J . Phys. Chem. 1994,98, 2018-2023
2018
ARTICLES Intramolecular Photoassociation and Photoinduced Charge Transfer in Bridged Diary1 Compounds, 7. A Semiempirical MO Study of Intramolecular Charge Transfer in the Excited Singlet States of Dinaphthylamines Donghai Chen,? Rovshan Sadygov, and Edward C. Limo*$ Department of Chemistry, The University of Akron, Akron, Ohio 44325-3601 Received: October 7, 1993; In Final Form: December 9, 1993”
A semiempirical MO study of the intramolecular charge transfer (CT) in the excited singlet states of dinaphthylamines has been carried out with the program systems MOPAC and ARGUS. The excited-state energies for various conformations of the molecules were obtained, in both the absence and the presence of a polarizable medium, by adding the transition energies calculated with the I N D O 1/S method to the groundstate energies calculated by means of the A M I method. The C T state corresponds to a twisted geometry in which one naphthalene moiety is conjugated with the amino bridge, while the other moiety is perpendicular to the first. The gas-phase energy of this twisted intramolecular C T (TICT) state is only slightly greater than that of the iowest excited singlet (SI) state of smaller dipole moment. In solvent of large dielectric constant, the TICT state is therefore predicted to be the lowest excited singlet state of the molecule. The computed oscillator strength of the absorption to the TICT state is much smaller than that to the lowest-energy excited state of an isolated molecule, so that the increased C T character of the SIstate in polar solvents is expected to lead to a decrease in the radiative decay rate of the state. These results are consistent with the experimental observation of a large fluorescence Stokes shift, and a reduction in the SIradiative decay rate, of the compounds in polar solvents relative to nonpolar solvents.
Introduction In an earlier publication’ of this series, we described the formation of a highly dipolar excited state of dinaphthylamines (DNAs) in solvents of large dielectric constants, as revealed by a large solvatochromic shift of the fluorescence spectra. The steady-state Stokes shift in various solvents followed the LippertMataga equations2
where and ;fl denote the absorption and emission maxima in wavenumbers, respectively, pe - pg is the difference in dipole moment between the excited and ground states, B and n are respectively the static bulk dielectricconstant and optical refractive index of the solvent, and a is the radius of a spherical cavity containing the dipole. Taking a to be 4.1 A, which is an effective radius based on a density of approximately 1.2 g/cm3, we find pe - pg (=Ap) to be ca. 12.6 and 10.4 D for 1,l’-DNA and 2,2’DNA, re~pectively.~These values of Ap are about a factor of 2 greater than the corresponding values for mononaphthylamines (6.0 D for 1-naphthylamineand 4.6 D for 2-naphthylamine,based on a = 3.8 A),’J and the results suggest that a significant fraction of an electron is being transferred from one naphthalene moiety to the other within the same DNA molecule. The lowest excited singlet (SI)state responsible for the strongly Stokes-shifted fluorescence in polar solvents was therefore assigned to an intramolecular charge transfer (CT) state.’ In nonpolar solvents, where the CT character of the excited state is relatively small, the &-state dipole moments of DNAs, as measured by time-
* To whom correspondence should be addressed.
t Permanent address: Malone College, Canton, OH 44709. t Holder of the Gwdyear Chair In Chemistry at The University of Akron. Abstract published in Advance ACS Abstracts, February 1, 1994.
