- Email: [email protected]
Solvation dynamics of the fluorenone radical anion by methanol: a direct MO dynamics study
THEO CHEM Journal of Molecular Structure (Theochem) 427 (1998) 19I - I98
ELSEVIER
Solvation dynamics of the fluorenone radical anion by methanol: a direct MO dynamics study Hiroto Tachikawa’ Graduate School
of Engineering, Hokkaido Univer.si~. Sapporo 060. Japan
Received 24 February 1997; accepted 8 May I997
Abstract Solvation dynamics of the fluorenone radical anion by the methanol molecule have been studied by direct MO dynamics calculations. A cluster composed of the fluorenone radical anion and a methanol molecule, [Fl-...MeOH], was considered as a model
of the solvation
[Fl-...MeOHl.,,,,,,d
-
system.
The solvation
process
after vertical
electron
attachment
to the neutral
system,
WI-. ‘.MeOHl,,l,,,d, was treated by direct MO dynamics calculation. The absorption spectrum of the
anionic system was monitored as a function of solvation time. The theoretical calculation shows that the potential energy is slightly decayed as a function of time due to the slight structural relaxation of Fl-, whereas the conspicuous spectral shift was not observed. This is due to the fact that the salvation structure of [Fl-...MeOH] resembles that of the neutral system. The salvation mechanism of the fluorenone radical anion is discussed and compared with that of the benzophenone radical anion. 0 1998 Elsevier Science B.V. Keyw0rd.v: Solvation
dynamics;
Fluorenone
radical anion; Direct MO dynamics
1. Introduction Solvation dynamics has been received much attention from both experimental and theoretical points of view [l]. It is, however, known that measurement of the real-time solvation dynamics is still difficult because the initial structure in the solvation is usually unknown. Recently, we have proposed a simple technique to observe the real-time solvation dynamics on the basis of the theoretical results [2]. The idea proposed by us is illustrated schematically in Fig. 1. The lower curve (a) indicates a potential energy curve along the solvation coordinates. The minimum point is a stable structure (A) for the neutral solvation ’ Fax: 00 8 I 1I 706 7897; e-mail: [email protected] 0166- I280/98/$19.00
system which is usually known. By capturing an excess electron, the potential energy is shifted up to curve b. At point B on curve b, the solute exists as a radical anion having an excess electron. Since the solvation structure of the solute anion is unstable relative to its relaxed structure (point C), structural relaxation (anion solvation) would occur. The solvation structure at point B is approximately the same as that of point A. Therefore measurement of the spectral shift from points B to C may provide direct information on the solvation process. By monitoring the UV/visible spectral shift caused by the anion solvation (re-orientation of the solvent molecules), one can obtain direct information on the real-time solvation dynamics. This is one of the anion solvation (electron attachment) techniques.
0 1998 Elsevier Science B.V. All rights reserved
PII SO1 66- 1280(97)00202-9
/\ /\ w
H. Tachikawa/Journal oj’Molecular Structure (Theochem) 427 (I 998) 191-I 98
192
C
II
__..-0 p\O/"--
H
Fluorenone...CH30H
(FI...MeOH)
solvation system. The result derived from the theoretical calculations is in good agreement with a recent experiment [3]. Fluorenone (Fl), which is similar to the benzophenone molecule, is solvated by several alcohol molecules, as is benzophenone. The time-dependent absorption spectra of the fluorenone radical anion (Fl-) after pulse-irradiation by using the pulse radiolysis technique were measured by several groups [4]. The absorption maximum appears at 560 nm at the earliest time and remains essentially stationary as time proceeds. The Fl- spectrum at 77 K in ethanol is very similar to that observed in MTHF glass at 77 K. No spectral shift was observed experimentally. This spectral feature is very different from that of benzophenone. In the present study, direct MO dynamics calculations were applied to a model solvation system composed of Fll and the methanol molecule in order to investigate the lack of spectral shift of Fll in alcohol. The quantum mechanical and dynamical studies of the FI- solvation system should provide detailed information on the solvation process.
2. Method of calculations
cpa 4Q
A
Fig. 1. Schematic
illustration
for a model of the anion solvation.
