An FT-IR and DFT based new approach for the detection of tautomer proportions in solution

An FT-IR and DFT based new approach for the detection of tautomer proportions in solution

Journal of Molecular Structure 1024 (2012) 151–155 Contents lists available at SciVerse ScienceDirect Journal of Molecular Structure journal homepag...

530KB Sizes 1 Downloads 18 Views

Journal of Molecular Structure 1024 (2012) 151–155

Contents lists available at SciVerse ScienceDirect

Journal of Molecular Structure journal homepage: www.elsevier.com/locate/molstruc

An FT-IR and DFT based new approach for the detection of tautomer proportions in solution Sedat Karabulut ⇑, Hilmi Namlı Balikesir University, Science and Art Faculty, Chemistry Department, Balikesir, Turkey

h i g h l i g h t s " A new and convenient method was improved to detect tautomer proportions in solution. " Experimental (FT-IR) and theoretical (DFT) methods were used together. " Absorbances (A) were detected by FT-IR and epsilon (e) values were calculated. " Acetylacetone was chosen as a model compound because of wide literature data. " The results were in a good harmony with literature data.

a r t i c l e

i n f o

Article history: Received 27 March 2012 Received in revised form 4 May 2012 Accepted 9 May 2012 Available online 17 May 2012 Keywords: Tautomerism FT-IR DFT Lambert–Beer Acetylacetone

a b s t r a c t Tautomer proportions of acetylacetone (acac) in six different solvents are investigated with a new method by means of experimental absorptions (A) and theoretical absorption coefficients (e). The specific absorption bands (key bands) for keto and enol tautomers were obtained from recorded FT-IR spectra in related solution at room temperature. The molar absorption coefficients for key bands of both keto and enol tautomers were calculated, which is impossible to obtain with experimental methods for individual isomers in equilibrium. The Lambert–Beer equation is used to detect tautomer proportions. The obtained results are in consistence with literature. The most stable enol tautomer is found to be (86%) in CCl4 and the keto tautomer is found to be most stable in DMSO (48%). Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction Tautomerism is a kind of isomerism and has an important role in organic chemistry, biochemistry, medicinal chemistry, pharmacology and molecular biology [1]. Understanding the mechanism of many organic reactions [2] and biochemical activity, which includes specific interactions with proteins, enzymes, and receptors [3] requires an understanding of tautomerization [2]. Different tautomers usually have different molecular fingerprints, hydrophobicities, pKa’s, 3D geometry and electrostatic properties [4]. This can be seen in a wide range of heterocyclic natural compounds and biomolecules. It is not always clear which tautomer is responsible from the biological activity, thermodynamically most stable or a less stable tautomer. Investigations of many important biological processes show that the energetically less stable tautomer is often an active intermediate and dictates the mechanism and the formation of the ⇑ Corresponding author. E-mail address: [email protected] (S. Karabulut). 0022-2860/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.molstruc.2012.05.029

product [5,6]. Thus it is vital to investigate the tautomer proportion even if it is a very small quantity. Tautomerism is one of special interest in protein–ligand interaction studies, because displacement of hydrogen may convert an acceptor into a donor and changes the interaction landscape of a protein–ligand complex [7]. This is one of the most important reasons that why molecular modeling community paid more attention to tautomerism and published a number of reviews [1,4] and methods about tautomer enumeration [8,9]. Most tautomeric molecules contain at least one electronegative atom and often two (e.g., oxygen and nitrogen), and the proton transfer is such a fast process that separation of the individual tautomers is very difficult and often even impossible. In such cases, tautomeric preferences are investigated by spectroscopic measurements [10–13]. Although tautomerism is exceptionally difficult to study, because tautomeric interconversions are usually very fast processes, the importance of applications encourage researchers to undertake new investigations on tautomerism [1]. Various techniques such as FT-IR [14], UV [15], NMR [16], X-ray [17] and HPLC [18] were used to study tautomerism. Theoretical

