The first (N═N)2– complex of a rare-earth metal with an end-on dinitrogen bridge, {K(crypt)}2{[(R2N)3Sc]2[μ-η1:η1-N2]} (crypt = 2.2.2-cryptand, R = SiMe3), has been isolated from the reduction of Sc(NR2)3 under dinitrogen at −35 °C and characterized by X-ray crystallography. The structure differs from the characteristic side-on structures previously observed for over 40 crystallographically characterized rare-earth metal (N═N)2– complexes of formula [A2Ln(THF)x]2[μ-η2:η2-N2] (Ln = Sc, Y, and lanthanides; x = 0, 1; A = anionic ligand such as amide, cyclopentadienide, and aryloxide). The 1.221(3) Å N—N distance and the 1644 cm–1 Raman stretch are consistent with the presence of an (N═N)2– bridge. The observed paramagnetism of the complex by Evans method measurements is consistent with DFT calculations that suggest a triplet (3A2) ground state in D3 symmetry involving two degenerate Sc—N2—Sc bonding orbitals. Upon brief exposure of the orange Sc3+ bridging dinitrogen complex to UV-light, photolysis to form the monomeric Sc2+ complex, [K(crypt)][Sc(NR2)3], was observed. Conversion of the Sc2+ complex to the Sc3+ dinitrogen complex was not observed with this crypt system, but it did occur with the 18-crown-6 (crown) analog which formed {K(crown)}2{[(R2N)3Sc]2[μ-η1:η1-N2]}. This suggests the importance of the alkali metal chelating agent in the reversibility of dinitrogen binding in this scandium system.

Over 70 years of chemical investigations have shown that plutonium exhibits some of the most complicated chemistry in the periodic table. Six Pu oxidation states have been unambiguously confirmed (0 and +3 to +7), and four different oxidation states can exist simultaneously in solution. We report a new formal oxidation state for plutonium, namely Pu2+ in [K(2.2.2-cryptand)][PuIICp″3], Cp″ = C5H3(SiMe3)2. The synthetic precursor PuIIICp″3 is also reported, comprising the first structural characterization of a Pu–C bond. Absorption spectroscopy and DFT calculations indicate that the Pu2+ ion has predominantly a 5f6 electron configuration with some 6d mixing.

We present the first unconstrained nonadiabatic molecular dynamics (NAMD) simulations of photocatalytic water oxidation by small hydrated TiO2 nanoparticles using Tully surface hopping and time-dependent density functional theory. The results indicate that ultrafast electron–proton transfer from physisorbed water to the photohole initiates the photo-oxidation on the S1 potential energy surface. The new mechanism readily explains the observation of mobile hydroxyl radicals in recent experiments. Two key driving forces for the photo-oxidation reaction are identified: localization of the electron–hole pair and stabilization of the photohole by hydrogen bonding interaction. Our findings illustrate the scope of recent advances in NAMD methods and emphasize the importance of explicit simulation of electronic excitations.

A new series of Ln3+ and Ln2+ complexes has been synthesized using the tris(aryloxide)arene ligand system, ((Ad,MeArO)3mes)3−, recently used to isolate a complex of U2+. The triphenol precursor, (Ad,MeArOH)3mes, reacts with the Ln3+ amides, Ln(NR2)3 (R = SiMe3), to form a series of [((Ad,MeArO)3mes)Ln] complexes, 1-Ln. Crystallographic characterization was achieved for Ln = Nd, Gd, Dy, and Er. The complexes 1-Ln can be reduced with potassium graphite in the presence of 2.2.2-cryptand (crypt) to form highly absorbing solutions with properties consistent with Ln2+ complexes, [K(crypt)][((Ad,MeArO)3mes)Ln], 2-Ln. The synthesis of the Nd2+ complex [K(crypt)][((Ad,MeArO)3mes)Nd], 2-Nd, was unambiguously confirmed by X-ray crystallography. In the case of the other lanthanides, crystals were found to contain mixtures of 2-Ln co-crystallized with either a Ln3+ hydride complex, [K(crypt)][((Ad,MeArO)3mes)LnH], 3-Ln, for Ln = Gd, Dy, and Er, or a hydroxide complex, [K(crypt)][((Ad,MeArO)3mes)Ln(OH)], 4-Ln, for Ln = Dy. A Dy2+ complex with 18-crown-6 as the potassium chelator, [K(18-crown-6)(THF)2][((Ad,MeArO)3mes)Dy], 5-Dy, was isolated as a co-crystallized mixture with the Dy3+ hydride complex, [K(18-crown-6)(THF)2][((Ad,MeArO)3mes)DyH], 6-Dy. Structural comparisons of 1-Ln and 2-Ln are presented with respect to their uranium analogs and correlated with density functional theory calculations on their electronic structures.

