Hybrid Generalized Gradient Approximation Research Articles

Density Functionals for Inorganometallic and Organometallic Chemistry

We present a database of 21 bond dissociation energies for breaking metal-ligand bonds. The molecules in the metal-ligand bond energy database are AgH, CoH, CoO+, CoOH+, CrCH3+, CuOH2+, FeH, Fe(CO)5, FeO, FeS, LiCl, LiO, MgO, MnCH3NiCH2+, Ni(CO)4, RhC, VCO+, VO, and VS. We have also created databases of metal-ligand bond lengths and atomic ionization potentials. The molecules used for bond lengths are AgH, BeO, CoH, CoO+, FeH, FeO, FeS, LiCl, LiO, MgO, RhC, VO, and VS and the ionization potentials are for the following atoms: C, Co, Cr, Cu, Ni, O, and V. The data were chosen based on their diversity and expected reliability, and they are used along with three previously developed databases (transition metal dimer bond energies and bond lengths and main-group molecular atomization energies) for assessing the accuracy of several kinds of density functionals. In particular, we report tests for 42 previously defined functionals: 2 local spin density approximation (LSDA) functionals, 14 generalized gradient approximation (GGA) methods, 13 hybrid GGA methods, 7 meta GGA methods, and 8 hybrid meta GGA methods. In addition to these functionals, we also examine the effectiveness of scaling the correlation energy by testing 13 functionals with scaled or no gradient-corrected correlation energy, and we find that functionals of this kind are more accurate for metal-metal and metal-ligand bonds than any of the functionals already in the literature. We also present a readjusted GGA and a hybrid GGA with parameters adjusted for metals. When we consider these 57 functionals for metal-ligand and metal-metal bond energies simultaneously with main-group atomization energies, atomic ionization potentials, and bond lengths we find that the most accurate functional is G96LYP, followed closely by MPWLYP1M (new in this article), XLYP, BLYP, and MOHLYP (also new in this article). Four of these five functionals have no Hartree-Fock exchange, and the other has only 5%. As a byproduct of this work we introduce a convenient diagnostic, called the B1 diagnostic, for ascertaining the multireference character in a bond.

Density functional study of structural and electronic properties of AlnN (1 ≤ n ≤ 12) clusters

AbstractLow‐lying equilibrium geometric structures of AlnN (n = 1–12) clusters obtained by an all‐electron linear combination of atomic orbital approach, within spin‐polarized density functional theory, are reported. The binding energy, dissociation energy, and stability of these clusters are studied within the local spin density approximation (LSDA) and the three‐parameter hybrid generalized gradient approximation (GGA) due to Becke–Lee–Yang–Parr (B3LYP). Ionization potentials, electron affinities, hardness, and static dipole polarizabilities are calculated for the ground‐state structures within the GGA. It is observed that symmetric structures with the nitrogen atom occupying the internal position are lowest‐energy geometries. Generalized gradient approximation extends bond lengths as compared with the LSDA lengths. The odd–even oscillations in the dissociation energy, the second differences in energy, the highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) gaps, the ionization potential, the electron affinity, and the hardness are more pronounced within the GGA. The stability analysis based on the energies clearly shows the Al7N cluster to be endowed with special stability. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

Databases for Transition Element Bonding: Metal−Metal Bond Energies and Bond Lengths and Their Use To Test Hybrid, Hybrid Meta, and Meta Density Functionals and Generalized Gradient Approximations

We propose a data set of bond lengths for 8 selected transition metal dimers (Ag(2), Cr(2), Cu(2), CuAg, Mo(2), Ni(2), V(2), and Zr(2)) and another data set containing their atomization energies and the atomization energy of ZrV, and we use these for testing density functional theory. The molecules chosen for the test sets were selected on the basis of the expected reliability of the data and their ability to constitute a diverse and representative set of transition element bond types while the data sets are kept small enough to allow for efficient testing of a large number of computational methods against a very reliable subset of experimental data. In this paper we test 42 different functionals: 2 local spin density approximation (LSDA) functionals, 12 generalized gradient approximation (GGA) methods, 13 hybrid GGAs, 7 meta GGA methods, and 8 hybrid meta GGAs. We find that GGA density functionals are more accurate for the atomization energies of pure transition metal systems than are their meta, hybrid, or hybrid meta analogues. We find that the errors for atomization energies and bond lengths are not as large if we limit ourselves to dimers with small amounts of multireference character. We also demonstrate the effects of increasing the fraction of Hartree-Fock exchange in multireference systems by computing the potential energy curve for Cr(2) and Mo(2) with several functionals. We also find that BLYP is the most accurate functional for bond energies and is reasonably accurate for bond lengths. The methods that work well for transition metal bonds are found to be quite different from those that work well for organic and other main group chemistry.

