Molecular and Electronic Structures of Macrocyclic Compounds Formed at Template Synthesis in the M(II)—Thiocarbohydrazide—Diacetyl Triple Systems: A Quantum-Chemical Analysis by DFT Methods

Abstract

Using density functional theory (DFT) B3PW91/TZVP, M06/TZVP, and OPBE/TZVP chemistry models and the Gaussian09 program, a quantum-chemical calculation of geometric and thermodynamic parameters of Ni(II), Cu(II), and Zn(II) macrotetracyclic chelates, with (NNNN)-coordination of ligand donor centers arising during template synthesis between the indicated ions of 3d elements, thiocarbohydrazide H2N–HN–C(=S)–NH–NH2 and diacetyl Me–C(=O)–C(=O)–Me, in gelatin-immobilized matrix implants was performed. The key bond lengths and bond angles in these coordination compounds are provided, and it is noted that in all these complexes the MN4 chelate sites, the grouping of N4 atoms bonded to the M atom, and the five-membered and six-membered metal chelate rings are practically coplanar. NBO analysis of these compounds was carried out, on the basis of which it was shown that all these complexes, in full accordance with theoretical expectations, are low-spin complexes. The standard thermodynamic characteristics of the template reactions for the formation of the above complexes are also presented. Good agreement between the data obtained using the above DFT levels is noted.

Full text

Citation: Mikhailov, O.V.; Chachkov,
D.V. Molecular and Electronic
Structures of Macrocyclic Compounds
Formed at Template Synthesis in the
M(II)—Thiocarbohydrazide—Diacetyl
Triple Systems: A Quantum-Chemical
Analysis by DFT Methods. Molecules
2023,28, 4383. https://doi.org/
10.3390/molecules28114383
Academic Editor: Ana Margarida
Gomes da Silva
Received: 7 May 2023
Revised: 22 May 2023
Accepted: 25 May 2023
Published: 27 May 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
molecules
Article
Molecular and Electronic Structures of Macrocyclic
Compounds Formed at Template Synthesis in the
M(II)—Thiocarbohydrazide—Diacetyl Triple Systems:
A Quantum-Chemical Analysis by DFT Methods
Oleg V. Mikhailov 1 ,*and Denis V. Chachkov 2
1Department of Analytical Chemistry, Certificatioin and Quality Management, Kazan National Research
Technological University, K. Marx Street 68, 420015 Kazan, Russia
2Kazan Department of Joint Supercomputer Center of Russian Academy of Sciences—Branch of Federal
Scientific Center “Scientific Research Institute for System Analysis of the RAS”, Lobachevskii Street 2/31,
420111 Kazan, Russia; de2005c@gmail.com
*Correspondence: ovm@kstu.ru
Abstract:
Using density functional theory (DFT) B3PW91/TZVP, M06/TZVP, and OPBE/TZVP
chemistry models and the Gaussian09 program, a quantum-chemical calculation of geometric and
thermodynamic parameters of Ni(II), Cu(II), and Zn(II) macrotetracyclic chelates, with (NNNN)-
coordination of ligand donor centers arising during template synthesis between the indicated ions of
3d elements, thiocarbohydrazide H
2
N–HN–C(=S)–NH–NH
2
and diacetyl Me–C(=O)–C(=O)–Me, in
gelatin-immobilized matrix implants was performed. The key bond lengths and bond angles in these
coordination compounds are provided, and it is noted that in all these complexes the MN
4
chelate
sites, the grouping of N
4
atoms bonded to the M atom, and the five-membered and six-membered
metal chelate rings are practically coplanar. NBO analysis of these compounds was carried out, on the
basis of which it was shown that all these complexes, in full accordance with theoretical expectations,
are low-spin complexes. The standard thermodynamic characteristics of the template reactions for
the formation of the above complexes are also presented. Good agreement between the data obtained
using the above DFT levels is noted.
Keywords:
template synthesis; Ni(II); Cu(II); Zn(II); thiocarbohydrazide; diacetyl; 3,10-dithio-6,7,13,14-
tetramethyl-1,2,4,5,8,9,11,12-octaazacyclotetradecatetraene-1,5,7,12; DFT method
1. Introduction
Previously, in [
1
], the template synthesis in the system Cu(II)–thiocarbohydrazide
H
2
N–HN–C(=S)–NH–NH
2
–diacetyl Me–C(=O)–C(=O)–Me in copper(II)hexacyanoferrate
(II) gelatin-immobilized matrix implants and the formation of a macrotetracyclic chelate of
the indicated metal ion were described, in which the ligand contained in it, namely, the
double-deprotonated form 3,10-dithio-6,7,13,14-tetramethyl-1,2,4,5,8,9,11,12-octaazacyclo-
tetradecatetraene-1,5,7,12 (
L2−
), coordinated to Cu(II) via four donor nitrogen atoms
(Figure 1
). The question of the specificity of the molecular structure of this complex (Cu
L
),
however, has not yet been resolved, because neither in [
1
] nor any other researchers have
been able to obtain single crystals of this compound suitable for XRD analysis. The com-
plexes considered in the article [
1
] belong to the category of metal-macrocyclic compounds
with a closed loop, in which the complex metal ion is located in the internal cavity of
the macrocyclic organic compound. Such complexes have a number of unique properties
that are not inherent in the complexes of the same metals with acyclic ligands and, for
this reason alone, are of considerable interest to modern fundamental chemistry. On the
other hand, these complexes and the macrocyclic ligands contained in them are quite close
in their structure to metal-porphyrins and metal-porphyrazines (complexes formed by
Molecules 2023,28, 4383. https://doi.org/10.3390/molecules28114383 https://www.mdpi.com/journal/molecules

Molecules 2023,28, 4383 2 of 13
porphyrin and porphyrazine, respectively) and can be considered as their peculiar “precur-
sors”. The field of the practical application of metal-porphyrins and metal-porphyrazines
is very significant (optics, luminescence, catalysis, medicine, sensorics, etc.), as a result
of which this group of coordination compounds is one of the most studied at present. In
this context, it seems interesting and important to obtain objective data on the structural
and geometric parameters of this chemical compound using quantum-chemical calcula-
tions using some version of the density functional theory (DFT), which is currently the
most popular method for calculating the molecular and electronic structures of 3d-element
complexes. On the other hand, it is very likely that in a similar way, i.e., as a result of the
combination of the above ligand synthons, accompanied by intramolecular dehydration
(Figure 2
), the same complexes of chemical elements adjacent to copper, nickel, and zinc
can be formed, although there is no information about this possibility either in [
1
] or in any
other publications devoted to template synthesis. Since it is these two 3delements that, in
terms of the complexes they form, are closest to Cu(II) complexes compared to those for
the other d-elements, it seems appropriate, first, to confirm the possibility of the existence
of Ni(II) and Zn(II) metal chelates with the above ligand
L2−
, and secondly, in case of a
positive answer to this question, compare the parameters of their molecular and electronic
structures, as well as their thermodynamic characteristics, with similar parameters for
the Cu
L
complex. The presentation of these data and their discussion will be carried out
further in the given article.
