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Inverted-sandwich-type and open-lantern-type dinuclear transition metal complexes: theoretical study of chemical bonds by electronic stress tensor

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Abstract

We study the electronic structure of two types of transition metal complexes, the inverted-sandwich-type and open-lantern-type, by the electronic stress tensor. In particular, the bond order \(b_\varepsilon\) measured by the energy density which is defined from the electronic stress tensor is studied and compared with the conventional MO-based bond order. We also examine the patterns found in the largest eigenvalue of the stress tensor and corresponding eigenvector field, the “spindle structure” and “pseudo-spindle structure”. As for the inverted-sandwich-type complex, our bond order \(b_\varepsilon\) calculation shows that relative strength of the metal-benzene bond among V, Cr, and Mn complexes is V > Cr > Mn, which is consistent with the MO-based bond order. As for the open-lantern-type complex, we find that our energy density-based bond order can properly describe the relative strength of Cr–Cr and Mo–Mo bonds by the surface integration of the energy density over the “Lagrange surface” which can take into account the spatial extent of the orbitals.

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Notes

  1. They are called M1 and Mo1 in Ref. [29].

  2. If calculated at the cc-pVDZ level, we see small regions with positive eigenvalue just like those of the Mo–Mo bond in Fig. 14. Since such regions do not appear at 6-31G(d,p), cc-pVTZ and cc-pVQZ levels, we believe they are numerical artifacts in the case of C2H2.

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Acknowledgments

Theoretical calculations were partly carried out using Research Center for Computational Science, Okazaki, Japan. This research work is supported partly by Collaborative Research Program for Young Scientists of ACCMS and IIMC from Kyoto University. This work is supported partly by Grant-in-Aid for Scientific research (No. 22550011), Grant-in-Aid for Specially Promoted Research (No. 22000009), and Grand Challenge Project (IMS, Okazaki, Japan) from the Ministry of Education, Culture, Sports, Science and Technology, Japan.

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Authors and Affiliations

  1. Department of Micro Engineering, Kyoto University, Kyoto, 606-8501, Japan

    Kazuhide Ichikawa, Ayumu Wagatsuma & Akitomo Tachibana

  2. Quantum Chemistry Research Institute, Kyoto, 615-8245, Japan

    Yusaku I. Kurokawa

  3. Fukui Institute for Fundamental Chemistry Organization, Kyoto University, Kyoto, 606-8103, Japan

    Shigeyoshi Sakaki

Authors
  1. Kazuhide Ichikawa
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  2. Ayumu Wagatsuma
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  3. Yusaku I. Kurokawa
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  4. Shigeyoshi Sakaki
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  5. Akitomo Tachibana
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Correspondence to Akitomo Tachibana.

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Dedicated to Professor Shigeru Nagase on the occasion of his 65th birthday and published as part of the Nagase Festschrift Issue.

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Ichikawa, K., Wagatsuma, A., Kurokawa, Y.I. et al. Inverted-sandwich-type and open-lantern-type dinuclear transition metal complexes: theoretical study of chemical bonds by electronic stress tensor. Theor Chem Acc 130, 237–250 (2011). https://doi.org/10.1007/s00214-011-0966-0

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