The structure and vibrational spectra of the 2,5-dimethylpyrazine (2,5-DMP) 1:1 adduct with 2,5-dichloro-3,6-dihydroxy-p-benzoquinone (CLA)

Article abstract of DOI:10.1016/j.chemphys.2010.12.003

The complexation of 2,5-dimethylpyrazine (2,5-DMP) with 2,5-dichloro-3,6-dihydroxy-p-benzoquinone (CLA) leads to the formation of the hydrogen bonded OH?N infinite chains without any proton transfer. In the high and medium frequency region of the IR spectra a characteristic Had?i's trio with maxima at ca. 2400, 1800 and 1150 cm^-1 is observed. The infrared, Raman and inelastic neutron scattering (INS) spectra are compared with those calculated by using the DFT methods applied to the crystalline state. The optimization of the structure by using this theoretical approach is also performed. Very good conformity of the experimental and theoretical structures is visible. The reproduction of vibrational spectra is also good except for the low frequency bands related to the CH₃ torsional modes. One gets relatively good agreement by using PWC(dnp) approach. Applications of other theoretical models leads to much higher values of CH ₃ torsional frequency.

Full text of DOI:10.1016/j.chemphys.2010.12.003

Chemical Physics 380 (2011) 34–39
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Chemical Physics
journal homepage: www.elsevier.com/locate/chemphys
The structure and vibrational spectra of the 2,5-dimethylpyrazine (2,5-DMP)
1:1 adduct with 2,5-dichloro-3,6-dihydroxy-p-benzoquinone (CLA)
a
b
b,
b
c
c
⇑
´
A. Pawlukojc , W. Sawka-Dobrowolska , G. Bator , L. Sobczyk , E. Grech , J. Nowicka-Scheibe
a Institute of Nuclear Chemistry and Technology, Dorodna 16, 03-195 Warsaw, Poland
b Faculty of Chemistry, University of Wrocław, F. Joliot-Curie, 1450 383 Wrocław, Poland
c Department of Inorganic and Analytical Chemistry, Westpomeranian University of Technology, Al. Piastów 42, 71-065 Szczecin, Poland
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 1 March 2010
In final form 15 December 2010
Available online 22 December 2010
The complexation of 2,5-dimethylpyrazine (2,5-DMP) with 2,5-dichloro-3,6-dihydroxy-p-benzoquinone
(CLA) leads to the formation of the hydrogen bonded OHꢀ ꢀ ꢀN infinite chains without any proton transfer.
ˇ
In the high and medium frequency region of the IR spectra a characteristic Hadzi’s trio with maxima at ca.
2400, 1800 and 1150 cmꢁ1 is observed. The infrared, Raman and inelastic neutron scattering (INS) spectra
are compared with those calculated by using the DFT methods applied to the crystalline state. The opti-
mization of the structure by using this theoretical approach is also performed. Very good conformity of
the experimental and theoretical structures is visible. The reproduction of vibrational spectra is also good
except for the low frequency bands related to the CH3 torsional modes. One gets relatively good agree-
ment by using PWC(dnp) approach. Applications of other theoretical models leads to much higher values
of CH3 torsional frequency.
Keywords:
Hydrogen bonds
2,5-dimethylpyrazine
Chloranilic acid
ˇ
Hadzi’s trio
Torsional modes of methyl groups
Inelastic neutron scattering
Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction
calculated and experimental frequencies of the vibrations. This
observation is valid over a broad frequency range with the excep-
Pyrazine and its derivatives merit being distinguished from the
point of view of crystal engineering and material sciences [1–5].
The same is related to 2,5-dichloro-3,6-dihydroxy-p-benzoquinone
(chloranilic acid – CLA) [6,7] and squaric acid (H2SQ) [8], which
possess two equivalent proton donor groups. Moreover CLA is
interesting from a biological point of view as a benzoquinone
derivative being an electron accepting system [9]. Both pyrazine
and CLA and H2SQ possess two centers with an ability to form
bridges of the hydrogen bond (HB) or charge transfer (CT) type.
The methyl derivatives of pyrazine and particularly tetrameth-
ylpyrazine (TMP) in complexes with either CLA [10,11] or H2SQ
[12,13] have been the subject of particular interest. TMP with
either p-nitrophenol [14] or picric acid [15] forms also an interest-
ing complex of the 1:2 composition. In the former case the TMP
molecule forms two hydrogen bonds without any proton transfer,
while in the latter case the protonation of both nitrogen atoms
takes place.
tion, however, of the CH3 torsional modes. The calculated frequen-
cies appeared to be much higher than the experimental ones.
