7 September 2001
Chemical Physics Letters 345 (2001) 81±88
www.elsevier.com/locate/cplett
Femtosecond charge transfer dynamics in arti®cial donor/acceptor systems: switching from adiabatic to nonadiabatic regimes by small structural changes T. Fiebig a,*, K. Stock b, S. Lochbrunner b, E. Riedle b a
b
Institut fur Physikalische und Theoretische Chemie, Technische Universitat Munchen, Lichtenbergstr. 4, D-85748 Garching, Germany LS fur BioMolekulare Optik, Sektion Physik, LMU Munchen, 80538 Munchen, Germany Received 21 May 2001; in ®nal form 11 July 2001
Abstract The dynamics of intramolecular charge transfer (CT) in a family of conjugated aromatic electron donor/acceptor (D/ A) systems has been studied by femtosecond pump-probe spectroscopy. Although the compounds have very similar structures we observed vastly dierent CT dynamics, ranging from a few 100 fs to the nanosecond time range. These results show that speci®c modi®cations in the substitution scheme can lead to alterations of the relevant D/A orbitals and thus to drastic changes in the excited state electronic coupling. As a result the CT process switches from the ultrafast adiabatic to the slow nonadiabatic regime. Ó 2001 Elsevier Science B.V. All rights reserved.
1. Introduction In the early 1960s charge transfer (CT) ¯uorescence was observed in both intra- and intermolecular donor/acceptor (D/A) systems. The discovery of dual emission in 4-N,N-dimethylaminobenzonitrile (DMABN) by Lippert et al. [1] and the discovery of intermolecular excited state complexes, so-called exciplexes [2], have laid the foundation for an active and exciting area in molecular sciences. The energetics of exciplex formation between D and A can in principle be understood and predicted when the redox potentials of the two moieties and the S1 energy of the initially excited molecule are known [3]. Hence,
*
Corresponding author. Fax: +49-89-289-13244. E-mail address: ®
[email protected] (T. Fiebig).
linear correlations were found between the exciplex emission maxima, the calculated exciplex energies, and the redox potential dierences Ox EARed ). While the term `exciplex' was origi(ED nally restricted to bimolecular excited complexes, it later became evident that exciplex emission can as well be present in ¯exibly, semirigidly and rigidly bonded D/A systems [4]. CT phenomena have also been extensively investigated in monomeric and oligomeric biaryls where aromatic subunits are connected through single r-bonds [5±10]. In contrast to DMABN and its derivatives, the CT emission maxima of various biaryls correlate well Ox with the redox potential dierence (ED EARed ) of their D and A aromatic subunits [7]. This ®nding implies that the CT state in those systems can be considered as an intramolecular exciplex. The key quantity that determines the coupling regime and therefore the way to describe excited
0009-2614/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 ( 0 1 ) 0 0 8 6 9 - 7
82
T. Fiebig et al. / Chemical Physics Letters 345 (2001) 81±88
state CT processes is the electronic coupling matrix element Vif between the initial and ®nal states [11±13]. Currently, there is a growing interest in details of the electronic coupling Vif , ranging from photosynthesis [12,14,15] to molecular electronics [16,17]. In many systems, D and A are spatially [18,19] and indirect well separated (10±20 A) coupling mechanisms (e.g., superexchange) apply. This kind of CT is found, e.g., in biological systems where the involved media can be DNA [20±22], proteins [23] or membranes [24]. Recently, we have presented a series of pyrenyl biphenyl esters where the electron donor (pyrene) is linked via a phenylene bridge to an aromatic oligoester [10]. By varying the substitution scheme, the electronic delocalization (i.e., the conjugation) in the excited states is strongly changed, and this is thought to result in large alterations of Vif . At the same time the energetics of the relevant excited molecular levels should not be signi®cantly in¯uenced by the substitution, and as a result any observed dierences in CT behavior can be interpreted solely as changes in Vif . In this Letter, we present our ®rst femtosecond time-resolved data that illuminate the actual dynamics of the CT process in three pyrenyl biphenyl ester systems. We have investigated 40 -pyren-1-ylbiphenyl-i,j-dicarboxylic dimethyl ester isomers with i 2,3 and j 3,4 that we abbreviate as 1e23, 1e24 and 1e34 (see Scheme 1). Using pumpprobe spectroscopy we observe an initial ultrafast
H3COOC COOCH3
1e23 H3COOC COOCH3
1e24 COOCH3 COOCH3
1e34 Scheme 1.
