zambach, P. Schmitt and H. Giinther, Helv. Chim. Acta 67 (1984) 1681.
30 August 1996
PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 259 (1996) 178-184
Assignment of the two lowest valence transitions of 1,1'-bicyclohexylidene: an ab initio MRD-CI investigation Frans J. Hoogesteger a, Joop H. van Lenthe b, Leonardus W. Jenneskens a, * a Debye Institute, Department of Physical Organic Chemistry, Utrecht University, Padualaan 8, 3584 CH Utrecht, The Netherlands b Debye Institute, Theoretical Chemistry Group, Utrecht University, Padualaan 8, 3584 CH Utrecht, The Netherlands Received 21 March 1996; in final form 1 July 1996
Abstract
In contrast to the vapor phase UV spectrum of tetramethylethene (2, broad band centered at 7.0 eV, f 0.3), 1,1'-bicyclohexylidene (1) possesses two absorption bands (5.95 eV, f 0.19 and 6.82 eV, f 0.26). For 1 MRD-CI (6-31G) calculations reveal that they have to be assigned to a "rr ~ rr * (9.28 eV, HOMO ~ LUMO, bu, f 0.849) and a ~r ~ cr * (10.49 eV, HOMO ~ L U M O + 1, b,, f 0.13) valence transition. Both transitions are perfectly polarized along the carbon-carbon double bond. In the case of 2 similar calculations reveal that the 7.0 eV band consists of two transitions (Tr ~ rr *, 9.75 eV, HOMO ~ LUMO, b2, f 0.900 and 7r ~ tr *, 10.16 eV, HOMO ~ LUMO + 1, b~, f 0.045). Whereas the rr ~ ~" * transition is perfectly polarized along the double bond, the "rr ~ tr * transition is polarized perpendicular to this bond.
1. I n t r o d u c t i o n
energy-loss spectroscopy the vapor phase spectrum
The UV absorption spectrum of 1,1'-bicyclohexylidene (1, IUPAC name Al't'-bicyclohexylidene)
of 1 has been interpreted. The 5.95 eV band was assigned to a 7r ~ -rr * transition, while the 6.82 eV band was attributed tentatively to a 'Tr(CH2)'--~ 7r * transition involving intramolecular charge transfer from the cyclohexyi moieties into the carbon-carbon
differs from that of tetramethylethene (2). Whereas for 2 both in the vapor phase and in solution only one broad band centered at 7.0 eV (oscillator strength f 0.3) is found, [1] two distinct transitions are ohserved in the case of 1 (vapor phase: 5.95 eV, f 0.19 and 6.82 eV, f 0.26, [2] and solution (solvent n-pentane) 6.01 eV and 6.85 eV, Fig. 1 [2,3]). Moreover, in the vapor phase spectrum of 1, both bands possess vibronic fine structure [2]. On the basis of photoelectron, multiphoton ionization and electron
• Corresponding author. Fax.: +31 302534533. Email: jen-
[email protected],
double bond. The presence of vibronic fine structure was rationalized by invoking Rydberg contributions [2,4,5]. However, solid-state polarized reflection UV spectroscopy of 1 (single crystal) also gave two distinct absorption bands positioned at 5.95 and 6.32 eV; both possessing vibronic fine structure! These transitions were shown to be perfectly polarized along the carbon-carbon double bond [6]. Since Rydberg contributions generally become undetectable in the condensed state, the solid state as well as the solution UV data of 1 strongly suggest that
0009-2614/96/$12.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S 0 0 0 9 - 2 6 1 4 ( 9 6 ) 0 0 7 4 9 - X
FJ. Hoogesteger et al./ Chemical Physics Letters 259 (1996) 178-184
12xl 03 -~
/ / ~
10a_.--Eo -~ 4 2
j ~
o 4.5
5.0
s.s
~
~
6.0
s.s
7.0
transition energy (eV)
Fig. 1. UV Absorption spectrum of 1. The UV absorption spectrum of 1 was recorded on a Cary 5 UV-Vis spectrophotometer in deaerated (three freeze-pump-thaw cycles) spectrophotometric grade n-pentane under a nitrogen atmosphere at 298 K.
both bands correspond to valence transitions. This is supported by their oscillator strengths f (-rr ~ ~r * transition; oscillator strength for Rydberg vs. valence transition f 0.08 vs. 0.2-0.3) [4,5]. Here we report the results of MRD-CI [7,8] calculations on both 1 and 2 to aid the interpretation of their experimental UV absorption spectra. It is shown that as a consequence of the incorporation of cyclehexyl moieties, i.e. in going from 2 to 1, the transition energies and oscillator strengths of especially the second and third vertical transitions are affected.