On the basis of the above model, we performed the direct MO dynamics calculation of the solvation process of the benzophenone radical anion (BP-) [2]. The theoretical calculations indicated that the spectral shift is mainly caused by the solvation structure around Bp-. This result suggests that the electron attachment (anion solvation) technique may provide important information on the
A 1: 1 cluster, composed of fluorenone and methanol molecules [Fl-...MeOH], was chosen as the model of the anion solvation system, as used in a previous paper for the benzophenone-methanol system [BP-. . .MeOH] [2]. First, the geometry for the corresponding neutral system [Fl...MeOH] was fully optimized by the PM3-MO method [5]. In general, the classical trajectory is performed on an analytically fitted potential energy surface as previously carried out by us [6]. However, it is not appropriate to predetermine the reaction surface of the Fl-...MeOH system due 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 [2]. In the direct dynamics calculations, we assumed that each atom moves as a classical particle on the PM3-MO multi-dimensional potential energy
H. Tachikawa/Journal
of Molecular Structure (Theochem) 427 (I 998) I91 - I98
B
0.0
0.5
Time / Fig. 2. Potential energies (PEs) calculated
surface. The equations molecule are given by m;dv,;/dt
of motion
1.5
1 .o
= F,,
dx,; ldt = V~i where xpr (CL= 1,2,3) are the three Cartesian coordinates of the ith atom with mass m, and Fpi (,u = 1,2,3) are the three components of the force acting on the ith atom. These equations were solved numerically by the Runge-Kutta method. The total energy and angular momentum are conserved throughout the simulations. No symmetry restriction was applied in the calculation of the gradients in the RungeKutta method. The time step size was chosen to be 1 fs, and a total of 20 trajectories was run. Excitation energy (E,,) and oscillator strength (f) at each reaction time were calculated with each geometry obtained for a snapshot at the PM3-CI level of theory.
-
2.0
ps
as a function of time for FI- (A) and (Fl-..,MeOH]
for n atoms in a
193
(B) by the PM3-MP method.
3. Results 3.1. The freejuorenone
radical anion (Fl-)
First, the structure of the neutral fluorenone molecule (Fl) was fully optimized by the PM3-energy gradient method. The C=O moiety of the carbonyl has a planer structure with a C=O distance of 1.2094 A. In the anionic state (Fl-), the C=O bond distance is slightly elongated by 0.030 A, whereas Table 1 CI coefficients and the excitation energies (Eex in eV) of the [FI-,..MeOH] complex calculated by the PM3-Cl method State Ground SOMO SOMO + 1 SOMO + 2 SOMO + 3 Eex
0.990 - 0.044 - 0.003 0.0
1St -
2nd 0.047 0.978 0.041 0.024 I .03
0.0 - 0.045 0.941 0.234 1.33
3rd 0.0 - 0.013 - 0.218 0.924 2.00
194
H. Tachikawa/Journal of Molecular Structure (Theochem) 427 (I 998) 191- 198
vC””
SOMO+l
H
d:_
4
H
H
.. .
H
0
SOM0+2
Fig. 3. Contour maps of important molecular orbitals contributing to the ground and low-lying the singly occupied molecular orbital of [Fl-.‘.MeOH] in the ground state.
SOM0+3
excited states of [Fl-.‘.MeOH].
SOMO denotes
H. Tachikawa/Journal
the whole structure of Fl- is still planer. This feature in Fl- is different from that of the benzophenone radical anion (BP-): the structure of Bp is very deformed by accepting an excess electron. The potential energy (PE) of Fl- starting from the neutral structure is calculated as a function of time by means of the direct MO dynamics method. The result is plotted in Fig. 2(A). The optimized structure of Fl is assumed as the initial structure in the direct MO dynamics calculation. The potential energy gradually decreases with increasing time and reaches a limiting value which is 3.1 kcal mol-’ lower than that of the initial state. This energy lowering is caused by the structural relaxation of Fl-. However, the energy difference and structural deformation are less than those of [Bp-...MeOH] [2].
0.0 ps
I
L
195
of Molecular Structure (Theochem) 427 (1998) 191-IYH
0.05 ps
i---_
3.2. Solvation structure [Fl.. .MeOH] < /
ofjuorenone
and methanol
The structure of [Fl...MeOH] was fully optimized by the PM3-MO method. The molecular distance, which is defined by the O-O distance, is calculated to be 2.7761 A, which is comparable to that of the benzophenone system. Fl in [Fl...MeOH] is very similar to free Fl. By capturing an excess electron, the solvation structure is usually deformed. However, the solvation structure [Fl-...MeOH] is hardly changed except for the C=O bond distance: the distance is slightly elongated by 0.033 A in the anionic system [Fl-. .MeOH]. The excitation energies are calculated by the PM3-CI calculation with the optimized
2.0 ps
-::-:--
Fig. 4. Snapshot of the solvation structure as a function of time.
