J . Phys. Chem. 1989, 93, 3915-3920 state. The nonradiative rate is large for a large molecule because the larger molecule has additional normal vibrations: (1) Some of them could be active normal modes in the sense of vibronic interaction. (2) Some of them are lower frequency normal modes. The low-frequency normal mode is effective for the nonradiative transition in the sense of energy conservation. (3) Many normal vibrations of a large molecule form an effective intramolecular heat bath through the vibration-vibration interaction in the ground state, and the molecular thermal energy dissipates easily to the solvent heat bath. The specific transfer efficiency Tobetween two luminophores in the absence of a third luminophore was obtained (eq 11 or 12). To is related to the distance between luminophores by eq 1. The values between S R I F and the analogues discrepancies of the TOAC (Table 111) are large. This suggests a conformational difference between S R I F and the analogues in the sense of the distance between three Phe and Trp in SRIF. The conformational study of S R I F by NMR7ss has given the structure of which the Nterminus does not interact with the rest of the molecule. The present result suggests that the Tyr residue at the N-terminus of the analogues causes the conformational change.
3915
Conclusion The present method of electronic energy transfer can give the intramolecular electronic energy-transfer efficiency T for the molecule that has three luminophores (eq 5 and 7). The fluorescence quantum yield in the absence of energy transfer & is obtained by using T (eq 8-10). The larger peptide has the smaller $o values for all luminophores. The specific energy-transfer efficiency To in the absence of the values third luminophore was obtained (eq 11 and 12). ToAC between Phe and Trp of Tyr-SRIF and [Tyr’ISRIF are smaller than that of SRIF. This shows the conformational difference between S R I F and the analogues. It is concluded that the Nterminal Tyr residue of the analogues can interact with the rest of the molecule and cause a conformational change of SRIF. The S R I F peptide with 14 amino acid residues is flexible in aqueous solution. Acknowledgment. We thank M. Morita for the measurements of the FAB/MS spectra of SRIF, Tyr-SRIF, and [Tyrl]SRIF. Registry No. SRIF, 38916-34-6; Tyr-SRIF, 58100-03-1; [Tyr’ISRIF, 59481-23-1.
Influence of Gap States on the Nonresonant Second Hyperpolarizabilities of Conjugated Organic Polymers David N. Beratan Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91 109 (Received: June 24, 1988; I n Final Form: November 18, 1988)
The presence of conjugation and substitution defects introduces “gap states” in finite polyenes that are shown to influence the size and sign of the second molecular hyperpolarizability, yxxxx.Using a one-electron tight-binding model, we calculate the dependence of yxxxxon the defect-state occupancy and energy in finite polyenes. Defects can cause a significant decrease or enhancement of yxxxxby impeding charge delocalization or by creating partly filled bands (mimicking the one-band limit), respectively. Concomitant sign changes in yxxxxare predicted. Calculations of these effects are made for molecules in which a central atom’s identity and electron occupancy are varied. The results suggest strategies for designing molecules that can be either photochemically or electrochemically switched between states with considerably different second hyperpolarizabilities.
1. Introduction Molecules with large electronic nonlinear polarizabilities are of great interest for their use in the manipulation of laser light for a host of optical switching, information processing, and other nonlinear optics applications.’ While great progress in the design and synthesis of donor-acceptor molecules with large quadratic nonlinearities has been made recently, guidelines for new types of molecules that exhibit cubic nonlinearities (second hyperpolarizabilities) have been more elusive. Most work to this point has focused on large delocalized r-electron systems. The goal of this paper is to calculate the hyperpolarizability of molecules related to unsaturated linear oligomers, to assist in the formulation of structure-property relationships for materials with large second hyperpolarizabilities. Recently, we examined a multi-“band” tight-binding model for the molecular hyperpolarizability of finite-length conjugated polymers.2 Predictions of the repeating unit and chain length dependence of the second molecular hyperpolarizability along the chain, the yxxxxtensor elements, were made.2J Many-electron (1) (a) Chemla, D. S.; Zyss, J. Nonlinear Optical Properties of Organic Molecules; Academic Press: New York, 1987; Vol. 1 and 2. (b) Nonlinear Optical Properties of Organic and Polymeric Materials; ACS Symposium Series 233; American Chemical Society: Washington, DC, 1983. (2) Beratan, D. N.; Onuchic, J. N.; Perry, J. W. J . Phys. Chem. 1987, 91, 2696. The signs in Table I should be negative (in units of e 4 a 4 / p I since 3 p1 < 0). Although that calculation uses a one-electron model, it is important to emphasize that two interaction parameters are included in the Hamiltonian to give a two-band system.