•Synthesis of bimetallic and trimetallic rare-earth metal hydrides.•Reduction of bimetallic yttrium, dysprosium, and terbium hydrides and chlorides.•DFT suggests reduction of bimetallics could lead to metal-metal bond character.•EPR evidence for a metal-based radical on yttrium.The reductive chemistry of [Cp'2Ln(μ–H)(THF)x]y [Ln = Y, Dy, Tb; Cp' = (C5H4SiMe3)1−; x = 2, 0 and y = 2, 3] was examined to determine if these hydrides would be viable precursors for 4fn5d1 Ln2+ ions that could form 5d1-5d1 metal–metal bonded complexes. The hydrides were prepared by reaction of the chlorides, [Cp'2Ln(μ–Cl)]2, 1-Ln, with allylmagnesium chloride to form the allyl complexes, [Cp'2Y(η3–C3H5)(THF)], 2-Ln, which were hydrogenolyzed. The solvent-free reaction of solid 2-Ln with 60 psi of H2 gas in a Fischer-Porter apparatus produced, in the Y case, the trimetallic species, [Cp'2Y(μ–H)]3, 3-Y, and in the Dy and Tb cases, the bimetallic complexes [Cp'2Ln(μ–H)(THF)]2, 4-Ln (Ln = Dy, Tb). The latter complexes could be converted to 3-Dy and 3-Tb by heating under vacuum. Isopiestic data indicate that 3-Y solvates to 4-Y in THF. Reductions of 4-Y, 4-Dy, and 4-Tb with KC8 in the presence of a chelate such as 2.2.2-cryptand or 18-crown-6 all gave reaction products with intense dark colors characteristic of Ln2+ ions. In the yttrium case, with either chelating agent, the dark green product gives a rhombic EPR spectrum (g1 = 2.01, g2 = 1.99, g3 = 1.98, A = 24.1 G) at 77 K. However, the only crystallographically-characterizable products obtainable from these solutions were Ln3+ polyhydride anion complexes of composition, [K(chelate)]{[Cp'2Ln(μ–H)]3(μ–H)}. Reduction of 1-Y with KC8 in the presence of 2.2.2-cryptand also yields an intensely colored product with an axial EPR spectrum (gx = gy = 2.05, Ax = Ay = 35.5 G; gz = 2.07, Az = 34.5) similar to that of (Cp'3Y)1− ion, but crystals were not obtained from this system.Download high-res image (129KB)Download full-size image

