Competing processes in the photochemistry of picolines and their N-methyl salts: photoinduced charge transfer, phototransposition and photohydration

Article abstract of DOI:10.1007/s11164-016-2669-6

Photochemical reactivity of a series of picolines and their N-methylated salts has been investigated by preparative irradiations and UV–vis spectroscopy. Understanding competing photochemical processes and knowledge of their relative efficiencies is important in the application of pyridines as photocages or in the synthesis of complex polycycles. Contrary to previous reports for the gas phase, picolines are not reactive in the phototransposition, presumably due to protonation of the pyridine nitrogen in the excited state. Deuterium exchange was observed upon irradiation in CD₃CN–D₂O, but it was rationalized by photoionization and radical formation. On the other hand, N-methylated picoline salts are not protonated upon excitation. They undergo photohydration and phototransposition (Φ_R?=?0.01–0.06). Upon irradiation of iodides, azabicyclic [3.1.0] hydration products were obtained. A difference in product distribution was observed between iodides and perchlorates, due to photoelimination of perchloric acid leading to the thermal aziridine ring opening. Moreover, excitation of iodide derivatives gives rise to change transfer transition forming iodide radicals that eventually give I₃ ^? with the quantum efficiency Φ_R?=?0.015–0.02.

Full text of DOI:10.1007/s11164-016-2669-6

Res Chem Intermed
DOI 10.1007/s11164-016-2669-6
Competing processes in the photochemistry of picolines
and their N-methyl salts: photoinduced charge transfer,
phototransposition and photohydration
1
Vesna Blazek Bregovic Nikola Basaric
1
•
ˇ
´
´
Received: 6 June 2016 / Accepted: 15 July 2016
Ó Springer Science+Business Media Dordrecht 2016
Abstract Photochemical reactivity of a series of picolines and their N-methylated
salts has been investigated by preparative irradiations and UV–vis spectroscopy.
Understanding competing photochemical processes and knowledge of their relative
efficiencies is important in the application of pyridines as photocages or in the
synthesis of complex polycycles. Contrary to previous reports for the gas phase,
picolines are not reactive in the phototransposition, presumably due to protonation of
the pyridine nitrogen in the excited state. Deuterium exchange was observed upon
irradiation in CD3CN–D2O, but it was rationalized by photoionization and radical
formation. On the other hand, N-methylated picoline salts are not protonated upon
excitation. They undergo photohydration and phototransposition (UR = 0.01–0.06).
Upon irradiation of iodides, azabicyclic [3.1.0] hydration products were obtained. A
difference in product distribution was observed between iodides and perchlorates,
due to photoelimination of perchloric acid leading to the thermal aziridine ring
opening. Moreover, excitation of iodide derivatives gives rise to change transfer
-
transition forming iodide radicals that eventually give I3 with the quantum effi-
ciency UR = 0.015–0.02.
Keywords Pyridine Á Pyridinium salt Á Excited state proton transfer Á
Excited state charge transfer Á Phototransposition Á Photohydration
Electronic supplementary material The online version of this article (doi:10.1007/s11164-016-2669-6)
contains supplementary material, which is available to authorized users.
´
Nikola Basaric
nbasaric@irb.hr
&
1
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´
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Department of Organic Chemistry and Biochemistry, Ruder Boskovic Institute, Bijenicka cesta
¯
54, 10 000 Zagreb, Croatia
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V. Blazek Bregovic, N. Basaric
Introduction
Pyridine and pyridinium derivatives are important in various biological processes.
For example, pyridinium salts are present in the structure in NAD? and NADP?
cofactors, which are essential for the functioning of all living cells. Since pyridines
and pyridinium derivatives are photochemically reactive, [1, 2] in principle,
excitation by light allows for the activation or deactivation of biochemical
processes involving NAD? and NADP? cofactors. Furthermore, biologically
important molecules from the family of vitamin B6 and its derivatives are
methylpyridines (also known as picolines), which are also prone to photochemical
reactions [3].
Interest in pyridine photochemistry was initiated by the discovery of photo-
chemical rearrangements giving Dewar-type products [4]. Later, in a seminal paper
by Kaplan et al. [5], photochemical rearrangement of pyridinium salts was reported.
Under basic conditions, pyridinium salt 1 undergoes rearrangement and hydration to
azabicyclo[3.1.0] derivative 3, via a cationic intermediate 2 (Eq. 1) [5, 6]. It is a
relatively simple reaction that delivers complex heterocyclic structures with well-
defined stereochemistry. Thus, Mariano et al. extended the scope of the pyridinium
salts photorearrangement and reported on acid- [7] or base-induced ring opening of
the photochemically formed aza-heterocycles, [8] whereas Simpson et al. [9] and
Burger et al. [10] used the photorearrangement as the key step in the synthesis of
natural compounds.
ð1Þ
Pyridinium photochemistry has been used in the development of photocages.
Falvey et al. developed photocages for alcohols and esters by applying single
electron transfer (SET) photochemistry of pyridinium salts in the presence of pyrene
and heterocyclic electron donors, [11] or ruthenium(II) sensitizers [12]. Boncella
et al. studied N-methylpicolinium triflate photocages for aliphatic amines [13].
Furthermore, photocages were developed wherein the electron donor and pyri-
dinium salt were in the same molecule [14]. Photodecaging of carboxylic acids was
accomplished by use of golden nanoparticles and pyridinium salts, [15] whereas
carboxylic acids, amino acids, and phosphates can be photodeprotected from
pyridinium photocages in the presence of cumarine and BODIPY derivatives [16].
Recently, Falvey et al. reported a simple approach for photodecaging of carboxylic
acids by use of visible light, based on charge transfer transition in pyridinium iodide
salts [17]. Consequently, a deeper understanding of photochemical transformation
of pyridine and pyridinium derivatives is of great relevance and could redirect
future studies in the life sciences.
123