0022-3654/89/2093-391 5$01.50/0
theories of this effect are being developed but as yet have not fully described the expected saturation of yxxxxwith chain length as the polyene chain becomes long, behavior that appears quite naturally in the one-electron t h e ~ r i e s . ~ (3) The sign of yxxxxpredicted by the one-electron theories is positive for chains of two or more double bonds as long as bond alternation is included. See: Reference 1. Risser, S.; Klemm, S.; Allender, D. W.; Lee, M. A. Mol. Cryst. Liq. Cryst. 1987, 150b, 631. This is in contrast to a study where a single interaction parameter is used: McIntyre, E. F.; Hameka, H.F. J . Chem. Phys. 1978, 68, 3481. The sign of yxxxxarrived at with many-electron theories is also positive but is sensitive to parameterization of the electronic integrals, basis set, amount of included configuration interaction, and inclusion of uelectrons in the calculation. See: Pierce, B. M. Nonlinear Optical Properties of Polymers. Mater. Res. Soc. Proc. 1988, No. 109. Analysis of whether this problem can be adequately expressed in a quasi particle theory, and the parameterization of such a theory, is discussed in: Wu, W.-K.; Kivleson, S. Mater. Res. SOC.Proc. 1988, No. 109, p 229. Heeger, A. J.; Kivelson, S.; Schrieffer, J. R.; Su,W.-P. Rev. Mod. Phys. 1988, 60, 781. (4) x,()),the orientation average of the nonresonant molecular hyperpolarizability, is known for solid plyacetylene not to be tremendously different from that for p-carotene measured in solution although direct comparison should be made with great caution: Perry, J. W., private communcation. Etemad, S.; Baker, G.L.; Jaye, D.; Kajzar, F.; Messier, J. SPIE 1987, 682, 44. Many-electron theoretical calculations have, presumably, not been performed on sufficiently long chains to show this saturation. See, for example: References 2 and 3. For the many-electron calculations see: Heflin. J. R.; Wong, K. Y.; Zamani-Khamiri, 0.; Garito, A. F. SPIE 1987, 825, 56. deMelo, C. P.; Silbey, R. J . Chem. Phys. 1988,88,2567. Zamani-Khamiri, 0.; Hameka, H. F. J. Chem. Phys. 1979, 71, 1607. Hurst, G. J. B.; Dupuis, M.; Clementi, E. J . Chem. Phys. 1988, 89, 385. For saturation of the hyperpolarizability with chain length in the simpler modles see: References 1 and 5b. Rustagi, K. C.; Ducuing, J. Opt. Commun. 1974, 10, 258.
0 1989 American Chemical Society
3916
The Journal of Physical Chemistr-v, Vol. 93, No. IO, 1989
One-electron theories neglecting bond alternation3 overestimate the size of yxxyyand therefore predict a negative value for the . quaspace-fixed third-order nonlinear susceptibility, x ( ~ ) For si-one-dimensional materials, such as polyacetylene derivatives, x ( ~is)actually dominated by the y,,, tensor element when proper account of bond alternation is made and its sign is predicted to be positive in the one-electron theory.* Materials for nonlinear optical applications4 differ from the idealized systems in two dominant ways. First, some quantity of intrinsic conjugation defects is expected to be present and to affect the hyperpolari~ability.~ Second, the terminal groups of the polymer (or other intentionally added substituents) may be different from the normal repeat unit of the conjugated system. An understanding of how these groups affect yxxxxis needed to develop molecular design principles and to interpret experimental data. In this paper, we calculate the effects of these perturbations on the electronic structure and the second molecular hyperpolarizability. We find that perturbations within the chain can influence both the magnitude and sign of y x x x x .Calculation of yxxxxis made for polyene systems with an atomic conjugation defect “impurity” (neutral or charged) at the center of the chain (structure I). This
WXWN
N
I “defect” might be a carbon atom or heteroatom at the site where the sense of conjugation switches. The defect may also be used to model more complicated organometallic or organic conjugated polymers.6 Tests of these predictions in modified polyenes are discussed. This paper is structured as follows: ( I ) In the Theoretical Section, we modify the technique used previously for finite polyenes to find the wave functions and yxxx,for polyenes with a conjugation defect and atomic substitution a t the center of the chain. (2) We calculate y,, for finite systems having these defects. The importance of the defect localized state energy relative to the valence and conduction band edges is shown. (3) In the Discussion and Applications of the Model section, we interpret the results, suggest experimental tests of the theory, and propose future studies. W e also address the scaling of y x x x xwith chain length in the presence of defects. This dependence is seen to be related to the dependence of the sign of y on the defect energy and the reduction of the problem to an “effective” one-band rather than two-band problem as the defect state approaches a band (becomes more delocalized). This result suggests some novel possibilities for creating transient excited states with enhanced hyperpolarizabilities.
