The first examples of crystallographically characterizable complexes Tb2+, Pr2+, Gd2+, and Lu2+ have been isolated, which demonstrate that Ln2+ ions are accessible in soluble molecules for all the lanthanides except radioactive promethium. molecular Tb2+ obtained from reaction Cp′3Ln (Cp′ = C5H4SiMe3, Ln rare earth) with potassium presence 18-crown-6 Et2O at −35 °C under argon: [(18-crown-6)K][Cp′3Tb], {[(18-crown-6)K][Cp′3Tb]}n, {[K(18-crown-6)]2(μ-Cp′)}{Cp′3Tb}. complex is analogous to...

Flash reduction of Cp'3U (Cp' = C5H4SiMe3) in a column potassium graphite the presence 2.2.2-cryptand generates crystalline [K(2.2.2-cryptand)][Cp'3U], first isolable molecular U(2+) complex. To ensure that this was not U(3+) hydride, [K(2.2.2-cryptand)][Cp'3UH], which could be crystallographically similar, hydride complex synthesized by addition KH to and H2 confirmed different compound. Density functional theory calculations indicate 5f(3)6d(1) quintet ground state for [Cp'3U](-) anion...

The Ln3+ and Ln2+ complexes, Cp′3Ln, 1, (Cp′ = C5H4SiMe3) [K(2.2.2-cryptand)][Cp′3Ln], 2, respectively, have been synthesized for the six lanthanides traditionally known in +2 oxidation states, i.e., Ln Eu, Yb, Sm, Tm, Dy, Nd, to allow direct structural spectroscopic comparison with recently discovered ions of Pr, Gd, Tb, Ho, Y, Er, Lu 2. 2-La 2-Ce were also prepared first all same coordination environment both +3 states. show unusual feature that Ln–(Cp′ ring centroid) distances are only...

We have computed the surface energies, work functions, and interlayer relaxations of clean (111), (110), (100) surfaces Al, Cu, Ru, Rh, Pd, Ag, Pt, Au. Many these metallic technological or catalytic applications. compare experimental reference values to those local density approximation (LDA), Perdew-Burke-Ernzerhof (PBE) generalized gradient (GGA), PBEsol (PBE for solids) GGA, SCAN meta-GGA, SCAN+rVV10 (SCAN with a long-range van der Waals vdW correction). The closest agreement uncertain is...

The strongly constrained and appropriately normed (SCAN) semilocal density functional [J. Sun, A. Ruzsinszky, J. P. Perdew \textit{Phys. Rev. Lett.} {\bf 115}, 036402 (2015)] obeys all 17 known exact constraints for meta-generalized-gradient approximations (meta-GGA) includes some medium range correlation effects. Long-range London dispersion interactions are still missing, but can be accounted via an appropriate correction scheme. In this study, we combine SCAN with efficient show that...

The first molecular complexes of holmium and erbium in the +2 oxidation state have been generated by reducing Cp′3Ln [Cp′ = C5H4SiMe3; Ln Ho (1), Er (2)] with KC8 presence 18-crown-6 Et2O at −35 °C under argon. Purification crystallization below gave isomorphous [(18-crown-6)K][Cp′3Ln] [Ln (3), (4)]. three Cp′ ring centroids define a trigonal-planar geometry around each metal ion that is not perturbed location potassium crown cation near one K–C(Cp′) distances 3.053(8)–3.078(2) Å. metrical...

Density functionals within the meta-generalized gradient approximation (MGGA) are widely used for ground-state electronic structure calculations. However, gauge variance of kinetic energy density τ confounds applications MGGAs to time-dependent systems, excited states, magnetic properties, and states with strong spin-orbit coupling. Becke Tao paramagnetic current construct a invariant generalized \documentclass[12pt]{minimal}\begin{document}$\hat{\tau }$\end{document}τ̂. We show that...

We derive a renormalized many-body perturbation theory (MBPT) starting from the random phase approximation (RPA). This RPA-renormalized extends scope of single-reference MBPT methods to small-gap systems without significantly increasing computational cost. The leading correction RPA, termed approximate exchange kernel (AXK), substantially improves upon RPA atomization energies and ionization potentials affecting other properties such as barrier heights where is already accurate. Thus, AXK...

Examination of the Y[N(SiMe3)2]3/KC8 reduction system that allowed isolation (N2)3− radical has led to first evidence Y2+ in solution. The deep-blue solutions obtained from Y[N(SiMe3)2]3 and KC8 THF at −35 °C under argon have EPR spectra containing a doublet giso = 1.976 with 110 G hyperfine coupling constant. react N2 generate (N2)2− complexes {[(Me3Si)2N]2(THF)Y}2(μ-η2:η2-N2) (1) {[(Me3Si)2N]2(THF)Y}2(μ-η2:η2-N2)[K(THF)6] (2), respectively, demonstrate reaction can proceed through an...

The random phase approximation (RPA) is an increasingly popular method for computing molecular ground-state correlation energies within the adiabatic connection fluctuation-dissipation theorem framework of density functional theory. We present efficient analytical implementation first-order RPA properties and nuclear forces using resolution-of-the-identity (RI) imaginary frequency integration. centerpiece our approach a variational energy Lagrangian invariant under unitary transformations...

