A gradient-corrected density functional study of indole self-association through N–H⋯π hydrogen bonding

11 May 2001

Chemical Physics Letters 339 (2001) 269±278

www.elsevier.nl/locate/cplett

A gradient-corrected density functional study of indole self-association through N±H


p hydrogen bonding Ljupco Pejov * Institut za hemija, PMF, Univerzitet `Sv. Kiril i Metodij', Arhimedova 5, P.O. Box 162, 91000 Skopje, Macedonia Received 7 December 2000; in ®nal form 7 March 2001

Abstract A B3LYP/6-31++G(d,p) study of indole dimer was performed. The optimized geometry reveals the existence of N±H


p hydrogen bond in which the benzenoid ring of one subunit acts as a proton acceptor, the interplanar angle  between the two monomeric units being 89.4° (a T-shaped structure), with the center-of-mass separation of 6.207 A. The counterpoise-corrected interaction energy is 2:15 kcal mol 1 …9:00 kJ mol 1 †. Anharmonic vibrational frequencies of monomeric and dimeric N±H oscillators, their change upon dimerization and the intensity enhancement are excellently reproduced by one-dimensional B3LYP/6-31++G(d,p) vibrational potentials. Ó 2001 Published by Elsevier Science B.V.

1. Introduction The general problem of the so-called `non-covalent' intermolecular interactions in chemical physics has received signi®cant attention in recent years, from both experimental and theoretical viewpoints [1]. Among all interactions classi®ed under the above heading, the hydrogen bonding one (of both `proper' [2] and the recently discovered `improper' type [3±5]) has been probably the one mostly studied. This is mainly due to the essential importance of this phenomenon in biological processes, as well as in the ®eld of molecular recognition [6,7] and organic synthesis [8]. A particularly important class of intermolecular interactions is that involving aromatic systems, the

*

Fax: +389-91-226-865. E-mail address: [email protected] (L. Pejov).

prototype of which is the widely studied benzene dimer [3,9±15]. Since aromatic rings containing heteroatoms occur in many chemical and biochemical phenomena, it is especially interesting to study the interactions between such domains, particularly with respect to self-association phenomena via hydrogen bonding. An ab initio HF SCF and MP2 study of the pyrrole dimer has been recently published [16], considering only the structural and energetic aspects of the self-associated species. We have recently published a combined AM1 theoretical and FT IR experimental study of indole self-association in CCl4 solutions, where both structural and vibrational spectroscopic aspects [17] were considered. Although the existence of N±H


p contact in the solid indole has been identi®ed earlier [18], the self-association of these molecular species in CCl4 via N±H


p interaction was for the ®rst time thoroughly studied in [17]. Indole itself, is a basic building block in a variety of complex, biologi-

0009-2614/01/$ - see front matter Ó 2001 Published by Elsevier Science B.V. PII: S 0 0 0 9 - 2 6 1 4 ( 0 1 ) 0 0 3 4 1 - 4

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L. Pejov / Chemical Physics Letters 339 (2001) 269±278

cally important molecules, and can be compared with the tryptophan residue within peptide structures. Interaction between the molecular units within indole dimer may thus serve as a prototype for more complex interactions involving systems with biological signi®cance. In this Letter, a gradient-corrected density functional study of indole dimer, self-associated via N± H


p hydrogen bonding is presented, aiming to provide a ®rm theoretical basis for the experimentally observed trends regarding both geometrical and energetic, as well as vibrational spectroscopic aspects. 2. Computational methodology The Kohn±Sham (KS) variant of density functional theory [19] was used throughout the present study. Becke's three-parameter hybrid adiabatic connection exchange functional (B3) [20] was used in combination with the Lee±Yang± Parr correlation functional (LYP) [21] ± B3LYP. The employed exchange and correlation functionals are gradient-corrected, i.e., the exchange-correlation energy is accounted for by one-electron integral involving electron densities qa ; qb and their gradients rqa ; rqb (the non-local character of the dynamical electron correlation [19]). The Kohn±Sham equations were solved iteratively for the gradient-corrected functionals (instead of performing a single integration after local spin density iterations) using the 631++G(d,p) basis set for orbital expansion. Note that the 6-31++G(d,p) basis includes a di€use `sp' shell on all heavy atoms and a di€use `s' shell on all hydrogens. It has been well recognized that it is of substantial importance to include di€use functions in the basis when studying intermolecular interactions, especially with respect to diminution of the basis set superposition errors. The `®ne grid' (75, 302) was used for numerical integration (75 radial and 302 angular integration points). Let us also brie¯y recall that B3LYP is a hybrid HF-DFT approach [19±21]. Namely, Becke`s three-parameter adiabatic connection exchange functional is of the form [20]

