J. Phys. Chem. 1994,98, 13157- 13161
13157
Modeling of the Franck-Condon Structure of the Electronic Transitions of an Oligomer of Polydiacetylene Francesco Zerbetto Dipartimento di Chimica "G. Ciamician", Universith di Bologna, Via F. Selmi 2, 40126, Bologna, Italy Received: August IS, 1994@
The Franck-Condon structures of the absorption and emission spectra of C14Hg (HC=C-CH=CH-CECCH=CH-C=C-CH=CH-CECH) are investigated through model calculations. Because of the relatively low resolution of the spectra available and to avoid a possible bias in the simulation, the Franck-Condon parameters are calculated by an ab initio procedure and by a more extensive set of semiempirical QCFFPI calculations. In the process, the QCFFPI model is upgraded to include the treatment of linear bendings. The calculated vibro-electronic spectra agree well with the experiment. In particular, the modeling reproduces the lack of mirror image between absorption and emission and the different behavior of the 0-0 band in the two spectra. Because of the success in the Franck-Condon simulation, the calculations are used to discuss the different nature of the excitation in the two lowest-lying electronically excited states of this prototypical molecule.
Introduction The understanding of the effects of electronic excitation in aromatic and conjugated molecules has been greatly enhanced by the joint impact of vibrationally resolved electronic spectroscopy and quantum chemical theory. Qualitative considerations can easily show that, in these systems, the excitation is highly delocalized over several CC bonds and transfers binding electron density from the double, Le., short, to the single, Le., long, bonds. The net effect is that the roles of these bonds are effectively reversed upon excitation. Despite this intuitive picture, unexpected effects may arise such as the frequency increase of the in-phase double bond stretch vibration in polyenes.' The addition of one, or more, acetylenic groups in the conjugated framework has two immediately perceivable consequences: the first is geometrical in nature and consists of the formation of linear CCC bonds; the second is the presence of extra x orbitals in the plane of the molecular frame. But for the case of polyynes, the extra x electrons do not participate in the main conjugation and in the low-lying electronic excitations of the main conjugated chain. It may not be straightforward to predict whether their contribution leads to an enhancement or to a reduction of any given molecular property (vide infra). Besides this rather basic consideration, the investigation of molecules containing one or more acetylenic groups is of interest also in view of the role that sp-hybridized carbon atoms may play in materials science and in the chemistry of the interstellar medium. In this work, I study the absorption and the emission spectra of a prototypical oligomer of polydiacetylene, namely, C14Hg (HCEC-CH=CH-CEC-CH=CH-C"C-CH=CHHCECH), and try to address the issue of the consequences to electron excitation of the presence of acetylenic bonds in the z system. The intent is to put on a solid basis the assignment of the experimental spectra of its capped tert-butyl derivative2and to further use the calculations to gather a better understanding of the role played by the acetylenic bonds in these molecules. To achieve these goals, I use ab initio molecular orbital calculations of the restricted Hartree-Fock (RHF) and the configuration interaction singles (CIS) types. Because of the
* Abstract published in Advance ACS Abstracts, November 1, 1994. 0022-3654/94/2098-13157$04.50/0
size of the molecule, ab initio calculations cannot fully explore the electronically excited state surface. I therefore employ a model that relates the excited state gradient (of the energy derived with respect to the nuclear coordinates) to the FranckCondon parameters which are required to simulate the spectra. With this robust result, I also upgrade the quantum consistent force fielax electrons (QCFFPI)3 to include sp-hybridized carbon atoms. This quantum chemical procedure has been greatly successful in disentangling the electronic spectra of polyenes.' It consists of a force field for the u electrons frame plus a quantum chemical procedure to treat the x electrons (selfconsistent field followed by configuration interaction). The modifications of the computer code bear mainly on the force field part. The linear bond treatment of the energy and its first and second derivatives was implemented according to the formulas proposed by Miller.4 The quantum chemical procedure was affected only because acetylenic carbon atoms have two x orbitals, orthogonal to one another, and the values of the x electron integrals do not depend any longer upon the CC torsional coordinate. The