Molecules 2023, 28, x FOR PEER REVIEW 2 of 13
other hand, these complexes and the macrocyclic ligands contained in them are quite close
in their structure to metal-porphyrins and metal-porphyrazines (complexes formed by
porphyrin and porphyrazine, respectively) and can be considered as their peculiar “pre-
cursors”. The field of the practical application of metal-porphyrins and metal-porphyra-
zines is very significant (optics, luminescence, catalysis, medicine, sensorics, etc.), as a re-
sult of which this group of coordination compounds is one of the most studied at present.
In this context, it seems interesting and important to obtain objective data on the structural
and geometric parameters of this chemical compound using quantum-chemical calcula-
tions using some version of the density functional theory (DFT), which is currently the
most popular method for calculating the molecular and electronic structures of 3d-element
complexes. On the other hand, it is very likely that in a similar way, i.e., as a result of the
combination of the above ligand synthons, accompanied by intramolecular dehydration
(Figure 2), the same complexes of chemical elements adjacent to copper, nickel, and zinc
can be formed, although there is no information about this possibility either in [1] or in
any other publications devoted to template synthesis. Since it is these two 3d elements
that, in terms of the complexes they form, are closest to Cu(II) complexes compared to
those for the other d-elements, it seems appropriate, first, to confirm the possibility of the
existence of Ni(II) and Zn(II) metal chelates with the above ligand L2−, and secondly, in
case of a positive answer to this question, compare the parameters of their molecular and
electronic structures, as well as their thermodynamic characteristics, with similar param-
eters for the CuL complex. The presentation of these data and their discussion will be
carried out further in the given article.
Figure 1. The structural formula of the complex formed during template synthesis in the Cu(II)–
thiocarbohydrazide–diacetyl system as described in [1].
Figure 1.
The structural formula of the complex formed during template synthesis in the Cu(II)–
thiocarbohydrazide–diacetyl system as described in [1].
Molecules 2023, 28, x FOR PEER REVIEW 2 of 13
other hand, these complexes and the macrocyclic ligands contained in them are quite close
in their structure to metal-porphyrins and metal-porphyrazines (complexes formed by
porphyrin and porphyrazine, respectively) and can be considered as their peculiar “pre-
cursors”. The field of the practical application of metal-porphyrins and metal-porphyra-
zines is very significant (optics, luminescence, catalysis, medicine, sensorics, etc.), as a re-
sult of which this group of coordination compounds is one of the most studied at present.
In this context, it seems interesting and important to obtain objective data on the structural
and geometric parameters of this chemical compound using quantum-chemical calcula-
tions using some version of the density functional theory (DFT), which is currently the
most popular method for calculating the molecular and electronic structures of 3d-element
complexes. On the other hand, it is very likely that in a similar way, i.e., as a result of the
combination of the above ligand synthons, accompanied by intramolecular dehydration
(Figure 2), the same complexes of chemical elements adjacent to copper, nickel, and zinc
can be formed, although there is no information about this possibility either in [1] or in
any other publications devoted to template synthesis. Since it is these two 3d elements
that, in terms of the complexes they form, are closest to Cu(II) complexes compared to
those for the other d-elements, it seems appropriate, first, to confirm the possibility of the
existence of Ni(II) and Zn(II) metal chelates with the above ligand L2−, and secondly, in
case of a positive answer to this question, compare the parameters of their molecular and
electronic structures, as well as their thermodynamic characteristics, with similar param-
eters for the CuL complex. The presentation of these data and their discussion will be
carried out further in the given article.
Figure 1. The structural formula of the complex formed during template synthesis in the Cu(II)–
thiocarbohydrazide–diacetyl system as described in [1].
Figure 2.
General scheme of the key reaction of template synthesis in the M(II)–thiocarbohydrazide–
diacetyl systems (M = Ni, Cu, Zns).

Molecules 2023,28, 4383 3 of 13
2. Results
We immediately note two circumstances that are of particular importance for our
further narration. First, each of the three different chemistry models we used, namely,
B3PW91/TZVP, M06/TZVP, and OPBE/TZVP, unambiguously predicts the possibility of
the existence of each of the three Ni
L
, Cu
L
, and Zn
L
complexes mentioned above. Second,
for each of these coordination compounds, all these three methods give practically the same
results, both qualitatively and quantitatively.
