17090
J. Phys. Chem. 1996, 100, 17090-17093
ARTICLES Dynamic Spectral Shift of Benzophenone Radical Anion Caused by the Solvent Molecule Reorientation. Semiempirical PM3-MO and Classical Trajectory Studies Hiroto Tachikawa Graduate School of Engineering, Hokkaido UniVersity, Sapporo 060, Japan ReceiVed: April 17, 1996; In Final Form: August 2, 1996X
The spectral shifts for the first electronic transition of the benzophenone anion radical (Bp-) caused by solvent geometrical reorientation have been investigated by means of semiempirical PM3-MO and classical trajectory calculations. A methanol molecule (MeOH) and the complex composed of Bp- and a methanol molecule (Bp-‚‚‚MeOH complex) were chosen as a solvent molecule and a solvated reaction system, respectively. The classical trajectories of the Bp-‚‚‚MeOH complex following vertical electron attachment to the neutral system have been calculated by the Runge-Kutta method on the PM3 multidimensional potential energy surfaces. The calculations suggested that the solvation structure of the neutral Bp‚‚‚MeOH complex is largely changed by accepting an excess electron: the binding site of the hydrogen bond of MeOH is changed from the nonbonding to the π* orbitals in carbonyl CdO. This structural change occurred as a unimolecule within the Bp-‚‚‚MeOH complex. With the change of the solvation structures, the absorption spectra of Bp- were gradually blue-shifted as a function of reaction time. The solvation mechanism was discussed on the basis of the theoretical results.
1. Introduction Absorption spectra of CdO carbonyl compounds have been extensively studied in a variety of solvents and indicate that low-lying excited states (e.g., nπ* and ππ* states) are largely affected by the solvents. This solvent effect appears as a spectral shift.1 It is considered that the dielectric constant of the polar solvent causes the spectral shift known as a solvatochromic shift.2 The spectral shift is also caused by forming a hydrogen bond between a CdO carbonyl group and a proton of the solvent. The n-π* and π-π* transitions in the carbonyl compounds are blue- and red-shifted by the hydrogen bond, respectively.3 Theoretical studies indicate that the blue-shift is due to the fact that an optimal hydrogen bond formed in the ground state is completely broken in the excited state.4 The origin of the spectral shifts in anion radicals of the CdO carbonyl compounds has not been clearly understood as compared with the neutral systems. Huddleson and Miller5 observed the time dependent absorption spectra of the benzophenone radical anion (Bp-) in ethanol by means of the pulse radiolysis technique. They found that the spectrum of the benzophenone anion generated by pulse irradiation is shifted as a function of time. The spectrum peaking at λmax ) 780 nm (1.59 eV) after pulse irradiation is immediately shifted to λmax ) 650 nm (1.91 eV) after 170 µs, meaning that the spectrum of the benzophenone anion radical is largely blue-shifted in ethanol. They concluded on the basis of the experimental results that the spectral shift is caused by the solvent dipole reorientation. Recently, Jonah and Lin6 investigated the solvation of the benzophenone anion in several alcohols by using pump-probe pulse radiolysis technique. The solvation process was faster for smaller alcohols. To understand the dependence of the X
Abstract published in AdVance ACS Abstracts, September 15, 1996.
