Download methods and models

Theoretical study of structure and intramolecular rearrangement of
coordination compounds of transition metals: methods and models
Koval Vitaliy Viktorovich1 and Starikov Andrey Georgievich2*+
1
Institute of Physical and Organic Chemistry. Southern Federal University. 194/2 Stachki Ave.
344090 Rostov on Don. Russian Federation.
2
Southern Scientific Center of Russian Academy of Sciences. 41 Chehova St.
344006 Rostov on Don. Russian Federation
Key words: transition metal complexes, quantum chemical calculations, density functional theory
Annotation
The applicability of different calculations schemas (HF, MP2, DFT, CAS and CCSD) for quantum
chemical study of transition metals coordination compounds structure and intramolecular rearrangement
have been considered. It is found, that B3LYP and B3LYP* functionals with 6-311++G(d,p) basis are
correct reproduces the characteristics of compounds with variable magnetic properties. It is shown that
theoretical study of transition metals coordination compounds with sterically overloaded ligands must to be
performed with full molecules geometry because bulky substituents may have essential influence on
stereochemistry of coordination unit and stabilization of spin states.
Introduction
The fast progress of computing machinery and the variety of application packages are
opening new horizons for theoretical study of structure and properties of coordination compounds.
Quantum chemical study of transition metals compounds and its reactions is supposing the using of
multideterminant approaches (CAS, CASPT2) or coupled cluster method (CCSD, CCSD(T)),
however a systematic consideration of metal-chelates rearrangements on this level is still technical
difficult task. In this connection a calibration of method permits to study correctly the real
compounds, consisting of several tens of atoms. Another problem of theoretical study of
coordination compounds of transition metals is model choice, which adequate describes its structure
and properties in crystalline state. In this study an applicability of different quantum chemical
approaches for study of transition metals compounds with open shell will have been shown on
series of experimental characterized systems.
Calculations with using of the one-determinant approximations
Important difference of metal coordination compounds from organic systems is
stereochemical non-rigidity, which have been conditioned by availability of “metal-donor atom”
bonds. “Elasticity” of such noncovalent interactions promotes to realization of intramolecular
rearrangements, accompanying by the changes in stereochemistry [1], spin state [2,3,4] or valence
isomerism [5-9] of complexes. One of most studied processes is the bis-chelate enantiomerization
[10]. Previously the intramolecular rearrangements of Be(II) and Zn(II) complexes have been
explored by MNDO[11] and RHF[12] methods, but this approximations are not applicable for study
of systems with open shell.
Relative energies of conformational isomers of Ni(II) 1, 2 and Co(II) 3, 4 bis-chelate aminovinylketonate complexes have been calculated for a choice of most appropriative method and
basis set for study of mechanism and energetic characteristics of spin-forbidden rearrangements of
transition metals.
1
H3C
H3C
N
O
N
O
Ni
Ni
O
N
O
N
CH3
CH3
1
2
H
H
N
O
N
O
Co
Co
O
N
O
N
H
H
3
4
According to the data of X-ray and magnetochemical studies these complexes in the
crystalline state are characterized by planar structure of coordination junction. The presence of
dynamic equilibrium between its low-spin planar and high-spin pseudo tetrahedral forms in noncoordinating solvents has been proved by NMR method [13, 14]. The measured difference of free
energies between conformational isomers of nickel complexes 1 and 2 is 2-5 kcal/mol, and in cobalt
complexes 3 and 4 – from -2 to +2 kcal/mol depending on substituents at carbon atoms of chelate
cycles.
The calculations by using HF, MP2 and DFT methods and different basis sets with
Gaussian03 program [15] have been made for study of approximation level influence on energy
characteristics of low- and high-spin forms of Ni(II) and Co(II) complexes [16]. As follows from
Table 1, the Hartree-Fock method overestimates the high-spin state stabilization energy regardless
of the used basis.
Table 1. Energy parameters of structures 1-4, calculated using HF, MP2 and DFT methods. Е – energy
difference between low- and high-spin states, EZPE - energy difference between low-and high-spin states,
taking into account zero-point energy of harmonic vibrations.