Table 2 Excitation energies (the first, second and third excited states are denoted by Eex ,, Eexz and Eex, in eV, respectively) and energy shifts (AE in eV) in the [FI-...MeOH] system calculated by the direct MO dynamics method. Oscillator strengths (/ x 10 in a.u) are given in parentheses Time/ps
SOMO +
Eex, 0.00 0.20 0.40 0.60 0.80 I .oo 1.50 2.00
I .49 I .77 I .49 1.68 1.58 I .65 I .6l 1.60
(0.57) (0.48) (0.65) (0.56) (0.67) (0.60) (0.62) (0.59)
I
SOMO + 3
SOMO + 2
AE
Eexz
0.00 0.28 0.00 0.19 0.09 0.16 0.12 0.11
2.10 2.29 2. I9 2.28 2.26 2.28 2.27 2.24
(0.58) (0.50) (0.53) (0.17) (0.37) (0.22) (0.32) (0.34)
AE
Eexi
0.00 0.19 0.09 0.18 0.16 0.18 0.17 0.14
2.74 2.55 2.64 2.58 2.59 2.57 2.60 2.60
AE (0.61) (0.53) (0.52) (0.86) (0.59) (0.78) (0.66) (0.72)
0.00 - 0.19 - 0.10 0.16 - 0.15 0.17 - 0.14 0.14
H. Tachikawa/Journal qf
196
MolecularStructure (Theochem) 427 (I 998) 191-I 98
Table 3 Excitation energies (the first, second and third excited states are denoted by Eex ,, Eexl and Eex, in eV, respectively) and energy shifts (AE in eV) in Fl- calculated by the direct MO dynamics method. Oscillator strengths (fx 10 in a.u) are given in parentheses Timelps
SOMO +
0.00 0.20 0.40 0.60 0.80 1.oo 1so 2.00
I
SOMO + 2
Eex ,
AE
Eexz
1.36 1.61 1.51 1.46 1.54
0.00 0.25 0.15 0.10 0.18 0.16 0.15 0.15
I .96 2.12 2.06 2.04 2.10 2.10 2.10 2.10
(0.51) (0.46) (0.47) (0.50) (0.47) 1.52(0.50) 1.5 I (0.49) 1.5I (0.49)
geometry of [Fl-...MeOH]. The results are summarized in Table 1 together with the CI coefficients for ground and low-lying excited states. Wavefunctions for the ground and low-lying excited states are mainly composed of four Hartree-Fock canonical solutions which are illustrated as contour maps in Fig. 3. As shown in Table 1, the ground state is only expressed by a single determinant which is composed of the singly occupied molecular orbital (SOMO). The ith excited state is also expressed by the electronic state in which an unpaired electron is occupied (SOMO + i). These excited states are mainly expressed by each single determinant. As is clearly seen in Fig. 3, the first and second electronic transitions are assigned to a local excitation band within the carbonyl C=O and a charge transfer band from the carbonyl C=O to the benzene rings,
\e”bn
_
anion
(0.81) (0.31) (0.57) (0.64) (0.46) (0.48) (0.47) (0.47)
SOMO + 3 AE
Eex,
0.00 0.16 0.10 0.08 0.14 0.14 0.14 0.14
2.61 (0.66) 2.58 (1.16) 2.67 2.68 2.63 2.64 2.63 2.63
!5E
(0.99) (1 .OO) (1.08) (1.03) (1.04)
(1.04)
0.00 _ 0.03 0.06 0.07 0.02 0.03 0.02 0.02
respectively. However, the intensity of the first band is negligibly small to observe as the absorption spectrum experimentally. The potential energy (PE) calculated as a function of time is given in Fig. 2(B). The energy is 4.2 kcal mol-’ lower than that of the starting point. This energy difference is similar to that for free Fl-, so that the solvent reorientation energy is negligibly small in [Fl...MeOH]. Snapshots of the solvation structure calculated as a function of time are given in Fig. 4. At time zero, the methanol coordinates to the non-bonding orbital of the carbonyl group with a hydrogen bond (denoted by n-form). The OH bond is located on the carbonyl sp2-plane. The snapshot at time = 1.0 ps indicates that the methanol molecule hardly moves around Fland the hydrogen bond is still remaining. This feature is also obtained at the time of 2 ps. These figures clearly indicate that the solvation structure is hardly changed by forming the anion radical. 3.3. Dynamic spectral shifts
T
t
e-
& n-form
t t e-
neutral
LJ x-form
Benzophenone Fig. 5. Schematic the [FI-...MeOH]
neutral
n-form
n-forr
Fluorenone
representation of the potential and [Bp-.‘.MeOH] systems.