internal conversion (IC) process (localized on pyrene), the CT process and the subsequent relaxation in the CT state. We observe strong variations in the CT dynamics and explain them in terms of the topology of the acceptor orbitals. 2. Experimental The experimental setup has been described in detail elsewhere [25,26] and only a short overview is given here. The pyrene derivatives were excited by pump pulses at 340 nm. The transmission changes induced by the subsequent processes were probed at four wavelengths ranging from 480 to 560 nm. This spectral range covers the blue and the red wings of the steady-state ¯uorescence of 1e24 and 1e34 as well as the spectral region for excited state absorption of pyrene [27] and its radical cation [28]. The tunable pump-probe spectrometer is based on two NOPAs [26,29] pumped by a home built Ti:sapphire laser system. The pump pulse (340 nm) was generated by frequency doubling the output of the ®rst NOPA and had a duration of 35 fs. Pump and probe pulses were focused to a spot size of 200 lm in diameter at the sample where the pump pulses had an energy of about 120 nJ. The tunable probe pulses stemming from the second NOPA were about 10 times weaker at the sample and had a pulse duration of typically 20 fs. The cross-correlation and the time zero were measured at the sample position by dierence frequency generation in a 25 lm thick BBO crystal yielding a typical cross-correlation width of 40 fs (FWHM). A sample cell with 1.25 mm thick fused silica windows and a light path of 1 mm was used. In order to determine the shift of the time zero caused by the entrance window and half of the solvent layer, the sample cell ®lled with acetonitrile was positioned in front of the BBO crystal, and the measured time shift was divided by two. To avoid dimerisation in the samples the experiments were carried out at low concentrations (<10 4 M). Therefore we had to use 1 mm cells to get an absorption for the pump pulses in the order of 50% and reasonable transmission changes in the order of 2%. Small dierences in the concentration of the
samples were corrected for in the ®nal data presented. Due to the group velocity dispersion in the solvent our time resolution was thereby smeared out to 100 fs. To check for solvent contributions to the pumpprobe signal we carried out additional measurements of pure acetonitrile and found only small transmission changes that were subtracted from the actual data. The results presented below were obtained with a magic angle geometry for the polarization of the pump and probe pulses to avoid transmission changes due to orientational relaxation. Comparing measurements with dierent polarization settings revealed that the orientational relaxation of the investigated compounds occurs on a time scale of 100 ps. Steady-state absorption spectra of the samples measured before and after the time-resolved experiments were compared with each other and no indications for degradation were found. The compounds have been synthesized, characterized and puri®ed by K uhnle and his coworkers at the Max-Planck-Institute for Biophysical Chemistry in G ottingen. 1 All compounds have been puri®ed by HPLC. Solvents were obtained from Merck (Uvasol, spectroscopic grade). All steady-state ¯uorescence spectra were obtained with a Perkin Elmer LS50 ¯uorimeter. The spectra were intensity corrected using a reference spectrum of a calibrated tungsten halogen lamp. The absorption spectra were recorded with a Varian Cary 5e spectrometer. 3. Results Fig. 1 shows the steady-state absorption and ¯uorescence spectra of 1e23, 1e24 and 1e34 dissolved in acetonitrile. The absorption spectra are characterized by the broadened vibrational structure of the S2 S0 transition of pyrene in solution. The long wavelength edges of the spectra are red-shifted as compared to unsubstituted pyrene.
1 The synthetic procedure used by Dr. K uhnle has never been published. Recently, several related compounds were synthesized as described in [30].
norm. absorption and fluorescence
T. Fiebig et al. / Chemical Physics Letters 345 (2001) 81±88
absorption
83
fluorescence
1e34
1 1e24
1e23 1php 0 350
400 450 500 550 600650 wavelength (nm)
Fig. 1. Steady-state absorption and emission spectra of 1e23, 1e24, 1e34 and the emission spectrum of 1-phenylpyrene (1php), measured in acetonitrile. All spectra have been normalized for easier comparison.
