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A TDDFT Study of the Fluorescence Properties of Three Alkoxypyridylindolizine Derivatives Pekka J. Aittala,*,† Oana Cramariuc,‡ Terttu I. Hukka,† Marilena Vasilescu,§ Rodica Bandula,§ and Helge Lemmetyinen† Department of Chemistry and Bioengineering, Tampere UniVersity of Technology, P.O. Box 541, 33101 Tampere, Finland, Department of Physics, Tampere UniVersity of Technology, P.O. Box 692, 33101 Tampere, Finland, and Institute of Physical Chemistry, Romanian Academy, Splaiul Independentei 202, 006021 Bucharest, Romania ReceiVed: NoVember 2, 2009; ReVised Manuscript ReceiVed: May 19, 2010
The fluorescence properties of three pyridylindolizine derivatives (one tricarbomethoxy-7-pyridyl-pyrrolopyridine and two dicarboethoxy-3-bromobenzoyl-7-pyridyl-pyrrolopyridines) have been investigated by applying density functional theory (DFT) and the time-dependent DFT (TDDFT). Performances of two hybrid-type functionals (BH&HLYP and B3LYP) and one generalized gradient approximation (GGA) functional (PBE) as well as three basis sets (SV(P), DZP, and TZVP) have been assessed. The solvent environment has been modeled with the conductor-like screening model (COSMO). Of the three functionals only BH&HLYP is able to yield reasonable estimates for all the studied indolizine derivatives whereas the success of the PBE and B3LYP functionals is highly dependent on the structure of the studied molecule. The SV(P) basis set provides geometrical changes as well as fluorescence maxima and Stokes shifts that agree with those obtained with DZP and TZVP. When a nonpolar solvent is used, COSMO is able to reproduce the experimental fluorescence maxima and Stokes shifts well. However, the agreement between the calculations and experiments is not as good when a solvent with higher polarity is used. 1. Introduction Indolizines, a group of heterocycles, have been widely investigated lately. They have been found useful in various medical and pharmaceutical applications.1-3 Additionally, indolizines and their derivatives are important in the field of material science owing to their unique photophysical properties. Because indolizines are highly fluorescent, they have been proposed as possible candidates for organic electronic device manufacturing. Although several applications are based on the optical properties of indolizines, only in a few studies have the relationship between the optical properties and the nature and positions of the substituents been investigated.4-7 The few theoretical studies of indolizines have been concentrating on syntheses, on the effects of substituents on the spectroscopic properties, on UV-vis absorption properties, and on the NMR properties.5,8-13 Correct mechanisms of the syntheses reactions of various indolizine derivatives have been identified by means of semiempirical8,9 and density functional theory (DFT)10 calculations. Rotaru et al.5 applied DFT for predicting the effect of the position and nature of the substituents on the spectroscopic properties of some indolizine derivatives. The UV-vis absorption spectra of some indolizine derivatives have been investigated by applying time-dependent DFT (TDDFT).11,12 Wiench et al.13 focused their studies on the chemical shifts, molecular geometries, and charge distributions of seven indolizine derivatives and of their monoprotonated forms by performing ab initio calculations. * To whom correspondence should be addressed,
[email protected]. † Department of Chemistry and Bioengineering, Tampere University of Technology. ‡ Department of Physics, Tampere University of Technology. § Institute of Physical Chemistry, Romanian Academy.
We have previously theoretically studied, by applying DFT and TDDFT,12 the structural and electronic properties of the ground states and the UV-vis absorption properties of three indolizine derivatives, which have been synthesized and experimentally investigated by Vasilescu et al.7 In this article we present our DFT and TDDFT results also on the fluorescence properties of the same indolizine derivatives. To the best of our knowledge, this is the first computational study concerning the fluorescence properties of indolizines. In contrast to the absorption spectrum which can be solved computationally by simply calculating the vertical excitations at the ground state geometry, solving of the fluorescence spectrum is more demanding because fluorescence calculations require the geometry optimization of the target excited state as a first step. Optimization of an excited state is more timeconsuming than that of the ground state because the vertical excitations must be calculated at each optimization cycle. In this sense, using TDDFT in fluorescence calculations seems a good option because of its good accuracy/efficiency ratio. Nevertheless, increasing of the basis set size slows down the TDDFT calculations quickly. Jacquemin et al. have shown, however, in their studies of 1,8-naphtalimide,14 benzene,15 and formaldehyde15 that the excited-state geometries and also the fluorescence energies are affected by the basis set size only little. They have also proposed that one could use a smaller basis set in the more demanding excited state optimizations and the final vertical excitations at that geometry could be calculated by using a larger basis set.15 The choice of an appropriate functional in TDDFT-based fluorescence calculations seems highly dependent on the studied system and not much consistency appears in the reported usage of functionals. For example, Jacquemin et al.14,15 have used the PBE0 functional in their studies, while Li et al.16 applied the
10.1021/jp9104536 2010 American Chemical Society Published on Web 06/04/2010
Fluorescence Properties of Indolizine Derivatives
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Figure 1. Two-dimensional molecular structures as well as the ground state (S0) and excited state (S1) structures of compounds I-III optimized at the BH&HLYP/SV(P) level in vacuum. The hydrogen atoms are omitted from the 2D structures for clarity. The torsion angle R that indicates the angle between the indolizine ring and the pyridyl substituent is shown in the 2D structures.