179
tively. Transition energies and oscillator strengths f, were calculated for the lowest two transitions per symmetry. Since the current MRD-CI program allows no more than 100 orbitals in the active configuration interaction (CI) space, low-lying MOs were frozen and high-lying MOs were discarded. In the case of 1 from the total of 148 MOs, the lowest 36 MOs (energy < - 0 . 5 1 Eh), were frozen and the 14 highest MOs (energy > 1.53 E h) were discarded. Thus, the active CI space consisted of 10 occupied MOs (20 active electrons) and 88 virtual MOs. A total of 15688 configuration state functions (CSFs) was selected. For 2 from a total of 78 MOs, the lowest 15 MOs (energy < - 0 . 5 7 E h) were frozen; no MOs were discarded. The active CI space contained 9 occupied MOs (18 active electrons) and 54 virtual MOs. A total of 34964 CSFs was selected. T o assess basis set effects on the calculated vertical transition energies, MRD-CI calculations on 3 (RHF/6-31G optimized geometry) were performed using the 6-31G and 6-31G* [11] basis sets, respectively, and on either its RHF/6-31G or R H F / T Z V P optimized geometry with the TZVP basis set (triplezeta valence basis set augmented with d-functions on the heavy atoms and p-functions on hydrogen) [12], respectively. In the case of 3 the two lowest MOs were frozen. Ground state and excited state charge distributions were calculated by a Mulliken population analysis [13].
3. Results and discussion
3.1. 1,1'-bicyclohexylidene (1): ground state
2. Computational All calculations were run on either a Silicon Graphics Power Challenge 75 MHz or a Cray YMP computer using the quantum chemical program system GAMESS-UK [9,10]. Geometries were optimized [ 1,1'-bicyclohexylidene (1, C 2h symmetry); tetramethylethene (2, D 2 symmetry) and ethene (3, D2h symmetry)] at the RHF/6-31G level (convergence criterion 0.001 hartree/bohr) and characterized as real minima by performing a Hessian calculation. MRD-CI calculations [7,8] were performed using the RHF/6-31G optimized geometries and molecular orbitals (MOs) of 1, 2 and 3, respec-
The geometry of 1 was optimized at the R H F / 6 31G level (C2h symmetry, Fig. 2). Selected bond lengths, valence and dihedral angles are presented in ~:~,~,, ~ ~ ~ ~ ~,~{,~ ~ - ~ ' ~ ~ " :~ . ~ ~ "L~ [12 ~,~,-~,,-~{~,~,~, ~
~.~ ~ ~ , 9 ~ - ~ \ ~ - ~ . / / 7~ : ~ " ' =~'f/' , ~,,s~-,,s
~ ~.~ Fig. 2. RHF/6-31G optimized geometryof 1.
~
180
F.J. Hoogesteger et al. / Chemical Physics Letters 259 (1996) 178-184
Table 1 R H F / 6 - 3 1 G bond lengths (A), valence angles (°) and dihedral angles ( ° ) f o r l,l'-bicyclohexylidene 1 (C2h symmetry) a
lengths (2(1)- c(2) c(2)-c(3)
1.34 [1.339] 1.52 [1.511; 1.514]
C(7)-C(11)
1.53 [1.523; 1.519]
Bond
C(3)-C(7)
Valence angles C(1)-C(2)-C(3) C(2)-C(3)-C(7) c(3)-c(7)-c(11) C(7)-C(11)-C(9) Dihedral angles C(4)-C(1)-C(2)-C(3) c(4)-c(1)-c(2)-c(5)
1.54 [1.529; 1.531]
124.9 [124.40; 124.55]
111.3 [112.27; 111.88] 111.5 [111.08; 111.17] 111.I [110.42] 180.01180.01 1.0[0.7]
a Single-crystal X-ray (C i symmetry) data between square brackets [14].
