Experimental and quantum chemical study of pyrrole self-association through N–H⋯π hydrogen bonding

Journal of Molecular Structure 651–653 (2003) 793–805 www.elsevier.com/locate/molstruc

Experimental and quantum chemical study of pyrrole self-association through N –H· · ·p hydrogen bonding Viktor Stefov, Ljupco Pejov*, Bojan Sˇoptrajanov Faculty of Science, Institute of Chemistry, Sts. Cyril and Methodius University, PMF, P.O. Box 162, Arhimedova 5, 1000 Skopje, Macedonia Received 3 September 2002; revised 13 November 2002; accepted 13 November 2002

Abstract An FT-IR study of pyrrole self-association in CCl4 solutions was carried out. According to the IR measurements, pyrrole forms self-associated dimeric species via N– H· · ·p hydrogen bonding. This was also confirmed by quantum chemical calculations for pyrrole monomer and dimer at B3LYP/6-31þ þG(d,p) level of theory. A T-shaped minimum was located on B3LYP/6-31þþ G(d,p) PES of pyrrole dimer characterized with a hydrogen bond of an N– H· · ·p type, with centers-of-mass ˚ , H· · ·p distance of 2.475 A ˚ , the interplanar angle between the two monomeric units separation of monomeric units of 4.520 A being 72.98. The anharmonic vibrational frequency shift upon dimer formation calculated on the basis of 1D DFT vibrational potentials is in excellent agreement with the experimental data (84 vs. 87 cm21). Harmonic vibrational analysis predicts somewhat smaller shift (68 cm21). On the basis of NIR spectroscopic data, anharmonicity constants for the 2n(N –H) and 2n(N– H· · ·p) vibrational transitions were calculated. The orientational dynamics of monomeric and self-associated pyrrole species was studied within the framework of the transition dipole moment time correlation function formalism. The period of essentially free rotation in the condensed phase reduces from 0.05 ps for the monomeric pyrrole to 0.02 ps for the proton-donor molecule within the dimer. q 2003 . Published by Elsevier Science B.V. All rights reserved. Keywords: Pyrrole; p-Type hydrogen bonding; Anharmonic vibrational frequencies; Vibrational anharmonicity; Orientational dynamics

1. Introduction The general significance of intermolecular interactions in chemical physics and essentially all of contemporary chemistry has been well recognized [1]. Of all intermolecular interactions, the hydrogen bonding ones (of both proper and improper or blueshifting type [2,3]) are of special importance because of their relevance to biochemically important phenomena, molecular recognition, organic * Corresponding author. Tel.: þ389-91-117-055; fax: þ 389-91226-865. E-mail address: [email protected] (L. Pejov).

synthesis, etc. The so-called p-type hydrogen bonding has been confirmed relatively recently [4 –7], having in mind the long awareness that the p-electronic clouds may serve as H-bonding protonacceptors as well as any other (more localized) electron density. It appears that the p-type hydrogen bonding could be of great relevance to biochemistry, as the interactions between aromatic domains within biochemically important molecular systems often involve a number of X –H· · ·p contacts (base– base interactions in DNA, packing of aromatic molecules within molecular crystals and tertiary structure of proteins) [8 – 11]. Continuing our previous

0022-2860/03/$ - see front matter q 2003 . Published by Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 2 8 6 0 ( 0 3 ) 0 0 2 9 2 - 8

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theoretical and experimental studies of various Hbonded systems [5 –7,11 – 15], particularly the X – H· · ·p ones [5 – 7,13], in this paper we present the results from a Fourier transform-infrared (FT-IR) spectroscopic and quantum chemical study of pyrrole self-association via N – H· · ·p hydrogen bonding. Pyrrole itself, as one of the simplest fivemember aromatic molecules has been studied a lot, partly due to its potential astrophysical relevance [16]. A number of low-resolution IR and Raman studies of this nitrogen heterocycle have been performed [17 – 23], accompanied by theoretical studies at both semi-empirical [24] and ab initio levels of theory [25 – 27]. Also, high-resolution investigations of this system in gas phase have been performed [28 –32], which enabled the rovibrational parameters for the fundamental N – H and C – H stretching bands, the first N –H overtone, as well as for the band corresponding to the n22 fundamental transition to be calculated. However, much less literature data exist regarding the selfassociation of pyrrole via N – H· · ·p hydrogen bonding [4,33,34], and especially the influence of this interaction on the anharmonic N – H stretching frequencies (of both the free and H-bonded N –H oscillator), as well as on the reorientational dynamics of pyrrole species in condensed phases. Only one theoretical paper has been devoted to selfassociation of pyrrole [5], but with a main emphasis on the energetic characteristics of this interaction, and not on the vibrational spectroscopic manifestations. We have recently thoroughly studied the self-association phenomena via N – H· · ·p type hydrogen bonding in the case of indole [6,14]. In this paper, we present the FT-IR spectra of pyrrole solutions in CCl4 in a wide concentration range. The spectral changes associated with the concentration increase are interpreted in terms of self-association between pyrrole species, which occurs through N – H· · ·p hydrogen bonding interaction. First N –H stretching overtones were also detected in the NIR region for the monomeric and both proton-donor and proton-acceptor species within the dimer, and on the basis of these data anharmonicity constants of the corresponding transitions were calculated. In order to get a deeper insight into the nature of this interaction, quantum chemical study of pyrrole monomer and dimer potential energy surfaces