Method/basis
HF/6-31G(d,p)
HF/6-311++G(d,p)
MP2(full)/6-31G(d,p)
MP2(full)/6-311++G(d,p)
B3LYP/SDD
B3LYP/6-31G(d,p)
B3LYP/6-311++G(d,p)
Experiment
1
E,
kcal/mol
-44.2
-44.4
-5.3
-1.6
-2.4
-0.4
2.3
2
Ezpe,
kcal/mol
-46.0
-46.2
-6.6
-2.9
-4.3
-2.3
0.6
2 – 5 kcal/mol
3
E,
kcal/mol
-50.2
-40.8
-11.7
-11.1
-1.7
-0.1
-1
4
Ezpe,
kcal/mol
-51.7
-41.4
-13.9
-12.4
-3.5
-1.7
-2.4
-2 - +2 kcal/mol
Accounting for electron correlation energy in second order Moller - Plesset perturbation
theory (MP2) leads to the reduction of energy gap between two forms of energy, but shows a
preference for high-spin configurations like the method of HF. Only calculations using B3LYP/62
311++G(d,p) method are in good agreement with data of NMR studies. Comparative benchmarking
of efficiency of others functionals for study of 1-4 conformational isomers showed that the simplest
LSDA (local spin density approximation) SVWN functional overrates stabilization energies of lowspin states. The results of calculations using GGA (generalized gradient approximation) functionals,
such as BP86, PBEPBE, BPW91 and BLYP, are some better, but obtained with their help values
overestimates the stabilization energies of 1 and 3 planar configurations also. The hybrid functional
B3P86, as B3LYP, give values, which are close to experimentally observed. These results testify
about the preference of method of density functional theory at use the one-determinant approaches
for study of rearrangements of transition metals compounds.
Although energy characteristics of the considered above intramolecular processes are well
reproduced by the B3LYP/6-311++G(d,p) method, used functional and basis set does not always
correctly predicts the spin states of complexes with spin-crossover [2]. For the correct description of
such systems Reiher et al. suggested to use a modified version of the B3LYP* functional [17, 18].
Performed by them calculations of bis(Isothiocyanato)-bis(1,10-phenanthroline-N,N')Fe(II)
complex have reproduced correctly the experimental data. The essence of the modification is in
decreasing of the Hartree-Fock contribution to the functional (being defined by coefficient c3) from
standard value of 0.20 [19] to 0.15.
ExcB3LYP = ExLSDA + c1Ex88 + c2EcLYP + (1-c2)EcVWN + c3[Eex.ex. – ExLSDA]
The reparametrized functional B3LYP* can more accurately predict the relative energies of
different forms of complexes, in which spin-crossover is possible, as well as better describes the
nearby spin states in the study of catalytic processes initiated by transition metals.
The efficiency of B3LYP* functional was considered at complexes of ferrous iron with the
coordination unit FeN6. It is known [2, 20], that the iron complexes with bipyridine and oxazole
changes from high-spin to low-spin state at pressure increasing or temperature decreasing. At the
same time, the complexes with pyridine [2] and imidazole [21] under similar external influences
remain high-spin.
Fig. 1
The calculations of Fe(II) complexes with bipyridine and oxazole, which have been
performed with using of the reparametrized B3LYP*/6-311++G(d,p) functional, showed that the
stabilization energy of low-spin forms of complexes with bipyridine 5 and oxazole 7 with respect
to high-spin 6 and 8 is 2.8 and 2.1 kcal/mol respectively (fig. 1). This is well consistent with the
presence of spin-crossover in these complexes. At the same time quantum-chemical study of the
complexes with pyridine and imidazole indicates about the preference of their high-spin structures
10 and 12. The calculated difference of energies between singlet and quintet states is -6.4 and 4.2 kcal/mol respectively. The obtained results correctly reproduce the experimental data and allow
to draw a conclusion that the absence of spin-crossover in Fe(II) complexes with pyridine and
imidazole is linked with essential stabilization of their high-spin forms.