Table 1. The RHF/6-31G results are in line with those derived from the single-crystal X-ray structure [14]. Note, however, that in the solid state 1 possesses C i symmetry. Only approximate C2h symmetry is found upon taking into account the presence of a non-crystallographic mirror plane. The lowest RHF/6-31G Koopmans [15] ionization potential (IP) of 1 [8.48 eV (14b u, HOMO w-type)] is well separated from the next IPs [10.89 eV (9bg, HOMO-1 ~-type) and 11.90 eV (14ag, HOMO-2 (r-type)] and are in satisfactory agreement with available photoelectron spectroscopy data of 1, 8.16, 9.8 and 1 1 . 1 eV) [2,16].
3.2. Influence o f basis sets on the 7r ~ 7r * transition energy o f ethene (3)
Although it is well established that accurate excitation energies can only be obtained using extended basis sets, [17] it should be stipulated that the inclusion of diffuse orbitals may lead to an admixture of Rydberg contributions, thus, complicating the identification of valence transitions. To circumvent this problem the 6-31G basis set was used. As shown by MRD-CI calculations for the w ~ w* transition of ethene (3, D2h symmetry, RHF/6-31G geometry, exp. w ~ w* transition energy 7.60 eV [18]) with various basis sets (6-31G, 6-31G* [11] and TZVP [12]), this will affect the values of the calculated transition energies (Table 2). Note that MRD-CI calculations on 3 using its RHF/TZVP, instead of RHF/6-31G, geometry and the TZVP basis set gave nearly identical w ~ w * transition energies (Table 2). 3.3. M R D - C I calculations on 1,1'-bicyclohexylidene (1)
The lowest vertical electronic excitations of 1 were calculated by performing MRD-CI calculations on its optimized RHF/6-31G ground state structure and MOs (see Section 2). A total of 21 reference configurations was defined from which the most important single and double excitations were selected by applying the method of Buenker and Peyerimhoff [19], leading to a total of 5431 CSFs of ag symmetry, 3409 of a, symmetry, 3413 of bu symmetry and 3435 of bg symmetry. Reference configura-
Table 2 MRD-CI energies ( E h) for the ground state and ~ ~ ~ * excited state of ethene (3) and vertical transition energies (eV) calculated using different basis sets a Basis set
Ground state 1A g b Excited state 1B ~, ('rr ,n" * ) ~r ~ ir * Transition energy c
6-31G
6-31G *
TZVP
- 78.194592 - 77.841886 9.60
- 78.290353 - 77.947848 9.32
- 78.347788 [ - 78.347729] d - 78.024005 [ - 78.022172] d 8.81 [8.85] d
a Geometry optimized at R H F / 6 - 3 1 G [ R H F / T Z V P ] level; D2h symmetry ( C = C 1.32 [1.32] ,~, C - H 1.07 [1.08] .& and H - C - C 121.9 [121.7]°). b RHF ground state energies (Eh): 6-31G -78.004456, 6-31G * -78.031666 and TZVP -78.061448 [-78.061515], respectively. c Experimental: 7.60 eV. [18] a MRD-C1 on R H F / T Z V P geometry.
F.J. Hoogesteger et al. / Chemical Physics Letters 259 (1996) 178-184
181
Table 3 MRD-CI energies(E h) and vertical transition energies (eV) of the two lowest excited states per symmetry for 1a
were calculated. The ground state energy (RHF -- 4 6 5 . 8 7 5 0 3 4 E h) moderately decreased to -- 4 6 5 . 9 3 8 3 7 8 E h u p o n C I . E x c i t e d s t a t e e n e r g i e s ,
State
Energy
symmetry
Transition
Osc. strength
Polari-
vertical transition energies,
energy
(f)
zati°nb
a n d p o l a r i z a t i o n s a r e p r e s e n t e d in T a b l e 3. W h e r e a s
oscillator strengths (f)
2Ag 1A u 2A u IB u 2Bu 1Bg
-465.410614 -465.500749 -465.488344 -465.597163 -465.552797 -465.560505
14.36 11.91 12.25 9.28 10.49 10.28
0.0000 0.1126 0.0086 0.8494 0.1282 0.0000
d_ .1_ II I[ -
t h e l o w e s t t r a n s i t i o n ( 9 . 2 8 e V , b u, f 0 . 8 4 9 4 ) c o r r e s p o n d s to a ~ r ~ " HOMO~LUMO transition
2Bg
-465.518276
11.43
0.0000
-
m e t r y f o r b i d d e n . T h e n e x t t r a n s i t i o n ( 1 0 . 4 9 e V , b u,
a n d is p e r f e c t l y p o l a r i z e d a l o n g t h e c a r b o n - c a r b o n double bond, the second lowest transition (10.28 eV, b g , cr ~ rr *, H O M O - 1 ~ L U M O , f 0 . 0 0 0 0 ) is s y m -
a MRD-CI ground state ( l A g ) energy: -465.938378 E h. b Notation used: II, polarized along C(1)-C(2) double bond; _1., polarized perpendicular to C(1)-C(2) double bond, in plane C(3)-
"iT ~ tr *, H O M O ~ L U M O + 1, f 0 . 1 2 8 2 ) is allowed and also perfectly polarized along the carbon-carbon double bond. For the assignment of
c ( 5 ) - c ( 4 ) - c ( 8 ) ; see Fig. 2.
