Synthesis and structure of heterocyclic derivatives of pyran-2-ones

ISSN 1070-4280, Russian Journal of Organic Chemistry, 2009, Vol. 45, No. 11, pp. 1663−1669. © Pleiades Publishing, Ltd., 2009.

Original Russian Text © Yu.A. Sayapin, Zyong Ngia Bang, V.N. Komissarov, I.V. Dorogan, V.V. Tkachev, G.V. Shilov, S.M. Aldoshin, V.I. Minkin, 2009, published in Zhurnal Organicheskoi Khimii, 2009, Vol. 45, No. 11, pp. 1671 − 1676.

Synthesis and Structure of Heterocyclic Derivatives of Pyran-2-ones Based on the Dimer of 4,6-Di(tert-butyl)-3-hydroxy-1,2-benzoquinone Yu. A. Sayapina, Zyong Ngia Banga, V. N. Komissarova, I. V. Dorogana, V. V. Tkachevb, G. V. Shilovb, S. M. Aldoshinb, and V. I. Minkina,c aInstitute

of Physical and Organic Chemistry at the Southern Federal University, Rostov-on-Don, 344090 Russia e-mail: [email protected] bInstitute of Problems of Chemical Physics, Russian Academy of Sciences, Chernogolovka, Moscow oblast, Russia cSouthern Scientific Center, Russian Academy of Sciences, Rostov-on-Don, Russia Received November 14, 2008

Abstract—Acid-catalyzed reaction of 6,10a-dihydroxy-3,4a,7,9-tetra(tert-butyl)-1,2,4a,10a-tetrahydrodibenzo[b,e][1,4]dioxine-1,2-dione with 2-methylquinoline derivatives led to the formation of a previously unknown system 6-[(Z)-2-(quinolin-2-yl)-1-hydroxyethen-1-yl]pyran-2-one. The molecular structure of 3,5-di(tert-butyl)-6-[(Z)-2(7,8-dimethyl-4-chloroquinolin-2-yl)-1-hydroxyvinyl]pyran-2-one was established by XRD method; the energy and structural characteristics of its isomers in the gas phase and in a polar solvent were calculated by quantumchemical methods (B3LYP/6-31G**). DOI: 10.1134/S107042800911013X

The synthesis and the study 3X spatially-hindered ortho-quinones is of obvious interest since the presence of highly reactive carbonyl groups and the nature of the substituents in the benzoquinone in the reaction of orthoquinones with 2-methyl-substituted nitrogen heterocycles significantly affect the direction of the reaction and result in the formation of diverse heterocyclic systems [1]. For a long time the dimeric structure of 3-hydroxy-4,6-di(tertbutyl)-1,2-benzoquinone that forms on the oxidation of

the corresponding 4,6-di(tert-butyl)-3-hydroxypyrocatechol was regarded as one among the possible dimeric forms and was ambiguously characterized [2–4]. The recent XRD study showed that the reaction of the oxidative dimerization of the spatially-hindered 4,6di(tert-butyl)benzene-1,2,3-triol (I) led to the formation of the corresponding 4,6-di(tert-butyl)-3-hydroxy-1,2benzoquinone (II) that underwent Diels–Alder hetero-

Scheme 1.

t-Bu OH t-Bu

OH OH

[O]

t-Bu

t-Bu

O O

HO O

Bu-t II

Bu-t O

t-Bu

t-Bu

6 9

Bu-t 7 8

Bu-t OH Bu-t

O * *

O O

1663

O

4 5 3 4a * 5a 2 10a * 9a 1

O OH 10 O IIIa

+

OH Bu-t I

O

OH

t-Bu

O OH IIIb

Bu-t

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SAYAPIN et al.

We presumed that the reaction of quinone III with 2methylquinolines IV would result in the 1,3-tropolone derivatives by the reaction of ortho-quinone ring expansion that we had previously discovered [7, 8]. It turned out however that the acid-catalyzed reaction of

cyclization yielding a racemic mixture of two chiral enantiomers (10aS,4aR)- and (10aR,4aS)-3,4a,7,9-tetra(tert-butyl)-6,10a-dihydroxy-1,2,4a,10a-tetrahydrodibenzo[b,e]-1,4-dioxine-1,2-diones (IIIa and IIIb) along Scheme 1 [5, 6].

Scheme 2.

