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REVIEW ARTICLE
Molecular structures of metal macrocyclic compounds with nitrogen,
oxygen, and sulfur atoms in macrocycles arising in Bself-assembly^
processes: quantum-chemical modeling
O. V. Mikhailov
1
Received: 27 November 2017 /Accepted: 30 January 2018 /Published online: 26 February 2018
#Springer Science+Business Media, LLC, part of Springer Nature 2018
Abstract
The results of quantum-chemical calculations of the molecular structures of d-metal macrocyclic chelate complexes with com-
partmental and macrocyclic (N,O)- and (N,S) donor atomic ligands arising as a result of Bself-assembly^process have been
systematized and generalized. It has been noticed that, generally, for such coordination compounds, molecular structures with
noncoplanar chelate nodes and noncoplanar macrocycles are more typical than those with coplanar ones. The review covers the
works of the author and other researchers carried out mainly over the past 20 years.
Keywords d-Element .Macrocyclic compound .Self-assembly .Molecular structure .DFT method
Introduction
As is well known macrocyclic p-, d-, and f-metal complexes
distinguished by the presence of three or more combined
(come together) metal chelate rings each of which share at
least two atoms with a neighboring chelate ring, have occu-
pied and continues to occupy a special position in modern
coordination chemistry a long time ago. These unique com-
pounds are very often obtained as a result of extremely spe-
cific chemical reactions in which at least one of the ligands in
the inner coordination sphere of such a complex is
Bassembled^from simpler Bbuilding blocks,^and this self-
assembly occurs only in the presence of certain metal ions.
(In coordination chemistry, more specific terms are used to
denote such a Bself-assembly,^namely, Btemplate synthesis,^
Btemplate process,^or Btemplate reaction^). Towards the end
of the twentieth century, the number of publications devoted
to the synthesis of macrocyclic metal complexes amounted to
thousands (in particular, more than 800 publications devoted
to this field of chemistry were cited in the monograph [1]). It
should be noted in this connection that the inner coordination
sphere of the vast majority of these compounds is formed by
3d-metal ions and polydentate organic ligands with N, O, and
S donor atoms [2–11].
To predict the physico-chemical properties of macrocyclic
metal complexes and to control the processes of their synthe-
sis (Bself-assembly^), information about their molecular struc-
tures is very important. However, in a number of cases, its
determination for such chemical compounds presents very
significant difficulties, since these compounds cannot be iso-
lated from the reaction system in the form of single crystals
suitable for carrying out XRD analysis. This situation, in par-
ticular, occurs when the Bself-assembly^of these compounds
is carried out in a polymer matrix, for example, in a gelatin
massif. In this regard, to determine the parameters of the mo-
lecular structures of macrocyclic metal complexes formed in
polymer layers, the quantum-chemical methods for calculat-
ing these structures became paramount, especially those based
on the density functional theory (DFT). This method has now
become very popular; it allows to predict with sufficient reli-
ability not only qualitative, but also quantitative characteris-
tics of the structures of macrocyclic metal complexes. There
are, of course, numerous studies in which quantum-chemical
modeling of macrocyclic metal complexes have been per-
formed to an extent using various versions of quantum-
chemical calculations. However, any systematization of the
published works devoted to quantum-chemical modeling of
the molecular structures of macrocyclic metal complexes of
*O. V. Mikhailov
olegmkhlv@gmail.com
1
Kazan National Research Technological University, Kazan, Russia
420015
Structural Chemistry (2018) 29:777–802
https://doi.org/10.1007/s11224-018-1091-7
3d-element ions with polydentate organic ligands containing
N, O, and S donor atoms, by using DFT method, was not
implemented up to now. In this connection, the present
review will be devoted to the generalization and discus-
sion of publications dealing with quantum-chemical cal-
culations of the molecular structures of namely such
macrocyclic metal complexes, and, in the first instance,
that were found as products of self-assembly in
biopolymer-immobilized matrices. Along with this, com-
plexes that are close to them in terms of chemical com-
position, which according to the data of such a calcula-
tion can arise in these specific conditions of complexa-
tion, will be considered here, too.
Specific of quantum-chemical calculation
of molecular structures of macrocyclic metal
complexes
In the works devoted to the quantum-chemical calculation of
the molecular structures of macrocyclic metal complexes, the
DFT was used in the B3LYP/6-31G(d) and DFT OPBE/TZVP
level of theory. In the first of these, the Becke exchange func-
tional [12] and the Lee-Yang-Parr correlation potential de-
scribed in [13] were used. In the framework of second variant,
quantum-chemical calculations were performed by the DFT
method using the standard TZVP extended spit-valence basis
set [14,15] and the OPBE nonhybrid functional [16,17]. In
the case of 3d-metal complexes, this level of theory has been
shown to give rather accurate relative energy stabilities of the
high- and low-spin states [17–21]. At the same time, the
OPBE/TZVP method reliably characterizes the geometric pa-
rameters of molecular structures of these compounds.
Calculations were performed with the Gaussian09 program
package [22]. The correspondence of the found stationary
points to energy minima was proved in all cases by the calcu-
lation of the second derivatives of energy with respect to the
atomic coordinates: all equilibrium structures corresponding
to minima on the potential energy surfaces had only real pos-
itive frequencies. The following multiplicities were consid-
ered for the M(II) complexes: 2, 4, and 6 for the Mn(II) and
Co(II) complexes; 1, 3, and 5 for the Fe(II) complex; 1 and 3
for the Ni(II) and Zn(II) complexes; and 2 and 4 for the Cu(II)
complex. Among the optimized structures, the structure with
the lowest energy was selected. The parameters of the molec-
ular structures with multiplicities other than 1 were always
calculated by the unrestricted (UHF) method; at multiplicity
1, the restricted (RHF) method was used. For complexes with
multiplicity 1, the unrestricted method in combination with
option GUESS=Mix was also used; in this case, the compu-
tational results were always analogous to the results obtained
by the restricted method. Also, the corrections for the disper-
sion were taken into account, they were envisaged in the
framework of the calculations. To visualize the structures,
various versions of the ChemCraft program were used. (It
should be noted in this connection that using this program,
images of the structures of the metal chelates that presented in
this paper were created.)
At present, macrocyclic metal complexes (chelates)
are commonly subdivided into two categories: chelates
with so-called open contour and chelates with so-called
closed contour. The first category involves chelate com-
plexes in which the complex-forming metal atom is lo-
cated at the rim of the macrocycle and is among the
atomsthatformit(formulaII.1); the second category
involves chelate complexes in which the complex-
forming metal atom is located inside the macrocycle
and is not involved in the formation of the macrocyclic
cycle (formula II.2). As a rule, metal chelates of the
first type contain three combined metal chelate cycles
and metal chelates of the second type contain four such
cycles.
CH
3
OO
O
N
HN
Cl
HN
M
CH
3
II.1
It may be subdivided into macrocyclic metal chelates,
also, by their assortment of combined metal chelate cycles
and, first of all, by the number of atoms in each of them,
which are denoted by digital indices in parentheses; the
number of these digital indices corresponds to the total
number of chelate cycles. So, a macrotricyclic metal com-
plex containing two 5-membered cycles and one 7-
membered cycle should be denoted as (575) or (557). A
macrotetracyclic metal complex with two 4-membered and
two 6-membered cycles can be denoted as (4646), (6464),
(4664), (6446), (4466), or (6644) depending on the ar-
rangement of these chelate cycles in the complex molecule
N
NN
N
M
N(CH3)2
Br
II.2
778 Struct Chem (2018) 29:777–802
and the order of numbering. In what follows, for definite-
ness, these chelate cycles are numbered beginning the up-
per left cycle and further counter clockwise; taking into
account this circumstance, the metal complexes represented
by formulas II.1and II.2should be referred to as
(576)macrotricyclic, and (6664)macrotetracyclic, respective-
ly. In addition, in the framework of each of these catego-
ries of macrocyclic metal chelates, two more subcategories
can be identified, namely, so-called symmetric and asym-
metric complexes; the former have a symmetry plane per-
pendicular to the plane in which the structural formula of
the given complex is shown and the latter lack such a
plane. In asymmetric complexes, the sets of atoms in met-
al chelate cycles with the same number of members can
be different as well as identical.
Molecular structures of metal macrocyclic
compounds with three combined cycles
Macrocyclic metal complexes of this type contain so-
called compartmental ligands in the inner coordination
sphere, which are acyclic polydentate organic com-
pounds distinguished by a spatial arrangement of do-
nor sites responsible for the formation of Bpre-orga-
nized chambers^for coordination of one or several
metal ions [9]. In all currently available studies deal-
ing with quantum-chemical calculations of biopolymer-
immobilized macrocyclic metal chelates, these ligands
are tetradentate and form, as a rule, the MN
2
S
2
,
MN
2
O
2
,orMN
4
chelate nodes, and the resulting coor-
dination compounds are macrotricyclic metal com-
plexes. In the overwhelming majority of these papers,
the molecular structures of the macrotricyclic chelates
of 3d-metals—Mn(II), Fe(II), Co(II), Ni(II), Cu(II), and
Zn(II)—have been considered [23–53]. Only in the lat-
est two works [54,55] the structures of 4d-metal
macrotricyclic compounds have been described. The
quantum-chemical calculation of molecular structures
in them has been performed using the DFT B3LYP/6-
31G(d) as well as DFT OPBE/TZVP level of theory.
The greatest attention has been attracted to
(565)macrotricyclic metal chelates and much less atten-
tion, to (555) macrotricyclic compounds; other types of
macrotricyclic complexes have been mentioned only
occasionally, and sometimes even in isolated cases. It
is precisely in this order we discuss them below.
(565)Macrotricyclic metal chelates Macrotricyclic metal che-
lates with this set of chelate rings have been discussed in
[23–28,30,31,35,37,38,44,46,47,49]. Most of these
papers have addressed Bsymmetric^complexes containing
chelate rings with an identical set of atoms [23–28,30,
31,37,38,47]; those were mainly complexes containing
the MN
2
S
2
chelate core. Most of these complexes are
noncoplanar, contrary to expectations based on the rigidity
of their structures. The degree of deviation from coplanar-
ity (for chelate nodes, it can be quantitatively characterized
by the difference (BAS–360°), where BAS is the X–M–Y
bond angle sum (X and Y are donor atoms, and M is the
metal atom in the corresponding chelate node). For chelate
rings, it can be evaluated by the difference between bond
angle sums in 5- and 6-membered chelate rings (BAS
5
and BAS
6
, respectively) and the sum of angles in the
corresponding planar polygon (540° and 720°, respective-
ly) turns out to be significant in many cases. Several tens
of degrees as, for example, in M(II) complexes with 2,8-
dithio-3,7-diaza-5-oxanonanedithioamide III.1[23,27].
Among these complexes are both metal chelates for which
(BAS–360°) < 0, so that their MN
2
S
2
chelate nodes have a
tetragonal-pyramidal structure, as in complex with 2,8-
dithio-3,5,7-triazanonane-dithioamide III.2[31], and metal
chelates with (BAS–360°) > 0 and a pseudotetrahedral or
even quasitetrahedral structure of the coordination nodes,
as, for example, with the deprotonated form of 2,3,7,8-
tetraaza-5-oxanonanedithioamide, isomeric to correspond-
ing complexes III.1[37]. Molecular structures of some
of these compounds have been shown in Fig. 1.
