J. Phys. Chem. 1992, 96, 10160-10165
10160
(27) Clark, R. J. H.; Dines, T. J. Angew. Chem.,Inr. Ed. Engl. 1986,25, 131. (28) (a) Westre, S. G.; Kelly, P. B.; Zhang, Y. P.; Ziegler, L. D. J. Chem. Phys. 1991,94, 270. (b) Westre, S. G.; Liu, X.; Getty, J. D.; Kelly, P. B. J .
Chem. Phys. 1991, 95, 8793. (29) Getty, J. D.; Kelly, P. B. Chem. Phys., in press. (30) Melinger, J.; Albrecht, A. C. J . Phys. Chem. 1987, 91, 2704. (31) Shin, K. S. K.; Zink, J. I. Inorg. Chem. 1989, 28, 4358.
Linear and Nonlinear Optical Properties of Cumulenes and Polyenynes: A Model Exact Study I. D. L.Albert,*” D. P~gh,*9~ J. 0. Morley,*and S.Ramaseshd Department of Pure and Applied Chemistry, University of Strathclyde, Glasgow GI IXL, Scotland, Research Centre, ICI Specialities, Blackley, Manchester M9 3DA. England, and Solid State and Structural Chemistry Unit, Indian Institute of Science, and Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560 01 2, India (Received: June 10, 1992; In Final Form: August 25, 1992)
Model exact static and frequencydependent polarizabilities,static second hyperplarizabilities and THG coefficients of cumulenes and polyenynes, calculated within the correlated Pariser-Parr-Pople (PPP) model defined over the r-framework are reported and compared with the results for the polyenes. It is found that for the same chain length, the polarizabilities and THG coefficients of the cumulenes are largest and those of the polyenynes smallest with the polyenes having an intermediate value. The optical gap of the infinite cumulene is lowest (0.75 eV) and is associated with a low transition dipole moment for an excitation involving transfer of an electron between the two orthogonal conjugated r-systems. The polyenynes have the largest optical gap (4.37 eV), with the magnitude being nearly independent of the chain length. This excitation involves charge transfer between the conjugated bonds in the terminal triple bond. Chain length and frequency dependence of a,,and T ~ , ~ ~ of these systems are atso reported. The effect of a heteroatom on the polarizability and THG coefficients of acetylenic systems is also reported. It has been found that the presence of the heteroatom reduces the polarizability and THG coefficients of these systems, an effect opposite to that found in the polyenes and cyanine dyes. This result has been associated with the different nature of the charge transfer in the acetylenic systems.
Introduction Conjugated organic molecules with large nonlinear optical (NLO) properties have attracted considerable interest from chemists and physicists in recent years.’-’ This has been due to the ease with which these molecules can be tailored for specific requirements in crystalline and noncrystalline bulk structures.6.’ Moreover, as a consequence of the molecular nature of these compounds in the solid state, the bulk properties can be addressed at the molecular level. Thus quantum chemical studies of the molecular hyperpolarizability have generated much interest during the early development of this field and provide a useful tool for analyzing a variety of diverse molecular systems. Theoretical modeling of the r-systems is nontrivial since the electron correlations are quite strong and even predicting the ordering of the energy levels requires extensive configuration interaction (CI).8-12This is prohibitive for smaller systems and impossible for larger systems. Thus many of the quantum chemical calculations resort to an incomplete or restricted set of excitations, the singly and doubly excited CI calculation being the mast commonly used.’+’’ However, it is necessary to perform a complete CI calculation to obtain the correct length dependence of these coefficients, as it is known that limited CI calculations are not size consistent. It has been demonstrated in recent years that a complete CI calculation within the r-framework based on the Pariser-Parr-Pople (PPP) model Hamiltonian with transferable parameters can accurately reproduce many of the prop erties of low-lying states of organic molecules found experimentally.10-1 2,16.17 The sum-over-states (SOS)method has been used extensively to calculate the NLO coefficient^.'^-'^*^^ In this method the perturbed electronic wavefunction is, in principle, expanded over University of Strathclyde.
