10155
J. Phys. Chem. 1992,96, 10155-10160
Vlbronk Coupllng of the Allyl Radical Excited States James D.Getty, XiPnming Liu, and Peter B. Kelly* Department of Chemistry. University of California, Davis, California 95616 (Received: June 23, 1992; In Final Form: September 17, 1992)
The nature of the allyl radical excited states has been examined by Raman spectroscopy. Fundamentals of non-totally symmetric normal modes are observed in the Raman spectra. The occurrence and intensiQ in non-totally symmetric fundammtalp is indicative of B-term scattering due to vibronic coupling. Analysis of the vibronic coupling is performed in terms of the Kramers-Heisenberg-Dirac formalism. The Raman spectra indicate that the vibronic coupling is from the weakly allowed 12B2state to either a molecular state arising from a combination of 3p atomic carbon orbitals or a valence state via non-totally symmetric vibrational modes. The vibrational frequencies for v9 and ul2 in the 12Bzstate have been determined to be 596 and 564 cm-' respectively.
Introduction The motivation for the study of the allyl radical is multifaceted. The allyl radical is an intermediate in both hydrocarbon combustion and photochemical reactions. The allyl radical is a benchmark molecule for both theoretical and experimental studies because it is the simplest conjugated *-electron hydrocarbon radical. The characterization of the ground and excited electronic states of the allyl radical is important to the understanding of free-radical chemistry. Resonance Raman spectroscopy can provide information on the allyl radical excited-state dynamics through examination of the intensities of the ground-state normal modes. The allyl radical (CH?CH-CH2) geometry from both ESR evidence' and ab initio calculations2 is bent with planar Ch symmetry. The valence r molecular orbital c o n f l t i o n consists of a bl bonding orbital, an a2 nonbonding orbital, and a bl antibonding orbital. The ground-state g2A2configuration is (bJ2(a2).' The allyl radical in the ground state is C, such that transitions from the ground 2A2state to the excited states with symmetries 2Bl,2B2,or 2A2arc one photon allowed. Excited states of 2AIsymmetry are inaccessiblevia one-photon akrption. Ab initio SCF-CI studies of Ha, Baumann, and Oth3report excitation energies and ionization potentials for the ground and 10 excited states of the allyl radical. Experimental studies have been performed on the one-photon-allowed 12B1valence state: the strongly allowed 22Blstate,- and the one-photon-forbidden 3s Rydberg 2AI In addition, matrix isolation infrared studies have yielded vibrational frequencies for the 2A2ground electronic ~ t a t e , ' ~ -and ' ~ photoelectron spectra of the allylic anion have displayed structure due to ground-state vibrations of the allyl radical.I6 Theoretical studies have examined the ground-state vibrational frequencies and electronic ~tructure~~"-~' as well as the excited-state allyl-cyclopropyl isomerizati~n.~'-~' A highresolution electron energy loss vibrational spectrum of the allyl radical has been observed from reactions of allyl chloride on Ag(1 Ha, Baumann, and 0 t h predict the lowest lying l2B1valence state to be at 396.1 nm? Currie and Ramsa9 have observed the one-photon-allowed 12BIstate via flash photolysis at 408.3 nm. Callear and Lees have assigned the strong absorption at 223 nm as the origin band of the 22Bl state with weak bands extending to 260 nm assigned to hot bands. Nakashima and Yoshihara' subsequently measured the oscillator strength of the ultraviolet bands at -223 nm. Resonance with the transition at 223 nm yields rcaonance Raman spectra of the allyl radical indicating that the initial excited-state dynamics are along the allyl-cyclopropyl disrotary isomerization.* Recent 1+1 resonant MPI spectra of the allyl radical performed by Chen et al. have demonstrated that the weak abporptions in the 24Ck260-nm range are not hot bands. They have assigned the band origin of the 22B, at 248.15 nm9and proposed that the band at 223 nm is due to a higher lying excited state. 0022-3654/92/2096-10155$03.00/0
