DFT-B3LYP, NPA-, and QTAIM-Based Study of the Physical Properties of [M(II)(H<sub>2</sub>O)<sub>2</sub>(15-crown-5)] (M = Mn, Fe, Co, Ni, Cu, Zn) Complexes
Bibliographic record
Abstract
A density functional theory study of the structure of the title compounds with the divalent metal ions in their high-spin ground state, obtained using B3LYP/6-311++G(d,p) in vacuo and in aqueous solution simulated using a polarized continuum medium, is reported for the first time. The modeling reproduces the pseudo pentagonal bipyramidal crystallographic structures very well, including some asymmetry in the equatorial bonds lengths to the crown ether O donors. The very marked asymmetry in the Ni(2+) structure due to a Jahn-Teller distortion of a d(8) system in a D(5h) ligand field is also well reproduced. The gas phase binding energies of the complexes follow the order Mn(2+) < Fe(2+) < Co(2+) < Ni(2+) < Cu(2+) > Zn(2+), in precise agreement with the Irving-William series. Both the NPA and Bader charges show there is ligand-to-metal charge transfer; however, the values obtained from the NPA procedure, unlike those obtained from Bader's quantum theory of molecules approach, do not correlate with the electronegativity of the metal ions, the stabilization energies of the solvated complexes or the ionic radii of the metal ions, and so appear to be less reliable. The nature of the bonding between the ligands and the metal ions has been explored using the topological properties of the electron charge density. The metal-ligand bond distances were found to be exponentially correlated with the electron charge density, its Laplacian, and with its curvature in the direction of the bond path at M-O bond critical points. While the bonding with coordinated H(2)O is predominantly ionic, that to the crown ether donor atoms has some covalent character the extent of which increases across the first transition series. The delocalization indices of M-O bonds in these complexes correlate reasonably well with the electron density and its Laplacian at the bond critical points; this therefore provides a rapid and computationally very efficient way of determining these properties, from which insight into the nature of the bonding can be obtained, obviating the need for time-consuming integration over atomic basins.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".