Complexes with negative (BAS–360°) values [23,24,31,
32] are less common in this category of macrocyclic metal
chelates than complexes with positive values of this pa-
rameter [25,26,35,37,38,44,46,47,49]. The N
2
S
2
or
N
4
group of donor atoms in tetragonal-pyramidal com-
plexes is often either exactly planar or has rather insignif-
icant deviations from coplanarity [23,24,31,32]. In tet-
rahedral complexes, the noncoplanarity of this moiety of
the metal chelate node is much more pronounced [25,26,
35,37,38,44,46,47,49]. As for the metal–donor atom
bond lengths in the chelate nodes, they monotonically de-
crease in going from Mn to Ni and monotonically increase
in going from Ni to Zn (which can be generally consid-
ered adequate to the change in M(II) radii), although in
some cases, there are deviations from this general rule. In
particular, in the M(II) chelates studied in [47], one of the
M–N bonds is the shortest in the Ni(II) complex
(186.6 pm), while the other bond is the shortest in the
Co(II) complex (191.9 pm). In M(II) chelates with
deprotonated 2,3,7,8-tetraaza-5-oxanonanedithioamide,
where the metal–nitrogen bond lengths are the same, a
more complicated behavior of these bond lengths along
the series is observed. They decrease in going from Mn
to Fe, increase from Fe to Co, decrease from Co to Ni,
and increase from Ni to Zn. A similar pattern is observed
for the metal–sulfur bonds, which are somewhat different
in each of these complexes [37].
Struct Chem (2018) 29:777–802 779
HN
S
SS
S
NH
HN NH
O
M
III.1
In accordance with theoretical expectations, the 5-
membered chelate rings in symmetric complexes of this type
turn out to be at least very similar to each other, if not complete-
ly identical. They have not only close (BAS
5
–540°) values but
also close bond angles formed by the ring atoms [23–28,30,
31,35,37,38,44,46,47,49]. As for coplanarity of chelate
rings, there are both the complexes with strictly planar rings
and the complexes with rings significantly distorted from co-
planarity. Any correlation is not observed between the degree
of noncoplanarity of the chelate node and degrees of
noncoplanarity of chelate rings in a complex. In the metal che-
lates under consideration, both the 5- and 6-membered chelate
rings are, as a rule, noncoplanar. There are only two
(565)macrotricyclic complexes where all three chelate rings
are strictly planar: the Fe(II) and Ni(II) complexes with 4,6-
dimethyl-2,3,7,8-tetraaza-3,6-nonadiene-1,9-dithioamide
(III.3), formed by self-assembly in the M(II) ion–
hydrazinecarbothioamide–2,4-pentanedione system [38].
Molecular structures of some of chelates III.3have been
presented in Fig. 2. In the (565)macrotricyclic complexes
formed by the other M(II) ions considered in the same paper,
namely, by Mn(II), Co(II), Cu(II), and Zn(II), the (BAS
5
–
540°) and (BAS
6
–720°) values for their 5- and 6-membered
rings, respectively, differ from zero, even if insignificantly.
(By 5.9°, 6.1°, and 0.2° in the Mn(II) complex; by 2.9°,
3.3°, and 0.0° in the Co(II) complex; by 1.8°, 2.4°, and 0.2°
in the Cu(II) complex; by 8.2°, 8.5°, and 0.2° in the Zn(II)
complex, respectively; all these values are positive). The rea-
son for this interesting structural effect has not yet been eluci-
dated. But it is noteworthy that, among all the
(565)macrotricyclic metal chelates calculated so far by the
DFT method, the complexes with 4,6-dimethyl-2,3,7,8-
tetraaza-3,6-nonadiene-1,9-dithiomide are the only ones
where the 6-membered ring contains two double bonds, and
it can be assumed that this circumstance somehow favors the
coplanarity of the above metal chelates. In the Co(II) complex
with the same compartmental ligand, the 5-membered chelate
rings deviate, even if slightly, from planarity, while the 6-
membered ring is ideally flat. The latter is all the more inter-
esting, given that the opposite situation (i.e., when both 5-
membered chelate rings in the complex would be coplanar
Fig. 2 Molecular structures of
Ni(II) and Zn(II) chelates with
general formulas III.3
Fig. 1 Molecular structures of
Cu(II) chelates with general
formulas III.1and III.2
HN
S
S
S
S
NH
HN NH
M
NH
III.2
H2NNH2
SS
N
M
H3C
N
CH3
NN
M = Fe, Ni
III.3
780 Struct Chem (2018) 29:777–802
while the 6-membered ring would nonplanar), for
(565)macrotricyclic metal chelates has been still not recorded.
Taking into account the statistical data presented in the publi-
cations cited above (namely, the fact that the noncoplanarity of
6-membered chelate rings is generally more pronounced than
that of 5-membered rings), this situation seems to be more
likely.
Quantum-chemical calculations of isomeric
(565)macrotricyclic metal chelates differing from one an-
other either in the composition of chelate nodes [24,28,
37] or in the orientation of substituents at the macrocyclic
rings [44,47] have been performed. In this respect, a
typical (and presumably most interesting) study was pre-
sented in [28]whereBsymmetric^metal chelates with dif-
ferent sets of chelate nodes, namely, MN
2
O
2
(III.4),
MN
2
S
2
(III.5), and MN
4
(III.6and III.7)wereconsid-
ered. According to computational data, isomer III.6for
any M(II) ion is the lowest-lying one on the energy scale
(Table 1). Although for the majority of the M(II) complex-
forming ions considered in [28], such a conclusion seems
to be quite expected, let us note that for Cu(II), which is
so-called Pearson soft acid, the more characteristic would
still be coordination through two nitrogen atoms and two
sulfur atoms, i.e., III.5. However, it is worth noting that,
in the case of this particular M(II), III.5is next in energy
after III.6and the energy difference E(III.5)–E(III.6)is
the smallest [28].
In conclusion of this paragraph, it should be noted that all
(565)macrotricyclic metal chelates either have a little number
of symmetry elements [namely, one plane of symmetry pass-
ing through the M atoms and the most distant atom of the 6-
membered chelate ring (group of symmetry C
s
)]. Sometimes,
one twofold axis and two symmetry planes (C
2v
) or are asym-
metric (i.e., have no elements of symmetry at all). This is
partially responsible for rather high electric dipole moments
μexhibited by these compounds (3.0 D or higher). Most of
them in the ground state have the same spin multiplicities as
the corresponding complex-forming agents in a tetragonal-
Table 1 Total energies E(in
hartrees) corrected for zero point
energies of complexes III.4–
III.7for different M(II). The
values in square brackets are
relative energies in kJ/mol (in all
cases, measured from the lowest
total energy Eof a complex taken
to be zero) [28]
M(II) E(III.4)E(III.5)E(III.6)E(III.7)
Mn(II) –2625.262776
[80.2]
–2625.276748
[43.5]
–2625.293321
[0.0]
–2625.291972
[3.5]
Fe(II) –2737.937547
[123.1]
–2737.949723
[91.1]
–2737.984433
[0.0]
–2737.953917
[80.1]
Co(II) –2856.956914
[147.7]
–2856.978534
[91.0]
–2857.013186
[0.0]
–2856.984953
[74.1]
Ni(II) –2982.480594
[131.3]
–2982.496610
[89.3]
–2982.530616
[0.0]
–2982.512103
[48.6]
Cu(II) –3114.603394
[117.8]
–3114.634830
[35.3]
–3114.648281
[0.0]
–3114.629101
[50.4]
Zn(II) –3253.465392
[136.5]
–3253.504677
[33.3]
−3253.517373
[0.0]
–3253.514115
[8.6]
HN
S
OO
S
NH
HN NH
O
M
III.4
HN
O
SS
O
NH
HN NH
O
M
III.5
N
O
S
S
O
N
HN NH
O
M
H
H
III.6
N
O
S
S
O
N
HN NH
O
M
H
H
III.7
Struct Chem (2018) 29:777–802 781
pyramidal or tetrahedral environment of donor atoms (6 for
the Mn(II) complexes, 2 or 4 for Co(II) complexes, 1 for
Ni(II), 2 for Cu(II), and 1 for Zn(II) complexes). Exceptions
are only Fe(II) chelates most of which have the triplet ground
state [28,35,37,38].
(555)Macrotricyclic complexes Macrocyclic metal chelates of
this type have also been addressed in a number of works
[32–34,36,40–42,45,46,48,50,54,55]. Most of these
works have focused on symmetric complexes with the
MN
2
S
2
chelate node formed by three 5-membered chelate
rings [32–34,36,41,48,50,54,55], although some
studies have considered asymmetric complexes [35,40,
42,45]. Typical examples of the symmetric complexes
are Mn(II), Fe(II), Co(II), Ni(II), Cu(II), and Zn(II) che-
lates with compartmental tetradentate chelants, such as
1,8-dimercapto-2,3,6,7-tetraaza-1,3,5,7-octatetraene-1,8-di-
amine [36]III.8and its 4,5-dimethyl-substituted derivative
III.9[34]. The asymmetric complexes can be exemplified
by chelate of the same M(II) ions with 8-imino-8-
mercapto-7-thio-2,3,6-triaza-3,5-octadienethioamide III.10
[42] and 4,5-dimethyl-1,8-diimino-1,8-dimercapto-2,3,6-
triaza-3,5-octadiene-7-thione III.11 [45]. Molecular struc-
tures of some of them are given in Figs. 3and 4. First
of all, let us note that, as distinct from (565)macrotricyclic
metal chelates generally exhibiting significant degrees of
deviation from coplanarity, all (555)macrotricyclic metal
chelates considered in [32–34,40–42,45,46,48,50,
54,55] show either a strictly planar chelate node or only
weak deviation of it from coplanarity. Moreover, they
commonly have planar or near-planar molecular structures,
both symmetric and asymmetric complexes. Qualitatively,
the structures of (555)macrotricyclic complexes depend rel-
atively slightly on both the nature and the electronic struc-
ture of the M(II) atom as well as on the composition of
the chelate node, be it MN
2
S
2
,MN
2
O
2
,orMN
4
. The
deviation from coplanarity is most pronounced for Zn(II)
complexes [33,40,45], for which (BAS–360°) > 0 (17.0°,
6.0°, and 6.8°, respectively) and, hence, the chelate nodes
have a pseudotetrahedral structure. In the vast majority of
(555)macrotricyclic metal chelates, both symmetric and
asymmetric, the groups of the chelant donor atoms N
2
S
2
,
N
2
O
2
,andN
4
turn out to be perfectly planar. All the three
5-membered chelate rings in them are either exactly planar
or have insignificant deviations (no more than 2°–3°) of
the (BAS
5
–540°) parameters from zero. In symmetric
complexes, geometrically analogous bond angles in
Boutermost^5-membered rings (i.e., those rings that share
only the M atom) are, as a rule, identical. It is interesting
that the 5-membered chelate ring that is formed as a result
of the so-called template cross-linking and contains, in
addition to M, two nitrogen atoms and two carbon atoms
sometimes shows even a smaller deviation from coplanar-
ity than the other two adjacent 5-membered chelate rings;
such a phenomenon was observed, in particular, in [34,
36]. For Mn(II), Fe(II), Co(II), Ni(II), Cu(II), and Zn(II)
chelates III.8with 1,8-dimercapto-2,3,6,7-tetraaza-1,3,5,7-
octatetraene-1,8-diamine, the bond angle sums BAS
5
in
each of the two outermost chelate rings are 539.7°,
539.8°, 539.5°, 540.0°, 540.0°, and 537.8°. In the third
ring, they are 540.0°, 539.8°, 540.0°, 540.0°, 539.6°, and
538.8°, respectively [36]. Only in one case, namely, in the
Cu(II) complex, is the deviation from coplanarity of the
third ring is more significant than that of the first two
ring. In all other cases, either the BAS
5
values are the
same (in the Fe(II) complex) or there or an opposite pro-
portion between these values.