AEXSlater ‡ …1

A†EXHF ‡ BDEXBecke88

‡ ECVWN ‡ CDECnon-local ;

…1†

where the constants A, B and C have been determined by ®tting to the G1 set of molecules. Obviously, it contains an admixture of the HF exchange, in contrast to the `pure DFT' methodologies. It has been found that the hybrid DFT methodology based on the B3LYP combination of functionals is the method of choice for prediction of a large number of molecular properties. Also the B3-LYP and B3-P86 combinations of functionals used with basis sets of DZ+P quality were shown to be fairly appropriate for studying the H-bonded and ionic type molecular clusters [22]. The geometries of indole monomer and dimer were optimized employing Schlegel's gradient optimization algorithm (the energy derivatives with respect to nuclear coordinates were computed analytically [23]). The absence of imaginary frequencies (negative eigenvalues of the Hessian matrix) con®rmed that the stationary points found correspond to real minima, instead of being saddle points. 2.1. Calculation of anharmonic vibrational frequencies and IR intensities 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 for the monomeric (free) N±H, dimeric hydrogen bonded (N±H


p) and dimeric `free' (non-H-bonded) N±H, as well as for the charge®eld perturbed monomeric N±H oscillators (vide infra), varying the N±H distance from 0.85 to 1.30  The obtained energies were least-squares ®tted A. to a ®fth-order polynomial in rNH . The resulting potential energy functions were subsequently cut after fourth order and transformed into Simons± Parr±Finlan (SPF) type coordinates q ˆ …rNH rNH;e †=rNH [24] (rNH;e being the equilibrium value), and the one-dimensional vibrational Schr odinger equation was solved variationally using the harmonic oscillator eigenfunctions as a basis. It

L. Pejov / Chemical Physics Letters 339 (2001) 269±278

has been well recognized that the SPF coordinates are superior over the `ordinary' bond stretch ones when variational solution of the vibrational Schr odinger 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 di€erences between the ground and ®rst excited vibrational levels. The anharmonicity constants (X) were computed from the equation m~NH ˆ x0;NH ‡ 2X ;

…2†

where x0;NH is the harmonic eigenvalue (obtained from k2 ). IR intensities, which are (within the electrical harmonic approximation) proportional to the squared dipole moment derivative were obtained according to the following relation:  2 1 NA p ol 1 As ˆ
4pe0 3c2 mH orNH rNH;e ln…10†  2 ol  19:1
; …3† orNH rNH;e where As is the molar absorption coecient (expressed in km mol 1 when ol=orNH is expressed in  1 ) while mH is the vibrating proton mass. The DA dipole moment derivatives were computed by a sixth-order polynomial least-squares ®t of the function l…rNH † and subsequent analytical di€erentiation at rNH;e . 2.2. Charge-®eld perturbation calculations and NBO analysis It is particularly interesting for all types of molecular interactions to be able to judge on the main `bonding' forces, i.e., mechanisms that are predominantly responsible for the interaction in question. Although several schemes have been developed for the total interaction energy decomposition into physically meaningful terms [25,26], no unique routine algorithm seems to exist that could provide an insight into the predominant forces in¯uencing anharmonic vibrational motions and the corresponding IR intensities. Within the present study, the so-called charge-®eld perturba-

271

tion approach (CFP) [27] is applied to study the electrostatic contribution to the total shift of the anharmonic N±H vibrational frequency upon selfassociation of indole. Although this approach has been applied for variety of di€erent purposes [12,27], it is shown in the present Letter that it gives quite useful results for the previously mentioned purpose as well. Within the CFP approach, the hydrogen-bond proton-accepting molecule was represented by a set of point charges, placed at the nuclear positions within the dimeric geometry. The sets of point charges were chosen such as to reproduce the molecular electrostatic potential of the proton-accepting unit at series of points selected applying three most frequently used point-selection algorithms ± CHelp, CHelpG and MK [28±30]. In order to judge on the direction and magnitude of the charge±transfer interaction, the natural bond orbital (NBO) analysis of monomeric and dimeric indole species was performed. All calculations were performed with the GA U S S I A N 98 series of programs [31] (and the NBO program, included in GA U S S I A N 98 [32]). 3. Results and discussion 3.1. Geometry The optimized geometry of indole dimer at B3LYP/6-31++G(d,p) level of theory is presented in Fig. 1. As can be seen, the planes of the two interacting monomers are stacked with an intersection angle close to 90° (89.4°), the nitrogen side of one monomer being directed to the benzenoid ring plane of the other, which is a clear geometrical indication for the existence of an N±H