The key parameters of the molecular structures calculated by the three different
DFT methods mentioned above, namely, the bond lengths and the angles between the
lines of these bonds (bond angles) for each of the three M
L
-type chelates (M = Ni, Cu,
Zn) considered by us with the above “template” ligand 3,10-dithio-6,7,13,14-tetramethyl-
1,2,4,5,8,9,11,12-octaazacyclotetradecatetraene-1,5,7,12, are presented in Table 1. All three
chemistry models unambiguously predict the coplanar coordination of donor nitrogen
atoms of this macrocyclic ligand with respect to the central metal ion, since in the MN
4
chelate nodes for the indicated M, the sum of four bond angles (N1M1N2), (N2M1N3),
(N3M1N4), and (N4M1N1), formed by donor atoms and M atoms (
BAS
), is exactly 360.0
◦
(which corresponds exactly to a flat quadrilateral). The same situation also takes place
for the sum of non-bonding angles (NBAS) formed by neighboring donor nitrogen atoms
(Table 1); consequently, the grouping of N
4
donor atoms is also coplanar. Wherein, in none
of the M
L
(M = Ni, Cu, Zn) complexes that we considered, it is rectangular—in each of
them, only pairwise equality of angles (NNN) takes place, and all these angles, of course,
are not equal to 90
◦
. This difference, as expected, is most pronounced in the case of Zn
L
and least strongly in the case of Ni
L
(Table 1). As for the M–N bond lengths, taking into
account the fact that they are equivalent to each other only in pairs, one should expect them
to be only pairwise equal, and the calculation results for each of the three variants of the
DFT chemistry models used in the work are in full agreement with this prediction. On the
other hand, in the series Ni(II)–Cu(II)–Zn(II), there is an increase in ionic radii, as a result of
which one can theoretically expect an increase in the lengths of these bonds; this conclusion
is also in good agreement with the data presented in Table 1. Unlike the metal–nitrogen
bonds, the lengths of the carbon–carbon, carbon–nitrogen, and nitrogen–nitrogen bonds
show a much weaker dependence on the nature of the 3d-element M, but pairwise equality
was also observed. The carbon–sulfur bond lengths in each of these complexes are the
same, which also seems quite natural.
Table 1. Key parameters of the molecular structures of Ni(II), Cu(II), and Zn(II) complexes with the
double-deprotonated form of the macrocyclic ligand, 3,10-dithio-6,7,13,14-tetramethyl-1,2,4,5,8,9,11,12
-
octaazacyclotetradecatetraene-1,5,7,12 (
L2−
) calculated by B3PW91/TZVP, M06/TZVP, and
OPBE/TZVP chemistry models.
Complex NiL CuL ZnL
Chemistry Model Chemistry Model Chemistry Model
Structural
Parameter B3PW91/TZVP M06/TZVP OPBE/TZVP B3PW91/TZVP M06/TZVP OPBE/TZVP B3PW91/TZVP M06/TZVP OPBE/TZVP
Bond lengths in the MN4chelate node, pm
(M1N1) 183.9 184.2 183.4 188.9 188.8 189.4 191.0 190.5 191.4
(M1N2) 183.5 184.2 182.6 190.9 191.4 190.9 197.5 198.2 197.7
(M1N3) 183.9 184.2 183.4 188.9 188.8 189.4 191.0 190.5 191.3
(M1N4) 183.5 184.2 182.6 190.9 191.4 190.9 197.5 198.2 197.6
Separate bond lengths outside the MN4chelate node, pm
(C1S1),
(C2S2) 165.9 165.7 165.9 166.0 165.7 166.1 166.0 165.7 166.0
(C1N5),
(C2N6) 137.8 138.0 137.7 139.8 140.0 140.0 141.6 141.7 141.8
(N2N6),
(N4N5) 135.6 135.7 135.1 134.9 134.9 134.2 134.3 134.3 133.8

Molecules 2023,28, 4383 4 of 13
Table 1. Cont.
Complex NiL CuL ZnL
Chemistry Model Chemistry Model Chemistry Model
Structural
Parameter B3PW91/TZVP M06/TZVP OPBE/TZVP B3PW91/TZVP M06/TZVP OPBE/TZVP B3PW91/TZVP M06/TZVP OPBE/TZVP
(C4C5),
(C3C6) 145.7 146.0 145.1 147.5 147.7 146.9 148.8 148.8 148.2
(C5N7),
(C6N8) 130.1 129.5 131.2 130.4 129.8 131.6 130.7 130.0 132.0
(C6C8),
(C5C9) 150.6 150.1 150.6 150.8 150.3 150.9 151.0 150.4 151.1
(C4C10),
(C7C8) 149.9 149.4 149.9 150.0 149.5 150.1 150.1 150.0 150.2
