Semiexperimental equilibrium structure of 1-methylisatin from gas-phase electron diffraction data and structural changes in isatin due to 1-methyl and 5-fluoro substituents as predicted by coupled cluster computations

ABSTRACT The molecular structure of 1-methylisatin (1) has been studied by gas-phase electron diffraction (GED) and quantum chemical computation up to the coupled cluster (CCSD(T)) level of theory. The semiexperimental equilibrium structure (Cs point group symmetry) has been determined from the GED data taking into account anharmonic vibrational corrections calculated in curvilinear coordinates with the B2PLYP force field. To observe fine structural effects due to the presence of different kinds of substituents, the accurate molecular structures of isatin (2) and 5-fluoroisatin (3) were also computed at the CCSD(T) level. The (O=)C–C(=O) carbon–carbon bonds of the pyrroline moiety in 1–3 are found to be remarkably longer than the typical single C–C bond. The electron donating methyl group causes a decrease of the C−N−C angle and an elongation of the N−C bond lengths in the pyrroline ring by 0.7° and up to 0.008 Å, respectively, whereas the electron withdrawing fluorine atom increases the ipso CCC angle by 2.5° in comparison to that in unsubstituted isatin. GRAPHICAL ABSTRACT


Introduction
Indoline-2,3-dione or indole-1H-2,3-dione, commonly known as isatin, is a well-known natural product found in plants [1,2]. It was isolated as a metabolic derivative of adrenaline in humans [3,4]. Being easily available, it is widely used as building blocks in organic synthesis. The recent literature shows a renewal of interest in isatin due to the development of stereoselective methodologies used in the synthesis of isatin derivatives with various [14,15] and computed at the M062X [16] and MP2 [17] levels (with the aug-cc-pVTZ basis set [18]). It was found that the most remarkable feature of these molecules is a relatively long (O = )C-C( = O) carbon-carbon bond (r a = 1.573(7), 1.581(11), 1.578(8), 1.574(12) Å for 5-R-isatin, where R = H, F, Cl, Br, respectively) if compared with respect to the mean value of the single C-C bond lengths of 1.52 Å in all molecules studied in the gas phase (see MOGADOC (Molecular Gas-phase Documentation) database [19]). This carbon-carbon bond elongation was first attributed to the repulsions by the electron lone pairs of the oxygen atoms [20]. Indeed, a survey of structural data in [19] points out the noticeably longer carbon-carbon bond distances for s-cis diketones than those for their s-trans conformers, in which this repulsion is absent. However, semiempirical and ab initio molecular orbital calculations [21] revealed that the electron lone pair repulsion cannot explain the observed lengthening of the (O = )C-C( = O) bond in isatin and several related molecules. A negative hyperconjugative interaction between the electron lone pairs of the oxygen atoms and the antibonding σ * orbital of the adjacent C-C bond is suggested to be the main reason for the relatively long C-C bond in both the s-cis and s-trans conformers of 1,2-diketones and other molecules. In our recent studies [14,15], the NBO (Natural Bond Orbitals) [22,23] analysis was performed in order to reveal peculiar features of molecular structures of isatin derivatives. The present work continues the analysis of structural changes in isatins due to the influence of different kinds of substituents, namely, R = 1-CH 3 and 5-F. The structure of 1-methylisatin (1) is known only in the solid state so far [24]. Therefore, the main aim of our study is the determination of the semiexperimental equilibrium structure of 1 by gas-phase electron diffraction (GED) taking into account anharmonic vibrational effects that allows benchmarking of the results of quantum chemical computations. The high accuracy of the high level ab initio computations will be exploited to reveal fine structural effects due to substitution, while very often these effects, being in magnitude comparable with GED uncertainties, cannot be seen in experimental structures. For a comparative analysis, the accurate structures of isatin (2) and 5-fluoroisatin (3) will be computed at the same level of theory.