0022-3654/94/2098-2018$04.50/0
resolved microwave conductivity: are relatively small, and they are comparable to those for the corresponding naphthylamine^.^ These results suggest that the nature of the SI-state changes in going from nonpolar to strongly polar solvents. In this paper, we present the results of semiempiricalquantum chemical calculations on the dipole moments and energies of the lower-lying excited singlet states of DNAs. It is shown that the CT state corresponds to a twisted geometry in which one naphthalene moiety is in conjugation with the lone-pair electrons of the amino (-NH-) bridge, while the other is approximately perpendicular to the first. For isolated molecules, this twisted intramolecularcharge transfer (TICT) state is only slightly higher in energy than the lowest excited state. In a medium of high dielectric constant, the TICT state with a large dipole moment is therefore expected to beeither thelowest excited stateor strongly mixed into it, consistent with the experimental observation of the highly polar fluorescent state. For the perpendicular conformation, the computed oscillator strength of the absorption to the TICT state is much smaller than that of the corresponding SO SIabsorption (invacuum),sothat the increasein theCTcharacter of the SIstate is expected to lead to a decrease in the radiative decay rate of the state. The result is in accord with the experimentalobservation that the SIradiativedecayrate, deduced from the quantum yield and mean lifetime of the fluorescence, decreases with increasing solvent polarity.1~3
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Computational Methods Because of the size of the molecular systems involved, it was necessary to use semiempirical methods for the study. The ground-state geometry was optimized using the AM1 Hamiltonian.5 Several starting geometries were used for the geometry optimization to ensure that the optimized structure corresponds to a global minimum. The starting geometries were built using Sybyl6 structure building program on a Silicon Graphics work0 1994 American Chemical Society
Charge Transfer in Dinaphthylamines
The Journal of Physical Chemistry, Vol. 98, No. 8, 1994 2019
TABLE 1: Bond Lengths (r, A) and Torsional Angles (0,
deg) for Ground-State Optimized and Dipolar Conformations of 1.1‘-DNA from AM1 SCF Calculations ~
bondlength r( 1-2) r(2-3) r(3-4) r(4-10) r(10-5) 45-6) 46-7) r(7-8) r(8-9) r( 9-1 0) r(9-4) r(8-11) r( 11-24) r(24-25) r(25-26) r(26-27) r(27-28) r(28-20) 420-2 1) 421-22) r(22-23) r(23-29) r(29-28) r(29-24)
a(8-1 1-24-29) 169.W 2706 1.374 1.414 1.372 1.424 1.420 1.372 1.408 1.394 1.445 1.419 1.423 1.406 1.405 1.392 1.409 1.371 1.420 1.423 1.372 1.414 1.374 1.423 1.419 1.447
1.374 1.414 1.371 1.424 1.420 1.372 1.408 1.393 1.445 1.420 1.424 1.417 1.428 1.388 1.412 1.371 1.421 1.423 1.372 1.415 1.373 1.423 1.419 1.441
bondangles
A
A
~~
(~(8-11-24-29) 169.00 270b 120.49 119.63 120.83 119.53 118.20 121.10 120.23 120.15 120.75 121.04 119.12 118.68 122.63 121.07 120.81 120.10 120.25 118.69 119.05 120.82 119.87 120.48 121.01 118.35 119.46
120.53 119.74 120.88 119.65 117.96 121.25 120.32 120.11 120.66 121.25 119.02 118.65 117.48 120.84 120.68 120.30 119.89 118.90 119.34 120.70 119.95 120.48 120.94 118.41 119.51
Ground-state optimized geometry. Dipolar conformation. station. For all starting geometries, preliminary optimizations were carried out with Sybyl/MOPAC 5.0 (QCPE No. 455),7 again on the Silicon Graphics workstation. Further geometry optimizations with a reduced gradient norm were performed using MOPAC version 6.0 on the Cray Y-MP8/865 computer at the Ohio Supercomputer Center. Geometries were optimized using internal coordinates, and calculations were terminated when the change in heat of formation on successive iterations was less than 1 X lo-’ kcal/mol, the change in density matrix elements on two successive iterations was less than 0.001, and the projected change in geometry is less than 1 X 10-5 A. All calculations were done with full optimization of geometrical variables (bond lengths, bond angles, and dihedral angles). The bond lengths and the bond angles corresponding to the geometry optimized conformation of 1,l’-DNA are presented in Table 1. The ground-state optimized geometry (global minimum) was then used to compute potential curves and dipole moments for the ground electronic state, the first excited state, and the dipolar state (vide infra), as a function of the torsional angle between the two naphthalene moieties (vide infra). For several torsional angles, a partial geometry optimization was also carried out for the ground-state 1,l’-DNA. These geometries were then used to compute the energies and dipole moments of the exicted states. This partial geometry optimization had no significant effect on the excited-state properties, and it was eliminated altogether for 2,2’-DNA. The potential curves and dipole moments for the ground state were all obtained from Sybyl/MOPAC 5.0 on the Silicon Graphics terminal (single-point HF calculation). The excitation energies, oscillator strengths, and the dipole moments in the excited states were computed by using ARGUS8/INDOl/S on the Cray Y-MP8/864 supercomputer and a Sun 4/260 workstation. All INDO 1/Scalculations were performed by using single excitation full SCF/CI (SCI), which includes the configurations with one electron excited from (any) occupied orbital to (any) unoccupied orbital. For each conformation, the total energy of the excited state was computed by adding the excitation energy from the INDOl /Scalculations to the ground-state energy (for the same conformation) from the AM1 calculations. The INDO 1/S
If
B
B
1
Figure 1. Ground-stateoptimizedgeometry (A) and dipolar conformation (B) of dinaphthylamines. Torsion angles 8-1 1-24-25 of 1,l’-DNA and 6-7-36-25 of 2,2‘-DNA were varied to obtain the dipolar geometries.
