Tension between predicting accurate ground state correlation energies and excitation energies from adiabatic approximations in TDDFT.

The connection between the adiabatic excitation energy of time-dependent density functional theory and the ground state correlation energy from the adiabatic connection fluctuation-dissipation theorem (ACFDT) is explored in the limiting case of one excited state. An exact expression is derived for any adiabatic Hartree-exchange-correlation kernel that connects the excitation energy and the potential contribution to correlation. The resulting formula is applied to the asymmetric Hubbard dimer, a system where this limit is exact. Results from a hierarchy of approximations to the kernel, including the random phase approximation (RPA) with and without exchange and the adiabatically exact (AE) approximation, are compared to the exact ones. At full coupling, the numerical results indicate a tension between predicting an accurate excitation energy and an accurate potential contribution to correlation. The AE approximation is capable of making accurate predictions of both quantities, but only in parts of the parameter space that classify as weakly correlated, while RPA tends to be unable to accurately predict these properties simultaneously anywhere. For a strongly correlated dimer, the AE approximation greatly overestimates the excitation energy yet continues to yield an accurate ground state correlation energy due to its accurate prediction of the adiabatic connection integrand. If similar trends hold for real systems, the development of correlation kernels will be important for applications of the ACFDT in systems with large potential contributions to correlation.

Utilizing Experiment and Theory to Evaluate Rhodamine B ethylenediamine as a Fluorescent Sensor for G-type Nerve Agents.

Nerve gas mimic binding with Rhodamine B ethylenediamine (1) was studied in organic media. Binding of the nerve gas mimic, diethyl chlorophosphate (DCP), with the probe generated a non-fluorescent intermediate and a fluorescent product. Fluorescent and non-fluorescent products generated were identified using mass spectrometry and X-ray crystallography. Time-dependent density functional theory calculations were also used to investigate the electronic structure of the fluorescent probe in the ground and lowest lying π → π* singlet excited state. Though good agreement between theory and experiment can be obtained for the intense peak in the experimental spectrum using non-hybrid functionals, care must be taken when modelling these complexes due to the appearance of an n → π* transition that is too low in energy and appears to fall in the shoulders of the π → π* transitions.

Effective mass path integral simulations of quasiparticles in condensed phases.

The quantum many-body problem in condensed phases is often simplified using a quasiparticle description, such as effective mass theory for electron motion in a periodic solid. These approaches are often the basis for understanding many fundamental condensed phase processes, including the molecular mechanisms underlying solar energy harvesting and photocatalysis. Despite the importance of these effective particles, there is still a need for computational methods that can explore their behavior on chemically relevant length and time scales. This is especially true when the interactions between the particles and their environment are important. We introduce an approach for studying quasiparticles in condensed phases by combining effective mass theory with the path integral treatment of quantum particles. This framework incorporates the generally anisotropic electronic band structure of materials into path integral simulation schemes to enable modeling of quasiparticles in quantum confinement, for example. We demonstrate the utility of effective mass path integral simulations by modeling an exciton in solid potassium chloride and electron trapping by a sulfur vacancy in monolayer molybdenum disulfide.

Adiabatic Connection without Coupling Constant Integration.

Using a second-order approximation to Random Phase Approximation renormalized (RPAr) many-body perturbation theory for the interacting density-density response function, we have developed a so-called higher-order terms (HOT) approximation for the correlation energy. In combination with the first-order RPAr correction, our new method faithfully captures the infinite-order correlation for a given exchange-correlation kernel, yielding errors of the total correlation energy on the order of 1% or less for most systems. For exchange-like kernels, our new method has the further benefit that the coupling-strength integration can be completely eliminated resulting in a modest reduction in computational cost compared to the traditional approach. When the correlation energy is accurately reproduced by the HOT approximation, structural properties and energy differences are also accurately reproduced, as we demonstrate for several periodic solids and some molecular systems. Energy differences involving fragmentation are challenging for the HOT method, however, due to errors that may not cancel between a composite system and its constituent pieces.

Properties of real metallic surfaces: Effects of density functional semilocality and van der Waals nonlocality.

