MOLECULAR PHYSICS

THEORETICAL STUDY OF THE DRIVING FORCES IN THEα- AND β-CYCLODEXTRIN : DICLOFENAC INCLUSION COMPLEXES

C. MORARI, D. BOGDAN, M. BOGDAN

National Research and Development Institute of Isotopic and Molecular TechnologiesP. O. Box 700, R-400293 Cluj-Napoca 5, Romania

e-mail: cristim@l30.itim-cj.ro

Received December 21, 2004

The nature of driving forces in complexes of α- and β-cyclodextrin withdiclofenac was investigated by ab initio calculation. Morokuma-Kitaura decompositionof the interaction energy between α (β)-CD and DCF is reported. The results showthat the dominant component of the binding energy is caused by charge transferprocess. The effect of the solvent upon the binding energy is discussed.

Key words: binding energy, cyclodextrin, diclofenac, Morokuma-Kitauradecomposition.

1. INTRODUCTION

Cyclodextrins (CD) are cyclic oligosaccharides composed of six, seven oreight α-1,4-linked glucose residues and are characterized by a truncated coneshape. In their cavity, the CD can accommodate a wide class of organicmolecules leading to inclusion complexes [1]. CD chemistry has caused muchinterest, not only due to its applications to pharmaceutical science andtechnology but also because the inclusion represents an ideal model mimickingenzyme-substrate interactions [2, 3].

The driving forces leading to the complexation have been attributed tofactors including van der Waals force [4], hydrophobic effect [5] anddipole-dipole interactions [6]. In a recent paper, Liu et al. [7] have pointed outthe importance of the charge transfer interaction for the complexation of α-CDwith several molecules like nitrobenzene or benzoic acid. The mechanism of thecharge transfer interaction can be summarized as follows: when a supermoleculeis built up from two components, a mixing of the filled orbital of the firstmolecule with the vacant orbitals of the second appear. This lead to a chargetransfer between the two monomers, hence an attractive force between the two

Paper presented at the 5th International Balkan Workshop on Applied Physics, 5–7 July2004, Constanþa, Romania.

Rom. Journ. Phys., Vol. 50, Nos. 9–10 , P. 995–1002, Bucharest, 2005

996 C. Morari, D. Bogdan, M. Bogdan 2

components arises. The aim of this paper is to emphasize the role of the chargetransfer interaction in the complexes α-CD : diclofenac (DCF) and β-CD : DCF,by means of the ab initio calculations. To this end, the driving forces that appearin the α-, β-CD : DCF complex were investigated using the Morokuma-Kitaura[8–10] analysis of the binding energy between CD and DCF.

According to the theory of Morokuma-Kitaura decomposition of bindingenergy between two monomers, when a supermolecule is formed from twomolecules, the electrons will lose their identity as belonging to one or othercomponent molecule. As a consequence the binding energy can be separated intofour types of interactions that describe the formation of a supermolecule:

(a) electrostatic interaction (Es), which is favored by large permanentcharges and dipoles;

(b) polarization interaction, which is favored by large volume andpolarizability of molecules (Epl);

(c) exchange energy, or Pauli repulsion (Ex);(d) charge-transfer interaction, discussed above (Ect);(e) a fifth term (Ehigh) is equal to the remaining interaction energy [10].Diclofenac, 2-(2′,6′-dichloroanilino) phenylacetic acid is a non-steroidal

anti-inflammatory drug used in different diseases such as rheumatoid arthritis,ankylosing spondylitis, osteoarthritis or sport injuries. Its geometry, with twotwisted aromatic rings plays an important role in this property [11].

Experimental studies in both α- and β-CD complexes [12–17] revealed thata 1:1 stoichiomeries characterize them. The α-CD : DCF complex was investigatedrecently by Arancibia et al. [12]. Their spectrofluorometric studies of theα-CD : DCF complex in aqueous solution reveals that both carboxyl andsecondary amino groups of the guest remain outside the cyclodextrin cavity.Large solubility of α-CD : DCF complex in water and high fluorescenceemission were mentioned as significant properties.

Investigations of β-CD : DCF were performed by several groups [13–17].The results suggest that hydrophobic effects and hydrogen bonding plays animportant role in the complexation process [14, 16]. By comparing results onα-CD : DCF [12] and β-CD : DCF [13]. Arancibia et al. suggested that theinteractions that occur in both complexes have a similar nature. Also theysuggested that in the case of β-CD : DCF the aromatic ring bonded to acetategroup resides within the β-CD cavity.