Hudgens and Dulcey'O have employed MPI to examine the one-photon-forbidden 3s Rydberg ZAlstate of the allyl radical. The study reported the electronic origin of the ZAlstate at 40085 cm-'. The CCC bend, v7, gave rise to the observed vibronic structure in the MPI spectrum. The 3s ZAl R2A2transition was further studied under higher resolution by Sappey and Weisshaar." The two-photon resonant spectra yielded the assignment of three vibrations for both the ground and excited states and a band origin for the 3s Rydberg state to lie at 40056.8 cm-I. The promotion of an electron from the a2nonbonding *-orbital to the nonbonding b2 orbital (5b2 la2) yields the 12B2state. The 5b2molecular orbital arises from a linear combination of 3s atomic orbitals on each carbon. Ab initio calculations of Ha, Baumann, and 0th3 predict the 12B2 g2A2transition to be at 235.7 nm with a small oscillator strength. Resonance Raman spectroscopy has been employed to examine the spectral range from 235 to 250 nm in an effort to examine the weakly allowed one-photon transitions of the allyl radical. Interpretation of the resonantly enhanced ground-state vibrational frequencies through the Kramer~-Heisenberg-Dira$~formalism yields insight to the coupling schemes responsible for the observed spectra. Intensity in the fundamentals of non-totally symmetric modes is indicative of B-term scattering and hence vibronic coupling. Symmetry considerations provide a possible interpretation of the vibronic coupling.
-
-
Theory
The Raman scattering intensity Im,for a transition between state Im) and In) is defined as Imn
a IOVO(VO
- ~mn)~CI(apu)mnI~ P"
(1)
where uo and vo - v,, are the frequency of the incident and scattered photon, respectively. The sum of the Kramers-Heisenberg-Dirac formalismZSis taken over all states and the apu component of the transition polarizability tensor is defined as
(gnl [Mulgelev)(4[Mpleglgm) hue, hvo ihcr,
+
+
where (evl[M.]&m) is the a-th component of the electronic transition dipole operator for the transition from vibronic level Igm) to vibronic level lev). The dephasing constant rev, is related to the lifetime of the vibronic state lev) by T = (2~cI',)-~. For resonance Raman scattering, the energy denominator for the second term in eq 2 becomes relatively large as huo approaches hv,, such that the first term dominates. Under resonance conditions the sum over all states may be taken over only one or two electronic states. (d
1992 American Chemical Society
Getty et al.
10156 The Journal of Physical Chemistry, Vol. 96, No. 25, 1992
The Herzberg-Teller perturbation approach is used to examine vibronic c o ~ p l i n g The . ~ ~electronic ~ ~ ~ dipole can be expanded as [Mplge
= [Mpl'ge
+ CCIMpIogs(hke,/~es)Qk + k s
(3)
where hk, = (ddH/dQ&)Q+ is the derivative of the Hamiltonian describing the interaction of the vibrational and electronic Hamiltonians with respect to the normal coordinate Q k such that the electronic states le) and Is) may couple. v, is the energy difference between the excited electronic state le) and the coupling state Is). The strength of the vibronic coupling is described by hk,/v,.27 The expansion (eq 3) may be substituted into the expression for the transition polarizability tensor (eq 2) yielding four terms which comprise the tensor, (a&," = A B C D. Only the A term and B term will be considered here; the reader is encouraged to refer to the review by Clark and Dinesz7 for an excellent discussion of the other terms which comprise the tensor. A-term Raman scattering is the often dominant contribution to the Raman intensity. The A-term component to the transition polarizability tensor is
excitation wavelennth (nm) 237.1 1
vibrational assinnment v1 CCC bend v I 2 CH2twist (sym) v9 CH2twist (asym) v7
+ VP
2v9
us CHI rock (sym) v4 CH2scissors (sym)
+ + +
v7
+ 2vq
2VlO 2v6 v6
231.29
vl
+ 2v9
CCC bend
v I 2CH2twist vg CHI twist Vl
(sym) (asym)
+ VI2
2v12 v6
ccc stretch (Sym)
us CH2 rock (sym)
