4044
J . Phys. Chem. 1993,97, 4044-4049
Comparative Theoretical Evaluation of Hyperpolarizabilities of Push-pull Polyenes and Polyynes. The Important Role of Configuration Mixing in the Excited States Monika Jain and Jayaraman Chandrasekhar' Department of Organic Chemistry, Indian Institute of Science, Bangalore 560 012, India Received: September 30, 1992
The potential use of push-pull polyenes and polyynes for second harmonic generation has been compared on the basis of hyperpolarizabilities computed for a large number of model systems of the type D(HC=CH),A and D ( m C ) , A (n = 2-8, and D = NH2, Br, or I; A = NO2 or CN). Geometries optimized at the AM1 level were used in a CI calculation including single and pair excitations involving up to 193 configurations. The sum-over-states expression was used to obtain the j3 values. While the trends in the computed j3 are the same for the two series of compounds, the values are generally smaller and increase less rapidly with increasing n for the polyynes. The results are interpreted in terms of the nature of the lowest excited states which contribute to j3 in these systems. Mixing of in-plane and out-of-plane u-u* excited configurations reduces the contribution of the lower excited states to j3. Push-pull polyynes with higher j3 values than the corresponding polyenes can be designed by the combined use of donor and acceptor groups such as I (or Br) and C N which can interact with both sets of orthogonal T MOs.
Introduction The design of organic nonlinear optical materials is of considerable current interest.' A fairly successful approach has been to concentrate on extended conjugated systems with donor and acceptor groups on opposite ends of the molecule. For example, push-pull substituted polyenes, polyphenylenes, stilbenes, etc., have large hyperpolarizabilities. When additional criteria, such as noncentrosymmetriccrystal packing and phase matching, are also met, these compounds are found to be quite efficient for second harmonic generation. Thus, push-pull polyenes with varying chain lengths have SHG efficiency several times that of urea.2-8 How about the possibility of using extended triple-bonded systems for designing molecules with large hyperpolarizabilities? From a simple bonding point of view, the presence of two sets of conjugating u units should prove to be effective for long-range substituent interactions. Recently a number of polyynes terminated by push-pull substituted phenyl groups have been investigated for SHG applications.*~9These derivatives have indeed been found to have significant j3. However, the values are not as large as in polyene systems with the same chain length. For example, push-pull substituted diphenylacetylenes have consistently smallerj3 than the corresponding stilbenes. Other extended polyenes have also been shown to exhibit diminished SHG when a triple bond is introduced in the chain.4 The relative inefficiency of diphenylpolyynesfor SHG has been interpreted on the basis of structural and spectroscopic studies. Electronic spectra reveal the presence of charge-transfer transitions,I0whileX-raystructuresindicatethepresenceofquinonoid distortions of the phenyl rings." These factors are expected to lead to significant j3. However, the acetylenic units show little bond length distortion. It has therefore been argued that the charge transfer is not highly delocalized but restricted to the donor and acceptor groups in the phenyl units. It has also been proposed that the interaction between x units formed by sp2and sp hybridized carbon atoms is poor and, hence, the polarization of the triple bond by push-pull substituents is rather small.8 While the above interpretation is reasonable, the intervening phenyl rings introduce some ambiguities. As is well established, the orientation of phenyl groups strongly influences the hyperpolarizability of a molecule.8J2 Although the crystal structures
reveal relatively parallel phenyl units, free rotation in the solution phase would affect the measured 8. It would be desirable to evaluatethe magnitudeof j3 in polyynes directly attached to strong donor and acceptor groups. Several such polyynes have indeed been synthesizedin recent years.13 We have therefore theoretically evaluated the j3 values of some of these derivatives, as well as those of several additionalmodel systems. The results are directly compared with those obtained for related polyenes. The computational study provides valuable insights into the nature of electronic excited states which are of fundamental importance in determining the trends in the j3 values in polyenes and polyynes. Useful generalizations for the design of polyynes with higher j3 are also obtained.
