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Structure of the Indole-Benzene Dimer Revisited Himansu S. Biswal,* Eric Gloaguen, and Michel Mons Laboratoire Francis Perrin, CEA/DSM/IRAMIS/SPAM—CNRS URA 2453, CEA/Saclay, 91191 Gif-sur-Yvette, France
Surjendu Bhattacharyya, Pranav R. Shirhatti, and Sanjay Wategaonkar Department of Chemical Sciences, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400 005, India
bS Supporting Information ABSTRACT: The structure of the indole-benzene dimer has been investigated using experimental techniques, namely, UV spectroscopy and infrared-ultraviolet (IR/UV) double resonance spectroscopy, combined with quantum chemical calculations such as MP2 and dispersion corrected DFT methods. The red shift of the indole N-H stretch frequency in the dimer provides direct evidence that the experimentally observed indole-benzene dimer is an N-H 3 3 3 π bound hydrogen bonded complex. Theoretical investigations suggest that the potential energy surface (PES) of the complex is rather flat along the coordinate describing the tilt angle between the molecular planes of indole and benzene, with several minima of similar energies, namely, parallel displaced (PD), right-angle T-shaped (T), and other intermediate structures which can be categorized as tilted T-shaped (T0 ) and tilted parallel displaced (PD0 ) structures. Three different computational methods, namely, RI-MP2, RI-B97-D, and PBE1-DCP, are used to arrive at a new structural assignment after assessing their performance in predicting the structure of the pyrrole dimer, for which accurate experimental data are available. By comparing the computed IR spectra of PD, T, and T0 / PD0 structures with the experimental IR spectrum, the tilted T-shaped (T0 ) structure was assigned to the indole-benzene dimer. The empirically dispersion-corrected functionals (RI-B97-D and PBE1-DCP) correctly reproduce the experimental IR spectrum whereas the popular post-Hartree-Fock, MP2 method gives disappointing results. These results are also in agreement with the experimental dissociation energy (D0) reported in the literature. The N-H stretch frequency of the indole-benzene dimer has been found to be a more pertinent parameter for the structural assignment than the dissociation energy (D0).
1. INTRODUCTION Noncovalent interactions between two aromatic (ar) systems are ubiquitous in the hydrophobic core of proteins.1-5 These interactions can be categorized as: (i) polarization, related to the Debye force, which controls the ar-X-H 3 3 3 π (X = C, N, and O) hydrogen bonding, in which one aromatic system acts as an H-bond donor and the other as an acceptor, and (ii) dispersion (London force), found in the interactions between two aromatic rings like in the benzene dimer.6-8 For instance, interactions between phenylalanine side chains, which are merely dispersion and quadrupole-induced-dipole interaction, have recently been shown to play a crucial role in the structure and the stability of peptides.9 The influence of the ar-X-H 3 3 3 π H-bonds are even more important in controlling the structure and reactivity of biomolecules as these interactions tend to orient both the aromatic systems more specifically than the London forces.10 As an example, the presence of ar-X-H 3 3 3 π H-bonds in protein chains play a pivotal role in stabilizing R-helices and β-sheets, which in turn provides them a well-defined shape.11 To study such interaction at the molecular level in proteins is still a quite challenging task for both the experimentalists and the r 2011 American Chemical Society
theoreticians. However, an alternative approach consists of studying relatively smaller molecular complexes which can be routinely synthesized under gas phase isolated conditions. These simple systems are ideal for modeling the aforementioned interactions and can serve as benchmark systems for quantum chemical methods. A lot of information about the structure, energetics, and the nature of the ar-X-H 3 3 3 π H-bonded interactions can be extracted by a combined approach of using the state-of-the-art experimental techniques such as IR/UV double resonance spectroscopy and ab initio calculations. In this context, the indole-benzene dimer is one of the simplest intermolecular complexes, which has recently drawn much attention from both spectroscopists and theoreticians to describe the aforementioned interactions at the molecular level.12-15 The indole-benzene dimer can indeed be considered as a model system for the Special Issue: David W. Pratt Festschrift Received: December 16, 2010 Revised: February 4, 2011 Published: March 17, 2011 9485
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Figure 1. Four different types of conformations of the indole-benzene dimer: two limiting cases (T and PD) and two intermediates (T0 and PD0 ). The T0 and PD0 conformations are found for the dispersion corrected DFT methods (RI-B97-D and PBE1-DCP) and RI-MP2 levels of theory, respectively, while T and PD conformations are found for both levels.
