1. Introduction

Maleimides are widely known as active electrophilic reagents to readily react with a variety of dienes and 1,3-dipoles including azomethine ylide, carbonyl ylide and, nitorenes, leading to various heterocycles [1]. We have explored the abundant synthetic potential of the new functionalized maleimides which can effectively be converted to fused pyridazine derivatives [2] and polymethine dyes [3, 4]. Herein we report the new series of dyes bearing push (pyrrole, indole)—pull (maleimide) systems. The computational investigations are also described for their first intense electric absorption peaks using TD-DFT [5], which is widely used in electronic transition energy predictions for many molecules [6, 7].

2. Synthesis and Electronic Spectra

A series of 4-methylthiomaleimides 1a–1c were found to undergo addition-elimination reactions with pyrrole 2a-2b and indoles 4a–4c to give new compounds 3a–3d and 5a–5g which are listed in Table 1 and the synthetic scheme is illustrated in Figure 1.

Table 1: Recaptulatives of the newly synthesized compounds along with the key geometrical parameters .

Figure 1: Synthesis diagram of 3a–3d and 5a–5g.

In details, compounds 1a and 1b reacted with pyrrole 2a under refluxing in acetic acid to afford methyl 1-methyl-4-(pyrrol-2-yl)-2,5-dioxo-1H-pyrrole-3-carbonitrile 3a and methyl 1-methyl-4-(pyrrol-2-yl)-2,5-dioxo-1H-pyrrole-3-carboxylate 3b, respectively, where the electrophilic attack of 1a and 1b to 2a selectively took place on 2-position of pyrrole ring. When using N-methylpyrrole 2b instead of 2a, the attack on the 2-position competes with that on 3-position of 2b. In the same way, methyl 1-methyl-4-(methylpyrrol-2-yl)-2,5-dioxo-1H-pyrrole-3-carboxylate 3d was obtained as mixture with the corresponding 1-methyl-4-(methylpyrrol-3-yl)-2,5-dioxo-1H-pyrrole-3-carboxylate. The reaction of indoles 4a–c smoothly proceeded in a manner similar as in the case of pyrroles. The electrophilic attack selectively took place at 3-position of indole ring. 1a reacted with 4a–c to give the corresponding compound 5a–c. The reaction yield was lowered in order of 5a > 5b > 5c, reflecting relative magnitude of steric hindrance at the 2-position. Reaction between 1c and 4a afforded the corresponding adduct 5d, but the yield was significantly lowered than 5a–c. 1b reacted with 4a–c to give the corresponding 5e–g in good yield. Details of the synthetic scheme are described in Supplementary Materials available online at doi:10.1155/2009/413219.

The UV/vis spectra were consistently measured in ethanol at room temperature. The first intense peaks of 5a–g appeared around 444–504 nm, bathochromically shifted from those of 3a–d, owing to their more extended -conjugation. The hyperconjugative effects of N-methyl group on maleimide ring invoked 26 nm bathochromic shift observed between 5a and 5d. The methyl and phenyl group at 2-position of indole ring induce 27 and 34 nm bathochromic shift, respectively, among 5a, 5b, and 5c. The substitution of COOMe to CN at 3-position on maleimide ring resulted in 14 nm shift, as observed between 5a and 5e.

3. Computational Details

The computations were carried out using GAUSSIAN03 program [8]. The Graphical representations of orbitals and of subtraction electron density were created by ChemCraft Software [9].

The ground-state geometry optimizations were carried out based on DFT using B3LYP hybrid functional combined with a series of Pople's standard basis sets (6-31G, 6-31G(d,p), 6-311G(d,p), 6-311G(2d,2p), 6-31+G(d,p), 6-311++G(d,p), and 6-311++G(2d,2p)). The optimized geometries were validated with the results that no negative vibration frequencies were found for all the molecules.

In TDDFT calculations on the DFT-optimized geometry,　a series of XC-functionals was employed; generalized gradient approximation (BLYP, PBE0, VSXC), hybrid type (B3PW91, B3LYP, O3LYP, MPW1PW91) and Handy's asymptotically corrected functional HCTH/407 to obtain the vertical excitation energies and their associated oscillator strengths.

