J. Phys. Chem. 1995,99, 11909-11915
11909
Molecular Orbital Calculation on 2-Nitrotriptycene: A New Molecular Unit for Nonlinear Optics Sophie Norvez" and Jacques Simon ESPCI, CNRS, URA 429, I O rue Vauquelin, 75231 Paris Cedex 05, France
Jean-Jacques AndrC and Andr6 Bieber ICs-CNRS, 6 rue Boussingault, 67083 Strasbourg Cedex, France Received: December 12, 1994@
2-Nitrotriptycene is 4 times as efficient as nitrobenzene for second harmonic generation in nonlinear optics. Molecular orbital calculations have been carried out to rationalize this result. A correlation has been established between the characteristics of the optical absorption peaks, the electron distribution of the frontier molecular orbitals, and the magnitude of the hyperpolarizability coefficients /3. The enhancement of the p-value seems to be due to a large electron transfer (0.9 e-) in the interaromatic ring charge transfer. The difference in dipole moment between the excited state and the ground state is consequently unusually large (17 D). The rather small corresponding extinction coefficients, however, lead to a p-value of about 10 & 3 x esu.
Introduction
EIO~
Molecules synthesized for second harmonic generation consist, in most cases, of various aromatic structures appropriately substituted with donor and acceptor groups.' The second-order hyperpolarizability coefficients are dominated by intramolecular charge transfers.2 Nonplanar molecules, such as triptycene derivatives, may also be used for second harmonic generation. Triptycene is made of three benzene rings in a D3h symmetry, in such a way that a charge transfer between them may be postulated. The question of the through space or through bond character of the charge transfer between the aromatic rings is a matter of controversy? Electric field induced second harmonic (EFISH) measurements have shown that 2-nitrotriptycene (1) presents nonlinear optical properties."
'0
8
8
4
2
0
c-
1
The hyperpolarizability coefficient of 1 (B = 10 x esu) is more than 4 times larger than the one of nitrobenzene' (B = 2.2 x esu). This enhancement can be associated either with a transannular charge transfer or may be due to the nitrobenzene moiety. The W spectrum of 2-nitrotriptycene (Figure 1) presents two bands at 288 and 322 nm with probable charge transfer character. The W spectra of triptycene derivatives are known to be generally the sum of the spectra of the three constitutive rings.5 Nitrobenzene presents an intense @Abstractpublished in Advance ACS Abstracts, June 1, 1995.
0022-365419512099-11909$09.0010
Figure 1. W spectra in CHZClz: 2-nitrotriptycene (full line), triptycene (dashed line), nitrobenzene (dotted line). In insert, part of the last spectrum in cyclohexane.
band at 260 nm (dotted line), a weak n-n* transition at 288 nm, and a n-n* transition around 330 nm (insert). The band at 322 nm in 2-nitrotriptycene is too large ( E = 4000) to be associated with a pure n-n* transition, even though interaction with the locally excited states of the other rings may enhance the probability of transition. The present work describes molecular orbital calculations to determine the influence of transannular charge transfer on the magnitude of the hyperpolarizability coefficients. Calculations have also been carried out on triptycene and nitrobenzene for comparison. 0 1995 American Chemical Society
11910 J. Phys. Chem., Vol. 99, No. 31, 1995
Norvez et al.
TABLE 1: Optimized Geometries Obtained in the AM1-RHF Approximationa
d f i a
''a
RP benzene, RI=H, R2=H aniline, R I = N H ~R2=H , nitrobenzene, RI=NOZ,R2=H nitroaniline, R I = N H ~R?=N02 , triptycene, RI=H nitrotriptycene; ring a,R,=N02 nitrotriptycene; ring /3, RI=H
a
b
C
d
e
f
1.395 1.390 1.393 1.384 1.410 1.419 1.418
1.395 1.415 1.405 1.421 1.384 1.383 1.385
1.395 1.415 1.405 1.421 1.397 1.412 1.402
1.395 1.390 1.393 1.384 1.389 1.401 1.391
1.395 1.394 1.395 1.406 1.397 1.399 1.402
1.395 1.394 1.395 1.406 1.384 1.386 1.385
6 (max- min) 0 0.025 0.012 0.037 0.026 0.036 0.033
a Bond lengths, expressed in A, are noted as shown for substituted benzene derivatives and for a third of the triptycene derivatives; the difference between the congest and shortest bonds is noted d(max-min).