Fig. 3 Molecular structures of
Fe(II) and Co(II) chelates with
general formula III.8
Fig. 4 Molecular structures of
Mn(II) and Cu(II) chelates with
general formula III.11
H2NNH2
SS
N
M
N
NN
III.8
782 Struct Chem (2018) 29:777–802
Theoretically, it is of interest to evaluate the relative stability
of isomeric metal chelates with both different compositions of
chelate nodes and different orientation of substituents at
macrocycles. This issue has been already discussed above when
we considered (565)macrotricyclic complexes; it should be not-
ed that in the case of (555)macrotricyclic metal chelates, much
more attention has been paid to this issue in the literature than in
the case of (565)macrotricyclic complexes. This is exemplified
by publications [32,34,40–42,45,48,50]. The most typical
here is article [40] dealing with M(II) complexes (M = Mn, Fe,
Co, Ni, Cu, Zn) with four tautomeric forms of a chelant but with
the same chelate nodes MN
2
S
2
III.12,III.13,III.14 and III.15
that can be formed by self-assembly in the M(II)–ethane-
dithioamide–hydrazinecarbothioamide–2,3-butanedione qua-
ternary systems. According to calculation, the lowest-lying
complex among them is III.13 in most cases, and only for
Zn(II) is structure III.12 more favorable (see Table 2). In some
of these asymmetric (555)macrotricyclic complexes, chelate
rings with the same number and set of atoms have different sets
of bond angles, but the sums of angles in these chelate rings
nevertheless turn out to be either exactly or nearly the same.
This unique situation is observed for the Mn(II), Fe(II), Co(II),
and Ni(II) complexes of type III.13. Here, the BAS
5
in all
chelate rings is exactly 540° [in which (BAS–360°) is either
zero (Mn(II) and Ni(II)) or nearly zero (Fe(II) and Co(II)].
Non-bonded angle sum in tetragons formed by the donor nitro-
gen and sulfur atoms (NBAS) is exactly 360°), as well as in the
analogous Cu(II) complex where BAS
5
in each of the three 5-
membered rings is 539.2° [40]. Besides, the most energetically
favorable structure for the Zn(II) chelate is not structure III.13,
as in the case of the other M(II), but structure III.12.In this
structure, the distance between the methyl carbon atom and the
thione sulfur atom (339.2 pm) is considerably shorter than that
in the other complexes (from 544.9 pm in the Mn(II) chelate to
551.2 pm in the Ni(II) complex). The key parameters of struc-
ture III.12 of the Zn(II) complex are much closer to the key
parameters of structure III.13 of the other M(II) than the key
parameters of structure the III.13 of the Zn(II) complex.
Table 2 Total energies E(in
hartrees) corrected for zero point
energies of complexes III.12–
III.15 for different M(II). The
values in square brackets are
relative energies in kJ/mol (in all
cases, measured from the lowest
total energy Eof a complex taken
to be zero) [40]
M(II) E(III.12)E(III.13)E(III.14)E(III.15)
Mn(II) −2852.228212
[27.3]
−2852.238629
[0.0]
−2852.207291
[82.3]
−2852.217230
[56.2]
Fe(II) −2964.985677
[23.2]
−2964.994515
[0.0]
−2964.964800
[78.0]
−2964.973315
[55.7]
Co(II) −3084.101701
[20.6]
−3084.109543
[0.0]
−3084.085542
[63.0]
−3084.084917
[64.7]
Ni(II) −3209.726188
[19.6]
−3209.733650
[0.0]
−3209.701443
[84.6]
−3209.708689
[65.5]
Cu(II) −3341.929552
[12.2]
−3341.934194
[0.0]
−3341.904007
[79.3]
−3341.908481
[67.5]
Zn(II) −3480.851082
[0.0]
−3480.835446
[41.0]
−3480.827048
[63.1]
−3480.816162
[91.7]
H
2
NNH
2
SS
N
M
H
3
C
N
CH
3
NN
III.9
HN
S
S
N
M
NH
2
S
NN
III.10
HN
S
S
N
M
NH
S
N
H
3
CCH
3
NH
III.11
HN
S
S
N
M
NH2
S
N
H3C
N
III.12
Struct Chem (2018) 29:777–802 783
As in the (565)macrotricyclic metal chelates, the
(555)macrotricyclic complexes show, on the whole, the
same trends in bond lengths between the central M
atom and the donor atoms (M–NandM–S). And name-
ly, the bond lengths decrease in going from Mn to Ni
andincreaseingoingfromNitoZn;therearealso
some deviations from this trend. Expected from general
theoretical considerations, the M–S bond lengths are
significantly longer than the M–NandM–O bond
lengths. The symmetric (555)macrotricyclic metal che-
lates described in the literature also have few symmetry
elements, namely, they have either one twofold axis in
combination with two mutually perpendicular symmetry
planes and, thus, group of symmetry C
2v
(if they are
perfectly planar) or only one plane of symmetry and
group of symmetry C
s
(if they are, on the whole, non-
coplanar). The asymmetric metal chelates with three 5-
membered rings, as a rule, should be devoid of symme-
try elements by definition; exceptions are only perfectly
planar complexes, which can have only one symmetry
plane passing through all atoms of the macrocycle and
the M atom. Since they lack the center of symmetry,
they are expected to have rather high electric dipole
moments (μ). Indeed, quantum-chemical DFT calcula-
tions predict significant dipole moments for both types
of complexes: for example, for the different complexes,
the dipole moments are within the limits from 2.35 (Ni)
to 2.91 (Fe) D [56],from1.47(Mn)to3.92(Ni)D
[50], from 2.94 (Co) to 3.83 (Cu) D [57], and from
2.73 (Zn) to 8.48 (Co) D [42]. (Interestingly, the next
value of dipole moment after the Zn(II) complex was
found for the Mn(II) complex, 7.90 D), and from 8.06
(Zn) to 9.08 (Co) D [40].) However, there are excep-
tions: for example, for the complexes described in [33],
the dipole moments are within the range from 0.30 (Ni)
to 3.96 (Zn) D. As can be seen from these values, there
is no correlation between the dipole moment and the
M(II) nature; the only trend that is observed is that μ
values for the symmetric complexes are generally lower
than those for the asymmetric complexes. Four of the
six central atoms M(II) considered in the above publi-
cations, namely Co(II), Ni(II), Cu(II), and Zn(II), in the
ground state have the same spin multiplicities as the
corresponding complex-forming atoms in a tetragonal-
pyramidal or tetrahedral environment of donor atoms
[2 for the Co(II) complexes, 1 for Ni(II), 2 for Cu(II),
and 1 for Zn(II)]. Exceptions against this background
are only the Mn(II) and Fe(II) chelates, which have,
respectively, a quartet and triplet ground state. The only
Fig. 5 Molecular structures of
Rh(II) and Ag(II) chelates with
general formula III.16 and III.17
Table 3 Total energies E(in hartrees) corrected for zero point energies
of complexes with the MN
2
S
2
(III.16)иMN
4
(III.17) chelate nodes for
different M(II) in the gas phase. The values in square brackets are relative
energies in kJ/mol (in all cases, measured from the lowest total energy E
of a complex taken to be zero) [54,55]
M(II) E(III.16)E(III.17)
Mo(II) −6021.249119 [0.0] −6021.237988 [29.2]
Tc(II) −6250.771513 [0.0] −6250.760050 [30.1]
Ru(II) −6487.654750 [0.0] −6487.635976 [49.3]
Rh(II) −6732.074667 [0.0] −6732.063863 [28.4]
Pd(II) −6984.231040 [0.0] −6984.229051 [5.2]
Ag(II) −7243.989341 [60.6] −7244.012438 [0.0]
Cd(II) −7511.621916 [66.9] −7511.647408 [0.0]
HN
S
S
N
M
NH
2
S
N
CH
3
N
III.13
HN
S
S
N
M
NH
S
N
H3C
NH
III.14
HN
S
S
N
M
NH
S
N
CH
3
NH
III.15
784 Struct Chem (2018) 29:777–802
exception here is the Mn(II) chelate described in [48],
which has a sextet ground state.
Two m ost recen t studies [54,55] have dealt with isomeric
(555)macrotricyclic 4d-M(II) chelates (M is Mo, Tc, Ru, Rh,
Pd, Ag, Cd) with the already mentioned compartmental
tetradentate ligand, 2,7-dithio-3,6-diaza-3,5-octadiene-1,8-
dithioamide, which have chelate nodes of different composi-
tions, namely, MN
2
S
2
[54]III.16 and MN
4
[55]III.17.The
examples of molecular structures of these complexes can see
on the Fig. 5.
Comparison of data for these chelates shows that for
Mo(II), Tc(II), Ru(II), Rh(II), and Pd(II), more energetically
stable are the complexes with the MN
2
S
2
chelate node, where-
as for the Ag(II) and Cd(II) complexes of the same composi-
tion, those with the MN
4
chelate node are more stable
(Table 3). An even more interesting fact that the [E(III.17)–
E(III.16)] values increase in going from Mo(II) to Ru(II) and
decrease in going from Ru(II) to Pd(II) but remain positive; in
going from Pd(II) to Ag(II) and then to Cd(II), [E(III.17)–
E(III.16)] changes the sign and its magnitude sharply in-
creases. In the complexes with the MN
2
S
2
chelate node, the
d(M–S) and d(M–N) bond lengths, being pairwise equal,
change differently along the Mo–Cd series. The former first
decrease and then increase and the minimal d(M–S) value is
observed for the Rh(II) complex; the latter decrease in going
from Mo to Ru, increase from Ru to Rh, decrease again from
Rh to Pd, and increase again from Pd to Cd, and the minimal
d(M–N) value is achieved for the Ru(II) complex. It is inter-
esting that something similar happens in complexes with the
MN
4
chelate node where the d(M–N) bond lengths are also
only pairwise equal: for one pair, in going from Mo to Cd, the
same pattern of changes in metal–nitrogen bond lengths is
observed as in the complexes with the MN
2
S
2
chelate node;
for the other, a pattern analogous to the change the metal–
sulfur bond length is observed. In full accordance with the
theoretical expectations, d(M–N) in all these metal chelates
is smaller than d(M–S) [54,55].
Macrotricyclic metal chelates with other sets of chelate rings
Publications focusing on the types of macrotricyclic metal
chelates, other than those considered in previous paragraphs,
are few in number, namely, [29,39,43,51–53], and the last
three of them were published in the same year as this review.
These studies present (454)macrotricyclic [53],
(464)macrotricyclic [51], (545)macrotricyclic [39],
(575)macrotricyclic [52], and (666)macrotricyclic [29,43]
3d-M(II) chelates. The array of works on these complexes is
still insufficient for any serious generalizations; therefore, the
review here is limited to a rather brief description of the
above-listed works in the above sequence.
(454)Macrotricyclic metal chelates III.18 with the com-
partmental chelant 1,2-di[(mercaptosulfo)amino]ethane are
probably the most exotic complexes among all macrotricyclic
metal chelates, and even not so much because they contain
two 4-membered chelate rings, but because these chelate rings
are Bcarbon-free^[53]. They can be divided into two groups,
the first of which constitute the Mn(II), Fe(II), and Zn(II)
complexes and the second, the Co(II), Ni(II), and Cu(II)
complexes.
The complexes of the first group are characterized by pro-
nounced Btetrahedricity^of the MN
2
S
2
chelate node, since for
them, the (BAS–360°) values are not only positive but also
very significant (34.4° for the Mn(II) complex, 37.3° for the
Fe(II) complex, and 25.8° for the Zn(II) complex). For the
complexes of the second group, the abovementioned tetrahe-
dral distortion also occurs, but it is much less pronounced and
the (BAS–360°) values differ only slightly from zero (9.3° in
the Co(II) complex, 2.5° for the Ni(II) complex, and 6.0° for
the Cu(II) complex). There is not less (if not more) striking
difference in the sum of the angles formed by the donor atoms
of the chelate ring (NBAS) between the complexes of the first
group [291.2° (Mn), 287.7° (Fe), 290.6° (Zn)] and the com-
plexes of the second group (341.6° (Co), 355.2° (Ni), 347.6°
(Cu)): more than 50° (!). That situation until now has not been
observed for any of the categories of Btemplate^metal che-
lates considered by us. In all these chelates, the four angles in
N
2
S
2
are pairwise equal, whereas for the angles composing the
MN
2
S
2
chelate node, such equality is observed only for two
angles of the four, and the other angles differ from each other.
