Solvatochromic Shift of DonorâAcceptor Substituted Bithiophene in

J. Phys. Chem. B 2008, 112, 4313-4322

4313

Solvatochromic Shift of Donor-Acceptor Substituted Bithiophene in Solvents of Different Polarity: Quantum Chemical and Molecular Dynamics Simulations Suci Meng and Jing Ma* Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistry of MOE, School of Chemistry and Chemical Engineering, Nanjing UniVersity, Nanjing, 210093, People’s Republic of China ReceiVed: October 30, 2007; In Final Form: January 16, 2008

The dependence of excitation energies of the solvatochromic dye, 5-dimethylamino-5′-nitro-2,2′-bithiophene (Me2N-2T-NO2) on the solvent polarity is demonstrated by time-dependent density functional theory (TDDFT) calculations in combination with molecular dynamics (MD) simulations. Three kinds of solvation models, namely, the continuum dielectric model, the discrete approach, and the combined discrete/continuum strategy, are employed to calculate the lowest dipole-allowed excitation energies of Me2N-2T-NO2 in seven solvents with the dielectric constant, , ranging from 2.23 to 111.00. Our calculations demonstrate the limitations of the continuum dielectric model in predicting the solvatochromic shift of Me2N-2T-NO2 in very polar solvents with > 35. The accuracy of the explicit solvent model is largely limited by the size of supermolecular cluster. The combined discrete/continuum solvent model gives a satisfactory description of the bathochromic shift of Me2N-2T-NO2 with increasing solvent polarity, in agreement with the experimental observations.

1. Introduction Donor-acceptor substituted oligothiophenes have attracted extensive experimental and theoretical interest because of their outstanding electronic and nonlinear optical properties.1-18 Usually, the π-conjugated systems are polarized by the donor (D) and acceptor (A) substituents, resulting in stronger intramolecular charge transfer and large dipole moment.16-21 Such D-π-A compounds may be described as a resonant form between (a) a neutral configuration, in which the central π-conjugated spacer displays a fully aromatic structure, and (b) a chargeseparated form, where the central backbone takes the quinoid structure. The relative weight of these two forms depends to a large degree on the surrounding environment (e.g., the external electric field and solvent dielectric field) for a D-π-A system (cf. Scheme 1). It has been demonstrated that the solute-solvent interactions have a significant influence on the UV/vis absorption spectra of D-π-A compounds,22-24 hence they are called the solvatochromic dyes. Among the large variety of donor-acceptor endcapped oligothiophenes, 5-dimethylamino-5′-nitro-2,2′-bithiophene (Me2N-2T-NO2) was found to show a pronounced positive solvatochromic shift, which extends almost over the whole visible range from a nonpolar (e.g., λ ) 446 nm in n-hexane) to a very polar solvent (e.g., λ ) 577 nm in formamide).22,23 Thus, Me2N-2T-NO2 is particularly suitable to be used as a probe for the determination of solvent polarity.24 The search for quantitative relationships between the solvent effects on UV/ vis/near-IR spectra and the solvent parameters has been hindered by the complexity of intermolecular solute-solvent interactions in solutions. It is well-known that the widely used approximate models, such as the continuum dielectric model, discrete approach, and the mixed discrete/continuum strategy (Scheme 2) have their strengths and weaknesses in treating the local and * Author to whom correspondence should be addressed. E-mail: [email protected].

SCHEME 1: Electronic Structures of Thiophene-Based D-π-A Systems in Media

bulk solvent effects.25-35 Therefore, the solvatochromic dye, Me2N-2T-NO2, is also a useful “indicator” to test the performance of different solvent models. Which kind of solVent model is capable to reproduce the gradual decrease in excitation energies with increasing solVent polarity? The solvent effects on Me2N-2T-NO2 have already been addressed by using the continuum dielectric model through quantum chemistry.19,36 The influence of solvents on the dipoleallowed transition energies of Me2N-2T-NO2 in several nonpolar and medium polar solvents (with the dielectric constant, ranging from 2.00 to 46.70) was described using the CNDO/ S-CI method in combination with the self-consistent reaction field (SCRF) in the image-charge representation.36 Recently, the lowest dipole-allowed excitation energies of Me2N-2T-NO2 in n-hexane, carbon tetrachloride, dichloromethane, and dimethyl sulfoxide have been also estimated by performing the timedependent density functional theory (TD-DFT) calculations within the framework of the polarized continuum model (PCM) at the B3LYP/6-31G** level.19 For those studied Me2N-2TNO2 solutions with a very limited range of from 2.23 to 46.70, the TD-DFT transition energies decreased with increasing solvent polarity, in agreement with the experimental observations.22,23 However, the present work will demonstrate that the lowest TD-DFT/PCM excitation energies attain a constant value

10.1021/jp710456p CCC: $40.75 © 2008 American Chemical Society Published on Web 03/13/2008

4314 J. Phys. Chem. B, Vol. 112, No. 14, 2008

Meng and Ma

SCHEME 2: Three Solvation Models: (a) Polarized Continuum Model (PCM); (b) Explicit Solvent Model; (c) Combined Discrete/continuum Strategy

of about 2.45 eV in the very polar solvents with > 35 (subsection 3.3). This is due to the neglect of short-range solute-solvent interactions in the continuum dielectric model. In fact, the local dipole-dipole interactions between solute and solvent are significant for Me2N-2T-NO2 in very polar solvents. In addition, the specific hydrogen bonds are formed in some highly polar solvents such as formamide. The solvent properties in the vicinity of the solute (usually called the first solvation shell) may be quite different from the bulk solvents. Hence, it is necessary to introduce the explicit solvent molecules, especially those around the solute in the more realistic solvent model. We aim to gain comprehensive understanding of the solvation effects on the electronic structures of Me2N-2T-NO2 from the viewpoint of the microscopic solvation structures and local solute-solvent interactions. The continuum dielectric model, the discrete approach, and their combined discrete/continuum strategy37-41 are employed in the present work. The PCM procedure, one of the most widely used continuum dielectric methods,42-48 is applied to study the solvent effects on electronic structures, especially the lowest dipole-allowed vertical excitation energies. Molecular dynamics (MD) simulations with hundreds of discrete solvent molecules are employed to investigate the solution configurations of Me2N2T-NO2 in solutions. On the basis of MD simulations, the supermolecular clusters (solute + solvents) are sampled along the trajectory from the solution configurations in the first solvation shell (cf. Scheme 2). Subsequently, the combined discrete/continuum solvation model, in which the cluster is embedded in the continuum dielectric filed, is applied to consider both the short-range and bulk solvent effects. We investigate the electronic structures of donor-acceptor substituted 2T in seven kinds of solvents spanning from nonpolar (carbon tetrachloride, CCl4: ) 2.23), polar (chloroform, CHCl3: ) 4.90; dichloromethane, CH2Cl2: ) 8.93;