(PES) was carried out, at B3LYP/6-31þ þ G(d,p) density functional level of theory. Both harmonic and anharmonic vibrational frequencies of the N – H stretching motions for the located minima on the monomer and dimer B3LYP/6-31þ þ G(d,p) PES were calculated on the basis of one-dimensional (1D) DFT N –H vibrational potentials. A natural bond orbital analysis (NBO) of the T-shaped minimum on the dimeric PES was performed as well, in order to analyse quantitatively the magnitude and direction of the charge transfer interaction within the dimer.

2. Experimental Room temperature FT-IR spectra of pyrrole solutions in CCl4 (in a wide concentration range) were recorded on a Perkin Elmer System 2000 FT-IR interferometer, with a resolution of 2 cm21, using a KBr cell (path length 0.024 mm). For a study of the NIR spectral region, CsBr or KBr cells (path lengths 0.5 and 1.0 mm, respectively) were used. In order to achieve good signal-to-noise ratio (especially for a study of the region of second-order N –H stretching transitions), 256 scans were accumulated and averaged. On the other hand, 64 scans appeared to be enough for the region from 4000– 400 cm21. Mathematical analysis of the spectra was performed with the GRAMS32 [35] and Mathcad7 [36] programming packages.

3. Computational details The geometry of pyrrole dimer (as well as of free monomeric pyrrole) was fully optimized at B3LYP/6-31þ þ G(d,p) level of theory, employing Schlegel’s gradient optimization algorithm (computing the energy derivatives with respect to nuclear coordinates analytically). The modified GDIIS algorithm was employed in productive searches for the stationary points on the considered PES [37], as it was found to be relatively flat by preliminary investigations. Kohn – Sham (KS) variant of density functional theory was employed throughout the study, using a combination of Becke’s three-parameter adiabatic connection exchange functional (B3, [38]) with

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the Lee– Yang –Parr (LYP, [39]) correlation onemethodology known under the B3-LYP acronym. The employed KS methodology is a hybrid one, as it includes an admixture of the HF exchange (in contrast to the ‘pure’ DFT methods). It has been shown that especially for studying intermolecular interactions, particularly the hydrogen bonding ones, appropriate choice of the ‘amount’ of the HF exchange is of substantial importance. However, the presently employed B3-LYP combination of functionals has been shown to perform remarkably well for a variety of different purposes [40]. The Kohn – Sham equations were solved selfconsistently for each particular purpose of the present study, using the standard 6-31þ þ G(d,p) basis set for orbital expansion, and the ‘fine’ (75, 302) grid for numerical integration (75 radial and 302 angular integration points). As a test of the character of the located stationary points on the explored PES-s, harmonic vibrational analyses were performed, the absence of imaginary frequencies (negative eigenvalues of the Hessian matrices) confirming that a true minimum is in question. Complete NBO analysis, including the secondorder perturbation theory analysis of the Fock matrix (or, more rigorously, its Kohn –Sham analog—hKS) within the NBO basis [41 – 47] as well as various NBO deletion analyses were performed for the minimum on the dimer PES. 3.1. Calculation of anharmonic vibrational frequencies Anharmonic N – H and N – H· · ·p stretching frequencies were obtained from pointwise DFT energy calculations, allowing the H atom to vibrate against the rigid residue of the monomer or dimer. Series of 10 energy calculations were performed ˚ , step 0.05 A ˚ ) for the (from r ¼ 0.85 to r ¼ 1.55 A monomeric (‘free’, i.e. free molecule) N – H, dimeric hydrogen bonded (N – H· · ·p) and dimeric free (non-H-bonded, i.e. the free N – H oscillator within the dimer) N – H oscillators, varying the N – ˚ . The obtained H distance from 0.85 to 1.30 A energies were least squares fitted to a fifth order polynomial in rNH. The resulting potential energy functions were subsequently cut after fourth order and transformed into Simons – Parr –Finlan (SPF)