The width of this longest wavelength absorption band is largest for 1e34 and smallest for 1e23. The key observation is that the three compounds have drastically dierent ¯uorescence properties [10]. 1e24 and 1e34 show a pronounced CT-type ¯uorescence band with a Stokes shifted maximum between 500 and 520 nm (which is strongly dependent on the solvent polarity, data not shown) while the ¯uorescence of 1e23 is spectrally more similar to the one of pyrene and in particular 1-phenylpyrene (1php, also shown in Fig. 1). For example, in acetonitrile the Stokes shift for 1e23 is 4200 cm 1 and increases to 9200 and 9500 cm 1 for 1e34 and 1e24, respectively. In addition 1e23 exhibits a weak red-shifted tail in the emission band that indicates dual emission from both a locally excited (LE) pyrene state and a CT state. In this Letter, we demonstrate that the strongly dierent steady-state emission properties result from dierences in the dynamics of these molecules on the ultrafast time scale. The close similarity of all three absorption bands and the CT emission bands of 1e24, 1e34 and 1e23 (red-shifted emission tail) supports our assumption that the energetics are not changed signi®cantly by the diering substitution sites. In Fig. 2 the pump-probe transients from )2 to 9 ps delay time are shown for all isomers for two dierent probe wavelengths and excitation at 340 nm. The curves for 1e24 and 1e34 are very
84
T. Fiebig et al. / Chemical Physics Letters 345 (2001) 81±88
0
1e23
0.001
1
0
1
λ probe= 480 nm
3
λ probe = 480 nm
2
2 x 0.5
2 1
1e24
0
1e23
1e34
8
1e23
0.001
λ probe = 530 nm
change of OD * 1000
∆OD
1e34
λ probe= 500 nm
4 0 8
λ probe= 530 nm
4
1e24 0
1e34
12 8
-2
0
2 4 delay time (ps)
6
8
Fig. 2. Transient absorption for the delay time range )2 to +9 ps for kprobe 480 and 530 nm. 1e24 and 1e34 show very similar dynamics while those of 1e23 deviate strongly.
similar while the ones for 1e23 deviate quite strongly. All curves show an instrument limited increase in optical density at time zero and an ultrafast initial change. For 1e23 the signal does not change signi®cantly after the ®rst few 100 fs while the signals for 1e24 and 1e34 show a large change for the whole interval shown. It will be shown below that this behavior is due to ultrafast CT in 1e24 and 1e34 and extremely slow CT (on our time scale) in 1e23. Generally, there are three contributions to the pump-probe signal: excited state absorption (ESA), stimulated emission, and ground state bleaching. Due to the choice of probe wavelengths, ground state bleaching cannot contribute to the observed signals. Since the molecules show significant ¯uorescence at 480 and 530 nm one must consider a contribution of stimulated emission to the signals. The increase in optical density shows, however, that the ESA is dominant over the
λ probe= 560 nm
4 0 0
1
2 0 delay time (ps)
1
2
Fig. 3. Delay time dependence of the transient absorption of 1e34 and 1e23 at kprobe 480, 500, 530 and 560 nm. In the depicted range up to 2.7 ps the behavior of the compounds diers signi®cantly.
stimulated emission which by itself would give rise to a decrease in optical density. The initial transient absorption is changed by the onset of stimulated emission and by the change of the ESA. In Fig. 3 the experimentally observed pumpprobe transients of 1e34 and 1e23 are shown on an expanded scale for all four probe wavelengths. The curves recorded for 1e24 are not shown since they are very similar to the ones of 1e34. We ®rst analyze the transients for 1e23 since they show simpler dynamics. The transient absorption appears within our time resolution and initially changes with a time constant of about 100 fs. It decreases at the longer wavelengths and slightly increases at 480 nm. This behavior is very similar to the one reported for unsubstituted pyrene [31] where it was interpreted as ultrafast IC
T. Fiebig et al. / Chemical Physics Letters 345 (2001) 81±88
from the optically excited S2 state to the S1 state. The ESA from the S1 state is peaked at 500 nm and the one from the S2 state at 585 nm [27,31]. Since the optical excitation in the investigated compounds is localized on the pyrene moiety, we conclude that the initial relaxation observed in our experiments is caused by the same IC process. Such a rapid IC process has also been found in other molecules [32,33]. We can further expect that this process occurs also in other pyrene derivatives, regardless of the subsequent CT dynamics. After the initial IC the signal for 1e23 barely changes on the time scale of our experiment. For 1e34 the dynamics are much more complex. We ®nd again an instrument limited appearance of transient absorption followed by the 100 fs IC relaxation. This is then followed by a fast contribution with a time constant that increases with the probe wavelength from 300 fs at 480 nm to 600 fs at 560 nm, and ®nally a 3 ps component which will be discussed below. We assign the 300±600 fs time to the intramolecular CT process. The experimental observation of a range of time constants for the dierent probe wavelengths is not surprising since intramolecular vibrational redistribution (IVR) is known to proceed on a similar time scale. The shape and peak position of both the LE and the CT state transient absorption bands will therefore change simultaneously during the CT process. Hence, the observed probe energy dependence of the CT dynamics re¯ects a convolution with IVR as expected for wave packet propagation on a multidimensional energy surface.