Competing processes in the photochemistry of picolines…
Herein, we report a general investigation of photochemical reactivity in a series
of a-, b-, and c-picolines 4–6, their methyl iodide, and perchlorate salts 7–9. The
investigation is conducted to probe for anticipated competing photochemical
reactions including excited state proton transfer (ESPT), charge transfer, photohy-
dration, and photorearrangement. Irradiations of 7–9 were conducted under different
conditions, and photoproduct formation studied by NMR and UV–vis spectroscopy.
The current investigation indicates occurrence of two competing photochemical
processes, charge transfer and photorearrangement, neither of which should be
neglected in the applications of pyridines photochemistry. Moreover, we observe an
interesting effect of the counterion and the meta effect of the methyl group to the
photochemical reactivity.
Experimental
General
1H and 13C NMR spectra were recorded on a Bruker Spectrometer at 300, 400, or
600 MHz. Picoline isomers 4–6 were purchased from the usual commercial sources
and were purified by distillation. Pyridinium iodide and perchlorate salts 7–9 were
prepared according to the known procedures [8, 18]. Experimental procedures for
the preparation of 7–9 and the corresponding NMR and UV–vis spectra are in the
supporting information. Solvents used for the photochemical experiments were of
HPLC grade. UV–vis spectra were recorded on a PG T80/T80 ? spectrometer, and
fluorescence on a Cary Eclipse Varian spectrometer. MS spectra were obtained on a
HPLC–MS–MS Agilent 1200 series, 6410.
123