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spectral shift as a function of solvent, they have made Monte Carlo computer simulations of a model dipolar solvent and pointed out that the position and orientation of the solvent dipole play an important role in determining the solvent spectral shift.7 The blue-shifts in the benzophenone radical anion were also observed by steady state spectroscopy at low temperature.8,9 Shida et al. measured the absorption spectrum of the anion radical in several glassy matrices and attributed the spectral shift to hydrogen bonding.8 A similar conclusion was obtained by Ichikawa et al.9 To explain the spectral shift, they suggested a structural model that the solvent alcohol is hydrogen-bonded to a π* orbital of the benzophenone anion radical occupied by unpaired electron. In the present study, the semiempirical molecular orbital (PM3 level) and classical trajectory calculations are performed for elucidating quantum-mechanically the origin of the spectral shifts in the benzophenone anion radical in alcohol. Quantum mechanical and dynamical studies of the anion solvation system would provide detailed information on the solvation process and the spectral shift. 2. Method of Calculation MO Calculations. The complex composed of benzophenone and methanol was chosen as a model of the solvation system. Geometries for both the neutral (Bp‚‚‚MeOH) and negatively charged (Bp-‚‚‚MeOH) systems were fully optimized by the semiempirical PM3 molecular orbital (MO) method. The excited state wave functions were obtained by means of the singly excited configuration interaction (SECI) method within the PM3 level of theory.10 The active spaces for the CI calculations were chosen for 12 orbitals with 7 electrons. The CI dimension was 72 in the present study. Classical Trajectory Calculations. In general, the classical trajectory is performed on an analytically fitted potential energy © 1996 American Chemical Society
Benzophenone Radical Anion surface as previously carried out by us.11 However, it is not appropriate to predetermine the reaction surface of the Bp-‚‚‚MeOH system owing to the large number of degrees of freedom (3N - 6 ) 72, where N is number of atoms in the reaction system). Therefore, in the present study, we applied the classical trajectory calculation with all degrees of freedom.12 In the trajectory calculations, first, a trajectory was calculated from the optimized geometry of the Bp‚‚‚MeOH complex up to 0.2 ps. At the start of the trajectory calculation, atomic velocities are adjusted to give a temperature of 77 K. This temperature is the usual one for experimental conditions in a low-temperature matrix.8,9 The initial geometries of the Bp-‚‚‚MeOH anionic system were randomly selected from the configurations generated within the time period of 0.2-0.3 ps by the trajectory calculation for the neutral system. Secondly, the trajectory of the Bp-‚‚‚MeOH anionic system was run for 2 ps. The potential energy (total energy) and energy gradient at each time step were calculated by the PM3-MO method. In the calculation of the classical trajectory, we assumed that each atom moves as a classical particle on the PM3 multidimensional potential energy surfaces. The equations of motion for n atoms in a molecule are given by
J. Phys. Chem., Vol. 100, No. 43, 1996 17091
Figure 1. Potential energy of the (Bp-‚‚‚MeOH) complex calculated as a function of time. The values at each point are calculated by PM3MO method.
mi dVµi/dt ) Fµi dxµi/dt ) Vµi where xµi (µ ) 1, 2, 3) are the three Cartesian coordinates of the ith atom with mass mi and the Fµi’s are the three components of the force acting on the ith atom. These equations were numerically solved by the Runge-Kutta method.9 No symmetry restriction was applied in the calculation of the gradients in the Runge-Kutta method. The time step size was 1 fs, and a total of 20 trajectories was run. Excitation energies and oscillator strengths at each reaction time were calculated with each geometry obtained for a snap-shot at the PM3-SECI level of theory. For comparison, the trajectories for the isolated benzophenone anion radical were also calculated in the same manner. 3. Results of the MO Calculations First, we performed the geometry optimization of the neutral complex composed of benzophenone and methanol molecules (Bp‚‚‚MeOH). The fully optimized parameters obtained by the PM3 method are as follows: r(CdO) ) 1.2219 Å, r(O‚‚‚HOMe) ) 1.8178 Å, and the dihedral angle between the two benzene rings is 82.7°. This structure was used for the initial geometry of the classical trajectory on the neutral system of Bp‚‚‚MeOH. The geometry optimization of the Bp-‚‚‚MeOH complex gave two different solvation structures: one is a structure where a hydrogen of MeOH coordinates to a nonbonding orbital of CdO carbonyl in Bp (n coordination form) and the other is a structure where the hydrogen coordinates to the π* orbital of the carbonyl CdO (π* coordination form). The π* coordination form is slightly energetically favored over the n coordination form. For the anionic system, the extensive features of the geometrical change from the neutral system can be summarized as follows. The CdO bond length is slightly elongated, and the sp2 orbital of the CdO carbonyl group is changed to a sp3 orbital. The dihedral angle of the two rings was 47.1°, which is closer to planer than that of the neutral Bp molecule. 4. Results of the Classical Trajectory Calculations The potential energy of the Bp-‚‚‚MeOH system for a sample trajectory at 77 K, calculated as a function of time, is plotted
Figure 2. Snap-shot of the solvation structure as a function of time.