upgraded QCFFPI method was used to optimize the molecular structure of So(lAg), S1(2Ag), and S2(1Bu) and to calculate the vibrational frequencies for these three electronic states. The agreement of the by-necessity smaller set of ab initio calculations with the QCFFPI ones allows to draw conclusions on the nature of the electronic excitation in this type of molecule. Theoretical Background I first obtained the Franck-Condon parameters, B, for the lA,-lBu transition of ClJ-Ig by ab initio molecular orbital calculations. The SO calculations were performed at HartreeFock level with the 6-31G* basis set of atomic orbitals5 The calculations for lB, were performed, with the same basis set, with the CIS (configuration interaction singly excited configurations) procedure6implemented in the Gaussian92 program.' All the singly excited configurations were used in the calculation. The CIS level of theory cannot describe the 2Ag state whose wave function contains a large amount of doubly excited configurations. As long as a C2 axis exists in the system, symmetry forbids the two states to interact electronically. The procedure to calculate the Franck-Condon parameters implies 0 1994 American Chemical Society
13158 J. Phys. Chem., Vol. 98, No. 50, I994
Zerbetto
the association of a harmonic oscillator to each normal mode. The equilibrium position of the totally symmetric modes can, upon electronic excitation, undergo a displacement. It is the amount of this displacement, Le., the change of bond lengths and bond angles, that governs the presence of bands due to a particular normal mode in the electronic spectra. Because of the size of the molecule studied, it is impractical to perform the extensive ab initio geometry optimization of the electronically excited state which is necessary to evaluate the changes in bond lengths and bond angles. I therefore use an approximate approach which holds so long as there is not frequency variation and no normal mode rotation upon electronic excitation. In such an instance, the energy gradient, with respect to the Cartesian coordinates, g, calculated for the final lB, state at the equilibrium position of SO is proportional to the displacement of the geometrical parameters. To show this, one must write the potential energy surface of the excited state both as a Taylor expansion
E = Eo
+ gx + '/,xHx + ...
(1)
and in dimensionless harmonic oscillator coordinates
E = Eo
+ Bvq + 1/2v2q2+ ...
(2)
where E is the energy, g is the energy gradient with respect to the nuclear coordinates, x is a displacement vector, H is the Hessian matrix, B is the vector of the displacements along the normal mode of the excited state potential energy surface with respect to the ground state one, v is the vibrational frequency, and q is the dimensionless coordinate of the harmonic oscillator. The relation between x and q is (3) where the constants n,c, and h have the usual meaning, L is the normal mode vector, and M is the 3N by 3N diagonal matrix of the atomic masses, with N number of atoms. Equating the first-order terms in eqs 1 and 2 and using eq 3 together with the proper conversion factors, one obtains 2408615 =
y3/2
M1/2L
(4)
where the frequencies are in wavenumbers, the energy gradient is in hartreehohr, and the atomic masses are in atomic units. The upgrade of the QCFFPI model was carried out by implementing the calculation of the energy, the first, and second derivatives with respect to nuclear displacements of the linear bending.4 The origin of the difficulty was in the fact that, in the standard formulation implemented in the program, a 180" bond angle yields a discontinuity in the transformation from Cartesian to internal coordinates. The acetylenic carbon atom requires a new parametrization. This was obtained by changing as little as possible the original one. In practice, the modifications to the Morse oscillators associated with the stretches mainly affected the values of the equilibrium positions. In keeping with the formulation of the QCFFPI model, the linear bend was treated as harmonic. This reduces to a single parameter, namely, the force constant, the description of the motion. In Table 1, I show the new values together with the analogous values for the sp2 carbon atom obtained from ref 3, from which I also take the symbols for sake of consistency. The Franck-Condon parameters were also calculated using the upgraded QCFFPI method. The B factors now reads
TABLE 1: C, and CsDzQCFF/PI Parameters bond csp2-c,p2~
c,p-csp csp-csp2
Cs$-H" Csp-H
D
a
81.94 87.94 87.94 103.1 113.1
1.756 1.756 1.756
bond angle C,$ -csp-csp2a 2 Csp2-Csp2-Ho Csp-Cs$-H Csp2-Csp-Csp Csp-Csp-H a
339 420 0.5Ko 52.8 52.8 24.0 24.0 42.0 30.0
csp2-csp~-csp
0.5Kb
0.5F 32.0 32.0 29.5 29.5
bo 1.466 1.38 1.43 1.08 1.065 40
2.56 2.56 2.18 2.18 0 0
From ref 3.