An analogous pairwise equality is also observed for the d(M–
N) and d(M–S) bond lengths, and d(M–N) < d(M–S) in all the
complexes considered. The values of d(M–N) in the Mn–Ni
series decrease, and in the Ni–Zn series, they increase; a sim-
ilar trend is observed for d(M–S), only the minimum here is
HN
S
SS
S
NN
M
NH
III.16
HN
S
SS
S
NN
M
NH
III.17
N
O
ON
O
S
S
MS
O
S
H
H
III.18
Struct Chem (2018) 29:777–802 785
achieved not in the Ni(II) complex, but in the Co(II) complex.
The longest bonds, both M–NandM–S, are observed in the
Mn(II) complex. The 4-membered chelate rings here are almost
identical to each other: the (BAS
4
–360°) values in each of them
are the same. In the Ni(II) and Cu(II) complexes where the
deviation of the MN
2
S
2
chelate node and the N
2
S
2
moiety from
coplanarity is much less pronounced than that in the Mn(II),
Fe(II), and Zn(II) complexes, the noncoplanarity of the 4-
membered rings is much more pronounced. (The deviation of
BAS
4
from 360° in these complexes exceeds 6°, whereas in the
Mn(II), Fe(II), and Zn(II) chelates, it does not exceed 3°.) For
the 5-membered rings, noncoplanarity is more pronounced than
for the 4-membered rings (the bond angle sum BAS
5
in them
differ from the sum of the interior angles in a flat pentagon by
more than 20°). Some of these molecular structures have been
presented in Fig. 6.
The (464)macrotricyclic M(II) chelates with 2,6-diaza-4-
oxaheptanethioic acid III.19 [51] are similar to the complexes
reported in [53]. As distinct from chelates III.18,almostallof
them are similar to each other; the (BAS–360°) values for them
are negative being −6.8° (Mn), −7.1° (Fe), −3.2° (Co), −0.9°
(Ni), and −3.6° (Cu), so that the MN
2
S
2
chelate nodes in each
complex has a quasi-planar structure with a small tetragonal-
pyramidal distortion. The N
2
S
2
group of the donor atoms in
them is exactly planar. The Zn(II)complex, which has a
completely different molecular structure, namely, III.20,with
two fused 6-membered rings and the (SOS)-coordination
mode of the donor chelant atoms to the complexing agent
stands apart from the other complexes. Here, the coordination
number (CN) of Zn(II) is 3, rather than 4, as is the case of the
other M(II) in chelates III.19 [49].
Although this complex can be attributed to macrocyclic metal
chelates, it is not macrotricyclic, but macrobicyclic, because it
contains only two 6-membered chelate rings. The interatomic
M–N distances in it are so significant (305.7 pm), so that chem-
ical bonds between these atoms should not be formed [51]. As for
complexes III.19 for the remaining five M(II) atoms, the angles
in the N
2
S
2
group in them are pairwise equal; the same pairwise
equality is also observed for the d(M–N) and d(M–S) bond
lengths. Characteristically, in complexes III.19 and III.18,the
shortest M–N bonds are in the Ni(II) complex, the shortest M–
S bonds are in the Co(II) complex; the longest M–NandM–S
bonds are observed in the Mn(II) complex. The 4-membered
chelate rings forming the macrocycle in any of complexes
Fig. 7 Molecular structures of
Fe(II) and Ni(II) chelates with
general formula III.21
Fig. 6 Molecular structures of
Co(II) and Zn(II) chelates with
general formula III.18
NH
HN
S
MS
S
S
O
III.19
NHHN
S
MS
S
S
O
III.20
786 Struct Chem (2018) 29:777–802
III.19 are completely identical to each other and are nearly planar,
since the (BAS
4
–360°) values in each of them are the same and
have a magnitude of less than 5°. The 6-membered rings here are
significantly noncoplanar, since the (BAS
6
–720°) magnitude for
each of these metal chelates exceeds 60°. The bond angles in each
of the 4-membered rings are different, while the bond angles in
the 6-membered rings are pairwise equal to each other; the bond
lengths forming these angles are also pairwise the same [51].
It is worth noting that, in all (545)macrotricyclic 3d-metal
chelates, namely, in M(II) complexes with 3,7-dimethyl-5-imi-
no-4,6-diaza-3,6-nonadienediol-2,8 III.21 [39], the chelate nodes
have either nearly planar or tetragonal-pyramidal orientation of
the donor N and O atoms with respect to the M(II) atom (Fig. 7);
the corresponding (BAS–360°) values are negative being −22.7°
(Mn), −0.5° (Fe, Cu), and −0.1° (Co, Ni, Zn). The NBAS values
are either exactly 360.0° (Fe, Co, Ni, Cu) or very close to 360.0°
(358.5° (Mn), 358.6° (Zn)), so that the N
2
O
2
group of the donor
atoms is also planar. As distinct from symmetric
(565)macrotricyclic metal chelates, hear the d(M–N) lengths, as
well as the d(M–O) lengths, are different, although in some cases,
they are pairwise close to each other. Remarkably, in the com-
plexes Mn(II), Fe(II), and Zn(II) complexes, d(M–N) > d(M–O),
whereas in the Co(II) and Ni(II)complexes, on the contrary,
d(M–N) < d(M–O), and in the Cu(II) complex, they are rather
close (though not equal) to each other. The shortest M–NandM–
O bonds are in the Co(II) complex and the longest, in the Mn(II)
complex. In the Mn–Zn series, in going from Mn to Co, d(M–N)
and d(M–O) decrease, and in going from Co to Zn, the former
increases, while the latter increases in the series Co–Cu and
decreases again in going from Cu to Zn [39]. The 4-membered
metal chelates are here nearly planar; as for the 5-membered
chelate rings, the complexes we study can be clearly divided into
two groups based on the geometry of these rings. In one group
(M = Fe, Co, Ni, Cu), both 5-membered rings are nearly planar;
in the second group (M = Mn, Zn), only one of them is planar,
while the other have a significantly different BAS (539.8° and
492.0° for Mn(II), 539.7° and 488.9° for Zn(II)). In the structures
of macrotricyclic complexes, this phenomenon has not been ob-
served so far. In this respect, complexes III.21 essentially differ
from metal chelates with one 6-membered and two 5-membered
rings, where, as indicated above, none of the chelate rings is
planar, and even more so from metal chelates with three 5-
membered rings each of which is nearly coplanar, and two of
them are identical.
Recently [52], quantum-chemical modeling has been per-
formed for the molecular structures of Mn(II), Fe(II), Co(II),
Ni(II), Cu(II), and Zn(II) chelates with the tetradentate com-
partmental ligand 6,9-dimethyl-2,4,4,10,11,13-hexaaza-
3,5,9,11-tetradecatetraene-3,12-dithiol capable of forming
macrotricyclic metal chelates III.22 with two 5-membered
rings and one 7-membered ring. It is worth noting that back
in 1970, the Ni(II) and Cu(II) complexes with this ligand were
experimentally synthesized by the template reaction of M(II),
N-methylthiocarbohydrazide, and 2,5-hexanedione [58].
However, no information on its structure since then has ap-
peared. According to [52], all compounds III.22 have a clear-
ly pronounced pseudotetrahedral coordination of the ligand
donor sites to the central atom; this feature is most pronounced
in the Fe(II) chelate and is least pronounced in the Ni(II)
chelate where the (BAS–360°) values are 41.4° and 2.1°, re-
spectively. The NBAS in the N
2
S
2
group in all these com-
plexes is, as a rule, noticeably smaller than 360.0°: for two
of them, namely, Fe(II) and Zn(II), thissum is even smaller
than 300.0°, so that the N
2
S
2
group is strongly distorted
(Fig. 8). The M–NandM–S bond lengths is all these com-
plexes, except the iron(II) and zinc(II) chelates, differ from
each other; in the Mn–Zn series, they decrease from Mn to
Co and increase from Co to Zn. In conformity with theoretical
expectations, d(M–S) is larger thand(M–N) by at least 20 pm.
None of the 5- and 7-membered chelate rings is planar; the 7-
membered rings in each of these complexes are noncoplanar
to a greater extent than the 5-membered rings. The least non-
coplanar 7-membered ring is revealed in the Mn(II) complex,
Fig. 8 Molecular structures of
Mn(II) and Cu(II) chelates with
general formula III.22
O
M
N
O
N
NH
CH
3
CH
3
H
3
C
H
3
C
III.21
Struct Chem (2018) 29:777–802 787
and it is most noncoplanar in the Zn(II) complex. As for the 5-
membered rings, they are completely identical by the bond
angles only in the Fe(II) and Zn(II) complexes and are some-
what different in the other four complexes. The reason for this
is unclear since, according to the formula of compounds
III.22, the 5-membered ring in each of them should be iden-
tical regardless of the nature of M(II). There is no correlation
between this feature of the Fe(II) and Zn(II) complexes and
their ground state electronic configurations (3d
4
and 3d
10
)as
compared with the ground state electronic configurations of
the rest of the M(II) ions. Undoubtedly, this difference is di-
rectly related to the inequality of both the d(M–N) and d(M–S)
bond lengths in four of the six complexes.
(666)Macrotricyclic metal chelates having III.23 and
III.24 formulas with MN
4
chelate nodes have been considered
in [29,43]. It has been demonstrated that, for the former,
corresponding compounds can exist from each of M(II) in
the Mn(II)–Zn(II) series [31], whereas, for the latter, com-
pounds can exist only for M(II) = Ni(II), Cu(II), and Zn(II)
[43]. (666)macrotricyclic metal chelates with the MN
2
S
2
che-
late node isomeric to complexes III.24 can independently
exist for none of the M(II) ions in the same Mn(II)–Zn(II)
series. For both III.23 and III.24, the pseudotetrahedral coor-
dination of the donor sites of the corresponding chelant to
M(II) is generally typical [29,43]. The (BAS–360°) values
in them are positive: in III.23, they are within the range from
4.3° (Fe(II)) to 35.8° (Zn(II)); in III.24,theychangefrom1.0°
(Zn(II)) to 48.2° (Ni(II)). The last of these complexes is unique
in its own way, because the (BAS–360°) value for it is the
highest among all values of this parameter for macrotricyclic
metal chelates calculated in the literature in general and very
close to the value of this parameter for an ideal tetrahedral
environment (49°28′). Apparently, with an increase in the total
number of rings cycles, the tendency to tetrahedral chelate
node increases and for (666)macrotricyclic metal chelates be-
comes most pronounced. This is facilitated by the trans ori-
entation of the donor chelant sites to the complexing agent
[46,49]. The M–N bond lengths in all these complexes are
different, and so are the bond anglesin the MN
4
chelate nodes,
the N4 groups of donor atoms, and the 6-membered chelate
rings, which, in each of these complexes, differ from each
other in sets of bond angles and in their sums [29,43]. All
considered chelates III.18–III.24 are, as a rule, asymmetric,
so that they are expected to have rather high dipole moments,
which is supported by quantum-chemical calculations [29,39,
43,51–53]. Structures of some of these metal chelates are
shown in Fig. 9.
In conclusion of this section, let us note that the ground
state for all Mn(II), Fe(II), Co(II), Ni(II), Cu(II), and Zn(II)
chelates considered in given paragraph are, as a rule, spin
sextet, quintet, doublet, singlet, doublet, and singlet, respec-
tively, which is typical for each of the above M(II). One of few
exceptions is Ni(II) chelate III.24, for which the ground state
Fig. 9 Molecular structures of
Co(II) and Cu(II) chelates with
general formula III.23 and III.24
H3CHN NHCH3
SS
N
M
H3C
N
CH3
NN
III.22
NH
NH
HN
C
S
HN HN NH
CS
NH
M
H
3
C
H
3
C
CH
3
N
III.23
S
S
S
S
NH HN
O
HN
NH
M
III.24
788 Struct Chem (2018) 29:777–802
is spin triplet. In some cases (in particular, for Fe(II) III.19,
Co(II) III.21, and Ni(II) III.24 chelates), the difference in
energy between the ground state and the nearest excited state
with spin multiplicity other than that of the ground state is
rather small (less than 10 kJ/mol), so that spin isomerism (spin
crossover) is possible.