method could not be used to calculate the ground-state energy at torsional angles where the distance between hydrogen atoms from two different naphthalene moieties is very small. Otherwise, thepotentialcurvesfrom theAM1 and theINDO l/Scalculations were found to be very similar in shape. Since the primary purpose of this work was to probe whether the formation of a low-lying TICT state is possible for the DNAs in a polarizable medium, the solvent was taken as a continuous dielectric. The solvation energies were therefore calculated using
which is applicable when the solvent relaxes fully about a solute dipole (with dipole moment p ) . Acetonitrile with static bulk dielectric constant ( E ) of 37.5 was taken as an example of polar solvents, and the cavity of radius a was assumed to be 4.7 A, which is an effective value based on a density of 1.2 g/cm3. The excited-state energies in acetonitrile were computed by adding the solvation energies to the corresponding excited-state energies of solvent-free systems.9
Results and Discussion ComputationalResults. The energies and the dipole moments of the low-lying excited singlet states of DNAs may be understood in a simple fashion in terms of a four-orbital model composed of two highest occupied MOs (HOMO and HOMO-1) and the two lowest unoccupied MOs (LUMO and LUMO+l). For the optimized ground-state geometry of DNA, shown in Figure 1, all four orbitals are delocalized over the molecule with nearly equal weight on the two naphthalene moieties (Figure 2). As one ring is rotated with respect to the other about the bridging N - C bonds, away from this optimized geometry (see Figure 1 for the definition of the torsional angle), the orbitals become more localized on one ring over the other. The HOMO and LUMO+l are more localized on the same ring, while the HOMO-1 and LUMO are more localized on the other. For the “90O”or ‘perpendicular” conformation in which the two naphthalene rings are approximately perpendicular to each other, the HOMO and LUMO+ 1 are localized almost exclusively on one ring and the HOMO-1 and LUMO are localized almost exclusively on the other ring. These results, which are shown in Figure 3, suggests that the HOMO LUMO excitation (responsible for the La absorption band of the molecule) involve the flow of charge between the two naphthalene rings.
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2020 The Journal of Physical Chemislry, Vol. 98, No. 8, 1994
Chen et al.
Figure2. Molecular orbital plots of 1.1'-DNA in the ground-state optimized geometry: (a) HOMO-I, (b) HOMO, (c) LUMO, (d) LUMO+I. Dark color indicates positive sign. and light color indicates negative sign (of = orbital).
Figure 3. Molecular orbital plots of I,I'-DNA in thedipolar (TICT) conformation: (a) HOMO-I, (b) HOMO, ( c ) LUMO, (d) LUMO+l. Dark color represents positive sign. and light color indicates negative sign.