2. Theoretical Section One-electron models for x ( ~predict ) the correct sign and order of magnitude for long-chain polyenes when bond alternation is included. One-electron models also apparently adequately explain enhancements of the frequency-dependent susceptibility due to multiphoton resonance^.^ W e use a one-electron method as a starting point for our investigations because it adequately describes the phenomenon (without adding subtle problems of basis set adequacy3) and allows investigation of large systems. A particularly appealing aspect of such models is their ability to encompass the short, long, and intermediate chain length regimes. Huckel and self-consistent field calculations (also known as tight-binding calculations) have been applied to conjugated hydrocarbons for (5) (a) Dalton, L. R. SPIE 1987,682, 7 7 . (b) Flytzanis, C. In Nonlinear Optical Properties of Organic and Polymeric Materials; Williams, D. J., Ed.; ACS Symposium Series 233; American Chemical Society: Washington, DC. 1983; p 167. (6) (a) Frazier, C. C.; Guha, S.; Chen, W. P.; Cockerham, M. P.; Porter, P. L.; Chauchard, E. A.; Lee, C. H. Polymer 1983, 24, 553. (b) Perry, J . W.; Stiegman, A. E.; Marder, S. R.; Coulter, D. R.; Beratan, D. N.; Brinza, D. E.: Klavetter, F. L.; Grubbs, R . H. SPIE 1988, 971. 17.
Beratan
1
E: lB11
Figure 1. Graphical depiction of eq 4 where f ( E ) corresponds to the right-hand side of the equation. Marked on thef(E) = 0 line a r e the energy eigenvalues for a chain of four double bonds. Eigenvalues for the even symmetry states of the system (C=C-),X*(-C=C), a r e given by the intersections of the dashed ( E - A ) line with the nine solid curves for A = 0. Odd symmetry states a r e unshifted from the values marked on thef(E) = 0 line, the eigenstates of an isolated tetraene. Changing A just shifts the dashed curve up or down.
some time.’ I n this section, we will expand on the one-electron tight-binding formulation of the hyperpolarizability problem that we used in ref 2 by using methods in common use to determine the electronic states of a defect-containing crystal.’ The tight-binding wave functions for the x-electron states of a finite-length polyene (two p2 orbitals per repeating unit) are, in a one-electron approximation* R
$* = ( 1 / J V ) ] \ ~[ C 4 i r )sin (ne) f
&(I)
sin ( ( N + 1 - n)O)]
n=l
(la) The values of 6 are determined by the boundary condition
PI sin [(N+ I ) O ]
+ p2 sin (NO) = 0
(1b)
and the energy of the state is a where a 2
=
a,z +
p22
+ 2d113*cos 6
(IC)
PI (PZ) is the exchange parameter for pz orbitals in a multiple (single) bond. There are N unique values of 0, 2N energy eigenvalues, and 2N eigenvectors of either even (+) or odd (-) parity. One strategy for determining the states in the presence
of a central conjugation defect is to construct the wave functions from a linear combination of the known states for the two isolated sides of the molecule plus the central atom, as in eq 2. The defect at the center (site 0) couples the halves of the molecule with the Hamiltonian H’ = Aailta,
+ /j’(aotuNL+ C.C.+ aOtalR+ c.c.)