Therefore it seems justified to examine the adduct of 2,5-DMP with
CLA, to prove generally this observation. In the present work we
decided to synthesize the crystalline 2,5-DMPꢀCLA adduct in order
to study the X-ray structure, which has been not known so far, as
well as to analyze the vibrational spectra obtained from the com-
plementary INS, infra-red and Raman techniques.
It should be noted that the infrared and Raman spectra at room
temperature of the pure component of the 2,5-DMPꢀCLA adduct –
2,5-dimethylpyrazine have been already recorded and the energy
levels of the methyl groups were obtained on the basis of a molec-
ular geometry [18].
2. Experimental and calculations
The crystalline 1:1 adduct of 2,5-dimethylpyrazine (2,5-DMP)
with 2,5-dichloro-3,6-dihydroxy-p-benzoquinone (CLA) was ob-
tained by a slow evaporation of acetone as a solvent containing
1:1 mixture of components.
The X-ray diffraction studies were performed on a Kuma KM4
CCD x-axis four circle diffractometer equipped with an Oxford
The complex of 2,6-dimethylpyrazine (26DMP) with chloranilic
acid [16,17] has been the object of studies as well. The main result
for this complex was the comparison of frequencies for the tor-
sional modes of methyl group with those calculated for the crystal-
line state. Generally one observes a good agreement between the
Cryosystem Cooler using graphite monochromated MoK
a radia-
⇑
tion. The data were corrected for Lorentz and polarization effects
as well as for absorption.
Corresponding author.
E-mail address: gb@wchuwr.chem.uni.wroc.pl (G. Bator).
0301-0104/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.chemphys.2010.12.003

´
35
A. Pawlukojc et al. / Chemical Physics 380 (2011) 34–39
The structure was solved by direct methods (SHELXS-97) and
refined by the full-matrix least-squares methods using the SHEL-
XL-97 [19] program. Non-hydrogen atoms were refined with aniso-
tropic thermal parameters. The hydrogen atoms attached to carbon
were placed at calculated positions and refined. Allowing them to
ride on the parent carbon atom. The hydrogen atom of O–H group
was located from difference map and refined. The crystal data and
structure refinement are summarized in Table 1. Crystallographic
data for the structural analysis have been deposited with the Cam-
bridge Crystallographic Data Centre, CCDC 767413.
approximation (LDA) at PWC functional (Perdew–Wang GGA
[26]). Calculations have been performed using DNP basis set as
implemented in DMol3.
3. Results and discussion
3.1. X-ray diffraction
The 2,5-DMP CLA adduct crystallizes in the triclinic space group
P-1 with only one formula unit per unit cell. The asymmetric unit
consists of a half neutral 2,5-DMP molecule and a half neutral CLA
molecule. Each molecule in the adduct lies on a crystallographic
center of inversion. The structure with atom numbering scheme
is shown in Fig. 1.
The selected bond lengths and angles together with the calcu-
lated ones for the crystalline state are presented in Table 2. The
consistency between corresponding lengths and angles is satisfac-
tory. The rings of 2,5-DMP and CLA lay almost in the same plane.
The angle between ring planes equals to merely 5.4(1)°.
The CLA and 2,5-DMP molecules are linked by an intermolecu-
lar O–Hꢀ ꢀ ꢀN hydrogen-bonding interaction (Fig. 2). Each nitrogen
atom of the 2,5-DMP molecule accepts one hydrogen bond from
the hydroxyl group of the CLA molecule. The O(4)–H(4)ꢀ ꢀ ꢀN(1) dis-
tance is indicating a moderate hydrogen bond, with a distance of
2.694(2) Å. The calculated values of the O–Hꢀ ꢀ ꢀN bond lengths
(2.678 Å) correspond well to the experimental ones. The O(4) atom
makes possible a formation of bifurcated hydrogen bonded system,
as it is also involved in an intramolecular O(4)–H(4)ꢀ ꢀ ꢀO(1) interac-
tions with a distance of 2.699(2) Å.