nitrobenzene, C6H5NO2: ) 34.82; dimethyl sulfoxide, DMSO: ) 46.70), to highly polar (water, H2O: ) 78.39; formamide, CHONH2: ) 111.00). It will be demonstrated that the combined explicit and implicit solvent model can give a satisfactory description of the shift in the lowest dipole-allowed excitation energies of Me2N-2T-NO2 with increasing solvent polarity. 2. Computational Details 2.1. Continuum Solvent Model. To evaluate the solvent effects on the electronic structures of Me2N-2T-NO2, the solute was treated by a quantum chemical method through the continuum dielectric model. For some closed shell D-π-A compounds, the RHF (restricted Hartree-Fock)fUHF (unrestricted Hartree-Fock) instability was noted.49,50 Our calculations at the HF/6-31G** level also display RHFfUHF instability for wave functions of Me2N-2T-NO2 in both the gas phase and formamide solution. But density function theory (DFT) does not show such instability for the studied systems. The B3LYP/ 6-31G** and UB3LYP/6-31G** (with broken symmetry) optimizations give the same value of ground-state energy. Thus, the restricted B3LYP calculations were carried out to investigate the electronic structures of Me2N-2T-NO2 in gas phase and solutions. Geometry optimizations and calculations of inter-ring torsional potentials of bithiophene (2T) and Me2N-2T-NO2 were performed in vacuo, and seven kinds of solvents were selected in PCM calculations at the B3LYP/6-31G** level. On the basis of the ground-state geometries, the natural bond order (NBO) charges of Me2N-2T-NO2 in gas phase and solutions were also estimated at the B3LYP/6-311+G** level. The lowest dipoleallowed vertical excitation energies of the isolated Me2N-2TNO2 and the supermolecular clusters (with discrete solvent molecules surrounding a solute) in various media were obtained

Solvatochromic Shift of Donor-Acceptor Bithiophenes

J. Phys. Chem. B, Vol. 112, No. 14, 2008 4315 TABLE 1: Validations of PCFF-Optimized Geometries of Me2N-2T-NO2 (in Gas Phase) and the Inter-ring Bond Length Alternation (BLA) Parameter, in Comparison with B3LYP/6-31G**, and MP2/6-31G** Optimizations. The Experimental Crystal Structure Data Are Also Listed for Comparisons

Figure 1. Evolution of the interaction potentials of Me2N-TNO2‚‚‚HNHCHO dimers as a function of the intermolecular distance, r. The interaction energy corresponds to the energy difference between the isolated molecules. The data are obtained from MP2/6-31G**, B3LYP/6-31G**, and PCFF calculations, respectively.

through TD-DFT/PCM calculations. A comparison of the TDDFT/PCM excitation energies of the embedded supermolecular clusters (explicit solvents + TD-PCM) was also made with the TD-DFT calculations of explicit solvent clusters in vacuo (explicit solvents + TD), in order to survey the influence of the long-range electrostatic interactions coming from the bulk media. All these calculations were carried out by using the Gaussian 03 program.51 2.2. Explicit Solvent Model. Usually, the solvated solute is surrounded by hundreds of solvent molecules. It is rather difficult to investigate the microscopic packing structures of solution by quantum chemical methods; thus, we resorted to the MD simulations. Validations of Force Field. In this work, we adopted the polymer consistent force field (PCFF),52 which had been tested in our previous study of the packing structures of R-oligothiophenes in the amorphous phase53 and solutions.54 To further validate the performance of PCFF in describing the intermolecular interactions between Me2N-2T-NO2 and solvents molecules, the MP2 (second-order Møller-Plesset perturbation theory), B3LYP, and PCFF potential energy curves of O‚‚‚H-N interactions in a dimeric cluster of Me2N-T-NO2‚‚‚HNHCHO as a function of the intermolecular distance, r, were depicted in Figure 1, respectively. The basis set superposition error (BSSE)55 was corrected by the counterpoise method56 for MP2 and B3LYP interaction energies. One can see from Figure 1 that PCFF potentials qualitatively agree with the MP2/6-31G** and B3LYP/6-31G** ones. The minima of all these potential energy curves are located at about 2.2 Å. On the other hand, the restrained optimizations were also performed by fixing the intermolecular distance, r, and minimizing other variables at the MP2/6-31G** and B3LYP/6-31G** level, respectively, as depicted in Figure S1a of the Supporting Information. Two minima are found (2.2 and 2.8 Å for the MP2 method; 2.1 and 2.8 Å for the B3LYP method). Starting from these minima, we obtain the fully optimized structures of dimers. The MP2/631G** full optimization gives only one minimum at 2.16 Å, while the B3LYP method gives two nearly degenerate minima (2.10 and 2.58 Å, cf. Figure S1b) with a very small energy difference of 0.16 kcal/mol. In conclusion, the PCFF can qualitatively describe the intermolecular interactions in the studied systems. The geometry parameters and the inter-ring bond length alternation (BLA) values of Me2N-2T-NO2 obtained from PCFF, B3LYP, and MP2 optimizations as well as the crystal X-ray data23 were compared in Table 1. The PCFF underestimates to some extent the quinonoid character of Me2N-2T-NO2, while

a The bond lengths are in units of angstroms and the dihedral angle is in units of degrees. b The B3LYP/6-31G** geometry of Me2N-2TNO2 was reported in ref 19. c Crystal structure of Me2N-2T-NO2 taken from ref 23.