popular B3LYP functional in a theoretical fluorescence study of oxyluciferin. On the other hand, Toivonen and Hukka17 studied large porphyrin-fullerene dyads and concluded that PBE outperforms the hybrid functionals PBE0 and B3LYP. Plo¨tner and Dreuw reported recently that GGA and hybrid functionals with a small fraction of Hartree-Fock (HF) exchange predict false minima in calculations of the excited state geometries of Pigment Yellow 101. The problem was proposed to arise from the well-known failure of TDDFT to model the charge transfer (CT) and was solved by applying a “half and half” hybrid functional BH&HLYP.18 Therefore, in our present calculations on the indolizine derivatives we have compared the performances of the “half and half” BH&HLYP (BH and HLYP) functional and the popular B3LYP hybrid functionals as well as the generalized gradient approximation (GGA) functional PBE. Additionally, the effect of the basis set size on the fluorescence energies has been investigated by applying the SV(P), DZP, and TZVP basis sets. All studied indolizine derivatives, 1,2,3-tricarbomethoxy-7(4-pyridyl)-pyrrolo[1,2-a]pyridine (I), 1,2-dicarboethoxy-3-(4bromobenzoyl)-7-(4-pyridyl)-pyrrolo[1,2-a]pyridine (II), and its isomer 1,2-dicarboethoxy-3-(4-bromobenzoyl)-5-(2-pyridyl)pyrrolo[1,2-a]pyridine (III) have been reported to be fluorescent7 and have relatively large Stokes shifts if compared to those of typical aromatic compounds, e.g., oligophenylenes.19,20 Structures of the studied compounds I-III are presented in Figure 1. 2. Theoretical Methods We used as starting geometries the minimum energy structures of I-III selected on the basis of the conformational investigation reported in our previous study of the same indolizine derivatives.12 The ground-state geometries and elec-
tronic structures were further optimized by applying DFT21,22 with the functionals and basis set used in the current study. Excited-state geometry optimizations, excitation energies, and oscillator strengths were calculated with TDDFT.23-25 The DFT and TDDFT calculations were performed by applying the “half and-half” hybrid BH&HLYP,26-30 Becke’s three-parameter hybrid26-29,31,32 (B3LYP), and the GGA type PBE26,27,33,34 and exchange-correlation functionals. Performances of the SV(P)35 (roughly 6-31G* quality), DZP,35 and TZVP36 (roughly 6-311G** quality) basis sets were investigated. Excited-state structures and fluorescence energies were obtained by using TDDFT with the following procedure. First, the geometry of each indolizine derivative was optimized at its first singlet excited state. Second, the electronic transitions were calculated by using the optimized excited-state geometry. In order to avoid root flipping,37 one or four higher excited states were also considered in the calculations of the excited-state structures. One higher state was considered in most of the excited-state optimizations. Some of the calculations were repeated by using four additional states in the search of the optimized excited-state structure, because the B3LYP calculated fluorescence maxima proved to be very sensitive to the compound. Calculations of the vibrational modes revealed no imaginary frequencies for the final equilibrium geometries of the excited states. The solvent effects in nonpolar cyclohexane (ε ) 1.9, µ ) 0 D) and in polar DMSO (ε ) 46.6, µ ) 3.96 D) were evaluated by means of the conductor-like screening model (COSMO).38,39 This method belongs to the class of continuum solvation models (CSM), where a cavity within the dielectric continuum of permittivity ε that represents the solvent is formed around the solute molecule. The charge distribution of the solute polarizes the dielectric solvent, and the response of the solvent is described
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TABLE 1: Selected Bond Lengths and Torsion Angles r in the Ground State (S0) and in the Lowest Excited State (S1) of I-III Optimized at the BH&HLYP/SV(P) Level in Vacuum, Cyclohexane, and DMSOa I
C9-N4 N4-C5 C5-C6 C6-C7 C7-C8 C8-C9 C9-C1 C1-C2 C2-C3 C3-N4 R a
II S1
S0
S0
III S1
S0
S1
vacuum
vacuum
cyclohexane
DMSO
vacuum
vacuum
cyclohexane
DMSO
vacuum
vacuum
cyclohexane
DMSO
1.38 1.37 1.36 1.42 1.37 1.41 1.41 1.40 1.38 1.39 152.7
1.37 1.37 1.37 1.41 1.45 1.37 1.44 1.41 1.38 1.41 174.4
1.38 1.37 1.37 1.41 1.45 1.37 1.44 1.40 1.38 1.41 174.9
1.38 1.37 1.37 1.41 1.45 1.37 1.44 1.40 1.38 1.40 174.1
1.39 1.38 1.37 1.43 1.39 1.41 1.42 1.41 1.41 1.40 151.7
1.37 1.37 1.37 1.41 1.44 1.37 1.44 1.40 1.39 1.40 170.5
1.38 1.37 1.37 1.41 1.44 1.37 1.44 1.40 1.39 1.40 170.8
1.38 1.37 1.37 1.41 1.44 1.37 1.44 1.40 1.39 1.40 173.5
1.39 1.38 1.36 1.42 1.36 1.41 1.40 1.42 1.38 1.39 140.0
1.37 1.38 1.41 1.37 1.41 1.38 1.43 1.40 1.39 1.40 165.2
1.37 1.39 1.41 1.37 1.41 1.38 1.43 1.40 1.39 1.40 165.5
1.38 1.39 1.41 1.37 1.41 1.37 1.43 1.40 1.39 1.40 163.4
Bond lengths are given in angstroms while angles are given in degrees.