p hydrogen bond (con®rmed by other calculations as well). Except for the equilibrium N±H distance, which changes from 1.0072 (for monomer) to  (for the H-donor within the dimer), the 1.0101 A other structural parameters show very subtle changes upon dimer formation, which is characteristic for weakly-bonded complexes. The six intermolecular parameters, de®ning the mutual orientation of the units within the dimer (Fig. 2) are presented in Table 1. These are: the distance between the centers of mass (CM's ± rCM ), the

272

L. Pejov / Chemical Physics Letters 339 (2001) 269±278 Table 1 The values of six intermolecular parameters, de®ning the mutual orientation of the monomeric units within the indole dimer, calculated at B3LYP/6-31++G(d,p) level of theory (see text and Fig. 2 for de®nition)  6.2072 RCM (A)  RH


p (A) 2.7125  RN…I†N…II† (A) 5.6369 / (deg) h (deg) a (deg)

Fig. 1. The optimized geometry of indole dimer in the T-shaped arrangement at B3LYP/6-31++G(d,p) level of theory.

Fig. 2. De®nition of intermolecular parameters, de®ning the mutual orientation of the units within the T-shaped indole dimer.

89.4 51.5 74.1

distance between the H atom from unit II and the benzenoid ring plane of unit I …RH


p †, the N(I)± N(II) distance, angle / between the planes of monomers I and II, angle h between the rCM directional vector and the monomer I plane, and the angle between the two N±H axes (a). Perhaps the most important parameter from the viewpoint of N±H


p hydrogen bonding is the RH


p distance. In the present case, the calculated value is  which is larger compared to the previ2.713 A, ously investigated N±H


p complexes, such as the molecular assembly of an aniline derivative (2.42  [33] and the pyrolle dimer (1.909 A)  [16], which A) indicates a much weaker interaction in the present case. Although the described minimum on the B3LYP/6-31++G(d,p) potential energy hypersurface of indole dimer would be expected to be favorable by dipole±quadrupole and quadrupole± quadrupole electrostatic interactions 1 and probably by the charge-transfer, the existence of other minima could not be excluded (stabilized an example by the dipole±dipole interaction). The search for the T-shaped minimum was, in fact, initiated by the preliminary AM1 results described in [17]. In fact, two other stationary points on the B3LYP/6-31++G(d,p) potential energy hypersurface of indole dimer were located as well, which are evidently favored by dipole±dipole interactions (Fig. 3a, b). However, these are much less stable than the T-shaped one (interaction energies are less than 1 kcal mol 1 for both of these structures),

1 The dipole±dipole interactions in the present case are of less importance due to the mutual arrangement of dipole moment vectors of the two monomers, which is quite far from the con®guration allowing optimal dipole±dipole stabilization.

L. Pejov / Chemical Physics Letters 339 (2001) 269±278

273

dimer potential energy hypersurface is in progress, employing some recently proposed functionals with improved long-range behavior. Note, however, that the present study yielded an excellent agreement of the indole monomer geometry parameters with the available microwave data [17]. Unfortunately, we were unable to ®nd any experimental data on the dipole or higher moments for this species, which could make possible to directly compare the calculated one-electron properties at B3LYP/6-31++G(d,p) level of theory. 3.2. Interaction energy

Fig. 3. Stationary points on the B3LYP/6-31++G(d,p) potential energy hypersurface of indole dimer stabilized by dipoledipole interactions.

the hypersurface being rather ¯at in their vicinity. Besides that, Fig. 3a, b do not involve hydrogen bonding interactions, which were experimentally detected [17]. Both the energetic arguments based solely on theoretical DFT data and the excellent agreement of the predicted shift of the m(NH) mode due to weak N±H


p hydrogen bond with the experimental data, thus favor the structure 1 as a global minimum on the explored hypersurface. All the data presented in the following will thus refer to the structure 1. A more detailed study of the indole