the two experimentally
observed
bands
the calcu-
lated first and third excited state are of interest (vide t i o n s w e r e c h o s e n to b e a s c l o s e a s p o s s i b l e to t h e
s u p r a a n d R e f s [2,6]). T h e m o s t i m p o r t a n t c o n f i g u r a -
HOMO
~ LUMO
tions for the ground state and these excited states are
lowed.
The
two
transition as far as symmetry lowest
states for each
al-
symmetry
p r e s e n t e d i n T a b l e 4. S i n c e f o r t h e r e f e r e n c e c o n f i g u -
Table 4 Most important configurations of the ground state and excited states of 1a c 2b
MO 9a u
14ag
9bg
14b u
15ag
2 2 2 2 2
2 2 2 2 2
2 -
. 2 1 1 -
Lowest lr --* "rr" (1B u) excited state 0.9451 R 2 2 2 0.0045 2 2 2 0.0005 R 2 2 1 0.0004 R 2 1 2 0.0002 R 2 1 2
1 l 2 2 2
1 . . -
rr ~ tr * (2B u) excited state 2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 1 2 1 2 2 2 2 1 2 2 2 2 1 2 1 2 2
. . . . 1 -
Ground state ( l A g ) 0.9513 R 2 0.0096 R 2 0.0034 2 0.0022 2 0.0004 R 2
Second lowest 0.9113 R 0,0177 0.0081 0.0020
0.0007 0,0003 0.0003 0.0003
R R R R
16ag
15b u
.
. . 1 . 2
.
.
1
.
.
. -
.
.
.
-
.
-
1
. 1
a Only configurations with c 2 >_ 0.0002 are tabulated. b Reference configurations of MRD-CI calculation are labeled 'R'; see text. c Singly occupied 2lag orbital.
. .
.
.
-
-
-
.
-
. .
-
.
1 .
1
-
.
. .
.
. 1
.
.
.
.
1 -
.
.
.
.
-
.
.
.
.
.
.
.
. .
.
. -
. .
. 1
.
.
.
1 1 -
.
. 1
.
. .
1Sag
. .
.
.
-
.
. .
10b e
. .
.
. .
.
.
.
17ag
.
.
.
.
.
. .
.
. .
.
.
.
.
.
.
10a u
.
.
. .
16b u
. .
. .