aromatic side chain interaction between the two naturally occurring amino acids tryptophan and phenylalanine, which bear indole and benzene as side chains, respectively. Another interesting aspect about this system is that it enables us to address the issue of competition between the two types of interactions described earlier. From the interplay between these two interactions and by analogy with the benzene dimer6,16-21 (excluding the ar-C-H 3 3 3 π interactions between indole and benzene), one can anticipate several conformations for the indole-benzene dimer (Figure 1) with two limiting cases: (i) a T-shaped NH 3 3 3 π H-bonded complex, with perpendicular molecular planes, and (ii) a π 3 3 3 π stacked or parallel displaced (PD) dimer. The PD dimer is mainly stabilized by the Londondispersion interaction while the N-H 3 3 3 π H-bonding is commonly considered as a mixed complex in the S22 data set,22-26 in which electrostatic and dispersion contributions are similar in magnitude. In addition to these extreme geometries, intermediate conformations (tilted parallel displaced, PD0 , or tilted T-shaped, T0 , see Figure 1) similar to the structure of the pyrrole dimer27 (tilted T-shaped, T0 ) are possible, in which the two molecular planes are neither parallel nor perpendicular to each other and the N-H of the donor can interact with one or more of the ring atoms of the acceptor, rather than with its centroid (Figure 1c). In an earlier publication, Braun et al.13 suggested that indolebenzene was in fact an N-H 3 3 3 π bound H-bonded dimer. The authors came to this conclusion by comparing the dissociation energy (D0) determined using mass-analyzed threshold ionization (MATI) spectroscopy with the ab initio quantum chemical calculations. The right-angle T-shaped N-H 3 3 3 π H-bonded dimer (Figure 1a) was in good agreement with the experimental D0 and was then assigned to the observed species. Such an assignment can be questioned for several reasons: first, the exploration of the potential energy surface was limited to only two structures, namely, PD and T conformations, and, second, the dissociation energy (D0) might not be sensitive enough to unambiguously distinguish the conformers, that are quite close in energy. In contrast, the N-H stretch being very sensitive to the
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environment of the NH bond, one can expect that the IR N-H stretch spectroscopy to be a more appropriate probe for structure elucidation. As far as theoretical description of the aromatic complexes is concerned, in which dispersion contribution is significant, a high level of theory such as the CCSD(T) level is required. However, geometry optimization and frequency calculation at the CCSD(T) level of theory for a system as large as the indole-benzene dimer is beyond our computational capacity. In such a situation one has to look for alternate methods that are cost-effective without sacrificing the accuracy. The strategy that is commonly followed consists of carrying out the geometry optimization and frequency calculation at a lower level (MP2 or RI-MP2), followed by single point energy calculation at the CCSD(T) level.13 As an alternative, dispersion corrected DFT methods28-35 have proven to describe dispersive interactions correctly. The B97-D method is specifically designed for dispersive systems and has been shown to be quite promising to describe peptide structures in the gas phase.9,36,37 In this case the London dispersion energy is empirically included by using an appropriately adjusted damping factor compared to the standard DFT methods. The PBE1-DCP is another dispersion corrected DFT, which involves the use of dispersion-correcting potentials (DCPs). The DCPs are local, atom-centered potentials which take into account long-range, weakly attractive potentials and shorter-range, weakly repulsive potentials. The PBE1-DCP method has recently shown to be very successful in predicting the structure and the energetics of different types of intermolecular complexes with significant dispersive interactions at low computational cost.25,33,34 Keeping in mind the relevance of the NH stretch spectroscopy for the structural assignment of the indole-benzene complex as well as the potentials of the new quantum chemistry methods in describing these systems, we have carried out a combined experimental and computational investigation of the indolebenzene dimer which enabled us to propose a new structural assignment. This paper is organized as follows. After an overview of the experimental and theoretical methods employed in this work, the results of the UV and IR/UV spectroscopy of the indole-benzene dimer are presented. An assessment of the different theoretical methods (RI-MP2, RI-B97-D, and PBE1DCP) is done using the pyrrole dimer as a reference system. Finally, the relevance of several types of experimental data (UV spectroscopy, energetic, and NH stretch spectroscopy) is discussed, leading to the proposed assignment.
