Benchmarking approximate density functional theory for s/d excitation energies in 3d transition metal cations

Studies on the Coordination Patterns of Diamine-Bridged Tetraphenoxy Ligands with Group 3 and 4 Metals

Alkane elimination reactions between the diamino- and dianilino-bridged tetrakis(phenolate) proligands 1a,b-H4 and precursors M(CH2SiMe3)3(THF)2, M(CH2C6H4-o-NMe2)3 (M = Sc and Y), and Hf(CH2Ph)4 were investigated. The diamino-bridged 1a-H4 afforded nonsymmetric complex 2a-Y2 incorporating two metal centers in different coordination environments. This one and other dinuclear compounds 2b-Sc2, 2a-Hf2, and 2b-Hf2 were characterized by NMR spectroscopy, elemental analysis, and X-ray diffraction study (for 2a-Y2 and 2b-Sc2) and turned out to be symmetric in solution. Compound 2a-Y2, upon treatment with 2 equiv of 2-phenylpyridine, afforded symmetric bis(aryl) product 3a-Y2, which was authenticated by NMR spectroscopy and X-ray crystallography. The mechanism of its formation was studied by DFT computations and presumably involves a cooperative reorganization process within the nonsymmetric parent 2a-Y2 to afford a symmetric isomer prior to its reaction with 2-phenylpyridine.

1,2-Palladasilacyclobutene: The Missing Link in the Pd-Catalyzed Annulation of Alkynes for the Silirene-to-Silole Transformation

The palladium-catalyzed annulation reaction of alkynes enables an attractive approach to siloles. Their access from silirenes and terminal alkynes proved rather general, involving reactive intermediates that have remained elusive to date. Starting from 1,2-bis(3-thienyl)silirene as a source of photochromic siloles, the mechanism of the annulation reaction has been revisited, and palladasilacyclobutenes resulting from the activation of the silirene could be isolated and thoroughly characterized (NMR, X-ray, and DFT). Their role as reactive intermediates and their fate in the course of the reaction were also studied in situ. In combination with in-depth DFT calculations, a clearer picture of the mechanism and the reactive key species is disclosed.

Computational Investigation of the Metal and Ligand Substitution Effects on the Structure and Electronic States of the Phosphoranimide Tetramer Complexes of Cu(I), Ni(I), Co(I), and Fe(I)

The structurally unique saddle-shaped paramagnetic tetrametallic clusters of Co(I) and Ni(I) with phosphoranimide ligands have been synthesized and proposed as catalyst precursors. The analogous Cu(I) nanocluster is planar and diamagnetic. These notable variations in geometry and ground electronic states indicate that the effect of metal and ligand substituents on the structure and electronic properties of these complexes requires investigation. We present a computational study of a series of these novel homoleptic complexes containing Co(I), Ni(I), and Cu(I) as well as Fe(I) coordinated to phosphoranimides with electron-donating and withdrawing substituents, conducted at the relativistic density functional theory level using ZORA-PBE/TZP. The optimized structures of the saddle-shaped Co(I) and Ni(I) and planar Cu(I) tetramers with linear N-M-N coordination are validated with respect to X-ray diffraction determinations. The ground-state analysis indicates that Cu(I) complexes are diamagnetic, whereas Ni(I) and Co(I) complexes are in high-spin states, in agreement with magnetic susceptibility measurements. The computational results show that Fe(I) complexes are saddle shaped and high spin. The Co(I) complex is stabilized by a metal macrocycle distortion from square to diamond, as elucidated from its Walsh diagram. The effects of metals and ligand substituents on the ground electronic state, metal center coordination environment, and energy of the complexes are investigated. The bulky tertiary butyl substituent causes the largest saddle-shape distortion of the tetramer marcocycle, which partially offsets its electron-donating effect. Macrocycle distortions with N-M-N site angles ranging from obtuse to alternating obtuse reflex are correlated with the increasing number of unpaired electrons. The phenyl-substituted complexes are expected to have the highest reactivity toward electrophiles. Understanding the interplay between structural and electronic parameters is intended to guide the development of synthetic cooperative systems for multielectron redox reactions, models of biological systems, and molecular magnets.