152

S. Karabulut, H. Namlı / Journal of Molecular Structure 1024 (2012) 151–155

calculations were also used to calculate some physical properties of tautomers which cannot be isolated easily [19]. The 1H NMR is still used frequently to study tautomerism because the intensity of 1H signals is strictly proportional to the relative concentration of a compound [16]. However 1H NMR is the most frequently used technique for tautomerization, it is not always the best option for all cases. The cost of NMR device and lack of deuterated form of some solvents (hexane) also insufficient time scale are some disadvantages of 1H NMR [16,20]. Because of this, generation of convenient methods for detection of equilibrium constants has always been an appealing topic for scientists, especially for b-dicarbonyl compounds. The tautomerism of b-dicarbonyl compounds has been one of the main subjects in physical organic chemistry [21]. The existence of both the keto and enol forms for b-dicarbonyl compounds was proved simultaneously in 1896 by Claisen, Wislicenus and Knorr for different molecules. Claisen also found that the ratio of the keto/enol tautomers depends on various factors such as temperature, nature of substituents and solvent [22]. The main factors that determines the conformation of enol form of b-dicarbonyls is formation of an intramolecular hydrogen bond that is in general the most abundant specie [23]. The conjugated p system and six membered ring shaped structure are also assist the enol form (Fig. 1). And the factor which determines the conformation of the keto form of b-dicarbonyls is the strong repulsion of the localized C@O bond dipoles [24]. The structure and reactivity of the acac have been important issues in many fields of science [19]. Acac is a good prototype to study tautomerization mechanism. Although acac is a prototype of b-diketones, it also belongs to the category of a, b-enone systems, due to the existence of an enolic form [25–27]. The enol form (Z-4-hydroxy-3-penten-2-one Fig. 2b) is stabilized by an internal hydrogen bond and is therefore the most stable form but it coexists with the b-diketone tautomer (2,4-pentanedione) in the gas phase or the liquid phase (Fig. 2a). For this system, tautomerization consists in a displacement of the proton of the OH group to the central carbon, which requires an electronic rearrangement. The keto/enol ratio of acac in solution varies on a very large scale depending on the solvent properties. As in some b-diketones, the keto/enol equilibrium can be completely reversed when going from polar solutions to the gas phase where the enol form is widely predominant [28]. The temperature dependence of the keto/enol equilibrium was also investigated in the gas phase [29]. Acac and its fluorinated analogs were studied as neat liquid and as supercritical CO2 solutions [30]. Acac is one of the most important reagents in analytical and coordination chemistry, and it is also used as one of the most powerful extractants [31]. Although the acac involves an intramolecular hydrogen bond, the transition state is not an intramolecular one, but probably involves solvent molecules (if it is possible) [32] or intermolecular hydrogen bonds (Fig. 3). The purpose of the present study is to improve a new and convenient method for the relative concentrations of tautomers in different solvents by examining the acac as a representative compound. The experimental vibrational band assignments have been performed by quantum calculations. While it is not possible to isolate a single tautomer for calibration, the absorption coeffi-

1

3 2

1

3 2

Fig. 1. Tautomerisation of b-dicarbonyls.

3

3

3

(a)

3

(b) Fig. 2. Tautomerisation of acac.

3 3 3

3 3

3

3 3

(a)

(b)

(c)

Fig. 3. The possible transition states of acac: (a) intra, (b) intermolecular with solvent (c) intermolecular with same molecule.

cients (e) were obtained from theoretical calculations and used in the Lambert Beer equation to find out the relative proportions of the tautomers. 2. Materials and methods All solvents and acac were purchased from Aldrich or Fluka as analytical purity and no further purification has been done. The vibrational absorption spectra of acac in solutions were recorded using a Perkin Elmer 1600 BX 2 FT-IR spectrophotometer. Solution spectra were obtained using 0.015 mm path length CaF2 cell with an average 32 scans, 4 cm1 resolution and 2 cm1 interval value. In all FT-IR measurements, the concentrations of the acac were 0.03 mol/L. Calculations were carried out with the Gaussian 03 [33] set of programs. All the input files generated with Chem Office 2008 and potential energy surface calculations were performed with semi-empirical AM1 method to prepare the best input geometry. The geometry optimizations and frequency calculations of tautomers of acac were carried out at the DFT B3LYP/6-311G++(2d,2p) level [34–38] with the conductor-like polarizable continuum model (CPCM) model [39]. 3. Results and discussion The molar absorption coefficient is a measurement of how strongly a chemical species absorbs light at a given wavelength. It is an intrinsic property of the species; the actual absorbance in a specific frequency (Am) of a sample is dependent on the molar absorption coefficient (em), path length (l) and the concentration (c) of the species via the Lambert–Beer law

Am ¼ em lc

ð1Þ

Keto and enol tautomers are the members of this equilibrium system and their relative concentrations depend on polarity of solvent and temperature. So the FT-IR spectrum of acac in solvent media has to be a total spectrum of two tautomers. In this total spectrum there is a correlation between the relative concentration and absorption band intensities. When Eq. (1) is applied for an absorption band in any frequency for acac system, it converts to Eq. (2), where AT (total absorbance) equal to the addition of Ak