* IC1 Specialities.
the complete set of eigenfunctions (ground and all excited states) of the unperturbed Hamiltonian. In practice, the method can only be expected to be successful if there is fairly rapid convergence as the excited states of increasing energy are added to the expansion. This criterion seems to be met in the case of first hyperpolarizabdity, where the main contribution comes from a small number of excitation associated with charge transfer across the molecule and where the two-level approximation (TLA)’9*20 has provided at least a qualitative guide to the interpretation of the phenomena such as second harmonic generation (SHG), but in other cases, particularly in the calculation of second hyperpolarizability, the slow convergence of the expansion leads to unresolved difficulties.2’q22Recent work by Ramasesha and Soos has made computation of NLO coefficients possible without explicitly computing the entire excitation s p e c ” and the associated transition dipole m ~ m e n t s . The ~ ~ .NLO ~ ~ coefficients are computed in the diagrammatic valence bond (DVB) basis, which is complete in the chosen PPP model and implicitly accounts for all the excitations. This technique has been successfully employed in the computation of the SHG?’ THG?6 EFISH?’ Pockels, and Kerr2*coefficients of a variety of conjugated r-systems. In this paper we report the results of our calculation on the frequencydependent polarizability and the THG coefficients of cumulenes and some acetylenic compounds and discuss the results at the molecular level.
Model Hamiltonion and the Computational Scheme The calculations have been carried out within the general framework of the Pariser-Parr-Pople (PPP) model, where the Hamiltonian is expressed in terms of the one-electron-transfer integrals (pivlpj)= tij = -2.40 + 3.20(rV- 1.397) (1) as in ref 25 and the two-electron Coulomb repulsion integrals
IIndian Institute of Science, and Jawaharlal Nehru Centre for Advanced Scientific Research.
0022-3654/92/2096-10160$03.00/0
(Pipjll/rijlPipI) = ( P i p i F j P j ) (0
1992 American Chemical Society
Vj
(2)
The Journal of Physical Chemistry, Vol. 96, No. 25, 1992 10161
Properties of Cumulenes and Polyenynes
I' 2' -----
fin eq 1 represents the mean field created by the nucleus and the a electrons. The orbitals referred to are the pz atomic orbitals (oriented normal to the molecular plane). Since in the PPP model, there is only one orbital per atom, i and j also label the carbon atoms. The intersite interaction potential V, is parametrized according to O h n as ~ ~ ~ V, = 14.397([28.794/(G + V,)2] + (3)
(I)
-
which reduces to the standard two-electron one-center integral Uij when rij = 0 and to 8 / r i j when rij m. The PPP Hamiltonian described above, which invokes the ZDO approximation, neglects interaction between two electrons with parallel or antiparallel spins in two different orbitals on the same atom and is valid only for systems with one r-orbital per site, such as the polyenes. For the cumulenes and polyenynes the interaction between two orthogonal ?r-orbitals that sometimes occurs on the same atom is represented at the INDO level of approximation by the one-center Coulomb and exchange integrals
Uiil= (pipitll/riizlpgit)= (pipi:pipi#) Kilt
(4)
= (ppjtJ1/ri&Jipi) = ( p i p i q i p i ! )
(5)
where the primed index, i', represents the p,-orbital on the atom for which i represents the p,-orbital. These integrals have been parametrized according to P ~ p l e . ~ ' The complete Hamiltonian can be conveniently written in the second quantized notation as
Mp!JpD0= E$@
+ iiCA c Uii1(fii- Zi)(fi(t- Z,) +
-
Kiit(Piif*Pijr ii'fA
(fij
+
fijt)}
(6)
where
(7)
(UIII)
(I#) Figure 1. Structures of the cumulenes (butatriene (I)), polyenyncs (vinylacetylene (11), 1,3-hexadien-5-yne (111), 1,3,5-octatrien-7-yne (IV), 1,5-hexadien-3-yne (V), and diacetylene (IX)), cyanoethylene (VI), cyanoimine (VII), and cyanobutadiene (VIII). TABLE I: BoDd Lein A of Cumulenes, Polyenynes, Cyanoethykw, Cyanobutrdieae, lad Cyanoimine Used in the Cnlcnlation molecule butatriene vinylacetylene 1.3-hexadien-5-yne 1,3,5-octatrien-7-yne 1,5-hexadien-3-yne diacetylene cyanoethylene cyanoimine cyanobutadiene
= ~&z>iu i
u
+ zztij(aTgju + HC) + z&fiipi-,,+ (ij)
i
CKj(fij - Zi)(fij - Zj) (8)
i>j
The operator a; (aiu)creates (annihilates) an electron in the p,-orbital of the ith carbon atom with spin a, q is the orbital energy or the Huckel a,and (ij)denotes summation over all bonds. Using this model Hamiltonian and the valence bond diagrams as the basis, the Hamiltonian matrix is set up by using standard procedures."J2 The resulting nonsymmetric matrix is solved for a few low-lying states by using the Rettrup algorithm." The exact dynamic first-order correction &(w) to the groundstate wavefunction (G) under the influence of a dynamic electric field E, cos or obeys the following equation:32
(H- EG + hio)#i(')(~) = -&IC)
(9)
where EG is the ground-state energy and ji is the dipole displacement operator given by Pi
= Fi - (GJriilG)
(10)
with where rip is the ith component of the position vector of the pth carbon atom. Since the VB basis is complete, it is possible to expand the correction vector q5 in terms of the VB basis. Substituting this expansion for 4, the expansion of the ground-state vector (G) transforms the eq 5 into a set of linear inhomogeneous equations, which are then solved by using the recent method of Ra~nasesha~~ to obtain #I). The PPP polarizability in terms of & I ) is then simply given by We can similarly compute the quantities related to the second-
r2
1.283 1.430 1.454 1.470 1.403 1.357 1.419 1.371 1.454
r3
r4
rs
r6
rl
1.209 1.342 1.431 1.208 1.337 1.437 1.329 1.441 1.215 1.200 1.169 1.169 1.342 1.431 1.164
order corrections to IC) that also satisfy an analogous inhomogeneous equation.