We have computed the surface energies, work functions, and interlayer surface relaxations of clean (111), (100), and (110) surfaces of Al, Cu, Ru, Rh, Pd, Ag, Pt, and Au. We interpret the surface energy from liquid metal measurements as the mean of the solid-state surface energies over these three lowest-index crystal faces. We compare experimental (and random phase approximation) reference values to those of a family of nonempirical semilocal density functionals, from the basic local density approximation (LDA) to our most advanced general purpose meta-generalized gradient approximation, strongly constrained and appropriately normed (SCAN). The closest agreement is achieved by the simplest density functional LDA, and by the most sophisticated one, SCAN+rVV10 (Vydrov-Van Voorhis 2010). The long-range van der Waals interaction, incorporated through rVV10, increases the surface energies by about 10%, and increases the work functions by about 3%. LDA works for metal surfaces through two known error cancellations. The Perdew-Burke-Ernzerhof generalized gradient approximation tends to underestimate both surface energies (by about 24%) and work functions (by about 4%), yielding the least-accurate results. The amount by which a functional underestimates these surface properties correlates with the extent to which it neglects van der Waals attraction at intermediate and long range. Qualitative arguments are given for the signs of the van der Waals contributions to the surface energy and work function. A standard expression for the work function in Kohn-Sham (KS) theory is shown to be valid in generalized KS theory. Interlayer relaxations from different functionals are in reasonable agreement with one another, and usually with experiment.

Fully relativistic complete active space self-consistent field for large molecules: quasi-second-order minimax optimization.

We develop an efficient algorithm for four-component complete active space self-consistent field (CASSCF) methods on the basis of the 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 that energies are minimized with respect to rotations among electronic orbitals and maximized with respect to rotations between electronic and positronic orbitals. Utilizing density fitting and parallel computation, we demonstrate that Dirac-Coulomb CASSCF calculations can be routinely performed on systems with 100 atoms and a few heavy-elements. The convergence behavior and wall times for octachloridodirhenate(III) and a tungsten methylidene complex are presented. In addition, the excitation energies of octachloridodirhenate(III) are reported using a state-averaged variant.

Structural, spectroscopic, and theoretical comparison of traditional vs recently discovered Ln(2+) ions in the [K(2.2.2-cryptand)][(C5H4SiMe3)3Ln] complexes: the variable nature of Dy(2+) and Nd(2+).

The Ln(3+) and Ln(2+) complexes, Cp'3Ln, 1, (Cp' = C5H4SiMe3) and [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, and Nd, to allow direct structural and spectroscopic comparison with the recently discovered Ln(2+) ions of Ln = Pr, Gd, Tb, Ho, Y, Er, and Lu in 2. 2-La and 2-Ce were also prepared to allow the first comparison of all the lanthanides in the same coordination environment in both +2 and +3 oxidation states. 2-La and 2-Ce show the same unusual structural feature of the recently discovered +2 complexes, that the Ln-(Cp' ring centroid) distances are only about 0.03 Å longer than in the +3 analogs, 1. The Eu, Yb, Sm, Tm, Dy, and Nd complexes were expected to show much larger differences, but this was observed for only four of these traditional six lanthanides. 2-Dy and 2-Nd are like the new nine ions in this tris(cyclopentadienyl) coordination geometry. A DFT-based model explains the results and shows that a 4f (n)5d(1) electron configuration is appropriate not only for the nine recently discovered Ln(2+) ions in 2 but also for Dy(2+) and Nd(2+), which traditionally have 4f (n+1) electron configurations like Eu(2+), Yb(2+), Sm(2+), and Tm(2+). These results indicate that the ground state of a lanthanide ion in a molecule can be changed by the ligand set, a previously unknown option with these metals due to the limited radial extension of the 4f orbitals.

Analytical First-Order Molecular Properties and Forces within the Adiabatic Connection Random Phase Approximation.