S. Karabulut, H. Namlı / Journal of Molecular Structure 1024 (2012) 151–155

153

(absorbance of keto tautomer) and Ae (absorbance of enol tautomer). The Ak and Ae are depend on the molar absorption coefficients (ek and ee), pathlength (l) and relative concentrations of tautomers (ck and ce)

AT m ¼ Akm þ Aem ¼ ðek lck Þ þ ðee lce Þ

ð2Þ

The first step in the analysis of a mixture with FT-IR based methods is examination of the infrared spectra of a single component so that a suitable absorption band for an individual tautomer has to be chosen as the ‘‘key band’’. It is essential for a key band as free as possible from overlapping with the bands of other tautomer and it should have at least a medium intensity. Such a key band can be employed for the quantitative analysis of two-component as well as multi-component mixtures [40]. The experimental FT-IR spectra of acac in different solvents were shown in Fig. 4. As seen from the Fig. 4, there are three absorption bands in 1500–1800 cm1 region. The absorption band at 1615 cm1 can be assigned as C@C stretching of enol tautomer. Two bands at 1705 cm1 and 1725 cm1 belong to the asymmetric and symmetric C@O stretching of keto tautomer respectively. The calculated vibrational spectra of keto and enol tautomers of acac at 1500–1800 cm1 region has been shown in Figs. 5 and 6 respectively. Asymmetric stretching of keto tautomer calculated at 1720 cm1 for each studied solvent (slightly changes by solvent). The C@C stretching of enol tautomer calculated at about 1640 cm1. The intramolecular hydrogen bond of enol tautomer of acac causes an overlap on C@C stretching band and C@O stretching band in experimental spectrum. So the shoulder shaped broad absorption band (about 1615 cm1) (Fig. 4) should be arises from an overlap of enol C@C and C@O stretching bands. With an intensive care, it is easy to find out that keto tautomer has no contribution at about 1640 cm1 and enol tautomer has no contribution at about 1720 cm1 (Figs. 5 and 6). Thus we can assume that the absorption band at 1615 cm1 belongs to enol and the 1705 cm1 belongs to the keto tautomer in experimental spectrum of acac (Fig. 4). So these two bands can be chosen as ‘‘key bands’’ for the absorbance values. As a result of this assumption, while there is no absorption of keto tautomer (Ak = 0) at about 1615 cm1 and enol tautomer (Ae = 0) at about 1705 cm1, the Eq. (2) can be converted to Eqs. (3) and (4) for enol and keto tautomers respectively.

A1615 ¼ 0 þ Ae ¼ 0 þ ðee ce lÞ ¼ ee ce l

ð3Þ

A1705 ¼ Ak þ 0 ¼ ðek ck lÞ þ 0 ¼ ek ck l

ð4Þ

1615 cm-1

1705 cm-1 -1

1725 cm

Fig. 4. Experimental FT-IR spectra of acac in different solvents between 1500 cm1 and 1800 cm1.

Fig. 5. The theoretical absorption bands of keto tautomer in 1500–1800 cm1 region.

Fig. 6. The theoretical absorption bands of enol tautomer in 1500–1800 cm1 region.

A simplified Eq. (5) can be obtained by dividing Eq. (3) to Eq. (4).

Ae =Ak ¼ ðee ce Þ=ðek ck Þ

ð5Þ

The absorption values (Ae and Ak) for each tautomer can be detected from the experimental FT-IR spectrum. For the solution of Eq. (5) the molar absorption coefficients for each keto and enol forms are needed. Since it is not easy to detect the molar absorption coefficient for a compound which cannot be isolated; the molar absorption coefficients for each tautomer have been calculated theoretically. When the calculated molar absorption coefficients were applied in Eq. (5), the concentrations of tautomers in equilibrium can be detected semi empirically. The relative keto/enol ratios were obtained using experimental absorptions and theoretical molar absorption coefficients and results were summarized in Table 1. As it can be seen from Table 1, detected enol concentrations (Ce%) are conspicuously similar to literature values. These results are encouraging and make it possible to imagine developing a convenient, cheap, practicable and an accurate method which can easily detect all kinds of tautomer proportions in all solvents. Harmony between the results of this study and literature values gives clues about the calculation of molar absorption coefficient of tautomeric molecules as good as possible in solvent media. These kinds of accurate calculation make it possible to study the spectroscopic and other physical properties of molecules without isolation. The isolation of organic molecules sometimes requires the usage of hazardous chemicals, solvents, and more time and labor.