The calculated energies and dipole moments of the low-lying excited singlet statesof solvent-free DNAsindicatethat theTICT state with a large dipole moment is the fifth excited singlet state (Ss).As expected, the CI coefficients of SI are largely (>70%) composed of HOMO LUMO excitations. Orbital occupancy numbers of the dipolar conformations are given in Table 2. The other low-lying excited singlet states, including SI,have dipole
-
-
moments that are similar to those of the ground state (rc 2 D) and considerably smaller than the excited-state dipole moments of the corresponding naphthylamines. The conformations of the TICTstatesareshownin Figure I . IntheseTICTconformations, one naphthalene ring is in conjugation with the lone-pair orbitals of the amino bridge, while the other ring is very nearly perpendicular to the first. Table 3 lists the charge distributions
Charge Transfer in Dinaphthylamines
The Journal of Physical Chemistry, Vol. 98, No. 8, 1994 2021
TABLE 2 Orbital Occupancy Numbers for CI State of the Dipolar Conformations of Dinaphthylamines from INDO 1/S CdCulati~’ 1 ,l’-DNA HOMO-1 HOMO LUMO LUMO+l
-2967
1
I
2,2’-DNA
so
SI
ss
so
SI
2.0 2.0 0.0 0.0
2.00 1.00 0.05 0.95
1.94 1.06 0.95 0.05
2.0 2.0 0.0 0.0
1.99 1.01 0.05 0.95
S5 1.90 1.10 0.96 0.04
Only the two highest occupied orbitals and the two lowest unoccupied orbitals are included in the CI calculations. a
TABLE 3: Charge Distributions on Con’ugated and Nonconjugated Naphthalene Moieties in hnaphthylamines, As Obtained by INDO l/S-SCI Calculations 1.1’-DNA
2
v
@ -2970 u
-
Y
-2971.
Sa
-2972.
-2973
2.2’-DNA
charge on left ring (e)c 0.0888 0.6563 0.0840 4 . 7 5 2 5 0.0798 4 . 7 6 2 8 0.0867 0.4895 charge on right ring (e)c charge on nitrogen bridge (e)c 4 . 1 6 8 6 0.1062 4 . 1 7 0 7 0.2629 a Ground-stateoptimizedconformation. b Dipolar conformation. See Figure 1 for structures.
%
w
-2e70‘ W
-2971.
--O
-150
-100
-50
0
50
100
150
:
0
Torsional Angle (in degrees)
Figure 7. Same as Figure 5, for 2,2’-DNA. -2071
w Torsionol Angle (in degrees)
Figure 4. Energies of solvent-free 1 ,l‘-DNA as a function of the torsional angle defined in Figure 1. SOis the ground electronic state, SIthe first excited singlet state, and SSthe fifth excited singlet state.
15-
h
0
w
I
55
10-
-u
g
i5
5-
50
100
150
200
250
300
350
400
Torsionol Angle (in degrees)
Figure 5. Dependence of dipole moment of solvent-free 1,l’-DNA on torsional angle.
for the ground and TICT states of the dinaphthylamines. Figure 4 and 5 respectively represent the energies and the dipole moments of SO,SI, and SSstates of solvent-free 1,1’-DNA, as a function of the torsional angle defined in Figure 1.
Corresponding plots for 2,2’-DNA are given in Figures 6 and 7. It should be noted that while the dipole moment of SODNA is small and insensitive to the change in the torsional angle, the Ss dipole moment is very sensitive to the variations in the torsional angle. The largest dipole moment is observed at torsional angles of about 85’ and 270° for 1,l’-DNA and at -looo and 9 5 O for 2,2’-DNA. In both 1,l’-DNA and 2,2’-DNA, theS& electronic energy gap is of the order of 1 eV for all conformations of solventfree molecules. In the presence of a polarizable medium of dielectric constant 37.5, there are drastic changes in the excited-state energies of the perpendicular conformation. More specifically, the TICT (Ss) state is greatly lowered in energy relative to the gas-phase value, and the TICT state becomes the lowest excited singlet state of the molecules, as shown in Figures 8 and 9. These results suggest that the nature of the emitting state (SI) should change in going from nonpolar to polar solvents for both 1,I-DNA and 2,2’-DNA. Table 4 lists the numerical values of the energies and the dipole moments of the So, SI, and Ss states and the oscillator strengths u> of transitions to these states for two different conformations (optimized ground-state geometry and the TICT geometry) of solvent-free 1 ,1’-DNA. Aside from the strong conformational dependence of the Ss dipole moment already noted, the most significant result of Table 4 is that the f value of the Ss transition is very small for the TICT conformation. These results predict that the formation of the TICT state is accompanied by a decrease in the radiative decay rate of the emitting state. Comparison to Experiment. The formation of intramolecular CT states is a well-known phenomenon among directly linked biaryl compounds.10 In such molecules, CT-state formation is favored when the two chromophores are able to twist into a
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Chen et al.