and
E$@
rl
1.318 1.342 1.340 1.337 1.337 1.199 1.334 1.282 1.339
(H- EG + h~2)4ij(~)(wl,w2) = -fi&j(l)(~l)
(12)
In terms of the second-order correction vector 4(2)ij,the dominant component of the THG coefficient, when the molecule is aligned along the x-axis, is simply written as ~
~
-
~ a) =~ (8)-1[(4~1!',(-30)lPx14~~(-2~,~)) ~ ( 3 ~ ~ w+ (4~~)(2w~)lPx14~')(-w)) + w -@I (13)
-
where w w indicates the terms generated by simply replacing w by -0. This method is exact in the chosen PPP model and the only assumption made in the entire computation is that the interaction of radiation with matter is dipole dominated. The largest calculation carried out by us is the computation of the frequency-dependent polarizability and the THG coefficients of hexapentaene with 10 r-orbitals, which spans a Hilbert space of 19404.
Results and Discussion Frequency-Dependent Polarizability and "€ICCoefficients of Cumuleaes and Polyenynes. The structures of the molecules investigated are shown in Figure 1 and their bond lengths in Table I. The bond angles at sp2and sp carbons are taken as 120° and 180°, respectively. In Tables I1 and I11 the dominant components of the static and frequency-dependent polarizability of the cumulenes and polyenynes are listed at three different frequencies. The dominant components of the static second hyperpolarizability and the THG coefficients are given in Tables IV and V. The static second hyperpolarizability cannot be calculated by the method described above, as it is not possible to solve for &2)(0). The static values of the polarizabilities are obtained from the finite field method" (using the same parametrization),but this technique cannot be used to obtain reliable values of the second hyperpolari~abilities.~~ The latter quantities are therefore found by expanding the THG coefficients in a Taylor series and eliminating the w2 term by computing the THG coefficient at two different frequencies. This is possible because of the fact that the energy denominators that occur in the expressions for the THG coeffi-
10162 The Journal of Physical Chemistry, Vol. 96, No. 25, 1992
Albert et al. TABLE IW Static Second HyperpoLrlPWty md THC coeffidcab (h 80) 8t Three Merent Frequaelea ho (ev) of Polyene6 md
system C=C=C
C=C==C==C
C=C-c=c
c--c--c=c=c c--c=c=c=C=C
c--c-c=c--c=C
ha 0.0 0.3 0.65 1.17 0.0 0.3 0.65 1.17 0.0 0.0 0.3 0.65 1.17 0.0 0.3 0.65 1.17
0.0
axx
axy
ayy
32.68 0.0 0.0 0.0 32.78 0.0 33.00 0.0 0.0 0.0 33.62 0.0 71.08 0.0 0.0 71.30 0.0 0.0 0.0 72.03 0.0 74.18 0.0 0.0 40.95 15.38 8.52 106.76 0.0 0.0 0.0 107.94 0.0 0.0 109.32 0.0 112.23 0.0 0.0 0.0 167.53 0.0 168.19 0.0 0.0 0.0 170.51 0.0 177.51 0.0 0.0 83.94 25.38 13.32
" , a
-a
system
38.41' C=c+
75.21' C=C=C=C
72.10: 73.39'
c=c--c=C C=C=C--C=C
186.24: 174.29'
'The static polarizability of the polyenes have been taken from ref 34. 'Dominant component of the static polarizability obtained from an ab initio calculation using the 3-21G b a ~ i s . ~ ~ CDominant .~' component of the static polarizability obtained from ab initio calculation using the STO-3G
C=C=C=C=C=C
c=C--c=C-c=c
0.0 0.3 0.65 1.17 0.0 0.3 0.65 1.17 0.0 0.3 0.0 0.3 0.65 1.17 0.0 0.3 0.65 1.17 0.0
Yuxx
Yuyy
0.056 0.058 0.065 0.091 0.657 0.694 0.828 1.538 0.476 0.559 0.818 0.859 1.010 1.715 3.255 3.566 4.681 284.2 3.009
0.0 0.0
Yywy
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.033 0.007 0.041 0.009 0.0 0.0 0.0 0.0
0.0 0.0
0.0 0.0 0.0 0.0 0.116
0.0 0.0 0.0 0.0 0.0 0.0 0.018
b
Yuu
-
-2.609
0.906
-14.56
4.976
'The THG coefficients of polyenea have been taken from ref 21. bDominant component of the second hypcrpolarizability obtained from an ab initio calculation using the 3-21G basis.36
TABLE IIk Static md Frequency-DependentPolulubUty (in au) at Three Merent Freqwncim ho (eV) of Pdyenyae~ system
c=c-c==c C4-C-C
C = C - c = C ~
c=C-c==c-c=c
ho 0.0 0.3 1.17 0.0 0.3 0.65 1.17 0.0 0.3 0.65 1.17 0.0 0.3 0.65 1.17
a, 50.83 51.23 52.08 40.28 40.35 40.68 41.69 82.15 82.44 83.42 86.33 84.68 85.57 86.60 89.68
ax"
0.0 0.0 0.0 -2.93 -2.93 -2.93 -2.92 4.06 4.08 4.18 4.47 -2.08 -2.09 -2.10 -2.14
a", ad* 0.0 69.17," 50.68' 0.0 0.0 7.62 44.65b 7.65 7.68 7.77 11.77 11.79 11.85 12.02 9.78 114.73," 85.3ob 9.97 10.01 10.13