Figure 2. The isoamplitude surfaces of HOMO and LUMO of I-III calculated for the S1 geometry with the BH&HLYP and B3LYP functionals and the SV(P) basis set in vacuum.
by the generation of screening charges on the cavity surface. Instead of dielectric boundary conditions, COSMO takes advantage of much simpler boundary conditions for a conductor and corrections for dielectric behavior are made afterward.40,41 Continuum solvation models should be sufficient for the studied compounds, because solute-solvent interactions do not include hydrogen bonding in this case which would require the inclusion of some explicit solvent molecules in the calculations. All calculations were carried out with Turbomole 5.9-6.0 software packages.42 3. Results and Discussion 3.1. Geometries of the Ground State and the First Excited State. The geometries of the ground (S0) and the first excited state (S1) of the three alkoxypyridylindolizine derivatives (see Figure 1 for the numbering of the atoms) were optimized with the BH&HLYP, B3LYP (ground state geometries from ref 12), and PBE functionals with the SV(P) basis sets; see Table 1 and Table S1 in the Supporting Information. In addition, the BH&HLYP functional was used to optimize the structures also with the DZP (compounds I-III) and TZVP (compound I) basis sets; see Table S2 in the Supporting Information. In the following, some selected bond lengths and torsion angles of I, II, and III optimized at the BH&HLYP/SV(P) level are presented and discussed together with the isoamplitude surfaces of HOMO and LUMO obtained via the BH&HLYP/SV(P) calculations for the S1 geometry; see Figure 2. The effects of the other functionals and basis sets on the geometries are highlighted in sections 3.1.1 and 3.1.2, respectively.
The S1 f S0 fluorescence of I-III consists of a one-electron transition from LUMO to HOMO. The two orbitals calculated at the same level of theory on the S0 geometry are practically identical with those presented in Figure 2 and are therefore omitted. When the equilibrium geometries of the S0 and S1 states of compounds I-III are compared, the largest changes are observed in the bonds of the indolizine ring on which the HOMO and LUMO orbitals have strong amplitudes. The calculations reveal that the orientations of both the carbomethoxyl and -ethoxyl groups are very similar in these states. The pyridyl ring is almost coplanar with indolizine in the S1 state of I; see Figure 1. Consequently, the torsion angle R (174.4°) in the S1 state is ∼22° larger than in the ground state (152.7°). When the S0 and S1 equilibrium geometries of I are compared, the average absolute changes in the bond lengths are about 0.02 Å; see Table 1. The largest changes, i.e., -0.08, +0.04, and -0.04 Å, occur in the C7-C8, C8-C9, and C9-C1 bonds, respectively. Thus, the S1 and S0 geometries of I have an inversed double-single bond pattern in the C7-C8-C9-C1 part of indolizine (see Table 1). When the geometries of the S1 and S0 states of II are compared, the following observations are made. The torsion angle R (170.5°) of II in the S1 state is ca. 20° larger than that in the ground state. The p-bromobenzoyl group of II has a planar structure in the S1 state and the substituent plane is tilted roughly by 50° with respect to the indolizine plane; see Figure 1. The spatial orientation of the p-bromobenzoyl substituent of II is therefore very similar in the both states. Comparison of the S1 and S0 geometries reveals average absolute changes in indolizine
Fluorescence Properties of Indolizine Derivatives bond lengths of ∼0.02 Å in II. In the S1 state of II the C7-C8 and C9-C1 bonds are shorter by 0.07 and 0.04 Å, respectively, than in the ground state whereas the C8-C9 bond is longer by 0.04 Å. As a result, the S1 and S0 geometries of II have an inversed double-single bond pattern between the C7-C8-C9-C1 carbons. In the S1 state the indolizine backbone of III twists slightly from the planar ground state structure and the torsion angle is larger than that in the ground state. The torsion angle R of III (165.2°) is roughly 25° larger than in the S0 state. The p-bromobenzoyl group is almost planar in III in the S1 state. However, the spatial orientation of the whole p-bromobenzoyl substituent with respect to indolizine is the same both in the S1 state and in the ground state. In III the average absolute differences in the bond lengths of indolizine between the S0 and S1 geometries are about 0.03 Å. The C6-C7 and C8-C9 bonds are lengthened by ∼0.04 Å. In contrast, the C5-C6, C7-C8, C9-C1, and C3-N4 bonds are shortened by 0.05, 0.05, 0.04, and 0.02 Å, respectively. The inversion of the double-single bond pattern covers a larger part of indolizine, i.e., C5-C6-C7-C8-C9-C1, in the S1 and S0 equilibrium geometries of III than in those of I and II. The structural changes which take place when the studied indolizines are excited to the first singlet excited state in vacuum or in nonpolar solvents are indications of the origin of the large Stokes shifts observed in the absorption and emission spectra of compounds of this kind. Despite the observed inversion in the double-single bond patter, the changes in bond lengths remain relatively small. Therefore, other structural characteristics such as the torsion angle between indolizine and pyridyl ring (variations of up to 25°) appear to be responsible for the large Stokes shifts. In the case of compounds II and III the p-bromobenzoyl hardly affects Stokes shift, because the relative orientation of the substituent with respect to the indolizine ring is almost identical in both the S0 and S1 states. 