Computational Details Two approaches are commonly employed for the calculation of molecular hyperpolarizabilities. In the finite field method,1bi8 the electronicenergy and the dipole moment of the molecule are calculated in the presence of a static electric field. Higher order polarizabilities are then obtained by a power series expansion. The alternative sum-over-statesa p p r ~ a c h l involves ~ - ~ ~ the use of a perturbation expansion in terms of the excited states of the molecule. Both methods have been used extensively for the calculationof 8 in conjunction with semiempirical (PPP, CNDO/ S, INDO, MNDO, AM1, etc.) as well as ab initio molecular orbital methods. Although the general trends in the results from the two approaches are similar, we prefer to use the SOS methodology in the present work. The perturbation expansion leads to greater insights into the factors contributing to j3, especially in terms of the electronic excited states, which are amenable to independent experimental evaluation using spectroscopic techniques.22 First, the geometry of each molecule under investigation was fully optimized using the AM 1method.24 Theoptimizedstructure was used in a CI calculation including single and pair excitations involving NMOSspanning the frontier orbitals (N = 8-1 8). Care was taken to ensure that degenerate sets of MOs were fully included in each case. Wave functions and energies of up to 129 of the lowest singlet excited states were used in a sum-over-states perturbation expression (eq 1) to obtain the molecular hyper-
0022-3654/93/2091-4044$04.0~/00 1993 American Chemical Society
Push-Pull Polyenes and Polyynes
The Journal of Physical Chemistry, Vol. 97, No. 16, 1993 4045
TABLE I: Calculated B,, for Push-Pull Substituted Polyenes (la-d) and Polyynes (2a-d) for Various Chain Lengthss n
In the above equation the subscripts i, j , and k are the Cartesian components, r a b corresponds to the dipole integral involving the states a and b, and the E values represent the electronic energies. The summation over P generates six terms obtained by permutationofthepairs(i,-2w), (j,w),and(k,w). Allofthecalculated hyperpolarizabilities are at photon energy of hw = 1.17 eV. The diagonal terms were so chosen that they correspond to the difference between the excited- and ground-state dipole moments; hence, the indices n and n’ may be restricted to run over the excited states only. Thus, r,, values are given by
la 2a lb 2b IC 2c Id 2d
2
3
4
5
6
7
8
27 29 13 15 15 28 13 23
126 78 71 52 33 53 31 51
359 159 211 114 70 92 66 94
734 304 470 226 128 151 135 161
1269 503 848 397 221 250 238 264
2015 783 1387 610 355 352 386 385
2861 1083 2074 861 552 471 600 526
All values are in units of 1.17 eV.
-Ap/e = r,, = (nlrln) - (0140) (2) Following the usual convention, the average quantity, BVe,, was computed using five,
=
(CB~)”*
1000
(3)
cm5 esu-I at an excitation energy of
1
i
j#i
The use of the AM1 procedure enables an all-valence description. The contributions from high-energy u and low-energy u* orbitals are taken into account. The method is also known to be appropriate for adequately describing conjugation effects. While doubly excited configurations do not directly contribute to the dipole integrals in eq 1, the inclusion of pair excitations in the CI procedure leads to a more reliable set of state energies and also to a balanced weight of the various configurations in the total wave functions. As a result of these factors, the above computational procedure yields reasonable /3 values for a wide variety of systems for which the experimental data are available.25 Calculations were carried out on a series of push-pull substituted polyenes, D(HC=CH),A (l),and the corresponding polyynes, D(C=C),A (2), with D = NHz and A = NO2 and C N
2
L -
for n ranging from 2 to 8. Additional calculations were carried out on polyynes and polyenes with D = I and Br and A = CN. To evaluate the methodology for predicting the energies and intensities of electronic transitions, a number of experimentally examined acetylenic derivatives (3 and 4) were also studied.