Molecular structures of metal macrocyclic
compounds with four combined cycles
The molecular structures of macrotetracyclic metal chelates
have, in general, the same specific features as the molecular
structures of macrotricyclic complexes. Most of them are also
nonplanar, and the degree of deviation from coplanarity for
them is sometimes rather significant (for 6- and 7-membered
chelate rings, it can be as high as almost 90°). For their MN
4
chelate nodes (M = Mn, Fe, Co, Ni, Cu, Zn), the most typical
is a pyramidal coordination with BASslessthan360°rather
than a planar or tetrahedral coordination with BASsequalor
larger than this value [56,59–76]. For both the pyramidal and
planar geometry of the chelate ring, the group of the nitrogen
atoms forming the chelate node is mainly exactly planar or
nearly planar.
(5656)Macrometracyclic metal chelates This most significant
category of macrotetracyclic metal chelates has been ad-
dressed in publications [56,59–61,65,68,71–74], most of
which (except only [61]) present structural data on symmetric
complexes. A typical example of such symmetric (5656)
macrotetracyclic metal chelates are M(II) complexes (M =
Fe, Co, Ni, Cu, Zn) with general formulas IV.1–IV.4with
1,4,8,11-tetraazatetradecane-2,3,9,10-tetrathione [71],
1,3,5,8,10,12-hexaazatetradecane-6,7,13,14-tetrathione [68],
1,8-dioxa-3,6,10,13-tetraazatetradecane-4,5,11,12-tetrathione
[59,72,74], and 1,8-dithia-3,6,10,13-tetraazatetradecane-
4,5,11,12-tetrathione [56], respectively.
Fig. 11 Molecular structures of
Co(II) and Zn(II) chelates with
general formula IV.5
Fig. 10 Molecular structures of
Ni(II) chelates with general
formula IV.1and IV.4
N
S
S
S
S
N
HN
NH
M
IV.1
N
S
S
S
S
N
HN NH
NH
M
NH
IV.2
Struct Chem (2018) 29:777–802 789
Molecular structures of some of these complexes have been
presented in Fig. 10.
The asymmetric chelates are exemplified by 3d-M(II) com-
plexes of general formula IV.5with 5,5,7,12,12,14-
hexamethyl-1,4,8,11-tetraaza-1,7-cyclotetradeca-diene-
2,3,9,10-tetrathione [61], some of them are shown in Fig. 11.
All these symmetric complexes are distinguished, in addition
to the mentioned general feature (a tetragonal-pyramidal struc-
ture of the chelate node) by nearly perfect identity of 5-
membered chelate rings: they pyramidal structure of the have
the same (BAS
5
–540°) values and the same sets of bond an-
gles between neighboring atoms in these chelate rings (al-
though both characteristics noticeably depend on the nature
of the central atom M). At the same time, these characteristics
for the 6-membered chelate rings in any of these metal che-
lates usually differ rather sharply from each other. (It is worth
noting in this context that, in all cases, those 6-membered
chelate rings that have N–H bonds with exocyclic hydrogen
atoms are distorted from coplanarity to a noticeably greater
extent than the rings that have no such bonds.) The group of
the four donor atoms in them is, as a rule, planar or very close
to planar; it is noteworthy that, for different M(II) atoms, this
group has different pairwise equal angles. For example, in
complexes IV.4, where NBAS is 360.0°, these angles are
89.6° and 90.4° (Mn), 90.6° and 89.4° (Fe), 91.6° and 88.4°
(Ni), 90.3° and 89.7° (Cu, Zn) [56].Thesespecificfeaturesare
also observed in asymmetric metal chelates IV.5[59]. As for
the M–N bond lengths in the MN
4
chelate nodes, they are at
best pairwise equal to each other. Nevertheless, they exhibit
the same trend in going along the Mn–Zn series as in the case
of macrotricyclic complexes: these bond lengths, on the
whole, decrease in going from Mn to Ni and hereafter increase
from Ni to Zn.
Practically all (5656)macrotetracyclic metal chelates de-
scribed in [56,59–61,65,68,71–74] are generally non-
coplanar since noncoplanar are their 5- and/or 6-membered
chelate rings. Among the few exceptions to this rule are
only the Fe(II), Co(II), Ni(II), and Cu(II) complexes with
3,10-dithio-6,7,13,14-tetramethyl-1,2,4,5,8,9,11,12-octaaza-
1,5,7,12-cyclodecatetraene IV.6[60] (Mn(II) and Zn(II)
chelates with the same chelant have a quasi-pyramidal
chelate node). The formation of these complexes by the
self-assembly in the ternary systems M(II)–
hydrazinecarbothiohydrazide–2,3-butanedione was report-
ed in [76]. In addition, these chelates are distinguished
among the complexes we studied by a unique feature that
has not been observed so far for planar macrotricyclic
complexes: the calculated electric dipole moments for
them are 0.00 D (in the Fe(II) complex), 0.01 D (in the
Co(II) complex), and 0.02 (in the Ni(II) and Cu(II) com-
plexes), i.e., nearly do not differ from zero [60]. It is
worth noting that for all other (5656)macrotetracyclic
Fig. 12 Molecular structures of
Fe(II) and Cu(II) chelates with
general formula IV.6
N
S
S
S
S
N
HN NH
O
M
O
IV.3
N
S
S
S
S
N
HN NH
S
M
S
IV.4
N
S
S
S
S
N
M
CH3
H3C
N
CH3
H3C
H3C
N
CH3
IV.5
790 Struct Chem (2018) 29:777–802
metal chelates mentioned in [56,59,61,65,68,71–74],
the (BAS–360°) are negative, and no complexes of this
type with (BAS–360°) > 0 have not been found thus far.
Some of molecular structures of chelates IV.6have been
imaged on Fig. 12.
The ground state in all Mn(II), Co(II), Ni(II), Cu(II), and
Zn(II) chelates IV.1–IV.4is, as a rule, spin sextet, doublet,
singlet, doublet, and singlet, respectively, which is typical for
each of the above M(II). However, the Fe(II) complexes (ex-
cept only that described in [59]) have a triplet ground state
untypical of this ion, and two Mn(II) complexes considered in
[61,73] have also untypical quartet ground state.
(5456)Macrotetracyclic metal chelates According to the data
presented in [62,64,67,69], for (5456)macrotetracyclic metal
chelates, which contain three types of chelate rings with dif-
ferent numbers of atoms rather than two types of rings in the
macrotricyclic and macrotetracyclic complexes considered
above, a tetragonal-pyramidal structure of the MN
4
chelate
node is also typical. As a rule, in the MN
4
chelate nodes of
these complexes, the differences (BAS–360°) < 0 and their
magnitudes are rather significant; the N
4
group of the donor
atoms is nearly coplanar, the 4-membered chelate rings are
also coplanar, while the 5-membered and especially 6-
membered ones are significantly distorted from coplanarity.
This is clearly exemplified by the data on M(II) complexes
IV.7with 5,7,9-triimino-1-oxa-3,6,8,11-
tetraazacyclododecane-4,10-dithione [62,67] that can be
formed by Bself-assembly^in the quaternary M(II) ion–2-
amino-2-thioethanamide–aminomethanamidine–methanal
(formaldehyde) systems. In these complexes, (BAS–360°) is
−22.4° (Mn), −18.2° (Fe), −11.4° (Co), −7.4° (Ni), −17.4°
(Cu), and −28.9° (Zn), and NBAS is either exactly 360.0°
(Fe, Ni, Zn) or nearly 360.0° (359.9° (Mn, Cu), 359.5°
(Co)), so that the N
4
group of the donor atoms can also be
considered planar. The d(M–N) bond lengths do not coincide
with each other, although in some cases that are pairwise close
to each other, the d(M–N) values for two nitrogen atoms in-
volved in the 6-membered ring are significantly larger than
those for two nitrogen atoms involved in the 4-membered
ring. The shortest M–N bonds are observed in the Ni(II) com-
plex and the longest, in the Zn(II) complex. The bond lengths
here also follow the Bclassical^trend: in the Mn–Zn series,
they decrease from Mn to Ni and increase from Ni to Zn. For
the 4-membered chelate rings, the magnitude of the degree of
deviation from coplanarity is at least 1.5° (in the Zn(II) com-
plex); for the 5-membered rings, this deviation is at least 11.6°
(in the Fe(II) complex); for the 6-membered rings, the devia-
tion is at least 71.3° (in the Mn(II) complex) [62]. It is worth
noting that, for each of these types of rings, minimal distor-
tions are observed for different M(II) ions. Structures of some
of these metal macrocyclic chelates are given in Fig. 13.
Geometrically analogous bond angles, both in the chelate
rings and beyond them, in all these complexes are pairwise not
equal to each other. The ground states in the
(5456)macrotetracyclic Co(II), Ni(II), Cu(II), and Zn(II) che-
lates are always spin doublet (Co(II), Cu(II)) and singlet
(Ni(II), Zn(II)) traditional for the tetragonal-pyramidal com-
plexes of these M(II) ions; the Mn(II) and Fe(II) complexes
have untypical quartet and triplet ground states, respectively
[62,64,67,69].
Fig. 13 Molecular structures of
Mn(II) and Ni(II) chelates with
general formula IV.7
N
H
3
C
CH
3
M
N
N
N
NN NH
N
H
S
S
CH
3
CH
3
IV.6
S
SS
S
NN
M
NN
IV.7
Struct Chem (2018) 29:777–802 791
Macrotetracyclic metal chelates with other sets of chelate
rings By analogy with (555)macrotricyclic metal chelates,
which commonly have a coplanar orientation of the chelant
donor sites with respect to the central M(II) atom (see
above), it can be expected than the same feature will be also
inherent (5555)macrotetracyclic metal chelates. Quantum-
chemical modeling of such complexes has been performed
only in [63,66]; therefore, it is obviously premature to make
any general conclusions about them regarding the coplanar-
ity of their molecular structures. However, we can state that
the molecular structures of the metal chelates described in
these works are actually coplanar. These studies have dealt
with symmetric 3d-metal chelates having general formula
IV.8(M = Mn, Fe, Co, Ni, Cu, Zn), where the Co(II) and
Ni(II) chelates exhibit strictly coplanar coordination of the
chelant donor sites with respect to M(II) and (BAS–360°) =
0. The other complexes show a tetragonal-pyramidal coordi-
nation with a deviation from coplanarity of up to 16.0° in
the Zn(II) complex). The NBAS in the each of these com-
plexes is exactly 360.0°, so that the N
4
group of the donor
atoms is perfectly planar. In the Mn(II) and Fe(II) com-
plexes, the angles in this group are pairwise equal to each
other, while in the other four complexes, all the angles are
90°. The M–N bond length in the same Co(II), Ni(II),
Cu(II), and Zn(II) complexes is exactly the same—a unique
feature that has not been observed for any of the macrocy-
clic metal chelates thus far. However, in the Mn(II) and
Fe(II) complexes, the M–N bond lengths as well as non-
bonded angles between the donor nitrogen atoms are only
pairwise equal to each other. The shortest M–N bonds are
observed in the Ni(II) complex and the longest, in the Zn(II)
complex; d(M–N) values decrease in going from Mn to Ni
and increase in going from Ni to Zn. By the character of the
5-membered chelate rings, each of which contains two do-
nor N atoms, two C atoms, and the M atom, chelates IV.8
can be clearly divided into two groups. In the first of them
(M = Co, Ni), all these rings are ideally planar, and in the
second group (M = Mn, Fe, Zn), in none of these rings, even
they are close to planarity, is the bond angle sum exactly
540.0°; moreover, they have somewhat different (BAS
5
–
540.0°) values. The Cu(II) complex holds an intermediate
position between the complexes of the first and second
groups: the sum of the interior angle in two 5-membered
rings is exactly 540.0° and in the other two rings, it is
somewhat [63,66]. It is worth noting that analogous bond
angles, both in the chelate rings and beyond them, in all
these complexes are, as a rule, equal to each other; the same
equality is observed between the bond lengths forming these
angles. Molecular structures of some of the given chelates
are shown in Fig. 14.