c._
182
FJ. Hoogesteger et al./ Chemical Physics Letters 259 (1996) 178-184
rations the sum of the squares of the CI coefficients (c 2) are larger than 0.9, the set of reference configurations ( ' R ' ) taken into consideration was adequate. The results provide compelling evidence that the two absorption bands observed for 1 both in the vapor phase and in the condensed state have to be assigned to a ~r ~ "rr * (HOMO ~ LUMO) and -rr ~ tr * (HOMO ~ L U M O + 1) transition. In agreement with the solid-state (single crystal) polarized reflection UV spectral data [6] these transitions are symmetry allowed and perfectly polarized along the carb o n - c a r b o n double bond. Hence, the previous as•
signment of the second transition as '-rr(CH2)' --~ ,rr , which was based on the assumption that excitation occurs from a 'ribbon-type' MO [20,21] discernible in compounds containing cyclohexane moieties, has to be incorrect [2]. The 'ribbon-type' MO in the case of 1 is related to the highest-filled MOs in cyclohexane (4eg) and is composed of " r r ( C H 2 ) ' a n d o ' ( C C ) local orbitals. According to photoelectron spectroscopy [21], the 'ribbon-type' MO is separated from the other ~r and tr MOs by a considerable energy gap, i.e. for I it is observed at 9.8 eV (6-31G, 10.89 eV, 9bg, HOMO-1 a-type) [2]. A survey of the most important configurations reveals that the 'ribbon-type' MO does not contribute (Tables 4 and 5, vide infra). Note that our MRD-CI calculations reveal that the tr ~ ~r* (HOMO-1 ~ LUMO) transition involving excitation from the 'ribbon-type' MO to the ~ * L U M O is symmetry forbidden (Table 3). Although for both transitions the absolute value of the MRD-CI transition energies deviate from the experimental values, the difference between both transitions is described reasonably well (rr ~ tr * transition energy minus ~r ~ rr * transition energy: exp. 0.87 eV and MRD-CI 1.21 eV, Table 3 and Ref. [2]). To assess charge redistributions upon excitation, a Mulliken population analysis of the CI wavefunction was performed [13]. The results show that the 7r ~ • r * (HOMO ~ LUMO) transition induces only a minor redistribution of electron density (Table 5). This is not surprising since both the H O M O and L U M O are primarily localized on the olefinic carbon atoms. In contrast, considerable charge redistribution is found for the 7r ~ tr * (HOMO ~ L U M O + 1) transition. Note that the ~ * L U M O + 1 is delocalized over the entire molecular framework and pos-
Table 5 Mullikenpopulation analysis of the ground state and the lowest ~r ~ ~r* (IB u) and ~ ~ tr* (2B u) excited states of 1
C(l); c(2) c(3); c(4); c(5); c(6)
Population Ground (It, I t ' ) statea stateb 5.995 -0.052 6.336 -0.002
(ax, tr*) stateb -0.198 -0.018
C(7); C(8); C(9); C(10)
6.293
- 0.025
- 0.031
c(11); c(12) H(13); H(14); H(15); H(16) H(17); H(18); H(19); H(20) H(21);H(22); H(23); H(24)
6.303 0.843 0.834 0.847
-0.022 +0.021 +0.007 +0.009
+0.005 -0.019 +0.140 +0.020
H(25); H(26); H(27); H(28) H(29); H(30) H(31); H(32)
0.854 0.846
+ 0.022
-0.006
Atom
0.847
+0.016 -0.004
0.000 +0.021
a Mulliken population, b Difference with ground state Mulliken population ( - : decrease in electron population; +: increase in electron population).
sesses both cr and 'rr'-type topology. A decrease in the electronic population of the two olefinic carbon atoms (C(1) and C(2) - 0 . 1 9 8 au) concomitant with an increase of the population on the four equatorial allylic hydrogen atoms (H(17)-H(20) + 0 . 1 4 0 au) is found. Thus, for the ~r -o tr * transition charge transfer occurs from the double bond into the cyclohexyl moieties [2]. The MRD-CI oscillator strength f for the rr ~ ~r * transition (0.8494) is larger than the experimental value ( f 0.19; vapor phase), while that of the ~r tr * transition ( f 0.1282) is smaller (exp. f 0.26) [1,2]. Since the quality of the 6-31G wavefunction is not sufficient for an accurate calculation of f , we refrain from further discussion. 3.4. A comparison between l,l'-bicyclohexylidene (1) and tetramethylethene (2) According to the MRD-CI results the two distinct valence transitions of 1 discernible in the UV region have to be assigned to a 7r--*-tr * and a 7r ~ tr * transition. The question arises whether these results are either unique to 1 or general to simple tetra-alkylated olefins. To gain insight the vertical transitions of tetramethylethene (2) were calculated foilowing the same approach as used for 1. The geometry of 2 was optimized in D a symmetry at the
FJ. Hoogesteger et al. / Chemical Physics Letters 259 (1996) 178-184
Table 6 MRD-CI energies ( E h) and vertical transition energies (eV) of the two lowest excited states per symmetry for 2 a State Energy symmetry
Transition energy
Osc. strength Polari(f) zation c
2AI IB t 2B~
-233.701057 -233.867100 -233.818473
14.68 10.16
0.0030 0.0450
3- L
IB2
-233.882086
2B 2 IB 3
-233.838799 - 233.833501
11.48 9.75 10.93
0.0554 0.9001 0.0031
3, ± II II
11.07
0.0073
3.