Quantum chemical calculations
The geometry optimizations for 1-3 molecules were performed at the level of second-order Møller-Plesset perturbation theory (MP2) [17] in conjunction with the cc-pVTZ (VTZ), cc-pVQZ (VQZ) [18] and cc-pwCVTZ (wCVTZ) [25] basis sets in the 'all-electron correlated' (AE) and/or 'frozen-core' (FC) approximations. A very time consuming structure optimisation by the coupled cluster method with single and double excitation [26] and a perturbative treatment of connected triples [27], CCSD(T)_FC, was carried out with the VTZ basis set. The effects of further basis set improvements, r e (T → Q) = [r e (VQZ) -r e (VTZ)], as well as the core-core and core-valence correlation effects, r e (corr) = [r e (AE/wCVTZ) -r e (FC/wCVTZ)], were estimated at the MP2 level, i.e. the CCSD(T)_FC/VTZ structure was extrapolated as follows yielding a structure of CCSD(T)_AE/wCVQZ quality: ( 1 ) The accuracy of this composite structure, based on the additivity of small corrections, was estimated to be very high, namely, of a few thousandths of Å for the bond lengths and a few tenths of degree for the bond angles (see for instance [28][29][30][31][32][33][34][35][36][37]). A summary of computed results is given in the online supplemental data (Tables S1-S3). The MP2 calculations were performed with the Gaussian 09 package (G09) [38], whereas the CFOUR programme [39] was used for the CCSD(T) computation.
Quadratic and cubic force fields were calculated with the B2PLYP double hybrid functional [40] and the correlation-consistent VTZ basis. The list of vibrational harmonic and anharmonic wavenumbers is archived in the supplemental data (Table S4).
Total corrections to experimental internuclear distances r a , ( r = r a -r e ), were calculated at the level of the first-order perturbation theory taking into account nonlinear kinematic effects using harmonic and anharmonic force constants [41][42][43][44] (for more details concerning r calculations, see also Ref. [45]). Anharmonic rovibrational corrections to the ground-state rotational constants X 0 = A 0 , B 0 , C 0 , X = X e -X 0 , and rootmean-square (rms) vibrational amplitudes (u h1 ) were also calculated in curvilinear coordinates using cubic and quadratic force constants, respectively. All these calculations were carried out with the SHRINK computer programme written by V. A. Sipachev [41][42][43][44]. The calculated vibrational corrections and rms amplitudes are presented in the supplemental data (Table S5).

Experimental procedure
The commercial sample 1 was additionally purified by recrystallization from ethanol and the expected purity was not less than 99.5%. The electron diffraction patterns were recorded at the Moscow State University on Table 1. Experimental conditions of gas-phase electron diffraction experiment for 1-methylisatin (1) at the long (LD) and short (SD) nozzle-to-film distances a . the EG-100M apparatus using the R 3 sector produced with high precision in the workshop at the University of Ulm. The electron wavelength was calibrated with the gaseous standard CCl 4 . The structural parameters of the CCl 4 molecule were taken from [46] being identical with those from Ref. [47]. The experimental conditions are described in Table 1.
Photo films (TASMA FT-41P) were scanned with the use of the Epson Perfection Photo 4870 commercial scanner in the 16-bit/4800-dpi gray scale scanning mode and with the use of the VueScan computer programme [48]. This programme permits to obtain data directly from the detector without any modifications. The data were processed as in [49,50] using a computer programme written by A.V. Belyakov. Preliminarily, the high resolution data were transformed by averaging of square regions of pixels as described in [48]. With this method mean transmittances and their standard deviations were collected. The latter were used as weights for smoothing of the transmittance surface using the 2D cubic splines [51]. The calibration of the scanner was carried out against the MD100 microdensitometer with the use of a 24 gray scale optical wedge of IT8 transmissive target on Kodak Ektachrome Professional E100G film [52]. Displacements of the scanner were corrected against a special ruler manufactured by LOMO. After the refinement of the centre in the electron diffraction pattern by a least squares method the data of scanning were transformed into a total intensity curve taking into account the 2D background. The atomic scattering factors were taken from [53].

Structural refinements
To calculate Cartesian coordinates of atoms, we used the algorithm described in [54]. For the ring closure the calculation of the coordinates is not terminated at the last atom in the ring, but is continued for three dummy atoms according to the same rules described in [54]. The problem of ring closure reduces to an iterative solution of nonlinear equations with respect to the dependent geometrical parameters so that the Cartesian coordinates of dummy atoms coincide with those of the first three atoms of the ring.    Table 2.
The fit of parameters of the molecular model was performed by the minimisation of the functional: where s = (4π/λ)sin(θ/2) is a function of the electron scattering angle θ; λ is the wavelength of electrons in the beam; sM(s) is intensity of electron scattering on molecules, so called 'reduced molecular intensity' [55]; w s is a weight function; and k is the scale factor. The goodness of the fit was characterised by the value of the R-factor : The structure refinements were carried out by means of a modified version of the KCED25 programme package [56,57]. The intensity data were multiplied by the weight factors of 1.0 and 0.5 for the long and short nozzle-tofilm distances, respectively. The final reduced molecular intensity sM(s) and radial distribution f (r) curves are shown in Figures 2 and 3, respectively. The molecular model of 1 with C s point group symmetry (see Figure 1 for atom numbering) was described by 23 independent parameters, i.e. by 15 bond lengths (C3a C7a, C7a-N1, C2-N1, C2-C3, C3a-C3, C7a Table 2. Semiexperimental equilibrium structure of (1) from GED data and computed equilibrium structures of 1-3 molecules a . 1.403 (7)   C7, C6 C7, C5 C6, C4 C5, C4 C3a, N1-C1, C2 = O2, C3 = O3, C1-H (average), C Ph -H (average)) and eight bond angles (C3a C7a-N1, C2-N1-C7a, C7 C7a C3a, C6 C7 C7a, C5 C6 C7, O2 = C2-N1, O3 = C3-C2, C1-N1-C2). Six bond angles (C3-C2-N1, C3a-C3-C2, C7a C3a-C3, C4 C5 C6, C3a C4 C5, C7a C3a C4) were derived from the ring closure conditions. Bond angles containing hydrogen atoms were assumed at the values of the extrapolated CCSD(T) structure (see Equation (1)). Small differences between similar geometric parameters were fixed at the values derived from the computed structure as can be seen in Table 2. Due to the strong correlation and large uncertainties, the average C-H bond length in the methyl group, the H-C-H bond angles, the C-N-C-H dihedral angles as well as the C1-N1-C2 bond angle were also assumed at the computed values.
Rms vibrational amplitudes were refined in groups. Differences between parameters in each group were fixed at the values calculated with the B2PLYP/VTZ force constants.