Molecular Orbital Calculations Calculation Procedure. All molecular orbital calculations have been performed within the framework of the semiempirical MNDO, AM1, and PM3 approximations6q7 using the QCPE MOPAC 6.0 p a ~ k a g e . ~An . ~optimization of geometry has been carried out on all the molecules both within the restricted Hartree-Fock (FU-IF) and the unrestricted Hartree-Fock (UHF) methods.I0 All optimized geometries discussed below correspond to real minima in the potential energy surface.11J2 Optimization of Geometry. The experimental molecular structures have been reported for benzene, triptycene, nitrobenzene, and nitr~aniline.'~-'~ The calculated optimized geometries have been compared with the experimental ones for these molecules. The MNDO approximation does not, in general, reproduce correctly the geometry of the NO2 group.I7 This has been presently verified on nitrobenzene, nitroaniline, and nitrotriptycene: the NO:! group is always found to be perpendicular to the aromatic ring in the MNDO approximation,whereas with AM1 and PM3 methods the NO2 is coplanar with the aromatic ring.I8 AM1 and PM3 give very similar results. However, in a few cases, some geometrical parameters (NO and CN bond lengths in C-NO2 or C-NH2) are closer to the experimental values with AM 1. Only AM1 results will be discussed further on. It has been checked that very different starting geometries lead to the same final geometry. Finally, RHF and UHF methods give very similar result^.^^-^^ The geometries obtained with the RHF method are shown in Table 1. For all molecules, the symmetries of the optimized geometries are in agreement with those e ~ p e c t e d . ~The ~ - ~aromatic ~ or quinonoid character may be visualized by the difference in the carbon-carbon bond lengths in the substituted benzene ring. Both substitution with amino and nitro groups induce a small quinonoid character (0.025 and 0.012 A, respectively). In 2-nitrotriptycene, the bond noted a in Table 1 is lengthened (f0.024 A) compared with benzene, due to the triptycene framework. This effect complicates the effect of the substitution in RI position (Table l), and no quinonoid character is observable on the ring but a bond alternation. The comparison between the experimental and the calculated geometries shows that the overall agreement is good (Figure 2). The bonds g of triptycene (Table 1) are unperturbed by substitution and are all equal (1.5 15 A). This value is close to the experimental one reported for triptycene (1.53 A). In nitrobenzene the NO bond lengths are well reproduced (1.202 versus 1.208 A). This bond is sensitive to a para substitution with an amino grou (experimental value 1.208 A in nitrobenzene versus 1.246 in p-nitroaniline), Calculation does not account for this electronic delocalization (1.202 1.204 A).
w
-
k
k
H
a
I2
H
H
H
H
k
H
H
(1.3731
k
c
il
Figure 2. Comparison of the experimental and the optimized geometries: (a) benzene,I3 (b) triptycene,I4 (c) nitr~benzene,'~ (d) nitroaniline.I6 Experimental bond lengths and angles are indicated in parentheses. For triptycene, one-third of the molecule is shown. Nitrotriptycene ' ' '
' ' ' I
O
O
' '
'
1is,;8'fO:03b
'
'
a;
'
0
'
; '
'
5.85
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O
5.80
0
-3582.501
' 0
0
11
0
5.70
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0 0
00
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5.65 5.60
ST
-i 0
Y
5.55
-a;10'.02
-40
-20
0
20
40
60
80
100
120
a Weg.1
Figure 3. Rotation barrier of NO2 in 2-nitrotriptycene: (circles) total energy Eta expressed in eV and (squares) dipole moment ,LA expressed in D. a is the angle between the nitro plane and the aromatic plane. Barrier of Rotation. The energy barrier for the rotation of both NO2 and N H 2 groups have been calculated. The results are shown in Figure 3 for the NO:! group in nitrotriptycene. Comparable results have been obtained for other molecules. The barrier is higher than 150 meV for the rotation of NO2 and in the range (300-400 meV) for NH2.
J. Phys. Chem., Vol. 99, No. 31, 1995 11911
MO Calculation on 2-Nitrotriptycene
.............. ............+ -%.
21 26
8
eV I 81
t
2.15 eV
'c)
.%.
....................52 *
a ' * -,,'
............ ..b
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25
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.... ...... 24
23
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22
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e t
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.......