795

type coordinates r ¼ (rNH 2 rNH,e)/rNH [48] (rNH,e being the equilibrium value), and the 1D vibrational Schro¨dinger equation was solved variationally using 15 harmonic oscillator eigenfunctions as a basis. It has been well recognized that the SPF coordinates are superior over the ‘ordinary’ bond stretch ones when variational solution of the vibrational Schro¨dinger equation is in question, since they allow for a faster convergence (with the number of basis functions used) and a greatly extended region of convergence. The fundamental anharmonic N – H stretching frequencies were computed from energy differences between the ground and first excited vibrational levels. The anharmonicity constants (X) were computed from the equation:

n~NH ¼ v0;NH þ 2X

ð1Þ

where v0,NH is the harmonic eigenvalue (obtained from the harmonic force constant). All quantum chemical calculations in this study were performed with the GAUSSIAN 98 suite of programs [49] (and the NBO code, included in GAUSSIAN 98 as link 607 [50]).

4. Results and discussion 4.1. FT-IR spectra of solvated monomeric and self-associated pyrrole species 4.1.1. The region of fundamental vibrational transitions In Fig. 1, the region of fundamental n(NH) vibrational transitions in the FT-IR spectra of pyrrole solutions in CCl4 with various solute concentrations are shown. As can be seen from this figure, in the case of a very diluted solution only a single, rather sharp band appears at 3495 cm1 which is due to monomeric N – H stretching fundamental vibrational transition. It is interesting to note at this point that the n(NH) mode exhibits the largest shift upon solvation in CCl4 (Dn˜ ¼ 2 36 cm21 with respect to the gasphase value) in comparison with all other intramolecular modes. As shown by our preliminary quantum chemical calculations based on continuum solvation models (the SCRF and IPCM

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Fig. 2. The stationary point on the pyrrole–CCl4 1:1 complex PES (at the presently implemented level of theory), corresponding to a structure with bifurcated H-bond.

Fig. 1. The region of fundamental n(NH) vibrational transitions in the FT-IR spectra of pyrrole solutions in CCl4 (the solute concentration increases from the uppermost curve downwards).

methodologies) within both the harmonic and the 1D anharmonic treatment of the n(NH) mode, such large downshift cannot be attributed to the continuous solvation [51] with CCl4. Obviously, the downshift has to be connected with a more specific interaction with the solvent molecules. In order to test such an assumption, we have also performed preliminary quantum chemical calculations for the 1:1 pyrrole –CCl4 complexes. The full results of the continuum solvation calculations, as well as of those including explicitly one or more solvent molecules will be published elsewhere [52]. For the purpose of this study, we just mention that the only stationary point on the pyrrole – CCl4 1:1 complex PES (at the presently implemented level of theory) corresponds to the structure with a bifurcated H-bond, shown in Fig. 2. However,

the vibrational frequency shift of the n(NH) mode upon interaction with CCl4 calculated for such complex on the basis of full 1D DFT anharmonic n(NH) potential is still too small as compared to the experimental data. A second band in the region of fundamental n(NH) vibrational transitions appears with the increase of pyrrole concentration (at 3408 cm21), which is attributed to the n(N –H· · ·p) hydrogen bonded oscillator, while the higher-frequency band (attributed to the non-hydrogen-bonded n(N – H) oscillator) exhibits a slight red shift to 3492 cm21. At still very low concentrations, it may be argued that practically only monomeric and dimeric solute forms exist. Further increase of pyrrole concentration leads to a subsequent, but this time only very slight red shift of the lower-frequency band, most probably because of formation of higher molecular associates. The outlined band assignments in this chapter are fully in line with the results from our quantum chemical calculations described in Section 4.2. The other spectral areas remain essentially unchanged in the course of formation of molecular dimers (Fig. 3), with an exception of the region in which bands due to out of plane g(N – H) bending modes appear. Upon increase of the solute concentration, two novel bands appear in this spectral region (Fig. 4), at somewhat higher frequencies (519 and 558 cm21) compared with the free g(N – H) value. We attribute these two bands to the g(N– H· · ·p) oscillator (558 cm1) and to the non-hydrogen-bonded g(N– H) oscillator within the dimer (519 cm21). Such assignment is in line with the results of the quantum chemical calculations presented in the next chapter. The association of pyrrole molecules in CCl4 is followed by a slight blue shift of the g(N – H) mode

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Fig. 3. The other areas in the FT-IR spectra of solvated monomeric pyrrole (upper curve) and the self-associated dimer (lower curve).

originating from the non-hydrogen bonded species (from 500 cm21 for the monomeric species to 502 cm21 for the dimer; see Fig. 4). Note that this mode is also significantly affected by the solvation (along with the n(N –H) mode, as mentioned before) as it is blue-shifted by 20 cm21 in comparison with the gas-phase frequency. Such blue shift is basically in line with a more specific solute –solvent interaction, such as H-bonding, which was outlined before. The band at 1421 cm21, which is due to a complex mode that includes d(N –H) motion, is practically not affected by molecular self-association. This may be attributed to the fact that the change in d(N – H) coordinate accounts only a little in the overall motion constituting this normal mode, and is thus essentially unaffected by the p-type hydrogen bonding.