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V. Blazek Bregovic, N. Basaric
Irradiation experiments in NMR tubes
Irradiation experiments were conducted in a Luzchem photochemical reactor
equipped with eight lamps (one lamp 8 W, output at 254 nm).
Picoline isomers 4–6 (1.0–2.4 mg) were dissolved in a mixture of CD3CN
(1 mL) and D2O (100 lL) in quartz NMR tubes (c = 1.91–2.34 9 10-2 M). The
solutions were irradiated in a Luzchem reactor at 254 nm over 5 min-2 h. After
different irradiation times, NMR spectra were recorded.
Pyridinium salts 7–9 (1.5–2.6 mg) were dissolved in a mixture of CD3CN
(500 lL) and D2O (50 lL) in quartz NMR tubes (c = 1.2–2.0 9 10-2 M). The
solutions were irradiated in a Luzchem reactor at 254 nm, and, after certain
irradiation intervals, NMR spectra were recorded.
In the preparative irradiation experiments, pyridinium salt 8a (376 mg, 0.04 M)
was dissolved in aqueous KOH solution (40 mL, 0.05 M). A quartz tube was filled
with the solution, purged with Ar for 30 min and sealed. After 8 h irradiation, the
solution was extracted with diethyl ether, ethyl acetate, and CH2Cl2. The collected
extracts were dried over Na2CO3, filtered, and the solvent was removed on a rotary
1
evaporator (without heating) to afford the residue that was analyzed by H NMR.
UV–vis experiments
A solution of 7a, 8a, or 9a in CH3CN–H2O (10:1, 3 mL) was divided into three
quartz cells for fluorescence spectroscopy. The first solution was purged with Ar,
the second with O2, and the third was not purged. The absorbances of the solutions
at 234 nm were adjusted to 0.75 (c & 5 9 10-5 M). The solutions were irradiated
in a Luzchem reactor at 254 nm in certain time intervals (2 min-2 h), and after each
irradiation UV–vis spectra were recorded.
Alternatively, to the solutions of 7a–9a in CH3CN (c & 5 9 10-5 M), different
amounts of H2O were added (corresponding to the volumetric ratio of 1, 5, 10, 20,
and 50 %). The solutions were irradiated at the same time in a Luzchem reactor at
254 nm. After certain irradiation intervals (2 min-2 h) UV–vis spectra were
recorded.
Measurements of reaction quantum efficiencies
Quantum efficiency for the hydration of 7a–9a was measured by a valerophenone
actinometer (U254 = 0.65 0.03) [19, 20]. For the actinometer, a solution of
valerophenone in CD3CN–D2O (10:1) c = 1.4 9 10-2 M) was used. Solutions of
7a–9a in CD3CN–D2O (10:1) were prepared with the same concentration
(c = 1.4 9 10-2 M, A254 [ 2). Quartz NMR tubes were filled with the solutions,
the solutions were purged with N2 15 min and the tubes were sealed. The solutions
were irradiated in a Luzchem reactor with four lamps at 254 nm 15 min
(valerophenone) or 2 h (7a–9a). After the irradiation, NMR spectra were taken.
From the conversion of reactant to photoproducts, quantum yields were calculated
(for the equations to calculate U, see the supporting information). The measure-
ments were performed in triplicate.
123

Competing processes in the photochemistry of picolines…
Quantum efficiency for the formation of I3- from 7a–9a was measured by a KI/
KIO3 actinometer KI/KIO3 (U254 = 0.74), [19, 21]. For the actinometer, a fresh
solution of KIO3 in borate buffer (0.01 M, pH 9.25) was prepared, and then, a
solution of KI (0.6 M) in the borate solution of KIO3. Fresh solutions of 7a–9a in
CH3CN–H2O (10:1) were prepared in cells for fluorescence spectroscopy in the
concentration range corresponding to A265 & 0.5 (c & 1 9 10-4 M). The volume
in cells was 2.5 mL, and the room temperature varied from 17 to 22 °C. The
solutions were purged with N2 15 min (or were not purged). Prior to the irradiations,
the UV–vis spectra were recorded. The solutions were irradiated in a Luzchem
reactor with one lamp at 254 nm 0.5, 1, and 2 min. During the irradiations the cells
were kept at a constant distance from the lamp and were covered by a dark paper at
three sides to ensure photon flux to the cell only from the front face. Concentration
-
of I3 was calculated from the absorbance increase at 352 nm, whereas decom-
position of 7a–9a was obtained from the decrease of absorbance at 235 or 228 nm
(for the equations to calculate U, see the supporting information). The measure-
ments were performed in triplicate.
Results and discussion
Absorption spectra of picolines 4–6 have an absorption band at &263 nm (253 nm
for 6) populating S1 state, which is not fluorescent. Attempts to record fluorescence
spectra failed. Pyridinium iodide salts exhibit two absorption bands, at 265 nm
(255 nm for 9a), corresponding to the pyridinium excitation, and at &235 nm
corresponding to a charge transfer transition due to the presence of iodide [17] (see
Figs. S1–S4 in the supporting information). Similar to 4–6, 7a–9a are not
fluorescent.
All irradiation experiments were performed by use of lamps with the output at
254 nm. Electronically excited states are often characterized by different acid–base
properties compared to the corresponding ground states [22]. Thus, pyridine
derivatives become more basic upon excitation to S1 (pKa S0 = 5.5, pKa S1 = 12.7)
[23]. Moreover, phototautomerization of 4 was investigated by computational
methods indicating that excitation to S1 or T1 lowers the activation barrier for the
formation of 4-T (Eq. 2) [24].
ð2Þ
Upon electronic excitation, the pyridine nitrogen in picolines is anticipated to
become more basic, whereas the methyl group may behave as a carbon photoacid
leading to the formation of 4-T, as shown in Scheme 1. Subsequent thermal
tautomerization of 4-T to 4 should lead to the regiospecific deuterium incorporation
in the methyl group in compound 4-D. Similarly, it is anticipated that pyridinium
123