3.1.1. The Effect of the Exchange-Correlation Functional. The S1 geometries of I predicted by B3LYP and PBE are very similar to the structure predicted by BH&HLYP. Comparison of the S0 and S1 equilibrium geometries of I reveals that, in contrast to BH&HLYP, B3LYP predicts large changes to the C9-N4 and C3-N4 bond lengths. These bonds are 0.02 Å shorter and 0.04 Å longer, respectively, in the S1 state than in the ground state. Of these three functionals, PBE yields the smallest changes to the bond lengths, as only N4-C5 and C7-C8 are 0.02 and 0.04 Å longer in the S1 state than in the S0 state whereas the other bonds are changed less. The torsion angles R obtained with B3LYP and PBE in the S1 state (170.2° and 171.8°, respectively) are ∼17° larger than those in the S0 state. The change in R is ca. 5° less than that obtained with BH&HLYP. Inspection of the S1 structure of II optimized at the B3LYP and PBE levels of theory reveals that the torsion angle R between the pyridyl ring and indolizine (151.4° and 156.1°, respectively) is 14-20° smaller than in the S1 state calculated by using BH&HLYP (170.5°). The p-bromobenzoyl group of II is perpendicular to indolizine in the S1 state when optimized with B3LYP, contrary to the geometries of the S1 state optimized with BH&HLYP and PBE which are tilted only by ca. 50°. Because of the electronic structure of the S1 state optimized with PBE and B3LYP and the overestimated fluorescence wavelengths (underestimated S1 energies) calculated for these geometries (see discussion in section 3.2.1), the S1 state obtained with these two functionals is a CT state which is probably a
J. Phys. Chem. A, Vol. 114, No. 26, 2010 7097 consequence of the failure to predict CT correctly with the density functionals without or with a low amount of HF exchange. There are no as clear differences in the S1 structures of III optimized with the three functionals as there are in the case of II. However, also the S1 states of III obtained with B3LYP and PBE turned out to be spurious CT states, see section 3.2.1. 3.1.2. The Effect of the Basis Set. The effects of the basis sets on the S0 and S1 geometries have been investigated by using the BH&HLYP functional. The structural characteristics calculated with DZP and TZVP basis sets are presented in Table S2 in Supporting Information. Because the excited-state optimizations with the TZVP basis set are very time-consuming and the basis set has only a minor effect on the wavelengths of the absorption and fluorescence maxima as well as on the Stokes shifts of I (see section 3.2.2), the S1 state was optimized with the TZVP basis set only for compound I. The bond lengths of the indolizine ring in the S0 and S1 states of I-III computed with the different basis sets differ by 0.01 Å at the most. In compound I the SV(P), DZP, and TZVP basis sets and in II and III the SV(P) and DZP basis sets predict largest changes in the same bonds in both states (see discussion in section 3.1). Moreover, all these basis sets predict similar differences in bond lengths. The quantitative differences in values of the torsion angles R obtained with the different basis sets (2-7°) are within the accuracy of the experimental evaluation of torsion angles and small considering difficulties in their exact computation even with highly correlated methods.43 In the S0 structures of I-III the torsion angle R between the pyridyl and indolizine rings decreases when the basis set size is increased; see Table 1 and S2 in the Supporting Information. Also in the S1 state of compound I the torsion angle R decreases but less (1-4°) than in the S0 state when the basis set size is increased. Hence, DZP and TZVP predict only slightly larger (ca. 4°) differences between the torsion angles of the geometries of the S1 and S0 states than SV(P) (25.3° and 25.9° vs 21.7°). For II the DZP yields ca. 5° larger R than SV(P) in the S1 state and the difference between the torsion angles of the S1 and S0 states is also larger when predicted with DZP (23°) than with SV(P) (19°). In the case of compound III the torsion angles R in the S1 state are practically the same 165.2° with both SV(P) and DZP. The difference between the torsion angles of the S1 and S0 states remains the same when the basis set size is increased. To summarize, already the smallest studied SV(P) basis set captures the changes in the geometries resulting from electronic transitions. This is useful since use of the SV(P) or DZP basis set instead of TZVP in the demanding excited-state optimizations decreases the computational effort significantly. 3.1.3. SolWent Effects. Both solvents (cyclohexane and DMSO) induce only minor changes to the S1 and S0 geometries of compounds I-III; see Table 1. In the S1 state structures optimized in both solvents the bond lengths of the indolizine ring are practically identical to those optimized in vacuum. Moreover, in both vacuum and solvent environments the torsion angle R is the same within 1°, 3°, and 2° in I, II, and III, respectively. However, the vibrational spectra of the S1 geometries of II optimized in cyclohexane and in DMSO revealed a single imaginary frequency. The coordinates were shifted along the imaginary mode after which the geometry optimizations yielded minimum structures without imaginary frequencies. 3.2. Optical Transition Energies. The wavelengths and energies of the fluorescence (S1 f S0) and absorption (S0 f S1) maxima, oscillator strengths, and Stokes shifts calculated
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TABLE 2: Absorption (S0 f S1) and Fluorescence (S1 f S0) Wavelengths λ (nm), Energies E (eV), Oscillator Strengths f, and Stokes Shifts ∆S (cm-1) of I-III Calculated in Vacuum by Using the PBE, B3LYP, and BH&HLYP Functionals with the SV(P), DZP, and TZVP Basis Sets (energy//geometry) S0 f S 1 compound I
II
III
a
S1 f S 0
functional
basis set
λ
E
f
λ
E
f
∆S
PBE B3LYP BH&HLYP BH&HLYP BH&HLYP BH&HLYP BH&HLYP PBE B3LYP BH&HLYP BH&HLYP BH&HLYP BH&HLYP PBE B3LYP BH&HLYP BH&HLYP BH&HLYP BH&HLYP
SV(P)//SV(P) SV(P)//SV(P) SV(P)//SV(P) DZP//SV(P) DZP//DZP TZVP//SV(P) TZVP//TZVP SV(P)//SV(P) SV(P)//SV(P) SV(P)//SV(P) DZP//SV(P) DZP//DZP TZVP//SV(P) SV(P)//SV(P) SV(P)//SV(P) SV(P)//SV(P) DZP//SV(P) DZP//DZP TZVP//SV(P)
404.3 353.9a 308.3 308.6 304.6 312.1 305.3 436.8 368.5a 318.1 318.4 316.1 323.6 496.3 398.3a 329.6 330.1 328.2 335.4
3.07 3.50 4.02 4.02 4.07 3.97 4.06 2.84 3.36 3.90 3.89 3.92 3.83 2.50 3.11 3.76 3.76 3.78 3.70
0.16 0.32a 0.40 0.39 0.38 0.40 0.39 0.08 0.48a 0.55 0.55 0.55 0.56 0.04 0.08a 0.13 0.13 0.13 0.12
551.6 412.7 362.2 363.1 362.3 367.8 366.3 814.5 719.1 372.5 373.2 372.3 380.3 857.8 607.2 462.8 462.6 463.4 470.7
2.25 3.00 3.42 3.41 3.42 3.37 3.38 1.52 1.72 3.33 3.32 3.33 3.26 1.45 2.04 2.68 2.68 2.68 2.63
∼0 0.30 0.43 0.43 0.43 0.43 0.44 ∼0 ∼0 0.51 0.51 0.52 0.50 ∼0 0.01 0.13 0.14 0.14 0.13
6605 4026 4827 4864 5229 4852 5455 10616 13231 4591 4612 4775 4607 8491 8638 8732 8677 8890 8570
From ref 12.