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8
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49
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bl
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& & P
............ 53 *
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.9.5
*
.I
.'I
-(..,'
-....
i
44 ................. + .,.....
., '... ......... ............ . 43 *
-1c
Figure 4. Molecular orbitals of nitrobenzene (symmetry CZ,),
As a comparison, the rotation barrier of the methyl group is as low as 1 meV.25The energy minimum for both substituents (NO;?,NH;?)is obtained when the substituent is coplanar with the aromatic ring. The permanent dipole moment is maximum at this geometry. The aim of this publication is to get some insight into the molecular origin of the optical nonlinear response rather than to compare quantitatively the experimental and theoretical results, and therefore we shall use simple SCF MO calculations. More sophisticated calculations would be necessary for quantitative evaluation of the properties. For instance, the assignment of the optical transitions would require extensive configuration interaction calculations taking into account not only some singly but also doubly excited states.26-28
I
'*.,
-1I35 eV
41 .......... *
Figure 5. Molecular orbitals of triptycene. At the right side, the MO of one of the three subunits is shown (symmetry D3h).
In the EFISH method, only the vectorial part of the hyperpolarizability tensor is measured, given by
For SHG,/?jij = /?j,;, then
Assuming Kleiman relations, it follows
Results and Discussion The calculated energy of the electronic levels as well as a schematic representation of the eigenfunctions are shown in Figures 4-6. The results for nitrobenzene (Figure 4) are in agreement with those previously obtained with a CNDO c a l c ~ l a t i o n .The ~ ~ ~first ~ ~ two transitions are associated with the symmetries B;?and AI in the CzVsymmetry group. In both cases, an electronic transfer from the aromatic moiety to the nitro group may be noticed. It is possible to relate the symmetry of the transition moment with the hyperpolarizability coefficients of the m ~ l e c u l e . ~If' z is assumed to be the direction of the ground state dipole moment:
The results for triptycene are presented Figure 5: the MO diagram of the triptycene may be deduced from the orbitals of three benzene rings in a D3h symmetry. The energies of the highest-occupied molecular orbitals can be related to the molecular ionization energies determined from photoemission spectroscopy (PE). The PE spectrum of triptycene shows in the energy region 7.8-9.8 eV two separated groups of bands whose intensity ratio is approximately 1:5.7.32 The first band probably corresponds to the ionization from the HOMO a'*, and the second group to the ionization from the five following highest n-MOs. There is a moderate agreement between the experimental and calculated ionization energies, with the usual restrictions associated with Koopman' s theorem. In the case of 2-nitrotriptycene (Figure 6), the electronic density of the frontier orbitals is not distributed over the three
Norvez et al.
11912 J. Phys. Chem., Vol. 99, No. 31, 1995
_
eV
I
-...
........+ ........ .... .... ............................. *
a'
63
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62
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61
0
eV I
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.953 951
=.>.
.9.59 -,
-9
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55
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= Y -. . .:............................. -, ...... .... -. ..., .%. ... ........... ................... ,53 .. ... .. .............. ........... ............+ 53 = - .' ,.....:. ..,,. ...............* 51 .P
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-11
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.
. .
,
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9.48
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. 9.94
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-.
10.26
-.
10.41
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10% 10.68
a* TrIpty cen e
Nltrotrlptycene
Nitrobenzene
-11
I%
._ .........
'.-. .:c......... ..,
%J
%
a"
a"
Figure 6. Molecular orbitals of 2-nitrotriptycene (symmetry Cs).