(3)
where at ( a ) creates (destroys) an electron a t the prescribed site. Multiplication of the full Schrodinger equation by &*, +,L*, and GkR* followed by integration gives for the N + 1 even states, (4)
(7) Salem, L. Molecular Orbital Theory of Conjugated Systems; W. A. Benjamin: Reading, MA, 1974. Yates, K. Hiickel Molecular Orbital Theory; Academic: New York, 1978. Wannier, G . H. Elements of Solid State Theory: Cambridge University Press: London, 1959. Smith, R . A. Wave Mechanics of Crystalline Solids, 2nd ed.; Chapman and Hall: London, 1969. Parr, R. G . The Quantum Theory of Molecular Electronic Structure; W. A . Benjamin: New York, 1964.
Hyperpolarizabilities of Conjugated Organic Polymers
The Journal of Physical Chemistry, Vol. 93, No. IO, 1989 3917
Equation 4 determines the even eigenvalues and eigenstates for which sin (NO,) a, = b, = (5) p ’ ( ~ , ) ‘ / 2 (-Ea,)
lo6
a is defined by eq I C for an isolated half of the molecule. The energy roots of the polynomial associated with eq 4 can be understood graphically’, as shown in Figure 1. The “band” states from each side of the molecule are weakly mixed by the defect, and an additional “midgap” state is introduced. A state below the valence levels and a state above the conduction levels are also added. For the odd symmetry eigenvalues of the system, H’ does not mix the unperturbed states so
10‘ .
and these states have the energy of the j t h unperturbed state of an isolated half of the chain. This strategy for writing the wave functions allows the dipole matrix elements between states to be written in terms of those between states for each half of the isolated molecule, i.e.
IO0
Ci is the normalization constant for the even symmetry states including the defect. Xjn is the dipole matrix between states j and n of the unperturbed polyene N double bonds long. The origin of the X coordinate system is at the defect site. These matrix elements, then, are equivalent to those calculated in ref 2 within an additive constant equal to the distance between the defect and the center of a conjugated half of the molecule. As discussed previously, the nonresonant contribution to yxxxxis proportional to the sum of fourth-order energy corrections to the occupied states ( m ) due to the field. Thus OmHmlHknHnmH1k m l#m k # m n#m
-
OmIwmkwmn
where the H values are the dipole matrix elements between the defect states, and Omis the occupancy of the mth electronic state. Because of the large band gap compared to K ~ T0,, is equal to 2 for all valence band states (and the one state below the valence band) and is 0, 1 (simple conjugation defect in polyene), or 2 for the gap state. It is 0 for all conduction band states. The energy denominator, wij, is the energy of state i minus that of state j .
3. Qualitative Properties of the Model yxxxxwith a Simple Midgap Conjugation Defect. We begin by applying this model to polyenes with simple sp2 carbon conjugation defects. For these materials, we estimated p2/pI = 0.79. A is zero in this case because the atom at the defect site is an sp2 carbon, which defines the zero of the energy scale. W e expect p’/pl, the interaction of the pz orbital at the defect site with its nearest neighbors, to be in the range between 0.79 and 1.0. This range is typical for both carbon and heteroatomic substituents,* and both values were examined. Because the impurity atom energy lies exactly midway between the valence and conduction bands of the polyene in this case, it mixes and splits those states but remains, itself, exactly midway between the bands. The midgap state is localized on the central defect but has amplitude on adjacent atoms as well.* Away from the defect site, the wave function amplitude decays approximately by the factor -p2/pl per double bond. The chain length dependence of yxxxxis shown in Figure 2. In this plot, the calculations for p’/pl equal to 0.79 (8) Streitwieser, A,, Jr. Molecular Orbital Theory f o r Organic Chemists; Wiley: New York, 1961. (9) Pople, J . A,; Walmsley, S . H. Mol. Phys. 1962, 5 , 1 5 .
1
Mid-gap defect m-
IO’ ;
..I..
z*
IO’ ;
IO’ ;
IO’ i
Figure 2.
-
yxxxx’,the molecular hyperpolarizability density (yxxxx/
for a polyene with N double bonds (solid line) and a polyene with N double bonds and a central conjugation defect (dashed line). The plots of the latter for 8’ = 0.79 and 1.0 a r e indistinguishable when plotted in this manner.