2. EXPERIMENTAL DETAILS The details of the experimental apparatus can be found elsewhere.38,39 Experimental techniques such as resonant twocolor two-photon ionization (2C-R2PI) time-of-flight mass spectrometry (TOFMS) and fluorescence detected infrared spectroscopy (FDIRS) were used to study the indole-benzene dimer in supersonic jet. The reagent indole was evaporated at 60-80 °C and coexpanded through a 500 μm pulsed nozzle (General Valve, series 9) via the expansion chamber and skimmer into the time-of-flight mass spectrometer using helium as a carrier gas. A 2-5% premixture of benzene in helium was used to generate the 1:1 complexes of indole and benzene. For the 2CR2PI experiments, a 10 Hz, nanosecond Nd3þ:YAG (Quantel Brilliant) pumped dye laser (Molectron DL18P) was used to provide the fixed ionization source (D0 - S1) and another 9486
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The Journal of Physical Chemistry A Nd3þ:YAG (Quantel YG781C) laser pumped dye laser (Quantel TDL70) was used to provide the tunable S1 - S0 excitation source. The two copropagating beams were spatially and temporally overlapped and were focused onto the molecular beam using a lens of 50 cm focal length. Typical pulse energies were ∼5-10 μJ for the excitation laser and ∼100 μJ for the ionization laser. The FDIRS was carried out in the expansion chamber itself. The IR spectra were recorded by monitoring the depletion of the fluorescence signal as a function of IR frequency between 3350 and 3550 cm-1 corresponding to the N-H stretch region. The tunable IR source was a ∼10 ns, 10 Hz seeded Nd3þ:YAG laser (Quanta-Ray PRO Series, PRO 230-10) pumped dye laser (Sirah, CSTR LG 18 532). The dye laser output was mixed with the 1064 nm output of the Nd3þ:YAG laser in a LiNbO3 crystal to generate the IR output by difference frequency generation. The N-H stretching region was covered using the styryl-8 dye (Exciton, Inc.). The UV and the IR lasers were temporally synchronized by a master controller (SRS DG-535). The typical backing pressure employed during the experiments was 2.5-3 atm. The typical working pressure in the source chamber and the TOFMS chamber was ∼6 10-5 and ∼2 10-6 Torr, respectively.
3. COMPUTATIONAL DETAILS Three different methods (RI-MP2/TZVPP, RI-B97-D/TZVPP, and PBE1-DCP/6-31G(d)) were used for the geometry optimization and the harmonic frequency calculation of the indolebenzene dimer. The post-Hartree-Fock Møller-Plesset level of theory (MP2) is very popular as it accounts for the correlation energy and is generally used for the systems where the dispersion interaction has a significant contribution although this method overestimates dispersion and is very sensitive to the basis set superposition error (BSSE) effects.40,41 The dispersion corrected DFT methods (RI-B97-D and PBE1-DCP), specifically designed to account for dispersion in large systems, have proven to be efficient methods to calculate the geometry and energy that are comparable to the CCSD(T) results on benchmark systems.25,28,29,33,34 Moreover, it has been shown that the PBE1DCP/6-31G(d) level of calculation gives energies of intermolecular complexes, comparable to those obtained at the CCSD(T)/CBS (CBS: Complete Basis Set) level of theory.25 These three methods were tested against the known structure of the pyrrole dimer. The geometry optimization and frequency calculations were carried out by RI-MP2/TZVPP, RI-B97-D/TZVPP (the TURBOMOLE 5.10 package42), and PBE1-DCP/6-31G(d) (the Gaussian03 program suite43) using both standard gradient and counterpoise (CP) gradient method according to Boys and Bernardi.44 The DCPs specifically developed for PBE1/6-31G(d) and counterpoise corrections were taken from ref 25. The binding energy (De) was corrected for the intermolecular basis set superposition error (BSSE).44 The dissociation energy (D0) was obtained by adding the difference in the zero point vibrational energy (ZPVE) of the dimer and the two monomers [ΔZPVE = ZPVEindole-benzene - (ZPVEindole þ ZPVEbenzene)] to the De value. No scaling factor is used for ZPVEs. For each method a constant scaling factor was applied to match the calculated monomer (indole or pyrrole) N-H stretch frequency with the experimental number. 4. RESULTS AND DISCUSSION 4.1. Electronic and Infrared Spectroscopy. Figure 2 displays the 2C-R2PI spectra of indole and its complex with benzene. The
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Figure 2. Two-color R2PI spectra of (a) indole and (b) indolebenzene dimer, recorded in their corresponding mass channel, m/z = 117 and 195, respectively. In all cases the ionization laser was kept at 27778 cm-1.