Figure 7. Comparison of the MO energies of nitrobenzene, triptycene,
and 2-nitrotriptycene. Although more precise calculations would be necessary to unambiguously assign the experimentally observed transitions, the present work permits to evidence the influence of the interring charge transfer. From the previous observations, it may be postulated that the main contribution to the hyperpolarizability of 2-nitrotriptycene is connected with interring CT transitions. Group theory allows to predict which optical absorption contributes to a particular hyperpolarizability coefficient. In D3h symmetry, the three /?coefficients arise from the irreducible representation E':
rings, but either on the nitrobenzene chromophore or on the two other aromatic rings. The HOMO 55 (fully represented) has, however, an electronic density largely concentrated (90%) on the unsubstituted rings. All transitions are allowed in the C, symmetry, it is therefore reasonable to assume that the first transitions observed in the UV spectrum of 2-nitrotriptycene are associated with a charge transfer from the unsubstituted rings to the nitrobenzene moiety, because these levels correspond to the frontier orbitals. & h e e * *XLx E' Similar calculations have already been performed on the 1,4G=Y X o h = (z,x) dihydro- 1,4-bi~(dicyanomethylene)triptycene.~~ The UV specL Z T . U Z . . E' trum of this molecule exhibits a band at 535 nm (log E = 3.4), which has been assumed to be a CT transition. The authors If a dipole moment stands along the z-axis, a CzVsymmetry have shown (self-consistent field-configuration interactionmust be considered. The E' representation then splits into AI dipole velocity -MO calculations) that a good agreement BI. between the observed and calculated UV spectra is obtained when through space interaction is taken into a c c o ~ n t . ~ ~ - ~ ~ c,, .xzJ Bl In the case of 2-nitrotriptycene, transitions purely centered on the nitrobenzene fragment would lie fairly high in energy. zur zyy uz AI (C2=z) The lowest energy transitions arise from triptycene type orbitals Finally in the C, symmetry of 2-nitrotriptycene, AI and B I (52-55) to either nitrobenzene type levels (56,57) or higher become A' and A": energy triptycene levels (58-61). The UV spectra of nitrotriptycene and triptycene have two peaks in common around c,. xzx xyx A" 270 nm which could be attributed to the second type of Y n YYY YU Y Y Z A' transition, while the first type is associated to the two broad z x x z y y z u t y z ~ A' b,z) within bands at longer wavelengths. These latter correspond to the plane interring charge transfer transitions, since HOMO'S are mainly Triptycene (D3h)and 2-nitrotriptycene (C,) have in common built from triptycene centered orbitals, and LUMO from three hyperpolarizability coefficients. By postulating that, in nitrobenzene fragment (Figure 7).
. . . . . ..
+
. . . . . . 9
. . .
MO Calculation on 2-Nitrotriptycene
J. Phys. Chem., Vol. 99, No. 31, 1995 11913
TABLE 2: Lowest Energy Transitions Calculated for 2-Nitrotriptycene (AM1-UHF Approximation) transitions energy (eV) symmetry 55
-
56 57 58 54 56 57 58 53 56 57 58 52 56 57 58 51 -56
8.47 9.23 9.41 8.89 9.65 9.83 8.90 9.66 9.84 8.92 9.69 9.87 9.25
TABLE 3: Calculated Amount of Charge Transfer during the Transition between the Frontier Orbitals nitrobenzene ring (A) unsubstituted rings (D)
A' A' A"
LUMO 56 HOMO 55 HOMO 53
A" A" A' A' A' A" A" A" A' A'
d(56-55)
d(56-53)
I (nm)
W+'Y(erg)
1"
288 322
4.56 x 103j 7.4 x 1033
0.082 0.070
a
-
0.030 0.902 0.993 -0.872 -0.963
TABLE 4: Absorption Bands of 2-Nitrotriptycene Which Mainly Contribute to the Hyperpolarizability/%Coefficient Measured by EFISH
the latter, triptycene still partly contributes to the hyperpolarizability properties, adding nitro group enhances the three components CS,,,@=,Pm) and generate seven new coefficients. In nitrotriptycene, the lowest energy transitions, 55 56 (8.47 eV), 54 56 (8.89 eV), 53 56 (8.90 eV), and 52 56 (8.92 eV), are of symmetry A', A", A', and A", respectively (Table 2). In all four cases, it corresponds to a charge transfer from the benzene rings to the nitrobenzene moiety. The transition of symmetry A" gives rise to the coefficients pxLxand Bqx which do not intervene in @ determined by EFISH, assuming that ,E stands in the (y, z ) plane. Consequently, only the absorption bands with A' symmetry can contribute to the experimentally measured hyperpolarizability coefficients; it follows that only 55 56 and 53 56 transitions are effective.