In both steps of geometry optimization and TDDFT calculations, solvent effects of ethanol were included using the nonequilibrium polarizable continuum model (PCM) [10].

4. Results and Discussion

4.1. A Model Compound 3a

As a prototypical study, 3a was examined in details to assess how the set of computational parameters affect on TDDFT excitation energies.

Two-key geometrical parameters, the single bond connecting two moieties (r) and the interring torsion angle (), are defined in Table 1. The two parameters are consistently referred to hereafter for the remaining compounds 3b–d and 5a–g. The bond length ( Å), considerably shorter than the standard single C–C bond length by c.a. 0.1 Å, indicates moderate electronic resonance between the two moieties. Table 2 shows the evolution of as a function of basis sets used in both geometry optimizations and TDDFT calculations. As for the basis set effect on the geometry optimizations, we notice the uniform role of polarization, valence-splitting, and diffuse functions. For instance, the most extensive TDDFT using 6-311++G(2d,2p) gave blue shift by 16 nm from 6-31G- to 6-31G(d,p)-optimized geometry. The valence-triple-zeta basis set 6-311G(d,p) instead of valence-double basis 6-31G(d,p) yielded 5 nm blue shift. 6-31+G(d,p) basis set, augmented by single-diffuse function, shifted inversely, giving 1 nm red shift relative to that of 6-31G(d,p). The blue-shift (polarization, valence-splitting) and red-shift effect (diffuse) were also observed in the case of thioindigo dyes [11]. Moving on to the basis set effect used in TDDFT, the basis set improvement gave 12 nm red shift going from 6-31G to 6-311++G(2d,2p) for the most expensive 6-311++G(2d,2p)-optimized geometry. In details, 6-311G(2d,2p) gave no red shift from 6-31G, an indication of the minor influence of polarization and double/triple zeta splitting. On the other hand, 6-31+G(d) gave considerable red shift of 10 nm in comparison with 6-31G, which means the critical role of diffuse function. These trends are also found in the case of diazonium ion with minor contribution of polarization and diffuse enhancement [11], anthraquinone derivatives with polarization and valence-splitting [12], but are sharp contrast to the case of thioindigo dyes where the three types of basis set enhancements (polarization, valence-splitting, and diffuse function) monotonically gave substantial red-shift effects [11]. The gap between the moderate-scale PCM-TD-DFT(B3LYP)/6-31+G(d,p)//PCM-DFT(B3LYP)/6-311G(d,p) and the most exhaustive calculation PCM-TD-DFT(B3LYP)/6-311++G(2d,2p)//PCM-DFT(B3LYP)/6-311++G(2d,2p) is less than 1 nm. We therefore can safely use PCM-TD-DFT(B3LYP)/6-31+G(d,p)//PCM-DFT(B3LYP)/6-311G(2d,2p) as a well-balanced scheme both accuracy and computational burden. The influence of XC-functionals for TDDFT calculations was subsequently examined consistently using the optimized geometry obtained by DFT(B3LYP)/6-311G(d,p). The mixing weight of exact (Hartree-Fock) exchange in XC hybrid functionals critically affects the calculated [11]; O3LYP with 11.67%, B3LYP with 20%, PBE0 with 25%, respectively. The calculated is shifted hypsochromically as the mixing percentage rises, 457 nm (O3LYP), 448 nm (B3LYP), and 439 nm (PBE0). Other functionals, GGA (BLYP), meta-GGA (VSXC), and asymptotically corrected functional (HCTH/407) predicted red-shifted , 485, 463, and 478 nm, respectively, in comparison to the experimental 459 nm. Slight influence of the correlation term to was indicated with the gap between B3LYP and B3PW91 being only 2 nm. These XC-functional influences are in a qualitative agreement to our previous TDDFT results [13].

Table 2: (in nm) dependence of 3a on the basis sets used for geometry optimization (DFT) and TD-DFT.