Fig. 4. The g(N –H) region in the FT-IR spectra of pyrrole solutions in CCl4 (the solute concentration increases from the uppermost curve downwards).

overtone. This band exhibits very slight red shift (to 6843 cm 1) upon self-association, which is accompanied with an appearance of another, much broader band at 6762 cm21. The spectroscopic data for these transitions, together with the anharmonicity constants, defined as: X¼

4.1.2. The region of second-order vibrational transitions involving the n(N– H) mode The spectral region in which bands due to secondorder vibrational transitions of the form 2 ˆ 0 (i.e. the first overtones) originating from the N – H stretching mode(s) are expected is shown in Fig. 5. The sharp band appearing at 6855 cm21 in case of solvated monomeric pyrrole species is due to the n(N – H) first

1 2

n~02 2 n~01

ð2Þ

(where n~0i denotes the wavenumber corresponding to the i ˆ 0 vibrational transition) are presented in Table 1. As can be seen, the anharmonicity constant for the 2n(N – H· · ·p) mode is somewhat lower (in absolute value) than that corresponding to the dimeric 2 ˆ 0 n(N –H) transition. Such finding is similar with the results for the self-associated secondary amines, as

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V. Stefov et al. / Journal of Molecular Structure 651–653 (2003) 793–805 Table 1 Relevant quantitative FT-IR spectroscopic data for the monomeric and dimeric pyrrole species solvated by CCl4 Mode/species

n~0i (cm21)

Monomer n(N–H) g(N –H) d(N–H)

3495 500 1421

13 19 17

Dimer n(N–H) n(N–H· · ·p) g(N –H)monomer g(N –H)free,dimer g(N –H· · ·p) d(N–H)

3492 3408 502 519 558 1421

13 63 21 24 42 19

Monomer 2n(N–H)

6856

37

267

Dimer 2n(N–H) 2n(N–H· · ·p)

6843 6762

53 141

271 227

a

Fig. 5. The spectral region of n(NH) second-order vibrational transitions in the FT-IR spectra of pyrrole solutions in CCl4 (the solute concentration increases from the uppermost curve downwards).

well as for the self-associated indole species, for which a decrease in anharmonicity of the hydrogen hydrogenbonded n(N –H) oscillator in comparison to the nonhydrogen bonded one was reported [13,53 –54]. 4.2. The B3LYP/6-31þ þ G(d,p) PES of pyrrole dimer—further evidence for the existence of a selfassociated N – H· · ·p hydrogen-bonded dimer In order to provide a deeper theoretical basis for understanding the pyrrole self-association, we relied on the quantum chemical calculations performed as described in the Computational details section at the B3LYP/6-31þ þ G(d,p) level of theory. According to quantum chemical calculations, a single minimum exists on B3LYP/6-31þ þ G(d,p) PES of pyrrole dimer, corresponding to a T-shaped structure in which the nitrogen side of one monomer is directed to the aromatic ring plane of the other (Fig. 6a, which is

FWHMa (cm21)

X (cm21)

Full width at half maximum intensity.

a clear geometrical indication for the existence of an N–H· · ·p hydrogen bond (confirmed by other calculations as well). Except for the equilibrium N – H distance, which changes from 1.0075 (for monomer) to ˚ (for the H-donor within the dimer), the other 1.0120 A structural parameters show subtle changes upon dimer formation, which is characteristic for weakly bonded complexes. In order to get an insight into the reliability of the optimized geometry of pyrrole dimer at the employed level of theory, the optimized geometry parameters for the monomeric free pyrrole unit (Fig. 6b) were compared with the available experimental data [27] (Table 2). As can be seen, the agreement of the presently applied level of theory with the experimental data is excellent, the results from the present study being of essentially identical quality with the MP2 ones reported for this system [26]. The six intermolecular parameters, defining the mutual orientation of molecular subunits within the dimer (Fig. 7) for the minimum located on B3LYP/631þ þ G(d,p) PES are presented in Table 3. These are the distance between the centers of mass (CM’s— RCM), the distance between the H atom from unit II and the aromatic ring plane of unit I (RH· · ·p), the N(I) – N(II) distance, angle f between the planes of