NyxxXx(”)) vs chain length
and 1.0 cannot be distinguished. The values of yxxxxfor chains containing six or more double bonds differ by 10% or less for the two values of p’. The sign of yxxxxis positive (negative in units of e4a4/P3),the same as in the pure chain case, and is dominated by the first term in eq 8. The calculation was made with the impurity orbital vacant (single cation), singly occupied (neutral doublet radical), and doubly occupied (singlet anion). yxxxxis independent of the occupancy because of exact cancellations in the perturbation sum for ym when m is the midgap orbital due to is proximity exactly between the band edges and the symmetry of the transition matrix elements involving the two bands. In reality, ionization of the defect site (or chemical substituents nearby such a defect) could alter A, the effective energy of the defect “atom”. Such effects are considered in the next part of this section. In the long-chain limit, we know that yxxxxis dominated by transition matrix elements arising from states at the band edge.235 Indeed, the defect localized state has large dipole matrix elements with the band edge states. They are roughly 3.15ea for a conjugation defect with eight double bonds on each side, compared to the direct HOMO-LUMO matrix element of 2.75ea for a 16 double bond length chain. Because of the energy denominators alone, the terms in eq 8 that involve the defect state could be expected to increase the hyperpolarizability density, yxxx:, by about 1 order of magnitude. In Figure 2, we see that this is the case for long chains. The hyperpolarizability density is defined as yxxxx.Ny,,,,(o), where N is the number of double bonds in the is the hyperpolarizability of an isolated double chain and yXxxx(O) bond. Preliminary results show enhancements of similar size when the defect is placed at the chain end.I0 Defect Energy Dependence of y-. When the Coulomb energy (A) of the defect is not equal to 0, the hyperpolarizability of the material can be tuned through several qualitatively different regions defined by varying (1) the occupancy of the defect state and ( 2 ) the proximity of the gap state to the valence or conduction states. As was seen in Figure 1, the defect causes three states to be split off from the bands. Of these three states, one is essentially localized and two are essentially delocalized. One level lies in the HOMO-LUMO gap ( E between Alp2 - &I) of the pure polyene, (10) The case of a defect at the chain end is similar to the above limit. The difference between the two cases is that the factor of 2 in eq 4 does not appear when the defect is at the chain end. Also, the corresponding perturbation expression includes additional terms. See: Beraian, D. N.; Lee, M. A,; Allender, D. A.; Risser, S. SPIE, in press. When the carbon defect is a t the chain end, yxxxxis also increased without a sign change. The numerical accuracy of the central defect calculation was verified by testing it in the limit of &/PI = 1 and comparing with the one-band result of ref 2.
Beratan
-
z
IO6
\
K
::
s
IO5
-& localized
Vacant gap state (16 double bonds)
b
1
a -& localized
E
lo’
Valence Band
Conduction Band
-delocalized
-localized
C
E Singly occupied gap state (16 double bonds)
C
lo’
1 Valence
Conduction
Band
Band
Figure 4. Positions of the three states split from the bands for the three possible limits in a two-band system interacting with a single defect atom. Arrows and shading symbolize occupied states. v and c refer to the valence and conduction bands, respectively. The three limits occur when s) A -e P,, (b) -P1 > A > P,, and (c) A > -81. TABLE I: Localized State Energy as a Function of A
k2.00 f 1 .oo f0.60
one below the lowest valence band state of the pure material, and one above the highest conduction band state of the pure material. The remaining states are weakly perturbed compared to the pure material.
f2.58 f 1.97 fO. 129
f0.15 0.00
k0.035 0.00
A and p’ determine the localized state energies. In Figure 3, we plot the hyperpolarizability density vs the energy of the localized state. This is the relevant energy to consider because, as discussed below, the localization of the defect state for fixed p’ is determined purely by the energy of the state, E . Since the defect is coupled relatively “strongly” to the band states, A and E are not approximately equal. If two conditions are met in these materials, the value of yxxxx can be significantly larger than that of the pure material or that of the exactly midgap defect material. This may result in both novel sign and chain length dependences of ymX. These conditions are that (a) the state in the gap is delocalized (that is, the position of the localized state, plotted in Figure 3, is above or below one
The Journal of Physical Chemistry, Vol. 93, No. 10, 1989 3919
Hyperpolarizabilities of Conjugated Organic Polymers TABLE 11: Effects on Y,.,,
of Molecular Modifications ~~
yxxxx relative to
examples
typical molecule
polyene
decreased somewhat decreased somewhat chem doped matl, excited polyacetylene states increased somewhat increased somewhat organometallics with low-energy MLCT or L M C T bands, where X = strong electron donor increased considerablyD or acceptor increased considerably increased considerably electron-transfer excited state, where D = porphyrin and Q = quinone, reached by increased considerably photoexcitation of D Molecules with donors and acceptors a t the chain end(s) are also expected to produce considerably enhanced hyperpolarizabilities.