Figure 3. FDIR spectra of (a) indole, (b) indole-benzene dimer, and (c) indole-H2O recorded while tuning the probe laser at the electronic band origin of the respective species.
S1 r S0 electronic origins of indole and indole-benzene dimer are observed at 35241 and 35077 cm-1, respectively. The observed R2PI spectrum for the indole-benzene is in excellent agreement with the previously reported spectrum.12 The red shift of the band origin of indole in the indole-benzene dimer is 164 cm-1 which is larger than that in the water complex (132 cm-1).45 A weak band, observed at 69 cm-1 to the blue side of the band origin of indole-benzene dimer was earlier assigned by Braun et al.12,13 as the intermolecular stretching frequency (σ1) of the T-shaped dimer. The FDIR spectra have been recorded for indole and indolebenzene in the N-H stretching frequency range (Figure 3). The FDIR spectrum of indole-H2O is also displayed for the sake of comparison with the well established NH 3 3 3 O H-bonded complex.45,46 The N-H stretches for the indole-benzene and indole-H2O complexes appear at 3479 and 3436 cm-1 and are red-shifted by 46 and 89 cm-1, respectively, with respect to the free N-H stretch of indole (3525 cm-1). It is observed that the red shifts of N-H stretch for the indole-benzene and pyrrolebenzene dimer47 are exactly same. To cross check this experimental red shift for the indole-benzene dimer, similar experiments are also performed on the 3-methylindole-benzene dimer (Figure S1 of Supporting Information). In this case the red shift is found to be 42 cm-1, which is consistent with the red shifts in the indole-benzene and pyrrole-benzene dimers. It is also worthwhile to mention that the red shifts of N-H stretches 9487
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Table 1. Comparison between the Experimental Parameters of the Pyrrole Dimer Such as the Measured Rotational Constants, the Geometrical Parameters Deduced from the Rotational Constants, the Observed N-H Stretching Frequencies, and Those Computed for the Three Different Methodsa rotational constants (MHz)b methods expt
A
B
C
geometrical parametersb
RMSPD
N-H frequency (cm-1)a,c
R (pm)
θ (deg)
j (deg)
(νN-H)D
(νN-H)A
RMSD 0
2972
722
674
0
412
12.0
55.4
3444
3524
PBE1-DCP/6-31G(d)
CP
2950
726
677
0.57
418
10.7
57.1
3446
3526
2
RI-B97-D/TZVPP
w/o CP
2954
732
682
1.11
415
13.8
51.2
3457
3525
9
CP
2953
731
681
1.02
415
13.8
51.1
3454
3528
8
RI-MP2/TZVPP
w/o CP CP
2964 2960
791 759
735 708
7.60 4.16
396 406
17.8 12.9
45.0 51.4
3419 3429
3519 3519
18 11
a
A constant scaling factor is used to match the computed N-H stretch of the monomer, pyrrole. Scaling factors: for RI-B97-D, 0.97541; RI-MP2, 0.95381; PBE1-DCP, 0.95078. RMSPD and RMSD are defined as the root mean squared percentage deviation and root mean squared deviation from the experimental values, respectively. b The experimental rotational constants and the geometrical parameters are taken from ref 27. c The experimental stretching frequencies of the pyrrole dimer are taken from ref 47.