B =0.172~"~(% - ~x$d'2L
(5)
where xfm are the Cartesian coordinates of the final state, in angstroms, and xh are the Cartesian coordinates of the initial state, in angstroms. For the Franck-Condon intensities of harmonic oscillators, a standard treatment is provided in a number of papers? Each spectral line calculated in the Franck-Condon simulation is then broadened by multiplying it by a Gaussian function, e-(v-v,)z/a2
G(v) = where v is the excitation wavenumber, in cm-', vo is the calculated excitation wavenumber, in cm-', and a is a constant, in cm-l, that accounts for the broadening, both homogeneous and inhomogeneous.
Results and Discussion To further the understanding of the electronic properties of this prototypical molecule, I use a combination of ab initio and semiempirical techniques. Their mutual agreement is used to strengthen the assignment of the absorption and emission spectra. Since more extensive excited state calculations are possible at semiempirical level, such an agreement is also used to support the conclusions reached at semiempirical level. The ab initio calculations yielded a total energy for the optimized structure of SO of -534.517 968 au and a vertical transition energy to the lB, state of 36 329 cm-'. To obtain the energy of the onset of the electronic transition, one should substract the Stokes shift, that is, '/&viB?, where i runs over all the normal modes. Before scaling (vide infra), the Stokes shift is calculated to be 31 19 cm-I. One should further subtract the difference of the zero-point energies of lAg and lB,. This quantity is not available in the present ab initio calculations. A study of the lAg-lB, transition of hexatriene'O and octatetraenell has shown that the energy difference in zero-point energy is at least 1000 cm-'. It is safe to subtract this amount from the energy gap. The most resolved spectroscopic data for this type of molecule were obtained by Kohler and Schilke.2 Their work was actually done on the capped ten-butyl derivative and was carried out in 3-methylpentane at 77 K. The 0-0 energy gap was found to be about 26 000 cm-'. The presence of the ten-butyl terminal groups and the influence of the solvent can easily decrease the gap of this very intense electronic transition by a couple of thousand of wavenumbers. Overall, one can conclude that the present calculation probably overestimates the transition energy by some 4000 cm-'. This estimate is in keeping with similar calculations on other conjugated systems.