in Figure 1. The values at each step are calculated by the PM3MO method. The potential energy for the trajectory started at time zero and gradually decreases with reaction time accompanied with oscillation. This energy change strongly suggests that the neutral geometry is not appropriate for the anion system and that the geometry of the anion at the initial point is spontaneously changed at 77 K to a more stable structure. For comparison, the same trajectory calculation was carried out at 4 K. However, the transfer of the methanol molecule in the complex did not occur because there is a very small activation barrier between the n and π* coordination forms. Snap-shots of the solvation structure calculated as a function of time are given in Figure 2. At time zero, the methanol hydrogen coordinates to the nonbonding orbital of carbonyl group with a hydrogen bond (the n coordination form). The OH bond is located on the carbonyl sp2 plane (upper figure). After 2 ps (lowest figure), the coordination structure finally reaches the π* coordination form, which corresponds to the most stable structure. Figure 2 (middle) shows a transient snap-shot from n to π* coordination forms. These figures clearly indicate that the solvation structure is considerably changed by forming the anion radical. In addition to the position of methanol, the structure of Bp- is slightly changed itself as a function of time. Shifts of the excitation energy caused by the structural change of the Bp-‚‚‚MeOH are given in Table 1 together with excitation energies. At time zero, the Bp-‚‚‚MeOH system with the neutral geometry has an excitation energy of 0.73 eV. After 2.0 ps (the end of the reaction), the excitation energy is calculated to 1.23 eV, meaning that the spectrum is largely blue-
17092 J. Phys. Chem., Vol. 100, No. 43, 1996
Tachikawa
TABLE 1: Excitation Energies (Eex in eV), Energy Shift (∆E in eV), and Oscillator Strength (f in au) Calculated by the Trajectory Calculationsa
a
time/ps
Eex
∆E
f
0.0 0.02 0.20 0.40 0.60 0.80 1.00 2.00
0.69 0.79 1.15 1.16 1.09 1.23 1.12 1.11
0.0 0.099 0.461 0.465 0.398 0.539 0.427 0.41
0.122 0.123 0.170 0.186 0.137 0.128 0.159 0.187
All values are averaged with the results of 20 trajectories.
Figure 3. Structural model of benzophenone anion solvation: (upper) solvation structure for neutral benzophenone by methanol; (lower) most stable solvation structure for benzophenone anion radical. The solvation structure is varied from the n coordination form to the π* coordination form in anion solvation.
shifted. It can be clearly seen in Table 1 that the change of the solvation structure causes a spectral shift in the Bp-‚‚‚MeOH system, although the intensities of the electronic excitation, i.e., oscillator strengths, are almost unchanged. For comparison, the trajectory calculations for the isolated benzophenone molecule were carried out in the same manner. The excitation energy was changed from 0.76 to 0.96 eV by the intramolecular structural relaxation, so the energy of the spectral shift caused by this unimolecular structural change is only 0.20 eV. 5. Discussion 5.1. Physical Origin of the Spectral Shift. In the present study, the classical trajectories of Bp- anion solvated by a methanol have been calculated in order to elucidate the spectral shift of Bp- in alcohol solution. First, we discuss the physical origin of the spectral shift. The present calculations clearly indicate that the first solvation structure of the Bp-‚‚‚MeOH formed at 77 K was spontaneously changed without an apparent activation barrier from n to π* coordination forms. This structural change destabilizes the first excited state because the hydrogen bond is broken at the excited state. In addition, the ground state is slightly stabilized by the interaction between the π*CO orbital and the hydrogen atom of MeOH so that the spectrum of Bp- is blue-shifted in alcohol solution. It can be concluded that the origin of the spectral shift is a position change of solvent molecule (i.e., the solvent molecule reorientation). A schematic representation of a model of solvent reorientation in the Bp-‚‚‚MeOH system is given in Figure 3. The final structure (i.e., the π* coordination form) corresponds to that