-
0.969 0.091 0 +0.878 $0.969
--
AP 18 16.3
Pcr (esu) 2.8 x 10-30 3.6 x
From spectral data. From MO calculations.
where W and f are deduced from the absorption spectrum; f may be calculated from the approximate formula
f = 4.6 x 10-
9 'max
M
7 %ax
where emax(in M-' L), AA,and Amax (in cm) are the intensity, the half-width, and the maximum wavelength of the charge transfer band. &trans may be deduced from molecular orbital calculations by calculating the amount of charge transferred during the transition. The first band observed in the W spectrum which is active in EFISH is due to the transition from the orbital 55 to the orbital 56. By calculating the electron density on each atom of nitrotriptycene in these two states, we Nonlinear Optical Properties of 2-Nitrotriptycene: A find that electron density is concentrated in unsubstituted part Model for the HOMO, and on nitrobenzene for the LUMO. It follows that during the transition, charge is transferred from the Quadratic hyperpolarizabilities of monosubstituted benzenes unsubstituted rings which may then be considered as donors have been rationalized by the equivalent intemal field (D), toward the nitrobenzene ring, which behaves as an acceptor In systems with several substituents, an additivity law can be moiety (A). Calculations are summed up in Table 3. As a used when the groups are in weak mutual interaction. When result, we find that 87% of the electron density is transferred the substituents are strong electron donors and acceptors, cross 56, and 96% during the transition interaction gives rise to an additional c o n t r i b ~ t i o n : ~ ~ ~ ~ . ~ ~ during the transition 55 53 56. Aptrans is related to the amount of charge transferred de and to the distance of transfer r (estimated as 3.9 A42):
-
-
-
-
@add is
the additive term and @mis a charge transfer contribution. This last term can be evaluated using the various methods proposed in literature.30s38-39 In all these methods, @mis related to the energies and oscillator strengths of all the electronic absorption bands.40 When charge transfer occurs mainly between two well-defined electronic states, the equation may be simplified to a two level models2 In a related approach, it can be postulated that the hyperpolarizability of nitrotriptycene is due to nitrobenzene being considered as isolated, and to some charge transfer between the two of the benzene rings and the nitrobenzene moiety. The unsubstituted triptycene contribution is considered negligible.4'
@ = @nitrobenzene + PCTtrans @CT
(3)
is related to the spectroscopic data by the equation (4)
where f is the oscillator strength and F ( W ) = W / { [ W 2- (2ho)2][W2- (ho)2]}
=
= 6 x 4.8 x lo-'' x 3.9 x
6 x 18.7 x lo-'' esu-cm = 18.76 D where 6 is the amount of charge transferred. The first absorption band at 322 nm is associated with the transition 55 56. For this transition, 6 = 0.87 and then &ms(322) = 16.3 D. The assignment of the other bands around 290 nm is difficult because of the large discrepancy between experimental and calculated values. It seems, however, clear that the broad peak is due to the nitrobenzene moiety since it is absent in the triptycene spectrum. The transitions (52-54) 56 must all arise around 290 nm. The EFISH active band is 53 56, giving rise to Aptrans(288) = 18.0 D. Equation 3 may be expressed as @ = @nitrobenzene -k @ c ~ ( 2 8 8+ ) @m(322).The transannular charge transfer contributions may then be deduced from the spectroscopic data (Table 4). It can be postulated that all induced polarizations occur along the same axis and that a simple addition may be made. The overall @-valueis found to be @ = (2.2 2.8 3.6) = 8.6 x esu, comparable with the experimental value ((10 f 3) x esu).
-
-
-
+
+
11914 J. Phys. Chem., Vol. 99,No. 31, 1995
Norvez et al.
TABLE 5: Experimental Dipole Moments for the Ground and First Excited States of Nitrobenzene (after Ref 43)
so SI
340 288 250
sz s3
4.21 4.0 f 0.1 9.0 f 2 8.18
n-n* n-n* n-n*
TABLE 6: Variation &-H of the Electron Density for the Indicated Transitions, As Deduced from MO Calculations. Comparison of the Ap Values Determined from Experimental Measurements or Derived from MO Calculations
I (nm) transition 340 B1 288
Bz 250 AI
NOz(A) benzene (D) Aps.e(DY AP,, (Wb LUMO24 HOMO21
0.284 0.829 8~-H -0.545 LUMO24 0.284 HOMO23 0 8~-H f0.284 LUMO24 0.284 HOMO22 0.034 8~-H +0.250
0.701 0.196 +0.505 0.701
1 -0.299 0.701 0.946 -0.245
0.2
8.4
4.8
4.8
4
4.0
Deduced from experimental data.43 Derived from MO calculations.