Results and Discussion 1. Hyperpolarizabilitiesof Push-pull Polyenes and Polyynes. The computed /3 values for the various push-pull substituted
n-+
6
a
Figure 1. Computed&,vschain length for push-pull substitutedpolyenes (la and IC) and polyynes (2a and 2c).
TABLE 11: Computed Transition Energies (Nanometers) Change in Dipole Moment (Debyes), Transition Moments (Atomic Units), and CI Coeffiisients of the Excited Singlet Configurations Obtained for Push-Pull Polyenes l a and l b n
x
All
Irl
C I coefficients P-R*
la
2 3 4 5 6 7 8
318 353 376 390 402 413 421
8.0 15.4 24.1 33.6 41.7 49.4 56.2
1.41 1.82 2.23 2.54 2.81 3.04 3.25
0.670 0.673 0.647 0.601 0.539 0.477 0.419
lb
2 3 4 5 6 7 8
303 336 361 381 394 407 417
4.8 10.0 16.6 23.7 30.4 37.0 42.9
1.37 1.85 2.26 2.58 2.86 3.09 3.30
0.643 0.669 0.657 0.627 0.586 0.544 0.501
A“
oW n+~*cocH3
L
polyenes (la-d) and polyynes (2a-d) with different numbers of double and triple bonds (n = 2-8) are given in Table I. All values are given in the customary units ( l W cm5 esu-I). The variations in the computed /3 for the polyenes follow the expected trends.2-8 Thus, 3/ increases rapidly with increasing chain length. For n = 2,3, and 8, the /3 values of the nitro,amino derivative, la, are 27, 126, and 2861, respectively. The increase in /3 with respect to the number of double bonds is not a linear one (Figure 1). The values follow a power law (j3 a nx), with an exponent of 2.87. These trends and numerical values compare very well with the reported PPP23 and CNDO/S*I studies on similar push-pull trans-polyenes having N,N-dimethylamino and nitro substituents on opposite ends of the molecule. The effect of the acceptor strength on /3 in polyenes is revealed by the data for the cyano derivatives, lb. The computed /3 values are uniformly smaller when the nitro group is replaced by a cyano
Jain and Chandrasekhar
4046 The Journal of Physical Chemistry, Vol. 97, No. 16, 1993
group. The decrease is about a factor of about 1.5-2 (Table I). For example, j3 is calculated to be 126 for the nitro compound l a (n = 3) but is only 71 for the corresponding cyano derivative (lb). Similarly, the @valuesare 2861 and 2074 for the nitro and cyano compounds with n = 8. These trends are on the expected line^,^^^,^ since the cyano group is a weaker ?r-acceptor than the nitro unit. Experimentally,a series of polyenes with the benzodithia group as donor and different acceptor groups (5) have been found to
TABLE III: Computed Transition Energies (Nanometers), Change in Dipole Moment (Debyes), Transition Moments (Atomic Units), and CI Coefficients of the Excited Singlet Configurations Obtained for Push-pull Polyynes 2a and 2b CI coefficient
za
n
x
Au
Id
TATn*
2
304 209 3 29 224 345 242 354 255 364 272 370 283 368 290
14.4 2.4 20.4 4.9 26.0 14.0 33.3 23.3 38.7 30.6 45.6 39.0 52.1 46.5
0.65 1.28 0.65 2.05 0.50 2.78 0.53 3.24 0.37 3.66 0.43 3.94 0.45 4.24
0.559 0.338 0.513 0.355 0.462 0.396 0.424 0.385 0.367 0.339 0.330 0.295 0.297 0.264
-0,372 0.367 -0.392 0.444 -0.412 0.491 -0.408 0.519 -0.407 0.475 -0.391 0.470 -0.374 0.458
310 200 334 22 1 353 242 362 259 373 275 375 286 375 295
8.0 3.8 12.5 7.8 17.0 12.7 22.4 17.7 27.4 22.3 32.8 27.8 37.8 33.5
0.32 1.56 0.35 2.42 0.23 3.04 0.25 3.47 0.22 3.78 0.19 4.08 0.13 4.37
0.530 0.369 0.514 0.427 0.477 0.428 0.452 0.410 0.413 0.367 0.384 0.345 0.354 0.326
-0,425 0.387 -0.426 0.468 -0,435 0.465 -0.427 0.466 -0.417 0.444 -0,407 0.43 1 -0.398 0.4 17
3 4 5 6
A = Acceptor
5
7 8 D = Donor
A = Acceptor,
2b
2 3
6 -