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799

Table 2 The calculated geometry parameters for pyrrole monomer at B3LYP/6-31þþ G(d,p) level of theory together with the available experimental data [31] Parameter

MW

MW-corrected

B3LYP/6-31þþ G(d,p)

r(N1–C2) r(C2–C3) r(C3–C4) r(N1–H6) r(C2–H7) r(C3–H8) /(N1C2C3) /(C2C3C4) /(C2N1C5) /(C2N1H6) /(N1C2H7) /(C2C3H8)

1.370 1.382 1.417 0.996 1.076 1.077 107.7 107.4 109.8 125.1 121.5 125.5

1.370 1.382 1.417 1.000 1.091 1.088 107.7 107.4 109.8 125.1 126.2 126.3

1.376 1.381 1.426 1.008 1.080 1.081 107.6 107.4 109.9 125.0 121.3 125.7

˚ , angles in degrees; see Fig. 6b for atomic All distances in A numbering scheme.

Fig. 6. (a) The T-shaped single minimum on B3LYP/631þ þG(d,p) PES of pyrrole dimer; (b) optimized geometry and atomic numbering of monomeric pyrrole.

monomers I and II, angle u between the RCM directional vector and the monomer I plane, and the angle between the two N – H axes (a). Undoubtedly, the most important parameter from the viewpoint of N – H· · ·p hydrogen bonding is the RH· · ·p distance. In ˚ , which the present case, the calculated value is 2.47 A is smaller compared to the previously investigated N – ˚ ) [5], which H· · ·p bonded indole dimer (2.71 A indicates a rather stronger interaction in the present case. However, this value is slightly larger than in the case of molecular assembly of an aniline derivative

Fig. 7. The six intermolecular parameters, defining the mutual orientation of molecular subunits within the pyrrole dimer.

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Table 3 The values of six intermolecular parameters, defining the mutual orientation of the monomeric units within the pyrrole dimer, calculated at B3LYP/6-31þþ G(d,p) level of theory together with the experimental values [37] Parameter

B3LYP/6-31þþ G(d,p)

Experimental

˚) RCM (A ˚) RH· · ·p (A ˚) RN(I)N(II) (A f (deg) u (deg) a (deg)

4.5202 2.4749 3.6865 72.88 1.73 71.09

4.116 – – 55.42 12.02 –

See text and Fig. 7 for definition.

˚ ) [55]. Agreement of the calculated structural (2.42 A parameters for pyrrole dimer in the present study with the experimental data (Table 3) is rather satisfactory. The described T-shaped minimum on the B3LYP/631þ þ G(d,p) potential energy hypersurface of pyrrole dimer would be expected to be favorable by dipole – quadrupole and quadrupole – quadrupole electrostatic interactions as well as by the charge transfer (the dipole –dipole interactions in the present case are of less importance than it would be a priori expected, due to the mutual arrangement of dipole moment vectors of the two monomers which is relatively far from the configuration allowing optimal dipole – dipole stabilization). The interaction energy calculated including the basis set superposition error (BSSE) corrections (accounted for by the standard full function counterpoise procedure of Boys and Bernardi [56]) at this level of theory is DE(BSSE) ¼ 2 12.82 kJ mol21 (the notation of Xantheas is adopted throughout this study [57]), while the overall deformation energy of monomeric units is Erel,tot ¼ 0.20 kJ mol21 and BSSE ¼ 2.19 kJ mol21. The dissociation energy computed upon inclusion of the zero-point vibrational energy (ZPVE) corrections (and the BSSE) is De ¼ 10.21 kJ mol21. These values are somewhat lower than those presented at MP2 level of theory [4]. This may be due to the inherent deficiencies in the DFT functionals with respect to treating the dispersion interaction in case of non-covalent intermolecular interactions. The relevant results from harmonic vibrational analysis of free pyrrole and the T-shaped minimum on the B3LYP/6-31þ þ G(d,p) PES are compared to the experimental data in Table 4. As can be seen, the agreement between theory and experiment is very

Table 4 The calculated harmonic vibrational frequencies for monomeric N– H, dimeric N–H· · ·p and dimeric free (non-H-bonded) N– H oscillators at B3LYP/6-31þþ G(d,p) level of theory, together with the experimental data (rNHe,SCF is the SCF value for the rNHe)

Monomer n(N–H) g(N– H) Dimer n(N–H) g(N– H) n(N–H· · ·p) g(N– H· · ·p)

rNHe,SCF ˚) (A

v0 (cm21)