Predicting Bond Dissociation Energies and Bond Lengths of Coordinatively Unsaturated Vanadium-Ligand Bonds

Understanding the electronic structure of coordinatively unsaturated transition-metal compounds and predicting their physical properties are of great importance for catalyst design. Bond dissociation energy D_e and bond length r_e are two of the fundamental quantities for which good predictions are important for a successful design strategy. In the present work, recent experimentally measured bond energies and bond lengths of VX diatomic molecules (X = C, N, S) are used as a gauge to consider the utility of a number of electronic structure methods. Single-reference methods are one focus because of their efficiency and utility in practical calculations, and multireference configuration interaction (MRCISD) methods and a composite coupled cluster (CCC) method are a second focus because of their potential high accuracy. The comparison is especially challenging because of the large multireference M diagnostics of these molecules, in the range 0.15-0.19. For the single-reference methods, Kohn-Sham density functional theory (KS-DFT) has been tested with a variety of approximate exchange-correlation functionals. Of these, MOHLYP provides the bond dissociation energies in best agreement with experiments, and BLYP provides the bond lengths that are in best agreement with experiments; but by requiring good performance for both the D_e and r_e of the vanadium compounds, MOHLYP, MN12-L, MGGA_MS1, MGGA_MS0, O3LYP, and M06-L are the most highly recommended functionals. The CCC calculations include up to connected pentuple excitations for the valence electrons and up to connected quadruple excitations for the core-valence terms; this results in highly accurate dissociation energies and good bond lengths. Averaged over the three molecules, the mean unsigned deviation of CCC bond energies from experimental ones is only 0.4 kcal/mol, demonstrating excellent convergence of theory and experiments.

Steric control in the metal–ligand electron transfer of iminopyridine–ytterbocene complexes

A systematic study of reactions between Cp*₂Yb(THF) and iminopyridine ligands featuring similar electron accepting properties but variable denticity and steric demand, has provided a new example of steric control on the redox chemistry of ytterbocenes.

Modeling σ-Bond Activations by Nickel(0) Beyond Common Approximations: How Accurately Can We Describe Closed-Shell Oxidative Addition Reactions Mediated by Low-Valent Late 3d Transition Metal?

Accurate modelings of reactions involving 3d transition metals (TMs) are very challenging to both ab initio and DFT approaches. To gain more knowledge in this field, we herein explored typical σ-bond activations of H-H, C-H, C-Cl, and C-C bonds promoted by nickel(0), a low-valent late 3d TM. For the key parameters of activation energy (ΔE^‡) and reaction energy (ΔE_R) for these reactions, various issues related to the computational accuracy were systematically investigated. From the scrutiny of convergence issue with one-electron basis set, augmented (A) basis functions are found to be important, and the CCSD(T)/CBS level with complete basis set (CBS) limit extrapolation based on augmented double-ζ and triple-ζ basis pair (ADZ and ATZ), which produces deviations below 1 kcal/mol from the reference, is recommended for larger systems. As an alternative, the explicitly correlated F12 method can accelerate the basis set convergence further, especially after its CBS extrapolations. Thus, the CCSD(T)-F12/CBS(ADZ-ATZ) level with computational cost comparable to the conventional CCSD(T)/CBS(ADZ-ATZ) level, is found to reach the accuracy of the conventional CCSD(T)/A5Z level, which produces deviations below 0.5 kcal/mol from the reference, and is also highly recommendable. Scalar relativistic effects and 3s3p core-valence correlation are non-negligible for achieving chemical accuracy of around 1 kcal/mol. From the scrutiny of convergence issue with the N-electron basis set, in comparison with the reference CCSDTQ result, CCSD(T) is found to be able to calculate ΔE^‡ quite accurately, which is not true for the ΔE_R calculations. Using highest-level CCSD(T) results of ΔE^‡ in this work as references, we tested 18 DFT methods and found that PBE0 and CAM-B3LYP are among the three best performing functionals, irrespective of DFT empirical dispersion correction. With empirical dispersion correction included, ωB97XD is also recommendable due to its improved performance.