display efficient optical second harmonic generation both in solution2 and in the solid state, provided they crystallized in a noncentrosymmetric space group.2 Another set of push-pull polyenes (6) has also been found to have high &values (EFISH) in DMSO solutions.5 This study also showed that j3 increases with increasing number of double bonds as well as the strength of the acceptor group. Push-pull substituted polyynes 2a and 2b are also computed to have significant @ values, especially when n is large (Table I). For the amino,nitro combination, the computed @ ranges from 29 ( n = 2) to 1083 (n = 8). However, the variation of @ with increasingn is smaller than in the correspondingpolyenes (Figure 1). For example, the computed value for 2a with n = 2 is close to that obtained for the corresponding diene. But the j3 value for n = 8 is nearly a third of that calculated for the polyene. The same trend is obtained for the amino,cyano combination of substituents. Although conjugated triple bonds are computed to lead to a large j3, extended conjugated does not seem to be as effective as in polyenes. Electronic polarization of triple bonds can perhaps be made more effective if both sets of orthogonal ?r MOs of triple-bonded systems are involved in substituent perturbations. The cylindrically symmetric molecules (2c and 2d) obtained with a halogen (I or Br) and a cyano substituent arecomputed to have substantial hyperpolarizabilities(Table I). These compounds show the usual increase in j3 with increasing n. More interestingly, the triplebonded series is found to have larger j3 values than the corresponding polyenes for n = 2 - 6 (Figure 1). Calculations on the series of bromo compounds with the cyano group as the ?r electron acceptor show similar trends. Up to n = 6, the triplebonded systems have larger 0 values. The present calculations confirm that push-pull substituted polyenes are in general superior to the corresponding polyynes for the design of moleculeswith the high @. However, it is possible to have polyyneswith large hyperpolarizability. With the correct combination of donor and acceptor groups and an optimum chain length, triple-bonded systems can indeed be made more effective for SHG applications. 2. Electronic Origin of the Variations in 8 for Polyenes and Polyynes. The perturbation expression for j3 involves energy differences as well as dipole integrals between the ground and several of the lower singlet excited states. The presence of lowenergy states (small E, - EO)which also have large transition moment integrals (large ro,) leads to a significant 8. The difference in the dipole moments of the ground and the lowest excited state (Ap) also contributes to the magnitude of j3. These
4 5 6 7 8
*.--?r,*
TABLE I V Computed Transition Energies (Nanometers), Change in Dipole Moment (Debyes), and Transition Moments (Atomic Units) Obtained for the 1od0,Cyaw Substituted Polyenes (IC) and Pobynes (2c) n x Afl Id IC
2 3 4 5 6 7 8
266 299 330 354 373 388 402
7.9 7.5 7.6 9.4 10.9 12.7 14.5
1.43 1.85 2.11 2.46 2.75 2.99 3.21
2c
2 3 4 5 6 7 8
197 218 237 253 270 28 1 289
9.3 11.3 13.0 14.7 17.1 19.3 21.4
2.1 1 2.66 3.11 3.53 3.92 4.19 4.45
data obtained with the AMl/CI procedure are given for representative examples (la and lb, Table 11; 2a and 2b, Table 111; ICand 2c; Table IV). The information provided includes the transition energies (in nanometers), change in dipole moment following excitation, and the dipole integral rO, associated with the transition. The last parameter is directly related to the oscillator strength. The computed variations in B for the polyenes are readily understood in terms of the data in Table 11. Two factors are found to contribute to the large increase in B with increasing chain length in la. As n increases, the donor and acceptor groups are separated by a larger distance (about 2.5 A per double bond). The dipole moment change on excitation shows a corresponding increase, about 8 D per C=C unit in l a (Table 11). Further, the energy difference between the HOMO and LUMO is reduced by extended conjugation. The combined effect of an increase in the magnitude of A p along with the red shift of the lowest energy transition accounts for the large increase in j3 values as n is made larger.