Bond angles in the MN4chelate node, deg
(N1M1N2) 94.1 94.1 94.1 94.7 94.7 94.7 95.1 95.2 95.0
(N2M1N3) 85.9 85.9 85.9 85.3 85.3 85.3 84.9 84.8 85.0
(N3M1N4) 94.1 94.1 94.1 94.7 94.7 94.7 95.1 95.2 95.0
(N4M1N1) 85.9 85.9 85.9 85.3 85.3 85.3 84.9 84.8 85.0
Bond angles
sum (BAS) 360.0 360.0 360.0 360.0 360.0 360.0 360.0 360.0 360.0
Non-bond angles in the N4grouping, deg
(N1N2N3) 90.1 90.0 90.2 89.4 89.2 89.5 88.1 87.7 88.2
(N2N3N4) 89.9 90.0 89.8 90.6 90.8 90.5 91.9 92.3 91.8
(N3N4N1) 90.1 90.0 90.2 89.4 89.2 89.5 88.1 87.7 88.2
(N4N1N2) 89.9 90.0 89.8 90.6 90.8 90.5 91.9 92.3 91.8
Non-bond
angles sum
(NBAS)
360.0 360.0 360.0 360.0 360.0 360.0 360.0 360.0 360.0
Bond angles in the 5-numbered (M1N4N5C1N1) chelate ring, deg
(M1N4N5) 110.5 110.3 110.9 109.0 108.9 109.1 107.9 107.6 107.8
(N4N5C1) 119.1 119.2 119.3 120.5 120.5 120.9 121.1 121.0 121.6
(N5C1N1) 109.7 109.8 109.1 111.1 111.1 110.7 111.9 112.0 111.6
(C1N1M1) 114.8 114.8 114.8 114.1 114.2 114.0 114.2 114.5 114.0
(N1M1N4) 85.9 85.9 85.9 85.3 85.3 85.3 84.9 84.8 85.0
Bond angles
sum
(VAS51)
540.0 540.0 540.0 540.0 540.0 540.0 540.0 540.0 540.0
Bond angles in the 5-numbered (M1N2N6C2N3) chelate ring, deg
(M1N2N6) 110.5 110.3 110.9 109.0 108.9 109.1 107.9 107.6 107.8
(N2N6C2) 119.1 119.2 119.3 120.5 120.5 120.9 121.1 121.0 121.6
(N6C2N3) 109.7 109.8 109.1 111.1 111.1 110.7 111.9 112.0 111.6
(C2N3M1) 114.8 114.8 114.8 114.1 114.2 114.0 114.2 114.5 114.0
(N3M1N2) 85.9 85.9 85.9 85.3 85.3 85.3 84.9 84.8 85.0
Bond angles
sum
(VAS52)
540.0 540.0 540.0 540.0 540.0 540.0 540.0 540.0 540.0
Bond angles in the 6-numbered (M1N1N7C5C4N2) chelate ring, deg
(M1N1N7) 128.5 128.3 128.8 127.0 126.8 127.1 126.1 125.9 126.6
(N1N7C5) 122.2 122.4 122.3 122.3 122.5 122.4 122.2 122.3 121.7
(N7C5C4) 127.0 127.2 126.8 129.5 129.5 129.6 131.6 131.6 132.1
(C5C4N2) 120.3 120.4 119.9 120.4 120.5 120.0 120.0 120.1 119.4
(C4N2M1) 127.9 127.6 128.1 126.1 126.0 126.2 125.0 124.4 125.2
(N2M1N1) 94.1 94.1 94.1 94.7 94.7 94.7 95.1 95.2 95.0
Bond angles
sum
(VAS61)
720.0 720.0 720.0 720.0 720.0 720.0 720.0 719.5 720.0

Molecules 2023,28, 4383 5 of 13
Table 1. Cont.
Complex NiL CuL ZnL
Chemistry Model Chemistry Model Chemistry Model
Structural
Parameter B3PW91/TZVP M06/TZVP OPBE/TZVP B3PW91/TZVP M06/TZVP OPBE/TZVP B3PW91/TZVP M06/TZVP OPBE/TZVP
Bond angles in the 6-numbered (M1N3N8C6C3N4) chelate ring, deg
(M1N3N8) 128.5 128.3 128.8 127.0 126.8 127.1 126.1 125.9 126.6
(N3N8C6) 122.2 122.4 122.3 122.3 122.5 122.4 122.2 122.3 121.7
(N8C6C3) 127.0 127.2 126.8 129.5 129.5 129.6 131.6 131.6 132.1
(C6C3N4) 120.3 120.4 119.9 120.4 120.5 120.0 120.0 120.1 119.4
(C3N4M1) 127.9 127.6 128.1 126.1 126.0 126.2 125.0 124.4 125.2
(N4M1N3) 94.1 94.1 94.1 94.7 94.7 94.7 95.1 95.2 95.0
Bond angles
sum
(VAS62)
720.0 720.0 720.0 720.0 720.0 720.0 720.0 719.5 720.0
Bond angles outside chelate rings, deg
(N1C1S1),
(N3C2S2) 130.6 130.6 130.9 130.7 130.6 131.1 130.8 130.7 131.4
(N5N4C3),
(N6N2C4) 121.6 122.1 121.0 124.8 125.2 124.6 127.2 127.6 127.1
(N4C3C7),
(N2C4C10) 118.8 118.7 119.1 118.6 118.5 118.9 118.8 119.3 119.0
(C3C6C8),
(C4C5C9) 118.8 118.4 119.6 117.3 117.0 117.9 116.1 115.6 116.6
(C8C6N8),
(C9C5N7) 114.1 114.4 113.6 113.2 113.5 112.4 112.2 112.8 111.3
(C6C3C7),
(C5C4C10) 120.9 120.8 121.0 121.0 121.0 121.1 121.3 120.6 121.5
With respect to five-membered [(M1N4N5C1N1), (M1N2N6C2N3)] and six-membered
[(M1N1N7C5C4N2), (M1N3N8C6C3N4)] metal chelate rings, it should be noted that all of
them, as well as the MN
4
chelate nodes, are also coplanar, since the sums of internal bond
angles in any of them are either equal to 540
◦
and 720
◦
, which coincides with the sum of the
internal angles in a flat pentagon and hexagon, respectively, or very slightly differs from
these values (as is the case for the Zn
L
complex calculated by the DFT M06/TZVP method).