OH O

t-Bu

R1

Bu-t

Cl

Bu-t

R3

O

OH O

N

CH3

CH3

O

O

O Bu-t

t-Bu Và_Ve

IVà_IVå

III

CH3

N H

R3

TsOH

+ O

Cl

R2

R2

Bu-t

R1

R1 = R2 = R3 = H (a); R1 = R3 = H, R2 = CH3 (b); R1 = R2 = H, R3 = CH3 (c); R1 = NO2: R2 = R3 = H (d); R2 = CH3, R3 = H (e); R2 = H, R3 = CH3 (f).

Scheme 3. OH III + IV (CH3_Q)

O

t-Bu

H+

O Bu-t OH O

t-Bu

O Bu-t

Bu-t

Bu-t

Bu-t

O OH OH H2C A Q OH

Bu-t O HO OH Bu-t H Q OH F

t-Bu

Bu-t

OH OH H HO Q

B OH t-Bu

OH

Bu-t OH

O Bu-t HO E

t-Bu

Bu-t

O

OH H Bu-t HO `C

Q

Bu-t OH

O HO

Q VI

t-Bu

t-Bu HO Q

Bu-t

O

Bu-t

Q

Bu-t _I

t-Bu

G

O

Bu-t

O

HO OH

OH

_I

_I

t-Bu

OH

Bu-t

O

OH HO

Bu-t

Bu-t

OH Q

OH

Bu-t O

O V

OH

O HO

D

Q

RUSSIAN JOURNAL OF ORGANIC CHEMISTRY Vol. 45 No. 11 2009

SYNTHESIS AND STRUCTURE OF HETEROCYCLIC DERIVATIVES OF PYRAN-2-ONES

3,4a,7,9-tetra(tert-butyl)-6,10a-dihydroxy-1,2,4a,10atetrahydrodibenzo[b,e]-1,4-dioxine-1,2-dione enantiomers (III) with 2-methylquinoline derivatives IV yielded previously unknown derivatives of [(Z)-2-(quinolin-2-yl)1-hydroxyvinyl]-pyran-2-ones Va–Vf (Scheme 2). Scheme 3 described the presumed multistage reaction mechanism leading to the formation of [(Z)-2-(quinolin2-yl)-1-hydroxyvinyl]pyran-2-one derivatives Va–Ve. Since the reaction product V does not contain chiral centers existing in the initial quinone III we believe that the reaction of the racemic mixture of IIIa and IIIb enantiomers takes the same routes in the reaction with quinoline derivatives IV leading to the target product. In the initial stage the aldol condensation of 2methylquinolines IV with quinone III affords adducts A. Intermediates A can undergo the cyclization along two pathways. By the first route adduct A forms norcaradiene derivatives B. Further transformation of intermediate B might occur by the opening of the norcaradiene ring with recyclization of the dioxine ring in the position 10a followed by the building up of a new heterocyclic framework, 8-oxabicyclo[3.2.1]octa-2,6-diene, in molecule C. The elimination of molecule of 4,6-di-(tertbutyl)benzene-1,2,3-triol (I) results in the substituted 8oxabicyclo[3.2.1]octa-1,3,6-triene D that through the thermal opening of the furan ring undergoes the rearrangement into final 3,5-di(tert-butyl)-6-[2-(quinolin2-yl)-1-hydroxy-vinyl]pyran-2-one (V). The formation of a tropolone ring VI might also occur if the opening of the norcaradiene in intermediate B would be accompanied with a 1,5-sigmatrope C–O shift of a hydrogen atom followed by the recyclization of the dioxine ring into the position 4a and by the elimination of the molecule of compound I in intermediate E. However we did not find yet tropolone VI in the reaction mixture, and presumably this reaction pathway is less energetically favorable. The second route of the formation of 3,5-di(tert-butyl)-6-[2-

Fig. 1. Molecular structure of 3,5-di(tert-butyl)-6-[(Z)-2-(7,8dimethyl-4-chloroquinolin-2-yl)-1-hydroxyvinyl]pyran-2-one (VcNH).

