randomly methylated-β-cyclodextrin binary system

randomly methylated-β-cyclodextrin binary system

Carbohydrate Research 346 (2011) 2746–2751 Contents lists available at SciVerse ScienceDirect Carbohydrate Research journal homepage: www.elsevier.c...

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Carbohydrate Research 346 (2011) 2746–2751

Contents lists available at SciVerse ScienceDirect

Carbohydrate Research journal homepage: www.elsevier.com/locate/carres

Structural and theoretical-experimental physicochemical study of trimethoprim/randomly methylated-b-cyclodextrin binary system Daniela Kubota a, Osmir Fabiano Lopes Macedo b, George Ricardo Santana Andrade b, Leila Souza Conegero c, Luis Eduardo Almeida b, Nivan Bezerra Costa Jr. a,b, Iara F. Gimenez a,b,⇑ a

NPGQ – Núcleo de Pós-graduação em Química, Universidade Federal de Sergipe (UFS), Av. Marechal Rondon s/n, Campus Universitário Prof. José Aloísio de Campos, CEP 49100-000 São Cristovão, SE, Brazil b P2CEM – Programa de Pós-graduação em Ciência e Engenharia de Materiais, Universidade Federal de Sergipe (UFS), Av. Marechal Rondon s/n, Campus Universitário Prof. José Aloísio de Campos, CEP 49100-000 São Cristóvão, SE, Brazil c Instituto de Química – Universidade Estadual de Campinas (UNICAMP), Cidade Universitária Zeferino Vaz s/n, Caixa Postal 6154, CEP 13084-862 Campinas, SP, Brazil

a r t i c l e

i n f o

Article history: Received 20 June 2011 Received in revised form 21 September 2011 Accepted 24 September 2011 Available online 2 October 2011

Keywords: Trimethoprim Randomly methylated-b-cyclodextrin Inclusion complex Phase-solubility diagram Semiempirical methods PM3-D

a b s t r a c t Here we report the structural characterization, physicochemical study and molecular modeling of the inclusion complex of trimethoprim in randomly methylated beta-cyclodextrin. The phase-solubility diagram obtained at pH 7.0 exhibited a linear behavior for the RAMEB concentrations studied suggesting a 1:1 stoichiometry and absence of aggregation in solution. From stoichiometric determination by the continuous variation method we confirmed a 1:1 stoichiometry. To make a detailed characterization of the inclusion mode, spectroscopic measurements by infrared and 1D and 2D 1H NMR spectroscopy provided evidence that the inclusion mode is characterized by inclusion of the trimethoxyphenyl ring in the cavity; interactions with methyl groups located in the border of the cavity were also detected. The structure proposed was also confirmed by semiempirical molecular modeling. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction Preparation of inclusion complexes of drug molecules using cyclodextrins (CDs) as hosts is a widely employed strategy to enhance the solubility, stability, and bioavailability of the guest molecules.1 However, parent cyclodextrins (a-, b-, and c-cyclodextrins) exhibit relatively low water solubilities, which consequently limit their use in pharmaceutical formulations.2 Thus, several cyclodextrin derivatives have been developed to overcome these limitations and among them b-CD derivatives are the most used due to factors such as price, availability, approval status, cavity dimensions, etc. An important factor to be considered when dealing with CD derivatives for use both in humans and in animals is the formation of stable crystalline complexes with cholesterol, which may form insoluble crystals in the kidneys causing nephrotoxicity. In this context, several hydroxypropylated and methylated CD derivatives are considered safe because, despite high affinities for cholesterol, the complexes formed are soluble. A modified b-CD that is considered one of the better solubilizers for hydrophobic drugs is heptakis(2,6-di-O-dimethyl)-b-CD (DIMEB)