J. Phys. Chem., Vol. 98, No. 50, 1994 13159
Franck-Condon Structures of C1&I8 TABLE 2: QCFF/PI Excitation Energies, in cm-l, for Cl.QH8 AE(lA,-2Ag) AE(1A,- 1B,,)
25000
1A. geometry
2A, geometry
lB,, geometry
32 086 30 856
23 186 26 658
26 738 28 121
1
20000
TABLE 3: Calculated Frequencies (in cm-') B FranckCondon Parameters, and Stokes Shifts (cm-') for the First Three Singlet States of CJIS B frequencies 1Ag0 2A, lB, 2156(2256) 2103(2164) 1549(1669) 1518 (1635) 1299(1301) 1294(1299) 1277(1271) 1130(1140) 991 (985) 893 (894) 680(732) 552(564) 528 (512) 407(415) 186(188) 161 (158) 61 (64) Stokes shift
2125 2118 2028 2068 1445 1489 1482 1480 1185 1270 1234 1224 1291 1283 1214 1188 1024 1006 941 916 678 679 558 555 537 531 417 413 183 185 162 161 59 59
lA,-lB, 1A -lBu lA,-lB, 2A,-lA, 6-31G* QCFFPI QCFFPI gradient gradient absorption emission
Q&W€"
0.98 0.30 0.12 0.85 0.38 0.14 0.05 0.09 0.22 0.51 0.01 0.06 0.03 0.23 0.28 0.86 0.34 2274
0.60 0.26 0.10 0.95 0.05 0.42 0.01 0.11 0.37 0.42 0.01 0.12 0.02 0.25 0.35 1.08 0.47 1614
0.73 0.16 0.47 0.58 0.44 0.40 0.04 0.01 0.32 0.37 0.00 0.06 0.00
0.25 0.21 0.61 0.09 1382
0.78 0.5 1 0.56 1.43 0.26 0.63 0.02 0.04 0.70 0.45 0.05 0.03 0.18 0.35 0.5 1 1.19 0.21 3537
15000
-t 10000
5000
0
In parentheses are the RHF/6-3 lG* values multiplied by 0.9.
The QCFFPI method was used to optimize the molecular geometry in So( lA,), S1(2Ag), and S2( lB,). The configuration interaction procedure included the lowest 100 singly and doubly excited configurations. In Table 2, one can find the calculated excitation energies for the optimized structures of the three states considered in this work. Interestingly, at the So(lA,) optimized geometry, the vertical excitation finds lB, lower than 2A,. This is compatible with the experiment where the 0-0 transition finds the 2A, state lower than the lB, state. It simply signals that the 2A, equilibrium geometry is more displaced with respect to the lAg geometry than that of the lB, state. This situation is analogous to that of polyenes.' The QCFFPI So(lAg), S1(2Ag), and S2(1B,) vibrational frequencies are given in Table 3. For So(lAg), also the RHF/ 6-31G* frequencies are shown after the usual scaling by 0.9. Substantial frequency shifts are observed upon excitation. As expected, they occur in the C W , C-C, and C-C frequency regions. Both excitations lower the C W and the C-C frequencies which are located above 2000 cm-I and around 1500 cm-', respectively. They also increase the C-C stretch frequencies which assume partial double bond character. Although in keeping with the intuitive notion of decreased double bond character, the frequency shift of the C=C vibrations differs from what happens in polyenes where it actually increases.' The reason for this increase has been discussed extensively before and will not be repeated here;' suffice it to notice that this is a first hint of a different behavior between oligomers of polydiacetylene and oligomers of polyacetylene. Also in Table 3, I show the B displacement parameters obtained ab initio and in the QCF'FPI calculation for the lA,-lB, transition. It is interesting to compare the results obtained by the two procedures using eq 4. The results are rather similar but for the C=C mode, which is more displaced in the ab initio calculation. This reduced QCFFPI activity is partially accounted for by the B factors obtained through full geometry
wavmumben
Figure 1. Simulation of the lAg-lB,, spectrum of cI4&. The vibronic line width is 300 cm-', and the intensity is in arbitrary units: 1, solid line, QCFFRI simulation based on Franck-Condon parameters calculated from the optimized geometries; 2, line with long dashes, QCFF/ PI simulation based on the lB, energy gradient to calculate the FranckCondon parameters; 3, line with short dashes, scaled ab initio simulation based on the lB, energy gradient to calculate the Franck-Condon parameters.