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V. Blazek Bregovic, N. Basaric
Scheme 1 Plausible ESPT reactivity of 4
Scheme 2 Plausible ESPT
reactivity of 7
Fig. 1 Anticipated
intermediates in the ESPT
photochemistry of 4–9
salts 7–9 behave as carbon photoacids. For example, deprotonation of 7 is
anticipated to give 7-T that should upon thermal protonation in D2O give 7-D with
the regiospecificaly deuterated methyl group (Scheme 2). It is plausible that meta
and para derivatives undergo similar photoreactions via the corresponding
intermediates 5-T–9-T (Fig. 1).
Anticipated ESPT reactivity and phototautomerization of 4–9 was probed by
irradiations in CD3CN–D2O. After the irradiation, the position and the extent of
deuteration was examined by NMR and MS, respectively. It should be noted that
protonation (deuteration) of pyridine nitrogen cannot be probed in such a way.
Interestingly, after the irradiation of 4–7, no deuterium incorporation in the methyl
group was observed, but it took place in the aromatic ring. Results are compiled in
Table 1. The plausible mechanism for deuteration of the aromatic ring may be
electrophilic aromatic substitution in S1, or a radical-cation mechanism similar to
123

Competing processes in the photochemistry of picolines…
Table 1 Deuterium content in 4–6 after irradiation in CD3CN–D2Oa
Comp.
%D (C-atom)b
% (Ion)
4
23 (C3), 23 (C4),
27 (C5), 37 (C6)
15 (C2), 20 (C4),
17 (C5), 17 (C6)
73 (C2,6), 63 (C3,5)
25 (M??1), 38 (M??2),
24 (M??3)
93 (M??1), 6 (M??2),
1 (M??3)
15 (M??1), 33 (M??2),
44 (M??3)
5
6
a
Irradiation at 254 nm for 2 h in CD3CN–D2O, performed in a quartz NMR tube
b
Obtained by integration of signals in 1H NMR spectra. The numeration of C-atoms follows IUPAC
guidelines, as shown in one example on Scheme 3
c
Obtained from MS
Scheme 3 Plausible mechanism for D-exchange in 4 upon irradiation in CD3CN–D2O
the one proposed for the deuteration of pyrroles and similar aza-heterocycles [25].
In such a mechanism, picolines are first oxidized to the corresponding radical-
cations 10 that undergo D-abstraction from CD3CN to give cations 11 and
eventually yield D-incorporated molecules (Scheme 3). Very low efficiency of
D-incorporation is in line with such a mechanism. Namely, photoionization of
pyridine should take place with low efficiency due to its relatively high oxidation
potential (in CH3CN, Eox = 1.82 V vs. Ag/AgCl) [26].
In addition to deuteration of 4–6, no other photochemical processes were
observed. In particular, phototransposition products were not formed, contrary to the
previous report by Pavlik et al. [27] on phototransposition of picolines in gas phase.
Obviously, photochemical reactivity in gas phase and protic solution differ
significantly, presumably due to the protonation of pyridine nitrogen in S1 [23].
Contrary to picolines, irradiation of the pyridinium derivatives 7–9 did not give
rise to deuterated compounds, but gave H2O-adducts and rearranged products. In
addition, during the irradiations of 7a–9a, the color of the solution changed from
transparent to yellow, indicating formation of I3- [28]. Therefore, we examined two
-
processes separately, photochemical formation of I3 by UV–vis spectroscopy and
formation of H2O-adducts by irradiation in quartz NMR tubes and recording NMR
spectra.
Upon irradiation of 7a–9a in NMR tubes, a new set of signals between 3 and
1
6 ppm in H NMR spectra was observed. Conversion to these primary photoprod-
ucts after 2 h irradiation was &10 % for 7a and 9a, whereas for the meta isomer 8a
123