Push-Pull Polyenes and Polyynes
The Journal of Physical Chemistry, Vol. 97, No. 16, 1993 4041 11+
x
no--+no>
1
2
*>I /fi
t 1 I n , --+ K i
2
Inoni)
Figure 2. Configuration mixing of the lowest excited singlet configurations in acetylene.
Similar trends are also found in the computed excited-state properties of l b (Table 11). The reduced u acceptor ability of the cyano group is reflected in the smaller ground-state dipole moments (not given in the table) as well as in smaller changes in dipole moments after excitation (compared to the nitro derivatives la). Interestingly, the excitation energies and the transition moment integrals are rather similar for the two series of compounds. Hence, the extent of u polarization in the excited states determines the relative values of @ in these systems. Along the same lines, the lower magnitude of @ in long-chain push-pull polyynes may be attributed to the poorer conjugating ability of triple bonds. The latter may arise from inferior overlap or from a larger HOMO-LUMO gap in an acetylenic unit compared to a C = C double bond.26 Lackof long-rangeelectronic polarization has indeed been inferred from ground-state geometries and 13C NMR spectral studies on push-pull p o l y y n e ~ . ~ ~ However, a comparison of Ap, transition dipoles, and excitation energies for polyynes and polyenes reveals a surprising trend. Two distinct u-u*-type transitions are computed to have significant oscillator strengths in polyynes. If the longer wavelength excitation is used for comparison, the magnitudes of p in la and 2a are not only similar but also increase roughly by about 7-8 units per n for both series. For example, the values of Ap are 24.1 and 25.7 D, respectively, for la and 2a (n = 4). The value of transition wavelength is generally higher in the polyenes. While this factor would contribute to the magnitude of @, the most dramatic difference between the polyenes and polyynes is in the computed transition moment integrals. The value of ron is much smaller, almost by a whole order of magnitude for the lowest energy u-u* transition in polyynes compared to polyenes. In polyynes, a large increasein the transition dipolewith increasing chain length is noted only for the higher energy excitation. The corresponding contribution to @ will therefore be smaller. The computed properties of the lower excited states in polyynes reveal theoperation of subtle effects in determining the magnitude of 8, rather than reduced electronic polarization or larger frontier orbital separation. The results can be best understood by consideringthe nature of the ulr* excited states of an acetylenic unit.28 The presence of two sets of u MOs (in-plane MOs, ui and ui*, and out-of-plane MOs, ?ro and uo*)in alkynes leads to different types of u-u* excitations. Configurations derived from ul-?ro*and uo-ui*-type excitations have a lower energy than those of ui-ui* and uolro*excitations. This is a direct consequence of lower electron repulsion when the electronsare placed in mutually
orthogonal orbitals. The lowest singlet states are obtained by allowing these configurations to interact with each other. Three distinct states result (Figure 2). The lowest is a 2,- state. This is followed by a doubly degenerate A,, state. One of its components may be viewed as the in-phase combination of the ui-?ro*and uolri* singlet configurations. The second corresponds to the out-of-phase combination of uilri* and u0lr,* excited singlet configurations. Much higher in energy than these singlet states is the symmetric combination of uilri* and ? r o l r o * excited