of the bands) and (b) the delocalized state close to a band is partially or fully unoccupied if it lies just above the valence band or (is partially or fully occupied if it lies just below the conduction band). These conditions are not surprising because we know that the qualitative chain length dependence of yxxxx(nonresonant) is different in 1-D semiconductors compared to 1-D metal^.^ Introducing a delocalized state with the opposite occupancy of the band very close to it makes the material like a 1-D metal. This causing state also makes the second term in eq 8 dominate yxxxx, a sign change in the hyperpolarizability. As in the case of the I-D metal, chains with these characteristics also do not show a saturation of yxxxJwith chain length at the lengths for which the pure and midgap localized defect materials do. These arguments for yxxxxenhancements hold at frequencies where resonant processes remain unimportant. In the long-chain limit, the decay of the localized-state wave functions9 (the three split-off states) per double bond is E, where 1 E2 Pi P2
(9)
PIP2
P2
PI
It is most useful to plot yxxxxvs E (the energy of the localized state), rather than vs A, because the degree of localization is defined by E . Table I gives several values of the energy of the central atom localized state as a function of A. These shifts (from a value approximately equal to A) indicate relatively strong mixing between the central atom and the conjugated chain. The relative positions of the split-off states with respect to the bands are shown in Figure 4. A strong dependence of the magnitude and sign of yxxxxon both the defect-state occupancy and the position of the localized state was found, as mentioned above. Sign differences are noted in Figure 3 by changes in the line type (solid or dashed).
4. Discussion and Applications of the Model When a single carbon atom conjugation defect is introduced into a polyene chain, yxxxJis enhanced by about 1 order of magnitude (for long chains) or less and the sign is unchanged. The effect is independent (in this approximation) of the ionization state of the defect. Often, the Coulomb energy of a defect site is parametrized to reflect the orbital occupancy, and this would eliminate the cancellation (see Figure 3c). Non-carbon substituents can be incorporated in conjugated polymers, and this would alter A as well. The potential enhancement of yxxxxfor such materials is substantially larger. One might also imagine chemically derivitizing the chain, resulting in a C-R bond at the point of attack. Alternatively, an atom in the chain might be purposefully replaced with a metal6 or heteroatom. Any of these cases would make the defect orbital energy (A) different from zero. Typical heteroatom substitutions (0,N) change A to between 1 and 2 (in units of pl).* Such an atom inserted between two polyene segments is expected to cause a decrease in yxxxirelative to that of an uninterrupted polyene with the same number of double bonds (see Figures 2 and 3a and Table I). The defect atom, as in the conjugation defect case, may have a variable number of electrons to interact with the hydrocarbon *-cloud. A nitrogen or oxygen free radical in conjugation with the polyene chain(s) is expected to cause 1 order of magnitude enhancement in yxxxx'(see Figure 3c). Similarly, conjugation
of stable nitroxide radicals (typical spin labels) conjugated with polyenes might lead to analogous enhancements. Other strategies for enhancing yxxxxwould require the attachment of powerful electron donors or acceptors to the polyene (carotenes with 11 double bonds might provide a useful framework for such experiments). By this we mean groups with filled energy levels close to the LUMO of the polyene (donors) or vacant energy levels close to the H O M O of the polyene (acceptors). In contrast to the heteroatoms, these levels would provide localized states in the band gap (of opposite occupancy compared to the nearby band) or could actually reduce (or oxidize) the polyene to yield hyperpolarizability enhancements. However, considerable loss of transparency well into the near-infrared can result from one-or two-electron oxidation of carotenes." This will be determined by the degree of charge transfer from or to the carotene. One might expect that attachement of species like T T