The Design of Candidate Optical Limiters
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39 Mat. Res. Soc. Symp. Proc. Vol. 374 01995 Materials Research Society
COMPUTATIONAL DETAILS The calculation of the second hyperpolarizability follows that of Kurtz et al. [18], where the energy of a molecular system in an electric field is given by:
E(F) = E(O),uj F1 - (--)oiFiF,(-)13..kfiFFk 2!
13! 3
(1)''JkFFjFkFI
4 !4
(1)
containing implied sums over repeated indices. The molecule is considered to be in a uniform electric field aligned along one of the axes of the system (by convention x ). The expressions are incorporated into AMI (Austin Model 1) Hamiltonian and solved to selfconsistency, and components with two different indices i j are obtained by applying a linear field in the ij plane along 450 between the axes. The mean value of the second hyperpolarizability is obtained from all components by: y= '{y
+ r,
+ y.
+ 2[yx~
+ y,]+
(2)
All calculations have been performed with MOPAC 93 [19]. RESULTS AND DISCUSSION Tolanes The 7 values calculated for the tolane derivatives (Figure 1) are summarized in Table 1. -
1C
0
(a)
(b)
Figure 1: A series of tolane derivatives: I (a)-(e) Indeed, large values are being observed, when compared to similar conjugated systems. The amount of n-electron conjugation in such compounds may be of importance for an understanding of the hyperpolarizabilities (e.g. as shown in [20]), and would be obvious if a variety of electron donor and acceptor substituents would be assessed [21 ]. However, for the unsubstituted molecular systems, the increase in 7 is clearly dependent on the number of biphenyl and acetylene moieties in these oligomers and not any changes in substitution. A comparison of bond lengths, and the corresponding bond orders in those systems show a
40
larger delocalization in the benzene rings, for example, the bond lengths in the phenyl ring in I(a) are 1.393 A, 1.405 A, 1.406 A, 1.393 A, and 1.395 A, while for I(e) they are 1.398 A, 1.393A, 1.393A, 1.398A, and 1.398 A. A comparison of the bond orders and partial atomic charges in the acetylene moiety in these derivatives show smaller changes, i.e. for Cl, C2, C3, and C4, the bond orders are ca. 1.04 for the single bond and 2.77 for the triple bond, while the partial atomic charges range between Cl: 0.025 to 0.030; C2: -.099 to -.106; C3: -.106 to -.112; and C4: 0.030 to 0.038 (all values are in electrons), for I(a)-(e), respectively. Note that bond orders and bond lengths are closely related, as shown, foe example, by Paolini's correlation [22]. Current investigations include calculations of these properties at a higher level of approximation, as well as further experimental evaluation [23]. Table 1: Calculated y for a series of tolane derivatives y (*10-36 esu) 36.2 38.1 42.0 75.2 82.5
Molecule I (a) (b) (c) (d) (e)
Semi-flexible, stiff-chain polymers The materials studied include substituted biphenyl (X, Y = H, CH 3 , NO 2 , or a halogen atom) and benzo-bisthiazole moieties [14], as shown in Figure 2. Rl R2
R3 R4
Molecule II
(a) (b) (c) (d) (e) (f)
(g) (h) (i) (j)
MI M2 M3 M4 M5 M6 M7 M8 M9
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