(quinolin-2-yl)-1-hydroxyvinyl]pyran-2-ones V may be described as a sequence of transformations A → F → G → D → V initiated by the formation of norcaradiene derivative F with the opening of the dioxine ring in the position 10a. The characteristic feature of 1H NMR spectra is the presence of the signal of the vinyl proton H2 in the region 5.72–5.74 ppm (Va–Vc) and 5.84–5.89 ppm (Vd–Vf), and also of the signal of the H42 proton of pyran-2-one in the region 6.92–6.99 ppm (Va–Vc) and 7.05–7.13 ppm (Vd–Vf). In solutions of compounds V a fast O–H...N exchange is observed revealed by the broadening of the proton signal of the hydroxy group in the region 15.30– 15.54 ppm of the 1H NMR spectra. Forms VOH–VNH are in a dynamic equilibrium (Scheme 4), however according to the XRD findings compound Vc (Fig. 1) in the crystalline state is present as (quinolin-2-ylylidene)acetylpyran-2-one VNH. The quinoline fragment, including atoms C11, C12, and O1, is located in a least-mean-square plane with an accuracy of 0.030 Å. In the molecule an intramolecular hydrogen bond H1...O1 exists with a distance of 1.87(3)

Scheme 4. R1

R

R2 R3

R1

R

CH3

N H

R2 R3

N CH3 H O t-Bu

O

1665

O Bu-t

VOH RUSSIAN JOURNAL OF ORGANIC CHEMISTRY Vol. 45 No. 11 2009

O t-Bu VNH

O

O Bu-t

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SAYAPIN et al.

Table 1. Some bond distances (d) and bond angles (ω) in structure Vc

Å, therewith the distance O 10 C11 equals 1.266(3) Å, somewhat longer that the common carbonyl bond [1.21– 1.23 Å, N1...O1 2.604(3) Å, angles N1H1O1 138(2)°, H1O1C11 99(1)°]. A least-mean-square plane can also be drawn through atoms O2O3C12–18; these atoms are located in the plane with an accuracy of 0.01 Å, atom C11 deviates from it by 0.09 Å. These two planes in the molecule form a torsion angle C10C11C12O2 of 70.3(3)°. The values of angles C 12 C 11 C 12 O 2 105.9(2)°, 11 C C12C13 132.9(2)° are worth special discussion. The attention is also drawn to the distortion of angles at the

C13–C18 bond contiguous to C11–C12 bond to 127.0(2) (C18C 13C 12) and 117.8(2)° C18C13C14. Evidently the reason of it is the mutual repulsion between atoms C11 and C 24 , therewith the distances between these nonhydrogen atoms and hydrogen atoms of the CH3 group of the tert-butyl fragment linked to atom C13, the nearest to this group, equal 2.49 (H...O1) and 2.55 Å (H...C11). For two other CH3 groups of this tert-butyl fragment situated in the gauche-configuration short contacts form H...H 2.06 and 2.55 Å between the hydrogen at the atom C14 and one ot the hydrogens of each CH3 group. The torsion angle C14C13C18C24 is 164.0(2)°. The second tertbutyl group has another orientation with respect to the plane of atoms, the torsion angle C14C15C17C20 is 12.5(3)°, the distances H...H between the hydrogen at the atom C14 and two hydrogens at the atom C20 equal 2.14 and 2.31 Å. This orientation of the second tert-butyl group forces the atom O3 to deviate to the opposite direction [angles O3C16C15 128.6(2)°, O3C16O2 115.5(2) deg] with the distances H...H 2.41 and 2.60 Å between the atom O3 and two hydrogen atoms attached to atoms C19 and C21. It is presumable that the steric strains in this fragment are a favorable factor that can for instance facilitate further rearrangements. The molecules have such spatial orientation that the nearest distance between the chlorine atom and one of the hydrogens at C26 of the neighboring molecule equals 3.09 Å. The main distances and angles in the molecule of compound Vc are presented in Table 1. The structural and energy characteristics of the tautomeric forms Vc in the gas phase and in a polar solvent (solvent dimethyl sulfoxide) have been established using B3LYP/6-31G** calculations whose results are presented in Fig. 2 and Table 2. According to the calculations in the gas phase the thermodynamically more stable tautomer of compound Vc is (quinolin-2-ylylidene)acetylpyran-2-one form (VNH) that is even more stabilized in the polar environment. This result is quite predictable taking into the consideration the difference in the dipole moments of isomers VNH and VOH (5.2 D and 4.7 D in the gas phase; 7.0 D and 6.2 D in DMSO solution respectively). The most significant changes in the structure VNH in going to the solution from the gas phase occur in the growth of the dihedral angle C10C11C12O2 (from 22.7 to 33.0°) and in lengthening of hydrogen bond H1...O1 (from 1.722 to 1.738 Å). In the crystal this parameter increased to 1.87 Å, and the value of the indicated dihedral angle grew to 70.3°. Both experimental and calculated data indicate the