2B 3
-233.787136
12.34
0.0005
3,
a Geometry optimized at the RHF/6-31G level; D 2 symmetry (C = C 1.34/~, C - C 1.51 /~, 3 C - H 1.09 ,~,, 1.08 ,~ and 1.09 ,~, C H 3 - C - C 124.3 °, C H 3 - C - C H 3 111.4 °, 3 H - C H 2 - C 109.8 °, 114.0 ° and 110.7 °, 3 H - C - H 107.3 °, 106.8 o and 107.9°); ground state(1A l) energies(Eh): RHF/6-31G,-234.086330; MRD-C1,
-234.240456. b Experimental 7.0 eV [1], see text. c Notation used: II, polarized along C - C double bond; 3,, polarized perpendicular to C - C double bond, in plane formed by C-atoms; 3, 3_, polarized perpendicular to both the C - C double bond and the plane formed by the C-atoms.
R H F / 6 - 3 1 G level (Table 6). From a total of 24 reference configurations 8919 CSFs of al symmetry, 8661 of bl symmetry, 8544 of b E symmetry and 8840 of b 3 symmetry were selected. For the two lowest states of each symmetry, state energies, vertical transition energies and oscillator strengths were calculated (Table 6). In analogy to 1, the lowest vertical excitation is a ~r ~ 7r * transition (9.75 eV, H O M O -~ LUMO, bE, f 0.9001) which is perfectly polarized along the carbon-carbon double bond. The next transition can be described as a "rr ~ t r * transition (10.16 eV, H O M O ~ L U M O + 1, b I, f 0.0450) and is polarized perpendicular to the plane formed by the carbon atoms. The third transition (10.93 eV, H O M O - I ~ L U M O , b 2 , f 0.0001) is a t r ~ 7r * transition. A1though it is perfectly polarized along the carboncarbon double bond, its oscillator strength is very low. These results show that, although for both 1 and 2 the "rr ~ zr * transition represents the lowest excited state, the second (1, tr -~ ,r *, f 0.0000 and 2, ~ tr ~, f 0.0450) and third (1, ~r ~ cr *, f 0.1282 and 2, ~r ~ 7r * f 0.0001) transitions are inter'
changed. In addition, due to the reduction in symmetry in going from 2 (D 2) to 1 (C2h) both the oscilla-
183
tor strengths and the polarization of the second and third transition are affected.
4. Conclusions MRD-CI calculations reveal that the two distinct transitions found in the UV region for 1,1'-bicyclohexylidene (1) have to be assigned to a ~r --* 7r * (HOMO ~ LUMO) and a ~r ~ cr * (HOMO L U M O + 1) transition. In line with experiment [6] b o t h transitions are perfectly polarized along the carbon-carbon double bond. T h e rr ~ tr" transition possesses charge-transfer character; charge redistribution from the double bond into the cyclohexylidene rings occurs. A comparison with MRD-CI resuits obtained for tetramethylethene (2) reveals that t h e introduction of cyclohexyl moieties in going from 2 to 1 affects both the transition energy and o s c i l l a t o r strength of especially the s e c o n d a n d third valence transitions.
Acknowledgements This work was sponsored by the Stichting Nationale Computerfaciliteiten (National Computing Facilities Foundation, NCF) for the use of supercomputer facilities, with financial support from the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (Netherlands Organization for Scientific Research, NWO).
References [l] M.B. Robin, R.R. Hart and N.A. Kuebler, J. Chem. Phys. 44 (1966) 1803. [2] M. Allan, P.A. Snyder and M.B. Robin, J. Phys. Chem. 89 (1985) 4900.
[3] F.J. Hoogesteger, R.W.A. Havenith, J.W. Zwikker, L.W. Jelmeskens, H. Kooijman, N. Veldman and A.L. Spek, J. Org. Chem. 60 (1995) 4375. [4] M.B. Robin, Higher excited states of polyatomic molecules, Vol. III (Academic Press, New York, 1985). [51 M.B. Robin, Chemical spectroscopy and photochemistry in the vacuum-ultraviolet, Eds. C. Sandorfy, P.J. Ausloos and M.B. Robin (Reidel, Dordrecht, 1974).
[6] P.A. Snyder and L.B. Clark, J. Chem. Phys. 52 (1970) 998.
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FJ. Hoogesteger et al./ Chemical Physics Letters 259 (1996) 178-184
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