1.008

3685 489

66 77

3629 -

1.008

3681 527 3617 578

74 99 328 24

3634 – 3462 -

1.012

I (km mol21)

v0,exp (cm21)

good. The calculated shifts of the g(N – H) mode frequencies upon self-association further support the outlined assignments of the corresponding bands in the previous chapter. As the N –H stretching motion (and the X – H motions in general) is known to be characterized by a pronounced mechanical anharmonicity, the good agreement between theoretical harmonic vibrational frequency shifts and the experimental (anharmonic) data may be in some cases due to cancellation of various errors. Therefore, we have performed anharmonic vibrational frequency calculations on the basis of 1D DFT vibrational potentials calculated for various n(N– H) oscillators within both the monomer and the p-hydrogen-bonded dimer. The results are given in Table 5, while the calculated vibrational potentials are presented in Fig. 8. It should be noted at this point that all the previous calculations were based on 1D N – Table 5 The calculated anharmonic vibrational frequencies for monomeric N–H, dimeric N–H· · ·p and dimeric free (non-H-bonded) N– H oscillators at B3LYP/6-31þþ G(d,p) level of theory, together with the corresponding harmonic eigenvalues, anharmonicity constants and the experimental data rNH,e ˚) (A

n (cm21)

v0 (cm21)

X (cm21)

nexp (cm21)

Xexp (cm21)

Monomer N–H

1.008

3550

3715

283

3495

267

Dimer N–H N–H· · ·p

1.008 1.012

3546 3466

3711 3646

282 290

3492 3408

271 –27

V. Stefov et al. / Journal of Molecular Structure 651–653 (2003) 793–805

Fig. 8. The calculated 1D DFT vibrational potentials for various N – H oscillators.

H· · ·p vibrational potential, i.e. the coupling with the intermolecular stretch was neglected. In cases like the present one, when intermolecular interaction is rather weak (also with the proton-donor atom being involved in a rather non-flexible ring structure), such vibrational coupling is indeed expected to be very small [5]. In Table 6, the experimentally measured shifts of the n(N – H) mode frequencies upon association are Table 6 The calculated (B3LYP/6-31þ þG(d,p), at harmonic and anharmonic level) and experimental changes in the n(N –H) frequencies upon dimer formation

Harmonic SCF approximation [n(N –H)monomer 2 n(N – H)dimer] (cm21) [n(N –H)dimer 2 n(N –H· · ·p)dimer] (cm21) [n(N –H)monomer 2 n(N – H· · ·p)dimer] (cm21)

B3LYP/6-31 þ þG(d,p)

Experimental

4 64 68

3 84 87

Harmonic approximation (1D DFT potentials) [n(N –H)monomer 2 n(N – H)dimer] (cm21) 4 [n(N –H)dimer 2 n(N –H· · ·p)dimer] (cm21) 65 [n(N –H)monomer 2 n(N – H· · ·p)dimer] (cm21) 69

3 84 87

Anharmonic calculations (1D DFT potentials) [n(N –H)monomer 2 n(N – H)dimer] (cm21) [n(N –H)dimmer 2 n(N –H· · ·p)dimer] (cm21) [n(N –H)monomer 2 n(N – H· · ·p)dimer] (cm21)

3 84 87

4 80 84

801

compared with theoretical data at various levels of sophistication (harmonic SCF approximation, harmonic approximation basing on the 1D DFT vibrational potentials as well as the full 1D anharmonic vibrational analysis). As can be seen, harmonic vibrational analysis fails to predict quantitatively the n(N– H) mode frequency shifts upon association via N – H· · ·p hydrogen bonding. However, anharmonic vibrational frequency shifts are in excellent agreement with the experimental FT-IR data. In fact, it has been recognized that DFT methods usually overestimate the vibrational frequency shifts of n(N– H) modes upon Hbonding due to inherent deficiencies in the currently used exchange-correlation functionals [58]. The excellent agreement in the present case may be attributed to the rather weaker character of the ptype hydrogen bond, as compared to the ordinary Hbond, with a more localized proton-accepting center. 4.3. Natural bond orbital analysis of the T-shaped pyrrole dimer To get at least a semi-quantitative picture of the direction and magnitude of the charge transfer interaction for the studied case, NBO analysis for the located minimum on B3LYP/6-31þ þ G(d,p) PES of pyrrole dimer was carried out. As revealed by the second-order perturbation theory analysis of the Kohn –Sham analog of the Fock matrix within the NBO basis (Table 7), the only significant charge transfer between the monomeric units is from monomer I to monomer II, or more precisely from aromatic ring p orbitals to the N – H antibonding sp orbital (p ! sp), as well as from p orbitals to a H Rydberg orbital (p ! Ryp). The estimated energetic effects due to these interactions are given by the second-order perturbation theoretical expressions of the form [41 –47]: DEcð2Þdonor !cacceptor < 22·

^ cacc l2 kcpdon lFl 1acc 2 1don

ð3Þ

where 1i is a diagonal NBO matrix element of the Fock operator F^ (or, more rigorously, the Kohn – Sham one-electron analog h^ KS ). All the NBO parameters related to the outlined discussion, calculated at B3LYP/6-31þ þ G(d,p) level of theory for pyrrole dimer are presented in Table 7. Since

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Table 7 Second order perturbation theory analysis of Fock matrix in NBO basis for the minimum on pyrrole dimer B3LYP/6-31þþ G(d,p) PES Donor orbital

Acceptor orbital

DE (2) (kcal mol21)

DE(acceptor–donor) (a.u.)

