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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. 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Ab initio MO calculations of effective exchange integrals between transition-metal ions via oxygen dianions: nature of the copper-oxygen bonds and superconductivity. Jpn. J. Appl. Phys. 1987. Vol. 26. P. 1362-1364. [30] Maseras F., Morokuma K. IMOMM - A new integrated ab-initio plus molecular mechanics geometry optimization scheme of equilibrium structures and transition-states. J. Comp. Chem. 1995. Vol. 16. P.11701179. [31] Ananikov V.P., Musaev D. G., Morokuma K. Real size of ligands, reactants and catalysts: Studies of structure, reactivity and selectivity by ONIOM and other hybrid computational approaches. J. Molecular Catalysis A: Chemical. 2010. Vol.324. P.104-119. [32] Harvey J. N., Aschi M., Schwarz H., Koch W. The singlet and triplet states of phenyl cation. A hybrid approach for locating minimum energy crossing points between non-interacting potential energy surfaces. Theor. Chem. Acc. 1998. Vol. 99. P. 95-99. [33] Kamenar B., Kaitner B., Ferguson G., Waters T.N. A redetermination of the structures of bis(salicylideneaminato)nickel(II) and monoclinic and orthorhombic forms of bis(Nmethylsalicylideneaminato)nickel(II). Acta Cryst. C: Cryst. Struct. Commun. 1990. Vol. 46. P.1920-1923. [34] Starikov A.G., Minyaev R.M., Minkin V.I. Theoretical modeling of the molecular, crystal structure and the square-planar to tetrahedral conformational rearrangement of trans-planar bis-(Nmethylsalicylaldiminato)nickel(II). Mendeleev Commun. 2009. Vol. 19. P. 64-66 [35] Ye B.-H., Chen X.-M., Xue G.-Q., Ji L.-N. Mononuclear nickel complexes assembled into twodimensional networks via hydrogen bonds and - stacking interactions. J. Chem. Soc. Dalton Trans. 1998. Vol. 17. P.2827-2832. 10 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