In the crystal structure of the title adduct, there are two inter-
molecular C–Hꢀ ꢀ ꢀO bridges, which link the 2,5-DMP and CLA moi-
eties into molecular chains extended along the b-axis. The chains of
the structural units are stabilized through the C–Hꢀ ꢀ ꢀO hydrogen
bonds. In Table 3 the other short contacts, found in the crystal
structure of the 2,5-DMPꢀCLA complex, are collected.
Infra-red spectra of 2,5-DMP CLA crystal were recorded at room
temperature with the FTIR spectrometer BRUKER IFS-113v over the
wavenumber range 4000–40 cmꢁ1 with a resolution of 1.0 cmꢁ1
.
For the mid-IR spectra the samples were studied as a suspension
in Nujol or Fluorolube between the KBr windows. The far-IR spec-
tra were taken in Nujol mulls between the polyethylene windows
over the wavenumber range 600–50 cmꢁ1
.
The Raman spectra of powder samples were recorded on a Nico-
let Magna 860 FT Raman spectrometer at room temperature.
Nd:YAG laser was the exciting source, with power of ca. 200 mW.
The back scattering geometry was applied. The resolution was
set up for 2 cmꢁ1
.
Neutron scattering data were collected at the pulsed IBR-2 reac-
tor in Dubna using the time-of-flight inverted geometry spectrom-
eter NERA-PR [20] at 20 K. The spectra were converted from
neutron per channel to S(Q,
x) scattering function per energy
transfer. At the energy transfer between 5 and 100 meV the rela-
tive INS resolution was estimated to be ca. 3%.
The total energy optimization and the frequency calculations
have been performed based on the density functional theory
(DFT) using the DMol3 program [21,22] as a part of Materials Stu-
dio package [23]. The results have been obtained for the crystalline
state within generalized gradient approximation (GGA) at BLYP
(Becke exchange [24] plus Lee–Yang–Parr correction functional
[25]) and PW91 functionals, as well as within the local density
Of some importance are also bridges formed between aromatic
C(16)–H(16) and methyl group C(17)–H(73) bonds with the O(1)
and O(4) oxygen atoms of CLA molecule. The corresponding
C–Hꢀ ꢀ ꢀO distances are equal to 3.030(2) Å and 3.292(2) Å, respec-
tively. The interactions between methyl groups of 2,5-DMP and
chlorine atoms of CLA (C(17)–H(71)ꢀ ꢀ ꢀCl(1), 3.935(2) Å) are the fac-
tors playing additional role in the linking the chains.
Table 1
Crystal data and structure refinement for 2,5-DMPꢀCLA adduct.
2,5-DMPꢀCLA
C6H8N2 C6H2Cl2O4
317.12
Empirical formula
Formula weight
Temperature, K
Wavelength (Å)
Crystal system
Space group
Unit cell dimensions
a (Å)
100(2)
0.71073
Triclinic
P-1
5.065(1)
b (Å)
8.092(2)
c (Å)
8.952(2)
a
b (°)
(°)
113.86(2)
102.04(1)
94.29(1)
322.93(14)
1
c
(°)
Volume (Å3)
Z
Calculated density, Mg mꢁ3
1.631
0.517
l
(mmꢁ1
)
Crystal size (mm)
h range for data collection (°)
Index range
0.40 ꢂ 0.12 ꢂ 0.10
4.18–26.5
ꢁ6 6 h 6 6
ꢁ10 6 k 6 10
ꢁ11 6 l 6 11
2188/1341
0.0324
Reflections collected/unique
Rint
Max and min absorption correction
Data/parameters
0.950, 0.829
1341/96
1.093
Goodness-of-fit on F2
Final R1 and wR2 indices [I > 2
R1 and wR2 indices (all data)
D
r
(I)]
0.0322, 0.0831
0.0396, 0.0858
0.246 and ꢁ0.258
qmax, D )
qmin (e Åꢁ3
Fig. 1. The structure of 2,5-DMP CLA unit with atom numbering showing
displacement ellipsoids at the 30% probability level.

´
36
A. Pawlukojc et al. / Chemical Physics 380 (2011) 34–39
Table 2
Table 3
Experimental and calculated (by using various models) bond lengths and angles for
2,5-DMPꢀCLA complex. (AÅ, °).
Hydrogen bonds and short contacts for 2,5-DMPꢀCLA adduct.