⇑ Corresponding author. E-mail address: [email protected] (I.F. Gimenez). 0008-6215/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.carres.2011.09.030

but the amorphous randomly methylated b-CD (RAMEB) is preferred because currently DIMEB cannot be produced with affordable prices.2 For this reason RAMEB has been chosen here as host for trimethoprim (TMP), a broad spectrum antibiotic widely used in the treatment of urinary tract infections as well as of certain types of pneumonia. The preparation of CD inclusion complexes may be advantageous considering that TMP has a very low aqueous solubility in addition to a bitter taste and both can be improved by CD encapsulation. This subject has been studied before both in solution3 and in the solid state4 with parent b-CD with improvements of the solubility and of the dissolution properties. On the other hand, the use of CD derivatives with higher solubility has also attracted attention and recently Longhi and co-workers5 reported the inclusion complex of TMP with hydroxypropyl-b-cyclodextrin showing the occurrence of aggregation behavior at relatively high concentrations of the host. Finally, Pinzauti and co-workers6 have also reported thermal properties and the temperature dependence of K1:1 apparent binding constant for RAMEB complexation of TMP. To our knowledge no theoretical-experimental study of structure and thermodynamic parameters of complexation have been reported until yet for this binary system. Thus we aim to contribute to a further understanding and possible applications of this complex.

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2. Results and discussion The phase-solubility diagram was determined in buffer solution at pH 7.0 (25 °C) (Fig. 1). The diagram obtained showed that the solubility of TMP increases linearly in the presence of RAMEB, which is expected with the formation of an inclusion complex and constitutes the primary evidence for the process. Additionally, the presence of a linear behavior also precludes the occurrence of aggregation in solution at the concentration range studied. Longhi and co-workers5 studied the complexation of TMP in 2-hydroxypropyl-b-cyclodextrin in a broad concentration range of the host, observing a deviation from the linear behavior, caused by aggregation in solution. From the phase-solubility diagram, we obtained the values for the association constant (K1:1 = 130 M 1) and for the complexation efficiency (C% = 21%). Pinzauti and co-workers6 studied the thermal behavior and phase-solubility for TMP/RAMEB complex prepared by tumble mixing, obtained a K1:1 value of 110 M 1 in water at 25 °C. The value is relatively close to that found here with a difference probably attributable to the change of medium.

0.0006

[TMP] mol L

-1

0.0005

0.0004

0.0003 0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

-1

[RAMEB] mol L

Figure 1. Phase-solubility diagram of TMP in the presence of RAMEB obtained at pH 7.0 (25 °C).

The principal stoichiometry of complexation has been evaluated by the continuous variation method yielding the plot shown in Figure 2a. On the basis of this method, the mole ratio of the drug corresponding to the maximum variation of the fluorescence intensity can be taken as the stoichiometry of the complex. Thus we can propose a 1:1 complexation stoichiometry. We also evaluated the in vitro release profile at pH 8.0 (to mimic the intestines) of TMP from the complex in comparison with free TMP. From the plots in Figure 2b we observe that complexation into RAMEB decreases the membrane permeability of TMP, decreasing the percent release of the drug at the time interval studied. This can be a result of the equilibrium association with the host, which in addition to the hydrophilic character of RAMEB slows down the drug permeation through the membrane. The inclusion complex collected by lyophilization has been characterized by standard techniques such as thermal analysis (TG/DTG and DTA) and FTIR spectroscopy. TG/DTG curves (Fig. 3a and b) show mainly that the inclusion complex decomposes at a temperature different from the free host and guest, as can be seen both in TG and DTG curves. This observation suggests that the complex behaves as a distinct species because otherwise the presence of both species as separate particles would generate a superposition of original peaks in the DTG curve. Also, the values of final mass residues confirm that the complex contains both species, because it presents an intermediate value between free RAMEB and free TMP. DTA curves (Fig. 4) provide additional evidence of complex formation because in general the absence of the peak associated with the melting transition of the free drug is taken as an evidence of inclusion. The reason for this is that the melting point as a physical constant is in general defined for a solid formed by the packing of identical molecules (in the case of molecular crystals such as many drugs). The melting temperature is thus reached when drug–drug interactions are broken and a sharp peak is recorded. In the complex, drug molecules interact with the cyclodextrin cavities and in principle there is no reason for those interactions lead to a melting temperature identical to the pure substance melting point. Figure 4 shows DTA curves for RAMEB, which decomposes without melting and as a result no peak is observed, TMP with the melting point observed as a peak at 200 °C and for the complex, for which no peak is observed, suggesting the presence of an inclusion complex. FTIR spectra were obtained for free host and guest and for the complex sample (Fig. 5a and b). In the spectrum of TMP the main

5

30

TMP

25

% TMP released

-1

[TMP]t.(F-F0) (10 mol.L )

4

-3

3

2

1

20

15

10

complex 5 0

0 0.0

0.2

0.4

0.6

TMP molar ratio

(a)

0.8

1.0

0

50

100

150

200

250

time (min)

(b)

Figure 2. (a) Job’s plot for the RAMEB/TMP system determined from fluorescence measurements; (b) in vitro release profiles determined at pH 8.0.