The interaction energy for the indole dimer (structure 1) was calculated including the basis set superposition error (BSSE) corrections, accounted for by the standard full function counterpoise procedure of Boys and Bernardi [34]. Despite the signi®cant debate in the literature regarding the most appropriate manner in which the binding energies may be corrected for this arti®cial e€ect due to the basis set extension (the primary BSSE), the Boys±Bernardi procedure is still the most widely used method at least for an estimation of the BSSE. Regardless of whether the full counterpoise correction is performed or a correction is performed including some orbital subset, the most ecient way to diminution of the BSSE, at least at the HF level, is the basis set enlargement. It has been shown that the counterpoise procedure should also be used when density functional levels of theory are applied to molecular clusters [22], though it does not show a regular dependence on the basis set enlargement. Within this approach, the BSSE-uncorrected (V) and -corrected …V cc † binding energies are given by [34] V ˆ Ec …Gc † …Em1 …Gc † ‡ Em2 …Gc ††; cc cc V cc ˆ Ec …Gc † …Em1 …Gc † ‡ Em2 …Gc ††;

…4† …5†

where Gc and Gm i denote the sets of coordinates characterizing the optimized geometries of the complex and ith monomer correspondingly, while the superscripts cc (counterpoise-corrected) denote that the corresponding energy has been calculated within the full dimer basis set (all of the basis

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L. Pejov / Chemical Physics Letters 339 (2001) 269±278

functions of the other monomer units present). The BSSE correction is thus BSSE ˆ V cc

V:

…6†

Obviously, the computed interaction energy in this manner contains the deformation energy of indole monomers upon complex formation. At B3LYP/6-31++G(d,p) level, the uncorrected interaction energy is 2:74 kcal mol 1 … 11:44 1 kJ mol †, while the BSSE-corrected value is 2:15 kcal mol 1 … 9:00 kJ mol 1 †. According to these results, the BSSE at the current level of theory is 0:58 kcal mol 1 …2:45 kJ mol 1 † or about 20% of the total interaction energy. The general conclusion which immediately follows is that the counterpoise-corrected interaction energy in the case of indole dimer is signi®cantly lower than the value reported for pyrrole dimer (although the values are not directly comparable, since the later was computed at MP2/6-31G(d,p) level of theory). This is also re¯ected in the much larger distance from the hydrogen-bonded proton to the ring plane. However, note that the relative magnitude of BSSE computed for indole dimer at B3LYP/631++G(d,p) level is signi®cantly lower than the value reported for pyrrole dimer. 3.3. N±H and N±H


p anharmonic vibrational frequencies and IR intensities The calculated anharmonic vibrational frequencies for the monomeric N±H oscillator, the

dimeric hydrogen bonded (N±H


p) and dimeric free (non-H-bonded) N±H oscillators, as well as for the charge-®eld perturbed N±H(


p) ones, together with the corresponding harmonic eigenvalues, anharmonicity constants and IR intensities are given in Table 2. Available experimental data from our previous studies are tabulated as well. The anharmonic vibrational potential energy parameters calculated at B3LYP/6-31++G(d,p) level are given in Table 3. In Table 4, a comparison is given between the predicted and experimentally found trends in the N±H stretching wave numbers upon dimer formation. The computed N±H stretching potentials for indole monomer and the N±H


p hydrogen bonded oscillator within the dimer, are presented in Fig. 4. In Fig. 5, variations of the dipole moment of the dimer with the changes in N±H distances for the studied N±H(


p) oscillators are presented. As can be seen from Tables 2±4, the agreement between the experimentally measured anharmonic N±H vibrational frequencies and the calculated B3LYP/631++G(d,p) ones is almost excellent. The last conclusion is especially valid for the changes in both the m(N±H) wave numbers and IR intensities upon dimer formation. Even the anharmonicity constants are excellently reproduced. A very slight change in the non-hydrogen bonded dimeric N±H stretching frequency …5 cm 1 † reveals the rather subtle geometry changes in the monomeric units upon self-association. However, the red shift of the N±H


p stretching frequency …65 cm 1 † follows

Table 2 The calculated anharmonic vibrational frequencies for monomeric N±H, dimeric N±H


p and dimeric free (non-H-bonded) N±H oscillators, as well as for the charge-®eld perturbed N±H(


p) ones, together with the corresponding harmonic eigenvalues, anharmonicity constants and IR intensities and the available experimental data from our previous studies [17] rNH;e  (A)