in the H2O complexes with pyrrole, indole, and 3-methylindole are very close (83, 89, and 84 cm-1 for the pyrrole-H2O,48 indole-H2O, and 3-methylindole-H2O dimers,45,46 respectively). This suggests that irrespective of the H-bond acceptor, pyrrole, indole, and 3-methylindole behave in a similar manner. Although the red shift of the N-H stretch in the indole-benzene dimer is almost half of the red shift observed for the indole-H2O dimer, it is large enough to indicate that the N-H is not free. Its significant value (46 cm-1) suggests, the observed species is not a PD conformation, for which only a slight shift is expected at most. On the other hand, this magnitude of the experimental red shift provides a direct evidence for an N-H 3 3 3 π H-bonded geometry. However, the question whether it is a right-angle, a tilted T-shaped, or a PD0 N-H 3 3 3 π H-bonded dimer is still open. In order to resolve this issue, we will rely on the comparison between the experimental IR shift and the theoretical predictions. 4.2. Assessment of the Computational Methods. The three different computational methods (RI-MP2/TZVPP, RI-B97-D/ TZVPP, and PBE1-DCP/6-31G(d) are evaluated using the pyrrole dimer as the reference system. The pyrrole dimer is chosen as the reference system for the following reasons: (i) same types of interactions are expected to be at play in the pyrrole dimer and the indole-benzene complex, and (ii) the microwavedetermined structure of the pyrrole dimer and its gas phase IR spectrum are available27,47,49 as benchmark data. The computed rotational constants have then been compared together with the three experimental27 structural parameters (Table 1), namely, R, the distance between the centers of mass of the monomers; θ, the angle between the directional vector joining the centers of mass of the monomers and the normal to the H-bond acceptor plane; φ, the angle between the planes of the H-bond donor and the H-bond acceptor (Figure 4). Similarly, the predicted vibrational frequencies are also compared (Table 1) with the experimental values.47,49 It can be noticed that most of the computed parameters obtained with CP-gradient are closer to the experimental values than those obtained using standard gradient. The computed parameters obtained from the PBE1-DCP method using standard gradient geometry optimization are not shown here as the DCPs are optimized for the CP-gradient procedure.25 The best match for the rotational constants with the experimental values is obtained from the PBE1-DCP-CP computation and the worst from the RI-MP2 level of theory. The limitations of the
Figure 4. Schematic representation of the geometrical parameters of the pyrrole dimer such as R, the distance between the center of mass of the monomers, θ, the angle between the directional vector joining the center of mass of the monomers and the normal to the H-bond acceptor plane, and φ, the angle between the planes of the H-bond donor and the H-bond acceptor. These structural parameters for the indolebenzene dimer are slightly different and redefined as follows: R, the distance between the geometrical centers of the pyrrole ring of indole and the benzene ring, θ, the angle between the directional vector joining the geometrical center of pyrrole ring in indole and benzene and the normal to the molecular plane of benzene, and φ, the angle between the molecular planes of the indole and benzene.
RI-MP2 method also appear in the computed vibrational frequencies (Figure 5). The computed N-H stretching frequency for the H-bond donor is highly underestimated at the RI-MP2 level whereas it is slightly overestimated by the RI-B97-D method. However, the N-H stretch frequencies predicted by the PBE1-DCP method nicely match the experimental values. The maximum discrepancy for the N-H stretch obtained at the RI-MP2 level is 25 cm-1, which is about ∼29% of the experimental N-H shift in the pyrrole dimer (87 cm-1). Both the RIB97-D-CP and PBE1-DCP-CP methods used in this study compare much better with the experimental parameters; the PBE1-DCP-CP level giving the best agreement. 4.3. Assignment of the Structure of the Indole-Benzene Dimer. Both the experimental and computational data are used to deduce the best possible description of the structure of the indole-benzene dimer. The details of the conformational exploration and the nomenclature used to label different 9488
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Figure 5. The experimental vibrational frequencies of the pyrrole dimer (dotted line) in the NH stretch region are compared with the IR stick frequencies calculated at the (a) PBE1/6-31G(d), (b, c) RI-B97-D/ TZVPP, and (d, e) RI-MP2/TZVPP levels of theory. For all these methods, a scaling factor is used to match the computed N-H stretch of the pyrrole with that of the experimental value (see footnote of Table 1). In the figure, CP denotes that the geometry optimization and frequency calculations are done using the counterpoise gradient, D and A denote the donor and acceptor N-H stretches of the pyrrole dimer, respectively. The experimental IR data for the pyrrole and the pyrrole dimer were taken from ref 47.