F (donor) or T C N Q (acceptor) would provide such extreme levels. It is difficult to predict whether formal oxidation (or reduction) will actually occur in these materials based purely on the redox potentials because it is difficult to quantify the effect of ion pairing in oxidized carotenes." Another class of molecules of possible relevance is organometallics with low-energy metal-to-ligand or ligand-temetal charge-transfer bands (MLCT or LMCT bands). These materials also would allow the tuning of the gap-state orbital by selecting the oxidation state of the metal or the composition of its ligands. Consider the ruthenium tris(bipyridine) complex with polyenesubstituted bipyridine ligands, for example. One might expect this system to have relatively low-energy charge-transfer bands, with the direction of the charge transfer determined by the oxidation state of the metal. Hence, such systems might allow probing of the effect on yxxxx of the defect-state proximity (defined by the oxidation state, ligand, and metal) to either the valence or conduction band. In the existing literature, some discussion of the influence of real excited states on the time response and size of yxxxrhas been given. Particular attention has been focused on the rise, evolution, and hyperpolarizability of the solitonic state of p ~ l y a c e t y l e n e . ~ ~ The current study suggests that a new class of transient large yxxxx materials might be made based on molecules having finite excited-state lifetimes. Molecules such as structure 11, in which a A
II relatively long-lived charge-transfer excited state is created rapidly (picoseconds-microseconds), would create a transient state with particularly enhanced yxxxxprovided that the charge transfe resulted in either (a) the creation of a partially occupied level very near the valence or conduction states of the polyene or (b) the (11) Grant, J . L.; Kramer, V. J.; Ding, R.; Kispert, L. D. J . Ani. Chem. SOC.1988, IIO, 2151.
3920
J. Phys. Chem. 1989. 93. 3920-3928
transient oxidation or reduction of a large conjugated system. Structure 11 is similar in many ways to the so called "triad" molecules in which electron transfer from an excited porphyrin to a quinone results in transient charge transfer to a carotene molecule (making carotene cation radical/porphyrin/quinone anion radical), which lives for milliseconds.12 Such a material would allow y x x x xto be optically switched between two different values. Prior to the creation of the charge-transfer excited state, the value of y x x x xwould be determined by Figure 3a. Following excitation and charge transfer, and for the duration of the charge-transfer excited-state lifetime, the hyperpolarizability would be determined by Figure 3c. Other examples of donor/acceptor pairs are Ru"/lrl L, (L = nitrogen-containing ligand)/methylviologen or aniline/nitrobenzene. It is essential, of course, that the photochemistry yield only reverisble oxidation/reduction of D, A, or the extended conjugated sections of the molecule. Such a molecule could also be synthesized with both a large nonresonant first hyperpolarizability ( x ( ~ )and ) switchable yxxxx.An oriented assembly of such molecules would display different nonlinear effects depending on the polarization of the incident light. The transient nonlinearities of other delocalized excited states are also of great interest.13 Table I1 summarizes these predictions. Other experiments and theoretical work of possible relevance include studies of the hyperpolarizabilities of cyanine dyes.14 Cyanines might correspond crudely to the model of Figure 3a, in which a low-lying occupied state(s) (energy below the valence band of the pure polyene) causes a decrease in yxxxx,although a two-substituent calculation is needed for reliable comparison. The detailed connection between a molecule's electronic structure and the anharmonicity of the corresponding effective oscillator is still somewhat open and will undoubtedly be explored further in the future.14 This semiempirical method has been shown to produce quantitative predictions that are testable. Conjugation defects are predicted to enhance yxxxx,at least in the low-defect concentration (12) Gust. D.; Moor, T. A.; Makings, L. R.; Liddell, P. A,; Nemeth, G. A,; Moore, A. L. J . A m . Chem. Soc. 1986, 108, 8028.