optimization (eq 5). Overall, the agreement can be considered satisfactory. It is interesting to notice the B parameters for the emission show an augmented activity of all the stretch regions. This agrees with the notion that the 2A, state corresponds to a doubly excited state. The Franck-Condon activity of the various vibrations cannot be easily obtained by a direct analysis of the experimental spectra. In particular, the large calculated activity of the 160 cm-' mode is hidden in the envelope of the 0-0 transitions. In the inspection of the experimental spectra, its oversight can even lead to a wrong evaluation of the frequency spacing. One should also remark that such an activity cannot be gathered from the spectra of related molecules such as polyenes. Indeed, similar calculations of the Franck-Condon activity of the vibrations of octatetraene isomers yielded, for the most active bending mode, located above 240 cm-', a B parameter of the order of 0.5-0.6." Two different spectral simulations are in order: The first should compare the three different approaches to calculate the spectrum of the lA,-lB, transition. The second should calculate the absorption and emission spectra of C14Hg. The first simulation is presented in Figure 1. The three calculations yield rather similar results. The ab.initio spectrum differs from the QCFFPI ones because it predicts more intensity in the C W stretch region than in the C=C region. Overall, however, their mutual agreement is satisfactory. The emission spectrum is presented in Figure 2, and the absorption spectrum is given in
Zerbetto
13160 J. Phys. Chem., Vol. 98,No. 50, 1994 25000
6000
5000
20000 Absorplbn speclfum
4000 15000
f-t
Q-t
3000
10000 2000
5000
1000
0
0
-
-
wsvmumben
wavenumben
Figure 2. QCFFPI simulation of the 2A, lA, emission spectrum of C ~ f i 8 . The vibronic line width is 300 cm-l, and the intensity is in arbitrary units.
Figure 3. They should be compared with Figure 1 in ref 2 where the spectra are shown side by side. The agreement is rather satisfactory. In particular, one can notice that the lack of mirror symmetry between absorption and emission is correctly reproduced. In fact, the 0-0 transition is the strongest band in absorption while it is not in emission. One should also note that the intensity of the 1500 cm-' region, that is, the C - C stretch region, is overestimated whereas the intensity of the region above 2000 cm-', that is, the CGC stretch region, is underestimated by the QCFFPI model. In practice, this means that the model tends to overestimate the polyenic nature of C14H8. Because of the successful spectral simulation, one may wish to gain a deeper insight into the properties of this prototypical molecule by examining more in detail the results of the calculations. In particular, the bond lengths presented in Table 4 can explain the effect of electron excitation in this system. In both of the electronically excited states considered in this work, only the two central acetylenic bonds participate in the excitation. When the single and the double bonds are considered, one can notice that the lB, state shows a near equilibration of all these bonds with the exception of C2-C3 bond, which is markedly longer than the others because it experiences the excitation to little extent. If one neglects the central C W bonds, it is readily seen that the bond length variation peaks in the center of the molecule. Hence, one may offer that the best picture for the IB, state consists of an excitation localized in the center of the chain which spreads out rather oblivious of the presence of the acetylenic bonds and tapers off at the end of the chain. The situation is markedly different in 2A, where
Figure 3. QCFFPI simulation of the lA, lB, absorption spectrum of CI&. The vibronic line width is 300 cm-', and the intensity is in arbitrary units.
TABLE 4: QCFFPI Calculated Bond Lengths, in A, of C I A in the First Three Singlet States ClCz C2C3 C3C4 C4C5 C& C6C7 C7C8
1A."
1B.6
2A,b
1.213 (1.189) 1.428 (1.434) 1.362 (1.329) 1.421 (1.431) 1.219 (1.193) 1.419 (1.431) 1.366 (1.330)
1.217 (0.004) 1.415 (-0.013) 1.388 (0.026) 1.390 (0.031) 1.236 (0.017) 1.378 (-0.041) 1.416 (0.050)
1.222 (0.009) 1.388 (-0.040) 1.419 (0.057) 1.364 (00.057) 1.244 (0.025) 1.361 (-0.058) 1.430 (0,064)
In parentheses are the RHF/6-31G* values. In parentheses are the bond lengths difference with respect to lA,.