Characteristically, these metal chelate rings are pairwise identical to each other, not only
in terms of the sum of bond angles but also in their sets, which depend relatively little on
the nature of M (Table 1). In view of the foregoing, the M
L
complexes under consideration
can be considered practically planar (although, given that they also include, among other
things, four methyl groups that are not a priori planar, it should be recognized that none
of them). This fact is very interesting; considering that, according to quite numerous data
presented in [
2
–
10
], macrotetracyclic chelate complexes of 3d elements with cyclic ligands
containing two five-membered and two six-membered metal chelate rings, contrary to
theoretical expectations, are non-coplanar, and in them, as a rule, all these four cycles
are non-coplanar. Each of the Ni
L
, Cu
L
, and Zn
L
complexes under consideration has
one second-order axis, a horizontal plane of symmetry, and a center of symmetry, and,
consequently, they all have the C
2h
symmetry group. In this circumstance, it is quite
understandable that according to the data of our calculation by the DFT B3PW91/TZVP as
well as and by the DFT M06/TZVP and DFT OPBE/TZVP, the dipole electric moment (
µ
)
of each of them practically does not differ from zero. Images of the molecular structures of
these metal chelates are presented in Figure 3.

Molecules 2023,28, 4383 6 of 13
Molecules 2023, 28, x FOR PEER REVIEW 5 of 13
relatively lile on the nature of M (Table 1). In view of the foregoing, the ML complexes
under consideration can be considered practically planar (although, given that they also
include, among other things, four methyl groups that are not a priori planar, it should be
recognized that none of them). This fact is very interesting; considering that, according to
quite numerous data presented in [2–10], macrotetracyclic chelate complexes of 3d ele-
ments with cyclic ligands containing two five-membered and two six-membered metal
chelate rings, contrary to theoretical expectations, are non-coplanar, and in them, as a rule,
all these four cycles are non-coplanar. Each of the NiL, CuL, and ZnL complexes under
consideration has one second-order axis, a horizontal plane of symmetry, and a center of
symmetry, and, consequently, they all have the C2h symmetry group. In this circumstance,
it is quite understandable that according to the data of our calculation by the DFT
B3PW91/TZVP as well as and by the DFT M06/TZVP and DFT OPBE/TZVP, the dipole
electric moment (µ) of each of them practically does not differ from zero. Images of the
molecular structures of these metal chelates are presented in Figure 3.
(a)
(b)
Molecules 2023, 28, x FOR PEER REVIEW 6 of 13
(c)
Figure 3. Molecular structure images of NiL (a), CuL (b), and ZnL (c) metal chelates calculated using
the DFT B3PW91/TZVP chemistry model.
The key data of the NBO analysis of these compounds, namely, the effective charges
on the metal atoms M1 and donor nitrogen atoms N1, N2, N3, and N4 obtained by DFT
B3PW91/TZVP, DFT M06/TZVP, and DFT OPBE/TZVP chemistry models, are presented
in Table 2; the full NBO analysis can be found in the Supplementary Materials. As ex-
pected, they differ quite significantly from those that would take place if all bonds be-
tween atoms were ionic. This circumstance indicates a very pronounced delocalization of
the electron density within the entire molecular structure of each of the complexes under
consideration. Images of higher occupied (HOMO) and lower vacant (LUMO) molecular
orbitals for the considered complexes are shown in Figure 4. It should be noted that the
NBO analysis data for all three NiL, CuL, and ZnL complexes obtained using the above
DFT variants also agree quite well with each other (Table 2).
Table 2. Key data of NBO analysis for the NiL, CuL, and ZnL complexes in the ground state accord-
ing to DFT B3PW91/TZVP, DFT M06/TZVP, and DFT OPBE/TZVP chemistry models.
Complex Chemistry Model The Charges on the Atoms, in Electron Charge Units (ē) <S**2>
M1 N1 N2 N3 N4
NiL B3PW91/TZVP +0.379 −0.316 −0.187 −0.316 −0.187 0.0000
M06/TZVP +0.382 −0.335 −0.198 −0.335 −0.198 0.0000
OPBE/TZVP +0.314 −0.265 −0.173 −0.265 −0.173 0.0000
CuL B3PW91/TZVP +0.729 −0.411 −0.257 −0.411 −0.257 0.7500
M06/TZVP +0.711 −0.425 −0.262 −0.425 −0.262 0.7500
OPBE/TZVP +0.672 −0.364 −0.245 −0.364 −0.245 0.7500
ZnL B3PW91/TZVP +1.088 −0.508 −0.321 −0.509 −0.321 0.0000
M06/TZVP +1.071 −0.524 −0.326 −0.524 −0.326 0.0000
OPBE/TZVP +1.085 −0.475 −0.318 −0.475 −0.318 0.0000
The values of the key thermodynamic parameters of the metal chelates considered
here, namely, the standard enthalpies, entropies, and Gibbs energies of their formation
ΔfH0298, Sf0298, ΔfG0298, are presented in Table 3. As can be seen from it, the values of Sf0298
obtained by different versions of the DFT are quite close to each other, while the values of
Figure 3.
Molecular structure images of Ni
L
(
a
), Cu
L
(
b
), and Zn
L
(
c
) metal chelates calculated using
the DFT B3PW91/TZVP chemistry model.

Molecules 2023,28, 4383 7 of 13
The key data of the NBO analysis of these compounds, namely, the effective charges
on the metal atoms M1 and donor nitrogen atoms N1, N2, N3, and N4 obtained by DFT
B3PW91/TZVP, DFT M06/TZVP, and DFT OPBE/TZVP chemistry models, are presented
in Table 2; the full NBO analysis can be found in the Supplementary Materials. As expected,
they differ quite significantly from those that would take place if all bonds between atoms
were ionic. This circumstance indicates a very pronounced delocalization of the electron
density within the entire molecular structure of each of the complexes under consideration.
Images of higher occupied (HOMO) and lower vacant (LUMO) molecular orbitals for the
considered complexes are shown in Figure 4. It should be noted that the NBO analysis
data for all three Ni
L
, Cu
L
, and Zn
L
complexes obtained using the above DFT variants also
agree quite well with each other (Table 2).
Table 2.