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364

90 80

60 50

TMP

40

COMPLEX

30 20

Mass difference

Mass (%)

RAMEB COMPLEX TMP

323

70

302

RAMEB

10 0 0

100

200

300

400

500

600

Temperature (ºC)

0

100

200

300

400

500

600

Temperature (ºC)

(a)

(b)

Temperature difference (a.u.)

Figure 3. TG (a) and DTG (b) curves for TMP, RAMEB and the complex.

RAMEB Complexo TMP

o

200 C

100

200

300

Temperature (ºC) Figure 4. DTA curves for TMP, RAMEB and the complex.

features observed are assigned to [email protected] and [email protected] from aromatic rings in the 1660–1400 cm 1 range, C–H stretching from aromatic rings at 3120 cm 1 and NH2 stretchings at 3472 and 3316 cm 1. In the RAMEB spectrum, main features are the O–H stretching (from residual non-methylated hydroxyl groups) centered at 3400 cm 1 and a large number of bands below 2000 cm 1 related to coupled modes from the cyclodextrin rings.7 The presence of the broad OH stretching band reveals that a considerable fraction of the hydroxyl groups remained non-methylated. In the spectrum of the complex (Fig. 5a and zoom in Fig. 5b), despite the predominance of RAMEB bands due to the presence of highly polar groups in the molecular structure, bands from TMP can be observed and have been marked with arrows in the Figure 5b. Differences in some bands especially those pairs at 1592/ 1564 cm 1 and 1460/1422 cm 1 assigned to [email protected] aromatic stretching in free TMP have fused in the complex at 1564 and 1414 cm 1, respectively, suggesting perturbations in aromatic rings which can be involved in the inclusion, as already observed by Longhi and coworkers.5 Finally in the region above 2500 cm 1 the spectrum of the inclusion complex shows a very broad band envelope, considerably broader than the O–H stretching band of RAMEB, probably corresponding to a superposition of spectral features from both

species: the broad O–H stretching band from RAMEB and TMP bands (NH2 stretching and aromatic C–H stretching bands). Inclusion complexes of TMP with different cyclodextrins were reported previously,3–6 but without a detailed experimental characterization of the inclusion mode. Longhi and co-workers5 focused on the study of aggregation behavior and observed changes in chemical shifts for 1H protons from TMP in NMR data, which allowed proposing the formation of an inclusion complex. In this context, one of the strongest pieces of evidence for the formation of the inclusion complex, with characterization of inclusion mode, has been provided by one and two-dimensional 1H NMR spectroscopic experiments (ROESY).8 The ROESY spectrum shown in Figure 6a and b exhibits off-diagonal correlations between protons that are in close proximity in space (in the order on 0.4 nm). Thus, correlations between protons from the guest and protons from the CD cavity are indicative of the formation of an inclusion complex. Here the ROESY plot shows correlations between H3 and H5 RAMEB protons located inside the cavity, (see Fig. 7 for proton numbering and Table 1 for tentative assignments) and protons and H5 TMP protons located in the trimethoxyphenyl ring. There are also cross-peaks between H5 proton from TMP and the Me2 group (methyl to carbon 2) from RAMEB, which is located close to the secondary opening. Finally there is also a weak correlation between H2 TMP proton and Me2 protons, along with absence of interactions with internal protons from the cavity (zoom image), indicating that this group is not included but is close to the secondary border of RAMEB. Those observations in addition to the absence of correlations with the Me6 groups (methyl to carbon 6) from RAMEB allow us to propose that the trimethoxyphenyl ring of TMP enters the cavity from the secondary rim. However, as the inclusion complex in solution behaves as a dynamic species, different penetration degrees can be suggested. It is worth mentioning that interactions of methoxy protons with protons in the RAMEB cavity cannot be unequivocally assigned due to the proximity of the respective signals which make the cross peaks to fall in the diagonal of the plot. Thus, those interactions are very likely to occur but cannot be evidenced from ROESY result. From the 1D 1H NMR spectra (not shown) we observed changes in the chemical shifts of both host and guest species (Table 1), including the methoxy protons from TMP. Concerning the direction of the observed changes, proton H2 from TMP is significantly upfield shifted which according to Longhi and co-workers5 indicated the proximity to a p-electron rich atom such as oxygen on the

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RAMEB/TMP

RAMEB/TMP

Transmittance

Transmittance

RAMEB

RAMEB

TMP

TMP

3500

3000

2000

1500

1000

?