Our NMR studies (M. Bogdan et. al, in press in J. Incl. Phenom.), pointedout that there is the possibility that the aromatic ring bonded to the acetate groupcan be accommodated also outside of the β-CD cavity. By means of ab initocalculation we try to give a satisfactory answer to this question too.

3 Driving forces in the α- and β-cyclodextrin 997

2. THEORY AND CALCULATION

The molecular modeling of the guest: host interaction by ab initio andsemiempirical methods was performed in three steps:

(i) The equilibrium structures of CD and DCF were set up. The structuresof α- and β-CD were taken from Cambridge Structural Database [18]. For thepresent calculation we made the approach that this structure changes very littleduring the complexation process. As a consequence of this approach, no furthertheoretical optimization was performed on these structures.

The initial structure of DCF was built up using the Hyperchem 5 program.This initial structure was optimized at ab initio level by using the DZ basis set[19]; for all calculations the GAMESS package was used [20].

For all calculations presented below two initial relative orientations of theCD : DCF complex were taken into account: (a) the secondary amino group ofDCF was oriented to the center of mass of the CD (through this paper we designthis as the orientation ‘1') and (b) the carboxyl group of DCF was oriented to thecenter of mass of the CD (the orientation ‘2').

(ii) The optimization strategy was to keep frozen all the internal coordinatesof the CD, while the relative orientation CD : DCF and the internal geometry ofthe DCF molecule were optimized using gradient methods.

Eight randomly chosen initial geometries of the complex were optimized atPM3 level, four for each orientation. The calculation was repeated for both typesof CD. In the next step, ab initio optimizations of the CD : DCF system wereperformed for both types of the CD and for both orientations. The starting pointin each case was the most stable PM3 – optimized geometry of the complex,from those described above. A minimal basis set (Slater type orbitals) with twofunctions for each atomic orbital (STO-2G) [21] was used. The reason of thischoice was the size of the system (about 150 atoms) which does not allows theuse of larger basis sets.

For the α-CD : DCF complex only the gas phase results are reported. Forthe β-CD : DCF complex, both gas phase and solvated molecule geometry werestudied. A qualitative discussion of the solvent effects was taken into account byusing the Born-Kirkwood-Onsager model [22]. According to this model, themolecular cavity is approximated by a sphere of radius a. The interactionbetween the molecular charge distribution and the electric field generated by thesolvent Er, is calculated by approximating the molecular charge distribution asan electric dipole. The dipole is located at the cavity center and has the value μ.Due to the ring shape of the CD, the model can be considered as a first approachfor qualitative discussion of the solvent effects upon the binding energy of thecomplex. The β-CD : DCF complex was encapsulated into a sphere with a radiusof a = 9.0 Å, while the dielectrical constant of the exterior medium was set to

998 C. Morari, D. Bogdan, M. Bogdan 4

εr = 80 (water). The value of 9.0 Å was computed from the densitymeasurements of DCF and CD aqueous solutions with 0.01 mM concentration.

(iii) For the STO-2G equilibrium geometry produced as described above(see Fig. 1) we performed a Morokuma-Kitaura [8, 10] decomposition of theinteraction energy for the CD : DCF complex, for all the cases discussed above.

It can be seen that DCF remains outside of the α-CD cavity for bothorientations, while the β-CD is accommodating the DCF molecule inside of thecavity only for orientation ‘2'.

Fig. 1. – Equilibrium geome-tries computed at HF/STO-2Gab initio level for α- andβ-CD : DCF complexes. Fromtop to bottom: α-CD : DCF,orientation ‘1', α-CD : DCF,orientation ‘2', β-CD : DCF,orientation ‘1', β-CD : DCF,orientation ‘2'. Left: lateral view. Right: top view.

5 Driving forces in the α- and β-cyclodextrin 999

RESULTS

Mulliken and Löwdin population analysis [24] gives a quantitative measureof the acid – base behavior of the two components in the complex. The sum ofMulliken populations for all atoms, computed at STO-2G level, was calculatedfor both CD and DCF. We found that CD receives a positive electronicpopulation, having the role of the Lewis acid in the complex, while the DCFmolecule act as a Lewis base and is donating electrons.

Table 1 summarizes the results of Mulliken and Löwdin populationanalysis of the complex CD : DCF for different configurations andcomputational models. The values lie all in the interval 0.03–0.04 with oneexception: β-CD : DCF system has a smaller value for orientation ‘1'. This valueis significantly changed by inclusion of the solvent effect, while it remainsroughly the same for orientation ‘2'.