Fig. 15 Molecular structures of
Mn(II) and Cu(II) chelates with
general formula IV.9
Fig. 14 Molecular structures of
Co(II) and Zn(II) chelates of type
IV.8
S
SS
S
NN
M
NN
IV.8
792 Struct Chem (2018) 29:777–802
The ground state for Mn(II), Fe(II), Co(II), Ni(II), and Cu(II)
chelates IV.8is in essence the same as in the case of the
(5656)macrotetracyclic metal chelates. The Zn(II) complex
shows a rather interesting feature: its ground state is a spin triplet,
and the difference in energy between this state and the nearest
singlet is significant (22.8 kJ/mol). Noteworthy is a very small
difference in energy (only 1.1 kJ/mol) between the ground state
and the nearest excited state with another spin for the Fe(II)
complex. Therefore, one can expect with high probability not
just manifestations of the spin crossover, but rather an unusual
one, with the transition from the triplet state to the singlet state,
which has not yet been noted in the experiment [66].
For (5454)macrotetracyclic compounds, the only known
example is represented by formula IV.9. For it, like for the
(5656)macrotetracyclic complexes, the tetragonal-pyramidal
structure ofthe chelate node is dominating [70]. The deviation
of the latter from coplanarity is significant: (BAS–360°) is −
42.4° (Mn), −39.8° (Fe), −35.4° (Co), −29.2° (Ni), −25.8°
(Cu), and −56.2° (Zn), even if the N
4
group itself is planar. In
five of the six complexes considered in [70], both 4-
membered rings as well as both 5-membered rings have
pairwise identical bond angle sums and bond angles them-
selves; both 4-membered rings are strictly planar, while both
5-membered rings are nearly planar with a deviation from
coplanarity of no more than 2.5°. Only the Zn(II) chelate
stands somewhat apart, for which the deviation from copla-
narity turns out to be noticeably larger than for the Mn(II),
Fe(II), Co(II), Ni(II), and Cu(II) complexes (Fig. 15).
It is noteworthy that, in these complexes, the d(M–N)
values for two nitrogen atoms trans to eachother are the same,
and the differеnce in d(M–N) between two pairs of bonds
ranges from 0.5 pm in the Co(II) chelate to 1.2 pm in the
Zn(II) chelate. The ground states for all these metal chelates
have the same spin multiplicity as the ground states of the
(5456)macrotetracyclic metal chelates [70].
In one of the most recent studies [75], quantum-chemical
modeling of the molecular structures of (5757) macrotetracyclic
metal chelates IV.10 was performed. For Ni(II), this complex
was obtained, in addition to already mentioned complex III.22
[58]. Metal chelates of this type and distinguished among all
theoretically studied macrotetracyclic metal chelates by that
they have a pseudotetrahedral structure of chelate nodes rather
than tetragonal-pyramidal as in complexes IV.1–IV.9.Thisis
supported by positive (BAS–360°) values for each of these
compounds, although it should be noted that they are low
(5.0° in the Mn(II) complex, 5.0° for Fe(II), 4.8° for Co(II),
4.7° for Ni(II), 5.2° for Cu(II), and 4.9° for Zn(II)) [75]. In
addition, complexes IV.10 have MN
2
S
2
chelate nodes rather
than MN
4
; as noted in the BMolecular structures of metal mac-
rocyclic compounds with three combined cycles^section, the
MN
2
S
2
chelate nodes can have a tetrahedral structure. The N
2
S
2
group of the donor nitrogen and sulfur atoms in these metal
chelates is also nonplanar: the NBAS value in each of them
differs from the sum of interior angles in a flat tetragon
(360.0°) by more than 9°. Both 7-membered chelate rings are
also noncoplanar. Moreover, the degree of deviation from co-
planarity for each of the rings in the same complex is rather
different, since its quantitative characteristics (BAS
7
–900°) dif-
fer significantly (by more than 50°!) from each other. [Namely,
−75.3° and −136.7°, −73.7° and −127.2°, −73.1° and −
129.0°, −73.2° and −127.6°, −69.8° and −138.3°, and −
73.7° and −138.0° in the Mn(II), Fe(II), Co(II), Ni(II), Cu(II),
and Zn(II) chelates, respectively.] Noteworthy is a very high—
more than 125° (!!)—degree of deviation from coplanarity for
the chelate rings containing two donor sulfur atoms, which has
not been observed heretofore in any of the macrocyclic metal
complexes, neither in macrotricyclic nor macrotetracyclic. In
Fig. 16 Molecular structures of
Fe(II) and Ni(II) chelates with
general formula IV.10
M
NN
NH
CH
3
CH
3
H
3
C
H
3
CNN
NH
IV.9
Struct Chem (2018) 29:777–802 793
both 7-membered rings of most of chelates IV.10,there
are three pairs of equal bond angles; an exception here
is only the Co(II) chelate: in both 7-membered rings of
this complex, all bond angles are different. The 5-
membered chelate rings in these metal chelates are also
nonplanar, although the degree of deviation from copla-
narity for them is much smaller than that for the 7-
membered chelate rings (the (BAS
5
–540°) magnitude
does not exceed 4°; all angles in these rings are differ-
ent. In all of them, except the Co(II), the 5-membered
rings have identical bond angles. The spin multiplicities
of the ground states in these complexes are the same as
in those of the (5656)macrotetracyclic chelates [75]. The
examples of molecular structures of such metal macro-
cyclic chelates have been shown in Fig. 16.
Concluding this section, we should note that, as a
rule, the metal chelates considered in it are not rich in
symmetry elements and contain only one plane of sym-
metry. Among the few exceptions to this rule are, in
particular, Co(II) and Ni(II) chelates IV.8.Inthemolec-
ular structures of these compounds, there are three two-
fold axes, three planes of symmetry, and the center of
symmetry (the remaining four complexes of this type
have one twofold axis and two symmetry planes), and
chelates IV.6, that have one twofold axis, one symmetry
plane, and the center of symmetry. Most of them are
asymmetric; therefore, rather high dipole moments
should be expected for all of them, which is definitely
confirmed by quantum-chemical calculations. Deviations
are observed only in two above-mentioned complexes
IV.8[66], in which the dipole moments are zero, and
also in some of complexes IV.9where they are relative-
ly small (0.31, 1.10, 1.99, and 1.56 D for the Mn(II),
Fe(II), Cu (II), and Zn(II) complexes, respectively) [70].
That is, they are not as great as one would expect,
given the low symmetry of the macrotetracyclic metal
chelates we consider.
Structural changes in macrocycles as a result
of Bself-assembly^process
As is known, one of the most important areas of modern
coordination chemistry and chemistry of macrocyclic metal
complexes is the transformation of polydentate organic
Fig. 17 Molecular structure of
chelants V.1(left),V.2(in center),
and V. 3(right)
Fig. 18 Molecular structures of
chelants V.4(left) and V. 5(right)
H3CHN NHCH3
SS
N
M
H3C
N
CH3
Br
Br
NN
IV.10
794 Struct Chem (2018) 29:777–802
ligands observed when they enter the inner coordination
sphere of a complex-forming metal ion. Among these trans-
formations are the structural changes in ligands caused by
complexation. This especially concerns those of them that
are themselves macrocyclic compounds with the so-called
chelating cage. This interesting and important issue, which is
actually necessary for the full understanding of the results of
these processes, seems to have not attracted any noticeable
attention of researchers up to the present time. To an extent,
this is probably due to the fact that it is not easy to observe
such structural changes in the experiment, because for this,
naturally, we need data on the spatial structure of both the
initial ligand and the complexes with different metal ions
formed by it (which are not often available). A very useful
tool for recording these changes could be quantum-chemical
calculations of the molecular structures of both the ligands and
complexes, but there are very few such works published to
date (we failed to find any work of other researchers in addi-
tion to our investigations concerning this issue). In this sec-
tion, we discuss the available papers on this subject, namely
[62–68,70,71,77]; all of them address only the metal chelates
considered in the BMolecular structures of metal macrocyclic
compounds with four combined cycles^section.
The incorporation of the M(II) metal ion into the Bchelating
cage^of a macrocyclic ligand (accompanied by elimination of
two hydrogen atoms bonded to the donor N atom) can result in
both the decrease and the increase in the degree of
noncoplanarity of its macrocycle. (In the ligand itself and its
complex, the degree of noncoplanarity can be quantitatively
characterized by the difference between the sum of its interior
angles in these compounds and the sum of interior angles in a
planar polygon with a number of vertices corresponding to the
number of atoms in a macrocycle.) The decrease in the degree
of noncoplanarity was observed for the metal chelates de-
scribedin[71,77], and the increase in the degree of
noncoplanarity was observed for the metal chelates described
in [68,77]. There are cases when complexation of some M(II)
atoms is accompanied by a decrease in the degree of
noncoplanarity of the macrocycle, while that of other M(II)
atoms, conversely, leads to an increase in the degree of
noncoplanarity [62–64,66,67,70]. The work [77] dealing
with (5656)macrotetracyclic complexes IV.1–IV.3with
chelants V.1–V. 3, respectively, seems to be the most detailed
in this respect.