singlet configurations. This state has 2,+ symmetry.29 By straightforward application of symmetry-based selection rules, dipole transitions from the ground state to the lowest two excited states are both forbidden. Only the excitation to the E,+ state is allowed and can have a sizeable transition dipole. Introduction of push-pull substituents on the acetylenic unit has interesting consequences. Substituents such as the nitro and amine groups can interact with only one set of u Mos. In oneelectron terms, the uoand uo*orbitals alone are affected. Of the four types of excited configurations, the singlet combination of the ?ro-?ro* would be stabilized to the greatest extent. As a result, only two of the excited states would be preferentially lowered in energy, viz., the symmetric and antisymmetric combinations of the ? r o l r o * and ai-*;* excited singlets (Figure 3). Of the various possible excitations, the lowest energy transition continues to remain forbidden. Although the degeneracy of the A, state is removed, the higher energy combination with predominantly ai?ro* and uolri* character is also predicted to have a low transition probability for excitation from the ground state. In contrast, transition to the lower energy component of the former A, state becomes partly allowed due to the reduced symmetry. The transition which is expected to be influenced most by the substituents is the one to the highest energy singlet. A large red shift and significant oscillator strength are anticipated for this excitation. In the above analysis, only the states derived from the highest energy u and the lowest energy u* orbitals from the in-plane and out-of-plane sets have been considered. Additional excited configurations involving lower lying filled and/or higher energy unfilled u orbitals may also have relatively low energies. These may lead to excited states lower than the 2,+ state derived from the HOMO and LUMO. However, these states would generally involve configurations of ui-uo*- or ?ro-ui*-type excitations. Correspondingly, the additional states would have negligible transition moments,ran, and would be unimportant in determining the electronicspectra as well as the hyperpolarizabilityof polyynes.
4048
Jain and Chandrasekhar
The Journal of Physical Chemistry, Vol. 97, No. 16, 1993
- - - - - - - - - - - I it nT> Figure 3. Configuration mixing of the lowest excited singlet configurations in unsymmetrical push-pull substituted acetylenes. The energies of the lro-lr,*
and
lr,-lro*
configurations are shown to be equal for the sake of simplicity. The CI coefficient CIis larger than C2.
TABLE V Comparison of the Experimental Spectral Wavelen hs and Intensitiess and Computed Transition Energies (Nanometers), Oscillator Strengths, Change in Dipole Moment &byes), Transition Moments (Atomic Units), and CI Coefficients of the Excited Singlet Configurations Obtained for Push-Pull Polyynes 3 and 4 calcd exptl molecule
h
CI coefficients t
3b, n = 2 314
9560
218
22890
348
5660
25 1
69670
326
10980
214
20380
354
7500
252
34600
3c, n = 3
4b, n = 2
4c, n = 3
h
osc str
Id
Au
347 306 272 204
0.00 0.14 0.00 0.98
0.03 0.64 0.03 1.36
13.1 14.2 8.5 7.8
369 324 297 223
0.00 0.15 0.00 1.62
0.02 0.68 0.02 1.82
17.2 20.6 11.7 8.3
340 305 277 207
0.00 0.15 0.00 0.87
0.02 0.64 0.04 1.29
11.1 15.6 9.4 4.9
361 334 323 223
0.00 0.08 0.00 2.26
0.02 0.5 1 0.03 2.15
15.6 19.7 13.3 10.0
7ro-lro*
lro-iri
*
*'I
*,* ,
*?-To*
0.677 0.558
-0.344
0.366
0.475
0.668 0.663 0.541
-0.377
0.363
0.493
0.677 0.679 0.548
-0.350
0.378
0.443
-0,660 0.661 0.506
-0.401
0.429
0.482
0.648
From ref 13.