The reactivity of the recently discovered Th2+ complex [K(18-crown-6)(THF)2][Cp″3Th], 1 [Cp′′ = C5H3(SiMe3)2-1,3], with hydrogen reagents has been investigated and found to provide syntheses of new classes of thorium hydride compounds. Complex 1 reacts with [Et3NH][BPh4] to form the terminal Th4+ hydride complex Cp″3ThH, 2, a reaction that formally involves a net two-electron reduction. Complex 1 also reacts in the solid state and in solution with H2 to form a mixed-valent bimetallic product, [K(18-crown-6)(Et2O)][Cp″2ThH2]2, 3, which was analyzed by X-ray crystallography, electron paramagnetic resonance and optical spectroscopy, and density functional theory. The existence of 3, which formally contains Th3+ and Th4+, suggested that KC8 could reduce [(C5Me5)2ThH2]2. In the presence of 18-crown-6, this reaction forms an analogous mixed-valent product formulated as [K(18-crown-6)(THF)][(C5Me5)2ThH2]2, 4. A similar complex with (C5Me4H)1– ligands was not obtained, but reaction of (C5Me4H)3Th with H2 in the presence of KC8 and 2.2.2-cryptand at −45 °C produced two monometallic hydride products, namely, (C5Me4H)3ThH, 5, and [K(2.2.2-cryptand)]{(C5Me4H)2[η1:η5-C5Me3H(CH2)]ThH]}, 6. Complex 6 contains a metalated tetramethylcyclopentadienyl dianion, [C5Me3H(CH2)]2–, that binds in a tuck-in mode.

The effect of nonadiabatic transitions on branching ratios, kinetic and internal energy distribution of fragments, and reaction mechanisms observed in acetaldehyde photodissociation is investigated by nonadiabatic molecular dynamics (NAMD) simulations using time-dependent hybrid density functional theory and Tully surface hopping. Homolytic bond breaking is approximately captured by allowing spin symmetry to break. The NAMD simulations reveal that nonadiabatic transitions selectively enhance the kinetic energy of certain internal degrees of freedom within approximately 50 fs. Branching ratios from NAMD and conventional “hot” Born–Oppenheimer molecular dynamics (BOMD) are similar and qualitatively agree with experiment. However, as opposed to the BOMD simulations, NAMD captures the high-energy tail of the experimental kinetic energy distribution. The extra “kick” of the nuclei in the direction of the nonadiabatic coupling vector results from nonadiabatic transitions close to conical intersections. From a mechanistic perspective, the nonadiabatic effects favor asynchronous over synchronous fragmentation and tend to suppress roaming.

Reduction of the Th3+ complex Cp′′3Th, 1 [Cp′′ = C5H3(SiMe3)2], with potassium graphite in THF in the presence of 2.2.2-cryptand generates [K(2.2.2-cryptand)][Cp′′3Th], 2, a complex containing thorium in the formal +2 oxidation state. Reaction of 1 with KC8 in the presence of 18-crown-6 generates the analogous Th2+ compound, [K(18-crown-6)(THF)2][Cp′′3Th], 3. Complexes 2 and 3 form dark green solutions in THF with ε = 23000 M−1 cm−1, but crystallize as dichroic dark blue/red crystals. X-ray crystallography revealed that the anions in 2 and 3 have trigonal planar coordination geometries, with 2.521 and 2.525 Å Th–(Cp′′ ring centroid) distances, respectively, equivalent to the 2.520 Å distance measured in 1. Density functional theory analysis of (Cp′′3Th)1− is consistent with a 6d2 ground state, the first example of this transition metal electron configuration. Complex 3 reacts as a two-electron reductant with cyclooctatetraene to make Cp′′2Th(C8H8), 4, and [K(18-crown-6)]Cp′′.

A new option for stabilizing unusual Ln2+ ions has been identified in the reaction of Cp′3Ln, 1-Ln (Ln = La, Ce; Cp′ = C5H4SiMe3), with potassium graphite (KC8) in benzene in the presence of 2.2.2-cryptand. This generates [K(2.2.2-cryptand)]2[(Cp′2Ln)2(μ-η6:η6-C6H6)], 2-Ln, complexes that contain La and Ce in the formal +2 oxidation state. These complexes expand the range of coordination environments known for these ions beyond the previously established examples, (Cp′′3Ln)1− and (Cp′3Ln)1− (Cp′′ = C5H3(SiMe3)2-1,3), and generalize the viability of using three anionic carbocyclic rings to stabilize highly reactive Ln2+ ions. In 2-Ln, a non-planar bridging (C6H6)2− ligand shared between two metals takes the place of a cyclopentadienyl ligand in (Cp′3Ln)1−. The intensely colored (ε = ∼8000 M−1 cm−1) 2-Ln complexes react as four electron reductants with two equiv. of naphthalene to produce two equiv. of the reduced naphthalenide complex, [K(2.2.2-cryptand)][Cp′2Ln(η4-C10H8)].