85
To understand the dierences we turn to the topology of the relevant molecular orbitals for the CT process. According to the simple one-electron picture for CT (see, e.g. [13]) the LUMO of the biphenyl ester moiety has to accept an electron from an occupied pyrene p-orbital. The LUMOs of the biphenyl esters of 1e23, 1e24 and 1e34 were calculated with the semiempirical AM1 method [34] and are shown in Fig. 4. They were obtained after full geometry optimization. While 1e24 and 1e34 have a large coecient on the connecting carbon atom which leads to a largely delocalized orbital, the LUMO of 1e23 is strictly localized on the outer aromatic ring. The overlap with the pyrene donor orbital is therefore negligible for 1e23, and no electronic coupling through p-orbital overlap is provided to mediate the CT process. In contrast, large overlap and strong electronic coupling exists for 1e24 and 1e34. As reported earlier [10], based on orbital topology arguments one would expect a dramatic variation of Vif caused by changes in the substitution scheme. Such variation could cause a change of the CT process from the adiabatic regime (where the dynamics proceed on a single energy surface) to the nonadiabatic regime 2 (where the rate becomes proportional to jVif j ).
1e23
1e24 4. Discussion 4.1. Molecular orbitals and electronic coupling From the experimental data we ®nd a 300±600 fs decay process for 1e24 and 1e34 after the initial relaxation from the optically excited S2 state to the S1 state and no such process for 1e23. We assign this to ultrafast CT in the ®rst two isomers while CT is slow in the latter one. This interpretation is in agreement with the observation of a largely Stokes shifted ¯uorescence in 1e24 and 1e34 and a LE-type ¯uorescence for 1e23.
1e34
Fig. 4. Calculated LUMOs for the biphenyl ester moieties of 1e23, 1e24 and 1e34. Note that the LUMO of 1e23 is highly localized while the LUMOs of 1e24 and 1e34 are strongly delocalized over both aromatic rings.
86
T. Fiebig et al. / Chemical Physics Letters 345 (2001) 81±88
4.2. 1e34 and 1e24 Guided by the femtosecond pump-probe measurements, the steady-state ¯uorescence spectra and the topology of the D/A orbitals, we propose the following model for photoinduced CT in 1e34 and 1e24 (see Fig. 5). The initial fs pump pulse at 340 nm creates a wave packet in a LE state that is electronically similar to the S2 state of pyrene. Following the excitation, there is an ultrafast IC S2 ! S1 on the time scale of 100 fs. The IC process is mediated by vibrational modes that most likely dier from the ones that are responsible for the CT process. The S1 state in turn is strongly coupled to the CT state due to large orbital overlap. As a result of this strong coupling the wave packet propagates along an adiabatic potential energy surface from the initial (LE) to the product (CT) well. The experimentally observed rate is weakly probe wavelength dependent due to the simultaneous IVR processes. In addition to the initial fs decay of the transient absorption (rise of stimulated emission) there
Fig. 5. Summary of all relevant dynamical processes. After photoexcitation coupling modes induce the motion of the wave packet from the S2 to the S1 state. Depending on the strength of the electronic coupling matrix element between the LE S1 state and the CT state the rate of the transfer process varies dramatically. Excited state absorption (white arrows pointing up) is observed from all states and dominates the stimulated emission (white arrows pointing down) from the LE and CT states. In the steady-state emission spectrum the spontaneous emission (wavy arrows) is observed.