TABLE 3: The Absorption (S0 f S1) and Fluorescence (S1 f S0) Wavelengths λ (nm), Energies E (eV), Oscillator Strengths f, and Stokes Shifts ∆S (cm-1) of I-III Calculated at the BH&HLYP/SV(P) Level in Two Different Solvent Environments and the Corresponding Experimental Values calculated S0 f S1 compound I II III a
experimental
S1 f S 0
S 0 f S1 a
solvent
λ
E
f
λ
E
f
∆S
λ
cyclohexane DMSO cyclohexane DMSO cyclohexane DMSO
308.4 310.5 318.6 319.5 328.6 329.0
4.02 3.99 3.89 3.88 3.77 3.77
0.41 0.45 0.56 0.54 0.13 0.11
359.5 354.3 371.7 368.3 460.6 445.2
3.45 3.50 3.34 3.37 2.69 2.78
0.47 0.47 0.51 0.54 0.13 0.13
4609 3981 4484 4147 8721 7933
338.8 342.8 373.8 381.6 359.8 356.2
S1 f S 0 a
E
λ
3.66 3.62 3.32 3.25 3.45 3.48
414 432 440 524 518 533
E
Inta,b
∆Sa
2.99 2.87 2.82 2.37 2.39 2.33
100 47 100 24 100 118
5361 6092 4025 7161 8488 9327
Obtained from ref 7. b Relative intensities.
in vacuum by using the BH&HLYP, B3LYP, and PBE functionals with the SV(P), DZP, and TZVP basis sets are presented in Table 2. Because the nonpolar cyclohexane is expected to have a minor effect on the fluorescence maxima, the values calculated for fluorescence in vacuum are compared with the experimental values measured in cyclohexane and reported in ref 7 The experimental values are given in Table 3. Owing to the broadness of the absorption bands of compounds I-III measured in cyclohexane, Stokes shifts were not reported in that medium. Therefore, we have used the reported7 absorption and fluorescence maxima and calculated estimates for the experimental Stokes shifts in cyclohexane. 3.2.1. The Effect of the Exchange-Correlation Functional. The effects of the functionals have been investigated by using the SV(P) basis set. The wavelengths of the absorption and fluorescence maxima, oscillator strengths, and Stokes shifts have been calculated with PBE, B3LYP, and BH&HLYP functionals, as presented in Table 2. The PBE functional predicts the longest wavelengths, i.e., lowest energies, for the absorption maxima of I-III; see Table 2. Depending on the compound, B3LYP yields 50-98 nm shorter wavelengths and BH&HLYP 96-167 nm shorter wavelengthsthanPBE.Thisisexpected,becausetheHOMO-LUMO gap increases when the amount of HF exchange in the functional
increases. The fluorescence maxima reveal even larger differences when results from the three functionals are compared; see Table 2. The wavelengths of the absorption (308.3 nm) and fluorescence (362.2 nm) maxima of compound I obtained by using BH&HLYP (Table 2) are 30.5 and 54.5 nm too short as compared to the experimental values of 338.8 and 414 nm (Table 3), respectively. Consequently, the calculated Stokes shift (4827 cm-1, Table 2) is 10% too small (534, 5361 cm-1, Table 3). The wavelength of the fluorescence maximum calculated with B3LYP (412.7 nm) compares extremely well with the experimental value. However, because the calculated wavelength of the absorption maximum (353.9 nm) is larger than the experimentally observed value, the calculated Stokes shift (4026 cm-1) is 25% too small (1335 cm-1). On the other hand, the PBE calculations overestimate the wavelengths of the absorption and fluorescence maxima by ∼70 and ∼140 nm, respectively. Consequently, the PBE calculated Stokes shift (6605 cm-1) is 23% larger than the experimentally measured value of 5361 cm-1. In addition, the fluorescence oscillator strength obtained with PBE, but not with BH&HLYP and B3LYP, is clearly smaller than the absorption oscillator strength. The fluorescence wavelength calculated with PBE deviates from the experimental value more than the ones obtained with BH&HLYP and B3LYP
Fluorescence Properties of Indolizine Derivatives because the correct excited state could not be reached with the PBE functional. The analysis of the molecular orbitals of the excited-state geometry, provided in Figure S1 in Supporting Information, reveals that the HOMO calculated with PBE exhibits σ or lone-pair character rather than π character. Hence, the fluorescence from S1 to S0 is in fact a n f π* transition, which is known to usually exhibit a rather low oscillator strength. On the contrary, the HOMO obtained with the BH&HLYP and B3LYP functionals has clear π character, as seen by analyzing the orbitals presented in Figure 2. Therefore, the fluorescence calculated with these two functionals represents the desired π f π* transition and the results reproduce the experimental data quite well. The geometrical changes observed in the optimized PBE structures support our analysis, namely, that the C-N bonds of the pyridyl ring are shorter roughly by 0.02 Å in the S1 state than in the S0 state. Substitution of the carbomethoxyl group at C3 (in I) with p-bromobenzoyl (in II) and the carbomethoxyl groups at C1 and C2 (in I) with carboethoxyl groups (in II) in the indolizine backbone shifts the experimental fluorescence maximum toward longer wavelengths.7 The wavelengths of the absorption (318.1 nm) and fluorescence (372.5 nm) maxima of compound II calculated with BH&HLYP are too short by 55.7 and 67.5 nm as compared to the experimental values of 373.8 and 440 nm, respectively. The calculated Stokes shift (4591 cm-1) is 14% (566 cm-1) longer than the experimental value 4025 cm-1. The B3LYP calculated fluorescence maximum of II (719.1 nm) is clearly overestimated if compared to the experiment. Furthermore, the B3LYP-calculated