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Transition metal complexes are widely used in the industry as catalysts and dyes. Predicting their properties includes calculating low-lying energy states, which is computationally intensive. Hence, we aim to provide a simple ligand field model of two Re(III) molecules, [ReCl \(_{6}\) ] \(^{3-}\) and ReCl \(_{3}\) (tppz) to accurately predict its low-lying energy states. Ab initio calculations were done with CASSCF and CASPT2. Two different model Hamiltonians were constructed with five different ligand field parameters: energy gap (J), spin-orbit coupling ( \(\lambda \) ), axial ( \(\varDelta \) ), and rhombic distortion ( \(\epsilon \) ), and orbital reduction factor ( \(\kappa \) ). A nine-by-nine matrix for the \(^{3}T_{1}\) configuration, and a fifteen-by-fifteen matrix for the \(t_{2g}^{4}\) configuration were obtained. The eigenvalues of the Hamiltonian were then fitted to the calculated energy states using a minimization function. The values for the \(^{3}T_{1}\) model fit extremely well, whereas the \(t_{2g}^{4}\) model has standard deviations ranging from 13 to 192. We obtained parameter values matching our predictions. The value of \(\lambda \) and \(\epsilon \) are close to 0 for [ReCl \(_{6}\) ] \(^{3-}\) , representing a perfect octahedral compound, and large for ReCl \(_{3}\) (tppz), which is not a perfect octahedral and will have some axial and rhombic splitting. We can expand our research by fitting the five parameters to other 5d \(^4\) transition metal complexes and including more states in the Hamiltonian.

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First Principles Investigation of Electronic Structure, Ligand Field and Magnetism of Re(III) Compounds

  • 会议论文

  • 发表日期：

    2025年

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  • Sze Ee, Josher Lo,
  • Yang En Ivan Ng,
  • Rutvij Manish Pradhan,
  • Liviu Ungur

摘要

Transition metal complexes are widely used in the industry as catalysts and dyes. Predicting their properties includes calculating low-lying energy states, which is computationally intensive. Hence, we aim to provide a simple ligand field model of two Re(III) molecules, [ReCl \(_{6}\) ] \(^{3-}\) and ReCl \(_{3}\) (tppz) to accurately predict its low-lying energy states. Ab initio calculations were done with CASSCF and CASPT2. Two different model Hamiltonians were constructed with five different ligand field parameters: energy gap (J), spin-orbit coupling ( \(\lambda \) ), axial ( \(\varDelta \) ), and rhombic distortion ( \(\epsilon \) ), and orbital reduction factor ( \(\kappa \) ). A nine-by-nine matrix for the \(^{3}T_{1}\) configuration, and a fifteen-by-fifteen matrix for the \(t_{2g}^{4}\) configuration were obtained. The eigenvalues of the Hamiltonian were then fitted to the calculated energy states using a minimization function. The values for the \(^{3}T_{1}\) model fit extremely well, whereas the \(t_{2g}^{4}\) model has standard deviations ranging from 13 to 192. We obtained parameter values matching our predictions. The value of \(\lambda \) and \(\epsilon \) are close to 0 for [ReCl \(_{6}\) ] \(^{3-}\) , representing a perfect octahedral compound, and large for ReCl \(_{3}\) (tppz), which is not a perfect octahedral and will have some axial and rhombic splitting. We can expand our research by fitting the five parameters to other 5d \(^4\) transition metal complexes and including more states in the Hamiltonian.