Calculations with using of the high-level approximations
Despite the correct reproducing of experimental data, the application of DFT method and
others one-determinant approaches for study of complexes of transition metals is limited because of
spin contamination. The calculated value of the square of the spin density may vary significantly
from the theoretical which points on the localization of the structures with the unstable wave
function. As a consequence, these calculations incorrectly reproduce the characteristics of the
complexes. The many-determinant methods of full active space CASPT2 and coupled cluster
methods CCSD(T), capable equally well to describe properties of various classes of compounds, are
freed from this disadvantage. However, despite the significant increasing in performance of
supercomputers, the calculations of rearrangements of transition metal complexes with such
3
approaches are sporadic and, as a consequence, there are no recommendations for choosing the
level of approximation.
H
H
N
O
Ni
Ni
O
N
O
N
N
O
H
H
13
14
The possibility of application of the complete active space method for the study of
rearrangements of the complexes with open shell was considered on the structures 1 and 2 by
CAS(8,10) method in 6-311+(d,p) basis. The calculations showed considerable (on 46 kcal/mol)
stabilization of high-spin form 2 in comparison with low-spin form 1, which contradicts to the
experiment. Also similar results were obtained for complex 13, which characterized by low-spin
configuration in the solution and in the crystalline state. The high-spin form of complex 14 is more
stable than low-spin 13 on 38 kcal/mol (table 2). This results show non-applicability of CAS
method in chosen approximation for study of such structures. The literature analyses have shown
[22] that the including of correlated procedures in calculation schema (CASPT2) gives good
agreement with experiment, but full optimization of geometry for complexes by such method is
unachievable currently.
Table 2. Energy parameters of structures 1-4, 13-16, calculated using CAS, CCSD and DFT
methods. Е – energy difference between low- and high-spin forms in kcal/mol.
1
Method/basis
CAS(8,10)/311+(d,p)
CCSD/6-31G(d,p)
CCSD/6-311++G(d,p)
B3LYP/6-311++G(d,p)
Experiment
2
3
4
E
E
E
E
-44
0.0
-9
0.0
-12.5 0.0
2.3
0.0
-1
0.0
*2–5
* -2 - +2
kcal/mol
kcal/mol
13
E
-38
9.4
-
14
15
E
0.0
0.0
16
E
-11
2.5
E
0.0
0.0
-
* Reference [14].
Another widely used approach, no subjected to spin contamination, is the coupled cluster
method. The geometry optimization of structures 1 and 2 by CCSD/6-31G(d,p) method showed a
preference of high-spin form of complex on 9 kcal/mol, that disagrees with experimental data.
Because of high requirements to supercomputer performance the calculation on 6-311++G(d,p)
level have been performed for -diketonate Ni(II) complex 15, characterized by “squaretetrahedron” equilibrium [23]. It was found that high-spin structure 16 is stabilized on 11 kcal/mol
relative to low-spin 15. Also the calculation of Co(II) complex points to a preference for high-spin
form 4 to low-spin form 3 on 12.5 kcal/mol.
Thus CAS and CCSD methods in basis up to 6-311++G(d,p) incorrect reproduce relative
energies of high- and low-spin forms of transition metal bis-chelates.
4
O
O
Ni
Ni
O
O
O
O
O
O
15
16
Wave function stability
As mentioned the calculation results by methods using the one-determinant approximation
(DFT, HF, MP2) are subjected to spin contamination that can lead to instability of wave function in
localized stationary points. Since there are multiple neighboring levels in transition metals, the
complexes on their base subjected to this effect more often than organic compounds.
In the study of intramolecular isomerization of -aminovinyliminate complex of cobalt 17
on quartet PES (potential energy surface) planar structure 18 was found, which is responsible to
transition state according to the analysis of the second derivative matrix (fig. 2). It was found that
calculated reaction barrier (32 kcal/mol) on detected path is essential higher than in analogous Nmethylsubstituted complexes [24,25]. The check of wave function stability in transition state 18 has
given negative result. The search of stable solution [Gaussian, stable=opt] has lead to structure 19,
which geometrically differs from structure 18 by elongation of Co–O bonds on 0.016Å. According
to data from table 3 the isomerization proceeds through transition state 19 with overcoming of
barrier 12 kcal/mol, what is in compliance with the calculation results of similar complexes [16].