Stokes shift of II (see Table 2) is over three times larger than that observed experimentally (see Table 3). Also PBE fails drastically in predicting the wavelength of the fluorescence maximum and Stokes shift of compound II even though the absorption maximum is relatively well predicted. Following the differences in the S1 geometries optimized with BH&HLYP, B3LYP, and PBE (see section 3.1.1), the electronic structures of the optimized S1 excited state obtained with these functionals are different; see Figure 2 and Figure S1 in Supporting Information. As in the case of compound I, PBE fails in optimizing the correct excited state and the obtained HOMO exhibits σ character, but BH&HLYP and B3LYP yield π character correctly for the HOMO orbital. The LUMO obtained with BH&HLYP is delocalized over a large part of the molecule, but the LUMO obtained with B3LYP (see Figure 2 and Figure S1 in Supporting Information) is localized entirely on p-bromobenzoyl. Hence, B3LYP predicts CT character for the S1 state, and the overlap between the orbitals involved in fluorescence, i.e., HOMO and LUMO, is practically zero and thus the oscillator strength is practically zero. Considering the highly overestimated wavelengths of the fluorescence maxima, i.e., too low S1 energies, obtained with the B3LYP functional, the S1 state of II obtained with B3LYP is a spurious CT state which is a consequence of the failure of TDDFT combined with the functionals with no or low amount of HF exchange44,45 to predict the CT correctly. Because of the differences in the optimized geometries of the excited states, we were concerned over the possibility of the root flipping; see section 2 for the computational procedure. Therefore, we increased the number of additional excited states (five states altogether) and repeated the S1 state optimization of II at the B3LYP level. However, increasing of the number of the additional states affects neither the S1 geometries of II nor the fluorescence maximum wavelengths. Moving the pyridyl ring from C7 (in II) to C5 (in III) induces a bathochromic shift of 78 nm to the experimental fluorescence
J. Phys. Chem. A, Vol. 114, No. 26, 2010 7099 maxima in cyclohexane.7 This is also predicted by the BH&HLYP calculations of II and III (90.3 nm, Table 2). Thus, the fluorescence maxima of III calculated with BH&HLYP are at higher wavelengths than those of II. Also PBE predicts a bathochromic shift, but B3LYP predicts a hypsochromic shift between the fluorescence maxima of II and III; however, these are less important because these two functionals failed in calculating the fluorescence properties of II. In the case of compound III, the wavelengths of the absorption (329.6 nm) and fluorescence (462.8 nm) maxima calculated with BH&HLYP are too short by 30.2 and 57.4 nm as compared to the experimental values of 359.8 and 518 nm, respectively. The absorption and fluorescence transition energies are 0.31 and 0.29 eV too high, respectively. The calculated Stokes shift (8732 cm-1) is only 3% (244 cm-1) longer than the experimental value 8488 cm-1. The B3LYP functional yields absorption (398.3 nm) and fluorescence maxima (607.2 nm) at much higher wavelengths than experimentally observed (see Table 3). Yet the calculated Stokes shift (8638 cm-1) is only 150 cm-1 larger than the experimental value. The PBE functional yields even higher wavelengths for absorption and fluorescence maxima but the calculated Stokes shift (8491 cm-1) is even closer to the experimental value 8488 cm-1 than the one obtained with B3LYP. Even though there were no clear differences in the S1 geometries of the compound III optimized with the three functionals (see section 3.1.1), PBE and B3LYP yield electronic structures for the optimized S1 state that differ from that obtained by using BH&HLYP; see Figure 2. Similar to compound II, the LUMO of the S1 state of III obtained with PBE (Figure S1 in Supporting Information) and B3LYP (Figure 2) is localized entirely on the p-bromobenzoyl. Hence, these two functionals predict CT character for the S1 state. In contrast, the LUMO calculated for the S1 geometry by using BH&HLYP is localized mainly on the indolizine and pyridyl rings just like the LUMO calculated for the S0 geometry (not shown). To summarize, PBE fails in optimizing the correct excited state for compounds I and II and predicts CT character for the S1 state of compound III. In addition, the B3LYP functional predicts CT character for the S1 state of compounds II and III. Considering that both functionals overestimate the wavelength of the fluorescence maximum, i.e., underestimate the S1 energy, this CT state is artificial and a consequence of the CT failure of TDDFT when combined with the traditional density functionals with no or low amount of HF exchange. Thus, although B3LYP outperforms BH&HLYP in predicting the wavelengths of the absorption and fluorescence maxima for compound I, a hybrid functional with a larger fraction of HF exchange (BH&HLYP) is mandatory to get a physically correct picture of the S1 f S0 fluorescence of compounds II and III. From a quantitative point of view, the absorption and fluorescence transition energies calculated with BH&HLYP are 0.31-0.57 and 0.29-0.43 eV higher than the experimental values, respectively. We agree with Plo¨tner and Dreuw18 that BH&HLYP hybrid functional is recommended for fluorescence calculations, although, in contrast to their study, in our investigations also the PBE and B3LYP functionals yielded minimum energy structures for the S1 states. The use of other functionals than BH&HLYP may in some cases yield more accurate results, but choosing the functional for fluorescence calculations has to be made with great care. 3.2.2. The Effect of the Basis Set. The effects of the basis sets on the optical transition energies have been investigated