conformations are outlined in section 4.3.1. Experimental data, such as the dissociation energy (D0) and the N-H stretching frequency of indole-benzene, are compared with the computed parameters (sections 4.3.2 and 4.3.3). The combined approach of experimental results and theoretical predictions provides a clear distinction between the different conformers of indole-benzene dimer and enables us to propose a new assignment (section 4.3.4). 4.3.1. Conformational Landscape. The structural assignment of the indole-benzene dimer by Braun et al13 was based on the computational data of only two structures, namely, T and PD. In the present work, a larger set of conformations has been considered. A conformational exploration for the indole-benzene dimer has been performed by starting geometry optimizations from 25 different trial geometries including N-H 3 3 3 π hydrogen-bonded and π-stacked structures. The geometry optimizations and the frequency calculations have been carried out using the three methods mentioned in the previous section. In all cases, the final structures converge on three different types of structures such as right-angle T-shaped (T), parallel-displaced (PD), and intermediate (tilted T-shaped (T0 ) or tilted parallel displaced (PD0 )) conformations (Figure 1). Table 2 shows some of the relevant geometrical parameters such as R, the distance between the geometrical centers of the pyrrole ring of indole and the benzene ring, θ, the angle between the directional vector joining the geometrical centers of pyrrole ring in indole and benzene and the normal to the molecular plane of benzene, and φ, the angle between the molecular planes of the indole and benzene. It is worth mentioning that the rotations of indole and benzene in their molecular planes are not described by these structural parameters R, θ, and φ. The (θ, φ) values for the T and PD conformations are almost the same at all the methods with φ values close to 90° for T and between 5 and 10° for PD. However, the intermediate structures are found to be method-dependent, with different sets of (θ, φ) values, i.e. (20°, 25°), (12°, 54°), and (10°, 58°) for the RI-MP2, RI-B97-D, and PBE1-DCP methods, respectively. The φ value of the intermediate structure obtained
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by the DFT-D methods is ≈55° and the structure seems to be slightly deviated from the right angle T-shaped structure (see Figure 1, panels a and c). This leads us to label this intermediate structure as the tilted T-shape (T0 ) conformation. The intermediate conformation for the RI-MP2 method exhibits a much smaller value of φ (≈25°), corresponding to another type of intermediate structure, between T0 and PD, and is therefore labeled as PD0 . This finding is consistent with the well documented37,50,51 overestimation of dispersion by MP2, favoring PD0 structures over T0 in the present case. It is worth mentioning that the T-conformation obtained with the PBE1-DCP method is not a minimum, rather a saddle point structure with two imaginary frequencies. 4.3.2. Dissociation Energy (D0). The PES of indole-benzene dimer can be characterized from the dissociation energies (D0) of the three stable conformations found in the system. These dissociation energies, displayed in Table 2, are obtained by adding the corresponding ΔZPVE corrections (without using any scaling factor for the respective ZPVEs) to their counterpoise corrected binding energies (De). The three minima exhibit comparable stabilities, however, with some differences depending on the method. RI-MP2 predicts a relatively flat surface. On the other hand, RI-B97-D and PBE1-DCP methods predict comparable stabilities for the T and T0 structures with a noticeable destabilization of the PD structure. Again, as already noticed for the structures of the different conformations, this energy difference should be ascribed to the trend of MP2 to overestimate dispersive interactions. These results, emphasizing the flatness of the PES, obviously affect the pertinence of the binding energy to be used as a