0
D–Hꢀ ꢀ ꢀA (Å)
D–H (Å)
Hꢀ ꢀ ꢀA (Å)
Dꢀ ꢀ ꢀA (Å)
<DHN (°)
Coordinates
Experimental Calculated
PWC(dnp) PW91(dnp) BLYP(dnp)
O(4)–H(4)ꢀ ꢀ ꢀN(1)
O(4)–H(4)ꢀ ꢀ ꢀO(1)
C(16)–H(16)ꢀ ꢀ ꢀO(1)
C(17)–H(73)ꢀ ꢀ ꢀO(4)
C(17)–H(71)ꢀ ꢀ ꢀCl(1)i
0.82(2)
0.82(2)
0.93
0.96
0.96
1.95(2)
2.25(2)
2.39
2.56
2.99
2.694(2)
2.699(2)
3.030(2)
3.292(2)
3.935(2)
151(2)
115(2)
126
133
167
N(1)–C(12)
C(12)–C(16)’’
C(16)–N(1)
C(12)–C(17)
C(1)–O(1)
C(1)–C(2)
C(2)–C(6)’
C(6)–C(1)
C(6)–O(4)
C(2)–C(l1)
1.354
1.394
1.333
1.496
1.216
1.470
1.348
1.511
1.328
1.722
1.342
1.395
1.330
1.477
1.232
1.442
1.366
1.497
1.350
1.398
1.338
1.491
1.236
1.449
1.367
1.509
1.354
1.400
1.343
1.499
1.239
1.452
1.368
1.518
Symmetry code: (i) x + 1, y + 1, z + 1.
Table 4
1.306
1.713
1.320
1.730
1.328
1.749
Classification of the fundamental modesa for the 2,5-DMP-CLA adduct crystal.
C(12)–C(16)’’–N(1)’’ 122.90
122.50
118.25
119.25
119.34
121.38
118.89
121.41
119.70
117.25
123.86
122.85
117.45
121.61
116.98
122.63
118.00
119.36
119.29
121.32
118.64
121.37
120.00
117.86
123.60
122.27
117.74
121.76
116.87
122.44
118.29
119.26
119.30
121.42
118.35
121.45
120.20
118.09
123.56
121.99
117.81
121.62
116.92
UCG
Lattice modes
Internal modes
Selection rules
C(16)–N(1)–C(12)
N(1)–C(12)–C(16)’’
C(17)–C(12)–N(1)
117.52
119.57
118.65
Ci
Ac
Lib
Trans
2,5-DMP
CLA
IR
Raman
Ag
Au
0
3
6
0
0
3
21
21
18
18
i
Xx,yy,zz,xy,yz,zx
i
C(17)–C(12)–C(16)’’ 121.76
X, Y, Z
C(6)–C(1)–C(2)
C(1)–C(2)–C(6)’
C(2)–C(6)–C(1)
O(1)–C(1)–C(6)
O(1)–C(1)–C(2)
O(4)–C(6)–C(2)’
O(4)–C(6)–C(1)
Cl(1)–C(2)–C(6)’
Cl(1)–C(2)–C(1)
118.12
121.27
120.61
118.51
123.36
122.32
117.08
121.99
116.74
a
UCG – Unit cell group; Ac – Acoustic modes, Lib – Librational modes; Trans –
Translational modes.
The observed frequencies of particular modes in INS, infra-red
and Raman spectra compared with calculated ones are presented
in Table 5.
The assignment of particular modes was based on the main con-
tribution derived from the normal coordinate analysis. None of
scaling factors was used. As Fig. 3 shows, in infra-red spectra a con-
tinuum of absorption spread from ca. 3000 cmꢁ1 down to ca.
500 cmꢁ1 is visible with clearly indicated submaxima, the first
one between ca. 3000 cmꢁ1 and 2100 cmꢁ1 with maximum at
2400 cmꢁ1, second one rather weak at 1825 cmꢁ1 and finally the
third one with overlapped narrow peaks of internal modes at ca.
Symmetry code: (‘) -x, -y, -z; (‘‘) -x, -y, -z.
3.2. Vibrational spectra
3.2.1. Selection rules for the 2,5-DMPꢀCLA adduct triclinic system,
space group P-1, Z = 1
Both 2,5-DMP and CLA molecules occupy Ci sites in the crystal
lattice. Formal classification of the fundamental modes (k = 0) are
listed in Table 4. In the INS spectra all modes are allowed, there
is no selection rules related to the symmetry of both a molecule
and the crystal structure.
