Several Molecular Orbital Computations for a Dinuclear Nickel(II) Complex

Hiroshi SAKIYAMA, Masato OSHIMA, Satoshi SUZUKI and Yuzo NISHIDA


1 Introduction

Dinuclear nickel(II) structures have attracted our interest since jack bean urease was found to include two nickel(II) ions at its active site [1], where ureases are known to catalyze the hydrolysis of urea. The crystal structures of ureases of various origins have been determined [2 - 4]. Interestingly, all of them have been found to possess dinuclear nickel(II) centers. Very recently, urease from Helicobacter pylori, which is considered to be a major predisposing cause of gastric ulcers, was also found to have a dinuclear nickel(II) center [4]. For the purpose of studying the relationship between a structure and a function, we often use synthetic model compounds that contain structures similar to the active-site structures. We previously prepared dinuclear nickel complexes [Ni2(bomp)(OCOMe)2]BPh4 and [Ni2(bomp)(OCOPh)2]BPh4 [bomp- = 2,6-bis [bis(2-methoxyethyl)aminomethyl]-4-methylphenolate] as model compounds for ureases and studied their magnetic properties and electronic spectra [5]. The effective magnetic moment per Ni of the complexes at room temperature were 3.27 and 3.35 mB, respectively, and the result indicated that two unpaired electrons were localized on each nickel(II) ion. Electronic spectra measured in DMF at room temperature were typical for an octahedral nickel(II) complex, and this result was consistent with the results of magnetic measurements. Therefore the ground term is a quintet at room temperature. Judging from the cryomagnetic data, we conclude that the ground term is a quintet in the temperature range from 15 K to 300 K.
Earlier we prepared an isostructural dinuclear zinc(II) complex as the first functional model for aminopeptidases [6], and performed several computations for the dinuclear zinc(II) complex using ab initio, DFT, semi-empirical, and molecular mechanics methods [7]. The computed structures were compared with a crystallographically obtained structure. Among the semi-empirical methods, PM5 and PM6 reproduced the crystal structure, the B3LYP/LANL2DZ method reproduced it very well, and the result by the MP2/3-21G method was best of all. In the present study, we performed several computations for the above-mentioned dinuclear nickel(II) complex (Figure 1) to understand its physicochemical properties.

Figure 1. Chemical structures of bomp- (left) and [Ni2(bomp)(OCOMe)2]+ complex cation (right).

2 Computational methods

A structure of the complex cation [Ni2(bomp)(OCOMe)2]+ was optimized using several computational methods, such as the ab initio, DFT, and semi-empirical methods. One of the crystallographically obtained structures was used initially for all the computations. First, we assumed quintet state because the crystal structures were determined at 100K and the ground state at 100 K was found to be a quintet from the magnetic measurement [5]. Optimizations by the ab initio and DFT methods were performed using Gaussian 03 software (Gaussian, Inc.), the Amsterdam Density Functional (ADF) program (Macrovision Corporation), and the WinGAMESS program [8, 9]. The methods used were MP2 [10 - 14], B3LYP [15 - 17], BLYP [18], BOP [19], LC-BLYP [20], and LC-BOP [20] with 3-21G, 6-31G, 6-31G(d), 6-31+G(d), 6-311+G(d), 6-311+G(2d), and LANL2DZ [21] basis sets, as well as LDA with TZP, TZ2P, and QZ4P basis sets. An optimization by semi-empirical methods was made using WinMOPAC software (Fujitsu Limited), MOPAC2007 software (Stewart Computational Chemistry) [22], and Winmostar software [23]. The methods used were AM1 [24], PM3 [25], PM5 [26], and PM6 [27].