B3LYP works very well. Consequently, the geometries of Me2N-2T-NO2 optimized from PCM-B3LYP/6-31G** calculations in solutions were directly applied as a rigid body in the following MD simulations. It is also demonstrated from Figure S2 that the choice of the flexible or rigid solute has only a slight effect on the statistic analyses of the solution configurations. MD Simulations. The MD simulations of Me2N-2T-NO2 in CCl4, CHCl3, CH2Cl2, C6H5NO2, DMSO, H2O, and CHONH2 solutions were performed in the canonical (NVT) ensemble at 298 K by using Andersen thermostat.57 Herein, the concentration of solution was assumed to be 0.1 M to mimic a dilute solution. The detailed information of the number of solvent molecules and the cell parameters were tabulated in Table S1. Equations of the motion were integrated using the velocity Verlet algorithm58 with the time step of 1 fs. The periodic boundary condition (PBC) was employed. All MD simulations were carried out using the discover module in Materials Studio package.59 The cutoff of van der Waals interactions was set to be 15.5 Å. The electrostatic interaction was evaluated by the Ewald summation.60 The 1-ns simulation was subsequently carried out after the equilibrium stage had been reached at the temperature of 298 K. Trajectories were collected every 50 fs. Finally, we employed trajectories of the 1 ns for the statistical analysis of solution structures. 2.3. Combined Discrete/Continuum Strategy. On the basis of MD simulations, a cluster model of solvated Me2N-2T-NO2, consisting of solvent molecules in the vicinity of nitro group, was sampled and then embedded in the further PCM calculations. The clusters were sampled at above 5-ps time intervals.40 The TD-DFT/PCM calculations were performed for the “embedded” clusters at the B3LYP/6-31G** level. The average excitation energies were then obtained from 50 snapshots.


Meng and Ma

Figure 3. Electrostatic (∆Ges) and nonelectrostatic (∆Gnones) contributions of solvation free energies of 2T and Me2N-2T-NO2 in different solutions (CCl4, ) 2.23; CHCl3, ) 4.90; CH2Cl2, ) 8.93; C6H5NO2, ) 34.82; DMSO, ) 46.70; H2O, ) 78.39; and CHONH2, ) 111.00). The data are obtained from the PCM calculations at the B3LYP/6-31G** level.

Figure 2. Evolutions of (a) bond length of inter-ring bond and (b) inter-ring bond length alternation (BLA) parameter for 2T and Me2N2T-NO2 with increasing the solvent polarity. The data are obtained from B3LYP/6-31G**/PCM calculations.

3. Results and Discussion 3.1. PCM Study of Ground States. Electronic Structures. The optimized geometries of 2T and Me2N-2T-NO2 in gas phase, CCl4, CHCl3, CH2Cl2, C6H5NO2, DMSO, H2O, and CHONH2 at the B3LYP/6-31G** level are displayed in Tables S2 and S3, respectively. Among them, the B3LYP/6-31G**/ PCM geometries of Me2N-2T-NO2 in CCl4, CH2Cl2, and DMSO have been reported.19 In comparison with 2T, the introduction of dimethylamino (Me2N) and nitro (NO2) groups leads to a significant variation in the geometry of the π-conjugated backbone. The remarkable influence of various solvents on the molecular geometries of Me2N-2T-NO2 is clearly shown in Figure 2, Tables S2 and S3, in contrast to the negligible changes in geometries of the unsubstituted 2T with increasing the medium polarity. The short bonds in the backbone of Me2N2T-NO2 are lengthened and long bonds are contracted as the dielectric constant increases. Different from 2T, the length of the inter-ring bond in Me2N-2T-NO2 decreases dramatically from nonpolar to highly polar solvents (cf. Figure 2a). This suggests that the torsional barrier of inter-ring bond in Me2N2T-NO2 should be higher than that of 2T, as demonstrated by the torsional potential curves plotted in Figure S3. Moreover, the change in torsional potentials of Me2N-2T-NO2 is more apparent than that of 2T with increasing the dielectric constant (Figure S3). The values of inter-ring BLA, δinter, defined as δinter ) (rRR - rRβ)/[(rRR + rRβ)/2],61-65 also tell the difference in geometry between 2T and Me2N-2T-NO2 (cf. Figure 2b). Obviously, the introduction of the donor and acceptor groups decreases the extent of long and short bond alternation, leading to the quinoid structure. Thus, the lowest dipole-allowed excitation energies of Me2N-2T-NO2 are expected to be lower than those of 2T, in line with the experimental observations

(e.g., 4.11 eV (for 2T) vs 2.34 eV (for Me2N-2T-NO2) in CHCl3).22,66,67 The very polar solvent makes the zwitterionic character of Me2N-2T-NO2 more obvious, which can be seen from the difference in NBO charges (cf. Table S4) between two terminal molecular fragments at the B3LYP/6-311+G** level. Therefore, it is not surprising to find from Table S4 that the magnitude of the dipole moment is enhanced with increasing the medium polarity. Solvation Free Energies. We calculate the solvation free energies, ∆Gsol of 2T and Me2N-2T-NO2 in seven solvents at the B3LYP/6-31G** level. The total solvation free energies of 2T and Me2N-2T-NO2 along with their dipole moments are listed in Table S5. It is clear that the value of ∆Gsol of Me2N2T-NO2 is much more sensitive to the solvent polarity than that of 2T. Furthermore, we compare the electrostatic (∆Ges) and nonelectrostatic (∆Gnones) components of solvation free energies of 2T with those of Me2N-2T-NO2, respectively, in a series of solvents, as schematically illustrated in Figure 3. It is well known that nonelectrostatic solvation free energy comprises cavitation (∆Gcav) and dispersion-repulsion (∆Gdis-rep) contributions, which are only correlated with the parameters of solute such as the radius of the cavity, the area of the molecular surface, or the molecular volume.27,68 Thus, the nonelectrostatic contributions (∆Gnones ) ∆Gcav + ∆Gdis-rep) for 2T and Me2N-2T-NO2 are nearly invariable in various solutions (cf. Figure 3). The electrostatic components of solvation free energies (∆Ges) mainly depend on the dipole moment, µ, of the solute and the dielectric constant, , of the medium,25,27 as shown in eq 1,

∆Ges ) -

[

]

- 1 µ2 - 1 2R 12 + 1 R3 2 + 1 R3

-1

(1)

where the parameters R and R denote the polarizability and radius of cavity, respectively. Figure 3 shows that the values of electrostatic contribution, ∆Ges of both 2T and its derivative increase with increasing the solvent polarity when is less than 35. But when the value of is further increased, the electrostatic solvation free energy, ∆Ges, reaches a nearly constant value (∼4.3 kcal/mol for 2T; ∼-11.3 kcal/mol for Me2N-2T-NO2). In the high-polarity limit, i.e., . 1, the factor of ( - 1)/(2 + 1) in eq (1) is close to 1/2, so that the electrostatic contribution of solvation free energy does not change much any more in those highly polar solvents, as shown in eq 2.