Key data of NBO analysis for the Ni
L
, Cu
L
, and Zn
L
complexes in the ground state according
to DFT B3PW91/TZVP, DFT M06/TZVP, and DFT OPBE/TZVP chemistry models.
Complex Chemistry Model The Charges on the Atoms, in Electron Charge Units (¯
e)
<S**2>
M1 N1 N2 N3 N4
NiL B3PW91/TZVP +0.379 −0.316 −0.187 −0.316 −0.187 0.0000
M06/TZVP +0.382 −0.335 −0.198 −0.335 −0.198 0.0000
OPBE/TZVP +0.314 −0.265 −0.173 −0.265 −0.173 0.0000
CuL B3PW91/TZVP +0.729 −0.411 −0.257 −0.411 −0.257 0.7500
M06/TZVP +0.711 −0.425 −0.262 −0.425 −0.262 0.7500
OPBE/TZVP +0.672 −0.364 −0.245 −0.364 −0.245 0.7500
ZnL B3PW91/TZVP +1.088 −0.508 −0.321 −0.509 −0.321 0.0000
M06/TZVP +1.071 −0.524 −0.326 −0.524 −0.326 0.0000
OPBE/TZVP +1.085 −0.475 −0.318 −0.475 −0.318 0.0000
Molecules 2023, 28, x FOR PEER REVIEW 7 of 13
ΔfH0298 and ΔfG0298 differ quite significantly from each other. Currently, it is not possible to
give preference to any of these methods in relation to these parameters. However, they
are all positive, and their modules are very significant. Characteristically, for each of the
complexes considered here, the smallest values of ΔfH0298 and ΔfG0298 are observed in the
case of using the DFT OPBE/TZVP and the largest in the case of using the DFT M06/TZVP.
Table 3. Standard thermodynamic parameters of formation for NiL, CuL, and ZnL complexes cal-
culated by B3PW91/TZVP, M06/TZVP, and OPBE/TZVP chemistry models.
Complex Chemistry Model ΔfH0298, kJ/mol Sf0298, J/mol∙К ΔfG0298, kJ/mol
NiL B3PW91/TZVP 769.1 745.5 966.6
M06/TZVP 891.0 742.7 1089.4
OPBE/TZVP 550.1 753.4 745.3
CuL B3PW91/TZVP 916.4 748.5 1114.1
M06/TZVP 1052.2 753.7 1248.3
OPBE/TZVP 753.3 760.5 947.4
ZnL B3PW91/TZVP 834.8 772.5 1027.9
M06/TZVP 983.9 766.1 1178.9
OPBE/TZVP 669.8 771.5 863.2
LUMO (alpha, beta) (−3.091) LUMO (beta) (−3.044) LUMO (alpha, beta) (−3.010)
LUMO (alpha) (−3.059)
Figure 4. Cont.

Molecules 2023,28, 4383 8 of 13
Molecules 2023, 28, x FOR PEER REVIEW 8 of 13
HOMO (beta) (−5.789)
HOMO (alpha, beta) (−5.670) HOMO (alpha) (−5.833) HOMO (alpha, beta) (−5.862)
NiL CuL ZnL
Figure 4. The pictures of HOMO and LUMO in the NiL, CuL, and ZnL complexes according to the
DFT B3PW91/TZVP chemistry model. The energy values of the given MOs (in brackets) are ex-
pressed in eV. The symbol “alpha” belongs to the electron having spin (+1/2), and the symbol “beta”
belongs to the electron having spin (−l/2).
The DFT B3PW91/TZVP and DFT M06/TZVP calculated standard thermodynamic
parameters of the template synthesis reactions leading to the formation of these complexes
(the general scheme of which is shown in Figure 2) as given in Table 4. As can be seen
from it, the values of each of these parameters calculated by these two versions of the DFT
are quite close to each other. That is, characteristically, for all these reactions, the relations
ΔrH0298 < 0, ΔrS0298 > 0, and ΔrG0298 < 0 take place. From this, in turn, it follows that for any
of the M = Ni, Cu, Zn considered by us, such reactions are thermodynamically allowed
not only under standard conditions with T = 298.16 K but also at any other temperature T,
since according to the Gibbs–Helmhol equation for an isobaric process
ΔrG(T) = ΔrH0 −
TΔrS0 the values of ΔrG(T) for these reactions will always be negative. It should be noted,
however, that the data presented in Table 4 refer to the gas phase, and therefore, our con-
clusion regarding the possibility of their implementation also applies to reactions occur-
ring precisely under such conditions.
Table 4. Standard thermodynamic parameters of template synthesis reactions of NiL, CuL, and ZnL
complexes in gaseous phase calculated by B3PW91/TZVP and M06/TZVP chemistry models.
Complex Chemistry Model ΔrH0 298, kJ ΔrSr0298, J/К ΔrG0 298, kJ
NiL B3PW91/TZVP −411.6 46.6 −425.5
M06/TZVP −393.1 65.6 −412.7
CuL B3PW91/TZVP −204.7 64.1 −223.8
M06/TZVP −191.2 91.2 −218.4
ZnL B3PW91/TZVP −77.0 80.5 −101.0
Figure 4.
The pictures of HOMO and LUMO in the Ni
L
, Cu
L
, and Zn
L
complexes according to
the DFT B3PW91/TZVP chemistry model. The energy values of the given MOs (in brackets) are
expressed in eV. The symbol “alpha” belongs to the electron having spin (+1/2), and the symbol
“beta” belongs to the electron having spin (−l/2).