3 Results and discussion

The crystal structure of the dinuclear nickel(II) complex [Ni2(bomp)(OCOMe)2]BPh4 was previously determined using the single-crystal X-ray method at 100±1 K [5], and the crystal was found to contain two crystallographically inequivalent complex cations, cation I and cation II, the structures of which are shown in Figure 2. Both cations look very similar to each other, and their bond lengths and bond angles differ within ~2% and ~5%, respectively (Table 1). In the complex cation [Ni2(bomp)(OCOMe)2]+, two nickel(II) ions are incorporated in a dinucleating ligand bomp-, and the nickel ions are bridged by one phenolic oxygen of the bomp ligand and two acetate ions. The Ni...Ni separation is 3.3515(3) A in cation I and 3.3592(3) A in cation II. These separations are slightly longer than that for the related dinuclear zinc(II) complex [3.2644(7) A] [6]. The coordination geometry around each nickel ion is distorted octahedral in both complex cations. Each complex cation has a pseudo-C2 symmetry, and the twisting angles between an aromatic plane and a plane, including two nickel ions and a phenolic oxygen atom, are 44° and 46° for cations I and II, respectively. The bomp ligand has four ether chelating arms: two of them are in equatorial positions, and the other two are in axial positions. In the case of the isostructural zinc(II) complex, significant axial elongation was observed. If we define the axial elongation as 100 × [(axial M-O distance)/(equatorial M-O distance) - 1] (M = Zn, Ni), the axial elongation was 6.6~11.0% for the zinc complex. In the case of the present nickel complex, the axial elongation was 2.6~2.8% for complex cation I but 0.6~0.7% for complex cation II. We previously concluded that the axial Zn-O(ether) bonds seemed to be ionic and weak and that the axial Ni-O(ether) bonds in the present nickel complex must have been weaker than the other coordination bonds. Therefore, the difference in the axial Ni-O(ether) bond lengths may have occurred between complex cations I and II even though both cations are in the same crystal.

Figure 2. Structures of the [Ni2(bomp)(OCOMe)2]+ complex cation; crystallographically observed structures for cations I (a) and II (b) and a computed structure using the B3LYP/LANL2DZ method (c).

Computed structures for the complex cation were obtained using the ab initio, DFT, and semi-empirical methods, and the results are summarized in Tables 1, - 3. All the DFT methods gave successful results assuming the quintet state. As an example, the structure obtained by B3LYP/LANL2DZ is shown in Figure 2c. The quality of the reproducibility was evaluated by the quality factor Q defined as , where a corresponds to the bond distances and angles. First, the results of the different basis sets were compared using the B3LYP method for 3-21G, 6-31G, 6-31G(d), 6-31+G(d), 6-311+G(d), 6-311+G(2d), and LANL2DZ (Figure 3). It should be noted that the larger the Q value, the better the quality. The 3-21G was not so good among these. The LANL2DZ reproduced the bond lengths and angles well, but the Ni...Ni separation was not reproduced so well. Generally, the 6-31G and the 6-31G(d) gave good results. The results of 6-31+G(d), 6-311+G(d), and 6-311+G(2d) were very similar to each other, and the results seemed to have converged. They were really good especially in their Ni...Ni separations and bond angles around Ni; however, they were less superior in their bond distances. In the case of coordination compounds, bond angles around a central metal ion are important. In the present case, addition of d polarization function improved the result a little; however, addition of diffusion function seemed less efficient. This may be because the complex is positively charged, and the steric requirement of the dinucleating ligand is strong. Therefore the 6-31G or the 6-31G(d) seemed to be sufficient for the present purpose.

Table 1. Deviations from the crystal structure for the computed structures.
Deviations in bond distancesa/%Deviations in bond anglesa/%
Around nickelatoms except forAround nickelatoms except for
LDA/TZP-3~0, -3~1-2~1, -3~1-5~4, -4~5-4~2, -6~2
LDA/TZ2P-3~0, -3~1-2~0, -3~1-5~4, -5~5-4~2, -6~2
LDA/QZ4P-3~0, -3~0-2~1, -3~1-5~4, -5~5-4~2, -6~2
B3LYP/3-21G-4~0, -4~2-1~4, -1~4-6~7, -6~8-3~6, -3~6
B3LYP/6-31G-1~2, -2~3-1~3, -1~3-2~3, -4~4-2~5, -3~5
B3LYP/6-31G(d)-2~2, -2~4-1~1, -2~1-3~3, -5~5-1~7, -2~7
B3LYP/6-31+G(d)-1~3, -1~5-1~1, -2~1-5~4, -6~5-2~5, -2~5
B3LYP/6-311+G(d)0~3, 0~4-1~1, -2~1-4~4, -6~5-2~5, -2~5
B3LYP/6-311+G(2d)-1~3, -1~5-1~1, -2~1-5~4, -6~5-2~5, -2~5
B3LYP/LANL2DZ-2~3, -2~30~3, 0~3-3~4, -4~5-2~5, -3~5
BLYP/6-31G-1~2, -1~30~4, 0~4-2~3, -3~4-2~4, -2~4
BLYP /6-31G(d)0~2, -1~30~2, 0~3-2~4, -3~4-1~4, -3~4
LC-BLYP/6-31G0~2, -1~30~3, 0~3-2~2, -3~4-3~4, -3~4
BOP/6-31G0~2, -1~30~4, 0~5-2~2, -3~4-2~4, -2~4
BOP /6-31G(d)0~2, -1~30~2, 0~3-2~4, -3~4-2~4, -3~4
LC-BOP/6-31G0~3, -1~30~3, 0~3-2~3, -4~4-3~4, -3~4
MP2/3-21G-4~2, -4~2-4~5, -4~5-5~7, -4~6-4~6, -4~5
AM1-3~35, -4~35-4~9, -3~8-21~25, -22~23-16~18, -16~17
a The former is based on cation I, and the latter on cation II.
b Deviations of cation I from cation II.
c The bridging mode of acetate ions changed as shown in Figure 5.