∆Ges( . 1) ≈ -

[

1 µ2 R 1- 3 2 R3 R

]

-1

(2)


Figure 4. (a) Radial distribution functions for oxygen atoms (O16 or O15 in Me2N-2T-NO2) to hydrogen atoms in CHCl3 and CH2Cl2 solutions (the statistical error is ( 0.05 Å); (b) probability distributions of O‚‚‚H-C angle of Me2N-2T-NO2 in CHCl3 and CH2Cl2 solutions within the first solvation shell. The data come from the statistical analysis of MD simulations in chloroform and dichloromethane solutions.

3.2. Local Solute-Solvent Interactions: MD Simulations. The solution configurations of Me2N-2T-NO2 in CCl4, CHCl3, CH2Cl2, C6H5NO2, DMSO, H2O, and CHONH2 were investigated by 1-ns MD simulations. The short-range solute-solvent interactions in the studied solutions can be characterized by means of some statistic analyses. Radial distribution functions (RDFs), g(r), are widely used to describe the probability of finding a given particle (atom or molecule) at a distance r from another given particle relative to the pure solvent (Figures 4a, 5a, and S4a). The molecular orientation of solvents populated around the solute can be also displayed by the local angular orientation, θ, as defined in Figures 4b, 5b, and S4b. In addition, the space distribution functions (SDFs)69 are very useful in visualizing the three-dimensional probability distribution of the atoms around a molecule (Figure 6). O‚‚‚H-C Interactions in Polar Solvents. The intermolecular O‚‚‚H-C interactions are not significant in chloroform, dichloromethane, and dimethyl sulfoxide solutions, as shown by the RDFs, gO‚‚‚H(r), for oxygen in Me2N-2T-NO2 to hydrogen in solvents in Figures 4a and S4a. As represented by the first peak of RDFs, the average distances of rO‚‚‚H are located at about

J. Phys. Chem. B, Vol. 112, No. 14, 2008 4317

Figure 5. (a) Radial distribution functions for oxygen atoms (O16 or O15 in Me2N-2T-NO2) to H4, H5, and H6 atoms in formamide (the statistical error is (0.05 Å); (b) probability distributions of O‚‚‚H-C and O‚‚‚H-N angles of Me2N-2T-NO2 in the first solvation shell. The data come from the statistical analysis of MD simulations in formamide solutions.

2.85 Å in both CHCl3 and CH2Cl2, 2.85-2.95 Å in DMSO within the first solvation shell, which are slightly larger than the sum of the van der Waals radii (H+O: 2.72 Å). The statistical probability distributions of O‚‚‚H-C angles, θ, in the first solvation shell in CHCl3, CH2Cl2, and DMSO solutions are depicted in Figures 4b and S4b. The average O‚‚‚H-C angles are distributed about 128° in CHCl3, 116° in CH2Cl2, and 110-120° in DMSO solutions, respectively. Hydrogen Bonding in Formamide Solution. Among the studied systems, formamide solution is of particular importance, because there exist two types of hydrogen bonding, O‚‚‚H-C and O‚‚‚H-N interactions with respect to H4 (H5) and H6, respectively (cf. Figure 5). In order to draw a qualitative picture of the hydrogen bonding interactions, Figure 5 depicts the radial distribution functions, gO‚‚‚H4 (gO‚‚‚H5) and gO‚‚‚H6 for oxygen in Me2N-2T-NO2 to hydrogen atoms in formamide, along with the probability distributions of O‚‚‚H-C and O‚‚‚H-N angles. The average value of rO‚‚‚H4 (2.55 Å) is shorter than that of rO‚‚‚H6 (2.95 Å), and the O‚‚‚H-N angle (about 130°) is larger than O‚‚‚H-C angle (about 110°). This implies stronger O‚‚‚H-N interactions than O‚‚‚H-C ones in formamide solutions, in agreement with the higher electronegativity of nitrogen than that of carbon. In addition, the more favorable dipole-dipole interactions between Me2N-2T-NO2 and CHONH2 molecules with the same dipole orientation give rise to the specific O‚‚‚ H4-N hydrogen bonding interactions rather than O‚‚‚H5-N ones (cf. Figure 5a). Such different intermolecular interactions


Meng and Ma

Figure 6. Three-dimensional probability distributions of hydrogen atoms in (a) CHCl3 and (b) CHONH2 molecules around the nitro group of Me2N-2T-NO2. The isosurface of SDFs is drawn at thresholds of 1.0. Only the backbone of solute is displayed for clarity.

TABLE 2: The Lowest Dipole-Allowed Excitation Energies and Oscillator Strengths (f) of Me2N-2T-NO2 Obtained from TD-DFT Calculations on PCM, the Explicit Solvent Model, and the Combined Model in Various Media. The Data Were Calculated at the B3LYP/6-31G** Level medium ()

TD-PCM (f)a

gas (1.00) CCl4 (2.23) CHCl3 (4.90) CH2Cl2 (8.93) C6H5NO2 (34.82) DMSO (46.70) H2O (78.39) CHONH2 (111.00)

2.78 (0.61) 2.57 (0.75) 2.50 (0.78) 2.48 (0.80) 2.45 (0.83) 2.45 (0.83) 2.45 (0.83) 2.45 (0.83)

explicit solvents + TD (f)b

explicit solvents + TD-PCM (f)b

expt

2.69 (0.51) 2.61 (0.69) 2.62 (0.71)

2.56 (0.57) 2.43 (0.79) 2.42 (0.82)

2.52 (0.59)

2.35 (0.81)

2.54c 2.34c 2.32,c 2.31d 2.23c 2.20c

2.48 (0.57)

2.34 (0.81)

2.15c

a The calculated excitation energies in ref 19 are 2.54 eV (f ) 0.77) in CCl , 2.46 eV (f ) 0.82) in CH Cl , and 2.42 eV (f ) 0.85) in DMSO, 4 2 2 respectively, using TD-DFT/PCM method at the B3LYP/6-31G** level. b The average values obtained from 50 different configurations with explicit solvent molecules in the first solvation shell. c UV-vis absorption maxima at 293 K in the corresponding solvents, taken from ref 22. d UV-vis absorption maxima measured in dichloromethane, taken from ref 11.