This example demonstrates the importance of stability analysis of wave function in the quantum
chemical study of coordination compounds of transition metals.
Fig. 2.
Table 3. Energy parameters of structures 17-19, calculated using DFT B3LYP/6-311++G(d,p) method. Etotal total energy, Е – energy difference, ЕtotalZPE - total energy, taking into account zero-point energy of
harmonic vibrations, ЕZPE - energy difference, taking into account zero-point energy of harmonic
vibrations. S2 – the value of a square of the spin density, - the lowest or imaginary frequency of harmonic
vibrations.
Structure
Etotal,
17
18
19
a.u.
-1836.640178
-1836.589129
-1836.620891
E,
kcal/mol
0.0
32.0
12.1
ЕtotalZPE,
a.u.
-1836.474316
-1836.423793
-1836.455477
EZPE,
kcal/mol
0.0
31.7
11.8
S2
3.76
3.78
3.76
,
cm-1
66
-57
-57
The Using of models
In the discussed above complexes of - aminovinylketones 1, 3, 13 and aminovinylimines the substituents at donor nitrogen atoms, coordinated to the metal, have a
significant effect on the energy characteristics of intramolecular rearrangements. At the same time
there are many complexes, in which ligands contains the bulky alkyl substituents, not connected
with coordination center directly. Such groups do not have pronounced donor or acceptor
properties, but taking them into account significantly increases the requirements to computer
resources, therefore, as a rule, in the quantum chemical calculations they are substituted by the
hydrogen atoms. Below the complexes will be discussed, which have structure and magnetic
properties have defined by bulky substituents.
Ni(II) and Cu(II) bis-chelates 20 with 2,4,6,8-tetra-tert-butyl-phenoxazine-1-on radicalanion ligands were synthesized previously [26,27]. It was found that the nickel complex is
5
diamagnetic due the strong antiferromagnetic interaction of unpaired electrons of ligands and
paramagnetic Ni(II). The magnetochemical study of Cu(II) complex in temperature range from 77
to 470K have shown the growing of magnetic moment from 1.87 B to 2.88 B, indicative of
antiferromagnetic ordering of unpaired electrons of ligand and metal. In order to establish the
reasons of the stabilization of the spin states the quantum chemical study of model structures have
been performed, in the models tert-butyl groups were replaced by the hydrogen atoms.
t-Bu
t-Bu
O
.
t-Bu
t-Bu
N
O
M
O
t-Bu
N
t-Bu
.
O
t-Bu
t-Bu
20, M=Cu, Ni
According to X-Ray data the Cu(II) complex 20 exists in cis-form. At the same time the
calculations by B3LYP/6-311++G(d,p) predicts that the ground state of complex is the structure 21
with trans-configuration of coordination unit. The parameter value of exchange interaction J for the
structure 21, calculated using the broken symmetry (BS) [28] approach, is 74 сm-1, which indicates
on its ferromagnetism. The model structure 22, being characterized by antiferromagnetic exchange
(J=-75см-1) and destabilized on 7.5 kcal/mol relative to the structure 21, corresponds to the cis-form
of complex 20 (M=Cu). Obviously the used model incorrect reproduces the properties of complex
20 (M=Cu). The structures, including two tert-butyl groups in each ligand, have been studied to
estimate the steric influence of alkyl substituents. The geometry optimization showed a presence of
only one stationary point 23 with cis-structure of coordination unit and antiferromagnetic exchange
interactions. As follows from fig. 3 the calculated geometric characteristics of structure 23 are in
good agreement with X-Ray data, which points on the necessity of the taking into account bulky
substituents in the theoretical study of complexes with sterically hindered ligands.
Fig. 3.
It was shown above that depending on the substituents at the nitrogen atoms of bis-chelate
Ni (II) complexes with the coordination unit MN2O2 can have both planar and pseodotetrahedral
structure and capable to the rapid isomerization, which passes with a change of spin state. The
principle difference of structure 20 (M=Ni(II)) from considered systems is the ligands
paramagnetism, influencing on the system multiplicity.