1150 cmꢁ1. This picture resembles the Hadzi’s trio, analyzed in
ˇ
several papers [27]. It indicates a specificity of strong O–Hꢀ ꢀ ꢀN
hydrogen bond present in our case and may suggest a presence
of a double minimum potential for the proton motion.
Fig. 2. Packing of the 2,5-DMP and CLA molecules in the crystalline lattice.

´
37
A. Pawlukojc et al. / Chemical Physics 380 (2011) 34–39
Table 5
Experimental and calculated frequencies for 2,5-DMPꢀCLA complex (cmꢁ1).
Approximate assignments
Experimental
INS
Calculated
PW91(dnp)
IR
Raman
PWC(dnp)
BLYP(dnp)
Translation and rotation (9 modes)
CH3tors. (25DMP)
CH3tors. (25DMP)
Ring tors. (CLA)
Ring tors. (CLA)
Ring tors. (25DMP)
Ring tors. (CLA)
C–Clbend. (CLA)
78
54–141
35
46
118
125
153
159
190
213
67–147
152
172
115
126
160
173
203
222
66–145
148
155
115
132
164
174
202
217
51
51
101
130
165
116
208
226
202
C–Owagg. (CLA)
C–Clbend. (CLA)
C–Obend. (CLA)
243
288
231
291
246
292
246
290
294
C–Obend. (CLA)
313
305
314
312
C–Clwagg. (CLA)
322
345
311
335
355
386
324
344
359
386
318
346
355
381
C–CH3bend. (25DMP)
Ring tors. (25DMP)
Ring def. (CLA)
344
357
337
385
C@Obend. (CLA)
Ring def. (CLA)
395
426
387
419
506
520
396
407
418
419
503
507
512
390
410
421
431
503
511
514
388
408
423
431
499
513
515
C–CH3bend. (25DMP)
Ring tors. (25DMP)
C–Owagg. (CLA)
C–CH3wagg. (25DMP)
Ring def. (CLA)
418
496
513
C–Clstr.(CLA)
528
526
533
531
Ring def. (25DMP)
C–Clwagg. (CLA)
554
573
553
583
553
584
544
581
Ring def. (25DMP)
C@Owagg. (CLA)
676
744
674
744
675
749
681
743
C–CH3str. (25DMP)
C–CH3wagg. (25DMP)
C@Obend. (CLA)
C@Owagg. (CLA)
C–Cstr. (CLA)
746
744
759
774
790
836
864
873
913
752
753
774
792
828
869
899
900
744
750
769
785
809
859
869
891
751
974
790
824
840
785
832
C–Clstr.(CLA)
C–CH3
(25DMP)
865
905
str.
C–Hwagg. (25DMP)
C–Hwagg. (25DMP)
C–Cstr. (CLA)
CH3rock. (25DMP)
CH3rock. (25DMP)
Ring def. (25DMP)
CH3rock. (25DMP)
890
990
923
955
988
953
982
995
939
972
984
1014
1001
1002
1006
1035
1088
1090
1112
1166
1233
1236
1254
1271
1281
1304
1329
1345
1358
1360
1376
1389
1397
1398
1421
1484
1564
1604
1623
1629
1672
1674
2311
2345
2944
2944
3027
1021
1029
1033
1044
1046
1046
1172
1218
1232
1245
1247
1250
1266
1283
1333
1342
1364
1374
1388
1442
1447
1449
1464
1476
1540
1596
1608
1634
1654
1655
2510
2542
3016
3016
3103
1027
1042
1043
1047
1055
1055
1182
1211
1221
1225
1239
1247
1253
1285
1302
1308
1357
1396
1406
1453
1455
1463
1474
1482
1520
1579
1591
1604
1629
1629
2518
2551
3013
3014
3081
CH3
(25DMP)
1054
1153
1227
1261
rock.