The magnitude of the expression (eq 4) is dependent upon the electronic transition moments (the transitions must be allowed), the energy denominator, and the Franck-Condon factors. A-term scattering will give rise to intensity in totally symmetric modes, and even overtones of both totally and non-totally symmetric normal modes. Note that the A-term scattering term does not have a vibronic coupling component. The B term contains the expression of vibronic coupling of a weakly allowed excited state to a strongly allowed excited. The B term of the polarizability tensor is
-
The "borrowed intensity" of the le) lg) is from the B-term contribution to the polarizability tensor. Examination of eq 5 indicates that in order for B-term to be significant both the transition from the ground state Ig) to the excited state le) and the transition from the ground state Ig) to the coupling state Is) must be allowed transitions. The magnitude of the B term is dependent upon the coupling of le) and Is) by mode k, hk,/u,; the electronic transition moments, [MpIo,; the energy denominator; and the vibrational overlap integrals, (nlQklv)(vlm) and (nlv) (vlQklm). The vibrational integrals in the harmonic oscillator approximation and without a major change in force constant for the non-totally symmetric modes are limited to unit change in the vibrational quantum number;z7thus the contributing integrals are (1IQklO) (010) ( I l l ) ( lIQklO)
(0-0)resonance (0-1) resonance
The vibrational integrals in eq 6 reveal that fundamentals of non-totally symmetric modes can now have significant intensity, unlike in A-term scattering where only even overtones of nontotally symmetric modes appear in the resonance Raman spectrum. However, for the non-totally symmetric fundamental Qk to be active the direct product of the non-totally symmetric fundamental Qr with the excited state Is) must be the same symmetry as the le) state. The summation over coupling states is reduced to a single term when the le) state is coupled to a single Is) state by a single vibrational mode, such that the B-term expression can be written with the (0-0) and (0-1) resonance integrals as
Vl
v4
+ 2VI2 CH3scissors (sym)
2VlO v6
+ 2v12
2v6
2vs v 4 + 2v12
240.5 1
V,
CCC bend
vI2 CHI twist (sym) v9
CH2twist (asym)
2v7 v7
+ VI2
obsd frecr (cm-9 ~~
421 518 549 911 1035 1066 1101 1245 1488 1524 1938 2128 2163 421 518 549 940 1035 1066 1245 1463 1488 1938 2099 2128 2488 2523 421 518 549 856 940 911 1035 1245 1488
4Frequenciesare within k 3 cm-I. The expression (eq 7) allows the occurrence of the fundamentals of non-totally symmetric modes to be rationalized in terms of vibronic coupling. Experimental Section The resonance Raman experimental layout for the study of gas-phase free radicals has been described in previous reports on the methyl and allyl radicals.828 The gas-phase allyl radicals are produced from a onephoton photolysis of the precursor allyl iodide. The fourth harmonic of a Nd:YAG laser is the photolysis source and arrives 15 ns prior to the far-ultraviolet probe. The probe laser is generated from a NdYAG pumped dye laser (LDS 750 dye), whose fundamental is doubled (KD'P) and mixed (BBO) with the second harmonic of the dye fundamental to produce the tunable far-ultraviolet probe. The Raman backscatter is imaged into a 1.0-m Czerny-Turner monochromator, dispersed by a grating operating in third order, and collected by a photomultiplier tube or a charge-coupled detector (Princeton Instruments Intensified CCD Model ICCD-576G). Results and MscuPsion Resonance Raman spectra of the allyl radical and the PrecUIgor allyl iodide at excitation wavelengths of 237.1 1,237.29, and 240.51 nm are presented in F w 1-3. The observed vibrational bands for each wavelength are listed in Table I. The initial resonance Raman wavelengths were selected on the basis of the multiphoton ionization spectra reported by Chen et al.9 The selection of the excitation wavelengths was a result of preliminary Raman excitation profiles to find excitation wavelengths that yielded maximum Raman intensity. The fgum display both the precu~or resonance Raman spectrum (lower trace) and the corrapondmg
The Journal of Physical Chemistry. Vol. 96, No. 25, 1992 10157
Nature of Allyl Radical Excited States
1
I
I
I
I
I ’ v1
CH,
ALLYL RADICAL
.