Molecular structures of all these chelants have been imaged
in Fig. 17. For metal chelates IV.1and IV.3, the degree of
deviation of the bond angle sum in the 14-membered
macrocycles from 2160° (the sum of interior angles in a flat
14-gon) is somewhat lower than that for the chelant. [In che-
lates IV.1, from 65.0° for the Cu(II) chelate to 70.9° for the
Fe(II) chelate, while in chelant V. 1,the deviation is 82.6°; in
chelates IV.3, from 64.2° for the Co(II) chelate to71.2° for the
Fig. 19 Molecular structures of
chelants V.6(left) and V. 7(right)
N
S
S
S
S
N
HN NH
H
H
V. 1
N
S
S
S
S
N
HN NH
NH
H
NH
H
V. 2
N
S
S
S
S
N
HN NH
O
H
O
H
V. 3
Struct Chem (2018) 29:777–802 795
796 Struct Chem (2018) 29:777–802
Table 4 Bonds lengths, valence, and torsion angles in the M(II) phthalocyaninemetal chelates. The bold font in brackets specifies experimental values,
regular font, calculated by DFT B3LYP/6-31G(d) method (first value) and DFT OPBE/TZVP method (second value)
MMn Fe Co Ni Cu
M–N bond lengths (pm)
(M1N1) 195.9; 195.5; (193.9) 193.8; 190.8; (192.7) 189.6; 191.5; (191.0) 190.4; 190.3; (183.0) 196.0; 196.2; (195.3)
(M1N2) 193.7; 193.7; (193.8) 193.8; 190.8; (192.6) 189.6; 191.5; (191.0) 190.4; 190.3; (183.1) 195.0; 196.2; (195.0)
(M1N3) 195.9; 195.5; (193.9) 193.8; 190.8; (192.7) 189.6; 191.5; (191.0) 190.4; 190.3; (183.0) 196.0; 196.2; (195.3)
(M1N4) 193.7; 193.7; (193.8) 193.8; 190.8; (192.6) 189.6; 191.5; (191.0) 190.4; 190.3; (183.1) 195.0; 196.2; (195.0)
C–N bond lengths (pm)
(N1C3) 138.5; 138.1; (138.9) 138.0; 138.2; (138.1) 138.8; 137.8; (138.4) 138.1; 137.7; (137.9) 137.5; 137.0; (138.8)
(N1C4) 138.5; 138.1; (139.7) 138.1; 138.3; (137.5) 138.8; 137.8; (137.1) 138.1; 137.7; (139.0) 137.6; 137.0; (138.9)
(N2C1) 139.5; 138.9; (139.1) 138.1; 138.3; (137.5) 138.8; 137.8; (137.1) 138.1; 137.7; (137.1) 138.3; 137.0; (137.9)
(N2C2) 139.5; 138.9; (139.2) 138.0; 138.3; (138.2) 138.8; 137.8; (138.4) 138.0; 137.7; (137.7) 138.3; 137.0; (138.1)
(N3C7) 138.5; 138.1; (138.9)138.0; 138.2; (138.1) 138.8; 137.8; (137.0) 138.1; 137.7; (137.9) 137.5; 137.0; (138.8)
(N3C8) 138.5; 139.1; (139.7) 138.1; 138.3; (137.5) 138.8; 137.8; (138.7) 138.1; 137.7; (139.0) 137.6; 137.0; (138.9)
(N4C5) 139.5; 138.9; (139.1) 138.1; 138.3; (137.5) 138.8; 137.8; (138.0) 138.0; 137.7; (139.5) 138.3; 137.0; (137.9)
(N4C6) 139.5; 138.9; (139.2) 138.0; 138.2; (138.2) 138.8; 137.8; (138.0) 138.1; 137.7; (137.7) 138.3; 137.0; (138.1)
(N5C2) 131.2; 131.1; (131.4) 132.2; 131.9; (132.1) 131.9; 131.7; (131.9) 131.8; 131.5; (136.8) 130.9; 132.3; (135.4)
(N5C3) 133.1; 132.7; (132.5) 132.2; 131.9; (132.2) 131.9; 131.7; (132.6) 131.8; 131.5; (137.7) 135.0; 132.3; (137.1)
(N6C6) 131.2; 131.1; (131.4) 132.2; 131.9; (132.1) 131.9; 131.7; (131.9) 131.8; 131.5; (136.8) 130.9; 132.3; (135.4)
(N6C7) 133.1; 132.7; (132.5) 132.2; 131.9; (132.2) 131.9; 131.7; (132.6) 131.8; 131.5; (137.7) 135.0; 132.3; (137.1)
(N7C4) 133.1; 132.7; (132.4) 132.2; 131.9; (132.0) 131.9; 131.7; (132.3) 131.8; 131.5; (138.0) 134.9; 132.3; (134.4)
(N7C5) 131.2; 132.8; (132.8) 132.2; 131.9; (132.4)131.9; 131.7; (132.5) 131.8; 131.5; (137.3) 130.8; 132.3; (134.9)
(N8C1) 131.2; 131.1; (132.8) 132.2; 131.9; (132.4) 131.9; 131.7; (132.3) 131.8; 131.5; (137.3) 130.8; 132.3; (134.9)
(N8C8) 133.1; 132.7; (132.4) 132.2; 131.9; (132.0) 131.9; 131.7; (132.5) 131.8; 131.5; (138.0) 134.9; 132.3; (134.4)
C–C bond lengths (pm)
(C9C10) 141.2; 141.0; (140.8) 140.4; 140.0; (139.0) 139.9; 140.1; (139.2) 140.0; 139.9; (138.3) 141.2; 140.6; (140.7)
(C11C12) 140.3; 140.2; (140.7) 140.4; 140.0; (139.3) 139.9; 140.1; (139.8) 140.0; 139.9; (138.9) 139.9; 140.6; (140.7)
(C13C14) 141.2; 141.0; (140.8) 140.4; 140.0; (139.0) 139.9; 140.1; (139.2) 140.0; 139.9; (138.3) 141.2; 140.6; (140.7)
(C15C16) 140.3; 140.2; (140.7) 140.4; 140.0; (139.3) 139.9; 140.1; (139.8) 140.0; 139.9; (138.9) 139.9; 140.6; (140.7)
(C9C17) 140.1; 139.9; (139.2) 139.6; 139.2; (139.5) 139.2; 139.5; (139.3) 139.6; 139.5; (139.4) 139.7; 139.4; (137.9)
(C17C25) 138.8; 138.8; (139.4) 139.3; 139.7; (138.7) 139.8; 139.2; (139.4) 139.3; 139.2; (139.2) 139.4; 139.3; (137.2)
(C25C26) 141.5; 141.0; (140.9) 140.9; 140.1; (139.4) 140.4; 140.5; (139.1) 140.9; 140.6; (140.7) 141.0; 140.5; (141.2)
(C26C18) 138.8; 138.8; (139.6) 139.3; 139.7; (139.7) 139.8; 139.2; (139.4) 139.3; 139.2; (139.5) 139.4; 139.3; (137.9)
(C18C10) 140.1; 139.9; (140.0) 139.6; 139.2; (139.4) 139.2; 139.5; (139.0) 139.6; 139.5; (138.5) 139.7; 139.4; (137.9)
C–H bond lengths (pm)
(C17H1) 108.5;108.8;(109.5) 108.5; 108.9; (–) 108.5; 108.8; (95.3) 108.5; 108.8; ( –) 108.6; 108.8; (102.8)
(C25H9) 108.7;109.0;(107.8) 108.7; 109.0; (–) 108.6; 109.0; (95.8) 108.7; 109.0; (–) 108.7; 109.0; (102.3)
(C26H10) 108.7; 109.0; (109.4) 108.7; 109.0; (–) 108.6; 109.0; (96.3) 108.7; 109.0; (–) 108.7; 109.0; (102.5)
(C18H2) 108.5;108.8;(108.0) 108.5; 108.9; (–) 108.5; 108.8; (95.1) 108.5; 108.8; (–) 108.6; 108.8; (102.8)
∠NMN valence angles (°)
(N1M1N4) 90.0; 90.0; (91.3) 90.0; 90.0; (90.9)90.0;90.0;(90.0) 90.0; 90.0; (89.3)90.0;90.0;(89.0)
(N4M1N3) 90.0; 90.0; (88.7) 90.0; 90.0; (89.1)90.0;90.0;(90.0) 90.0; 90.0; (90.7)90.0;90.0;(91.0)
(N3M1N2) 90.0; 90.0; (91.3) 90.0; 90.0; (90.9)90.0;90.0;(90.0) 90.0; 90.0; (89.3)90.0;90.0;(89.0)
(N2M1N1) 90.0; 90.0; (88.7) 90.0; 90.0; (89.1)90.0;90.0;(90.0) 90.0; 90.0; (90.7)90.0;90.0;(91.0)
VA S 360.0; 360.0; (360.0) 360.0; 360.0; (360.0) 360.0; 360.0; (360.0) 360.0; 360.0; (360.0) 360.0; 360.0; (360.0)
∠NNN non-valence angles (°)
(N1N4N3) 90.7; 90.5; (90.5) 90.0; 90.0; (90.0)90.0;90.0;(90.0) 90.0; 90.0; (90.2)90.2;90.0;(90.1)
(N4N3N2) 89.3; 89.5; (89.5) 90.0; 90.0; (90.0)90.0;90.0;(90.0) 90.0; 90.0; (89.8)89.8;90.0;(89.9)
(N3N2N1) 90.7; 90.5; (90.5) 90.0; 90.0; (90.0)90.0;90.0;(90.0) 90.0; 90.0; (90.2)90.2;90.0;(90.1)
(N2N1N4) 89.3; 90.5; (89.5) 90.0; 90.0; (90.0)90.0;90.0;(90.0) 90.0; 90.0; (89.8)89.8;90.0;(89.9)
Mn(II) chelate, while in chelant V. 3, the deviation is 98.3°.] It
should be noted in this connection that the minimal and max-
imal deviation from coplanarity for chelants V. 1and V. 3is
observed for different M(II) ions [71,77]. For V. 1and V. 3,
the trends in differences between the sum of interior angles in
the 14-membered macrocycle of the chelant and the sums of
interior angles in the 14-membered macrocycles of the corre-
sponding metal chelate along the Mn –Zn series are also
different. For chelates IV.1, these differences decrease in
going from Mn to Fe, increase from Fe to Cu, and decrease
again from Cu to Zn, whereas for chelates IV.3,theyincrease
in going from Mn to Co and decrease from Co to Zn. For
metal chelates IV.2, a different pattern is observed: the devia-
tion of the bondangle sum in their 14-membered chelate rings
from 2160° (from 72.6° in the Co(II) complex to 82.7° in the
Mn(II) complex) every time turns out to be somewhat larger
than for the chelant itself (72.4°). Besides, the magnitudes of
these differences decrease from Mn(II) to Co(II), increase
Table 4 (continued)
MMn Fe Co Ni Cu
NVAS 360.0; 360.0; (360.0) 360.0; 360.0; (360.0) 360.0; 360.0; (360.0) 360.0; 360.0; (360.0) 360.0; 90.0; (360.0)
Valence angles in the 6-numbered cycle (M1N1C4N7C5N4) (°)
(N1M1N4) 90.0; 90.0; (91.3) 90.0; 90.0; (90.9)90.0;90.0;(90.0) 90.0; 90.0; (89.3)90.0;90.0;(89.0)
(M1N4C5) 126.2; 126.1; (125.2) 126.3; 126.7; (125.4) 127.0; 126.4; (127.8) 126.7; 126.6; (130.4) 125.9; 125.6; (127.5)
(N4C5N7) 127.5; 127.6; (127.9) 127.5; 127.6; (128.0) 127.6; 127.8; (126.2) 127.7; 127.9; (126.9) 128.5; 127.9; (127.2)
(C5N7C4) 123.1; 123.0; (122.7) 122.5; 121.4; (122.2) 120.8; 121.5; (121.1) 121.2; 121.0; (116. 0) 122.1; 123.0; (122.0)
(N7C4N1) 127.2; 127.4; (127.7) 127.5; 127.6; (127.9) 127.6; 127.8; (128.4) 127.7; 127.9; (126.9) 127.6; 127.9; (126.5)
(C4N1M1) 125.9; 125.8; (125.2) 126.2; 126.7; (125.5) 127.0; 126.4; (125.8) 126.7; 126.6; (130.5) 125.9; 125.6; (127.8)
VAS
1
719.9; 719.9; (720.0) 720.0; 720.0; (719.9) 720.0; 719.9; (719.3) 720.0; 720.0; (720.0) 720.0; 720.0; (720.0)
Valence angles in the 5-numbered cycle (C3N1C4C9C10) (°)
(C3N1C4) 108.2; 108.4; (107.5) 107.6; 106.6; (107.3) 106.1; 107.1; (107.3) 106.5; 106.8; (99.9) 108.0; 108.8; (106.1)
(N1C4C9) 109.2; 109.1; (109.5) 109.8;110.4;(110.0) 110.6; 110.1; (109.3) 110.5; 110.3; (11 5.9) 109.6; 109.2; (111.4)
(C4C9C10) 106.7; 106.7; (106.6) 106.4; 106.3; (106.6) 106.3; 106.3; (106.2) 106.3; 106.3; (102.6) 106.4; 106.4; (106.5)
(C9C10C3) 106.7; 106.7; (107.0) 106.4; 106.3; (106.5) 106.3; 106.3; (106.5) 106.3; 106.3; (106.5) 106.4; 106.4; (105.5)
(C10C3N1) 109.2; 109.1; (109.3) 109.8;110.4;(109.6) 110.6; 110.1; (108.2) 110.4; 110.3; (115 .1) 109.6; 109.2; (110.4)
VAS
2
540.0; 540.0; (539.9) 540.0; 540.0; (540.0) 539.9; 539.9; (537.5) 540.0; 540.0; (540.0) 540.0; 540.0; (539.9)
Valence angles in the 6-numbered cycle (C9C10C18C26C25C17) (°)
(C9C10C18) 121.0; 120.1; (120.8) 121.2; 121.2; (121.4) 121.4; 121.3; (119. 6) 121.4; 121.3; (119.9) 121.0; 121.1; (120.0)
(C10C18C26) 117.7; 117.8; (11 7.5) 117.6; 117.7; (117 .0) 117.5; 117.5; (119.2) 117.4; 117.5; (120.9) 117.8; 117.7; (118. 0)
(C18C26C25) 121.3; 121.3; (121.3) 121.2; 121.1; (121.2) 121.1; 121.2; (11 9.4) 121.2; 121.2; (119 .0) 121.2; 121.2; (120.7)
(C26C25C17) 121.3; 121.3; (121.3) 121.2; 121.1; (121.8) 121.1; 121.2; (120.0) 121.2; 121.2; (11 9.9) 121.2; 121.2; (119.7)
(C25C17C9) 117.7; 117.8; (117 .3) 117.6; 117.7; (11 6.9) 117.5; 117.5; (11 9.7 ) 117.4; 117.5; (119. 9) 117.8; 117.7; (11 8.5 )
(C17C9C10) 121.0; 121.0; (121.8) 121.2; 121.2; (121.7) 121.4; 121.3; (119. 6) 121.4; 121.3; (120.4) 121.0; 121.1; (120.8)
VAS
3
720.0; 719.3; (720.0) 720.0; 720.0; (720.0) 720.0; 720.0; (717.5) 720.0; 720.0; (720.0) 720.0; 720.0; (720.0)
Selected torsion angles (°)
(M1N1C4N7) 0.0; 0.0; (1.1) 0.0;0.0;(0.0) 0.0;0.0;(11 .0) 0.0;0.0;(0.0) 0.0;0.0;(2.7)
(N1C4C9C17) 180.0; 180.0; (176.9) 180.0; 180.0; (178.8) 180.0; 180.0; (175.8) 180.0; 180.0; (180.0) 180.0; 180.0; (172.9)