postulated by Ichikawa et al. for explaining the spectral shift.9 At the neutral system, the hydrogen-bonded structure where the OH group of MeOH orients toward the n orbital is most stable, whereas the π* coordination form becomes the energetically more favored structure in the anionic system. If an excess electron is injected into the neutral system, the solvation structure is gradually varied toward the π* coordination form. It should be emphasized here that the solvent molecule is spontaneously transferred within the Bp-‚‚‚MeOH complex at 77 K. The present trajectory calculations strongly suggested that the molecular reorientation is dominant in the spectral shift in the Bp-‚‚‚MeOH system. In addition, the final stable structure is the π* coordination form with the O-H bond orientation. 5.2. Comparison with Experiments. The energy size of the spectral shift was 0.41 eV in the present calculation, which is close to the experimental values (0.32-0.38 eV),5,9 although the excitation energies were slightly underestimated in the PM3CI calculations. A more accurate wave function (e.g., ab initio CI calculation with large basis sets) may be required to obtain a more realistic excitation energy. A similar calculation for a system composed of a formaldehyde anion and a water molecule is now in progress.15 The preliminary calculation at the ab initio CI/6-311G(d,p) level suggested that the formaldehyde anionwater system causes a spectral shift and a change of the solvation structure as well as the Bp-‚‚‚MeOH system. This suggests that the PM3 trajectory calculation provides a reasonable feature of the Bp-‚‚‚MeOH solvation. A model for the spectral shift of Bp- in alcohol was proposed in the present study, i.e., the spectral shift is mainly caused by the solvent molecule reorientation around the CdO carbonyl group. The model can reasonably explain the experimental features obtained by Jonah and Lin6,7 and by Huddleson and Miller5 as mentioned in the results section. In 1992, on the basis of computer Monte Carlo simulations, Jonah and Lin suggested that the spectral shift is assigned to the position and the orientation of the dipole functional group. Our model is consistent with their results. The solvent dipole reorientation and more solvent molecules surrounding the Bp-‚‚‚MeOH complex may be the secondary matter in the spectral shift. This is due to the fact that the hydrogen bonding energy with a methanol is mostly dominant in the solvation energy. This suggests that the 1:1 Bp-‚‚‚MeOH complex may be a reasonable model for Bp- in alcohol. In the present model system, the solvent relaxation time was about 2 ps, which is much shorter than the experimental value.7b In solution, Bp- is surrounded by a large number of solvent alcohol molecules. The alcohol molecules may prevent the relaxation of the solvent and anion molecules. In addition, the excess energy generated by the structural change of Bp-‚‚‚MeOH may rapidly transfer to the bath modes of solvent molecules. Hence, the relaxation time is largely affected by the solvent molecules. This solvent effect may cause the long relaxation time. In 1975, Newton performed an ab initio MO calculation of the solvated electron system composed of four water molecules and an electron.13 He suggested that the dipole orientation is favored in the solvated electron system. The recent quantum molecular dynamic calculations14 on the solvated electron system, including a large number of solvent molecules, suggested that the OH orientation is dominant. In the present system, we have considered only the 1:1 Bp-‚‚‚MeOH system to treat the reaction dynamics of Bp- in methanol solution. This may cause the underestimation of the relaxation time of the anion system as discussed above. A method to treat more large
Benzophenone Radical Anion solvent molecule systems would be required to obtain more reliable results. 6. Summary On the basis of the theoretical calculations reported here, we can make the following conclusions. (i) The solvation structure for the neutral Bp‚‚‚MeOH system is not appropriate for the anionic Bp-‚‚‚MeOH system, so a structural relaxation occurs. This relaxation corresponds to a reorientation of the solvent around the Bp anion. Although the solvation structure for the neutral system is composed of a geometry where a hydrogen of the methanol molecule coordinates the nonbonding orbital of the CdO carbonyl in Bp, the most stable structure for the anionic system is a geometry whose hydrogen coordinates the π* orbital of Bp- (π* coordination form). (ii) The excitation energy of the Bp- is largely blue-shifted by the solvent reorientation (π* coordination form). This energy shift is mainly caused by an unstable energy level of the excited state due to the fact that the hydrogen bond is broken at the first excited state. The π* interaction in the ground state of Bp-‚‚‚MeOH is slightly stabilized. (iii) The excitation band observed as a blue-shift in experiments is attributed to a transition from the π* orbital localized in the CdO carbonyl to a π* orbital delocalized in the two benzene rings. Therefore, this is an intramolecular charge transfer band from the CdO carbonyl to the benzene rings. Acknowledgment. The author is indebted to the computer center at the Institute for Molecular Science (IMS) for the use of the computing facilities. The author also acknowledges partial support from a Grant-in-Aid for Encouragement of Young Scientists from the Ministry of Education, Science and Culture of Japan.