can be also shown by the SDFs of hydrogen around nitro group of Me2N-2T-NO2 in formamide solution, illustrated by the gOpenMol package70 in Figure 6. The solvent molecules in the vicinity of nitro group populate around two sides of the plane of solute, exhibiting the ellipse-like distribution. In formamide solution, it is clear that the hydrogen atom in the amido group (H4, shown in white) is closer to the nitro group than is the hydrogen atom in the carbonyl group (H6, shown in green). 3.3. TD-DFT Excitation Energies. Continuum vs Explicit Solvent Models. As mentioned in Introduction, the previous work discussed the solvation effects only spanned from nonpolar ( ) 1.89) to medium polar solutions ( ) 46.70).19 Here, the solvent effects on Me2N-2T-NO2 are extensively investigated with up to highly polar solutions ( ) 111.00). The TD-DFT lowest dipole-allowed vertical excitation energies of Me2N-2TNO2 in gas phase and in seven dielectric media (at the B3LYP/ 6-31G** level), along with available experimental data, are summarized in Table 2. The TD-DFT/PCM results display that the lowest dipoleallowed singlet transition energies of Me2N-2T-NO2 produce a bathochromic shift from )2.23 (CCl4) to 34.82 (C6H5NO2) solvents, which qualitatively agrees with the experimental observations.22,23 Moreover, the oscillator strengths become larger with increasing medium polarity. However, TD-DFT/

Figure 7. Evolution of the lowest dipole-allowed excitation energies, Eex (eV) of Me2N-2T-NO2 as a function of the dielectric constant, of solvent. The data were obtained from TD-PCM (hollow square) and explicit solvents + TD-PCM (solid triangle) calculations at the B3LYP/ 6-31G** level, respectively. The inset presents the experimental excitation energies in various solvents, taken from ref 22.

PCM transition energies converge to a constant value of about 2.45 eV in the case of > 35, different from the continuous decline along the whole range in experiments,22,23 as sketched in Figure 7. The simultaneously anisotropic characters of solvent medium and the local intermolecular interactions cannot be properly described in the continuum solvent model. Therefore,


J. Phys. Chem. B, Vol. 112, No. 14, 2008 4319

Figure 8. (a) Explicit solvation models and (b) combined discrete/continuum strategy with different size of supermolecular clusters. The TD-DFT and TD-PCM excitation energies are calculated at the B3LYP/6-31G** level.

the PCM method may have some limitations in describing the solutions with high polarity and short-range solute-solvent interactions. The TD-DFT calculations on the explicit solvent models evidently overestimate the lowest dipole-allowed electronic excitation energies, with the average deviations of about 0.27 eV from the experimental spectra, probably because of the insufficient retention of crucial subset of explicit molecules in the supermolecular cluster (cf. the second volume of Table 2). The increase in the size of the cluster does improve the accuracy of the explicit solvent model, as shown in Figure 8a. In other words, TD-DFT excitation energies of the explicit supermolecular cluster depend to a large degree on the cluster size. For example, the excitation energy of Cluster I with 7 solvent molecules is about 2.60 eV; on going to Cluster II with 13 solvent molecules, the excitation energy is decreased to 2.57 eV, and the excitation energy is further lowered to 2.54 eV by adding more solvent molecules in Cluster III. However, the quantum chemical calculations on the explicit solvent models with an even larger cluster are impractical, because the computational cost increases exponentially with the system size. On the other hand, the background point charges are introduced for those crucial solvent molecules in the neighborhood of the selected supermolecular cluster to simulate the effects of electrostatic interactions (Figure 8, Table S6). In this model, the solvent molecules around the nitro group are explicitly treated in the first solvation shell, while other adjacent solvents are represented by the electrostatic potential (ESP) partial charges. For the studied system, the background point charges have little influence on the TD-DFT excitation energies as shown in Table S6. Thus, the usage of the background point charges is not sufficient to account for the long-range solutesolvent interactions.

In conclusion, the TD-DFT calculations on both the continuum and the explicit solvation models cannot effectively evaluate the solvatochromic shift of Me2N-2T-NO2 in solutions, especially in highly polar solvents. The Combined Implicit/explicit Solvent Model. A compromise way to consider both local and bulk solvent effects is the combination of the discrete model with the continuum model. The TD-DFT/PCM calculations are performed for the clusters sampled from MD simulations, and the average excitation energies are listed in the third volume of Table 2. The evolution of the lowest singlet transition energies in CCl4, CHCl3, CH2Cl2, DMSO, and CHONH2 is depicted in Figure S5 as a function of the simulation time. The fluctuation of transition energies relative to the average value is less than 5%. The combined explicit and implicit solvent model is demonstrated to have better performance than the PCM calculations in describing the decreasing excitation energies of Me2N-2TNO2 in solutions as the solvent polarity increases (Figure 7). The S0fS1 absorption band is mainly assigned to the transition from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO) state. It is found that the evolution of the HOMO-LUMO gaps, ∆EH-L, is similar to the trend of the lowest vertical transition energies (cf. Table S7). These results indicate that both the short-range and long-range solvation effects should be considered in order to properly describe the observed solvatochromic shifts of Me2N-2T-NO2. It should be mentioned that TD-DFT calculations have some intrinsic limitations in predicting the lowest dipole-allowed transition energies of the cluster models.71 Moreover, the current exchange-correlation functionals are still insufficient in describing the weak intermolecular interactions such as hydrogen bonding and van der Waals interactions in the supermolecular