energy curves of
Excitation energies and energy shifts of the excitation energy caused by the structural change of the [Fl-...MeOH] system are given in Table 2. At time zero, the [Fl-...MeOH] system with the neutral geometry has an excitation energy of 1.49 eV for the first electronic excitation. After 2.0 ps (the end of the solvation), the excitation energy is calculated to 1.60 eV, meaning that the spectrum is slightly blue-shifted, although the shift is much smaller than that for Bp- [2]. The second and third
H. TachikawdJournal
cfMolecular
excited states also have the same tendency. These are due to the fact that the solvation structure is hardly changed as clearly shown in Fig. 4. For comparison, the trajectory calculations for the isolated fluorenone molecule was carried out in the same manner. The results are summarized in Table 3. The excitation energy was changed from 1.36 to 1.51 eV by the intramolecular structural relaxation, so that the energy of the spectral shift caused by this unimolecular structural change is only 0.20 eV.
4. Discussion In a previous paper, we carried out similar dynamics calculations of the [Bp-...MeOH] system. The results can be summarized as follows: the solvation structure for the neutral system [Bp...MeOH] is not appropriate for the anionic system [Bp-...MeOH], so that a structural relaxation occurs. This relaxation in [Bp-...MeOH] is caused by both the structural deformation of Bp- and a reorientation of the solvent around the Bp anion. The solvation structure of [Bp...MeOH] has a hydrogen bond where a hydrogen of the methanol molecule coordinates the nonbonding orbital of the carbonyl C=O in Bp which is called the n-form. The most stable structure for the anionic system is a geometry whose the hydrogen coordinates the a* orbital of Bp- (*-form). The spectral shift is mainly caused by the reorientation from n- to 7r-forms. In the present study, the dynamics of the Fll anion solvated by methanol has been studied in order to elucidate the spectral behavior of Fl- in alcohol solution. The direct dynamics calculations indicated that the spectral shift of Fll interacting with MeOH is negligibly small because the structural deformation of Fll is small and the reorientation does not occur in [Fll-..MeOH]. This feature, which is very different from that of BP-, is in good agreement with the experiment [4]. A schematic illustration of the potential energy curves is given in Fig. 5. In the neutral state, both complexes have solvation structures with the n-form. In the anionic state, the energy minimum of [Bp-,..MeOH] is in the a-form, whereas the minimum of Fll is still located in the n-form. Therefore, structural deformation has not occurred in Fl-. The
Structure (Theochem) 427 (1998) 191-198
197
present calculations clearly indicated that this is the origin of lack of spectral shift in Fll. In the present calculation we have introduced some approximations to treat the reaction dynamics and to construct the potential energy surface. It is assumed that the atoms move as classical particles on the potential energy surface. In the calculation of the potential energy surface, we employ the semiempirical PM3 calculations. More elaborate calculations with accurate wavefunctions, such as ab initio dynamics calculations and quantum mechanical treatment, are needed to obtain a deeper insight into the solvation process. Despite the approximations employed here, it is shown that a theoretical characterization enables us to obtain valuable information on the mechanism of the real-time solvation dynamics.
Acknowledgements The author is indebted to the Computer Center at the Institute for Molecular Science (IMS) for the use of the computing facilities. I also acknowledge a partial support from a Grant-in-Aid from the Ministry of Education, Science, Sports and Culture of Japan.