The optimized TDDFT scheme above-mentioned characterized the low-lying six singlet excited states for 3a, as in Table 3. The first, fourth, and sixth transitions originate from the transitions on the whole molecular plain. The first intense peak, dominantly describable with the HOMO-LUMO excitation, has large oscillator strength (f) of 0.34. The second local excitation (LE) originates from HOMO-1 (mainly distributed on pyrrole ring) to LUMO with moderate f of 0.069. The third peak is of character with negligibly small f of 0.0002. The fourth transition derives from HOMO-3 (mainly distributed on maleimide ring) to LUMO with moderate f of 0.256. The fifth peak is of character with negligibly small f of 0.0002. The sixth transition has moderate f of 0.0281. The first computed transition at 448 (PCM-TD-DFT(B3LYP)/6-31G(d,p)) nm is ascribed to the first intense visible band at 459 nm, the fourth transition to the second band at 309 nm, and the sixth transition to the third UV band at 263 nm. The second, third, and fifth transitions with small f are thought to be hidden in the spectra.

Table 3: Low-lying valence singlet excited states of 3a.

4.2. Other Maleimide Derivatives 3b–3d and 5a–g

Following the assessment in the previous subsection, we consistently applied PCM-TD-DFT/6-31+G(d)//PCM-DFT(B3LYP)/6-311G(d,p) to the remaining molecules 3b–3d and 5a–g. Table 4 shows the interring bond lengths and the tortional angles along with the HOMO and LUMO levels. The TDDFT-predicted first peak positions are listed in Table 5 along with the experimental ones and the statistical parameters.

Table 4: Key geometrical parameters , HOMO, LUMO energy levels of (3a–d) and (5a–g).

Table 5: Calculated (nm) dependence on XC functionals for (3a–3d) and (5a–5g).

3a and 3b with little intramolecular steric hindrance hold nearly planar geometry while 3c and 3d have twisted geometries because of the steric repulsion between methylpyrrole and maleimide ring. The interring bond lengths of 3a and 3b are therefore appreciably shorter than those of 3c and 3d because the -conjugation in the molecular plain is fully restored. Concerning the theoretical dependence on XC hybrid functionals, O3LYP functional (with low mixing ratio of exchange term) showed excellent agreements for planar molecules 3a and 3b but appreciably longer for distorted compounds 3c and 3d. PBE0 and MPW91PW91 (with high mixing ratio of exchange term), inversely, gave worse agreement in case of 3a and 3b while a better agreement for 3c and 3d. The hybrid functionals B3PW91, B3LYP, and O3LYP gave underevaluated peaks in this order, with the peaks being blue-shifted proportional to the mixing ratio of an exact exchange term. Using the other functionals, the amplitude of displacement is severely large; BLYP-, VSXC-, and HCTH-predicated peaks showed large deviations particularly for 3c and 3d. In our previous TDDFT study [13], we found some specific features and limitations of theoretical for the newly prepared maleimide derivatives, where the molecules with large twist angle showed better agreement owing to efficient charge separation between the two moieties while PBE0 and MPW91PW91 gave better agreements than other functionals and the agreements worsen for planar compounds. All types of XC-fuctionals employed failed to reproduce hypsochromic shift of 3c and 3d in comparison with 3a and 3b. This is because theoretical of near-planar 3a and 3b are underevaluated while those of twisted 3c and 3d overvaluated, leading to this fictitious switching.

5a–5g apparently hold distorted geometry with the two -moieties being well separated. The qualitative agreements (within 40 nm deviations between theory and experiment) were obtained using PBE0 and MPW1PW91. The theoretical peaks however were overvaluated with all the XC-functionals, particularly for 5g using VSXC and HCTH functionals by more than 100 nm deviations. The theoretical displayed systematic red-shifted tendencies in the order B3PW91<B3LYP<O3LYP for hybrid functionals, which is proportional to the mixing ratio of an exact exchange term, as in case of 3a–3d.

The relative errors and the relative standard deviations in Table 5 indicate that a qualitative agreement is obtained between theoretical and experiment for 3a, 3b, and 3c, while other molecules show a worse agreement. This is due to the considerable red-shift deviations when using VSXC and HCTH functionals which are not well optimized for twisted -conjugated systems.

5. Conclusion

New maleimide derivatives bearing pyrrole and indole ring were synthesized and assessed for their UV/vis spectra experimentally and computationally. Experimental UV/vis were observed in 435–504 nm. TDDFT analysis (PCM-TD-DFT/6-31+G(d,p)//PCM-DFT(B3LYP)/6-311G(d,p)) for the first intense peak of the compounds was done to obtain semiquantitative agreements between experimental and theoretical for the compounds.