Meng and Ma concentration, temperature, etc., may also affect the electronic structures of Me2N-2T-NO2. 3.4. Influence of Intermolecular Distances on the Excitation Energies. To investigate the influence of intermolecular distances on transition energies, the lowest dipole-allowed excitation energies are calculated for Me2N-2T-NO2‚‚‚HNHCHO dimers as a function of the intermolecular distance, r, using the TD-DFT method at the B3LYP/6-31G** level. As displayed in Figure 9a, the electronic excitation energies undergo a red shift as the solute-solvent distance decreases. In particular, the change is apparent when the intermolecular distance is very short (e.g., r ) 1.6 Å). In the process of long-wavelength electronic excitations, the main contributions are involved in the transitions of HOMOfLUMO (both are localized on Me2N-2T-NO2) and HOMO-2 (localized on CHONH2)fLUMO, respectively. When the intermolecular distance is in the range of r > 2.0 Å, the intramolecular charge transfer dominates the lowest vertical excitation energies. Obviously, the contribution of intramolecular HOMOfLUMO transition decreases with decreasing the intermolecular distance (cf. Figure 9b). In the case of r ) 1.6 Å, the contribution of HOMO-2fLUMO transition (characterized by a significant intermolecular charge transfer between CHONH2 and Me2N-2T-NO2) increases steeply. That is why the excitation energies of Me2N-2T-NO2 exhibit a significant red shift when the solute and solvent molecules come closer. The evolution of the solute-solvent interactions with the intermolecular distance can also be demonstrated by the NBO analyses of the orbital interaction energies in Figure 9c. The intermolecular nOfσ*N-H interaction between the oxygen lone pair orbitals (nO) and the N-H antibonding orbitals (σ*N-H) is important for the Me2N-2T-NO2‚‚‚HNHCHO dimers. The orbital interaction energy of nOfσ*N-H decreases and gradually converges to a constant with increasing the intermolecular distance. So, it is easy to understand the significant charge transfer from the oxygen lone pair orbitals, nO, of the nitro group to the proximate N-H antibonding orbitals, σ*N-H, of formamide in the case of r ) 1.6 Å. 4. Conclusions

Figure 9. Evolution of (a) excitation energies, Eex, (b) transition contributions, and (c) orbital interaction energies of Me2N-2T-NO2‚‚‚ HNHCHO dimers as a function of the intermolecular distance, r. The excitation energies were calculated by using TD-DFT method at the B3LYP/6-31G** level. The contour plots are drawn for the dominant orbital interactions between the oxygen lone pair orbitals (n1(O), right) and the N-H antibonding orbitals (σ*(N-H), left).

clusters.72 In addition, the intermolecular interactions in the formamide solution may also be underestimated by PCFF force field. For example, the closet O‚‚‚H-N distances obtained from the B3LYP/6-31G** and MP2/6-31G** geometry optimizations are significantly shorter than 2.55 Å (which is predicted by PCFF), even in the clusters with 14 formamide molecules (cf. Figure S6). Other environmental factors such as viscidity,

In this work, the solvatochromic dye, Me2N-2T-NO2, is employed to test the performance of the explicit, implicit, and their combined solvation models in describing the solvent effects on the lowest dipole-allowed vertical excitation energies. A variety of solvents (CCl4, CHCl3, CH2Cl2, C6H5NO2, DMSO, H2O, and CHONH2) are selected with the dielectric constant, , ranging from 2.23 to 111.00. It has been demonstrated that both the explicit and the continuum solvent models do not work well in predicting the solvatochromic shift of Me2N-2T-NO2 in highly polar solvents. In the continuum dielectric model, the anisotropic characters of solvent medium and the short-range intermolecular interactions cannot be properly described. For the explicit solvent model, the TD-DFT excitation energies depend to a large degree on the size of cluster, and the quantum mechanical treatment is still impractical for particularly large clusters at the present stage. Therefore, the solvation effects on Me2N-2T-NO2 are investigated from the viewpoint of the microscopic solvation structure and the short-range solutesolvent interactions by combining quantum chemistry (TD-DFT/ PCM /6-31G**) with MD simulations. It has been demonstrated that the combined explicit and implicit solvent model can satisfactorily describe the solvatochromic shift of Me2N-2TNO2. The calculated excitation energies of Me2N-2T-NO2 through TD-DFT/PCM calculations on the “embedded” supermolecular clusters at the B3LYP/6-31G** level show a batho-

Solvatochromic Shift of Donor-Acceptor Bithiophenes chromic shift as the solvent polarity increases, in agreement with the experimental observations.22,23 The molecular dynamics simulations reveal that the local intermolecular interactions between solute and solvents are not negligible in polar solvents. The specific hydrogen bonds (O‚‚‚H-N interactions) are formed in the formamide solution. Both the local and bulk solvent effects are important in describing the solvatochromic shifts of Me2N-2T-NO2 in polar solutions. Acknowledgment. This work was supported by the National Natural Science Foundation of China (Grants 20433020 and 20573050), the Chinese Ministry of Education (Grant NCET05-0442), and the National Basic Research Program (Grant 2004CB719901). Note Added after ASAP Publication. This paper was published ASAP on March 13, 2008. Table 1 was updated. The revised paper was reposted on March 18, 2008. Supporting Information Available: Evolution of interaction potentials of Me2N-T-NO2‚‚‚HNHCHO dimers as a function of the intermolecular distance, r, and the optimized geometries using MP2 and B3LYP methods (Figure S1); radial distribution functions of Me2N-2T-NO2 in CHCl3 and CH2Cl2 from the rigid and flexible simulations (Figure S2); the torsional potentials of 2T and Me2N-2T-NO2 in gas phase and in various solutions (Figure S3); radial distribution functions of Me2N-2T-NO2 in DMSO and the probability distributions of O‚‚‚H-C angle in the first solvation shell (Figure S4); evolution of the lowest dipole-allowed singlet excitation energies of Me2N-2T-NO2 as a function of the simulation time in CCl4, CHCl3, CH2Cl2, DMSO, and CHONH2 solutions using the combined discrete/ continuum strategy (Figure S5); the optimized structures of solute-solvent clusters with different size at the B3LYP/631G** or MP2/6-31G** level (Figure S6); the selected models in MD simulations and supermolecular clusters (Table S1); the optimized geometrical parameters of 2T and Me2N-2T-NO2 in gas phase and the selected seven kinds of solvents at the B3LYP/ 6-31G** level (Tables S2 and S3); the calculated NBO charges of molecular fragments and dipole moments of Me2N-2T-NO2 in different media (Table S4); dipole moments and solvation free energies of the ground states for 2T and Me2N-2T-NO2 in gas phase and solutions using the PCM method (Table S5); the TD-DFT excitation energies on the explicit solvent models with or without background ESP point charge and the combined solvation models at the B3LYP/6-31G** level (Table S6); the HOMO-LUMO gaps of Me2N-2T-NO2 obtained from B3LYP/ 6-31G** calculations on the three solvent models in various media (Table S7). This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Meier, H. Angew. Chem., Int. Ed. 2005, 44, 2482. (2) Mandal, K.; Kar, T.; Nandi, P. K.; Bhattacharyya, S. P. Chem. Phys. Lett. 2003, 376, 116. (3) Rettig, W.; Kharlanov, V.; Effenberger, F.; Steybe, F. Chem. Phys. Lett. 2005, 404, 272. (4) Bolı´var-Marinez, L. E.; dos Santos, M. C.; Galvaõ, D. S. J. Phys. Chem. 1996, 100, 11029. (5) Hernańdez, V.; Casado, J.; Effenberger, F.; Lo´pez Navarrete, J. T. J. Chem. Phys. 2000, 112, 5105. (6) Raposo, M. M. M.; Fonseca, A. M. C.; Kirsch, G. Tetrahedron 2004, 60, 4071. (7) Hernańdez, V.; Casado, J.; Effenberger, F.; Lo´pez Navarrete, J. T. Synth. Met. 2001, 119, 551. (8) Wu¨rthner, F.; Effenberger, F.; Wortmann, R.; Kra¨mer, P. Chem. Phys. 1993, 173, 305.