154

S. Karabulut, H. Namlı / Journal of Molecular Structure 1024 (2012) 151–155

Table 1 Experimental (meexp and mkexp ) and related theoretical (metheo and mktheo ) enol and keto frequencies, experimental absorbances (Aeexp and Akexp ) and related theoretical molar absorption coefficients (etheo and ktheo ), detected relative enol concentrations (Ce (%)), literature values for relative enol concentrations in individual solvent (Lit. (%)).

meexp (cm1) mkexp (cm1) metheo (cm1) mktheo (cm1) Aeexp ) Akexp )

e k

theo theo

Ce (%) Lit.a (%) a

Benzene

Chloroform

Methanol

Dichloromethane

Acetonitrile

Dimethylsulfoxide

1618 1708

1620 1704

1622 1706

1618 1708

1622 1708

1620 1702

1654 1738 0.54 0.11

1646 1728 0.86 0.26

1640 1718 0.16 0.06

1644 1720 0.77 0.30

1640 1718 0.11 0.10

1640 1718 0.19 0.18

2105 1954 82 89–97

2286 2339 77 83–87

2512 2628 74 68–74

2448 1844 66

2441 2648 54 53–62

2453 2688 54 60–63

[24].

Developing such theoretical methods should rescue scientist at least some of these disadvantages. 4. Conclusion The primary objective of this study is suggesting a new method for detection of the relative concentration of isomers in equilibrium. For this purpose, acac was choosen as model compound. The extensive literature about the tautomeric ratios of the acac has provided a great chance to compare the obtained results. While the C@O stretchings bands of each tautomer appears at different frequencies (Figs. 5 and 6) in calculated spectra gave chance to assume that the keto tautomer has no remarkable contribution at the experimental enol C@O stretching band (Fig. 4) or vice versa. The predominant tautomeric form is found to be the enol form in all studied solvents. It is observed that the absorption bands of enol form which is affected from intramolecular hydrogen bonds appeared as broad absorption bands in experimental FT-IR spectra [28]. Enol content of the solution decreases with increasing polarity of solvent. The more polar solvent means more interaction with solvated molecule and keto tautomer has carbonyls and acidic hydrogens for this interaction. Otherwise the enol tautomer is more stable in less polar solvents because of its intramolecular interactions. Acac is a good model for testing the accuracy of a method which is for detection of the enol content of a tautomeric system. The results of this new method are in harmony with literature values (Table 1) for acac. It is aspected to get similar good results for other tautomeric systems and make it easier to investigate the enol content of a compound in solvent media.

References [1] E.D. Raczynska, W. Kosinska, B. Osmialowski, R. Gawinecki, Chem. Rev. 105 (2005) 3561. [2] (a) J. March, Advanced Organic Chemistry, Reaction, Mechanism and Structure, fourth ed., J. Wiley, New York, 1993; (b) F.A. Carey, R. Sundberg, J. Advanced Organic Chemistry, third ed., Plenum Press, New York, 1993. [3] (a) W. Saenger, Principles of Nucleic Acid Structure, Springer, New York, 1994; (b) W.O. Foye, T.L. Lemke, D.A. Williams, Principles of Medicinal Chemistry, Williams & Wilkins, Baltimore, MD, 1995; (c) H. Weinstein, D. Chou, C.L. Johnson, S. Kang, J.P. Green, Mol. Pharmacol. 12 (1976) 738; (d) K.J. Watling, The RBI Handbook of Receptor Classification and Signal Transduction, RBI, Natick, MA, 1998; (e) A.F. Pozharskii, A.T. Soldatenkov, A.R. Katritzky, Heterocycles in Life and Society, Wiley, New York, 1997. [4] C.M. Yvonne, J. Comput. Aided Mol. Des. 23 (2009) 693–704. [5] (a) D.J. Kuo, I.A. Rose, J. Am. Chem. Soc. 100 (1978) 6288; (b) D.J. Kuo, E.L. O’Connell, I.A. Rose, J. Am. Chem. Soc. 101 (1979) 5025; (c) D.J. Kuo, I.A. Rose, J. Am. Chem. Soc. 104 (1982) 3235;

[6]

[7] [8] [9] [10]

[11]

[12]