*Dominant component of the static polarizability obtained from an ab initio calculation using the 3-21G 'Dominant component of the static polarizability obtained from ab initio calculation using the STO-3G b a s i ~ . ~ * * ~ ~
cients show that all the THG coefficients are even functions of o. The resultant expression for the static second hyperpolarizability is23 T x x x x ~ ~ ~=o [~Woz 2~r ( W d
- ~ l Z T ( ~ z ) l (-~%*) zZ (14)
It can seen from Tables 11-V that both the polarizability and THG coefficients of the cumulenes are much larger than those of the polyenynes at all chain lengths and at all the frequencies. While there are no experimental reports on the frequency-dependent polarizability and THG coefficients of these compounds to compare with, both ab initio and INDO calculations (Prasad et a1.36J7and Delhalle et a1.38.39)of the static polarizability and second hyperpolarizability of some of the compounds have been reported in the literature. These values are given in the table for comparison. It can be seen from the Tables I1 and I11 that while the polarizability values are in reasonably good agreement, with those reported by Delhalle et al., they are consistently smaller than the values reported by Prasad et al. However, the second hyperPdarizability values show greater differences as compared with those of Prasad et al. The ab initio and INDO polarizabilities are expected to be larger since they also include the H atoms in the calculation, thereby including the polarization due to the C-H bond. Moreover, it is also known that electron correlations reduce the polarizability and hyperpolarizabilityof conjugated
system C=C-C=
C=c-C=C
c==c-c=c-C=c
ho 0.0
0.3 0.65 1.17 0.0 0.3 0.65 1.17 0.0 0.3
c=C-c=c-G=€
0.65 1.17 0.0 0.3 0.65 1.17
Yxxu
Yuyy
0.205 0.21 1 0.236 0.357 0.326 0.339 0.386 0.608 2.299 2.429 2.912 5.648 2.093 2.218 2.680 5.679
0.0 0.0 0.0 0.0 0.023 0.024 0.028 0.049 0.080 0.088 0.1 14 0.268 0.106 0.114 0.145 0.349
rsb
Yyyyy
Yuxx
0.0
0.823
0.0
0.0 0.0 0.0
0.0 0.0 0.0 0.003 0.003 0.004 0.006 0.004 0.005 0.005 0.008
1.754b
'Dominant component of the second hyperpolarizability obtained from an ab initio calculation using the 3-21G basis.)6 'Dominant component of the second hyperpolarizability obtained from an INDO calculation." It can be sem from the calculations of Prasad et al. that the second hy-perpolarizability values obtained from ab initio calculations are markedly different from those obtained from INDO calculations, which has been explained as due to the deficiency of the minimal basis set used in the calculation. However, as mentioned earlier, while the finite field method gives better values of the static polarizability the second hyperpolarizability values are not numerically stable. It is also interesting to note that while the polarizabilities of polyenynes and cumulenes obtained from ab initio are in good agreement with the polarizabilities obtained from our calculations, they are, however, about 40% larger in the case of the polyenes. This is to be expected as the contribution of the u-electrons to the polarizability in the case of the polyenynes and the cumulenes is expected to be lower than those to the polyenes, which has been recently found to be only 30%.40 Thus our calculation of the static and frequencydependent polarizability and the THG coefficients being exact in the chosen PPP model should prove to be more reliable. To help elucidate the reasons for the relatively large polarizabilities and THG coefficients of the Cumulenes compared with the polyenynes and polyenes, the optical gaps of all three classes of compounds are plotted in Figure 2 as a function of the reciprocal of the number of atoms in the chain. The polyenynes for which
The Journal of Physical Chemistry, Vol. 96, No. 25, 1992 10163
Properties of Cumulenes and Polyenynes
TABLE M: Magdtade of tbe Tnaritioa Dipole Moment (In debyer)&to,tk itb Strk, wbicb Ill the Optidly Allowed Excited State far the cllrrmkacs,Pdyeaes,rad Polyayncr system
ith state
Po-,
5.316 4.295 5.683 3.241 0.286 7.280 1.692 3.604
Y
I
0.00
0.05
0.10
0.15
0.20
Y.