J. Phys. Chem. B, Vol. 112, No. 14, 2008 4321 (9) Steybe, F.; Effenberger, F.; Beckmann, S.; Kra¨mer, P.; Glania, C.; Wortmann, R. Chem. Phys. 1997, 219, 317. (10) Steybe, F.; Effenberger, F.; Gubler, U.; Bosshard, C.; Gu¨nter, P. Tetrahedron 1998, 54, 8469. (11) Hartmann, H.; Eckert, K.; Schro¨der, A. Angew. Chem., Int. Ed. 2000, 39, 556. (12) Stecher, R.; Drewnick, F.; Gompf, B. Langmuir 1999, 15, 6490. (13) Norambuena, E.; Rezende, M. C. J. Phys. Org. Chem. 1998, 11, 419. (14) George, J. E.; Drago, R. S. Inorg. Chem. 1996, 35, 239. (15) Ruiz Delgado, M. C.; Ramı´rez, F. J.; Hernańdez, V.; Casado, J.; Enrı´quez, F.; Lo´pez Navarrete, J. T. J. Mol. Struct. 2005, 744-747, 393. (16) Zhu, W.; Jiang, Y. Phys. Chem. Chem. Phys. 2000, 2, 47. (17) Ruiz, Delgado, M. C.; Hernańdez, V.; Casado, J.; Lo´pez Navarrete, J. T.; Raimundo, J.-M.; Blanchard, P.; Roncali, J. Chem. Eur. J. 2003, 9, 3670. (18) Casado, J.; Hernańdez, V.; Kim, O.-K.; Lehn, J.-M.; Lo´pez Navarrete, J. T.; Delgado Ledesma, S.; Ponce Ortiz, R.; Ruiz Delgado, M. C.; Vida, Y.; Pe´rez-Inestrosa, E. Chem. Eur. J. 2004, 10, 3805. (19) Ortı´, E.; Viruela, P. M.; Viruela, R.; Effenberger, F.; Hernańdez, V.; Lo´pez Navarrete, J. T. J. Phys. Chem. A 2005, 109, 8724. (20) Lipin´ski, J.; Bartkowiak, W. Chem. Phys. 1999, 245, 263. (21) Meier, H.; Mu¨hling, B.; Kolshorn, H. Eur. J. Org. Chem. 2004, 1033. (22) Effenberger, F.; Wu¨rthner, F.; Steybe, F. J. Org. Chem. 1995, 60, 2082. (23) Effenberger, F.; Wu¨rthner, F. Angew. Chem., Int. Ed. Engl. 1993, 32, 719. (24) Reichardt, C. SolVents and SolVent Effects in Organic Chemistry; VCH: Weinheim, 2003. (25) Orozco, M.; Luque, F. J. Chem. ReV. 2000, 100, 4187 and references therein. (26) Reichardt, C. Chem. ReV. 1994, 94, 2319 and references therein. (27) Tomasi, J.; Persico, M. Chem. ReV. 1994, 94, 2027 and references therein. (28) Cramer, C. J.; Truhlar, D. G. Chem. ReV. 1999, 99, 2161 and references therein. (29) Hush, N. S.; Reimers, J. R. Chem. ReV. 2000, 100, 775 and references therein. (30) Tomasi, J.; Mennucci, B.; Cammi, R. Chem. ReV. 2005, 105, 2999 and references therein. (31) Zeng, J.; Craw, J. S.; Hush, N. S.; Reimers, J. R. J. Chem. Phys. 1993, 99, 1482. (32) Klamt, A. J. Phys. Chem. 1995, 99, 2224. (33) Zeng, J.; Hush, N. S.; Reimers, J. R. J. Am. Chem. Soc. 1996, 118, 2059. (34) Cossi, M.; Rega, N.; Scalmani, G.; Barone, V. J. Comput. Chem. 2003, 24, 669. (35) Luque, F. J.; Negre, M. J.; Orozco, M. J. Phys. Chem. 1993, 97, 4386. (36) (a) Nandi, P. K.; Das, K. K.; Bhattacharyya, S. P. J. Mol. Struct. (THEOCHEM) 1999, 466, 155. (b) Nandi, P. K.; Chattopadhyay, T.; Bhattacharyya, S. P. J. Mol. Struct. (THEOCHEM) 2001, 545, 119. (37) Bandyopadhyay, P.; Gordon, M. S. J. Chem. Phys. 2000, 113, 1104. (38) Ekanayake, K. S.; Lebreton, P. R. J. Comput. Chem. 2006, 27, 277. (39) (a) Alemań, C. Chem. Phys. Lett. 1999, 302, 461. (b) Alemań, C. Chem. Phys. 1999, 244, 151. (c) Alemań, C. Chem. Phys. 2000, 253, 13. (d) Alemań, C.; Galembeck, S. E. Chem. Phys. 1998, 232, 151. (40) (a) Mennucci, B.; Martıńez, J. M. J. Phys. Chem. B 2005, 109, 9818. (b) Mennucci, B.; Martıńez, J. M. J. Phys. Chem. B 2005, 109, 9830. (c) Mennucci, B.; Martıńez, J. M.; Tomasi, J. J. Phys. Chem. A 2001, 105, 7287. (41) Improta, R.; Barone, V. J. Am. Chem. Soc. 2004, 126, 14320. (42) Cossi, M.; Barone, V.; Cammi, R.; Tomasi, J. Chem. Phys. Lett. 1996, 255, 327. (43) Mennucci, B.; Cance`s, E.; Tomasi, J. J. Phys. Chem. B 1997, 101, 10506. (44) Cance`s, E.; Mennucci, B.; Tomasi, J. J. Chem. Phys. 1997, 107, 3032. (45) Cossi, M.; Barone, V. J. Chem. Phys. 1998, 109, 6246. (46) Mennucci, B.; Cammi, R.; Tomasi, J. J. Chem. Phys. 1999, 110, 6858. (47) Cammi, R.; Mennucci, B. J. Chem. Phys. 1999, 110, 9877. (48) Cossi, M.; Rega, N.; Scalmani, G.; Barone, V. J. Chem. Phys. 2001, 114, 5691. (49) Smith, M. A.; Jasien, P. G. J. Mol. Struct. (THEOCHEM) 1998, 429, 131. (50) Dwyer, T. J.; Jasien, P. G.; Kirkowski, S. M.; Buxton, C. M.; Arruda, J. M.; Mitchell, G. W. J. Am. Chem. Soc. 1998, 120, 12942. (51) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.;