The values of the key thermodynamic parameters of the metal chelates considered
here, namely, the standard enthalpies, entropies, and Gibbs energies of their formation
∆f
H
0298
,S
f0298
,
∆f
G
0298
, are presented in Table 3. As can be seen from it, the values of S
f0298
obtained by different versions of the DFT are quite close to each other, while the values of
∆f
H
0298
and
∆f
G
0298
differ quite significantly from each other. Currently, it is not possible
to give preference to any of these methods in relation to these parameters. However, they
are all positive, and their modules are very significant. Characteristically, for each of the
complexes considered here, the smallest values of
∆f
H
0298
and
∆f
G
0298
are observed in the
case of using the DFT OPBE/TZVP and the largest in the case of using the DFT M06/TZVP.
Table 3.
Standard thermodynamic parameters of formation for Ni
L
, Cu
L
, and Zn
L
complexes
calculated by B3PW91/TZVP, M06/TZVP, and OPBE/TZVP chemistry models.
Complex Chemistry Model ∆fH0298, kJ/mol Sf0298, J/mol K ∆fG0298 , kJ/mol
NiL B3PW91/TZVP 769.1 745.5 966.6
M06/TZVP 891.0 742.7 1089.4
OPBE/TZVP 550.1 753.4 745.3
CuL B3PW91/TZVP 916.4 748.5 1114.1
M06/TZVP 1052.2 753.7 1248.3
OPBE/TZVP 753.3 760.5 947.4
ZnL B3PW91/TZVP 834.8 772.5 1027.9
M06/TZVP 983.9 766.1 1178.9
OPBE/TZVP 669.8 771.5 863.2

Molecules 2023,28, 4383 9 of 13
The DFT B3PW91/TZVP and DFT M06/TZVP calculated standard thermodynamic
parameters of the template synthesis reactions leading to the formation of these complexes
(the general scheme of which is shown in Figure 2) as given in Table 4. As can be seen
from it, the values of each of these parameters calculated by these two versions of the DFT
are quite close to each other. That is, characteristically, for all these reactions, the relations
∆r
H
0298
< 0,
∆r
S
0298
> 0, and
∆r
G
0298
< 0 take place. From this, in turn, it follows that for
any of the M = Ni, Cu, Zn considered by us, such reactions are thermodynamically allowed
not only under standard conditions with T= 298.16 K but also at any other temperature T,
since according to the Gibbs–Helmholtz equation for an isobaric process
∆r
G(T) =
∆r
H
0
−
T
∆r
S
0
the values of
∆r
G(T) for these reactions will always be negative. It should be
noted, however, that the data presented in Table 4refer to the gas phase, and therefore,
our conclusion regarding the possibility of their implementation also applies to reactions
occurring precisely under such conditions.
Table 4.
Standard thermodynamic parameters of template synthesis reactions of NiL, CuL, and ZnL
complexes in gaseous phase calculated by B3PW91/TZVP and M06/TZVP chemistry models.
Complex Chemistry Model ∆rH0298, kJ ∆rSr0298, J/K ∆rG0298, kJ
NiL B3PW91/TZVP −411.6 46.6 −425.5
M06/TZVP −393.1 65.6 −412.7
CuL B3PW91/TZVP −204.7 64.1 −223.8
M06/TZVP −191.2 91.2 −218.4
ZnL B3PW91/TZVP −77.0 80.5 −101.0
M06/TZVP −66.7 96.0 −95.3
According to our data, the ground state of the Ni
L
and Zn
L
chelates in each of the
DFT variants used by us is a spin singlet and that of the Cu
L
chelate is a spin doublet, so
that all of them belong to the category of low-spin complexes. This is confirmed by the
calculation data of the <S**2> parameter, which is equal to 0.0000 in the case of the Ni
L
and
Zn
L
complexes and 0.7500 in the case of CuL, which correspond to the spin multiplicities
M
S
= 1 and M
S
= 2, respectively. Wherein, the difference in the energies of structures
with a spin multiplicity different from that of the ground state (triplet in the case of Ni
L
and Zn
L
, quartet in the case of Cu
L
) is 132.3, 146.7, and 144.7 kJ/mol (according to DFT
B3PW91/TZVP), 148.7, 157.3, and 200.1 kJ/mol (according to DFT B3PW91/TZVP), and
101.6, 120.7, and 124.3 kJ/mol (according to DFT OPBE/TZVP), respectively. As can be
seen from these data, the nearest excited state in each of the complexes under study is much
higher than the ground state, so that spin cross-over (spin isomerism) is impossible here in
principle. That is, interestingly, the largest differences between the energies of the ground
and nearest excited states with a different spin multiplicity, as well as for the parameters
∆f
H
0298
and
∆f
G
0298
, take place in the case of using the DFT M06/TZVP and the smallest
in the case of using the DFT OPBE/TZVP.