0.25
0.30
0.35
I
Figure 2. Optical gap (in eV) of the cumulenes (squares), polyenes (cross), and polyenyna (asterix) as a function of the reciprocal of the number of atom (W).
system C==C--C--C
C=CbC=C
m
cyanoimine
charge density GS Es 1 .W24 1.1413 0.9976 1.2579 1 .m 0.6007 1.oooO 0.6007 0.9976 1.2579 1 .OO24 1.1413 1 .oO04 1.0260 1 .m 1.0176 0.9999 1.1222 0.9999 0.8354 1 .oooO 0.8236 0.9999 1.1748 0.9502 0.9160 1.0286 0.9908 0.8360 0.6994 0.8518 1.1330 1.1626 1.3298 1.1754 0.9314 0.7396 0.9094 1.2474 1.2924 0.8310 1.2020 0.8372 0.3292 1.1626 0.6770 1.1754 1.5898
the optical g a p are plotted are vinylacetylene (11), Whexa-
dien-5-yne(In),and 1,3,5-0ctatrien-7-yne (IV). The extrapolated values of the optical g a p of the cumulenes, polyenynes, and polyenes are 0.75,4.37,and 2.86 eV, mpectively. The cumulenes and polyenes show a similar, marked decrease of the optical gap with chain length, while the polyenyne gap remains almost constant. This trend cannot be attributed merely to the smaller value of bond alternation in cumulenes (2.7%) compared to that in polyenynes (-10%) or in polyenes (7%). This is because the simple relation between the bond alternation 6 and the optical gap, E, = 4pp, in the infinite limit becomes inappropriate owing to the strong Correlations and the complexity in these systems. The transition corresponding to the low optical gap in cumulenes is likely to be due to the transfer of an electron from the *-system f d by the fi-orbitalsto the *-system formed by the pz-orbitals (Table VI). The smaller transition dipolesof cumulcna ampared to those of polyenes for the optically allowed transition lends credence to this conjecture (Table VII). Table VI1 also shows the presence of midgap states in both cumulenes and polyenynes as in the case of polyenes. The insensitivity of the gap in polyenynes with smalla number of carbon atoms to the chain length may be attributed to the localkition of the transition on the triple bond at the end of the chain. Support for this comes from the
a
a, 42.92 74.18 41.69 52.08
ayy
Yuu
8.84 0.0 7.77 0.0
1.009 1.539 0.608 0.357
Y*ur'
Yyyyy
0.016 0.0 75.21 -2.609 0.001 44.64 0.0 69.17," 50.68'
"Dominant components of the static polarizability and second hyperpolarizability obtained from an ab initio c a l ~ u l a t i o n . ~Dominant ~ components of the static polarizability obtained from ab initio calculation using the STO-3G basis.39
'
charge density calculation presented in Table VI. We note that the charge densities of the orbitals participating in the triple bond are different in the ground and excited state while those of the other orbitals remain roughly the same in both the states. This, however, may not be true of longer chains where the lower excitation energy of the polyene subsystem could become signifcant. In Table VIII, we present the polarizability and THG coefficients of butadiene, butatriene (I), vinylacetylene (11), and diacetylene (IX)to examine the trend shown by the polarizability and THG coefficients by the three systems, namely, polyenes, polyenynes, and cumulenes. We find that the polarizability of butatriene is greater than that of diacetylene, which is in turn greater than that of butadiene and vinylacetylene. For the THG coefficients, butatriene is still largest but diacetylene is smaller than vinylacetylene and butadiene. While the calculations of Bodart et al. also show that the polarizabilities of diacetylene are larger than those of butadiene, the calculation of Prasad et al. show an opposite trend. The lower optical gaps of diacetylene (4.515 eV) compared to butadiene (5.40 eV) seem to be a reason for the larger polarizability of diacetylene. It is, however, not clear why it does not also favor the THG coefficient. It is indeed misleading to correlate the optical