References [I] (a) C. Lienau, A.H. Zewail, _I.Phys. Chem. IO0 (I 996) 18629. (b) A. Matemy, C. Lienau, A.H. Zewail, J. Phys. Chem. 100 (1996) 18650. (c)Q. Liu, C. Wan, A.H. Zewail, J. Phys. Chem. 100 (1996) 18666. [2] H. Tachikawa, J. Phys. Chem. 100 (1996) 17090. [3] Z. Xujia and C.D. Jonah. Chem. Phys. Lett. 245 (1995) 42 I. [4] (a) M. Ogasawara. H. Yoshida. S. Karolczak. C. Stradorski. J. Kroh, Radiat. Phys. Chem. 21 (1984) 7 I I. (b) J.L. Marignier, B. Hickel, Chem. Phys. Lett. 86 (1982) 95. (c) M. Hoshino, S. Arai, M. Imamura, J. Phys. Chem. 7X (1974) 1473. [5] (a) J.J.P. Stewart, J. Comput. Chem. IO (1989) 209. (b) J.J.P. Stewart, J. Comput. Chem. IO (1989) 221. (c) M.J. Frisch. G.W. Trucks, M. Head-Gordon. P.M.W. Gill. M.W. Wong, J.B. Foresman. B.C. Johnson, H.B. Schlegel, M.A. Robb, E.S. Replogle, R. Gomperts, J.L. Andres, K. Raghavachari, J.S. Binkley, C. Gonzalez, R.L. Martin, D.J. Fox. D.J. Defrees, J. Baker. J.J.P. Stewart. J.A. Pople, An ab initio molecular orbital calculation program; GAUSSIAN 92. Revision F.3. Gaussian Inc., Pittsburgh, PA, 1992. [6] (a) H. Tachikawa, Chem. Phys. 21 I (1996) 305. (b) H. Tachikawa, J. Phys. Chem. 99 (1995) 255. (c)
198
H. Tachikawa/Joumal
of Molecular Structure (Theochem) 427 (1998) 191-198
H. Tachikawa, T. Hamabayashi, H. Yoshida, J. Phys. Chem. 99 (1995) 16630. (d) H. Tachikawa, H. Takamura, H. Yoshida, J. Phys. Chem. 98 (1994) 5298. (e) H. Tachikawa, N. Ohta, Chem. Phys. Lett. 224 (1994) 465. (f) H. Tachikawa,
A. Ohtake, H. Yoshida, J. Phys. Chem. 97 (1993) 11944.(g) H. Tachikawa, N. Hokari, H. Yoshida, J. Phys. Chem. 97 (1993) 10035. (h) H. Tachikawa, M. Ogawasawa, J. Phys. Chem. 94 (1990) 1746.
ELSEVIER
Solvation dynamics of the fluorenone radical anion by methanol: a direct MO dynamics study Hiroto Tachikawa’ Graduate School
of Engineering, Hokkaido Univer.si~. Sapporo 060. Japan
Received 24 February 1997; accepted 8 May I997
Abstract Solvation dynamics of the fluorenone radical anion by the methanol molecule have been studied by direct MO dynamics calculations. A cluster composed of the fluorenone radical anion and a methanol molecule, [Fl-...MeOH], was considered as a model
of the solvation
[Fl-...MeOHl.,,,,,,d
-
system.
The solvation
process
after vertical
electron
attachment
to the neutral
system,
WI-. ‘.MeOHl,,l,,,d, was treated by direct MO dynamics calculation. The absorption spectrum of the
anionic system was monitored as a function of solvation time. The theoretical calculation shows that the potential energy is slightly decayed as a function of time due to the slight structural relaxation of Fl-, whereas the conspicuous spectral shift was not observed. This is due to the fact that the salvation structure of [Fl-...MeOH] resembles that of the neutral system. The salvation mechanism of the fluorenone radical anion is discussed and compared with that of the benzophenone radical anion. 0 1998 Elsevier Science B.V. Keyw0rd.v: Solvation
dynamics;
Fluorenone
radical anion; Direct MO dynamics
1. Introduction Solvation dynamics has been received much attention from both experimental and theoretical points of view [l]. It is, however, known that measurement of the real-time solvation dynamics is still difficult because the initial structure in the solvation is usually unknown. Recently, we have proposed a simple technique to observe the real-time solvation dynamics on the basis of the theoretical results [2]. The idea proposed by us is illustrated schematically in Fig. 1. The lower curve (a) indicates a potential energy curve along the solvation coordinates. The minimum point is a stable structure (A) for the neutral solvation ’ Fax: 00 8 I 1I 706 7897; e-mail: [email protected] 0166- I280/98/$19.00
system which is usually known. By capturing an excess electron, the potential energy is shifted up to curve b. At point B on curve b, the solute exists as a radical anion having an excess electron. Since the solvation structure of the solute anion is unstable relative to its relaxed structure (point C), structural relaxation (anion solvation) would occur. The solvation structure at point B is approximately the same as that of point A. Therefore measurement of the spectral shift from points B to C may provide direct information on the solvation process. By monitoring the UV/visible spectral shift caused by the anion solvation (re-orientation of the solvent molecules), one can obtain direct information on the real-time solvation dynamics. This is one of the anion solvation (electron attachment) techniques.