relevant assignment parameter. Comparison with the experimental data however remains interesting from the perspective of the theoretical assessment of the T and T0 conformations. The D0 values for the T and T0 conformations obtained at the RI-B97-D and that for T0 conformation obtained at the PBE1-DCP method are compared with the experimental value. The D0 for T at PBE1-DCP is not considered as it is a saddle point structure. The computed D0 values of T0 conformations by both RI-B97-D and PBE1DCP methods match reasonably well with experiment, with an underestimation of ca. 0.3 kcal/mol. The larger discrepancy for the PD structure (1.7 kcal/mol) seems to disqualify this structure. In the case of RI-MP2, the overall flatness of the PES hinders any tentative assignment based merely on energetics. In addition, one can notice the apparent overestimation of D0 in RI-MP2, by at least 0.6 kcal/mol for the T structure and the agreement between the experimental and computed D0 values is rather poor for the RI-MP2 method. Owing to these disappointing performances of the binding energy, spectroscopic parameters will be used as an alternative and a better choice for the final assignment. 4.3.3. N-H Stretch Frequency of Indole. The experimental N-H stretch frequency of the dimer is compared with those obtained with the dispersion corrected DFT methods, which have been validated on the pyrrole dimer system (Figure 6 and Table 2). A constant scaling factor is used to match the computed N-H stretch of the monomer, indole. The scaling factor is deduced by dividing the respective computed values of N-H stretch frequencies of indole for the different methods with the experimental value. The same scaling factors are used for the dimer, i.e., 0.97584, 0.95403, and 0.94963 for RI-B97-D, RIMP2, and PBE1-DCP methods, respectively. The experimental red shift of the N-H stretching frequency (46 cm-1) of the 9489
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Table 2. The Computed Rotational Constants, Geometrical Parameters, N-H Stretching Frequencies, and Dissociation Energy of the T, PD, and the Intermediate (T0 /PD0 ) Conformations of the Indol-Benzene Dimer Obtained for the Three Different Methodsa13 rotational constants (MHz) A
methods
B
C
geometrical parameters R (pm) θ (deg) j (deg)
expt
N-H frequency (cm-1)b (νN-H)D
δ
1168
359
304
449
0.8
89.9
3506
%δ
D0 c
3479
PBE1-DCP-CP/6-31G(d) T
dissociation energy (kcal/mol)
5.21 27
d
T0
1165
379
322
428
9.6
58.4
3485
6
4.87
-6.4
PD
896
587
468
376
29.9
7.8
3525
46
3.91
-25.0
RI-B97-D-CP/TZVPP
T T0
1182 1171
358 382
305 325
446 426
0.3 12.3
89.7 53.8
3498 3487
19 8
4.88 4.85
-6.3 -6.9
887
580
461
386
32.2
8.4
3520
41
3.52
-32.4
RI-MP2-CP/TZVPP
T
1193
365
310
440
1.3
88.8
3483
4
5.79
11.1
PD0
1149
447
380
382
20.3
24.7
3464
-15
6.12
17.5
PD
903
541
473
366
28.4
5.8
3521
42
6.22
19.4
PD
a
The computed N-H stretching frequencies (a constant scaling factor is used to match the computed N-H stretch of the monomer, indole)a and the dissociation energies are compared with the experimental values. The experimental dissociation energy of the indole-benzene dimer was taken from the reference. δ and % δ are defined as the error and percentage of error from the experimental values, respectively. b Scaling factors: RI-B97-D, 0.97584; RIMP2, 0.95403; PBE1-DCP, 0.94963. c The experimental dissociation energy (D0) is taken from ref 13. d Since conformation T is a saddle point for the PBE1-DCP-CP/6-31G(d) method, its D0 value is meaningless.
Figure 6. The experimental IR spectra for the (a) indole and (c) indole-benzene dimer in the NH stretch region are compared with the IR stick spectra calculated at the (d) PBE1-DCP-CP/6-31G(d), (e) RIB97-D-CP/TZVPP, and (f) RI-MP2-CP/TZVPP levels of theory for the three minima of the PES. For all the methods a scaling factor (see footnote of Table 2) is used to match the computed N-H stretch frequency of indole with the experimental value. In the figure, CP denotes that the geometry optimization and frequency calculations are done using the counterpoise gradient procedure.