gaps directly to these coefficients, since in cumulenes the low optical gaps are also associated with a very small transition dipole moment. However, from the results of the calculation on larger systems, it can be concluded that among the three different types of conjugated systems, for a given number of carbon atoms, cumulenes have the largest THG coefficients and polyenynes the smallest with polyenes lying in between the two. The existence of two orthogonal conjugated chains (T,, and rz)in cumulenes appears to be a possible reason for their larger NLO coefficient. Figure 3 shows the frequency dependence of the polarizability of the 1.5-hexadien-fyne (V) and diacetylene (IX);Figure 4 shows the frequency dependence of the THG coefficients of these compounds. It can be seen from the plot that the polarizability shows a smooth variation as a function of the excitation frequency since all the frequencies are far from the one photon resonance. A larger dispersion is found in the case of 1,5-hexadien-3-yne where the onephoton excitation energy at ho = 2.0 eV is closer to the highat field frequency. The dispersion behavior of the THG coefficients dearly show the twct and the thrcaphoton resonances in all three compounds. apsaacllec of the PohripMaity d T H G c o e m ~ of Cumubmeu. It is well-known that both the polarizability and THG coefficients exhibit a power law dependence on the length
10164 The Journal of Physical Chemistry, Vol. 96, No. 25, 1992
. i
75
a so
Albert et al.
1 AI-
1
0.9
1.0
1.1
1.2
1.3
1.t
In
0 1
i
0.00
0.25
0.75
0.50
1.00
1.25
1.75
1.50
2.00
1.5
1.6
1.7
1.8
1.9
L,
Figure 6. log-log plot of yuu vs L, for cumulenes at an excitation frequency of 0.65 eV. L, is in A and yxxxxin au.
Ilm I e.V.
Figwe 3. Dominant component of the polarizability (in au) as a function of the excitation frequency (in eV) for 1,5-hexadien-3-yne(squares) and diacetylene (cross). system cyanoethylene +0000,
30000
r
800
cyanoimine
4
.2 < I
cyanobutadiene
20000
1 0000
4
O +
0 25
0 SO
0 75
I 00
1 25
I
I 75
50
2 00
bs /e V
Figure 4. Plot of the dominant component of the THG coefficient (in au) and the excitation frequency (in eV) for 1,5-hexadien-3-yne (cross) and diacetylene (squares). The axis on the left corresponds to 1,s-hexadien-3-yne and the one on the right to diacctylenes.
3.2 0.9
Qxx
38.58 38.88 39.20 38.20 38.51 39.42 80.15 8 1.08 83.85
a, 7.38 7.41 7.49 6.87 6.90 6.97 11.59 11.65 11.82
Yuu
Yyyyy
277.44 314.65 476.61 147.74 172.15 293.34 2239.81 2681.19 5073.16
0.28 0.33 0.48 -0.93 -0.97 -1.16 3.15 3.64 5.86
Inflwm of the Hetermtom on the Polarizability and THG Coefficients of Polyenynes. The dominant components of the
I m 0 00
hw 0.3 0.65 1.17 0.3 0.65 1.17 0.3 0.65 1.17
1.0
1.1
1.2
1.3
I.+
In
1.5
1.6
1.7
1 8
1.9
L
Figure 5. Plot of In uu versus In Lx with an in au and Lx in A for the cumulenes at an excitation frequency of 0.65 eV.
of the molecule. The exponents predicted from free electron calculations are 3 and 5 for polarizability and the THG coefficients. In Figures 5 and 6 the length dependence of the polarizability and the THG coefficients of cumulenes at an excitation frequency of 0.65 eV are shown. Although the polarizability shows a power law dependence on the lengtb of the molecule as expected, the THG coefficients show deviations from liiear dependence in the l w o g plot. The latter could be because the THG coefficients are more strongly lengtb dependent, so that the f i i t e size effects are magnified. From the THG coemcients of the two largest systems we have studied, pentatetraene and hexapentaene, the exponent is found to be 4.4, which is slightly larger than the exponents of 3.8 obtained in the case of polyenes. The exponent for the polarizability at 1.8 is rather smaller than the value of 2.1 obtained for the polyenes.