is a slower 3 ps component. The fact that this component appears as a decay of the emission at shorter wavelength (480 nm) and as a corresponding rise at longer wavelength (530 nm) indicates that the overall emission spectrum is shifting towards longer wavelengths. This timedependent Stokes shift is however, slower than the typical solvation times observed for acetonitrile [35]. We therefore attribute this time constant to structural relaxations that involve mainly intramolecular modes. Based on what is known about the relaxation of biarylic compounds it is reasonable to assume that twisting motions are involved in stabilizing the CT state leading possibly to the formation of a twisted intramolecular CT (TICT) state [6,9]. To further test this hypothesis, experiments in solvents of dierent viscosity as well as temperature dependent measurements need to be carried out. 4.3. 1e23 As in 1e34 and 1e24 the initial excitation creates a wave packet in the pyrene-like S2 state of 1e23. Following the ultrafast IC there are no dynamics in the excited state on the ultrafast time scale at any of the wavelengths we studied. However, the appearance of weak dual ¯uorescence in the steady-state spectrum indicates a slow CT process on the time scale of nanoseconds. By changing the substitution scheme we have slowed down the CT dynamics from 1013 to less than 109 s 1 . Although we must consider dierences in the free energy (DG0 ) for CT (as a result of the changes in the substitution schemes), these effects can hardly account for the vastly dierent dynamics observed in 1e23 vs. 1e24 and 1e34. This important conclusion is supported by the spectral position of the (weak) CT emission of 1e23 which is in the same range as the ones for 1e24 and 1e34 (see Fig. 1). For intramolecular exciplexes there should be a correlation between the emission maxima and the free energy for CT [7]. It could be argued that the small electronic coupling in 1e23 is caused by a vanishing overlap between the two biphenylic benzene rings due to out-of-plane twisting. Such a twisting could originate from steric hindrance induced by the
T. Fiebig et al. / Chemical Physics Letters 345 (2001) 81±88
bulky ester substituent in ortho position to the interaromatic r-bond. This mechanism would explain dierent CT dynamics for 1e23 and 1e34. However, the close similarity between the dynamics of 1e24 and 1e34 prove unequivocally that this steric hindrance is not decisive for the CT process. 5. Conclusion In conclusion, the three structurally very similar pyrenyl biphenyl esters presented in this study show vastly dierent dynamics on the fs time scale as predicted earlier from steady-state ¯uorescence spectra and the topology of their D/A orbitals. By comparing 1e24 and 1e34 we have shown that ± although widely assumed ± sterical eects due to bulky substituents around an interaromatic rbond have practically no in¯uence on the initial CT dynamics. However, the dynamics can be dramatically changed by varying the position of an electron-withdrawing (or electron-donating) substituent on one of the aromatic subsystems. Such changes can alter the orbital topologies and thereby the overlap between the relevant D/A orbitals. As a result the electronic coupling element is altered dramatically and the CT process can be switched from the adiabatic to the nonadiabatic regime. Future experiments will also include detailed investigations of electronic coupling eects on the recombination dynamics of these compounds which occur on the nanosecond time scale. Acknowledgements We warmly thank Dr. W. K uhnle (MPI G ottingen) for the synthesis, characterization and puri®cation of the samples and Tanja Bizjak and Uli Schmidhammer for valuable experimental assistance. We also gratefully acknowledge the continuous support by Prof. Wolfgang Zinth and the ®nancial support by the Deutsche Forschungsgemeinschaft (DFG). TF is grateful for ®nancial support from the Emmy Noether-Program by the DFG.