3. Calculation Method
When performing calculations, we used a variant of the density functional theory
(DFT), which combines the standard extended valence-split basis set TZVP and the most
modern hybrid functional M06, described in detail in [
11
], which, according to its authors, is
best suited for calculations of 3d-element compounds. For comparison, we also used another
version of the DFT, namely, with B3PW91 functional, which is described in detail in [
12
–
14
]
and used by us, in particular, in recently published papers [
15
–
17
]. The use of this variant
of the DFT, in this case, is due to the fact that, according to [
12
–
14
] and our experience,
it allows, as a rule, to obtain the most accurate (i.e., close to experimental) values of the
geometric parameters of molecular structures, as well as significantly more accurate values
of thermodynamic and other physicochemical parameters compared to other variants

Molecules 2023,28, 4383 10 of 13
of DFT chemistry models. In addition to them, we also carried out calculations of the
molecular and electronic structures of the macrocyclic metal chelates by the OPBE/TZVP
method, which combines the above TZVP basis and the non-hybrid OPBE functional [
18
,
19
],
which, according to the data of works [
19
–
23
], in the case of 3d elements gives a fairly
accurate ratio of the energy of the high-spin state with respect to the energy of the low-spin
state and, at the same time, reliably characterizes the geometric parameters of the molecular
structures of the metal complexes observed by us. The calculations were carried out using
the Gaussian09 software package [
24
]. As in our previous articles, in which the above
calculation methods [
15
–
17
] were used, the correspondence of the found stationary points
to the energy minima in all cases was proved by calculating the second derivatives of the
energy with respect to the atomic coordinates; in this case, all the equilibrium structures
corresponding to the minimum points on the potential energy surfaces had only real (and,
moreover, always positive) frequency values. From the optimized structures, the structure
with the lowest total energy was chosen for further consideration. In accordance with the
theory of the structure of the atoms, Ni(II), Cu(II), and Zn(II) which are the complexes
under examination, should correspond to 3d
8
, 3d
9
, and 3d
10
electronic configurations,
respectively. In this context, spin multiplicities 1 and 3 in the case of Ni(II) and Zn(II) and
spin multiplicities 2 and 4 in the case of Cu(II) are considered for the given central metal
ions during the calculation. Among the structures optimized at these multiplicities, the
lowest-lying structure was selected. To calculate the parameters of molecular structures
with multiplicity greater than 1, we used the unrestricted method (UM06,UB3PW91, and
UOPBE). The energetically most favorable structure has always been checked according
to the STABLE = OPT procedure; in all cases, the wave functions corresponding to these
structures were stable. Natural Bond Orbital (NBO) analysis was carried out, using the NBO
3.1 version in the framework of the Gaussian09 program [
24
] according to the methodology
described in [
25
]. The standard thermodynamic parameters of a formation (
∆f
H
0298
,S
f0298
,
and
∆f
G
0298
) for the Ni(II), Cu(II), and Zn(II) macrocyclic compounds under study were
calculated employing the method [26].
4. Conclusions
Interest in metal macrocyclic compounds and prediction of their physicochemical
characteristics (including the calculation of molecular and electronic structures using
quantum-chemical calculations of various levels) continues to be consistently high on
the part of researchers, as evidenced by a number of recent works, in particular, [
27
–
40
],
and this article is just one of many devoted to the above topics. In summary, we would
like to emphasize that the above-mentioned data of quantum-chemical calculations per-
formed using three different variants of density functional theory, namely, B3PW91/TZVP,
M06/TZVP, and OPBE/TZVP chemistry models, unambiguously predict the possibility
of the existence of macrocyclic metal complexes Ni(II), Cu(II), and Zn(II) with macro-
cyclic tetradentate ligand, double-deprotonated form 3,10-dithio-6,7,13,14-tetramethyl-
1,2,4,5,8,9,11,12-octaazacyclotetradecatetraene-1,5,7,12 (L
2−
) with the ratio M(II): L
2−
= 1:1,
resulting from template synthesis in the ternary systems M(II)–thiocarbohydrazide–diacetyl
(M = Ni, Cu, Zn). Wherein, the reactions of template synthesis in each of these three ternary
systems are accompanied by a decrease in enthalpy and an increase in the entropy of the
reaction system; the latter circumstance is unusual for template processes, which, as a rule,
are accompanied by a decrease in this thermodynamic parameter. Based on the values
of
∆f
H
0298
,S
f0298
, and
∆f
G
0298
, it can be expected that the NiL complex will be the most
stable among them, the CuL complex will be the least stable, and the ZnL complex will
occupy an intermediate position. Remarkably, only the least stable of these complexes is
currently known [
1
]. In this regard, there is every reason to hope that the other two will
also be obtained, and at present it is important to confirm the theoretical prediction made
in the experiment.
The key structural fragments of these complexes, namely, chelate nodes,
two 5-membered
and two 6-membered metal chelate rings, are practically coplanar (which is also uncon-

Molecules 2023,28, 4383 11 of 13
ventional for metal chelates containing the listed atomic groups). The values of the key
parameters of molecular structures (bond lengths and bond angles) in the compounds
under consideration depend little on the nature of M(II) in their composition. Thus, the
decisive role in the formation of these structures belongs, as expected, to the macrocyclic
ligand itself.
Supplementary Materials:
The following supporting information can be downloaded at: https:
//www.mdpi.com/article/10.3390/molecules28114383/s1, NBO Analysis Data of ML complexes.
Author Contributions:
Conceptualization, O.V.M.; methodology, O.V.M. and D.V.C.; software, D.V.C.;
validation, O.V.M. and D.V.C.; formal analysis, O.V.M. and D.V.C.; investigation, O.V.M. and D.V.C.;
resources, D.V.C.; data curation, D.V.C.; writing—original draft preparation, O.V.M. and D.V.C.;
writing—review and editing, O.V.M.; visualization, O.V.M. and D.V.C.; supervision, O.V.M.; project
administration, O.V.M.; funding acquisition, D.V.C. All authors have read and agreed to the published
version of the manuscript.
Funding: This research received no external funding.
Institutional Review Board Statement: This study did not require institutional approval.
Informed Consent Statement: Not applicable.
Data Availability Statement: No unpublished data were created or analyzed in this article.
Acknowledgments:
All quantum-chemical calculations were performed at the Joint Supercomputer
Center of the Russian Academy of Sciences—Branch of Federal Scientific Center “Scientific Research
Institute for System Analysis of the RAS” which is acknowledged for technical support. The contri-
bution of author Denis V. Chachkov was funded by the state assignment to the Federal Scientific
Center “Scientific Research Institute for System Analysis of the RAS” for scientific research. Moreover,
this study was carried out using the equipment of the Center for Collective Use “Nanomaterials
and Nanotechnology” of the Kazan National Research Technological University with the financial
support of the Ministry of Science and Higher Education of the Russian Federation under agreement
No. 075-15-2021-699.
Conflicts of Interest:
The authors declare that they have no conflict of interest, financial or otherwise.
Sample Availability: Not applicable.
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