2022 The Journal of Physical Chemistry, Vol. 98, No. 8, 1994
TABLE 4 Computed Energies, Dipole Moments, and Oscillator Strengths for the Grouad-State Optidzed and Dipolar Conformations from INM) l/S-SCI Calculations‘ 1 ,1’-DNA
so -2972.475 energy (eV) dipole moment (D) 1.33 oscillator strength U, -2972.421 energy (eV) 1.63 dipole moment (D) oscillator strength U,
SI
2,2’-DNA
s3
S1
s4
SI
so
SI
sz
s3
S4
ss
Ground-State Optimized Geometries -2969.003 -2968.866 -2968.81 1 -2968.763 -2967.89 -2972.604 -2968.872 -2968.698 -2968.531 -2968.242 -2968.082 1.61 0.87 0.88 1.6 6.68 0.707 2.59 2.36 1.59 1.49 1.34 0.441 0.084 0.077 0.066 0.027 0.091 0.084 0.287 0.093 1.385 Dipolar-State Geometries -2968.619 -2968.655 -2968.497 -2968.309 -2967.971 -2972.454 -2968.689 -2968.848 -2968.681 -2968.492 -2967.852 1.58 2.36 1.59 1.49 16.16 1.26 2.71 0.94 2.48 0.96 15.69 0.061 0.084 0.287 0.093 0.006 0.039 0.011 0.229 0.098 0.077
All ground-state (SO)energies were calculated by AM1, whereas the energies of SIthrough Ss states were obtained by adding the excitation energy from INDO 1/S to the ground-state energy (for the same conformation).
-2973’
.
50
IW
1M
2w
2M
m
sea
I
4w
Torsional Angle (in degrees)
Figure 8. Energies of the ground and excited states of 1,l’-DNA in solvent of dielectric constant 37.5.
.-. P
+
-2969
v
4 p -2970 -2971
the vicinity of the TICT state. Thus, there are reasonable agreements between the calculation and experiment. The calculations also support the experimental conclusion that the increase in dipole moment in going from S, to SI,Le., Ap, is substantially greater in DNAs than in the corresponding naphthylamines (see Introduction). Qualitatively, the greater dipole moments of the TICT states of DNAs relative to the excitedstate dipole moments of thenaphthylamines are easily rationalized. In the TICT conformations of the DNAs, one naphthalene (Np) moiety is in conjugation with the lone-pair orbital of the N H bridge, while the other N p moiety is essentially perpendicular to the first. Thus, in the TICT state of DNAs, the NpNH group acts as an electron donor and the N p moiety as an electron acceptor, as is evident from the charge distributions in Table 3. The larger dipole moments of the DNAs relative to the naphthylamines are simply a reflection of the fact that the NpNH group (or alternatively naphthylamine) is a much better electron donor than the NH2 group (or alternatively ammonia) in the CT interaction with the electron acceptor naphthalene. The radiative decay rate of the SI state can be deduced from the ratio of the measured quantum yield (@)and mean lifetime (7)of fluorescence ( k , = a/.). The results of such measurements indicate that the radiative decay rate decreases with increasing solvent po1arity.l~~For 1,l’-DNA the value of k, decreases by a factor of about 3 when the reaction field parameter or solvent function, (e - 1)/(2e 1) - (n2 - 1)/(2nZ+ l), is changed from 0.17 to 0.31.j This observation is also consisteqt with the theoretical prediction that the increase in the TICT character of the SI state leads to a decrease in the radiative decay rate due to the very small oscillator strength of the TICT state. A question of considerable interest is the degree to which the charge is separated in the SI states of DNAs in acetonitrile. For the completely charge-separated state of DNAs, we would expect a dipole moment of ca. 26 D for 1,l’-DNA based on the 5.5-A center-to-center separation of the two naphthalene moieties at the TICT geometry. The estimated dipole moments are therefore significantly smaller than this value, indicating that the TICT state involves a substantial, but certainly not complete, transfer of a charge between the two naphthalene chromophores. Consistent with this conclusion, picosecond transient absorption spectra of S , DNAs in acetonitrile do not reveal clear evidence of ion pairs (corresponding to naphthylamine cation and naphthalene anion).I4