0 1998 Elsevier Science B.V. All rights reserved
PII SO1 66- 1280(97)00202-9
/\ /\ w
H. Tachikawa/Journal oj’Molecular Structure (Theochem) 427 (I 998) 191-I 98
192
C
II
__..-0 p\O/"--
H
Fluorenone...CH30H
(FI...MeOH)
solvation system. The result derived from the theoretical calculations is in good agreement with a recent experiment [3]. Fluorenone (Fl), which is similar to the benzophenone molecule, is solvated by several alcohol molecules, as is benzophenone. The time-dependent absorption spectra of the fluorenone radical anion (Fl-) after pulse-irradiation by using the pulse radiolysis technique were measured by several groups [4]. The absorption maximum appears at 560 nm at the earliest time and remains essentially stationary as time proceeds. The Fl- spectrum at 77 K in ethanol is very similar to that observed in MTHF glass at 77 K. No spectral shift was observed experimentally. This spectral feature is very different from that of benzophenone. In the present study, direct MO dynamics calculations were applied to a model solvation system composed of Fll and the methanol molecule in order to investigate the lack of spectral shift of Fll in alcohol. The quantum mechanical and dynamical studies of the FI- solvation system should provide detailed information on the solvation process.
2. Method of calculations
cpa 4Q
A
Fig. 1. Schematic
illustration
for a model of the anion solvation.
On the basis of the above model, we performed the direct MO dynamics calculation of the solvation process of the benzophenone radical anion (BP-) [2]. The theoretical calculations indicated that the spectral shift is mainly caused by the solvation structure around Bp-. This result suggests that the electron attachment (anion solvation) technique may provide important information on the
A 1: 1 cluster, composed of fluorenone and methanol molecules [Fl-...MeOH], was chosen as the model of the anion solvation system, as used in a previous paper for the benzophenone-methanol system [BP-. . .MeOH] [2]. First, the geometry for the corresponding neutral system [Fl...MeOH] was fully optimized by the PM3-MO method [5]. In general, the classical trajectory is performed on an analytically fitted potential energy surface as previously carried out by us [6]. However, it is not appropriate to predetermine the reaction surface of the Fl-...MeOH system due 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 [2]. In the direct dynamics calculations, we assumed that each atom moves as a classical particle on the PM3-MO multi-dimensional potential energy
H. Tachikawa/Journal
of Molecular Structure (Theochem) 427 (I 998) I91 - I98
B
0.0
0.5
Time / Fig. 2. Potential energies (PEs) calculated
surface. The equations molecule are given by m;dv,;/dt
of motion
1.5
1 .o
= F,,
dx,; ldt = V~i where xpr (CL= 1,2,3) are the three Cartesian coordinates of the ith atom with mass m, and Fpi (,u = 1,2,3) are the three components of the force acting on the ith atom. These equations were solved numerically by the Runge-Kutta method. The total energy and angular momentum are conserved throughout the simulations. No symmetry restriction was applied in the calculation of the gradients in the RungeKutta method. The time step size was chosen to be 1 fs, and a total of 20 trajectories was run. Excitation energy (E,,) and oscillator strength (f) at each reaction time were calculated with each geometry obtained for a snapshot at the PM3-CI level of theory.
-
2.0
ps
as a function of time for FI- (A) and (Fl-..,MeOH]
for n atoms in a
193
(B) by the PM3-MP method.
3. Results 3.1. The freejuorenone
radical anion (Fl-)
First, the structure of the neutral fluorenone molecule (Fl) was fully optimized by the PM3-energy gradient method. The C=O moiety of the carbonyl has a planer structure with a C=O distance of 1.2094 A. In the anionic state (Fl-), the C=O bond distance is slightly elongated by 0.030 A, whereas Table 1 CI coefficients and the excitation energies (Eex in eV) of the [FI-,..MeOH] complex calculated by the PM3-Cl method State Ground SOMO SOMO + 1 SOMO + 2 SOMO + 3 Eex
0.990 - 0.044 - 0.003 0.0
1St -
2nd 0.047 0.978 0.041 0.024 I .03
0.0 - 0.045 0.941 0.234 1.33
3rd 0.0 - 0.013 - 0.218 0.924 2.00
194
H. Tachikawa/Journal of Molecular Structure (Theochem) 427 (I 998) 191- 198
vC””
SOMO+l
H
d:_
4
H
H
.. .
H
0
SOM0+2
Fig. 3. Contour maps of important molecular orbitals contributing to the ground and low-lying the singly occupied molecular orbital of [Fl-.‘.MeOH] in the ground state.
SOM0+3
excited states of [Fl-.‘.MeOH].
SOMO denotes
H. Tachikawa/Journal
the whole structure of Fl- is still planer. This feature in Fl- is different from that of the benzophenone radical anion (BP-): the structure of Bp is very deformed by accepting an excess electron. The potential energy (PE) of Fl- starting from the neutral structure is calculated as a function of time by means of the direct MO dynamics method. The result is plotted in Fig. 2(A). The optimized structure of Fl is assumed as the initial structure in the direct MO dynamics calculation. The potential energy gradually decreases with increasing time and reaches a limiting value which is 3.1 kcal mol-’ lower than that of the initial state. This energy lowering is caused by the structural relaxation of Fl-. However, the energy difference and structural deformation are less than those of [Bp-...MeOH] [2].