0
500
--
I
1000
1500
2000
2500
3000
WAVENUMBER
Figure 1. Resonance Raman spectrum of the allyl radical (upper trace) at 237.1 1 nm, displaying strong intensity in the fundamental of v9 at 549 cm-I, as well as overtones, and combinations of v9. The lower trace is the resonance Raman spectrum of the precursor allyl iodide.
‘ I ALLYL RADICAL
ALLYL IODIDE
1
0
I
500
1000
1500
2000
2500
CH,
3000
WAVENUMBER
Figure 2. Resonance Raman spectrum of the allyl radical (upper trace) at 237.29 nm, displaying strong intensity in the fundamental of v12 at 518 cm-I, as well as overtones, and combinations of v12. The lower trace is the resonance Raman spectrum of the precursor allyl iodide.
allyl radical resonance Raman spectrum (upper trace) at each wavelength. The assignment of the fundamental vibrational transitions is aided by the ab initio calculations of Ystenes and Fjorstad” and Takada and Dupuk2 The resonance Raman spectra (Figures 1-3) from 237 to 240 nm display a dramatic change in the intensity of the Raman scattering with a change in the excitation wavelength. The observed variation in Raman intensities is intimately related to the magnitude of the molecular dephasing constant rW. A large dephasing constant will result in a broad resonance, and thus the
remnance Raman spectra will not change significantly with change in excitation frequency. However, if the lifetime of the excited state is relatively long, the resonance Raman spectra will exhibit narrow resonan- in particular vibrational modes as the probe laser wavelength is changed. The rovibrationally resolved MPI spectra of Chen et a1.9 exhibit features with a spectral bandwidth of approximately 0.5 an-]; the small magnitude of rW indicates that the excited-state lifetime is relatively long. Examination of Figure 1 shows that at 237.1 1 nm the fundamental, overtones, and combinations of v9, the CHI asymmetric twist, are the modes
10158 The Journal of Physical Chemistry, Vol. 96, No. 25, 1992
Getty et al.
VI
CH,
ALLYL IODIDE
I
0
I
I
500
1000
1500
2500
2000
3000
WAVENUMBER
Figure 3. Resonance Raman spectrum of the allyl radical (upper trace) at 240.51 nm, the electronic origin of the resonance Raman spectrum of the precursor allyl iodide.