1
-2972 -
SO
conformation in which the two ?r systems are orthogonal (minimum overlap rule11). The term “twisted intramolecular charge transfer (TICT)” is commonly used to describe this type of CT state.I2 The results of the present calculations indicate that the dinaphthylamines also exhibit TICT-state formation in polar solvents. The S1-state dipole moments (pc) of DNAs have not been measured in polar solvents. However, an estimate can be made by combining A p (=pc - pg) values from the Stokes shift data with the measured ground-state dipole moment (pg = 1.2 D).13 The values so deduced are 13.8 and 11.6 D for 1,l’-DNA and 2,2’-DNA, respectively. The calculated dipole moment (- 16 D) of the TICT state represents an upper limit of the dipole moment of the emitting (viz., SI)state, as there are thermally accessible excited states having much smaller dipole moments in
Conclusion The purpose of this work was to probe computationally whether the formation of a low-lying intramolecular C T state is energetically possible for dinaphthylamines in polar solvents. The results of the study reveal that a low-energy CT state can indeed be formed by twisting one naphthalene moiety with respect to the other about the amine bridge. In solvents of high dielectric constant, this TICT state with a large dipole moment and perpendicular geometry is predicted to be the lowest excited state
Charge Transfer in Dinaphthylamines of the molecules. The results of the semiempirical molecular orbital calculations are qualitatively in accord with the conclusions from experiment. It is our intention tocombine the results of the molecular orbital calculations with a molecular dynamics program to simulate the effects of various solvents on the time evolution of the TICT state.
Acknowledgment. The authors are grateful to Dr. John Warman for the microwave conductivity measurements and for his suggestions concerning the analyses of the Stokes shift data. We are also grateful to the Ohio Supercomputer Center for a generous grant of computer time. This work was supported by a grant (DE-FG02-89ER 14024) from the Office of Basic Energy Sciences of the Department of Energy.
References and Notes (1) Dresncr, J.; Modiano, S. H.; Lim, E. C. J. Phys. Chem. 1992, 96, 4310.
The Journal of Physical Chemistry, Vol. 98, No. 8, 1994 2023 (2) (a) Lippert, E. Z . Naturforsch. 1955, IOA, 5412. (b) Mataga, N.; Kaifu, Y.; Koizumi, M. Bull Chem. Soc. Jpn. 1956, 29,465. (3) Cai, J.; Wang, S.;Lim, E. C. Unpublished results based on new measurements in a series of aprotic solvents. (4) Warman, J. M. Private communications. ( 5 ) Dewar, M. J. S.;Zoebisch, E. G.; Healy, E.F.; Stewart, J. J. P. J. Am. Chem. Soc. 1985,107, 3902. (6) T r i p Associates, St. Louis, MO 63144. (7) Stewart, J. J. P. Frank J. Seiler Research Laboratory, United States Air Force Academy, Colorado Springs, CO 80840. (8) Thompson,M.A. MoleculerScienceR#rchCenter, BattellePacific Northwest Laboratories, Richmond, WA 99352. (9) Majumdar, D.; Sen, R.; Bhattacharyya, K.; Bhattacharyya, S.J. Phys. Chem. 1991,95,4323. (10) Rettig, W.; Zander, M. Ber. Bunsen-Ges. Phys. Chem. 1983, 87, 1143. (1 1) Grabowski, Z. R.; Rotkiewicz, K.; Siemiarczuk, A.; Cowley, D. J.; Bauman, W. Noun J. Chim. 1979, 3,443. (12) Siemiarczuk, A,; Grabowski, Z. R.; Krowczynski, A.; Asher, M.; Ottalenghi, M. Chem. Phys. Lctt. 1977,51, 315. (13) McClellan, A. L. Tables of Experimental Dipole Moments; Rahara Enterprises: El Cemto, CA, 1974; Vol. 2. (14) Modiano, S. H.; Dresner, J.; Lim, E.C. Unpublished results.