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by using the BH&HLYP functional. The wavelengths of the absorption and fluorescence maxima, oscillator strengths, and Stokes shifts have been calculated with three different basis sets at three different geometries, as presented in Table 2. Because the excited state optimizations employing the TZVP basis set are very time-consuming and the basis set has only a minor effect on the wavelengths of the absorption and fluorescence maxima as well as on the Stokes shifts, as proved by the TZVP// TZVP calculations for compound I, these calculations are not presented for compounds II and III. The absorption and fluorescence maxima obtained with the SV(P)//SV(P), DZP//DZP, and TZVP//TZVP calculations are the same within few nanometers for compound I. The wavelengths of the absorption maxima of compound I are the same within 4 nm (SV(P)//SV(P) 308.3 nm, DZP//DZP 304.6 nm, and TZVP//TZVP 305.3 nm), and ∼30 nm shorter than the experimental maximum wavelength, 338.8 nm. The wavelengths of the fluorescence maxima are also the same within 4 nm and roughly 50 nm shorter than the experimental value 414 nm. The calculated Stokes shifts increase in the order of SV(P)// SV(P) < DZP//DZP < TZVP//TZVP, but the differences in Stokes shifts are rather small because the wavelengths of the absorption and fluorescence maxima are hardly affected by the basis set. In the case of compounds II and III the wavelengths of the absorption maxima obtained with SV(P)//SV(P) and DZP//DZP differ only by 3 nm (II) and ∼1 nm (III). Furthermore, the wavelengths of the fluorescence maxima are the same within 1 nm. The SV(P)//SV(P)-calculated Stokes shifts are smaller than the ones obtained with DZP//DZP, but as in the case of compound I the differences in Stokes shifts are rather small (184 and 158 cm-1 in II and III, respectively) because the wavelengths of the absorption and fluorescence maxima are hardly affected by the basis set. The use of the DZP or TZVP basis set in the excitation energy calculations at the SV(P) geometry yields almost systematically slightly longer absorption and fluorescence wavelengths than the full DZP and TZVP calculations, but the differences are negligible because in all cases the wavelengths of the absorption and fluorescence maxima are underestimated roughly by the same amount, i.e., 30 nm (II) and 50 nm (III) with respect to the experimental value. Thus, the use of the SV(P) basis set both in geometry optimizations and in excitation energy calculations emerges as a good choice since the use of a larger basis set, i.e., DZP or TZVP, does not practically improve either the calculated fluorescence maxima or Stokes shifts. 3.2.3. SolWent Effects. The wavelengths and energies of the fluorescence (S1 f S0) and the absorption (S0 f S1) maxima, oscillator strengths, and Stokes shifts calculated in cyclohexane and in DMSO are presented in Table 3 along with the corresponding experimental data. Simulating of the solvent environment with COSMO affects the wavelengths calculated in vacuum only slightly. The experimental fluorescence maxima of compound I in cyclohexane and in DMSO are 413 and 432 nm, respectively. The calculations underestimate them by 50 nm (359.5 nm) and 80 nm (354.3 nm), respectively; see Table 3. Additionally, the calculated oscillator strength is equal in both solvents, whereas experiments show stronger fluorescence in cyclohexane. The Stokes shift calculated in cyclohexane (4609 cm-1) is 752 cm-1 (14%) smaller than the experimental value (5361 cm-1). Because the calculations yield too low a wavelength for the fluorescence maximum in DMSO, the calculated Stokes shift (3981 cm-1) is 2111 cm-1 (35%) smaller than the experimental value (6092
Aittala et al. cm-1). The calculations also predict a larger Stokes shift in cyclohexane than in DMSO, contrary to the experiments. The experimental fluorescence maxima of compound II in cyclohexane and in DMSO are at 440 and 524 nm, respectively. The Stokes shifts are 4025 and 7161 cm-1, respectively. The maxima of the calculated absorption wavelengths of II in cyclohexane (318.6 nm) and in DMSO (319.5 nm) are located ∼55 and ∼62 nm below the experimental values, respectively. Simultaneously, the calculations underestimate the wavelengths of the fluorescence maxima by ca. 70 nm in cyclohexane (371.7 nm) and by ca. 150 nm in DMSO (368.3 nm). Consequently, the calculated Stokes shift in cyclohexane (4484 cm-1) is only 459 cm-1 (11%) higher than the experimental value. In DMSO (4147 cm-1), however, the calculated Stokes shift is as much as 3014 cm-1 (42%) smaller than the experimental value. The experimental fluorescence of II is more intense in cyclohexane than in DMSO. The calculations fail to reproduce this for II and yield a slightly larger fluorescence oscillator strength in DMSO than in cyclohexane. As in the case of compound