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 an efficient analytical implementation of first-order RPA molecular properties and nuclear forces using the resolution-of-the-identity (RI) approximation and imaginary frequency integration. The centerpiece of our approach is a variational RPA energy Lagrangian invariant under unitary transformations of occupied and virtual reference orbitals, respectively. Its construction requires the solution of a single coupled-perturbed Kohn-Sham equation independent of the number of perturbations. Energy gradients with respect to nuclear displacements and other first-order properties such as one-particle densities or dipole moments are obtained from partial derivatives of the Lagrangian. Our RPA energy gradient implementation exhibits the same [Formula: see text] scaling with system size N as a single-point RPA energy calculation. In typical applications, the cost for computing the entire gradient vector with respect to nuclear displacements is ∼5 times that of a single-point RPA energy calculation. Derivatives of the quadrature nodes and weights used for frequency integration are essential for RPA gradients with an accuracy consistent with RPA energies and can be included in our approach. The quality of RPA equilibrium structures is assessed by comparison to accurate theoretical and experimental data for covalent main group compounds, weakly bonded dimers, and transition metal complexes. RPA outperforms semilocal functionals as well as second-order Møller-Plesset (MP2) theory, which fails badly for the transition metal compounds. Dipole moments of polarizable molecules and weakly bound dimers show a similar trend. RPA harmonic vibrational frequencies are nearly of coupled cluster singles, doubles, and perturbative triples quality for a set of main group compounds. Compared to the ring-coupled cluster based implementation of Rekkedal et al. [J. Chem. Phys. 2013, 139, 081101.], our method scales better by two powers of N and supports a semilocal Kohn-Sham reference. The latter is essential for the good performance of RPA in small-gap systems.

Communication: Random phase approximation renormalized many-body perturbation theory.

We derive a renormalized many-body perturbation theory (MBPT) starting from the random phase approximation (RPA). This RPA-renormalized perturbation theory extends the scope of single-reference MBPT methods to small-gap systems without significantly increasing the computational cost. The leading correction to RPA, termed the approximate exchange kernel (AXK), substantially improves upon RPA atomization energies and ionization potentials without affecting other properties such as barrier heights where RPA is already accurate. Thus, AXK is more balanced than second-order screened exchange [A. Grüneis et al., J. Chem. Phys. 131, 154115 (2009)], which tends to overcorrect RPA for systems with stronger static correlation. Similarly, AXK avoids the divergence of second-order Møller-Plesset (MP2) theory for small gap systems and delivers a much more consistent performance than MP2 across the periodic table at comparable cost. RPA+AXK thus is an accurate, non-empirical, and robust tool to assess and improve semi-local density functional theory for a wide range of systems previously inaccessible to first-principles electronic structure calculations.

Identification of the +2 oxidation state for uranium in a crystalline molecular complex, [K(2.2.2-cryptand)][(C5H4SiMe3)3U].

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

Completing the series of +2 ions for the lanthanide elements: synthesis of molecular complexes of Pr2+, Gd2+, Tb2+, and Lu2+.

The first examples of crystallographically characterizable complexes of Tb(2+), Pr(2+), Gd(2+), and Lu(2+) have been isolated, which demonstrate that Ln(2+) ions are accessible in soluble molecules for all of the lanthanides except radioactive promethium. The first molecular Tb(2+) complexes have been obtained from the reaction of Cp'3Ln (Cp' = C5H4SiMe3, Ln = rare earth) with potassium in the presence of 18-crown-6 in Et2O at -35 °C under argon: [(18-crown-6)K][Cp'3Tb], {[(18-crown-6)K][Cp'3Tb]}n, and {[K(18-crown-6)]2(µ-Cp')}{Cp'3Tb}. The first complex is analogous to previously isolated Y(2+), Ho(2+), and Er(2+) complexes, the second complex shows an isomeric structural form of these Ln(2+) complexes, and the third complex shows that [(18-crown-6)K](1+) alone is not the only cation that will stabilize these reactive Ln(2+) species, a result that led to further exploration of cation variants. With 2.2.2-cryptand in place of 18-crown-6 in the Cp'3Ln/K reaction, a more stable complex of Tb(2+) was produced as well as more stable Y(2+), Ho(2+), and Er(2+) analogs: [K(2.2.2-cryptand)][Cp'3Ln]. Exploration of this 2.2.2-cryptand-based reaction with the remaining lanthanides for which Ln(2+) had not been observed in molecular species provided crystalline Pr(2+), Gd(2+), and Lu(2+) complexes. These Ln(2+) complexes, [K(2.2.2-cryptand)][Cp'3Ln] (Ln = Y, Pr, Gd, Tb, Ho, Er, Lu), all have similar UV-vis spectra and exhibit Ln-C(Cp') bond distances that are ~0.03 Å longer than those in the Ln(3+) precursors, Cp'3Ln. These data, as well as density functional theory calculations and EPR spectra, suggest that a 4f(n)5d(1) description of the electron configuration in these Ln(2+) ions is more appropriate than 4f(n+1).