Theoretical treatment of one electron redox transformation of a small molecule using f-element complexes

DFT calculations can provide useful insights into low-valent f-element single electron transfer reactivity.

Benchmark study of the performance of density functional theory for bond activations with (ni,pd)-based transition-metal catalysts

The performance of 23 density functionals, including one LDA, four GGAs, three meta-GGAs, three hybrid GGAs, eight hybrid meta-GGAs, and ten double-hybrid functionals, was investigated for the computation of activation energies of various covalent main-group single bonds by four catalysts: Pd, PdCl⁻, PdCl₂, and Ni (all in the singlet state). A reactant complex, the barrier, and reaction energy were considered, leading to 164 energy data points for statistical analysis. Extended Gaussian AO basis sets were used in all calculations. The best functional for the complete benchmark set relative to estimated CCSD(T)/CBS reference data is PBE0-D3, with an MAD value of 1.1 kcal mol⁻¹ followed by PW6B95-D3, the double hybrid PWPB95-D3, and B3LYP-D3 (1.9 kcal mol⁻¹ each). The other tested hybrid meta-GGAs perform less well (M06-HF: 7.0 kcal mol⁻¹; M06-2X: 6.3 kcal mol⁻¹; M06: 4.9 kcal mol⁻¹) for the investigated reactions. In the Ni case, some double hybrids show larger errors due to partial breakdown of the perturbative treatment for the correlation energy in cases with difficult electronic structures (partial multi-reference character). Only double hybrids either with very low amounts of perturbative correlation (e.g., PBE0-DH) or that use the opposite-spin correlation component only (e.g., PWPB95) seem to be more robust. We also investigated the effect of the D3 dispersion correction. While the barriers are not affected by this correction, significant and mostly positive results were observed for reaction energies. Furthermore, six very recently proposed double-hybrid functionals were analyzed regarding the influence of the amount of Fock exchange as well as the type of perturbative correlation treatment. According to these results, double hybrids with <50–60 % of exact exchange and ∼30 % perturbative correlation perform best.

Insights into the mechanism of reaction of [(C5Me5)2Sm(II)(thf)2] with CO2 and COS by DFT studies

Reaction mechanisms for the oxidative reactions of CO(2) and COS with [(C(5)Me(5))(2)Sm] have been investigated by means of DFT methods. The experimental formation of oxalate and dithiocarbonate complexes is explained. Their formation involve the samarium(III) bimetallic complexes [(C(5)Me(5))(2)Sm-CO(2)-Sm(C(5)Me(5))(2)] and [(C(5)Me(5))(2)Sm-COS-Sm(C(5)Me(5))(2)] as intermediates, respectively, ruling out radical coupling for the formation of the oxalate complex.

Ring-opening polymerization of ε-caprolactone catalyzed by sulfonic acids: computational evidence for bifunctional activation

The mechanism of ring-opening of ε-caprolactone by methanol catalyzed by trifluoromethane and methane sulfonic acids has been studied computationally at the DFT level of theory. For both elementary steps, the sulfonic acid was predicted to behave as a bifunctional catalyst. The nucleophilic addition proceeds via activation of both the monomer and the alcohol. The ring-opening involves the cleavage of the endo C-O bond of the tetrahedral intermediate with concomitant proton transfer. In both cases, the sulfonic acid acts as a proton shuttle via its acidic hydrogen atom and basic oxygen atoms. The computed activation barriers are consistent with the relatively fast polymerizations observed experimentally at room temperature with both catalysts.

A DFT study of the reactivity of actinidocenes (U, Np and Pu) with pyridine and pyridine N-oxide derivatives

The ortho C-H bond activation of several pyridine and pyridine N-oxide derivatives mediated by Cp(2)An(IV)(CH(3))(2) and Cp(2)An(III)(CH(3)) (Cp = C(5)H(5) and An = U, Np, Pu) have been investigated at the DFT level. For uranium(IV) complex, an excellent agreement with experimental observations is found, and particularly in the case of 2-picoline where only ortho sp(2) C-H activation is observed without any sp(3) C-H activation. These differences of reactivity can be explained by the charges distribution at the metathesis transition state level. A predictive study of the reactivity of neptunium and plutonium complexes with pyridine and pyridine N-oxide is reported. This study shows that neptunium and plutonium have almost the same reactivity. The C-H activation mediated by actinide (III) complexes have found to be more kinetically and thermodynamically favorable than for actinide (IV) complexes. The influence of 5f electrons on organoactinide reactivity is found to be small by comparing implicit and explicit treatment of 5f electrons.