with sisnificant intensity. In contrast, tuning 0.18 nm to the red, the fundamental, overtones, and combination of v12, the CH2 symmetric twist, are the modes that are most prevalent (Figure 2). The observed dramatic resonance enhancement is indicative of a small dephasing constant and has been exploited to selectively enhance various vibrational modes in order to calculate groundstate anharmonic constants.29 The MPI work performed by Blush, Minsek, and Chen provides an estimate for the excited-state line width^.^ The natural line widths of the trahsitions become larger with decreasing wavelength. The MPI bands observed at 234-238 nm were significantly broader than the 0.5 cm-'survey laser line width. The MPI bands at 242-248 nm show rotational structure in accordance with the 0.1-cm-' laser resolution used to reexamine those bands. The theory of resonance secondary radiation developed by Melinger and Albrecht classifies the emission as predominantly rt8onBnce Raman scattering when the excitation line width is less than the natural line width of the transition.M The excitation laser line width was 0.1 cm-'.The spectra taken with 237.1 1-, 237.29-, and 240.51-nm excitation are described in terms of resonance Raman scattering since the natural line width for those bands is greater than or equal to 0.5 cm-'. The spectra taken with excitation at wavelengths longer than 242 nm are expected to be dominated by the resonance fluorescence component since the line width of the observed structure is less than 0.1 cm-'. The interpretation of the spectra in terms of the vibronic couplings and excited-state vibronic assignments are the same for resonance fluorescence and resonance Raman scattering. In general, the most intense and most common resonance Raman spectra can be described in terms of A-term scattering which arises from resonance with a single allowed electronic transition. Only the fundamentalof totally symmetric modes and the even overtones of non-totally symmetric modes would have significant intensity. For molecules with C, symmetry in both the ground and excited electronic states, transitionsfrom the 2A2 ground state to excited states of 2A2,2BI,and 2B2symmetry are one photon allowed. In particular, the predicted electronic states in the 237-nm range are the onephoton forbidden 12AIand the weakly allowed 12Bzstate.' Thus, by theoretical arguments alone resonance Raman spectra in the -240-nm energy range would be expected to be due to the weakly allowed 12B2 g2A2tran+-
satu mrmd by MPI
12B2state. The lower trace is the
S U l a pndisrd by
Ab Mib cakulumr
Figure 4. Energy level diagram of the allyl radical excited states. The left column is the states observed by Chen et al. (ref 9). The right column is the state ordering predicted by Ha et al. (ref 3). The electronic band origins are given in electronvolts (eV).
sition. Figure 4 displays the relevant energy levels. The state symmetriea are thesameas thosepredicted by Ha, Baumann,and 0th;' however, experimental results of Chcn et a1.9 have located the band origins of some of these stat- and thus indicated a reordering of the electronic states. Intensity in the fundamental of a non-totally symmetric mode is indicative of B-term Resonance Raman spectra with excitation at 237.1 1 nrn yield stmng intensity in -tal, overtones, and combinations of ug (a2 symmetry), the CH2 asymmetric twist.In contrast, resonance Raman spectra at 237.29
The Journal of Physical Chemistry, Vol. 96, No. 25, 1992 10159
Nature of Allyl Radical Excited States nm display strong intensity in fundamental, overtones, and combinations of v I 2(bl symmetry), the CHI symmetric twist. The Raman-active non-totally symmetric fundamental is a result of the vibronic coupling of a weakly allowed electronic state to a strongly allowed coupling state of the appropriate symmetry via the fundamental. In order for the B term to have a significant contribution to the Raman intensity, both the weakly allowed excited state and the coupling state must obey onephoton selection rules. Examination of eq 7 reveals that the magnitude of the B-term scattering is also dependent upon the strength of the coupling (hkw/vw),the energy denominator, and the vibrational overlap integrals. Assuming the harmonic oscillator approximation, the vibrational integrals will be such that transitions with only unit change in vibrational quantum number are allowed. Thus, the Franck-Condon factors will be nonzero and the fundamental of a non-totally symmetric mode can be allowed. The integrals in the (0-0) resonance (eq 6 ) can be considered in terms of the symmetries of the integrand functions. The ground-state vibrational level will be the totally symmetric repmentation, and excitation to the zero level in the intermediate state will yield a nonzero overlap integral. Raman scattering enhanced by vibronic coupling from an a2 displacement coordinate Qk from the