(N1C3C10C18) 180.0; 180.0; (177.3) 180.0; 180.0; (178.6) 180.0; 180.0; (157.8) 180.0; 180.0; (180.0) 180.0; 180.0; (180.0)
(N7C4C9C17) 0.0; 0.0; (1.9) 0.0;0.0;(0.0) 0.0;0.0;(3.4) 0.0;0.0;(0.0) 0.0;0.0;(0.0)
(N5C3C10C18) 0.0; 0.0; (3.5) 0.0;0.0;(1.9) 0.0;0.0;(2.6) 0.0;0.0;(0.0) 0.0;0.0;(0.0)
(H1C17C9C10) 180.0; 180.0; (178.9) 180.0; 180.0; (–) 180.0; 180.0; (165.0) 180.0; 180.0; (–) 180.0; 180.0; (178.5)
(H10C26C18C10) 180.0; 180.0; (178.9) 180.0; 180.0; (–) 180.0; 180.0; (153.4) 180.0; 180.0; (–) 180.0; 180.0; (180.0)
(H2C18C10C9) 180.0; 180.0; (179.4) 180.0; 180.0; (–) 180.0; 180.0; (180.0) 180.0; 180.0; (–) 180.0; 180.0; (180.0)
(C9C4N1M1) 180.0; 180.0; (177.6)180.0; 180.0; (178.1) 180.0; 180.0; (168.1) 180.0; 180.0; (180.0) 180.0; 180.0; (176.5)
(C10C3N1M1) 180.0; 180.0; (177.5) 180.0; 180.0; (177.9) 180.0; 180.0; (159.9) 180.0; 180.0; (180.0) 180.0; 180.0; (176.3)
(H1C17C9C4) 0.0; 0.0; (3.3) 0.0;0.0;(–) 0.0;0.0;(4.6) 0.0;0.0;(–) 0.0;0.0;(0.0)
(H2C18C10C3) 0.0; 0.0; (2.1) 0.0;0.0;(–) 0.0;0.0;(7.0) 0.0;0.0;(–) 0.0;0.0;(0.0)
The sign (–) means that there is no corresponding experimental data
Struct Chem (2018) 29:777–802 797
from Co(II) toNi(II), decrease again from Ni(II) to Cu(II), and
increase again from Cu(II) to Zn(II). Thus, the complexing of
the above 3dM(II) ions with chelants V. 1and V. 3is accom-
panied by a decrease in the degree of distortion of their
macrocycles; on the contrary, the complexing with chelant
V. 2enhances the distortion [77]. The macrocycles in both
the chelants themselves and the corresponding metal chelates
are geometrically convex polygons. However, in
macrotetracyclic metal chelates IV.7,aswellasincorrespond-
ing chelant V. 4, the 12-membered macrocycle is not convex,
since its bond angle sum in all cases exceeds (and noticeably)
the sum of interior angles of a flat 12-gon (1800°). [This
difference is 28.7° in the Mn(II) complex, 24.3° in the Fe(II)
complex, 22.7° in the Co(II) complex, 29.8° in the Ni(II)
complex, 42.6° in the Cu(II) complex, and 44.5° in the
Zn(II) complex [60,65]. An analogous trend is also observed
for the related complexes with chelant V. 5[64]. However,
there are also differences between them. And namely, the
complexing of chelant V. 4with four of the six M(II) ions leads
either to a decrease in the degree of noncoplanarity of the
macrocycle (M = Mn, Fe, Co) or to its retention unaltered
(M = Ni) [62], the complexing with the other two M(II) ions
leads to an increase in the degree of noncoplanarity. In the case
of chelant V.5,suchanincreaseisobservedonlyforM=Zn
[64]. Note that the degrees of deviation of the macrocycle
from coplanarity in both chelants are the same (29.8°).
Molecular structures of both these chelants have been present-
ed in Fig. 18.
Nonconvex 12- and 10-membered macrocycles have also
been reported for (5555)- and (5454)macrotetracyclic com-
plexes IV.8and IV.9with chelants V. 6and V. 7,respectively;
specific features of their molecular structures were discussed
in [70]and[63,66], respectively. In the latter, the bond angle
sum in all cases significantly exceeds the sum of interior an-
gles of a flat 10-gon (1440°) (by 170.9° in the chelant, 170.2°
in the Mn(II) complex, 155.4° in the Fe(II) complex,
155.9° in the Co(II) complex, 157.9° in the Ni(II) com-
plex, 179.8° in the Cu(II) complex, 197.4° in the Zn(II)
complex); in the first four metal chelates, this deviation
from 1440° is smaller than in the chelant, while in the
last three metal chelates, it is larger than in the chelant
[70]. A similar situation has been observed for chelant
V. 6[63,66](
Fig.19). Thus, it can be stated that the
complexation of the above 3dM(II) ions with V. 6and
V. 7can be accompanied by both a decrease and an
increase in the degree of distortion of its structure.
(5656)Macrotetracyclic metal chelates IV.6with chelant
V. 8stand apart against this background: the chelant itself
as well as its M(II) complexes is nearly flat [60,65], so
that, as is seen, complex formation does not result in any
significant change in the degree of coplanarity of the
macrocycle. It is worth noting in this context that, accord-
ing to our (until unpublished) data, a similar situation
SS
HN
NH
O
HN
NH
NH
HN NH
V. 4
S
SS
S
HN NH
O
NH
HN NH
V. 5
S
SS
S
NN
HN
NH
V. 6
NN
NH
CH
3
CH
3
H
3
C
H
3
CNH HN
NH
V. 7
798 Struct Chem (2018) 29:777–802
exists in the case of (6666)macrotetracyclic complexes of
the same M(II) with phthalocyanine V. 9.
Comparing the results of quantum-chemical calculations at
all and of ones by means of DFT method with corresponding
experimental data is now the only way to verify the adequacy
of these calculations. Unfortunately, structural data related to
macrocyclic metal chelates considered above are absent in the
literature. Nevertheless, such a comparison in this case is still
possible with the example of macrocyclic chelates of 3d-ele-
ment ions M(II) with the phthalocyanine V. 9already men-
tioned, since for some of them [namely, for Mn(II), Fe(II),
Co(II), Ni(II) and Cu (II)] such data are available [78–83].
Macrocyclic metal chelates with this ligand are, as is easy to
see, also more complex than any other macrocyclic com-
pounds that have been considered above. The results of these
calculations using two of both theory levels, namely DFT
B3LYP/6-31G(d) and DFT OPBE/TZVP have been presented
in the Table 4. As can be seen from the data presented in it, the
key parameters of the molecular structures of these macrocy-
clic metal chelates (bond lengths, valence, and torsion angles)
calculated by these methods are in good agreement with the
experimentally determined ones. Besides, using the DFT
OPBE/TZVP method as a whole gives better agreement with
experiment than using the DFT B3LYP/6-31G(d)method.In
connection with this circumstance, it can be assumed that if
the variants of the DFT method considered in this paper give a
good agreement between the calculated and experimental
structural data for such complex compounds as metal chelates
M(II) phthalocyanine, then for the simpler macrocyclic metal
chelates there will be no less good similar accordance.
In favor of such a conclusion, the comparison of the results
of quantum-chemical calculations of the Ni(II)-
hydrazinomethanethioamide chelate with using different
levels of the DFT theory (B3LYP/6-31G(d), B3LYP/6-
31G(d)//LanL2DZ, B3LYP/6-31G(d)// SDDAll, B3LYP/cc-
pVTZ, B3PW91/6-31G(d), B3LYP/6-311++G(d,f,p),
wB97XD/6-31G(d), OPBE/TZVP), with experimental struc-
tural data for this compound [57], is evidence [84].
Conclusions
As can be seen from the foregoing, the structures of
macrotricyclic and macrotetracyclic metal chelates with
tetradentate compartmental or macrocyclic ligands (chelants)
and (NNNN)- and (NXXN)-coordination to the central M(II)
ion (X = O or S, M is a 3d-metal from the Mn–Zn series) are,
on the whole, rather unique. Such a situation occurs both for
open-chain chelates and those with a closed contour. It, in
essence, have no analogues among the Btraditional^bis(-
chelate) complexes formed by the same complex-forming
atoms with bidentate ligands containing the same donor N,
O, and/or S atoms. This manifests itself in the fact that, with
rare exceptions, they have noncoplanar molecular structures,
which are determined, to a much greater extent, by the nature
of the corresponding compartmental or macrocyclic ligand
(chelant) than by the nature of the complex-forming M(II)
atom. All appearances, in most cases namely the chelant
Bdetermines^also the geometric type of the metal chelate
node (tetragonal-pyramidal, planar, or tetrahedral) in the com-
plexes formed by it. It is characteristic that quite often, con-
trary to expectations, not only these metal chelates as a whole
turn out to be noncoplanar, but also key moieties of their
structures, such as single metal chelate rings, are also nonco-
planar. This is true not only for asymmetric, but also, in some
cases, for symmetric complexes.
Theoretically, one can expect that the nature of the polymer
will also exert a certain influence on the structural parameters
of macrocyclic metal complexes immobilized in the polymer
matrix [85–88]. At present time, however, by means of
quantum-chemical modeling, it is not possible to take into
account the influence of structural parameters of gelatin or
other polymers on the structures of those macrocyclic metal
chelates that are formed in these polymer matrices during the
corresponding chemical reactions. On the one hand, this has
been connected with the fact that the corresponding level of
DFT theory is still under elaboration. On the other hand, even
HN
H3C
CH3
N
N
N
NNH NH
N
H
S
S
CH3
CH3
V. 8
N
N
NH
HN
N
NN
N
V. 9
Struct Chem (2018) 29:777–802 799
with its presence, the difficulties of quantum-chemical calcu-
lations with its use will repeatedly increase and at this stage of
their development will require very large computer capacities
that can hardly be accessed by modern researchers. So that,
taking into account the influence of the specificity of the poly-
mer matrix on the structure of macrocyclic metal chelates is
already a perspective for the future.
Of course, the final commentary on the specific features of
the molecular structures of macrocyclic metal chelates can be
continued, but it is also quite enough for the statement that the
theoretical structural chemistry of the abovementioned class
of coordination compounds clearly deserves to be developed
henceforward.
Funding information The present review was carried out with financial
support in the framework of draft no. 4.5784.2017/8.9 to the competitive
part of the state task of the Russian Federation on the 2017–2019 years.
Compliance with ethical standards
Conflict of interest The author declares that he has no conflict of
interest.
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