This model allows us to estimate the second-order hyperpolarizability of triptycene derivatives, and evaluates the importance of the transannular charge transfer in the nonlinear properties of these compounds. Conclusion Molecular orbital calculations showed that the low energy bands in the W spectrum of 2-nitrotriptycene are associated with a transannular charge transfer. This rationalizes the enhancement of the second-order hyperpolarizability observed for nitrotriptycene comparatively to nitrobenzene. Although more accurate results may be expected from calculations including configuration interaction, the comparison between experimental and calculated values would be more difficult since extensive mixing of the orbitals occurs. We have introduced a term btrans, which refers to the charge transfer between the highest occupied and lowest unoccupied orbitals during the transition. We have shown, by comparison with nitrobenzene, that this approximation gives a satisfactory agreement with experimental values. In the case of 2-nitrotriptycene, MUans is due to a transannular charge transfer. Its remarkably high value (17 D) derives from the important electron redistribution during the inter-ring transition.
Appendix. Calcdation of Aptram The validity of the previous model has been checked in the nitrobenzene: we used previously employed CNDO which included configurationinteraction over the first nine singlet excited states; the first three optical bands of nitrobenzene are composed of the transitions 21 24 (Bl), 23 24 (Bz),and 22 24 (AI) (see Figure 4). The experimental dipole moments of the different electronic states of nitrobenzene are available from the literature43(Table 5 ) . From these experimental determinations, the b,,, expected for the 340, 288, and 250 nm bands of nitrobenzene are 0.2, 4.8, and 4 D, respectively. By studying as previously the HOMO-LUMO transition from the benzene ring to the NO2 group, the variation ~ L - Hof the electron density may be calculated from the charge densities on each atom in the ground and excited states (Table 6): the charge transfer occurs over case of
-
-
-
approximately 3.4 A; it can be deduced from (6) that AptrmSis equal to 8.4, 4.8, and 4.0 D for the BI, Bz, and AI bands, respectively. The results are in good agreement with the experimental values for the AI and BZ bands. A problem remains concerning the n-Jc* transition at 340 nm. It must, however, be remarked that the relative signs of the dipole moments in SO and SI states of nitrobenzene are not known with certainty. If the two dipoles have opposite signs, the Ap value is 8.21 D for the transition B1 (340 nm), in good agreement with the one expected from charge density calculations. Apms calculated for 2-nitrotriptycene is very large (-17 D) compared with conventional CT molecules. This results from the large electronic density change (0.9 e-) occuning over fairly large distances (3.9 A) during the inter-ring charge transfer transition. In nitroaniline derivatives, the amount of electron transfer is significantly smaller (0.24 e- for p-nitroaniline). References and Notes (1) Chemla, D. S., Zyss, J., Eds. Nonlinear Optical Properties of Organic Molecules and Crystals; Academic Press: Orlando, FL, 1987. (2) Oudar, J. L.; Chemla, D. S . J . Chem. Phys. 1977, 66 (6), 2664. (3) (a) de Wit, J.; Wynberg, H. Tetrahedron 1972, 28, 4617. (b) Dessau, R. M. J . Chem.Phys. 1971,54 (12), 5430. (c) Stock, L. M.; Suzuki, J. J . Am. Chem SOC.1965,87, 3909. (d) Wilcox, C. F., Jr. J . Chem. Phys. 1960,33, 1874. (e) Kitaguchi, N. Bull. Chem. SOC.Jpn. 1989,62,800. (0 Iwamura, H.; Makino, K. J . Chem. Soc., Chem. Commun. 