zero level in the excited state to one quanta of the a2mode in the ground state will also yield a nonzero integral and thus intensity in a non-totally symmetric fundamental. S i considerationsapply to bl normal modes. However, in order for the non-totally symmetric fundamental QI; to contribute to B-term scattering it must also be of the appropriate symmetry to couple the two excited states. Thus, the direct product of the coupling vibration (the non-totally symmetric fundamental), Qk, and the weakly allowed excited state, le), must be of the same symmetry as the strongly allowed coupling state, Is). The E-term scattering can be used to describe the intensity in the non-totally symmetric fundamentals and in turn the vibronic coupling. The predicted energy3of the 12B2state lies in the range of the o k e d spectra at 237 nm (Figures 1 and 2). The oscillator strength of the 12B2is predicted to be small3such that vibronic coupling of this weakly allowed state to a strongly allowed coupling state via the a2 (v9, the CHI asymmetric twist at 549 an-’)and/or bl (v12, the CH2 symmetric twist at 518 cm-’) fundamental is responsible for the observed intensity. Applying eq 7, the symmetry of the coupling state is 237.1 1 nm must be of the same symmetry as the direct product B2 X a> Thus, the resonance Raman spectra at 237.1 1 nm are a result of the 12B2 R2A2 transition vibronically coupled to the strongly allowed 22B1state via v9, the CH2 asymmetric twist a2 fundamental. In turn, the rescnance Raman spectra at 237.29 nm are a result of the 12B2 X2A2transition vibronically coupled to the 22A2state (B2 X bJ via v12, the CHI symmetric twist bl fundamental. The 22A2 state arises from an excitation of the electron from the valence a1molecular orbital to the a2molecular orbital. The a2molecular orbital is a linear combination of 3p carbon atomic orbitals. The absorption bands at 237.1 1 and 237.29 nm are assigned to transitions from the origin level of the ground state to one quanta in v9 and v12 in the 12Bzexcited state. Intensity in a fundamental without significant intensity in the overtones or combination modes is indicative of an electronic band The allyl radical spectra at 240.51 nm display intensity in the fundamentals of both v9 and v12, but weak intensity in the overtones and combinations. The assignment of the electronic origin at 240.51 nm to the 12B2state is supported by the 1+1 MPI spectra of the allyl radical where the electronic origin of the 12B2 state is given at 240.56 nm.9 The resonance Raman spectra of the perdeutero allyl radical at 240.70 nm (corresponding to the predicted 12B2origin) also lacks significant intensity in the overtones supporting the electronic origin assignment. Based on the B-term symmetry considerations the resonance Raman spectrum at 237 nm is assigned to vibronic bands of the 12Bzstate, with the electronic origin at 240.51 nm. The 0-1 resonance (eq 6) is observed at 237.1 1 nm for v9. The energy difference between the electronic band origin and the 0-1 resonance yields the vibrational frequency of 596 cm-’for v9 in the 12B2state. The 0-1 resonance
-
-
for vI2is identifkd by the vibronic coupling evident at 237.29 nm. The excited-state frequency for v12 is -564 cm-’ corresponding to the energy difference between the 0-1 resonance and the 0 4 resonance. The approximate vibrational frequencies for the 12B2 state arc comparable to those observed by Sappey and Weisshaar for the 3d Rydberg 12AIstate (v9 558 cm-l, v12 508 cm-l).ll The allyl radical electronic states correlate to the states of the cyclopropyl radical through both the conrotary and disrotary isomerization pathways?1*22The distortion of the allyl radical along either isomerization pathway can provide a mechanism for the coupling of the electronic states of the allyl radical. The 12B2 excited state of the allyl radical is expected to cross the 12Alstate and the 22B1states along the disrotary isomerization pathway. The 12B2state correlates with an excited state of the cyclopropyl radical and is of A” reduced symmetry when distortion of the molecule in the disrotary configuration is considered. The 12A1 state and the 22B1state correlate to lower excited states of the cyclopropyl radical and are of A’ reduced symmetry. The expected curve crossings of these electronic states would allow vibronic coupling through a2 and bl vibrations of the type observed for v9 and v12.
Conclusion Resonance Raman spectroscopy has been employed to examine the weakly allowed 12B2state. Observation of the fundamentals of both a2 and bl non-totally symmetric vibrational modes is evidence of B-term scattering due to vibronic coupling. The intensities in the resonance Raman spectrum reflect vibronic coupling of the 12B2to the 22B1state via an a2 mode (v9), and to the 22A2state via a bl mode (v12). The vibrational frequencies for v9 and vI2 in the 12B2state have been determined.