complex relative to the free N-H of the indole monomer indicates a significant H-bond interaction between the N-H group of indole and the benzene moiety. The PD conformation shows no significant red shift of the N-H stretch frequency, which excludes it as the experimentally observed indole-benzene complex. The predicted red shift of the T-conformation, at 27 and 19 cm-1 with the RI-B97-D and PBE1-DCP, respectively, is still far from that obtained by experiment. On the other hand, the predicted N-H stretch frequency of T0 is very close to the
experimental value (within 8 cm-1). This gives clear evidence for T0 to be assigned as the structure of indole-benzene dimer. Figure 6 also shows that RI-MP2 provides a different spectral picture (Figure 6f). The experimental shift is bracketed by the theoretical PD0 and T predictions, the latter being relatively close (4 cm-1 below). Owing to the trend of RI-MP2 to overestimate of the spectral shift, by ca. 20% according to the pyrrole-dimer benchmark, this finding disqualifies the T structure and seems to favor the remaining PD0 structure. Even if the agreement remains relatively poor (once the overestimation is taken into account), one has to realize that the PD0 structure predicted by RI-MP2 is probably farther from the correct description of the experimentally produced dimer than the T0 structure predicted by PBE1DCP and RI-B97-D methods. 4.3.4. Final Assignment. The comparison between experimental (energetics and spectral) data and PBE1-DCP and RI-B97-D predictions, assessed on both the geometry and spectroscopy of the pyrrole dimer and the energetic of indole-benzene, finally provides a consistent set of evidence, which allows us to propose a new assignment of the experimentally observed indole-benzene dimer. The dimer is reassigned to an N-H 3 3 3 π H-bonded complex, having an intermediate tilted T-shaped structure T0 that is best described by PBE1-DCP and RI-B97-D methods. The T0 and PD0 conformations differ largely for the tilt angle, i.e., φ ≈ 55° versus φ ≈ 25°. At this point it is hard to completely rule out either the intermediate PD0 conformation predicted by RI-MP2 method or the conformations having the tilt angle between 25° and 55°. On the other hand, the better agreement between the experimental N-H stretch and D0 values with the computed values for T0 conformation leads it to a more favorable and reasonable assignment. One thing is clear from this study is that the T and PD conformations are not the experimentally observed indole-benzene dimer. However, more accurate assignment for T0 versus other intermediate conformations will await microwave and high-resolution UV spectroscopy investigations on this dimer. According to the dispersion corrected DFT methods used, the tilt angle φ value (≈55°) is very close to that of the 9490
dx.doi.org/10.1021/jp1119684 |J. Phys. Chem. A 2011, 115, 9485–9492
The Journal of Physical Chemistry A pyrrole dimer, suggesting very similar structures for these two N-H 3 3 3 π H-bonded complexes. This tilt angle originates from the delicate balance between the N-H 3 3 3 π H-bonding and the π 3 3 3 π stacked interaction between the indole and benzene rings. The maximum red shift of the N-H stretch for T0 conformation compared to T and PD conformation also shows that it is the strongest H-bonded dimer among them.
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’ ACKNOWLEDGMENT H.S.B., E.G., and M.M. acknowledge the French National Research Agency (ANR) for financial support (Grant ANR-08BLAN-0158). The authors thank Dr. Richard J. Plowright for the thorough reading of this paper. ’ REFERENCES
5. CONCLUSIONS IR-UV double resonance experiments combined with the quantum chemical methods designed for a correct description of the dispersion interaction enabled unraveling a detailed description of the indole-benzene dimer structure. (i) On the basis of a relevant experimental parameter, namely, the red shift of the indole N-H stretch frequency in the dimer with respect to that of the monomer, it is inferred that the experimentally observed indole-benzene dimer is an N-H 3 3 3 π H-bonded complex rather than a PD dimer. (ii) Three different methods of calculations, namely, RI-MP2 and RI-B97-D and PBE1-DCP have been tested against the microwave and IR data of the pyrrole dimer. The structural parameters, rotational constants, and vibrational spectrum of the pyrrole dimer obtained using dispersion corrected DFT methods are very close to the experimental values, whereas those obtained using the RIMP2 level are not as satisfactory. In addition, the geometry optimization using the counterpoise gradient gave better results than the standard gradient. (iii) All the methods of calculations, showed that the T, T0 / PD0 , and PD conformations of indole-benzene dimer are close in energy. This suggests that the PES is almost flat along the φ angle coordinate that describes the tilt angle between the indole and benzene planes. Therefore, the energy criterion is not good enough for a categorical assignment of the structure; instead, the IR spectroscopic data have been used for that purpose. (iv) In contrast with the previous investigation that was solely based on the energetics measurements and theoretical predictions,13 the present comparison between the computed IR spectrum and experimental observation allowed us to reassign the indole-benzene dimer to the NH 3 3 3 π bound H-bonded complex with a tilted T-shaped structure with a tilt angle between molecular planes of indole and benzene (φ) of the order of 55°. High resolution experimental data like those obtained by Professor David Pratt’s lab52,53 and microwave spectroscopy17,54 would be of a great interest to address this issue. ’ ASSOCIATED CONTENT
bS
Supporting Information. FDIR spectra of 3-methylindole and 3-methylindole-benzene dimer and the Cartesian coordinates of different conformations of indole-benzene dimer discussed in this paper. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected],
[email protected].
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