SYNTHESIS AND STRUCTURE OF HETEROCYCLIC DERIVATIVES OF PYRAN-2-ONES

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Table 2. Total energy corrected for the energy of zero vibrations (Etot + ZPE) (a.u.) and relative energies (ΔE) (kcal mol−1) of isomers of Vc calculated by the method B3LYP/6-311G** for gas phase and DMSO solution

existence in compound VNH of a resonance-stabilized [9] intramolecular bond O...H...N. It is proved by a short contact O...N considerably less than the sum of van der Waals radii. The calculated value of this parameter in DMSO (2.608 Å) virtually coincided with the XRD data (2.604 Å). Analogous structural features were previously observed in the derivatives of 2-(quinolin-2-yl)-β-tropolone [7] where the distance O–N was 2.455–2.460 Å, and it was among the shortest for the systems with intramolecular hydrogen bonds. EXPERIMENTAL IR spectra were recorded on a spectrophotometer 75IR from mulls in mineral oil. 1H NMR spectra were registered on a spectrometer Varian Unity-300 from solutions in CDCl 3. Mass spectra were obtained on a Finnigan MAT INCOS 50 instrument. The column chromatography was carried out on Al2O3 of II–III grade of Brockmann activity. The melting points were measured in capillaries on a PTP device and were reported uncorrected. XRD analysis of compound Vc. Parameters of the unit cell and three-dimensional array of intensities were measured on an automatic diffractometer Enraf-Nonius CAD-4 (λ MoKα radiation, graphite monochromator). Light-yellow transparent monoclinic crystals: C 26 H 30 ClNO 3 , M 439.96; a 12.504(3), b 15.816(3), c 13.162(3) , β 113.66(3)°. V 2384.2(9) 3 , Z 4, dcalc 1.226 g/cm 3, μ(MOK α) 1.87 cm –1, space group P-21/c. Intensities of 3408 reflections were measured in the range 2θ ≥ 48° by ω/2θ scanning from a single crystal of the size 0.7 × 0.24 × 0.25 mm. After excluding the systematically quenched reflections and averaging of the pairs of equivalent reflections hk0 and h¯ k0 (Rint 0.037) the working array of the measured F2hkl and σ(F 2) contained 3100 independent reflections , of which 2319 with F2 > 4σ(F2) were used in further calculations. The structure was solved by the direct method using the

Fig. 2. Structural characteristics of tautomer forms of compound Vc in the gas phase by the data of B3LYP/6-31G**. Bond lengths in angstroms, dihedral angles in degrees.

program SHELXS-97 [10] and refined by the full-matrix least-mean-squares method with respect to F2 by the program SHELXL-97 [10] in the anisotropic approximation for nonhydrogen atoms. In the crystal structure Vc all hydrogen atoms were localized form the Fourier difference synthesis of the electron density. Further the coordinates and the isotropic thermal parameters for all H atoms save the hydrogen attached to N 1 were calculated by the least-mean-squares method in the rider model [10]. In the last cycle of the full-matrix refinement the absolute deviations of all 100 varied parameters of Vc were less than 0.001σ. The final refinement parameters: R1 0.043, wr2 0.115 for observed reflections with I ≤ 2σ(I); R1 0.059, wr2 0.123 for all measured reflections: quality of the refinement s 1.036 and 1.036 respectively.