Fig. 4.
The geometry optimization of the model complex of nickel showed, that the structure 24,
characterized by trans-planar coordination unit, has the lowest total energy on the triplet PES. The
analysis of spin density distribution in structure 24 showed its absence on the metal atom. The
structure 25, destabilized relative to trans-form 24 on 14.0 kcal/mol, corresponds to cis-form. This
indicates that such configuration is disadvantageous.
6
According to X-Ray data the structure 20 (M=Ni(II)) has pseudo-tetrahedral structure,
which is typical for high-spin tetracoordinated complexes of nickel. The calculations on quintet PES
have resulted to the structure 26, destabilized relative to planar structure 24 on 5.8 kcal/mol. The
spin density distribution in structure 26 shows the localization of two unpaired electrons on metal
and by one – on ligands. The calculation of parameter J according to the formula Yamaguchi [29]
showed that in the structures 24 and 26 the exchange interactions have an antiferromagnetic
character; the values of constants are -598 и -182 сm-1 respectively. This indicates on the
diamagnetism of the complex regardless of its stereochemistry, it is fully consistent with magnetic
measurements. Thus the calculations of model complex are reproducing it magnetic properties
correctly, but are predicting the stereochemistry incorrectly.
In order to determine the role of alkyl fragments in the stabilization of different spin states of
complex the model structures with the tert-butyl groups have been studied. The performed
calculations showed that the structure 27, which is a minimum on triplet PES, corresponds to the
complex with low-spin of metal. As follows from fig. 3, it are characterized by the cis-position of
ligands, meanwhile trans-form is not stabilized due to the steric hindrances, being created by
volumetric alkyl groups. The search of the high-spin form of complex has lead to the structure 28
with the pseudo-tetrahedral structure of coordination unit; the structure 28 is stabilized relative to
the structure 27 on 0.5 kcal/mol. These results are in full agreement with experimental data and
testify about the determinative role of bulky substituents during formation of complexes of type 20.
The promising approach for theoretical study of complexes of transition metals with big
number of atoms is QM/MM method [30], permitting to calculate different parts of molecule by
varied methods. Its application substantially reduces the requirements to computer resources
because of modeling of some atom groups on the lower approximation level, even by methods of
molecular mechanics. Recently the review [31] was published, in it the efficiency of this approach
has been shown for process study of metal complex catalysis. However, though the considerable
winning in time the QM/MM method has a number of restrictions, considerably restrictive for it
application in the study of transition metals coordination compounds with variable magnetic
properties. Most essentially hindrances are the impossibility of check of wave function stability in
the stationary points and an absence of an implementation of MECP search algorithm [32] using
this method in current software products. We can expect that next progress of this combined
approach will allow to eliminate above-mentioned disadvantages.
Effects of packing
The stereochemical nonrigidity of coordination compounds promotes that depending on the
synthesis method and the conditions of growing the monocrystals with different spatial structure
can be isolated [33]. In a number of cases on the ground of X-ray data it is difficult to discover the
factors that lead to the stabilization of different molecules conformations. So, it is known that bis(N-methylsalicylaldiminato) Ni(II) 28 can exist in two polymorphous modifications with transplanar (CSD Refcode - MSLDNI16) and distorted (CSD Refcode - MSLDNI17) structures. At the
same time the calculation of single molecule of complex using different approximations
permanently leads to trans-planar configuration.
28
28a
The clusters, consisting of ten molecules of complexes, have been calculated to
ascertainment of existence causes of two modification of complex 28 by DFT (B3LYP/6-31g(d,p))
7
method [34]. Optimized geometrical characteristics of the central molecules of associates
(structures 29’ and 30’) practically coincided with the corresponding experimental data (fig. 5).
This result allowed to conclude that the metal-chelate cycles of bis-(N-methylsalicylaldiminato)
Ni(II) molecules 28 are planar in fact, and the stepped distortion, observed in the solid stage, is an
effect of the crystal packing, which can be reproduced only by calculations of molecular associates
with large number of the molecules of metal-chelate complexes.