Table 1

Sum of the total Mulliken and Löwdin electronic populations over theatoms of DCF for different complexes and computational models ispresented. Notations: ' or. “1” means orientation ‘1' and ' or. ‘“2”'

means orientation ‘2'

Complex Mulliken Löwdin

α-CD : DCF, or. ‘1' –0.0469 –0.0446

α-CD : DCF, or. ‘2' –0.0418 –0.0448

β-CD : DCF, or. ‘1' –0.0136 –0.0120

β-CD : DCF, or. ‘2' –0.0424 –0.0493

β-CD : DCF + SOLV., or. ‘1' –0.0334 –0.0319

β-CD : DCF + SOLV., or. ‘2' –0.0435 –0.0504

The results of Morokuma-Kitaura decomposition of the binding energy forboth complexes CD : DCF are given in Table 2.

A graphical representation of these results is given in Fig. 2. By comparingthe results for the two complexes it can be seen that the nature of the interactionsis the same in both complexes, while the numerical values follow a regular trend.In all the cases, the dominant component is the charge transfer one while thePauli repulsion is significant in all these cases.

The energetical gap between the two orientations is larger for the β-CD : DCF system than that for the α-CD : DCF. The Heitler-London interactionbetween the two components is the sum of the electrostatic and exchangeenergies, EHL = Ex + Es. It can be seen from Fig. 2 that the Heitler-Londoninteraction energy has a positive value for all four cases under investigation.

1000 C. Morari, D. Bogdan, M. Bogdan 6

Table 2

Results of Morokuma-Kitaura decomposition for the CD : DCF complexes are presented. First tworows: orientation ‘1'. Second two rows: orientation ‘2'. The notations are: Es – electrostaticenergy; Ex – exchange repulsion energy; Epl – polarization energy; Ect – charge transfer energy;Ehigh – high order coupling energy; Etot – total binding energy of the complex. The energies are

given in [kcal/mole]

Complex Es Ex Epl Ect Ehigh Etot

α-CD : DCF –6.73 16.56 –0.52 –16.76 0.06 –7.38

β-CD : DCF –2.80 9.14 –0.12 –9.30 0.22 –2.86

α-CD : DCF –10.40 24.35 –0.38 –22.51 –0.86 –9.80

β-CD : DCF –14.85 39.75 –0.61 –32.74 –2.81 –11.26

Fig. 2. – The Morokuma-Kitaura components of the binding energy forboth α- and β-CD : DCF complexes are represented in the picture.Energies are expressed in [kcal/mole]. The notations are the same as those

used in the Table 2.

The total binding energy was estimated also in the presence of water byusing the Born-Kirkwood-Onsager model. Due to the limitations of the model[26] only a qualitative discussion can be made. The energy of the complex andthe energies of the CD and DCF were computed separately. The binding energieswithin this model were E1 = –0.58 kcal/mole for orientation ‘1' and E2 == –5.73 kcal/mole for orientation ‘2'.

These values are a qualitative indication of the influence of the solventupon the binding energy: if the solvent effects are included, the binding energiesbecome significantly smaller, for both geometries of the β-CD : DCF complex.

7 Driving forces in the α- and β-cyclodextrin 1001

4. CONCLUSION

The geometry and the nature of the driving forces for the α- and β-CD : DCFcomplexes were investigated by ab initio methods. As revealed by previousstudies [12], we found that at equilibrium both relative orientations (labeled intext as orientation ‘1' and orientation ‘2') are possible for both systems.

The nature of the binding energy of the complex was investigated using theMorokuma-Kitaura decomposition. Our results for gas-phase compoundsshowed that charge-transfer is the most important driving force in the CD : DCFcomplexation process. The Morokuma-Kitaura components of the bindingenergy are similar in the α-CD : DCF and β-CD : DCF complexes. Thecomponents of the binding energy follow a regular trend, explicitly given inFig. 2, with β-CD : DCF orientation ‘2' as the most stable complex andβ-CD : DCF orientation ‘1' having the smallest binding energy.

The inclusion of the solvent effects in the calculations leads to a significantdecrease of the binding energy for the β-CD : DCF complex.

Acknowledgements. Authors thanks to Dr. M. Caira for help. Ministry of Education andResearch of Romania provided support for this work in the framework of grants CNCSIS 126 /2003 and BIOTECH program (No. 01–8–CPD–041).

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