Table 2. Comparison of the crystal structure and the computed structures.
MethodNi...Ni separation/ADihedral angle between the aromatic ring plane and the Ni-O-Ni plane/°
X-ray (cation I)3.3515(3)44
X-ray (cation II)3.3592(3)46
BOP /6-31G3.40044
BOP /6-31G(d)3.35245
LC-BOP /6-31G3.40545

Table 3. Equatorial and axial Ni-O(ether) distances and axial elongation. a
MethodEquatorial Ni-O distance/AAxial Ni-O distance/AAxial elongation/%
X-ray (cation I)2.128~2.1312.186~2.1882.6~2.8
X-ray (cation II)2.130~2.1462.145~2.1580.6~0.7
LC-BLYP/6-31G2.128~2.1482.195~2.2082. 2~3.8
BOP /6-31G2.135~2.1572.200~2.2192.0~2.9
BOP /6-31G(d)2.141~2.1652.206~2.2231.9~3.9
LC-BOP /6-31G2.033~2.1372.205~2.2224.0~8.5
a Axial elongation is defined as 100 × [(axial Ni-O distance)/(equatorial Ni-O distance) - 1].

Figure 3. Comparison of the basis sets using the B3LYP method. Structural optimization was made for [Ni2(bomp)(OCOMe)2]+ complex cation using Gaussian 03 software. The quality factor Q is defined as , where aobs and acalc correspond to the observed and calculated bond lengths and angles.

Figure 4. Comparison of the methods using the 6-31G basis set. Structural optimization was made for [Ni2(bomp)(OCOMe)2]+ complex cation using WinGAMESS program. The quality factor Q is defined as , where aobs and acalc correspond to the observed and calculated bond lengths and angles.

Next, the results of the different methods were compared for B3LYP, BLYP, and BOP using the 6-31G basis set; the results of long-range correction methods were also compared (Figure 4). If we compare the results by the B3LYP, BLYP, and BOP methods, B3LYP was the best, and the order was B3LYP > BLYP > BOP. Especially, in the bond angles around Ni, the order was significant. The LC methods improved the quality in the bond angles; however, the quality in Ni...Ni separation and in bond distances around Ni became slightly worse. Totally, the B3LYP and the LC-BLYP seemed good.
Semi-empirical computational optimization was made on the basis of the AM1, PM3, PM5, and PM6 methods. When the structure was optimized using the PM3, PM5, or PM6 method, the structures of the bridging acetate ions were broken (Figure 5), and the results were not satisfactory. In the case of the AM1 method, the bridging structure was not broken, but the obtained Ni-N bonds and Ni-O bonds were much longer than the crystal structure. In our previous work on the isostructural dinuclear zinc(II) complex, the PM5 and the PM6 methods gave successful results; however, none of the semi-empirical methods gave a reasonable structure for the present dinuclear nickel(II) complex.

Figure 5. Bridging structure of cation I (a) and calculated bridging structures by PM3 (b), PM5 (c), and PM6 (d). Other atoms are not shown for clarity.

In this work, computationally obtained structures were compared with a crystallographically obtained structure at 100 K. Judging from the magnetic data for the nickel complex, the ground state at 100 K is a quintet, and the exchange interaction between the two nickel(II) ions is ferromagnetic [J = 1.75 cm-1 (H = -2JS1.S2)] [5]. When we assume the singlet state, the computed structures were not reasonable; no successful results were obtained when the ground state was assumed to be a triplet. All the reasonable structures computed in this study were obtained by assuming the quintet state, which is consistent with the ferromagnetic exchange interaction.

4 Conclusion

The molecular structures of a dinuclear nickel(II) complex were obtained using eighteen computational methods, and the computed structures were evaluated by comparing the non-hydrogen bond lengths, bond angles, Ni...Ni separation, twist angle, and axial elongation. The B3LYP and LC-BLYP methods were the best among those investigated. Concerning the basis set, 6-31G and 6-31G(d) seemed to be sufficient due to the strong steric requirement of the dinucleating ligand. None of the semi-empirical methods reproduced the crystal structure. All the reasonable structures were obtained by assuming the quintet state, which was consistent with the ferromagnetic exchange interaction.


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