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 the (N═N)2– complexes [(C5Me5)2Ln]2(μ-η2:η2-N2). This demonstrates that productive organolanthanide photochemistry is not limited to complexes of the unusual (η3-C5Me4H)− ligand in the heteroleptic complexes (C5Me5)2(C5Me4H)Ln and (C5Me5)(C5Me4H)2Ln. Photolytic activation of (C5Me5)2Ln(η3-C3H5) (Ln = Y, Lu) in the presence of isoprene provides a rare photopolymerization route to polyisoprene. Sulfur can also be reduced by photolysis of (C5Me5)2Ln(η3-C3H5) (Ln = Y, Lu) to generate the (S)2– complexes, [(C5Me5)2Ln]2(μ-S), which have variable Ln–S–Ln angles depending on crystallization conditions.

The tris(cyclopentadienyl) yttrium complexes Cp3Y(THF), CpMe3Y(THF), Cp″3Y, Cp″2YCp, and Cp″2YCpMe [Cp = C5H5, CpMe = C5H4Me, Cp″ = C5H3(SiMe3)2] have been treated with potassium graphite in the presence of 2.2.2-cryptand to search for more stable examples of complexes featuring the recently discovered Y2+ ion first isolated in [K(18-crown-6)][Cp′3Y] and [K(2.2.2-cryptand)][Cp′3Y], 1-Y (Cp′ = C5H4SiMe3). Reduction of the tris(cyclopentadienyl) complexes generates dark solutions like that of 1-Y, and the EPR spectra contain doublets with g values between 1.990 and 1.991 and hyperfine coupling constants of 34–47 gauss that are consistent with the presence of Y2+. [K(2.2.2-cryptand)][Cp″2YCp], 2-Y, was characterizable by X-ray crystallography. Reduction of the Cp″3Gd, Cp″2GdCp, and Cp″2GdCpMe complexes containing the larger metal gadolinium were also examined. In each case, dark solutions and EPR spectra like that of [K(2.2.2-cryptand)][Cp′3Gd], 1-Gd, were obtained, and [K(2.2.2-cryptand)][Cp″2GdCp], 2-Gd, was crystallographically characterizable. None of the new yttrium and gadolinium complexes displayed greater stability than 1-Y and 1-Gd. Exploration of this reduction chemistry with indenyl ligands did not give evidence for +2 complexes. The only definitive information obtained from reductions of the CpIn3Ln (CpIn = C9H7, Ln = Y, Ho, Dy) complexes was the X-ray crystal structure of {K(2.2.2-cryptand)}2{[(C9H7)2Dy(μ–η5:η1-C9H6)]2}, a complex containing the first example of the indenyl dianion, (C9H6)2–, derived from C–H bond activation of the (C9H7)1– monoanion. Density functional theory analysis of these results provides an explanation for the observed hyperfine coupling constants in the yttrium complexes and for the C–H bond activation observed for the indenyl complex.

The Ln3+ and Ln2+ 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 Ln2+ 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 n5d1 electron configuration is appropriate not only for the nine recently discovered Ln2+ ions in 2 but also for Dy2+ and Nd2+, which traditionally have 4f n+1 electron configurations like Eu2+, Yb2+, Sm2+, and Tm2+. 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.

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 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.