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V. Blazek Bregovic, N. Basaric
Scheme 4 Competing photohydration and phototransposition of 7a and 9a
Scheme 5 Photohydration of 8a
it was &50 %. From 7a or 9a, in addition to primary products formed in yields
lower than 10 %, competing phototransposition took place, giving mixtures of all
three isomers 7a–9a (Scheme 4). Our observation is in agreement with a preceding
theoretical report that photolysis of meta-alkylated pyridinium salts takes place
without nitrogen migration [29]. Attempts to isolate the primary photoproducts after
preparative irradiations in CH3CN–H2O failed. In the isolation process, the primary
products rearranged in a transposition reaction giving mixtures of 7a–9a. Similarly,
upon heating of a NMR tube containing only starting molecule 8a and primary
products 14 and 15, a mixture of 7a–9a was obtained (Scheme 5).
123

Competing processes in the photochemistry of picolines…
In principle, primary photoproducts could be associated to the hydration products
1
12–16, or iodide adducts such as 17 (Scheme 4). Similarity of the signals in H
NMR to H2O-adducts described in precedent literature [5] encouraged us to assign
the primary products to 12–16. To verify this assignment, the irradiation of 8a has
been conducted under basic conditions, the same as in the report by Kaplan et al. [5]
where I-adducts are not expected due to the presence of a large excess of the better
nucleophile, OH-. Indeed, the same products were obtained in the irradiation of
neutral and basic solution, indicating that the primary products are correctly
assigned to H2O-adducts. Additional evidence that the primary products are H2O-
adducts came from the lack of their formation upon irradiation in neat CH3CN.
Prolonged irradiation resulted only in the inefficient phototranspositon. Note that
12–16 have in principle different diastereomeric forms. Since we did not manage to
separate the H2O-adducts, we were not able to assign their stereochemistry.
However, it is known that nucleophile attacks the azabicyclic [3.1.0] cation
stereospecifically, anti- to the aziridine ring, as shown, for example, in Eq. (1)
[5, 7–10].
Efficiency of the photohydration was determined by use of a valerophenone
actinometer [19, 20]. Results are compiled in Table 2. It is interesting to note that
photohydration of meta- isomer 8a takes place about 2–3 times more efficiently than
for the ortho or para isomers. This result represents one more example of a meta-
effect in photochemistry [30, 31]. The observation is probably due to the positive
inductive effect of the methyl substituent that stabilizes the cationic intermediate,
more pronounced in 8-cat then in 7-cat or 9-cat. Our observation of meta-effect is
also in agreement with precedent theoretical investigation [29].
Photochemical reactivity of iodide salts 7a–9a in charge transfer reactions was
investigated by recording UV–vis spectra during the irradiation, where formation of
I3- species was clearly observed. For example, Fig. 2 shows the changes in spectra
upon irradiation of 8a, where a decrease of absorbance at 235 and 265 nm indicate a
disappearance of I- and pyridinium chromophores, whereas an increase of
absorbance at 290 and 360 nm indicates formation of I3-. In particular, the
absorption band at 235 nm corresponds to a charge transfer transition [32]. It is
clearly demonstrated by UV–vis spectra at different H2O content where the
absorption band shifts hypsochromically with the increase of solvent polarity (See
Fig. S4 in the supporting information). Thus, upon excitation, an electron is
transferred from I- to the pyridinium forming a radical pair. Escape of the iodine
radicals from the cage leads to the formation of I2 and I3- (Scheme 6). However, by
1H NMR we did not detect the presence of any bispyridine or reduction product,
Table 2 Quantum yield of
photohydration (UH2O) of 7a–
Compound
UH2O
9aa
7a
8a
9a
0.027 0.003
0.06 0.02
a
Determined by use of a
valerophenone actinometer
0.014 0.003
(U254 = 0.65 0.03) [19, 20]
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V. Blazek Bregovic, N. Basaric
Fig. 2 Changes in the UV–vis
spectra of 8a upon irradiation in
CH3CN–H2O (9:1). The
irradiation was performed at
254 nm and the spectra were
recorded in the irradiation
intervals of 0.5–5 min
Scheme 6 Charge transfer
transition in 8a leading to the
formation of I3
-
indicating that the recombination of pyridyl radicals does not take place or leads to
the formation of high molecular weight products.
-
Whereas charge transfer transition and formation of I3 are important in the
application of pyridinium salts as photocages, [17] it is an energy wasting process
in the synthetic applications. Therefore, we determined quantum efficiency for the
-
chromophore disappearance and formation of I3 from 7a to 9a by use of a KI/
KIO3 actinometer (Table 3) [20, 21]. Moreover, we investigated the influence of
solvent polarity and presence of O2 to the reaction efficiency. Irradiations were
performed in N2-purged, air-saturated and O2-purged solutions where we
examined the efficiency of the iodine formation, as well as the decay of the
Table 3 Quantum efficiency for the compound degradation (Ud) and I3- formation (UI) for 7a–9a in N2-
purged and air-saturated solutionsa
Compound
Udb
Udc
UIb
UIc
7a
8a
9a
a
0.075 0.005
0.10 0.01
0.07 0.01
0.14 0.04
0.10 0.05
0.10 0.03
0.02 0.01
0.02 0.01
0.02 0.01
0.015 0.05
0.015 0.05
0.018 0.06
Irradiated at 254 nm and determined by use of a KI/KIO3 actinometer (U254 = 0.74) [20, 21]
b
c
N2-purged solution
Air-saturated solution
123