Density functional theory for transition metals and transition metal chemistry

We introduce density functional theory and review recent progress in its application to transition metal chemistry. Topics covered include local, meta, hybrid, hybrid meta, and range-separated functionals, band theory, software, validation tests, and applications to spin states, magnetic exchange coupling, spectra, structure, reactivity, and catalysis, including molecules, clusters, nanoparticles, surfaces, and solids.

Highly accurate first-principles benchmark data sets for the parametrization and validation of density functional and other approximate methods. Derivation of a robust, generally applicable, double-hybrid functional for thermochemistry and thermochemical kinetics

We present a number of near-exact, nonrelativistic, Born-Oppenheimer reference data sets for the parametrization of more approximate methods (such as DFT functionals). The data were obtained by means of the W4 ab initio computational thermochemistry protocol, which has a 95% confidence interval well below 1 kJ/mol. Our data sets include W4-08, which are total atomization energies of over 100 small molecules that cover varying degrees of nondynamical correlations, and DBH24-W4, which are W4 theory values for Truhlar's set of 24 representative barrier heights. The usual procedure of comparing calculated DFT values with experimental atomization energies is hampered by comparatively large experimental uncertainties in many experimental values and compounds errors due to deficiencies in the DFT functional with those resulting from neglect of relativity and finite nuclear mass. Comparison with accurate, explicitly nonrelativistic, ab initio data avoids these issues. We then proceed to explore the performance of B2x-PLYP-type double hybrid functionals for atomization energies and barrier heights. We find that the optimum hybrids for hydrogen-transfer reactions, heavy-atoms transfers, nucleophilic substitutions, and unimolecular and recombination reactions are quite different from one another: out of these subsets, the heavy-atom transfer reactions are by far the most sensitive to the percentages of Hartree-Fock-type exchange y and MP2-type correlation x in an (x, y) double hybrid. The (42,72) hybrid B2K-PLYP, as reported in a preliminary communication, represents the best compromise between thermochemistry and hydrogen-transfer barriers, while also yielding excellent performance for nucleophilic substitutions. By optimizing for best overall performance on both thermochemistry and the DBH24-W4 data set, however, we find a new (36,65) hybrid which we term B2GP-PLYP. At a slight expense in performance for hydrogen-transfer barrier heights and nucleophilic substitutions, we obtain substantially better performance for the other reaction types. Although both B2K-PLYP and B2GP-PLYP are capable of 2 kcal/mol quality thermochemistry, B2GP-PLYP appears to be the more robust toward nondynamical correlation and strongly polar character. We additionally find that double-hybrid functionals display excellent performance for such problems as hydrogen bonding, prototype late transition metal reactions, pericyclic reactions, prototype cumulene-polyacetylene system, and weak interactions.

Consistent van der Waals radii for the whole main group

Atomic radii are not precisely defined but are nevertheless widely used parameters in modeling and understanding molecular structure and interactions. The van der Waals radii determined by Bondi from molecular crystals and data for gases are the most widely used values, but Bondi recommended radius values for only 28 of the 44 main-group elements in the periodic table. In the present Article, we present atomic radii for the other 16; these new radii were determined in a way designed to be compatible with Bondi's scale. The method chosen is a set of two-parameter correlations of Bondi's radii with repulsive-wall distances calculated by relativistic coupled-cluster electronic structure calculations. The newly determined radii (in A) are Be, 1.53; B, 1.92; Al, 1.84; Ca, 2.31; Ge, 2.11; Rb, 3.03; Sr, 2.49; Sb, 2.06; Cs, 3.43; Ba, 2.68; Bi, 2.07; Po, 1.97; At, 2.02; Rn, 2.20; Fr, 3.48; and Ra, 2.83.