500

Wavenumber (cm-1)

1700

1400

1300

1200

(b)

Figure 5. (a) FTIR spectra (KBr disks) for TMP, RAMEB and the complex (4000–400 cm

border of the cavity. On the other hand, all other protons are downfield shifted indicating a change in the polarity probably due to inclusion in the cavity. An interesting feature is that the chemical shift of H2 proton from TMP is also considerably changed, which corroborates observations from ROESY data, because although this proton remains outside the cavity, it interacts with groups located in the border of the cavity such as Me2.

1500

Wavenumber (cm-1)

(a)

Figure 6. (a) 1H–1H ROESY for the complex (4000–400 cm

1600

1

); (b) zoom of the highlighted region in (a).

1

); (b) zoom of the cross-peaks region of relevant interactions.

Semiempirical molecular modeling of the inclusion complex with a permethylated b-cyclodextrin has been performed using different available methods. The results are summarized in Table 2. Comparing conventional methods (AM1, PM3, PM6 and RM1) on the basis of the enthalpy associated to the reaction formation of the complex from separate host and guest molecules, the results indicate that the NH2-out configuration is the preferred one from

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N

(1) H2N

N

(3) NH2

(5) H

(6) OMe OMe (7)

C (4) H2

H (2)

H (5)

OMe (6)

(b)

(a)

Figure 7. Representations of the structure of (a) glucopyranose unit of cyclodextrins; (b) TMP along with proton numbering.

Table 1 1 H NMR chemical shifts (CD3OD) for RAMEB and TMP free and in the complex Molecule

Proton

d free (ppm)

d complex (ppm)

RAMEB

H1 H2 H3 H4 H5 H6

5.072–5.079 3.612–3.622 3.885–3.982 3.507–3.574 3.811 3.310–3.381

5.083–5.094 3.670–3.673 3.875–3.960 3.506–3.550 3.815 3.310–3.383

TMP

H1 H2 H3 H4 H5 H6 H7

— 7.455 — 3.310 6.532 3.794 3.645

— 7.431 — Masked 6.538 3.800 3.650

dispersive correction to make semiempirical methods suitable for the calculation of intermolecular interaction energies with very good results compared to the performance of high level ab initio methods. To our knowledge there is only one report of the use of a similar method to study interactions between units present in cyclodextrin structure and aromatic ring, with results comparable to CCSD(T) method.10 Here, compared to the current semiempirical methods, we observe that PM3-D confirms the inclusion orientation in addition to giving a higher stabilization degree for the preferred mode, which shows the importance of dispersion forces for complexation. In fact the current methods yielded values for enthalpy change very close to each other considering the two possible orientations, which revealed only a slight degree of stabilization and suggests that the relevant forces have not been considered. Figure 8 shows a modeled structure of the inclusion complex in the NH2-out orientation (PM3-D). Despite approximations such as the consideration of a permethylated host, it is illustrative to observe this kind of model structure because the common planar representations of inclusion complexes are too oversimplified and do not properly allow us to understand how the intermolecular interactions take place. For instance, it is clear that the TMP molecule is placed in the cavity in an inclined position so that only one of the two H5 hydrogen atoms from the trimethoxyphenyl ring is close to RAMEB cavity protons. Probably the inclination of TMP molecule is a result of the presence of volumous methoxy groups, which are responsible for most of the interactions inside the cavity (which could not to be assigned undoubtedly in ROESY plots). 3. Conclusions

Table 2 Values of enthalpy (DH) obtained by different semiempirical methods for process of formation of the inclusion complex from separate RAMEB and TMP Me-BCD-TMP NH2in

