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Unrestricted density functional theory calculations have been carried out to investigate the reactivity of Th, Th+, and Th2+ toward the methane dehydrogenation process. A close description of the reaction mechanisms together with the analysis of the electronic factors offer insights into the reactivity of the thorium species. All possible spin states of the metal centers were considered as well as the effect of spin−orbit interactions on the transition-state barrier heights. The three reactions investigated are found to be exothermic, with the best thermochemical conditions observed for Th2+ around 105 kJ mol−1. The Th+ + CH4 reaction is found to be kinetically more favorable than that for the neutral Th atom. The DFT results indicate a direct participation of 5f electrons/orbitals in the reactivity of thorium species. The presence of electrons in 5f orbitals has an important effect on the insertion activation barrier, providing an electrostatic repulsion toward the closed-shell methane. The NBO results show that 5f orbitals play an important role in the overall strengths of the Th−C and Th−H chemical bonds, favoring thermochemical conditions of these reactions.

We have performed Car-Parrinello molecular dynamics simulations at ambient conditions for four-, five- and six-coordinated Cu(II) aqua complexes. The molecular geometry has been investigated in terms of Cu-O, Cu-H bond lengths and O-Cu-O bond angles and compared with earlier experimental measurement results and theoretical calculations. We find that the average Cu-O and Cu-H bond lengths increase with increasing coordination number. We have also observed relatively faster structural transition in the case of five-coordinated complex between trigonal bipyramidal and square pyramidal geometry. This result deviates from the findings of the earlier report (A. Pasquarello et al., Science, 2001, 291, 856) on copper(II) in aqueous solution and we attribute these differences to the neglect of solvent environment in our calculations. The averaged absorption spectra for the copper(II) aqua complexes have been computed using spin-restricted density functional linear response formalism taking 100 snap shots from a trajectory of 0.48 ps. We find that the calculated spectra are significantly different, showing clear features that distinguish each coordination model. Comparison with the experimentally reported absorption spectra is made wherever it is possible and the results obtained favor the distorted fivefold-coordination arrangement for the molecular structure of the Cu(II) ion in aqueous solution.

Density functional theory (DFT) and Hartree−Fock effective core potential calculations have been performed to investigate the reactivity of neutral f-block atoms toward methane C−H bond activation. The first step of the methane dehydrogenation process, which corresponds to an oxidative insertion, was studied for all lanthanide and actinide thorium atoms. The DFT/B3LYP-correlated results indicate more favorable kinetic and thermochemical conditions for the insertion of the lanthanides with a three non-f valence electron 2D([f n ]s2d1) as compared to a two non-f1S([f n +1]s2d0) electronic configuration. Among all the lanthanides, only 2D([f n ]s2d1)La, Ce, Gd, and Lu may react exergonically with methane; the lowest activation barrier is calculated for La and Ce atoms (ΔG ⧧ = 25 kcal·mol-1). A semiquantitative analysis from a simple two-state model shows that an indirect participation of the 4f-orbitals is expected to modify the [4f n +1]s2d0 reactivity of the Pr, Nb, and Tb−Tm lanthanides as a configuration mixing with the [4f n ]s2d1 electronic configuration may be quite effective. The most interesting result obtained in this work is for the insertion of the [5f   0]7s26d2 thorium into the methane C−H bond, where an essentially barrierless (ΔG ⧧ = 0.3 kcal·mol-1) and considerably exergonic (ΔG = − 38 kcal·mol-1) reaction is predicted to occur. The performance of a Th neutral atom overshadows the catalytic power of the best of the lanthanides, Ce, in the [4f   0]6s25d2 electronic configuration. One of the most important factors for this effectiveness comes from the 5f-orbital radial overlap onto the 7s6d valence shell, which enhances the ability of thorium as a catalyst for methane C−H bond activation.

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The density functional restricted-unrestricted approach for treatments of spin polarization effects in molecular properties using spin restricted Kohn–Sham theory has been extended from linear to nonlinear properties. It is shown that the spin polarization contribution to a nonlinear property has the form of a quadratic response function that includes the zero-order Kohn–Sham operator, in analogy to the lower order case where the spin polarization correction to an expectation value has the form of a linear response function. The developed approach is used to formulate new schemes for computation of electronic g-tensors and hyperfine coupling constants, which include spin polarization effects within the framework of spin restricted Kohn–Sham theory. The proposed computational schemes are in the present work employed to study the spin polarization effects on electron paramagnetic resonance spin Hamiltonian parameters of square planar copper complexes. The obtained results indicate that spin polarization gives rise to sizable contributions to the hyperfine coupling tensor of copper in all investigated complexes, while the electronic g-tensors of these complexes are only marginally affected by spin polarization and other factors, such as choice of exchange-correlation functional or molecular structures, will have more pronounced impact on the accuracy of the results.

Density functional theory (DFT) calculations have been performed to investigate the reactivity of early actinide ions (Ac+−Pu+) toward methane C−H bond activation. The first step of the methane dehydrogenation process, corresponding to an oxidative insertion, was studied for all ground and excited spin electronic states of these actinide ions. We find that Pu+ 7D (5f67s1) may react endoergonically with methane, whereas exoergonic reactions are observed for the other actinide ions investigated. The activation barriers are computed to be higher than 20 kcal mol− 1, except for Th+ 4F 6d27s1 and U+ 4I 5f37s2 ions, for which an effectively barrierless process (ΔG ⧧ < 2.5 kcal mol− 1) was predicted for Th+, while small values (ΔG ⧧ < 15 kcal mol− 1) were computed for U+. The analyses of results indicate a direct participation of 5f electrons and 5f orbitals in the reactivity of the early actinide ions. While the 5f electrons give rise to a repulsive electrostatic interaction with the closed-shell methane, increasing the size of the activation barrier, a strong participation of 5f orbitals in the actinide chemical bonds makes the thermochemical conditions of the insertion process unfavorable. Th+ is observed to be the most efficient actinide ion toward methane C−H bond activation. We find four salient factors responsible for this effectiveness: (i) its 4F [Rn]6d27s1 ground electron configuration, (ii) an “early” transition structure in the insertion process, (iii) a proper 5f orbital mix with the 6d7s valence shell, leading to enhanced strengths of the Th−H and Th−C bonds, and (iv) the absence of electrons in 5f orbitals.