m …cm 1 †

x0 …cm 1 †

X …cm 1 †

I …km mol 1 †

mexp …cm 1 †

Xexp …cm 1 †

Monomer N±H

1.0071

3515.6

3659.3

)71.9

20.65

3491.0

)67.6

Dimer N±H N±H


p

1.0073 1.0105

3510.8 3450.8

3659.6 3603.0

)74.4 )76.1

18.10 90.50

3489.5 3423.6

CFP CHelp CHelpG MK

1.0083 1.0090 1.0100

3499.2 3489.7 3475.7

3643.1 3633.9 3620.4

)71.9 )72.1 )72.3

26.83 29.78 33.79

L. Pejov / Chemical Physics Letters 339 (2001) 269±278

275

Table 3 Anharmonic vibrational potential energy parameters calculated at B3LYP/6-31++G(d,p) level of theory for various N±H oscillators (see text) k2  1† …mdyn A

k3  2† …mdyn A

k4  3† …mdyn A

k5  4† …mdyn A

Monomer N±H

3.7656

)8.212

11.98

)10.0

Dimer N±H N±H


p

3.7661 3.6506

)8.238 )8.089

11.77 11.74

)8.9 )10.0

CFP CHelp CHelpG MK

3.7323 3.7134 3.6859

)8.149 )8.116 )8.070

11.92 11.88 11.83

)10.0 )10.0 )10.0

Table 4 The calculated (B3LYP/6-31++G(d,p)) and experimental changes in the m(N±H) frequencies and IR intensities upon dimer formation 1

‰m…N±H†monomer m…N±H†dimer Š (cm ) ‰m…N±H†dimer m…N±H


p†dimer Š (cm 1 ) ‰m…N±H†monomer m…N±H


p†dimer Š (cm 1 ) I…N±H


p†dimer =I…N±H†dimer I…N±H


p†dimer =I…N±H†monomer

B3LYP/6-31++G(d,p)

Experimental

4.8 60.0 64.8

1.5 65.9 67.4

5.00 4.38

4.49 4.0

CFP calculations CHelp ‰m…N±H†monomer m…N±H


p†dimer Š (cm 1 ) I…N±H


p†dimer =I…N±H†monomer

16.4 1.30

67.4 4.0

CHelpG ‰m…N±H†monomer m…N±H


p†dimer Š (cm 1 ) I…N±H


p†dimer =I…N±H†monomer

25.9 1.44

67.4 4.0

MK ‰m…N±H†monomer m…N±H


p†dimer Š (cm 1 ) I…N±H


p†dimer =I…N±H†monomer

39.9 1.64

67.4 4.0

 upon dimerthe re (N±H) change of ca. 0.0035 A ization. It should be noted at this point that all the previous calculations were based on one-dimensional N±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 and the monomer units massive (also with the proton-donor atom being involved in a rather non-¯exible ring structure), such vibrational coupling is indeed expected to be very small. This assumption is actually supported by the experimental data on the self-associated indole species in CCl4 . Namely, the m(N±H


p† band can be excellently modeled by

least-squares ®tting to a single Lorentzian (Cauchy) function [17], indicating a practically negligible interaction with a lower-frequency intermolecular mode. As mentioned before, in order to elucidate whether a purely electrostatic interaction could be responsible for the observed vibrational frequency shifts and IR intensity changes, a series of CFP calculations were performed. As can be expected (Table 2), the computed values for the anharmonic N±H stretching frequencies are somewhat dependent on the point-selection algorithm in the charge-assignment schemes. It has been well recognized that no unique method exists for parti-

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L. Pejov / Chemical Physics Letters 339 (2001) 269±278

Fig. 4. The computed B3LYP/6-31++G(d,p) N±H stretching potentials for indole monomer (a) and the N±H…


p† hydrogen bonded oscillator within the T-shaped dimer (b).