Hole localization in [AlO4] defects in silica materials

First-principles calculations based on cluster models have been performed to investigate the ground state and the optically excited states of the [AlO(4)](0) hole in alpha-quartz and in the siliceous zeolite ZSM-5. The structure and spectroscopic properties of this defect have been studied using the recently developed Becke88-Becke95 one-parameter model for kinetics (BB1K) functional of Zhao et al., [J. Phys. Chem. A 108, 2715 (2004)]. Our results show that the BB1K method is significantly more reliable and more accurate than the standard density-functional theory (DFT) functionals at reproducing the localized spin density on one oxygen atom and the hyperfine coupling constants associated with the hole. Furthermore, we find that the BB1K results are in close agreement with experiments, and with the self-interaction-free unrestricted Hartree-Fock (UHF) and unrestricted second-order Møller-Plesset perturbation theory (UMP2) calculations. For the first time, we present results of the ground-state paramagnetic properties of the Al defect in ZSM-5. Similar to the theoretical work for defective alpha-quartz, we find that the BB1K, UHF, UHFLee-Yang-Parr, and UMP2 calculations show a localized hole on one oxygen neighboring the Al, while even the best to date thermochemically derived hybrid generalized gradient approximation density-functional, B97-2, predicts a different model where the hole is distributed over two oxygen. We have further considered the optical transitions of the [AlO(4)](0) center in alpha-quartz and ZSM-5. In both systems, our BB1K time-dependent density-functional theory (TDDFT) and configuration interaction singles (CIS) calculations predict that the most likely transition involves electron transfer from the hole-bearing oxygen to other neighboring oxygen ions. This reinforces the experimental conclusions obtained for defective alpha-quartz. Notably, the two lowest, most dominant excitation energies calculated by BB1K-TDDFT (1.99 and 3.03 eV) show excellent agreement with experiment (1.96 and 2.85 eV [B. K. Meyer, J.M. Spaeth, and J.A. Weil, J. Phys. C: Solid State Phys. 17, L31 (1987)]) clearly outperforming the CIS method and other DFT calculations available in the literature.

Assessment of various density functionals and basis sets for the calculation of molecular anharmonic force fields

AbstractIn a previous contribution, we established the suitability of density functional theory (DFT) for the calculation of molecular anharmonic force fields. In the present work, we have assessed a wide variety of basis sets and exchange‐correlation functionals for harmonic and fundamental frequencies, equilibrium, and ground‐state rotational constants, and thermodynamic functions beyond the rigid rotor‐harmonic oscillator (RRHO) approximation. The fairly good performance of double‐zeta plus polarization basis sets for frequencies results from an error compensation between basis set incompleteness and the intrinsic error of exchange‐correlation functionals. Triple‐zeta plus polarization basis sets are recommended, with an additional high‐exponent d function on second‐row atoms. All conventional hybrid generalized gradient approximation (GGA) functionals perform about equally well: high‐exchange hybrid GGA and meta‐GGA functionals designed for kinetics yield poor results, with the exception of of the very recently developed BMK functional, which takes a middle position along with the HCTH/407 (second‐generation GGA) and TPSS (meta‐GGA) functionals. Second‐order Møller–Plesset perturbation theory (MP2) performs similarly to these functionals but is inferior to hybrid GGAs such as B3LYP and B97‐1. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

Density functional study of structural and electronic properties of NanMg (1⩽n⩽12) clusters

Low-lying equilibrium geometric structures of NanMg (n=1–12) clusters obtained by an all-electron linear combination of atomic orbital approach, within spin-polarized density functional theory, are reported. The binding energy, dissociation energy, and stability of these clusters are studied within the local spin density approximation (LSDA) and the three-parameter hybrid generalized gradient approximation (GGA) due to Becke-Lee-Yang-Parr (B3LYP). Ionization potentials, electron affinities, hardness, and static dipole polarizabilities are calculated for the ground-state structures within the GGA. It is observed that for clusters with n<9, symmetric structures with the magnesium atom occupying the internal position are higher in energy (typically by less than 1 eV) than those where Mg occupies a peripheral position. It is found that the relative ordering of the isomers is influenced by the nonlocal exchange-correlation effects for small clusters. Generalized gradient approximation extends bond lengths and widens the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), as compared to the LSDA gap. The odd-even oscillations in the dissociation energy, the second differences in energy, the HOMO–LUMO gaps, the ionization potential, the electron affinity, and the hardness are more pronounced within the GGA. The stability analysis based on the energetics clearly shows the Na6Mg cluster to be endowed with special stability, which occurs because of an electronic shell closure.