a strong bond alternation reappears. In this state, the roles of single and double bonds are reversed. Interestingly, the bond lengths at the two sides of the central acetylenic units are nearly equal. If one considers the lack of effects of the excitation at the end of the chain, it appears that the three C-C=C-C fragments behave rather similarly upon excitation. One may therefore offer that the best picture for the 2A, state consists of excitations localized in the butadienic fragments which interact through the central acetylenic bonds whose role, in turn, is to effectively clamp the excitation inside the three fragments. Conclusions I have used ab initio and QCFFPI calculations to examine the nature of the two lowest-lying excited states of C1&. To accomplish this, I have used a simple technique to calculate ab initio the Franck-Condon parameters required to simulate the lA,-IB, spectrum. In the process, I have also upgraded the QCFFPI model to include linear bending and sp-hybridized
Franck-Condon Structures of C ~ ~ H S
J. Phys. Chem., Vol. 98, No. 50, 1994 13161
carbon atoms. The QCFFPI procedure was used to optimize the geometry and calculate the vibrational frequencies of the three lowest-lying singlet states of the molecule at hand. The good agreement between the different simulations of the 1A,lB, spectrum shows that the QCFFPI Hamiltonian can be used to obtain further information on the excited states of molecules containing sp-hybridized carbon atoms. In particular, it simulates well the differences between the 2A, lA, emission spectrum and the lAg lB, absorption spectrum and finds features hidden under the complexity of the experimental spectrum which are not shared by the most closely closely related molecules, namely, the polyenes. It also helps to assess the effect of electron excitation in this molecule. It is found that the two lowest-lying electronic states differ rather markedly. The lB, state almost ignores the presence of the acetylenic bonds and forms an exciton localized at the center of the chain; the 2Ag state, instead, can be described as an excitation equally delocalized on each of the three butadienic fragments of the molecule.
-
-
References and Notes (1) Orlandi, G.; Zerbetto, F.; Zgierski, M. Z. Chem. Rev. 1991, 91, 867 and references therein.
(2) Kohler, B. E.; Schilke, D. E. J . Chem. Phys. 1987, 86, 5214. (3) Warshel, A.; Karplus, M. J . Am. Chem. SOC.1972, 94, 5612. (4) Miller, K. J. J. Comput. Chem. 1990, 11, 336. (5) Hehre, W. J.; Ditchfield, R.; Pople, J. A. J . Chem. Phys. 1972, 56, 2257. Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta 1973, 28, 213. Gordon, M. S.Chem. Phys. Lett. 1980, 76, 163. (6) Foresman, J. B.; Head-Gordon, M.; Pople, J. A.; Frisch, M. J. J. Phys. Chem. 1992, 96, 135. (7) Gaussian 92, Revision B: Frisch, M. J.; Trucks, G. W.; HeadGordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.;Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian, Inc., Pittsburgh, PA, 1992. (8) Zerbetto, F.; Zgierski, M. Z. Chem. Phys. Lett. 1988, 144, 437. Zerbetto, F.; Zgierski, M. Z. Chem. Phys. Letr. 1988, 151, 526. Zerbetto, F.; Zgierski, M. Z. Chem. Phys. Lett. 1989, 157, 515. Zgierski, M. Z.; Zerbetto, F. J. Chem. Phys. 1993, 98, 14. Zgierski, M. Z.; Zerbetto, F. J. Chem. Phys. 1993, 99, 3721. (9) Hemley, R. J.; Lasaga, A. C.; Vaida, V.; Karplus, M. J . Phys. Chem. 1988, 92, 945. Zerbetto, F.; Zgierski, M. Z. Chem. Phys. 1988, 127, 17. (10) Zerbetto, F.; Zgierski, M. Z. J . Chem. Phys. 1993, 98, 4822. (11) Zerbetto, F.; Zgierski, M. Z. J . Chem. Phys. 1994, 101, 1842.