Dinitrogen reduction via photochemical activation of heteroleptic tris(cyclopentadienyl) rare-earth complexes.

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 in which N2 is reduced to (N═N)(2-) and (C5Me4H)(-) is oxidized to (C5Me4H)2. Density functional theory indicates that this unusual example of rare-earth photochemistry can be rationalized by absorptions involving the (η(3)-C5Me4H)(-) ligands.

Density functional theory and X-ray analysis of the structural variability in η5,η5,η1-tris(ring) rare earth/actinide tetramethylpyrrolyl complexes, (C5Me5)2M(NC4Me4).

(C5Me5)2M(NC4Me4) complexes (M = Y, Sm, Ce, U) were synthesized to act as structural models for the (η(5)-C5Me5)2M(η(1)-C5Me5) intermediate postulated to give pseudoalkyl reactivity to sterically crowded (C5Me5)3M complexes. This synthesis was accomplished through reaction of the tetraphenylborate complexes, [(C5Me5)2M][(µ-Ph)2BPh2], with potassium tetramethylpyrrolyl, KNC4Me4. X-ray crystallographic studies on the resulting (C5Me5)2M(NC4Me4) complexes showed that, although the two (C5Me5)(-) rings bind to the metal with η(5) coordination and tetramethylpyrrolyl has a primary η(1) coordination, the complexes are not symmetrical in the solid state, and disparate M-N-C(ring) angles within a complex orient a (NC4Me4)(-) ring carbon and methyl carbon near the metal in a pseudo-η(3) binding mode. Moreover, these (C5Me5)2M(NC4Me4) complexes display unexpectedly large structural variations not only between metals but also between crystals grown from the same mother liquor. Large variations are observed in the M-N-C(ring) angles that lead to close metal ring carbon distances [105.6(1)-115.7(2)°] as well as in the M-N-(NC4Me4 ring centroid) angles (152.2-167.3°). The synthesis and structure of 4d, 4f, and 5f metal examples are described, and the results are compared to predictions from the density functional theory. The reasons for the variable structures displayed by the (C5Me5)2M(NC4Me4) complexes are discussed.

Harnessing the meta-generalized gradient approximation for time-dependent density functional theory.

Density functionals within the meta-generalized gradient approximation (MGGA) are widely used for ground-state electronic structure calculations. However, the gauge variance of the kinetic energy density τ confounds applications of MGGAs to time-dependent systems, excited states, magnetic properties, and states with strong spin-orbit coupling. Becke and Tao used the paramagnetic current density to construct a gauge invariant generalized kinetic energy density τ. We show that τ(W)≤τ, where τ(W) is the von Weizsäcker kinetic energy density of a one-electron system. Thus, replacing τ by τ leads to current-dependent MGGAs (cMGGAs) that are not only gauge invariant but also restore the accuracy of MGGAs in iso-orbital regions for time-dependent and current-carrying states. The current dependence of cMGGAs produces a vector exchange-correlation (XC) potential in the time-dependent adiabatic Kohn-Sham (KS) equations. While MGGA response properties of current-free ground states become manifestly gauge-variant to second order, linear response properties are affected by a new XC kernel appearing in the cMGGA magnetic orbital rotation Hessian. This kernel reflects the first-order coupling of KS orbitals due to changes in the paramagnetic current density and has apparently been ignored in previous MGGA response implementations. Inclusion of the current dependence increases total computation times by less than 50%. Benchmark applications to 109 adiabatic excitation energies using the Tao-Perdew-Staroverov-Scuseria (TPSS) MGGA and its hybrid version TPSSh show that cMGGA excitation energies are slightly lower than the MGGA ones on average, but exhibit fewer outliers. Similarly, the optical rotations of 13 small organic molecules show a small but systematic improvement upon inclusion of the magnetic XC kernel. We conclude that cMGGAs should replace MGGAs in all applications involving time-dependent or current-carrying states.