(d) S.J. Grabowski, T.M. Krygowski, B. Steüpien, J. Phys. Org. Chem. 13 (2000) 740. (a) E. Haslam, The Shikimate Pathway, Halsted Press, Wiley, New York, 1974; (b) U. Weiss, J.M. Edwards, The Biosynthesis of Aromatic Compounds, Wiley, New York, 1980. F. Milletti, A. Vulpetti, J. Chem. Inf. Model. 50 (2010) 1062–1074. F. Milletti, L. Storchi, G. Sforna, S. Cross, G. Cruciani, J. Chem. Inf. Model. 49 (2009) 68–75. M. Haranczyk, M. Gutowski, J. Chem. Inf. Model. 47 (2007) 686–694. (a) A.R. Katritzky, J.M. Lagowski, Adv. Heterocycl. Chem. 1 (1963) 311, 339; (b) A.R. Katritzky, J.M. Lagowski, Adv. Heterocycl. Chem. 2 (1) (1963) 27; (c) J. Elguero, C. Marzin, A.R. Katritzky, P. Linda, Advances in Heterocyclic Chemistry, Academic Press, New York, 1976 (Supp. 1); (d) V.I. Minkin, L.P. Olekhovich, Y.A. Zhdanov, Molecular Design of Tautomeric Compounds, D. Reidel Publishing Co., Dordrecht, Holland, 1988; (e) H. Backer, Rec. Trav. Chim. 68 (1949) 827; (f) F. Farina, J.C. Vega, Tetrahedron Lett. (1972) 1655; (g) P. Seckarova, R. Marek, K. Malioakova, E. Kolehmainen, D. Hockova, M. Hocek, V. Sklenar, Tetrahedron Lett. 45 (2004) 6259. (a) A.R. Katritzky, M. Karelson, P.A. Harris, Heterocycles 32 (1991) 329; (b) J. Elguero, A.R. Katritzky, O.V. Denisko, Adv. Heterocycl. Chem. 76 (2000) 1; (c) W. Friedrichsen, T. Traulsen, J. Elguero, A.R. Katritzky, Adv. Heterocycl. Chem. 76 (2000) 85; (d) V.I. Minkin, A.D. Garnovskii, J. Elguero, A.R. Katritzky, O.V. Denisko, Adv. Heterocycl. Chem. 76 (2000) 157; (e) R.M. Claramunt, J. Elguero, A.R. Katritzky, Adv. Heterocycl. Chem. 77 (2000) 1; (f) I. Shcherbakova, J. Elguero, A.R. Katritzky, Adv. Heterocycl. Chem. 77 (2000) 51; (g) B. Stanovnik, M. Tisler, A.R. Katritzky, O.V. Denisko, Adv. Heterocycl. Chem. 81 (2001) 253. (a) S. Patai, The Chemistry of the CdO group, John Wiley & Sons, London, 1966; (b) Z. Rappoport, The Chemistry of Enols, Wiley, New York, 1990; (c) S. Patai, The Chemistry of the Thiol Group, John Wiley & Sons, London, 1974; (d) J. Zabicky, The Chemistry of Amides, John Wiley & Sons, London, 1970; (e) J.H. Boyer, The Chemistry of the Nitro and Nitroso Groups, Interscience Publishers, New York, 1969; (f) S. Patai, The Chemistry of Amino, Nitroso, Nitro Compounds and their Derivatives, John Wiley & Sons, New York, 1982; (g) S. Patai, The Chemistry of Amino, Nitroso, Nitro and Related Groups, John Wiley & Sons, Chichester, UK, 1996 (Suppl. F2); (h) S. Patai, Z. Rappoport, Nitrones, Nitronates and Nitroxides, John Wiley & Sons, Chichester, UK, 1989; (i) S. Patai, Z. Rappoport, The Chemistry of Amidines and Imidates, John Wiley & Sons, Chichester, UK, 1991; (j) A.G. Cook, Enamines, second ed. New York, 1998.; (k) S. Patai, The Chemistry of Hydrazo, Azo, and Azoxy Groups, Wiley, New York, 1975.