4322 J. Phys. Chem. B, Vol. 112, No. 14, 2008 Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03; Revision D. 01; Gaussian, Inc.: Wallingford, CT, 2004. (52) Sun, H. Macromolecules 1995, 28, 701. (53) (a) Zhang, G.; Pei, Y.; Ma, J. J. Phys. Chem. B 2004, 108, 6988. (b) Zhang, G.; Ma, J.; Wen, J. J. Phys. Chem. B 2007, 111, 11670. (54) Meng, S.; Ma, J.; Jiang, Y. J. Phys. Chem. B 2007, 111, 4128. (55) Simon, S.; Duran, M.; Dannenberg, J. J. J. Chem. Phys. 1996, 105, 11024. (56) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553. (57) Andersen, H. C. J. Chem. Phys. 1980, 72, 2384. (58) Allen, M. P.; Tildesley, D. J. Computational Simulation of Liquids; Oxford: New York, 1987. (59) Materials studio, version 4.0, Accelrys Inc., San Diego, 2006. (60) Karasawa, N.; Goddard, W. A., III. J. Phys. Chem. 1989, 93, 7320. (61) Andre´, J. M.; Delhalle, J.; Bre´das, J. L. Quantum Chemistry Aided Design of Organic Polymers-An Introduction to the Quantum Chemistry of Polymers and its Applications; World Scientific Publishing Co. Pte. Ltd.: Singapore, 1991; Vol. 2. (62) Bre´das, J. L. J. Chem. Phys. 1985, 82, 3808. (63) Albert, I. D. L.; Marks, T. J.; Ratner, M. A. J. Phys. Chem. 1996, 100, 9714. (64) Marder, S. R.; Perry, J. W.; Tiemann, B. G.; Gorman, C. B.; Gilmour, S.; Biddle, S. L.; Bourhill, G. J. Am. Chem. Soc. 1993, 115, 2524.

Meng and Ma (65) Zhang, G.; Ma, J.; Jiang, Y. Macromolecule 2003, 36, 2130. (66) Grebner, D.; Helbig, M.; Rentsch, S. J. Phys. Chem. 1995, 99, 16991. (67) Hutchison, G. R.; Ratner, M. A.; Marks, T. J. J. Phys. Chem. A 2002, 106, 10596. (68) (a) Floris, F.; Tomasi, J. J. Comput. Chem. 1989, 10, 616. (b) Floris, F. M.; Tomasi, J.; Ahuir, J. L. P. J. Comput. Chem. 1991, 12, 784. (c) Floris, F. M.; Tani, A.; Tomasi, J. Chem. Phys. 1993, 169, 11. (69) See, for example: (a) Svishchev, I. M.; Kusalik, P. G. J. Chem. Phys. 1993, 99, 3049. (b) Gubskaya, A. V.; Kusalik, P. G. J. Phys. Chem. A 2004, 108, 7151. (c) Gubskaya, A. V.; Kusalik, P. G. J. Phys. Chem. A 2004, 108, 7165. (d) Liu, X.; Zhang, S.; Zhou, G.; Wu, G.; Yuan, X.; Yao, X. J. Phys. Chem. B 2006, 110, 12062. (e) Liu, Z.; Huang, S.; Wang, W. J. Phys. Chem. B 2004, 108, 12978. (f) Soper, A. K. J. Chem. Phys. 1994, 101, 6888. (g) Yokogawa, D.; Sato, H.; Sakaki, S. J. Chem. Phys. 2006, 125, 114102. (h) Vishnyakov, A.; Lyubartsev, A. P.; Laaksonen, A. J. Phys. Chem. A 2001, 105, 1702. (70) Laaksonen, L. J. Mol. Graphics 1992, 10, 33. (71) See, for example: (a) Yam, C. Y.; Yokojima, S.; Chen, G. J. Chem. Phys. 2003, 119, 8794. (b) van Faassen, M.; de Boeij, P. L.; van Leeuwen, R.; Berger, J. A.; Snijders, J. G. Phys. ReV. Lett. 2002, 88, 186401. (c) Dreuw, A.; Weisman, J. L.; Head-Gordon, M. J. Chem. Phys. 2003, 119, 2943. (d) Casida, M. E.; Gutierrez, F.; Guan, J.; Gadea, F.-X.; Salahub, D.; Daudey, J.-P. J. Chem. Phys. 2000, 113, 7062. (72) See, for example: (a) Kohn, W.; Meir, Y.; Makarov, D. E. Phys. ReV. Lett. 1998, 80, 4153. (b) Milet, A.; Korona, T.; Moszynski, R.; Kochanski, E. J. Chem. Phys. 1999, 111, 7727. (c) Wu, X.; Vargas, M. C.; Nayak, S.; Lotrich, V.; Scoles, G. J. Chem. Phys. 2001, 115, 8748. (d) Hesselmann, A.; Jansen, G.; Schu¨tz, M. J. Chem. Phys. 2005, 122, 014103. (e) Williams, H. L.; Chabalowski, C. F. J. Phys. Chem. A 2001, 105, 646. (f) Grimme, S. J. Comput. Chem. 2004, 25, 1463. (g) Paizs, B.; Suhai S. J. Comput. Chem. 1998, 19, 575. (73) Samdal, S.; Samuelsen E. J.; Volden H. V. Synth. Met. 1993, 59, 259

Solvatochromic Shift of DonorâAcceptor Substituted Bithiophene in

Recommend Documents

Solvatochromic Shift of DonorâAcceptor Substituted Bithiophene in