DH kcal/mol

AM1 PM3 PM6 RM1 PM3-D

0.4123 8.622 4.937 1.150 38.90

Me-BCD-TMP NH2out 1.210 9.044 8.398 0.9850 61.90

most of the methods, except from AM1. On the other hand, none of those methods were originally developed to account for dispersion forces, which are particularly important in the case of supramolecular systems. In this context, McNamara9 included an empirical

A TMP/RAMEB inclusion complex has been prepared, characterized and studied in terms of physicochemical properties. We observed from a phase-solubility study a linear increase in the TMP solubility, pointing out that RAMEB can be used as a suitable solubilizer for TMP also modulating its release properties. Structural characterization together with computer modeling evidenced that inclusion orientation involves penetration of trimethoxyphenyl group in the CD cavity. Current semiempirical methods (AM1, PM3, PM6, and RM1) and PM3-D methods were applied to calculate the enthalpy of inclusion complex formation, pointing out the preferred inclusion orientation. The stabilization degree of the complex compared to the separate species was very significant from PM3-D compared to the current methods, confirming the inclusion mode determined experimentally.

Figure 8. Side and front view of the molecular structure modeled for the TMP/RAMEB inclusion complex (PM3-D).

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4. Experimental

4.4. In vitro release studies

Trimethoprim and randomly methylated-b-cyclodextrin were purchased from Sigma and used without any previous treatment. Buffer solutions were prepared using dibasic sodium phosphate (ISOFAR). All aqueous solutions were prepared using ultrapure water generated by a Milli Q purification system.

Here we used double-compartment systems separated by Spectrapore dyalisis bags with exclusion pore diameter of 1000 Da and made triplicate tests. In each test 5 mL of a solution (free TMP or complex) of a concentration chosen so as to contain an equivalent amounts of the drug, was placed inside the dialysis bag along with 5 mL of borate buffer solution at pH 8.0. The bags were then immersed into 250 mL of the same buffer at 37 °C under gentle stirring and aliquots were taken at time intervals until an equilibrium concentration was reached. The concentration of TMP has been determined in each aliquot by reading the absorbance at 287.5 nm and converted into percent TMP released considering the total TMP amount added in each case. Plots of percent TMP released as a function of time were plotted for discussion.

4.1. Phase-solubility studies The phase-solubility isotherm was determined in 1.0 mmol L 1 phosphate buffer (pH 7.0). Briefly, a fixed solid amount of TMP was added to aqueous medium (1.0 mmol L 1 buffer solution) containing increasing concentrations of RAMEB. The TMP mass was chosen to ensure a five-fold excess relative to the RAMEB mol number in the most concentrated solution. Suspensions were protected from light and stirred for 24 h at room temperature, being afterward filtered over 0.45 lm membranes for UV/ vis determination of the TMP concentration in the liquid phase. The instrument used was a Lambda 45 Perkin Elmer Spectrophotometer. 4.2. Stoichiometry The main stoichiometry has been determined by the continuous variation method. This method, developed by Job,11 is based on measuring the variation of some property that depends directly on the formation of the complex such as the fluorescence emission parameters or the NMR chemical shift for some nucleus in the guest structure. The chosen property must be measured for a series of equimolar mixtures prepared by mixing solutions of guest and of the host with the same initial concentration. After mixing stock solutions, variable proportions keeping total volume constant the mixtures were stirred for 24 h. After this contact time the fluorescence emission of TMP was measured and compared with the measurements made for a blank series, in which the TMP solution was diluted with water just like the series with RAMEB solution. The DF = F Fo (the difference in intensity emission in the presence and in the absence of RAMEB) was plotted against R (the drug mole ratio), giving a maximum at the preferred stoichiometry due to the highest yield of product. Fluorescence measurements were carried out by exciting the solutions at 281 nm using a Perkin Elmer LS 55 Luminescence Spectrometer.

