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We present benchmark databases of Zn-ligand bond distances, bond angles, dipole moments, and bond dissociation energies for Zn-containing small molecules and Zn coordination compounds with H, CH3, C2H5, NH3, O, OH, H2O, F, Cl, S, and SCH3 ligands. The test set also includes clusters with Zn-Zn bonds. In addition, we calculated dipole moments and binding energies for Zn centers in coordination environments taken from zinc metalloenzyme X-ray structures, representing both structural and catalytic zinc centers. The benchmark values are based on relativistic-core coupled cluster calculations. These benchmark calculations are used to test the predictions of four density functionals, namely B3LYP and the more recently developed M05-2X, M06, and M06-2X levels of theory, and six semiempirical methods, including neglect of diatomic differential overlap (NDDO) calculations incorporating the new PM3 parameter set for Zn called ZnB, developed by Brothers and co-workers, and the recent PM6 parametrization of Stewart. We found that the best DFT method to reproduce dipole moments and dissociation energies of our Zn compound database is M05-2X, which is consistent with a previous study employing a much smaller and less diverse database and a much larger set of density functionals. Here we show that M05-2X geometries and single-point coupled cluster calculations with M05-2X geometries can also be used as benchmarks for larger compounds, where coupled cluster optimization is impractical, and in particular we use this strategy to extend the geometry, binding energy, and dipole moment databases to additional molecules, and we extend the tests involving crystal-site coordination compounds to two additional proteins. We find that the most predictive NDDO methods for our training set are PM3 and MNDO/d. Notably, we also find large errors in B3LYP for the coordination compounds based on experimental X-ray geometries.

Abstract:The ground and lower excited states of Fe 2 , Fe 2 -, and FeO + were studied using a number of density functional theory (DFT) methods. Specific attention was paid to the relative state energies, the internuclear distances (r e ), and the harmonic vibrational frequencies (ω e ). A number of factors influencing the calculated values of these properties were examined. These include basis sets, the nature of the density functional chosen, the percentage of HartreeFock exchange in the density functional, and constraints on orbital symmetry. A number of different types of generalized gradient approximation (GGA) density functionals (straight GGA, hybrid GGA, meta-GGA, and hybrid meta-GGA) were examined, and it was found that the best results were obtained with hybrid GGA or hybrid meta-GGA functionals that contain nonzero fractions of HF exchange; specifically, the best overall results were obtained with B3LYP, M05, and M06, closely followed by B1LYP. One significant observation was the effect of enforcing symmetry on the orbitals. When a degenerate orbital (π or δ) is partially occupied in the 4 Φ excited state of FeO + , reducing the enforced symmetry (from C 6v to C 4v to C 2v ) results in a lower energy since these degenerate orbitals are split in the lower symmetries. The results obtained were compared to higher level ab initio results from the literature and to recent PBE+U plane wave results by Kulik et al. (Phys. Rev. Lett. 2006, 97, 103001). It was found that some of the improvements that were afforded by the semiempirical +U correction can also be accomplished by improving the form of the DFT functional and, in one case, by not enforcing high symmetry on the orbitals.

The electrostatically embedded many-body expansion (EE-MB), at both the second and third order, that is, the electrostatically embedded pairwise additive (EE-PA) approximation and the electrostatically embedded three-body (EE-3B) approximation, are tested for mixed ammonia-water clusters. We examine tetramers, pentamers, and hexamers for three different density functionals and two levels of wave function theory, We compare the many-body results to the results of full calculations performed without many-body expansions. Because of the differing charge distributions in the two kinds of monomers, this provides a different kind of test of the usefulness of the EE-MB method than was provided by previous tests on pure water clusters. We find only small errors due to the truncation of the many-body expansion for the mixed clusters. In particular, for tests on tetramers and pentamers, the mean absolute deviations for truncation at second order are 0.36-0.98 kcal/mol (average: 0.66 kcal/mol), and the mean absolute deviations for truncation at third order are 0.04-0.28 (average: 0.16 kcal/mol). These may be compared to a spread of energies as large as 4.24 kcal/mol in the relative energies of various structures of pentamers and to deviations of up to 8.57 kcal/mol of the full calculations of relative energies from the best estimates of the relative energies. When the methods are tested on hexamers, the mean unsigned deviation per monomer remains below 0.10 kcal/mol for EE-PA and below 0.03 kcal/mol for EE-3B. Thus the additional error due to the truncation of the expansion is small compared to the accuracy needed or the other approximations involved in practical calculations. This means that the EE-MB expansion in combination with density functional theory or wave function theory for the oligomers provides a useful practical model chemistry for making electronic structure calculations and simulations more affordable by improving the scaling with respect to system size.

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