87
References [1] E. Lippert, W. L uder, H. Boos, in: A. Mangini (Ed.), Advances in Molecular Spectroscopy, Pergamon Press, Oxford, 1962, p. 443. [2] H. Leonhardt, A. Weller, Ber. Bunsenges. Phys. Chem. 67 (1963) 791. [3] A. Weller, in: M. Gordon, W.R. Ware (Eds.), The Exciplex, Academic Press, New York, 1975, p. 23. [4] J.W. Verhoeven, T. Scherer, R.J. Willemse, Pure Appl. Chem. 65 (1993) 1717. [5] K. Tominaga, G.C. Walker, W. Jarzeba, P.F. Barbara, J. Phys. Chem. 95 (1991) 10475. [6] W. Rettig, Top. Curr. Chem. 169 (1994) 253. [7] T.v.d. Haar, A. Hebecker, Y. Il'ichev, Y.-B. Jiang, W. K uhnle, K.A. Zachariasse, Recl. Trav. Chim. Pays-Bas 114 (1995) 430. [8] A. Onkelinx, G. Scheitzer, F.C.D. Schryver, H. Miyasaka, M.V.d. Auweraer, T. Asahi, H. Masuhara, H. Fukumura, A. Yashima, K. Iwai, J. Phys. Chem. A 101 (1997) 5054. [9] M. Maus, W. Rettig, G. Jonusauskas, R. Lapouyade, C. Rulliere, J. Phys. Chem. A 102 (1998) 7393. [10] T. Fiebig, W. K uhnle, H. Staerk, Chem. Phys. Lett. 282 (1998) 7. [11] J. Jortner, Biochim. Biophys. Acta 594 (1980) 193. [12] R.A. Marcus, N. Sutin, Biochim. Biophys. Acta 811 (1985) 265. [13] M.D. Newton, Chem. Rev. 91 (1991) 767. [14] D.N. Beratan, J.N. Onuchic, J.N. Betts, B.E. Bowler, H.B. Gray, J. Am. Chem. Soc. 112 (1990) 7915. [15] M.R. Wasielewski, Chem. Rev. 92 (1992) 435. [16] A. Aviram, M. Ratner (Eds.), Molecular Electronics: Science and Technology, New York Academy of Sciences, New York, 1998. [17] J. Jortner, M. Bixon (Eds.), Electron Transfer ± from Isolated Molecules to Biomolecules, Wiley, New York, 1999. [18] J. Bolton, G. McLendon, N. Mataga (Eds.), Electron Transfer in Inorganic, Organic and Biological Systems, American Chemical Society, Washington, DC, 1991. [19] C.C. Moser, J.M. Keske, K. Warncke, R.S. Farid, P.L. Dutton, Nature 355 (1992) 796. [20] P.F. Barbara, E.J.J. Olson, Adv. Chem. Phys. 107 (1999) 647. [21] C. Wan, T. Fiebig, S.O. Kelley, C.R. Treadway, J.K. Barton, A.H. Zewail, Proc. Natl. Acad. Sci. USA 96 (1999) 6014. [22] M. Bixon, B. Giese, S. Wessely, T. Langenbacher, M.E. Michel-Beyerle, J. Jortner, Proc. Natl. Acad. Sci. USA 96 (1999) 11713. [23] G. McLendon, Acc. Chem. Res. 21 (1988) 260. [24] J. Schrenzel, L. Srrander, B. Ban®, O. Nusse, R. Fouyouzi, D.P. Lew, N. Demaurex, K.H. Krause, Nature 392 (1998) 734. [25] S. Lochbrunner, A.J. Wurzer, E. Riedle, J. Chem. Phys. 112 (2000) 10699.
88
T. Fiebig et al. / Chemical Physics Letters 345 (2001) 81±88
[26] E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sp orlein, W. Zinth, Appl. Phys. B 71 (2000) 457. [27] P. Foggi, L. Pettini, I. Santa, R. Righini, S. Califano, J. Phys. Chem. 99 (1995) 7439. [28] T. Shida, Electronic Absorption Spectra of Radical Ions, Elsevier, New York, 1988. [29] T. Wilhelm, J. Piel, E. Riedle, Opt. Lett. 22 (1997) 1494. [30] M. Beinho, W. Weigel, M. Jurczok, W. Rettig, C. Modrakowski, I. Br udgam, H. Hartl, A.D. Schl uter, Eur. J. Org. Chem. (accepted).
[31] F.V.R. Neuwahl, P. Foggi, Laser Chem. 19 (1999) 375. [32] W. Fu, K.-L. Kompa, S. Lochbrunner, A.M. M uller, T. Schikarski, W.E. Schmid, S.A. Trushin, Chem. Phys. 232 (1998) 161. [33] M. Schmitt, S. Lochbrunner, J.P. Shaer, J.J. Larsen, M.Z. Zgierski, A. Stolow, J. Chem. Phys. 114 (2001) 1206. [34] MO P A C 6.0: QCPE program #455. [35] S.J. Rosenthal, X. Xie, M. Du, G.R. Fleming, J. Chem. Phys. 95 (1991) 4715.