[13] (a) S.J. Yeh, H.H. Jaffe, J. Am. Chem. Soc. 81 (1959) 3279; (b) M.J. Kabachnik, T.A. Mastryukova, A.E. Shipov, T.A. Malentyeva, Tetrahedron 9 (1960) 10; (c) T.A. Mastryukova, Yu.N. Sheinker, I.K. Kuznetsova, E.M. Peresleni, T.B. Sakharova, M.I. Kabachnik, Tetrahedron 19 (1963) 357; (d) M. In Charton, in: N.B. Chapman, J. Shorter (Eds.), Correlation Analysis in Chemistry: Recent Advances, Plenum Press, New York, 1978, p. 175; (e) J. In Oszczapowicz, The Chemistry of Amidines and Imidates, John Wiley & Sons, Chichester, UK, 1991. p. 623; (f) C. Reichardt, Solvent Effects in Organic Chemistry, Verlag Chemie, Weinheim, Germany, New York, 1979. [14] J. Emsley, J.F. Neville, J. Mol. Struct. 161 (1987) 193–204. [15] S. Coussan, Y. Ferro, A. Trivella, M. Rajzmann, P. Roubin, R. Wieczorek, C. Manca, P. Piecuch, K. Kowalski, M. Wloch, S.A. Kucharski, M. Musial, J. Phys. Chem. A 110 (2006) 3920–3926. [16] R.M. Claramunt, C. Lopez, M.D. Santa Maria, D. Sanz, J. Elguero, Progr. Nucl. Magn. Reson. Spectrosc. 49 (2006) 169–206. [17] R. Boese, M.Y. Antipin, D. Bla1ser, K.A. Lyssenko, J. Phys. Chem. B 102 (1998) 8654–8660.

S. Karabulut, H. Namlı / Journal of Molecular Structure 1024 (2012) 151–155 [18] [19] [20] [21] [22]

[23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33]

M. Moriyasu, A. Kato, Y. Hashimoto, J. Chem. Soc. Perkin Trans. II (1986) 515. X.B. Chen, W.H. Fang, D.L. Phillips, J. Phys. Chem. A 110 (2006) 4434–4441. J. Emsley, N.J. Freeman, J. Mol. Struct. 161 (1987) 193–204. P. Cornago, R.M. Claramunt, L. Bouissane, I. Alkorta, J. Elguero, Tetrahedron 64 (2008) 8089–8094. (a) L. Claisen, Liebigs Ann. Chem. 291 (1896) 25; (b) W.L. Wislicenus, Ann. Chem. 291 (1896) 147; (c) L. Knorr, Liebigs Ann. Chem. 293 (1896) 70. V. Lacerda Jr., M.G. Constantino, G.V.J. Da Silva, A.C. Neto, C.F. Tormena, J. Mol. Struct. 828 (2007) 54–58. Y. Pocker, G.T. Spyridis, J. Am. Chem. Soc. 124 (2002) 10373–10380. W. Egan, G. Gunnarsson, T.E. Bull, S. Forsen, J. Am. Chem. Soc. 99 (1977) 4568– 4572. B. Cohen, S. Weiss, J. Phys. Chem. 88 (1984) 3159–3162. N.N. Shapetko, V.P. Bazov, Zh. Fiz. Khim. 63 (1989) 2832–2835. R.R. Lozada-Garcia, J. Ceponkus, W. Chin, M. Chevalier, C. Crepin, Chem. Phys. Lett. 504 (2011) 142–147. G.W. Mines, H. Thompson, Proc. Roy. Soc. Lond. A 342 (1975) 327. C.H. Matthew, R.Y. Clement, Anal. Chem. 76 (2004) 4684–4689. M. Kato, Ind. Eng. Chem. Fundamen. 19 (1980) 253–259. R.M. Claramunt, C. Lopez, S. Lotta, M.D. Santa Maria, I. Alkortab, J. Elguero, Helv. Chim. Acta 88 (2005) 1931. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery, Jr., T. Vreven, K. N. Kudin, J. C. Burant, J. M.

[34] [35] [36] [37] [38] [39] [40]

155

Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, C. Gonzalez, and J. A. Pople, Gaussian 03, Revision C.02, Gaussian, Inc., Wallingford, CT, 2004. W.J. Hehre, L. Radom, P.v.R. Schleyer, J.A. Pople, Ab Initio Molecular Theory, Wiley, New York, 1986. F. Jensen, Introduction to Computational Chemistry, John Wiley & Sons, London, 1999. R.G. Parr, W. Yang, Density Functional Theory of Atoms and Molecules, Oxford University Press, New York, 1989. C. Lee, W. Yang, R.G. Parr, Phys. Rev. 37 (1988) 785. A.D. Becke, Phys. Rev. B 38 (1988) 3098. V. Barone, M. Cossi, J. Phys. Chem. A 1998 (1995) 102. C.N.R. Rao, Chemical Applications of Infrared Spectroscopy, Academic Press, New York and London, 1963.