O–Hwagg. (CLA)
O–Hwagg. (CLA)
O–Hbend. (CLA)
C–Cstr.(CLA)
C–Cstr.(CLA)
Ring str. (25DMP)
Ring str. (25DMP)
O–Hbend. (CLA)
C–Hbend. (25DMP)
C–Hbend. (25DMP)
C–Ostr. (CLA)
1236
1302
1332
C–Ostr. (CLA)
Ring str. (25DMP)
CH3bend. (25DMP)
CH3bend. (25DMP)
CH3bend. (25DMP)
CH3bend. (25DMP)
CH3bend. (25DMP)
Ring str. (25DMP)
CH3bend. (25DMP)
Ring str. (25DMP)
C@Cstr. (CLA)
1365
1404
1393
1455
1459
1465
1489
1494
1539
1550
Ring str. (25DMP)
C@Cstr. (CLA)
C@Ostr. (CLA)
1622
1630
1634
C@Ostr. (CLA)
O–Hꢀ ꢀ ꢀNstr.
ꢃ2500
ꢃ2500
O–Hꢀ ꢀ ꢀNstr.
C
C
m–Hstr.
m–Hstr.
2923
3076
C–Hstr.
(continued on next page)

´
A. Pawlukojc et al. / Chemical Physics 380 (2011) 34–39
38
Table 5 (continued)
Approximate assignments
Experimental
INS
Calculated
PW91(dnp)
IR
Raman
PWC(dnp)
BLYP(dnp)
C–Hstr.
3027
3070
3071
3105
3106
3103
3147
3148
3166
3167
3082
3123
3125
3195
3196
C
C
C
C
m–Hstr.
m–Hstr.
m–Hstr.
m–Hstr.
Fig. 3. Comparison of the infra-red and Raman spectra in the wavenumber range between 100 and 3500 cmꢁ1. The absorption arising from Nujol is shown as dotted line.
The comparison of the infra-red and Raman spectra in the med-
ium frequency range is shown in Fig. 3 as well, allowing a possibil-
ity of quantitative comparison of observed peaks.
The INS spectrum, in the frequency range up to 1200 cmꢁ1
,
compared with simulated ones by using various models merits a
special treatment (Fig. 4).
The experimental spectrum shows particularly strong band at
51 cmꢁ1, which should be ascribed to the torsional/librational
vibrations of methyl groups. The best reproduction is obtained by
using the PWC functional. Remaining two other PW91 and BLYP
models lead to very high frequencies of CH3 torsional mode, three
times as high as experimental values. In the case of the other
modes all three models yield highly similar frequencies.
4. Conclusions
The 2,5-DMP and CLA molecules form in the crystalline lattice
the infinite equivalent hydrogen bonded chains with the O–Hꢀ ꢀ ꢀN
length equal to 2.694(2) Å. These strong bridges find a reflection
in the infrared continua that suggest a double minimum potential
in the excited vibrational state. According to the Zundel’s theory
[28] such bridges are characterized by a very high polarizability
and as a consequence by the unusual width of stretching vibra-
tional bands. In addition to the O–Hꢀ ꢀ ꢀN hydrogen bonds the bifur-
cate O–Hꢀ ꢀ ꢀO bridges, strongly bent, are present.
The origin of a trio on the broad continuous absorption can be
explained as due to the splitting of the energetic levels in the
excited vibrational state. Simultaneously one should take into
account the coupling with the overtone of the C–Hwagg. mode that
leads to a creation of an Evans hole on the absorption curve and an
appearance of the pseudoband located at 1825 cmꢁ1
.
In the present paper we did not analyze the behavior of hydro-
gen bonds with the participation of the C–H groups. Here we want
to tell that analogous features of the C–H groups engaged into
Fig. 4. The INS spectrum confronted with simulated ones by using various models.

´
39
A. Pawlukojc et al. / Chemical Physics 380 (2011) 34–39
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´
[10] M. Prager, A. Pawlukojc, L. Sobczyk, E. Grech, H. Grimm, J. Phys.: Condens.
The analysis of the structure and vibrational modes has been
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line state. Both the calculated structure and the mode frequencies
are well consistent, except the CH3 torsional mode. Relatively good
agreement was achieved only by using the PWC functional.
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Acknowledgments
The calculations were performed on computers of the Wroclaw
Centre for Networking and Supercomputing, under Calculating
Grant No. 2006/5, and in Interdisciplinary Centre for Mathematical
and Computational Modeling, Warsaw University, under Calculat-
ing Grant No. G30-15. MATERIALS STUDIO package was used under
POLAND COUNTRY-WIDE LICENSE.
´
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This work was supported by the Polish Ministry of Science and
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