0.0 ps
I
L
195
of Molecular Structure (Theochem) 427 (1998) 191-IYH
0.05 ps
i---_
3.2. Solvation structure [Fl.. .MeOH] < /
ofjuorenone
and methanol
The structure of [Fl...MeOH] was fully optimized by the PM3-MO method. The molecular distance, which is defined by the O-O distance, is calculated to be 2.7761 A, which is comparable to that of the benzophenone system. Fl in [Fl...MeOH] is very similar to free Fl. By capturing an excess electron, the solvation structure is usually deformed. However, the solvation structure [Fl-...MeOH] is hardly changed except for the C=O bond distance: the distance is slightly elongated by 0.033 A in the anionic system [Fl-. .MeOH]. The excitation energies are calculated by the PM3-CI calculation with the optimized
2.0 ps
-::-:--
Fig. 4. Snapshot of the solvation structure as a function of time.
Table 2 Excitation energies (the first, second and third excited states are denoted by Eex ,, Eexz and Eex, in eV, respectively) and energy shifts (AE in eV) in the [FI-...MeOH] system calculated by the direct MO dynamics method. Oscillator strengths (/ x 10 in a.u) are given in parentheses Time/ps
SOMO +
Eex, 0.00 0.20 0.40 0.60 0.80 I .oo 1.50 2.00
I .49 I .77 I .49 1.68 1.58 I .65 I .6l 1.60
(0.57) (0.48) (0.65) (0.56) (0.67) (0.60) (0.62) (0.59)
I
SOMO + 3
SOMO + 2
AE
Eexz
0.00 0.28 0.00 0.19 0.09 0.16 0.12 0.11
2.10 2.29 2. I9 2.28 2.26 2.28 2.27 2.24
(0.58) (0.50) (0.53) (0.17) (0.37) (0.22) (0.32) (0.34)
AE
Eexi
0.00 0.19 0.09 0.18 0.16 0.18 0.17 0.14
2.74 2.55 2.64 2.58 2.59 2.57 2.60 2.60
AE (0.61) (0.53) (0.52) (0.86) (0.59) (0.78) (0.66) (0.72)
0.00 - 0.19 - 0.10 0.16 - 0.15 0.17 - 0.14 0.14
H. Tachikawa/Journal qf
196
MolecularStructure (Theochem) 427 (I 998) 191-I 98
Table 3 Excitation energies (the first, second and third excited states are denoted by Eex ,, Eexl and Eex, in eV, respectively) and energy shifts (AE in eV) in Fl- calculated by the direct MO dynamics method. Oscillator strengths (fx 10 in a.u) are given in parentheses Timelps
SOMO +
0.00 0.20 0.40 0.60 0.80 1.oo 1so 2.00
I
SOMO + 2
Eex ,
AE
Eexz
1.36 1.61 1.51 1.46 1.54
0.00 0.25 0.15 0.10 0.18 0.16 0.15 0.15
I .96 2.12 2.06 2.04 2.10 2.10 2.10 2.10
(0.51) (0.46) (0.47) (0.50) (0.47) 1.52(0.50) 1.5 I (0.49) 1.5I (0.49)
geometry of [Fl-...MeOH]. The results are summarized in Table 1 together with the CI coefficients for ground and low-lying excited states. Wavefunctions for the ground and low-lying excited states are mainly composed of four Hartree-Fock canonical solutions which are illustrated as contour maps in Fig. 3. As shown in Table 1, the ground state is only expressed by a single determinant which is composed of the singly occupied molecular orbital (SOMO). The ith excited state is also expressed by the electronic state in which an unpaired electron is occupied (SOMO + i). These excited states are mainly expressed by each single determinant. As is clearly seen in Fig. 3, the first and second electronic transitions are assigned to a local excitation band within the carbonyl C=O and a charge transfer band from the carbonyl C=O to the benzene rings,
\e”bn
_
anion
(0.81) (0.31) (0.57) (0.64) (0.46) (0.48) (0.47) (0.47)
SOMO + 3 AE
Eex,
0.00 0.16 0.10 0.08 0.14 0.14 0.14 0.14
2.61 (0.66) 2.58 (1.16) 2.67 2.68 2.63 2.64 2.63 2.63
!5E
(0.99) (1 .OO) (1.08) (1.03) (1.04)
(1.04)
0.00 _ 0.03 0.06 0.07 0.02 0.03 0.02 0.02
respectively. However, the intensity of the first band is negligibly small to observe as the absorption spectrum experimentally. The potential energy (PE) calculated as a function of time is given in Fig. 2(B). The energy is 4.2 kcal mol-’ lower than that of the starting point. This energy difference is similar to that for free Fl-, so that the solvent reorientation energy is negligibly small in [Fl...MeOH]. Snapshots of the solvation structure calculated as a function of time are given in Fig. 4. At time zero, the methanol coordinates to the non-bonding orbital of the carbonyl group with a hydrogen bond (denoted by n-form). The OH bond is located on the carbonyl sp2-plane. The snapshot at time = 1.0 ps indicates that the methanol molecule hardly moves around Fland the hydrogen bond is still remaining. This feature is also obtained at the time of 2 ps. These figures clearly indicate that the solvation structure is hardly changed by forming the anion radical. 3.3. Dynamic spectral shifts
T
t
e-
& n-form
t t e-
neutral
LJ x-form
Benzophenone Fig. 5. Schematic the [FI-...MeOH]
neutral
n-form
n-forr
Fluorenone
representation of the potential and [Bp-.‘.MeOH] systems.