Fig. 5.
Another dependence example of the structure of coordination compound from packing is the
structure 31 [35]. It is mixed ligand Ni(II) complex with 2,2’-bipyridine, in which the acetate
groups are counterions, and the completion to an octahedron have been realized at the cost of two
water molecules. According to the X-Ray data [35], the complex has asymmetrical structure (fig.
6): the bond lengths between nickel atom and donor atoms of ligands are in the range 2.07-2.08 Å.
The gas-phase calculations by B3LYP/6-31g(d,p) and B3LYP/6-311++g(d,p) methods (structure
32) predicts the presence of C2v symmetry and the increase of distance to 2.15 Å between nickel
atom and oxygen atoms of water. In order to establish the reasons of the disagreement of calculated
and experimental geometries of complex the crystallographic cell have been studied, which is
include the dimers, stabilized by intermolecular hydrogen bonds, according to the X-Ray data.
Fig. 6.
The geometry optimization of an associate, composed of two molecules of complex, by
B3LYP/6-31g(d,p) method had lead to structure 33 (fig. 6), which is in agreement with the data of
X-ray structural studies. This allows us to conclude that symmetry decrease of complex 31 in
crystalline state is due to intermolecular bonds, generated by the coordinated molecules of water.
Conclusions
The applicability research of different computation schemas for quantum chemical modeling
of structure, properties and intramolecular rearrangements of coordination compounds of transition
metals showed that method DFT is most suitable currently. The B3LYP functional and the B3LYP*
modification in combination with the 6-311++G(d,p) basis are allowed to reproduce correctly the
properties of discussed complexes. The application of the Hartree-Fock method with different
correlated schemas (HF, MP2 and CCSD) is presented as unwarranted, because these
approximations incorrectly predicts the relative energy of high- and low-spin forms of test
complexes. The using of CASPT2 and CCSD(T) “uncompromising” methods in the extended basis
(6-311++G(3df,3pd), aug-cc-pvNz) is long-run prospect because insufficient performance of
current computer systems.
It is shown that theoretical study of coordination compounds with sterically overloaded
ligands should carry out using complete geometry of molecules, because the substituents may have
influence on the three-dimensional structure of complexes and the stabilization of spin states. The
geometry of metal complexes with ligands, able to make multiple donor-acceptor (hydrogen) bonds,
can be reproduced only by the calculations of molecular associates with a rather great number of the
molecules.
Acknowledgment
This work has been supported by Russian Foundation for Basic Research (projects 09-03-00684а
and 09-03-12109 ofi-m).
8
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Caption to Figures
Fig. 1 The characteristics of structures 5 - 12, calculated by DFT B3LYP*/6-311++G(d,p) method. LS- lowspin singlet state, HS- high-pin quintet state. Bond lengths are given in angstrom here and further.
Fig. 2. The characteristics of structures 17 – 19, calculated by DFT B3LYP/6-311++G(d,p) method.
Fig. 3. The characteristics of structures 21 – 23, calculated by DFT B3LYP/6-311++G(d,p) method. On
structure 23 the hydrogen atoms are omitted for clarity. The experimental data are given in square brackets
[27].
Fig. 4. The characteristics of structures 24, 26-28, calculated by DFT B3LYP/6-311++G(d,p) method. S – the
multiplicity of structure, on structures 27 and 28 the hydrogen atoms are omitted for clarity. The
experimental data are given in square brackets [26].
Fig. 5. (a) The structure of complex 28 with trans-planar (left) and stepped-twisted (right) molecular
configurations [33]. (b) The geometries of central molecules 29’ and 30’, calculated by B3LYP/6-31g(d,p)
method and discovered during X-ray analysis (shown in brackets) [33]. The calculated value of angle α in
30’ is 162º.
Fig. 6. The geometrical characteristics of structure 31, according to X-Ray data [35], and the geometrical
characteristics of structures 32,33, calculated by B3LYP/6-311++G(d,p) method and B3LYP/6-31G(d,p)
method relatively.
11