J. Phys. Chem., Vol. 100, No. 43, 1996 17093 References and Notes (1) See, for example, the following. SolVent Effects in Organic Chemistry; Reichardt, C., Ed.; Weinheim: New York, Verlag Chemie, 1978. (2) For a review, see the following. Suppan, P. J. Photochem. 1990, 50, 293. (3) (a) Brealey, G. J.; Kasha, M. J. Am. Chem. Soc. 1955, 77, 4462. (b) Becker, R. S. J. Mol. Spectrosc. 1959, 3, 1. (4) (a) DeBlt, S. E.; Koppman, P. A. J. Am. Chem. Soc. 1990, 112, 7515. (b) Blair, J. T.; Krogth-Jespersen, K.; Levy, R. M. J. Am. Chem. Soc. 1989, 111, 6948. (c) Fukunaga, H.; Morokuma, K. J. Phys. Chem. 1993, 97, 59. (d) Sanchez, M. L.; Aguilar, M. A., Olivares del Valle, F. J. J. Phys. Chem. 1995, 99, 15758, and references therein. (5) Huddleston, R. K.; Miller, J. Radiat. Phys. Chem. 1981, 17, 383. (6) Jonah, C. D.; Lin, Y. Chem. Phys. Lett. 1992, 191, 357. (7) (a) Lin, Y.; Jonah, C. D. J. Phys. Chem. 1992, 96, 10119. (b) Xujia, Z.; Jonah, C. D. Chem. Phys. Lett. 1995, 245, 421. (8) (a) Shida, T.; Hamil, W. J. Am. Chem. Soc. 1966, 88, 3683. (b) Shida, T.; Iwata, S. J. Am. Chem. Soc. 1973, 95, 3473. (9) Ichikawa, T.; Ishikawa, Y.; Toshida, H. J. Phys. Chem. 1988, 92, 508. (10) (a) Stewart, J. J. P. J. Comput. Chem. 1989, 10, 209. (b) Stewart, J. J. P. J. Comput. Chem. 1989, 10, 221. (11) (a) Tachikawa, H. J. Phys. Chem. 1995, 99, 255. (b) Tachikawa, H.; Hamabayashi, T.; Yoshida, H. J. Phys. Chem. 1995, 99, 16630. (c) Tachikawa, H.; Takamura, H.; Yoshida, H. J. Phys. Chem. 1994, 98, 5298. (d) Tachikawa, H.; Tomoda, S. Chem. Phys. 1994, 182, 185. (e) Tachikawa, H.; Lunnel, S.; Tornkvist, C.; Lund, A. J. Mol. Struct.: THEOCHEM 1994, 304, 25. (f) Tachikawa, H.; Ohtake, A.; Yoshida, H. J. Phys. Chem. 1993, 97, 11944. (g) Tachikawa, H.; Hokari, N.; Yoshida, H. J. Phys. Chem. 1993, 97, 10035. (12) Chen, W.; Hase, W. L.; Schlegel, H. B. Chem. Phys. Lett. 1994, 228, 436. (13) Newton, M. D. J. Phys. Chem. 1975, 79, 2795. (14) See, for examples, the following. (a) Romero, C.; Jonah, C. D. J. Chem. Phys. 1989, 90, 1877. (b) Barnett, R. N.; Landman, U.; Nitzan, A. J. Chem. Phys. 1988, 89, 2242. (c) Rossky, P. J.; Schnitker, J. J. Phys. Chem. 1988, 92, 4277. (15) Tachikawa, H. To be published.
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