Competing processes in the photochemistry of picolines…
photochemically formed I3-. Results in Table 3 and Fig. S7 in the supporting
-
information indicate that I3 is formed with similar efficiency when the solution
contained O2, suggesting that no quenching or negligible quenching of the excited
state took place.
Monitoring of the absorbance of 8a after the irradiation at 254 nm indicates that
some intermediates or primary products formed in the photochemical reaction are
not stable. Their decay was monitored over 1 h wherein we observed slower kinetics
in the presence of O2 than in the Ar-purged solution (see Fig. S8 in the supporting
information). However, we were not able to isolate intermediates in the charge-
transfer photochemistry or get more confident spectroscopic proofs for their
structure.
-
Efficiency of the I3 formation was also tested at different H2O contents and
different 8a substrate concentrations. Whereas in the tested substrate concentration
range no significant influence to the reaction efficiency was observed, H2O
-
concentration affected the charge transfer transition and the efficiency for the I3
-
formation. At higher H2O concentration the efficiency of the I3 formation
decreases (see Fig. S9 in the supporting information), presumably due to competing
photohydration. Thus, at higher H2O concentration, disappearance of the substrate
was more efficient.
Irradiation of pyridine iodide salts at 254 nm gives rise to the charge transfer
transition and formation of iodine. On the contrary, perchlorate has a high oxidation
potential rendering such a transfer energetically impossible. Therefore, we
performed photochemical experiments with pyridinium iodide and perchlorate
isomers to probe for the counter-ion effect. Interestingly, NMR spectra after the
irradiation indicate formation of different products than from the iodide salts. Again,
attempts to isolate the products failed. However, the observed difference can be
associated to acid-catalyzed aziridine opening by photorelease of a strong acid,
HClO4, as shown in Scheme 7. 1H NMR spectrum after irradiation of 8b showed th
presence of two compounds in approximate ratio 1:1 with characteristic signals
clearly corresponding to 18 and 19, in agreement with precedent literature [7].
Scheme 7 Photohydration of 8b followed by aziridine ring opening
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V. Blazek Bregovic, N. Basaric
Conclusions
Photochemical reactivity of a series of picolines and their N-methylated salts has
been investigated. Picolines are not reactive in phototransposition, probably due to
protonation of pyridine nitrogen in the excited state. Deuterium exchange was
observed upon irradiation in CD3CN–D2O, presumably due to photoionization and
radical formation. On the other hand, N-methylated picoline salts are not protonated
upon excitation. They undergo photohydration and phototransposition. A difference
in reactivity was observed between perchlorate and iodide salts. Upon irradiation of
iodides, azabicyclic[3.1.0] hydration products were obtained, whereas due to
photoelimination of perchloric acid thermal aziridine ring opening takes place.
Excitation of iodide pyridinium salts gives rise to change transfer transition forming
iodide radicals that eventually give I3-. Revealing the photochemical reactivity of
these simple chromophores is of significant importance in the application of these
molecules as photocages or in the synthesis of complex polycycles.
Acknowledgments These materials are based on work financed by the Croatian Ministry of Science
Education and Sports (MZOS) and the Croatian Science Foundation (HRZZ Grants 02.05/25 and IP-
2014-09-6312).
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