1978, 720. (g) Tanaka, J.; Ozeki-Minakata, K.; Ogura, F.; Nakagawa, M. Spectrochim. Acta 1973, 29A, 897. (i) Harada, N.; Tamai, Y.; Uda, H. J. Am. Chem. SOC.1980, 202, 506. (i)Quast, H.; Fuchsbauer, H. L. Chem. Ber. 1986, 129, 1016. (k) Klanderman, B. H.; Perkins, W. C. J . Org. Chem. 1969, 34, 630. (4) Norvez, S.;Barzoukas, M. Chem. Phys. Lett. 1990, 165 (l), 41. (5) Wilcox, C. F., Jr.; Craig, A. C. J . Org. Chem. 1961, 26, 2491. (6) Dewar, M. J. S.;Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P. J . Am. Chem. SOC. 1985, 107, 3902. (7) Stewart, J. J. P. J . Comput. Chem. 1989, 10, 209 and 221. (8) Stewart, J. J. P. MOPAC 6.0 QCPE 1990, 455. (9) All calculations were performed on HP9000-720 and HP9000-735 computers. (10) Geometries were considered to be optimized when GNORM = SCF convergence has been required to satisfy that the change in energy on successive iterations was less than lo-' kcalmol-I and the change in density matrix elements on two successive iterations less than (1 1) The nature of the extrema has been checked as in ref 12, p 119. (12) Clark, T. A Handbook of Computational Chemistly; John Wiley: New York, 1985. (13) Kitai'gorodsky, A. I. Molecular Crystals and Molecules; Academic Press: New York, 1973. (14) Anzenhoffer, K.; de Boer, J. J. Z. Kristallogr. 1970, 131, 103. (15) Trotter, J. Acta Crystallogr. 1959, 12, 884. (16) Trueblood, K.; Goldish, E.; Donohue, J. Acta Crystallogr. 1961, 14, 1009. (17) Stewart, J. J. P. J . Cornput.-Aided Mol. Des. 1990, 4, 1. (18) See Table 8, p 73, in ref 17. (19) This is not the case for other compounds such as porphyrin" derivatives and phthalocyanine?' For a discussion, see ref 12, p 185. (20) Reynolds, C. H. J. Org. Chem. 1988, 53, 6061. (21) Bieber, A.; Hajji, L.; And& J. J., to be published. (22) For triptycene, for example, the symmetry D3h is obtained with a high accuracy with eigenvectors following algorithm23whereas the geometry obtained with other optimization procedures (namely BFGS in MOPAC (24)) does not predict the correct geometry. (23) Baker, J. J . Comput. Chem. 1986, 7, 385. (24) Shanno, D. F. J . Optim. Theory Appl. 1985,46, 87 and references therein. (25) Lu, K. T.; Eiden, G . C.; Weisshaar, J. C. J . Phys. Chem. 1992, 96, 9742. (26) Dick, B. Diplomarbeit, Koln Universitat, 1977. (27) Dick, B.; Hohlreicher, G. Theor. Chim. Acta (Berlin) 1979, 53, 221. (28) See for example: Morley, J. 0.;Pavlides, P.; Pugh, D. J . Chem. SOC., Faraday Trans. 2 1989, 85, 1789. (29) Sieiro, C.; Fernhdez-Alonso, J. I. Chem. Phys. Lett. 1973, 18 (4), 557. (30) Lalama, S.J.; Garito, A. F. Phys. Rev. A. 1979, 20 (3). 1179. (31) Simon, J.; Bassoul, P.; Norvez, S. New. J . Chem. 1989, 13, 13. (32) Kobayashi, T.; Kubota, T.; Ezumi, K. J . Am. Chem. SOC. 1983, 105, 2172.
MO Calculation on 2-Nitrotriptycene (33) Inagaki, S.; Yamamura, K.; Nakasuji, K.; Nakazawa, T.; Murata, I. J . Am. Chem. SOC.1981, 103, 2093. (34) Murata, I. Pure Appl. Chem. 1983, 55, 323. (35) Harada, N.; Uda, H.; Nakasuji, K.; Murata, I. J. Chem. Soc., Perkin Trans. 2 1989, 1449. (36) Oudar, J. L.; le Person, H. Opt. Commun. 1976, 15, 258. (37) Levine, B. F. Chem. Phys. Lett. 1976, 37, 516. (38) Oudar, J. L. J . Chem. Phys. 1977, 67 (2), 446. (39) Morrell, J. A,; Albrecht, A. C. Chem. Phys. Lett. 1979, 64, 46.
J. Phys. Chem., Vol. 99, No. 31, 1995 11915 (40) Oudar, J. L.; Zyss, J. Phys. Rev. A 1982, 26, 2016. (41) Norvez, S. Thesis, Universitk Pierre et Marie Curie (ESPCI), Paris, 1991. (42) The distance between the ring centers (4.5 A) has been projected on the transfer axis. (43) Seliskar, C. J.; Khalil, 0. S . ; McGlynn, S.P. Excited States; Lim, C., Ed.; Academic Press: New York, 1974; Vol. I, p 261.
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