polarizability and THG coefficients of vinylacetylene (11), cyanoethylene (VI), and cyanoimine (MI)at threedifferent excitation frequenciesare shown in Table IX. It can be seen from the table that the presence of a heteroatom either at the ends of the chain or at the ends and in the middle reduces the polarizability and the THG coefficients of vinylacetylene, the effect being more pronounced in the case of the THG coefficients. This is contrary to our earlier studies on cyanine where it was found that the heteroatom at the ends of the chain aids polarization and leads to an increase in the polarizability and the THG coefficients wlule substitution at the middle of the chain raiuca both the coemcients. In order to understand the reason for this behavior we have calculated the charge densities of the three systems in the ground and excited states. The charge density results (Table VI) show that the charge-transfer patterns in the case of polyenynes are quite different from those in the polyenes or cyanine dyes. While charge transfer in the case of polyenes and cyanine dyes, occurs from a p-orbital on one center to a porbital on a different center, the charge transfer in the case of the polyynic systems occurs between two gorbitals situated on the same center. This leads to a reduction in the polarization and hence a reduction in polarizability and the THG coefficients in polyynic systems. This is further confirmed by the fact that both the polarizability and the THG coefficients of I1 are lower than those of butadiene. The polarizsbility calculation of Fowler and Diercksm using a coupled Hartr#-Fodr method also shows that systems have a larger polarizability than the *N systems." In order to show that this is true of larger systems also, we have computed the polarizability and THG coefficients of cyanobutadiene. The polarizability and THG coefficients of VI11 are lower than the corresponding coefficients of 111, confirming that the above interpretation holds good in the case of longer chains.
collelmioll The present study of the polarizabilities and THG coefficients of cumulenes and polyenynes is based on a complete *-electron CI calculation within the PPP parametrization. Other approaches (Prasad and Delhalle) have been based on all valence electron bases with ab initio or more elaborate semiempirical techniques
J. Phys. Chem. 1992, 96, 10165-10176 but with no configuration interaction and therefore they neglect electron correlation effects. A comparison with the results from these studies has been given in the previous section. The present calculations predict that the cumulenes should have polarizabilities and THG coefficients substantially larger than those of the polyenes and polyenynes. It is found that, in contrast to the behavior of the polyenes, the charge transfer in the polyynic systems is between the orthogonal *-orbitals on the same carbon atom. This leads to a reduction in the polarization and hence to a reduction in the polarizability and THG coefficients. The coefficients are further reduced in the polyynic systems when one or more carbon atoms are replaced by heteroatoms.
R W NO. I, 2873-50-9;11,689-97-4;111, 10420-90-3;IV, 2002357-8;V, 821-08-9;VI, 107-13-1;VII, 43730-26-3;VIII, 1615-70-9; IX, 460-12-8. Refereoces and Notes (1) Williams, D. J., Ed. Nonlinear Optical Properties of Organic and Polymeric Materials; ACS Symposium Series 233;American Chemical Society: Washington, DC, 1983. (2) Chemla, D. S.,Zyas, J., Eds. Nonlinear Optical Properties of Organic Molecules and Crystals; Academic Press: Orlando, 1987. (3) Prasad, P. N., ulrich, D. R., Eds. Nonlinear Optical and Electroactiue Polymers; Plenum Press: New Yorlc, 1988. (4) Messiar, J., Kajzar, F., Prasad, P. N., Eds. Organic Molecules for Nonlinear Optics and Photonics; NATO AS1 Series; Kluwer Academic Publishers: London, 1990; Vol. 194. (5) Hann, R. A., Bloor, D., Eds. Organic Materials for Nonlinear Optics; The Royal Soc. Chem.: London, 1988. (6) Nicoud, J. F.; Tweig, R. J. In Nonlinear Optical Properties of Organic Molecules and Crystals; Chemla, D. S.,Zyss, J., Us.; Academic Press: London, 1987;Vol. 1, p 227. (7)Cheng, L.-T. In Organic Molecules for Nonlinear Optics and Photonics; Messier, J., Kajzar, F., Prasad, P. N., Eds.; AS1 Series; Kluwer Academic Publishers: London, 1990; p 121. (8) Matsen, F. A. Ace. Chem. Res. 1978, 11, 387. (9) Hudsen, E. S.;Kohler, E. E.; Schulten, K. Excited States 1982, 6, 1. (10)Soos, Z.G.;Ramasesha, S.Phys. Rev. Lett. 1983, 51, 2374. (11) Ramasesha, S.;Soos, Z. G. J. Chem. Phys. 1984,80, 3278.