4.5. Molecular modeling Because RAMEB forms an amorphous solid composed by a mixture of randomly methylated derivatives, b-CD crystallographic structure was obtained from CSD (Cambridge Crystallographic Database) and used as starting point for molecular modeling of inclusion complexes considering a permethylated structure. TMP molecular structure has been built using CaChe Worksystem 6.1 (Fujitsu LTD, Japan) and further optimized using the same software with MM3 method to yield a suitable starting structure for the guest. Two orientations of TMP molecule were considered in the inclusion complexes: one with the diaminopyrimidine ring included in the cavity (NH2 in) and the other with inclusion of the 3,4,5-trimethoxybenzyl ring (NH2out) and initially the structures were fully optimized with MM3 method. Then the resulting structures were used as starting points for optimization with the following semiempirical methods implemented in the MOPAC2009 program: AM1,12 PM3,13 RM1,14 PM6,15 and PM3-D.9 Calculations were performed allowing free drug rotation inside the cavity without imposing any restriction on the atomic positions and bond angles for the host molecule. Acknowledgments Authors are grateful to Finep, Capes, CNPq and Fapitec for financial support. We would like to thank Professor I. O. Mazali (IQ/Unicamp) for NMR measurements. D. Kubota, O. F. L. Macedo and G. R. S. Andrade acknowledge Capes and CNPq for fellowships. References

4.3. Preparation and isolation of solid inclusion complex Samples of the inclusion complex for characterization have been prepared by the suspension method. This has been carried out by adding solid TMP into aqueous RAMEB solutions in the 1:1 mol proportion, considering the preferential stoichiometry determined by continuous variation method. After stirring under dark conditions at room temperature for 24 h the suspensions were filtered over 0.45 lm membranes and freeze-dried by the use of a Terroni system. The resulting solid was characterized as follows. FTIR spectroscopy was carried out in the form of KBr pellets measuring the spectra in the 4000–400 cm 1 range with 4 cm 1 resolution Perkin Elmer Spectrum BX equipment. Thermal analysis (TG and DTA) were carried out in a 2960 TA Instruments using platinum cells, heating rate of 10 °C min 1 under 100 mL min 1 of N2. 1H one- and two-dimensional (ROESY) NMR spectra in CD3OD with TMS standard were acquired with a Varian INOVA 500 MHz using 2 s relaxation delay and 2.00 ms mixing time.

1. Uekama, K.; Hirayama, F.; Irie, T. Chem. Rev. 1998, 98, 2045–2076. 2. Szejtli, J. J. Mater. Chem. 1997, 7, 575–587. 3. Li, N.; Zhang, Y.-H.; Xiong, X.-L.; Li, Z.-G.; Jin, X.-H.; Wu, Y.-N. J. Pharm. Biomed. Anal. 2005, 38, 370–374. 4. Li, N.; Zhang, Y.-H.; Wu, Y.-N.; Xiong, X.-L.; Zhang, Y.-H. J. Pharm. Biomed. Anal. 2005, 39, 824–829. 5. Garnero, C.; Zoppi, A.; Genovese, D.; Longhi, M. Carbohydr. Res. 2010, 345, 2550–2556. 6. Mura, P.; Maestrelli, F.; Cirri, M.; Furlanetto, S.; Pinzauti, S. J. Thermal Anal. Calorim. 2003, 73, 635–646. 7. Egyed, O. Vibrat. Spectrosc. 1990, 1, 225–227. 8. de Araujo, M. V. G.; Vieira, E. K. B.; Lazaro, G. F.; Conegero, L. S.; Almeida, L. E.; Barreto, L. S.; da Costa, N. B.; Gimenez, I. F. Bioorg. Med. Chem. 2008, 16, 5788– 5794. 9. McNamara, J. P.; Hiller, I. H. Phys. Chem. Chem. Phys. 2007, 9, 2362–2370. 10. Raju, R. K.; Hillier, I. H.; Burton, N. A.; Vincent, M. A.; Doudou, S.; Bryce, R. A. Phys. Chem. Chem. Phys. 2010, 12, 7959–7967. 11. Job, P. Ann. Chim. 1928, 9, 113–203. 12. Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. G.; Stewart, J. J. P. J. Am. Chem. Soc. 1985, 107, 3902–3909. 13. Stewart, J. J. P. J. Comput. Chem. 1989, 10, 209–220. 14. Rocha, G. B.; Freire, R. O.; Simas, A. M.; Stewart, J. J. P. J. Comput. Chem. 2006, 27, 1101–1111. 15. Stewart, J. J. P. J. Mol. Modeling 2007, 13, 1173–1213.