Varying the Lewis base coordination of the Y2N2 core in the reduced dinitrogen complexes {[(Me3Si)2N]2(L)Y}2(µ-η2:η2-N2) (L = benzonitrile, pyridines, triphenylphosphine oxide, and trimethylamine N-oxide).

The effect of the neutral donor ligand, L, on the Ln(2)N(2) core in the (N═N)(2-) complexes, [A(2)(L)Ln](2)(µ-η(2):η(2)-N(2)) (Ln = Sc, Y, lanthanide; A = monoanion; L = neutral ligand), is unknown since all of the crystallographically characterized examples were obtained with L = tetrahydrofuran (THF). To explore variation in L, displacement reactions between {[(Me(3)Si)(2)N](2)(THF)Y}(2)(µ-η(2):η(2)-N(2)), 1, and benzonitrile, pyridine (py), 4-dimethylaminopyridine (DMAP), triphenylphosphine oxide, and trimethylamine N-oxide were investigated. THF is displaced by all of these ligands to form {[(Me(3)Si)(2)N](2)(L)Y}(2)(µ-η(2):η(2)-N(2)) complexes (L = PhCN, 2; py, 3; DMAP, 4; Ph(3)PO, 5; Me(3)NO, 6) that were fully characterized by analytical, spectroscopic, density functional theory, and X-ray crystallographic methods. The crystal structures of the Y(2)N(2) cores in 2-5 are similar to that in 1 with N-N bond distances between 1.255(3) Å and 1.274(3) Å, but X-ray analysis of the N-N distance in 6 shows it to be shorter: 1.198(3) Å.

Expanding rare-earth oxidation state chemistry to molecular complexes of holmium(II) and erbium(II).

The first molecular complexes of holmium and erbium in the +2 oxidation state have been generated by reducing Cp'(3)Ln [Cp' = C(5)H(4)SiMe(3); Ln = Ho (1), Er (2)] with KC(8) in the presence of 18-crown-6 in Et(2)O at -35 °C under argon. Purification and crystallization below -35 °C gave isomorphous [(18-crown-6)K][Cp'(3)Ln] [Ln = Ho (3), Er (4)]. The three Cp' ring centroids define a trigonal-planar geometry around each metal ion that is not perturbed by the location of the potassium crown cation near one ring with K-C(Cp') distances of 3.053(8)-3.078(2) Å. The metrical parameters of the three rings are indistinguishable within the error limits. In contrast to Ln(2+) complexes of Eu, Yb, Sm, Tm, Dy, and Nd, 3 and 4 have average Ln-(Cp' ring centroid) distances only 0.029 and 0.021 Å longer than those of the Ln(3+) analogues 1 and 2, a result similar to that previously reported for the 4d(1) Y(2+) complex [(18-crown-6)K][Cp'(3)Y] (5) and the 5d(1) La(2+) complex [K(18-crown-6)(Et(2)O)][Cp″(3)La] [Cp″ = 1,3-(Me(3)Si)(2)C(5)H(3)]. Surprisingly, the UV-vis spectra of 3 and 4 are also very similar to that of 5 with two broad absorptions in the visible region, suggesting that 3-5 have similar electron configurations. Density functional theory calculations on the Ho(2+) and Er(2+) species yielded HOMOs that are largely 5d(z(2)) in character and supportive of 4f(10)5d(1) and 4f(11)5d(1) ground-state configurations, respectively.

Isolation of (CO)1- and (CO2)1- radical complexes of rare earths via Ln(NR2)3/K reduction and [K2(18-crown-6)2]2+ oligomerization.