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Quantum-chemical calculations were performed using a hybride functional B3LYP [11–13] in the basis 6-31G** applying the program package GAUSSIAN 03. The calculation for solution was carried out using CPCM model [14] with the dimethyl sulfoxide parameters of the solvent (å 46.7). 3,5-Di(tert-butyl)-6-[(Z)-2-(8-methyl-4-chloroquinolin-2-yl)-1-hydroxyvinyl]pyran-2-one (Va). A solution of 1.9 g (10 mmol) of 2,8-dimethyl-4chloroquinoline (IVa), 5.7 g (12 mmol) of quinone III, and 0.20 g of p-toluenesulfonic acid in 10 ml of o-xylene was boiled for 2 h. The solution was cooled, the solvent was distilled off, 5 ml of chloroform was added, and the solution was subjected to chromatography on a column packed with alumina (eluent chloroform) collecting the bright-yellow fraction. The solvent was evaporated. Yield 0.51 g (12%). Yellow crystals, mp 174–176°C (2-propanol). 1H NMR spectrum, δ, ppm: 1.34 s [18H, 3',5'-C(CH3)3], 2.64 s [3H, 8"-CH3], 5.74 s (1H, H2), 6.98 s (1H, H4'), 7.20–7.60 m (3H, Hquinoline), 7.86 m (1H, H3"), 15.40 br.s (1H, OH). Mass spectrum, m/z (Irel, %): 425 (40), 407 (10), 381 (25), 366 (35), 218 (100), 190 (40), 154 (25), 57 (20), 41 (10). Found, %: C 70.24; H 6.42; Cl 8.14; N 3.12. C25H28ClNO3. Calculated, %: C 70.49; H 6.63; Cl 8.32; N 3.29. M 425.18. −Vf were obtained similarly. Compounds Vb− 3,5-Di(tert-butyl)-6-[(Z)-2-(6,8-dimethyl-4chloroquinolin-2-yl)-1-hydroxyvinyl]pyran-2-one (Vb). Yield 11%. Yellow crystals, mp 197–199°C. IR spectrum, ν, cm–1: 1700, 1620, 1567, 1540, 1460, 1367, 1340, 1300. 1H NMR spectrum, δ, ppm: 1.34 s [18H, 3',5'-C(CH3)3], 2.47 s (3H, 6"-CH3), 2.62 s (3H, 8"-CH3), 5.72 s (1H, H2), 6.99 s (1H, H42 ), 7.37 s (1H, Hquinoline), 7.38 s (1H, Hquinoline), 7.66 s (1H, H3"), 15.54 br.s (1H, OH). Mass spectrum, m/z (Irel, %): 439 (70), 395 (20), 380 (35), 232 (98), 204 (80), 179 (35), 168 (55), 151 (95), 137 (55), 121 (30), 109 (55), 57 (97), 41 (93). Found, %: C 70.76; H 6.64; Cl 7.88; N 2.78. C 26 H 30 ClNO 3 . Calculated, %: C 70.98; H 6.87; Cl 8.06; N 3.18. M 439.19. 3,5-Di(tert-butyl)-6-[(Z)-2-(7,8-dimethyl-4chloroquinolin-2-yl)-1-hydroxyvinyl]pyran-2-one (Vc). Yield 11%. Yellow crystals, mp 171–173°C. IR spectrum, ν, cm–1: 1700, 1620, 1567, 1527, 1460, 1380, 1340, 1327, 1300. 1H NMR spectrum, δ, ppm: 1.35 s [18H, 3',5'-C(CH3)3], 2.50 s (3H, 7"-CH3), 2.55 s (3H, 8"-CH3), 5.72 s (1H, H2), 6.92 s (1H, H42 ), 7.23 C (1H, Hquinoline), 7.38 C (1H, Hquinoline), 7.76 m (1H, H32 2 ),