energy curves of
Excitation energies and energy shifts of the excitation energy caused by the structural change of the [Fl-...MeOH] system are given in Table 2. At time zero, the [Fl-...MeOH] system with the neutral geometry has an excitation energy of 1.49 eV for the first electronic excitation. After 2.0 ps (the end of the solvation), the excitation energy is calculated to 1.60 eV, meaning that the spectrum is slightly blue-shifted, although the shift is much smaller than that for Bp- [2]. The second and third
H. TachikawdJournal
cfMolecular
excited states also have the same tendency. These are due to the fact that the solvation structure is hardly changed as clearly shown in Fig. 4. For comparison, the trajectory calculations for the isolated fluorenone molecule was carried out in the same manner. The results are summarized in Table 3. The excitation energy was changed from 1.36 to 1.51 eV by the intramolecular structural relaxation, so that the energy of the spectral shift caused by this unimolecular structural change is only 0.20 eV.
4. Discussion In a previous paper, we carried out similar dynamics calculations of the [Bp-...MeOH] system. The results can be summarized as follows: the solvation structure for the neutral system [Bp...MeOH] is not appropriate for the anionic system [Bp-...MeOH], so that a structural relaxation occurs. This relaxation in [Bp-...MeOH] is caused by both the structural deformation of Bp- and a reorientation of the solvent around the Bp anion. The solvation structure of [Bp...MeOH] has a hydrogen bond where a hydrogen of the methanol molecule coordinates the nonbonding orbital of the carbonyl C=O in Bp which is called the n-form. The most stable structure for the anionic system is a geometry whose the hydrogen coordinates the a* orbital of Bp- (*-form). The spectral shift is mainly caused by the reorientation from n- to 7r-forms. In the present study, the dynamics of the Fll anion solvated by methanol has been studied in order to elucidate the spectral behavior of Fl- in alcohol solution. The direct dynamics calculations indicated that the spectral shift of Fll interacting with MeOH is negligibly small because the structural deformation of Fll is small and the reorientation does not occur in [Fll-..MeOH]. This feature, which is very different from that of BP-, is in good agreement with the experiment [4]. A schematic illustration of the potential energy curves is given in Fig. 5. In the neutral state, both complexes have solvation structures with the n-form. In the anionic state, the energy minimum of [Bp-,..MeOH] is in the a-form, whereas the minimum of Fll is still located in the n-form. Therefore, structural deformation has not occurred in Fl-. The
Structure (Theochem) 427 (1998) 191-198
197
present calculations clearly indicated that this is the origin of lack of spectral shift in Fll. In the present calculation we have introduced some approximations to treat the reaction dynamics and to construct the potential energy surface. It is assumed that the atoms move as classical particles on the potential energy surface. In the calculation of the potential energy surface, we employ the semiempirical PM3 calculations. More elaborate calculations with accurate wavefunctions, such as ab initio dynamics calculations and quantum mechanical treatment, are needed to obtain a deeper insight into the solvation process. Despite the approximations employed here, it is shown that a theoretical characterization enables us to obtain valuable information on the mechanism of the real-time solvation dynamics.
Acknowledgements The author is indebted to the Computer Center at the Institute for Molecular Science (IMS) for the use of the computing facilities. I also acknowledge a partial support from a Grant-in-Aid from the Ministry of Education, Science, Sports and Culture of Japan.
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