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1704. (16) Ramamha, S.;Sooe, Z. G. Chem. Phys. 1984,91, 35. (17) Ramasesha, S.; Albert, I. D. L.; Sinha, B. E. Mol. Phys. 1991, 72, 537. (18) Pierce, E. J. Chem. Phys. 1989, 91, 791. Beratan, D.N. J. Phys. Chem. 1989, 93, 3915. (19) Oudar, J. L. J. Chem. Phys. 1977,67,446. (20)Oudar, J. L.;Chemla, D. S. Opt. Commun. 1975, 13, 1651. (21) Morley, J. 0.; Pavlidts, P.; Pugh,D. Int.J. Quanrum Chem., in press. (22) Morley, J. 0.; Pavlides, P.; Pugh, D. J. Chem. Soc., Faraday Trans. 2 1989,85, 1789. (23)Soos,2. G.; Ramasesha, S. J. Chem. Phys. 1989,90, 1067. (24)Ramasesha, S.; Soos, 2. G . Chem. Phys. Lett. 1988, 153, 171. (25)Albert, I. D. L.; Ramasesha, S.;Das, P. K. Phys. Rev. 1991,843, 7013. (26) Albert, I. D. L.; Das, P. K.; Ramasesha, S. J. Opt. Soc. Am. E, submitted for publication. (27)Ramasesha, S.;Albert, I. D. L. Phys. Rev. 1990, 842, 8587. (28)Albert, I. D. L.; Ramasesha, S.Chem. Phys. Lett., in press. (29) Ohno, K. Theor. Chim. Acta 1964, 2,4550. (30)Pople, J. A.; Bcveridge, D. L. Approximate Molecular Orbital The ory; McGraw Hill: New York, 1970. (31) Rettrup, S.J. Compur. Phys. 1982, 45, 100. (32) Langhoff, P. W.; Epstien, S. T.; Karplus, M. R N . Mod.Phys. 1972, 44, 602. (33) Ramasesha, S.J. Compur. Chem. 1990,11,545. (34) Ramamha, S.; Albert, I. D. L. Chem. Phys. Lett. 1989, 154, 501. (35) Albert, I. D. L.; Ramasesha, S.Mol. Cryst. Liq. Cryst. 1989, 168, 95. (36)Chopra, P.; Carlacci, L.; King, H. F.; Prasad, P. N . J. Phys. Chem. 1989, 93, 7120. (37) Karna, S.P.; Laskowski, Z.; Talapatra, G. B.; Prasad, P. N. J . Phys. Chem. 1991.95. 6508. (38)Deldaile, J.; Bodart, V. P.; Dory, M.; Andre, J. M.; Zyss, J. Int. J . Quantum Chem. 1986,19, 313. (39) Bodart, V. P.; Delhalle, J.; Andre, J. M.; Zyss, J. Can. J. Chem. 1985, 63. 1631. (40) Albert, I. D. L.; Ramasesha, S.Chem. Phys. Lett. 1991,182, 351. (41) Fowler, P. W.; Diercksen, G. H. F. Chem. Phys. Lett. 1990,167,105.
Infrared Spectra of [nlstaffanes
-
Murthy S. Gudipati," Steven J. Hamrock, V. Balaji, and Josef M i ~ h l * * ' ~
Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309-021 5 (Received: June 12, 1992; In Final Form: September 9, 1992)
The IR spectra of the first five oligomers of [ l.l.l]propellane ([nlstaffanes, n = 1-S), and some of their bridgeheaddeuteriated derivatives, have been measured in argon matrix isolation. IR transition moment directions were obtained using stretched polyethylene as solvent. Assignments were based on a simple model of interacting subunits and on comparison with 3-21G HF calculations. IR peaks particularly suitable for use in the determination of orientation of the staffane moieties in supramolecular assemblies have been identified.
Introduction (n]Staffanes2are rigid-rod molecules acctssible by oligomerization3 of [l.l.l]propellane.4 The structures of the first five members of the homologous series (1-5) are shown. The first member of the series is bicyclo[1.1Jlpentane, which has been known for a long timea5 Terminally fimctionalized [nlstaffanes promise to be useful not only as rigid spacers, say, in studies of charge transfer6 and spin density propagation,' but also as novel constituents of various types of supramolecular assemblies.* In the latter applications, the ability to determine supramolecular order is essential. Since an understanding of the anisotropy of IR absorption due to the individual constituentscan be very helpful in this regard: we have decided to record and analyze the IR spectra of the first five members of the [nlstaffane series. In order to improve the resolution of the individual spectral peaks of these relatively large but thermally stable molecules, we have measured the spectra in
1
2
3 4 5
-c+Q+c+
argon matrix isolation. In order to help with the assignments, we have measured the IR polarization directions using stretched
0022-365419212096- 10165$03.00/0 Q 1992 American Chemical Society