The pattern described above is confirmed by the electronic spectral properties of a number of polyynes directly substituted by a donor,acceptor combination. The calculated spectral parameters for two series of compounds, 3 and 4, are compared with experimental data in Table V u t 3Typically, these compounds show two features: a long-wavelength band followed by an intense higher energy band. The calculations reveal the presence of a number of low-energy excited states, but the oscillator strengths for many of the transitions are predicted t o be low. Only two low-energy transitions are computed to have fairly significant transition moments. The longer wavelength transition corresponds to the state derived from the out-of-phase combination of ro-ro* and A~-P,* singlet configurations on the basis of the computed CI coefficients (Table V). The in-phase combination of the corresponding configurations leads to the higher energy singlet with a large transition dipole. With thespectral assignment shown in Table V, there is good agreement between computed and experimental transition energies. The computed oscillator strengths also generally parallel the trends in the observed i n t e n ~ i t i e s .These ~ ~ results provide a useful calibration for the present theoretical method for adequately accounting for excitedstate properties which are essential for the computation of @.
The effect of substituents on the excited-state energies of acetylenes discussed above provides a rationale for the computed variations in the hyperpolarizabilities of these systems. In spite of the presence of several low-energy excited configurations, only two states contribute significantly to 8. Although these states lead to large charge transfer as indicated by the magnitude of Ap, the longer wavelength transition is a remnant of a forbidden transition of the unsubstituted system. The corresponding transition dipoleis smaller, especially compared to that in polyenes. More importantly, the transition dipole of the longer wavelength excitation of the polyyne becomes progressively smaller as the chain length is increased (Table 111). This is because the corresponding excited state involves an out-of-phase mixing of ro-rg* and ~i-ai*configurations. The contribution from the latter increases with increasing chain length. The admixture consistently reduces the transition dipolerb. Therefore, thelarger @ values obtained for higher n result almost exclusively from the red shift and increased transition dipole associated with the higher excited state of these systems. The variations in the computed for the linear molecules 2c and 2d are also understandable on the basis of thier excited-state properties. The donor and acceptor groups interact equally with
Push-Pull Polyenes and Polyynes the two sets of T MOs of the polyynes. Consequently, the outof-phase combination of A,--A,* and ~ i - q * excited singlet configurations has a zero transition dipole rOn. The corresponding excitation cannot therefore contribute to 8, unlike in the case of the less symmetrical polyynes, 2a and 2b. This factor is offset by the greater effectiveness of the symmetric combination of the above configurations in these systems (i.e., 2+state). The degree of charge transfer on excitation to this state in the triple-bonded systems is significantly larger compared to the T-T* transitions in the polyenes with the same chain length (compare A p values in Table IV). Although the transition energies are smaller in the polyenes, the magnitudes of the transition moment integrals are higher in the polyynes. Hence, the hyperpolarizabilities of polyenes and polyynes with iodo and cyano substitution for similar chain lengths are comparable.
Conclusions Push-pull substituted polyynes arecomputed to have significant
fl values. However, the corresponding polyenes have larger hyperpolarizabilities. A detailed analysis of the calculated properties of excited states, viz., relative energy, change in dipole moment, and transition dipole integrals, reveals that lack of longrange electronic polarization is not the principal reason for the lower fl in nitro,amino- and nitro,cyano-substituted long-chain polyynes. Configuration mixing plays a crucial role in determining the transition dipoles of the excited states. In spite of the presence of a number of low-energy excited singlet states in polyynes, only two contribute in a significant measure to 8. The lower energy excitation becomes less effective with increasing chain length due to out-of-phase admixture of in-plane a--A*excited configurations. The relative behavior of polyenes and polyynes can be modified by the use of substituents which can interact with the orthogonal set of T MOs. Model systems with iodo and bromo groups as donors and the cyano group as the acceptor confirm that the polyynes would have hyperpolarizabilities comparable to the corresponding polyenes. For SHG applications, polyynes directly connected to strong donor and acceptor substituents, such as the experimentally known compounds 3 and 4, may be well suited. Due to difficulties involving synthesis and constraints imposed by reactivity and stability considerations, only modest chain lengths may be amenable for experimental applications. Under these circumstances, linear iodo derivatives with three to four C=C units would prove to be interesting candidates.
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