^ kdonlFlaccl (a.u.)

q (e)

p(ring) p(ring) p(ring) p(ring)

sp(NH) sp(NH) Ryp(H) Ryp(H)

1.39 1.06 0.21 0.11

0.75 0.74 1.58 1.63

0.030 0.026 0.016 0.012

0.0032 0.0025 0.0002 0.0001

See text for details and definitions.

the overall charge transfer can be essentially described by interactions between the previously mentioned orbitals, it is expected that the sum of the corresponding energy terms should be almost equal to the total charge transfer energy. The quantities of transferred charge from a given donor to a given acceptor orbital may be estimated again using elementary perturbation theory arguments, leading to the following approximate formula: ! ^ cacc l 2 kcpdon lFl qcdonor !cacceptor < 2 ð4Þ 1acc 2 1don The calculated values for the present case are also given in Table 7. Obviously, the magnitude of p ! sp(N – H) charge transfer within the dimer is only about 0.006e (the sum of all contributions, i.e. all q 2 s in this table), which is quite relevant from the stabilization aspect. It has been emphasized that even seemingly small values of transferred charge (0.001 – 0.01e) lead to chemically significant stabilization energies [41 –47]. We have further proceeded with the NBO energetic analysis of pyrrole dimer by successively deleting particular matrix elements from the Kohn – Sham analog of the NBO Fock matrix, diagonalizing the new Fock matrix to obtain a new density matrix, and passing this final density matrix through a single SCF step. The difference between the energy obtained by such ‘deletion’ procedure and the energy obtained from the starting density matrix is a good estimation of the total energy contribution of the deleted terms [41 –47]. We have performed three calculations of the deletion type. Within the first one, we have removed all Fock matrix elements between high occupancy NBOs of each monomer to the low-occupancy NBOs of the other (which corresponds to removing the

effects of all intermolecular delocalizations). The second and third steps corresponded to deleting all Fock matrix elements between high occupancy NBOs of the proton-donor unit to the low occupancy NBOs of the proton-acceptor, and between high occupancy NBOs of proton-acceptor to the low occupancy NBOs of the proton-donor. In such a way, we have estimated both the total CT energy (between both fragments within the dimer), as well as each of the ‘one-directional’ contributions. The results are summarized in Table 8. In line with the previously outlined conclusions, essentially the whole charge transfer occurs onedirectionally, the p ! sp interaction being by far the most significant. Of course, all of these conclusions about the degree of charge transfer are not to be taken in an absolute quantitative sense. They are valuable only in the course of estimating the relative contributions to the total CT energy of intermolecular delocalizations in one or another direction, and not of the overall CT contribution to the total interaction energy. This is so since, first of all, a single SCF step through which the new density matrix is passed does not lead to a full convergence, and also due to inherent characteristics of the NBO algorithm [41 – 47]. Table 8 Results from the NBO energetic deletion analysis for the minimum on pyrrole dimer B3LYP/6-31þ þG(d,p) PES Deleted Fock matrix elements

DE(B3LYP) (kcal mol21)

Donor ! acceptor and acceptor ! donor Donor ! acceptor Acceptor ! donor

6.78 5.73 1.09

See text for details and definitions.

V. Stefov et al. / Journal of Molecular Structure 651–653 (2003) 793–805

4.4. Orientational dynamics of monomeric and associated pyrrole species It has been well recognized that a study of the dynamics of solute species in a given solvent may yield useful information for the solute– solute and solute – solvent interactions. However, to probe the molecular motions at the picosecond time scale, the Heissenberg formulation of quantum mechanics is more appropriate than the Schro¨dinger one. In the present study, the orientational dynamics of both monomeric and selfassociated pyrrole species was explored using the transition dipole moment time correlation function approach [59]. Following Gordon’s approach, the transition dipole moment correlation function corresponding to a given transition observable in IR spectrum (i.e. corresponding to an IR band) is defined as [59]: ð  ^~ð0Þ·m ^~ðtÞl¼Re km ð5Þ I~ðn~Þexpð2i·2pcDn~tÞdn~ band

where Dn~¼ n~2 n~0 (n~0 being the band center), the integration is performed over the whole band, while kl denotes ensemble average. The symbol I_ðn~Þ denotes normalized intensity: Iðn~Þ I~ðn~Þ¼ ð Iðn~Þdn~

