Ab initio and DFT theoretical methods for geometry evaluation of inorganic compounds with first series transition metals
2021 - 144155
e-Pôster
Resumo
The lack of enough experimentally resolved equilibrium structures (reexp) for organometallics or coordination compounds undermines any serious attempt to evaluate ab initio and DFT prediction ability about such compounds. When such studies are performed three strategies are typically used: either they are performed using benchmarks based on non-metal compounds, or benchmarks that include inorganic compounds with more common experimentally related structures, like r0, rα, rg, etc, that are most probably still significantly far from equilibrium structures. A third approach is based on high quality calculated structures, at CCSD(T) level or above, with QZ and 5Z basis-sets, that are too expensive and slow to achieve convergence, and are still far from CBS.
We performed an extensive literature study to build a database of experimentally resolved equilibrium structures of inorganic compounds with a metal center, with nearly 1000 references. Such database is still growing and is available for any interested researcher (please e-mail the main author).
Based on a selected number (30) of inorganic diatomics, with a first-series transition metal, 14 ab-initio/DFT methods on a typical Jacob ladder approach, with def2-triple zeta basis-sets, were evaluated for the hydride, chloride and carbide series. Preliminary results indicate that GGA (BP86-D3 and BPE-D3) and meta-GGA (TPSS) have the best prediction ability based on MAD and RMSD statistics.
Carbide series gave worst results, which was determined to be caused by almost degeneracy of the fundamental states and its multiconformational nature, according to the B1-test proposed by Truhlar and collaborators,1 since DFT methods are fundamentally uniconformational. Such difficulties also apply to the experimental studies, since only NiC and FeC reexp are known, while hydride and chloride series are almost complete.
The inclusion of the relativistic effect in the studied ML compounds, according to the Douglas-Kroll-Hess approach (DKH2), significantly improves the MAD and RMSD results, with almost 50% decrease in the deviation; and is recommended even in the transition metals first series.
[1] – N. E. Schultz, Y. Zhao, D. G. Truhlar, J. Phys. Chem. A, 205, 109, 11127.
Instituições
- 1 Universidade Federal Fluminense
Eixo Temático
- Química Inorgânica - INO
Palavras-chave
Equilibrium structure
database
Inorganic diatomics
DFT
First transition series
Discussões Científicas de Qualidade
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João Madureira
Hi Leonardo
This matter is a complex one and you would probably find a better answer with a physicist not a chemist, as I am. Nevertheless, I might tell you that in relativistic quantum mechanics, the basics comes from the Dirac equation. Compared to the Bohr approach, the electron spin emerge naturally as the fourth quantum number. For a n-electrons situation, the one electron spin orbitals (alpha or beta spin) are replaced by four component spinors (alpha+, beta+, alpha- and beta-).
While Dirac himself has neglected the importance of relativistic effects on atoms and molecules, such effect has proven important for heavy elements (high Z) particularly on the electrons with low n quantum numbers, due to their higher probability density near the nucleus. Higher charge of the nucleus impose an increased velocity, which means an increased electron relativistic mass and a radial contraction of the orbitals. Because of that, lanthanides relativistic effects must be taken into account.
For a multi-electron situation, the approach is to add the Dirac equations for each single
electron to the electron-electron repulsion. Direct electronic calculations based on this Hamiltonians are too expensive. The typically small relativistic contribution can be approximated performing a four to two transformation of the Dirac components, using the theory of effective Hamiltonians. More popular examples of such approach are the zeroth order regular approximation (ZORA) or the Douglas-Kroll-Hess (DKH).
On the present work, the calculations were performed with Orca 4.2 only. The program includes both ZORA and DKH approaches (in fact a revised version, DKH2). Such corrections have to be included on your input file directly on the basis set of your preference. You should check if such basis set is redefined to include relativistic effects and is parametrized for the element you need to study!
Orca’s manual shows a full list of basis sets, including the relativistic ones. Another good starting point is the "Basis Set Exchange" site. You´ll have to choose between a full electron or ECP. Several all-electrons orbitals with ZORA or DKH (DKH2, DKH3) can be found there for lanthanides: SARC, Sapporo, etc.
All the best
João Madureira