15.49 br.s (1H, OH). Mass spectrum, m/z (Irel, %): 439 (40), 395 (15), 380 (25), 232 (70), 204 (48), 190 (14), 168 (28), 151 (35), 137 (20), 121 (15), 109 (25), 57 (100), 41 (70). Found, %: C 70.64; H 6.72; Cl 7.76; N 2.82. C26H30ClNO3. Calculated, %: C 70.98; H 6.87; Cl 8.06; N 3.18. M 439.19. 3,5-Di(tert-butyl)-6-[(Z)-2-(8-methyl-5-nitro-4chloroquinolin-2-yl)-1-hydroxyvinyl]pyran-2-one (Vd). Yield 17%. Yellow crystals, mp 191–193°C. 1H NMR spectrum, δ, ppm: 1.35 s [18H, 3',5'-C(CH ) ], 3 3 2.69 s (3H, 8"-CH3), 5.89 s (1H, H2), 7.13 s (1H, H42 ), 7.39–7.57 m (3H, Hquinoline), 15.30 br.s (1H, OH). Found, %: C 63.56; H 5.70; Cl 7.46; N 5.84. C25H27ClN2O5. Calculated, %: C 63.76; H 5.78; Cl 7.53; N 5.95. 3,5-Di(tert-butyl)-6-[(Z)-2-(6,8-dimethyl-5-nitro4-chloroquinolin-2-yl)-1-hydroxyvinyl]-pyran-2-one (Ve). Yield 19%. Yellow crystals, mp 214–216°C. 1H NMR spectrum, δ, ppm: 1.35 s [18H, 3',5'-C(CH ) ], 3 3 2.38 s (3H, 6"-CH3), 2.65 s (3H, 8"-CH3), 5.85 s (1H, H2), 7.12 s (1H, H42 ), 7.38 s (1H, Hquinoline), 7.45 s (1H, H quinoline), 15.39 br.s (1H, OH). Found, %: C 64.28; H 5.90; Cl 7.14; N 5.56. C26H29ClN2O5. Calculated, %: C 64.39; H 6.03; Cl 7.31; N 5.78. 3,5-Di(tert-butyl)-6-[(Z)-2-(7,8-dimethyl-5-nitro4-chloroquinolin-2-yl)-1-hydroxyvinyl]-pyran-2-one (Vf). Yield 18%. Yellow crystals, mp 208–210°C. 1H NMR spectrum, δ, ppm: 1.35 s [18H, 3',5'-C(CH 3 ) 3 ], 2.53 s (3H, 7"-CH3), 2.59 s (3H, 8"-CH3), 5.84 s (1H, H2), 7.05 s (1H, H42 ), 7.32 s (1H, Hquinoline), 7.38 s (1H, Hquinoline), 15.38 br.s (1H, OH). Found, %: C 64.20; H 5.94; Cl 7.06; N 5.48. C26H29ClN2O5. Calculated, %: C 64.39; H 6.03; Cl 7.31; N 5.78. The study was carried out under the financial support of the program no.8 of the Presidium of the Russian Academy of Sciences “Development of methods of production of chemical substances and creation of new materials”, program of purposeful expenditure of the Presidium of the Russian Academy of Sciences “Support for young scientists”, projects of the Ministry of Education and Science RNP.2.2.2.3.10011 and of CRDF program of the Ministry of Education of BRHE 2007 Post Doctoral Fellowship Y4-C04-01, and of the grant for the support of leading scientific schools NSh4849.2006.3. REFERENCES 1. Minkin, V.I., Komissarov, V.N., and Sayapin, Yu.A., Arkivoc., 2006, vol. VII, p. 439.


SYNTHESIS AND STRUCTURE OF HETEROCYCLIC DERIVATIVES OF PYRAN-2-ONES 2. Critchlow, A., Haslam, E., Haworth, R.D., Tinker, P.B., and Waldron, N.M., Tetrahedron, 1967, vol. 23, p. 2829. 3. Waldron, N.M., J. Chem. Soc. C, 1968, p. 1914. 4. Shif, A.I., Lyubchenko, S.N., and Olekhnovich, L.P., Zh. Obshch. Khim., 1997, vol. 67, p. 1166. 5. Shif, A.I., Lyubchenko, S.N., Borbulevich, O.Ya., Shishkin, O.V., Lysenko, K.A., and Olekhnovich, L.P., Izv. Akad. Nauk, Ser. Khim., 1999, p. 139. 6. Tkachev, V.V., Aldoshin, S.M., Shilov, G.V., Komissarov, V.N., Sayapin, Yu.A., and Minkin, V.I., Izv. Akad. Nauk, Ser. Khim., 2007, p. 267. 7. Minkin, V.I., Aldoshin, S.M., Komissarov, V.N., Dorogan, I.V., Sayapin, Yu.A., Tkachev, V.V., and Starikov, A.G., Izv. Akad. Nauk, Ser. Khim., 2006, p. 1956.

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8. Komissarov, V.N., Bang, D.N., Minkin, V.I., Aldoshin, S.M., Tkachev, V.V., and Shilov, G.V., Mendeleev Commun., 2003, p. 219. 9. Sobczyk, L., Grabowski, S.J., Krygowski, T.M., Chem. Rev., 2005, vol. 105, p. 3513. 10. Sheldrick, G.M., The SHELX-97 Manual, Göttingen: Univ. of Gottingen, 1997. 11. Becke, A.D., Phys. Rev. A, 1991, vol. 91, p. 651. 12. Becke, A.D., J. Chem. Phys., 1993, vol. 98, p. 5648. 13. Lee, C., Yang, W., and Parr, R.G., Phys. Rev. B, 1988, vol. 37, p. 785. 14. Barone, V. and Cossi, M., J. Phys. Chem. A, 1998, vol. 102, p. 1995.