ð6Þ

band

In other words, the information on the dynamics of molecular motions in condensed phases is obtained by a Fourier inversion of the spectral band shape. More precisely, the spectral density of a given band, and the correlation function of the relevant (for that case) transition moment operator are mutual Fourier transforms [60,61]. However, it is not generally easy, nor always possible, to attach a physical meaning to the obtained result [62]. Also, it is not even an easy task to select a band to probe the molecular dynamics, as several requirements must be satisfied for that purpose [59]: first of all, the spectral band contour must correspond to only one specific oscillator (‘the single oscillator’ condition—the band used to probe the molecular dynamics must not be overlapped with those corresponding to other transitions). All of these conditions are fulfilled for the n(N –H) modes in the present case. The natural logarithms of transition dipole moment time correlation functions obtained by

803

Fourier inversion of the normalized band profiles corresponding to monomeric n(N –H), dimeric nonhydrogen bonded n(N – H) as well as of the n(N – H· · ·p) 1 ˆ 0 vibrational transitions are shown in Fig. 9. Since the transition moment of the n(N– H) mode component is parallel to the N – H axis (and also to the axis of molecular permanent dipole moment), the corresponding correlation function describes the orientational motion of this axis as the molecule rotates around the two axes perpendicular to this one [63 –70]. In case of a pure Lorentzian (Cauchy) profile, the corresponding dipole time correlation function has the form [59 –61]:   ^~ðtÞl ¼ exp 2 t km^~ð0Þ·m ð7Þ tl where tl is the Lorentzian relaxation time, related to the bandwidth by:

tl ¼ 2pcDn~1=2

ð8Þ

In the presently studied case, the long-time behavior of the dipole correlation function is exponential, while the short time one is Gaussian. Thus, the time evolution of the transition dipole moment operator (determined essentially by molecular orientational motion) may be divided into two distinct time regimes. During the brief initial period, it is the free rotation of the solute species that determines the kinetics of the transition dipole moment rotation [63 –70] and the accuracy of a statistical estimate of the directional change of the selected transition dipole moment is governed by the intrinsic inertial properties of the free molecular species. The short time dynamics of species in condensed phases generates a Gaussian decay rate of the transition dipole moment time correlation function [59]. At longer times, on the other hand, the reorientation becomes random, as a result of the influence of the neighboring molecules in condensed phase, resulting in an exponential decay of the dipole time correlation function and a Lorentzian frequency spectrum-rotational diffusion [59]. The intermediate time regime needs much more complex dynamical description [59]. It can be concluded from Fig. 9 that the stochastic processes leading to the exponential decay become predominant after approximately 0.05 ps for the monomeric pyrrole species. In other words, the intrinsic inertial properties (‘free

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rotation’ leading to reorientation of the transition dipole moment in question), determine the dynamics of the solvated species within this time interval. In the case of proton-accepting molecule of the associated species, this value remains essentially unchanged, while for the proton-donor one, it is reduces to 0.02 ps. In fact, these findings are in line with the formation of a sort of ‘directional N – H· · ·p hydrogen bond’, leading to further hindering of molecular rotation in the condensed phase.

5. Conclusions The self-association of pyrrole molecules in CCl4 solution was studied with FT-IR spectroscopy and quantum chemical calculations. Intermolecular interaction between pyrrole molecules occurs via N – H· · ·p hydrogen bonding, mostly influencing the n(N– H) stretching mode, which is red-shifted by 87 cm21 with respect to the monomer value. Anharmonicity constant of the 2n(N –H· · ·p) vibrational transition is significantly smaller than the corresponding value for the 2n(N – H) transition. Quantum chemical calculations at B3LYP/6-31þ þ G(d,p) level of theory confirm the existence of a T-shaped N–H· · ·p hydrogen bonded minimum on the considered PES. Excellent agreement of the predicted frequency shift for the n(N –H) mode upon hydrogen bonding with the experimental data is obtained if anharmonic vibrational frequencies are calculated on the basis of 1D DFT vibrational potentials. The period of essentially free rotation in the condensed phase reduces from 0.05 ps for the monomeric pyrrole to 0.02 ps for the proton-donor molecule within the dimer, as revealed by the analysis of the corresponding transition dipole moment time correlation functions.

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Fig. 9. The natural logarithms of transition dipole moment time correlation functions corresponding to monomeric n(N– H) (a), dimeric non-hydrogen bonded n(N –H) (b) and the n(N –H· · ·p) 1 ˆ 0 vibrational transitions (c).

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