Fig. 5. Variations of the dipole moment of T-shaped dimer with the changes in N±H distances for the studied N±H and N±H…


p† oscillators.

tioning the total (continuous) charge distribution of a molecular system into discrete point charges associated with atomic centers within it. Still, the electrostatic potential-derived charges may be considered as the most appropriate choice for the present purpose, since they have been obtained by ®tting to the molecular electrostatic potential (which is a quantum-mechanical observable), and they reproduce the last quantity in the region outside the van der Waals surface of the molecule. Because of such generation algorithm, the

electrostatic potential-derived atomic charges account quite satisfactory for the e€ects due to multipole moments generated by the molecular charge distribution. However, though the CFP values for the anharmonic N±H frequencies di€er, it is obvious that according to these calculations the purely electrostatic interaction (without charge transfer) between the N±H


p oscillator and the monomer I unit could be only responsible for about up to 50% of the observed red shift (of course, the last estimation should not be taken in quantitative sense). Thus, the charge transfer interaction is of considerable importance. This is especially true when IR intensity changes are in question. The rather large experimentally measured enhancement in the IR intensity of the m(N±H) mode upon dimerization, reproduced excellently when both monomeric units are explicitly accounted for in quantum mechanical calculations, cannot be reproduced at all by the CFP models. Such conclusions are fully in line with the previous studies of dimeric systems, in which it has been pointed out that the electrostatic interactions are more important in a `static' sense, while the variation in the charge transfer upon excitation of vibrational modes (in a dynamic sense) is of cardinal importance for IR intensity enhancement upon dimerization [35]. In order to get at least a semi-quantitative picture of the direction and magnitude of the charge transfer for the studied case, NBO analysis of the indole monomer and dimer was performed (for the B3LYP/6-31++G(d,p) optimized geometries). However, since the NBO program implemented in GA U S S I A N 98 cannot handle nearly-linear dependent bases, the NBO analysis was based on the B3LYP/6-31G(d,p) density. As revealed by the second-order perturbation theory analysis of the Kohn±Sham analog of the Fock matrix within the NBO basis (Table 5), the only signi®cant charge transfer between the monomeric units is from monomer I to monomer II, or more precisely from a benzenoid ring p orbital to the N±H antibonding r orbital …p±r †, and from the benzenoid ring p orbital to a H Rydberg orbital …p±R†. The estimated energetic e€ects due to these interactions are given by the second-order energy expressions [35]:

L. Pejov / Chemical Physics Letters 339 (2001) 269±278

277

Table 5 Second-order perturbation theory analysis of Fock matrix in NBO basis at B3LYP/6-31G(d,p)//B3LYP/6-31++G(d,p) level of theory (see text) Donor orbital

Acceptor orbital

DE…2† …kcal mol 1 †

DE (acceptor±donor) (a.u.)

hpCC jF^jacci (a.u.)

p(CC) p(CC)

r (NH) R(H)

)1.54 )0.11

0.74 1.52

0.032 0.012

DEpr  2


DEpR  2


D E2 pCC jF^jrNH epCC

erNH

D E2 pCC jF^jRH epCC

eR H

;

…7†

;

…8†

where i is a diagonal NBO matrix element of the Fock operator F^ (or, more rigorously, the Kohn± Sham analog h^KS ). Since the overall charge transfer can be essentially described by interactions between these orbitals, it is expected that the sum of the previous two terms should be almost equal to the total charge-transfer energy. The populations of the most relevant orbitals for the present CT interaction in the cases of indole monomer and dimer are presented in Table 6. Obviously, the magnitude of p(CC)±r (NH) charge transfer within the dimer is 0.0043 e, which is quite relevant from the stabilization aspect. It has been emphasized that even seemingly small values of transferred charge (0.001±0.01 e) lead to chemically signi®cant stabilization energies [35]. 4. Conclusions A T-shaped minimum on the B3LYP/ 6-31++G(d,p) potential energy hypersurface of Table 6 Populations of the relevant for the CT interaction indole monomer and dimer orbitals calculated with NBO analysis at B3LYP/6-31G(d,p)//B3LYP/6-31++G(d,p) level of theory (see text) Orbital

r (NH) R(H)

Population (e) Monomer

Dimer unit I

Dimer unit II

0.0152 0.0015

0.0151 0.0015

0.0195 0.0021

indole dimer has been located by the gradient optimization technique. Within this geometry, the two monomeric units are associated via N±H


p hydrogen bonding. The experimentally observed changes in the anharmonic m(NH) vibrational frequencies and IR intensities upon dimerization are almost excellently reproduced by the present level of theory when both monomeric units are explicitly considered. Purely electrostatic interaction between monomers, mimicked by the charge®eld perturbation approach could neither account for the red shift of the m(NH) vibrational frequencies or for the signi®cant enhancement of the m(N±H


p) IR intensity. NBO analysis of indole monomer and dimer reveals a signi®cant onedirectional charge transfer of p±r type, whose variation upon vibrational excitation governs the IR intensity enhancement.