(13) (a) Schott, M.; Wegner, G. In Nonlinear Optical Properties o f o r ganic Molecules and Crysfals;Chemla, D. S., Zyss, J., Eds.; Academic Press: New York, 1987; Val. 2, p 3. (b) Kobayashi, T. SPIE 1986, 682, 12. (14) (a) Mehendale, S . C.; Rustagi, K. C. Opt. Commun. 1979,28,359. (b) Stevenson, S. H.; Donald, D. S . ; Meredith, G. R. Nonlinear Optical Properties of Polymers. Mater. Res. SOC.Proc. 1988, No. 109, p 103.
limit, and will not change the sign of the longitudinal hyperpolarizability. Oxidation or reduction of the polymer will cause sign changes and could cause large enhancements. The theory can be made more quantitative for specific molecules (e.g., Pd polyynes6) by determining the energies and extinction coefficients of the defect-polyene charge-transfer bands. Energetic trends for other free-radical and spin-paired defects have also been calculated. Placing localized electron states near bands of holes or localized holes near bands of electrons enhances y x x x xby enhancing delocalization of that localized state. Large transient changes in hyperpolarizability may be achievable by creating transient charge-separated states in a direction orthogonal to the direction of chain delocalization. Enhancements may also be produced by preparing delocalized excited states, thus simulating a I-D metal-like hyperpolarizability with the characteristic chain length d e p e n d e n ~ e . * +As ~ . ~low-lying charge-transfer transitions are introduced, or as oxidation/reduction of bands occurs, significant loss of transparency may result. This problem may not be too severe in relatively short-chain materials or materials in which the valence and conduction bandwidths are different.15 The treatment in this paper has assumed that the frequencies of the intrinsic resonant absorption processes of the molecules are well removed from the frequencies of the fields involved in the nonlinear process. If this is not the case, the nonresonant theory used here is inappropriate. For states split off slightly from a band and having the opposite occupancy of the band, resonant processes are indeed a possible source of complication. Resonant enhancement and the time evolution of the polarization in cases such as this are under study.
Acknowledgment. Helpful discussions of this work with S. R. Marder, J. N. Onuchic, and J . W. Perry are gratefully acknowledged. The research described in this paper was performed by the Jet Propulation Laboratory, California Institute of Technology, as part of its Innovative Space Technology Center, which is sponsored by the Strategic Defense Initiative Organization Innovative Science and Technology office through an agreement with the National Aeronautics and Space Administration (NASA). (15) For example, if the valence band is narrower than the band gap, a range of optical energies might exist in which nonresonant hyperpolarizabilities could be probed.
Vibrational Spectra and Scaled 3-216 ab Initio Harmonic Force Field for 2-Methyloxetane and Several Deuterated Isotopomers R. Anthony Shaw, Nan Ibrahim, and Hal Wieser* Department of Chemistry, University of Calgary, Calgary, Alberta, Canada T2N I N 4 (Received: June 28, 1988: In Final Form: November 18, 1988) Infrared absorption spectra have been measured, both in the vapor phase and in solution, for 2-methyloxetane and three selectively deuterated isotopomers. The ab initio optimized structures and harmonic vibrational force fields have been evaluated at the 3-21G level for both 2-methyloxetane and the parent molecule, oxetane. The local symmetry force constants of 2-methyloxetane were scaled initially by using factors optimized for the analogous vibrational coordinates of oxetane, and the Calculated frequencies were used as a guide in assigning the spectra. A final reoptimization of the scaling factors provided a force field which reproduces 101 firm assignments with an average,deviation of 4.5 cm-'. These assignments are corroborated by calculated infrared absorption intensities, evaluated by using 3-21G calculated atomic polar tensors in conjunction with the optimized force field, showing good qualitative agreement with the experimental spectra. Introduction The accuracy of a b initio force constants has been amply demonstrated, both by direct comparisons with empirically derived values,'.2 and subsequently by a number of studies ofsmall to medium-sized Although the diagonal force ( I ) Pulay, P.; Meyer, W. J . Mol. Specfrosc. 1971, 40, 59-70. (2) Meyer, W.; Pulay. P. Theor. Chim. Acta 1974, 32, 253-264.
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are generally overestimated, the errors have been shown to be quite systematic and may be corrected by scaling the force constant matrix to optimize agreement with experimental f r e q u e n c i e ~ . ~ . ~ (3) For reviews see, for example: (a) Fogarasi, G.; Pulay, P. Vibrational Spectra and Structure; Durig, J, R,,Ed,; Elsevier: Amsterdam, 1984; Val, 14, pp 125-219. (b) Fogarai, G.; Pulay, P. Annu. Reo. Phys. Chem. 1984, 35, 191-213. (c) Hess, B. A,; Schaad, L. J.; Carsky, P.; Zahradnik, R. Chem. Reu. 1986, 86, 709-730.
0 1989 American Chemical Society