Isostructural vanadium, niobium and tantalum complexes of bis(3,5-di-tert-butyl-2-phenol)amine ([ONO]H3), were prepared and characterized to evaluate the impact of the metal ion on redox-activity of the ligand platform. New vanadium and niobium complexes with the general formula, [ONO]MCl2L (M = V, L = THF, 1-V; M = Nb, L = Et2O, 1-Nb) were prepared and structurally analysed by X-ray crystallography. The solid-state structures indicate that the niobium derivative is electronically analogous to the tantalum analog 1-Ta, containing a reduced (ONO) ligand and a niobium(V) metal ion, [ONOcat]NbVCl2(OEt2); whereas, the vanadium derivative is best described as a vanadium(IV) complex, [ONOsq]VIVCl2(THF). One-electron oxidation was carried out on all three metal complexes to afford [ONO]MCl3 derivatives (3-V, 3-Nb, 3-Ta). For all three derivatives, oxidation occurs at the (ONO) ligand. In the cases of niobium and tantalum, electronically similar complexes characterized as [ONOsq]MVCl3 were obtained and for vanadium, ligand-based oxidation led to the formation of a complex best described as [ONOq]VIVCl3. All complexes were characterized by spectroscopic and electrochemical methods. DFT and TD-DFT calculations were used to probe the electronic structure of the complexes and help verify the different electronic structures stemming from changes to the coordinated metal ion.

Recent experiments and calculations have established the transition from two-dimensional (2D) to three-dimensional (3D) structures at a cluster size of 8 and 12 atoms for gold cluster cations and anions. For neutral gold clusters, however, experimental data are scarce, and existing theoretical studies disagree on the 2D–3D crossover point. We present the results of global structure optimizations of neutral gold clusters Aun for n = 9–13 using a genetic algorithm and meta-generalized density functional theory. The relative energies of the lowest-lying isomers are computed using the revTPSS functional and the random phase approximation (RPA). Thermal, scalar relativistic, and spin–orbit effects are included, and basis set extrapolations are performed for the RPA calculations. For the 2D–3D transition of gold cluster cations and anions, this methodology yields near-quantitative agreement with cross section and electron diffraction measurements. For neutral gold clusters, the 2D and 3D structures are predicted to be almost isoenergetic at n = 11 gold atoms, while clusters with n > 11 are manifestly 3D. Thus, neutral gold clusters turn 3D at an unusually large size of 11 gold atoms.

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 U2+ complex. To ensure that this was not the U3+ 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 U2+ complex and was confirmed to be a different compound. Density functional theory calculations indicate a 5f36d1 quintet ground state for the [Cp′3U]− anion and match the observed strong transitions in its optical spectrum.

The first examples of crystallographically characterizable complexes of Tb2+, Pr2+, Gd2+, and Lu2+ have been isolated, which demonstrate that Ln2+ ions are accessible in soluble molecules for all of the lanthanides except radioactive promethium. The first molecular Tb2+ 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 Y2+, Ho2+, and Er2+ complexes, the second complex shows an isomeric structural form of these Ln2+ complexes, and the third complex shows that [(18-crown-6)K]1+ alone is not the only cation that will stabilize these reactive Ln2+ 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 Tb2+ was produced as well as more stable Y2+, Ho2+, and Er2+ analogs: [K(2.2.2-cryptand)][Cp′3Ln]. Exploration of this 2.2.2-cryptand-based reaction with the remaining lanthanides for which Ln2+ had not been observed in molecular species provided crystalline Pr2+, Gd2+, and Lu2+ complexes. These Ln2+ 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 Ln3+ precursors, Cp′3Ln. These data, as well as density functional theory calculations and EPR spectra, suggest that a 4fn5d1 description of the electron configuration in these Ln2+ ions is more appropriate than 4fn+1.