Results and discussion
According to calculations (see above), 1 is a rather rigid molecule with the lowest vibrational wavenumber of 102 cm −1 (B2PLYP/VTZ). The absence of imaginary frequencies confirms that the structure with C s point group symmetry corresponds to a minimum on the potential energy surface.
The comparison of data in Table 2 shows an excellent agreement between the determined semiexperimental and estimated CCSD(T)_AE/wCVQZ equilibrium bond lengths of 1. Differences between these parameters are about three times less than the estimated experimental errors of 0.007 Å. Differences between the bond angles are outside of the experimental uncertainties by a few tenths of a degree, except for the C4 C5 C6 and C5 C4 C3a angles with relative large discrepancies of up to 1.4°outside of the estimated experimental error.
The equilibrium (O = )C-C( = O) bonds in the pyrroline moiety of 1.560(7) and 1.559 Å for 1 and 1.554 and 1.562 Å for 2 and 3, respectively, are remarkably longer in comparison with the mean magnitude of the single C-C bond lengths of 1.52 Å (without vibrational corrections which reduce this value by ≈ 0.01 Å) evaluated in the MOGADOC database [19] for thousands of gas-phase compounds.
The explanation of this result is given in our previous studies by the NBO analysis for glyoxal, pyrrole-2,3dione and 5R-isatines (R = H, F, Cl, Br) [14,15]. It was shown that the elongation of the (O = )C-C( = O) bond cannot be attributed alone to the electrostatic repulsion of the electron lone pairs of the oxygen atoms and occurs mainly due to hyperconjugation, i.e. due to delocalisation of the oxygen electron lone pairs of π-type into the corresponding carbon-carbon antibonding orbital, n π (O) → σ * * (C-C).
Comparison of the computed structures of CCSD(T) _AE/wCVQZ quality shows a decrease of the C7a−N1− C2 angle and an elongation of the N−C bond lengths in the ring by 0.7°and by up to 0.008 Å, whereas the electron withdrawing fluorine substituent increases the C4 C5 C6 bond angle by 2.5°in comparison to that in unsubstituted isatin (see Figure 4). The same tendencies were revealed in benzene and heterocyclic derivatives due to electronegative and electropositive substituents [59][60][61].

Concluding remarks
For the first time, the molecular structure of 1methylisatin is studied by an experimental method in the gas phase. The high accuracy of the semiexperimental equilibrium structure, determined from gas-phase electron diffraction data taking into account anharmonic vibrational effects, allows the benchmarking of the results of quantum chemical computations (up to CCSD(T)_AE/wCVQZ quality). Furthermore, the high accuracy of the computed structures of isatin and its 1-methyl and 5-fluoro derivatives makes possible the revealing of fine structural effects comparable in magnitude with experimental uncertainty. The electron donating methyl group causes a decrease of the C−N−C angle and an elongation of the N−C bond lengths in the pyrroline ring by 0.7°and by up to 0.008 Å, whereas the electron withdrawing fluorine substituent increases the ipso C C C angle by 2.5°in respect to that in unsubstituted isatin.
Similar to previously studied isatin derivatives, the very long (O = )C-C( = O) bond length in 1-methylisatin can be explained mainly by the delocalisation of the oxygen electron lone pairs of π -type into the corresponding carbon-carbon antibonding orbital, n π (O) → σ * *(C-C).