The structural phase transitions of different materials, including metal to metal, semiconductor, and semiconductor transitions, were explored using methods based on the random approximation. Transition pressures for Si, Ge, SiC, GaAs, ${\mathrm{SiO}}_{2}$, Pb, C, BN from their stable low-pressure phases certain high-pressure computed with several semilocal density functionals adiabatic connection fluctuation-dissipation formulation functional theory at zero temperature. In addition...

New syntheses of complexes containing the recently discovered (N(2))(3-) radical trianion have been developed by examining variations on LnA(3)/M reductive system that delivers "LnA(2)" reactivity when Ln = scandium, yttrium, or a lanthanide, M an alkali metal, and A N(SiMe(3))(2) C(5)R(5). The first examples reduction dinitrogen with aryloxide ligands (A OC(6)R(5)) are reported: combination Dy(OAr)(3) (OAr OC(6)H(3)(t)Bu(2)-2,6) KC(8) under was found to produce both (N(2))(2-) products,...

Deep-blue solutions of Y(2+) formed from Y(NR(2))(3) (R = SiMe(3)) and excess potassium in the presence 18-crown-6 at -45 °C under vacuum diethyl ether react with CO -78 to form colorless crystals (CO)(1-) radical complex, {[(R(2)N)(3)Y(μ-CO)(2)][K(2)(18-crown-6)(2)]}(n), 1. The polymeric structure contains trigonal bipyramidal [(R(2)N)(3)Y(μ-CO)(2)](2-) units axial ligands linked by [K(2)(18-crown-6)(2)](2+) dications. Byproducts such as ynediolate,...

We develop an efficient algorithm for four-component complete active space self-consistent field (CASSCF) methods on the basis of Dirac equation that takes into account spin-orbit and other relativistic effects self-consistently. Orbitals are optimized using a trust-region quasi-Newton method with Hessian updates so energies minimized respect to rotations among electronic orbitals maximized between positronic orbitals. Utilizing density fitting parallel computation, we demonstrate...

We review the theory and application of adiabatic exchange-correlation (xc-) kernels for ab initio calculations ground state energies quasiparticle excitations within frameworks connection fluctuation dissipation theorem Hedin's equations, respectively. Various different xc-kernels, which are all rooted in homogeneous electron gas, introduced but hereafter we focus on specific class renormalized kernels, particular rALDA rAPBE. The drastically improve description short-range correlations as...

The implementation of the frozen-core option in combination with analytic gradient random-phase approximation (RPA) is reported based on a density functional theory reference determinant using resolution-of-the-identity techniques and an extended Lagrangian. reduces dimensionality matrices required for RPA gradient, thereby yielding reduction computational cost. A frozen core also size numerical frequency grid accurate treatment correlation contributions Curtis-Clenshaw quadratures, leading...

In order to remedy some of the shortcomings random phase approximation (RPA) within adiabatic connection fluctuation-dissipation (ACFD) density functional theory, we introduce a short-ranged, exchange-like kernel that is one-electron self-correlation free and exact for two-electron systems in high-density limit. By tuning parameter our model recover an limit homogeneous electron gas correlation energy, obtain nonlocal, energy-optimized reduces errors RPA both inhomogeneous solids. Using...

Dinitrogen can be reduced by photochemical activation of the trivalent rare-earth-metal bis(pentamethylcyclopentadienyl) allyl complexes (C5Me5)2Ln(η3-C3H4R) (Ln = Y, Lu; R H, Me) to form (N═N)2– [(C5Me5)2Ln]2(μ-η2:η2-N2). This demonstrates that productive organolanthanide photochemistry is not limited unusual (η3-C5Me4H)− ligand in heteroleptic (C5Me5)2(C5Me4H)Ln and (C5Me5)(C5Me4H)2Ln. Photolytic (C5Me5)2Ln(η3-C3H5) Lu) presence isoprene provides a rare photopolymerization route...

Dinitrogen can be reduced by photochemical activation of the Ln(3+) mixed-ligand tris(cyclopentadienyl) rare-earth complexes (η(5)-C5Me5)(3-x)(C5Me4H)(x)Ln (Ln = Y, Lu, Dy; x 1, 2). [(C5Me4R)2Ln]2(μ-η(2):η(2)-N2) products (R H, Me) are formed in reactions which N2 is to (N═N)(2-) and (C5Me4H)(-) oxidized (C5Me4H)2. Density functional theory indicates that this unusual example photochemistry rationalized absorptions involving (η(3)-C5Me4H)(-) ligands.

A series of transition metal chloro complexes with the tetradentate tripodal tris(2-amino-oxazoline)amine ligand (TAO) have been synthesized and characterized. X-Ray structural analyses these compounds demonstrate formation mononuclear [M(II)(TAO)(Cl)](+), where M(II) = Cr, Mn, Fe, Co, Ni, Cu Zn. These exhibit distorted trigonal-bipyramidal geometry, coordinating through an apical tertiary amine, three equatorial imino nitrogen atoms, axial chloride anion. All possess intramolecular...

Without extensive fitting, accurate prediction of transition metal chemistry is a challenge for semilocal and hybrid density funcitonals. The Random Phase Approximation (RPA) has been shown to yield superior results functionals main group thermochemistry, but much less known about its performance metals. We have therefore analyzed the behavior reaction energies, barrier heights, ligand dissociation energies obtained with RPA compare our several functionals. Particular attention paid...