Deep-blue solutions of Y(2+) formed from Y(NR(2))(3) (R = SiMe(3)) and excess potassium in the presence of 18-crown-6 at -45 °C under vacuum in diethyl ether react with CO at -78 °C to form colorless crystals of the (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 with axial (CO)(1-) ligands linked by [K(2)(18-crown-6)(2)](2+) dications. Byproducts such as the ynediolate, [(R(2)N)(3)Y](2)(µ-OC≡CO){[K(18-crown-6)](2)(18-crown-6)}, 2, in which two (CO)(1-) anions are coupled to form (OC≡CO)(2-), and the insertion/rearrangement product, {(R(2)N)(2)Y[OC(═CH(2))Si(Me(2))NSiMe(3)]}[K(18-crown-6)], 3, are common in these reactions that give variable results depending on the specific reaction conditions. The CO reduction in the presence of THF forms a solvated variant of 2, the ynediolate [(R(2)N)(3)Y](2)(µ-OC≡CO)[K(18-crown-6)(THF)(2)](2), 2a. CO(2) reacts analogously with Y(2+) to form the (CO(2))(1-) radical complex, {[(R(2)N)(3)Y(µ-CO(2))(2)][K(2)(18-crown-6)(2)]}(n), 4, that has a structure similar to that of 1. Analogous (CO)(1-) and (OC≡CO)(2-) complexes of lutetium were isolated using Lu(NR(2))(3)/K/18-crown-6: {[(R(2)N)(3)Lu(µ-CO)(2)][K(2)(18-crown-6)(2)]}(n), 5, [(R(2)N)(3)Lu](2)(µ-OC≡CO){[K(18-crown-6)](2)(18-crown-6)}, 6, and [(R(2)N)(3)Lu](2)(µ-OC≡CO)[K(18-crown-6)(Et(2)O)(2)](2), 6a.

Synthesis, structure, and physical properties for a series of trigonal bipyramidal M(II)-Cl complexes with intramolecular hydrogen bonds.

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 of these compounds demonstrate the formation of the mononuclear complexes [M(II)(TAO)(Cl)](+), where M(II) = Cr, Mn, Fe, Co, Ni, Cu and Zn. These complexes exhibit distorted trigonal-bipyramidal geometry, coordinating the metal through an apical tertiary amine, three equatorial imino nitrogen atoms, and an axial chloride anion. All the complexes possess an intramolecular hydrogen-bonding (H-bonding) network within the cavity occupied by the metal-bound chloride ion. The metal-chloride bond distances are atypically long, which is attributed to the effects of the H-bonding network. Nuclear magnetic resonance (NMR) spectroscopy of the Zn complex suggests that the solid-state structures are representative of that observed in solution, and that the H-bonding interactions persist as well. Additionally, density functional theory (DFT) calculations were carried out to probe the electronic structures of the complexes.

Synthesis of the (N2)3- radical from Y2+ and its protonolysis reactivity to form (N2H2)2- via the Y[N(SiMe3)2]3/KC8 reduction system.

Examination of the Y[N(SiMe(3))(2)](3)/KC(8) reduction system that allowed isolation of the (N(2))(3-) radical has led to the first evidence of Y(2+) in solution. The deep-blue solutions obtained from Y[N(SiMe(3))(2)](3) and KC(8) in THF at -35 °C under argon have EPR spectra containing a doublet at g(iso) = 1.976 with a 110 G hyperfine coupling constant. The solutions react with N(2) to generate (N(2))(2-) and (N(2))(3-) complexes {[(Me(3)Si)(2)N](2)(THF)Y}(2)(µ-η(2):η(2)-N(2)) (1) and {[(Me(3)Si)(2)N](2)(THF)Y}(2)(µ-η(2):η(2)-N(2))[K(THF)(6)] (2), respectively, and demonstrate that the Y[N(SiMe(3))(2)](3)/KC(8) reaction can proceed through an Y(2+) intermediate. The reactivity of (N(2))(3-) radical with proton sources was probed for the first time for comparison with the (N(2))(2-) and (N(2))(4-) chemistry. Complex 2 reacts with [Et(3)NH][BPh(4)] to form {[(Me(3)Si)(2)N](2)(THF)Y}(2)(µ-N(2)H(2)), the first lanthanide (N(2)H(2))(2-) complex derived from dinitrogen, as well as 1 as a byproduct, consistent with radical disproportionation reactivity.