I, the calculations predict that the Stokes shift of II decreases when the solvent polarity increases, which is contrary to the experimental observations. The oscillator strengths of III do not follow the trends observed in the experimental fluorescence intensities in cyclohexane and DMSO; i.e., calculations predict equal intensities in cyclohexane and DMSO. In addition, the calculations predict larger Stokes shift in cyclohexane than in DMSO. As a result of the underestimated absorption and fluorescence maxima, the Stokes shift of III calculated in cyclohexane (8721 cm-1), is 233 cm-1 (3%) higher than the experimental Stokes shift (8488 cm-1). In DMSO the difference between the calculated (7933 cm-1) and the experimental (9327 cm-1) Stokes shifts is even larger, 1394 cm-1 (15%). The wavelengths of the absorption and fluorescence maxima and the Stokes shifts of compounds I-III calculated in cyclohexane agree reasonably well with the experimental results. However, the fluorescence properties calculated in cyclohexane do not improve from the ones calculated in vacuum. The wavelengths of the fluorescence maxima calculated in DMSO are, however, consistently underestimated. Consequently, the calculated Stokes shifts are clearly underestimated in DMSO. In addition, the calculations predict larger Stokes shifts for I-III in a nonpolar solvent than in a polar solvent, which is contrary to the experiments. 4. Conclusions We have theoretically studied the fluorescence properties of three alkoxypyridylindolizine derivatives (I-III). The calculations were carried out by applying DFT and TDDFT. Performances of the BH&HLYP, B3LYP, and PBE functionals as well as the SV(P), DZP, and TZVP basis sets in fluorescence calculations were investigated. The solvent environment (cyclohexane and DMSO) was simulated with COSMO. The wavelengths of the fluorescence maxima and Stokes shifts of the studied indolizine derivatives I-III calculated by using BH&HLYP are in rather good agreement with the experiments though the functional has a tendency to overestimate the optical transition energies. In contrast, the success of the PBE and B3LYP functionals is highly dependent on the structure of the studied molecule. The B3LYP functional performs very well in the calculations of the fluorescence properties of I but both B3LYP and PBE fail drastically when the properties of II and III are calculated. In contrast to BH&HLYP, these two functionals predict charge transfer character for the lowest
Fluorescence Properties of Indolizine Derivatives excited state of II and III. Consequently, we recommend the use of the BH&HLYP functional for the TDDFT-based fluorescence calculations at least in the case of these kinds of compounds. The use of exchange-correlation functionals with a smaller amount of HF exchange may in some cases improve the results, but failure of such functionals seems to be unpredictable as even small changes in the molecular conformations can trigger problems in calculations. Although there are some differences in the bond lengths optimized with SV(P), DZP, and TZVP, the trends in the bond lengths in S1 f S0 fluorescence are the same, regardless of the basis set. Moreover, using of a larger basis set than SV(P) in the geometry optimizations or in the excitation energy calculations yields hardly any improvement for the wavelengths of the fluorescence maxima or the Stokes shifts of the studied compounds. Thus, it is sufficient to use the smallest SV(P) basis set both in the demanding excited state optimizations and in the calculations of the wavelengths of the absorption and fluorescence maxima. Performance of COSMO depends on the solvent polarity applied. The wavelengths of the absorption and fluorescence maxima and the Stokes shifts of I-III calculated in a nonpolar cyclohexane are in good agreement with the experiment. The fluorescence properties calculated in cyclohexane, however, do not improve from the ones calculated in vacuum. In a solvent with a higher polarity, i.e., DMSO, the calculated fluorescence maxima wavelengths are underestimated without exception at the level of theory used in this study. In addition, the calculations predict larger Stokes shifts in a nonpolar solvent than in a polar solvent for the compounds I-III, which is not supported by the experimental data. Acknowledgment. The IT Center for Science Ltd (CSC), governed by the Finnish Ministry of Education, is acknowledged for providing the computing resources. Financing of this research by the Academy of Finland is greatly appreciated. Supporting Information Available: Structural characteristics of compounds I-III calculated with the PBE and B3LYP functionals as well as with the DZP and TZVP basis sets and isoamplitude surfaces of HOMO and LUMO calculated for the S1 geometries of I-III at the PBE/SV(P) level of theory. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Michael, J. P. Nat. Prod. Rep. 1999, 16, 675. (2) Nasir, A. I.; Gundersen, L.-L.; Rise, F.; Antonsen, Ø.; Kristensen, T.; Langhelle, B.; Bast, A.; Custers, I.; Haenen, G. R. M. M.; Wikstro¨m, H. Bioorg. Med. Chem. Lett. 1998, 8, 1829. (3) Østby, O. B.; Dalhus, B.; Gundersen, L.-L.; Rise, F.; Bast, A.; Haenen, G. R. M. M. Eur. J. Org. Chem. 2000, 9, 3763. (4) Cheng, Y.; Ma, B.; Wudl, F. J. Mater. Chem. 1999, 9, 2183.
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