References [1] K. M uller-Dethlefs, P. Hobza, Chem. Rev. 100 (2000) 143. [2] S. Scheiner, Hydrogen Bonding ± A Theoretical Perspective, Oxford University Press, Oxford, 1997.  [3] P. Hobza, V. Spirko, H.L. Selzle, E.W. Schlag, J. Phys. Chem. A 102 (1998) 2501. [4] P. Hobza, Z. Havlas, Chem. Phys. Lett. 303 (1999) 447.  [5] P. Hobza, V. Spirko, Z. Havlas, K. Buchhold, B. Reimann, H-D. Barth, B. Brutschy, Chem. Phys. Lett. 299 (1999) 180. [6] F. Diederich, Angew. Chem., Int. Ed. Engl. 27 (1988) 362. [7] A.V. Mueldorf, D. Van Engen, J.C. Warner, A.D. Hamilton, J. Am. Chem. Soc. 110 (1988) 6561. [8] P.L. Anelli, P.R. Ashton, R. Ballardini, V. Balzani, M. Delgago, M.T. Gandol®, T.T. Goodnow, A.E. Kaifer, D. Philp, M. Pietraszkiewicz, L. Prodi, M.V. Reddington, A.M.Z. Slawin, N. Spencer, J.F. Stoddart, C. Vincent, D.J. Williams, J. Am. Chem. Soc. 114 (1992) 193. [9] K.H. Fung, H.L. Selzle, E.W. Schlag, J. Phys. Chem. 87 (1983) 5113. [10] K.S. Law, M. Schauer, E.R. Bernstein, J. Chem. Phys. 81 (1984) 4871.

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[11] K.O. B ornsen, H.L. Selzle, E.W. Schlag, J. Chem. Phys. 85 (1986) 1726. [12] P. Hobza, H.L. Selzle, E.W. Schlag, J. Chem. Phys. 93 (1990) 5893. [13] B.F. Henson, G.V. Hartland, V.A. Venturo, P.M. Felker, J. Chem. Phys. 97 (1992) 2189. [14] P. Hobza, H.L. Selzle, E.W. Schlag, J. Phys. Chem. 97 (1993) 3937. [15] P. Hobza, H.L. Selzle, E.W. Schlag, J. Am. Chem. Soc. 116 (1994) 3500. [16] H. Park, S. Lee, Chem. Phys. Lett. 301 (1999) 487.  [17] V. Stefov, Lj. Pejov, B. Soptrajanov, J. Mol. Struct. 555 (2000) 363. [18] A. Lautie, M.F. Lautie, A. Gruger, S.A. Fakhri, Spectrochim. Acta 36A (1980) 85. [19] J.M. Seminario, P. Politzer, Modern Density Functional Theory: A Tool for Chemistry, Elsevier, Amsterdam, 1995 (Chapters 1±4). [20] A.D. Becke, Phys. Rev. A 38 (1988) 3098. [21] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785.

 [22] P. Hobza, J. Sponer, T. Reschel, J. Comp. Chem. 16 (1995) 1315. [23] H.B. Schlegel, J. Comp. Chem. 3 (1982) 214. [24] G. Simons, R.G. Parr, J.M. Finlan, J. Chem. Phys. 59 (1973) 3229. [25] K. Kitaura, K. Morokuma, Int. J. Quantum Chem. 10 (1976) 325. [26] W.J. Stevens, W.H. Fink, Chem. Phys. Lett. 139 (1987) 15. [27] U. Dinur, Chem. Phys. Lett. 192 (1992) 399. [28] L.E. Chirlian, M.M. Francl, J. Comp. Chem. 8 (1987) 894. [29] C.M. Breneman, K.B. Wiberg, J. Comp. Chem. 11 (1990) 361. [30] U.C. Singh, P.A. Kollman, J. Comp. Chem. 5 (1984) 129. [31] M.J. Frisch, et.al., GA U S S I A N 98 (Revision A.9), Gaussian, Inc., Pittsburgh, PA, 1998. [32] E.D. Glendening, et al., NBO, Version 3.1. [33] L.R. Hanton, C.A. Hunter, D.H. Purvis, J. Chem. Soc., Chem. Commum. (1992) 1134. [34] S.F. Boys, F. Bernardi, Mol. Phys. 19 (1970) 553. [35] L.A. Curtiss, D.J. Pochatko, A.E. Reed, F. Weinhold, J. Chem. Phys. 82 (1985) 2679.