Acknowledgment. We thank Professor P. Chen (Harvard University) for helpful discussions and exchange of data. We express our gratitude to the National Science Foundation (CHE8923059) for the financial support of this work. Registry No. Allyl radical, 1981-80-2.
References md Notes (1) Fessenden, R. W.; Schuler, R. H. J . Phys. Chem. 1968, 39, 2147. (2) Takada, T.; Dupuis, M. J. Am. Chem. Soc. 1983, 105, 1713. (3) Ha, T. K.; Baumann, H.; Oth, J. F. M. J. Chem. Phys. 1986,85,1438. (4) Cume, C. L.; Ramsay, D. A. 1.Chem. Phys. 1966,45, 488. ( 5 ) Calltar,A. B.; Lee, H. K. Tram. Faraday Soc. 1968,64,308. Callear, A. B.; Lee, H. K. Nature 1967, 213,693. (6) van den Bergh, H. E.; Callear, A. B. Trans. Faraday Soc. 1970,66, 268 1. (7) Nakashima, N.; Yoshibara, K. h e r Chem. 1987, 7 , 177. (8) Getty, J. D.; Burmeister, M. J.; Westre, S. G.; Kelly, P. B. J. Am. Chem. Soc. 1991,113, 801. (9) Minsck, D. W.; Blush, J. A.; Chen, P. J. Phys. Chem. 1992,92,2025. Also see preceding paper in this issue. (10) Hudgens, J. W.; Dulccy, C. S.J . Phys. Chem. 1985,89, 1505. (11) Sappey, A. D.; Weisshaar, J. C. J. Phys. Chem. 1987, 91, 3731. (12) Mal’stcv, A. K.; Korolov, V. A.; Nefedov, 0. M. Bull. Acad. Sci. USSR,Chem. Ser. 1982, 31,2131. (13) Maier, G.; Reisenauer, H. P.; Rohde, B.; Dehnicke, K. Chem. Ber. 1983, 116, 732. (14) Holtzhauer, K.; Cometta-Morini, C.; Oth, J. F. M. J. Phys. Org. Chem. 1990,3, 219. (15) Huang, J. W.; Graham, W. R. M. J . Chem. Phys. 1990, 93, 1583. (16) Oakes, J. M.; Ellison, G. B. J. Am. Chem. Soc. 1984, 106, 7734. (17) Ystenes, M.; Fjorstad, E. Specrrochim. Acta 1990, 46A, 47. (18) Cometta-Morini, C.; Ha, T. K.; Oth, J. F. M. J . Mol. S t r c r . THEOCHEM. 1989,188,79. (19) Sim, F.; Salahub, D. R.; Chin, S.; Dupuis, M. J. Chem. Phys. 1991, 95, 4317. (20) Szalay, P. G.; Csaszar, A. G.; Fogarasi, G.; Karpfen, A.; Lischka, H. J. Chem. Phys. 1990,93, 1246. (21) Famell, L.; Richards, W. G . J. Chem. Soc., Chem. Commun. 1973, 334. (22) Merlet, P.; Peyerimhoff, S.D.; Buenker, R. J.; Shih, S.J . Am. Chem. Soc. 1974,96, 959. (23) Olivella,S.;Sole, A.; Bofdl, J. M. J. Am. Chem. Soc. 1990,112,2160. (24) Carter, R. N.; Anton, A. B. J . Am. Chem. Soc. 1992, 114, 4410. (25) (a) Tang, J.; Albrecht, A. C. In Raman Spectroscopy; Szymanski, H., Ed.;Plenum: New York, 1970; Vol. 2, p 33. (b) Lee,D.; Albrecht, A. C. In Advances in Infrared and Raman Spectroscopy; Clark, R. J. H., Hater, R. E., Eds.; Wiley: New York, 1985; Vol. 12, p 179. (26) Herzberg, G.; Teller, E. Z . Phys. Chem. 1933, 21, 410.
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
‘Indian 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)
, ~ ~