Adiabatic nuclear potential energy surfaces (PESs) defined via the Born–Oppenheimer (BO) approximation are a fundamental concept underlying chemical reactivity theory. For a wide range of excited-state phenomena such as radiationless decay, energy and charge transfer, and photochemical reactions, the BO approximation breaks down due to strong couplings between two or more BO PESs. Non-adiabatic molecular dynamics (NAMD) is the method of choice to model these processes. We review new developments in quantum–classical dynamics, analytical derivative methods, and time-dependent density functional theory (TDDFT) which have lead to a dramatic expansion of the scope of ab initio NAMD simulations for molecular systems in recent years. We focus on atom-centered Gaussian basis sets allowing highly efficient simulations for molecules and clusters, especially in conjunction with hybrid density functionals. Using analytical derivative techniques, forces and derivative couplings can be obtained with machine precision in a given basis set, which is crucial for accurate and stable dynamics. We illustrate the performance of surface-hopping TDDFT for photochemical reactions of the lowest singlet excited states of cyclohexadiene, several vitamin D derivatives, and a bicyclic cyclobutene. With few exceptions, the calculated quantum yields and excited state lifetimes agree qualitatively with experiment. For systems with ∼50 atoms, the present TURBOMOLE implementation allows NAMD simulations with 0.2–0.4 ns total simulation time using hybrid density functionals and polarized double zeta valence basis sets on medium-size compute clusters. We close by discussing open problems and future directions.

(C5Me4H)3U, 1, reacts with 1 equiv of NO to form the first f element nitrosyl complex (C5Me4H)3UNO, 2. X-ray crystallography revealed a 180° U–N–O bond angle, typical for (NO)1+ complexes. However, 2 has a 1.231(5) Å N═O distance in the range for (NO)1– complexes and a short 2.013(4) Å U–N bond like the U═N bond of uranium imido complexes. Structural, spectroscopic, and magnetic data as well as DFT calculations suggest that reduction of NO by U3+ has occurred to form a U4+ complex of (NO)1– that has π interactions between uranium 5f orbitals and NO π* orbitals. These bonding interactions account for the linear geometry and short U–N bond. The complex displays temperature-independent paramagnetism with a magnetic moment of 1.36 μB at room temperature. Complex 2 reacts with Al2Me6 to form the adduct (C5Me4H)3UNO(AlMe3), 3.

We compile a 109-membered benchmark set of adiabatic excitation energies (AEEs) from high-resolution gas-phase experiments. Our data set includes a variety of organic chromophores with up to 46 atoms, radicals, and inorganic transition metal compounds. Many of the 91 molecules in our set are relevant to atmospheric chemistry, photovoltaics, photochemistry, and biology. The set samples valence, Rydberg, and ionic states of various spin multiplicities. As opposed to vertical excitation energies, AEEs are rigorously defined by energy differences of vibronic states, directly observable, and insensitive to errors in equilibrium structures. We supply optimized ground state and excited state structures, which allows fast and convenient evaluation of AEEs with two single-point energy calculations per system. We apply our benchmark set to assess the performance of time-dependent density functional theory using common semilocal functionals and the configuration interaction singles method. Hybrid functionals such as B3LYP and PBE0 yield the best results, with mean absolute errors around 0.3 eV. We also investigate basis set convergence and correlations between different methods and between the magnitude of the excited state relaxation energy and the AEE error. A smaller, 15-membered subset of AEEs is introduced and used to assess the correlated wave function methods CC2 and ADC(2). These methods improve upon hybrid TDDFT for systems with single-reference ground states but perform less well for radicals and small-gap transition metal compounds. None of the investigated methods reaches “chemical accuracy” of 0.05 eV in AEEs.

We investigate the photodynamics of vitamin D derivatives by a fully analytical implementation of the linear response time-dependent density functional theory surface hopping method (LR-TDDFT-SH). Our study elucidates the dynamics of the processes involved in vitamin D formation at the molecular level and with femtosecond resolution. We explain the major experimental findings and provide new insights that cannot directly be obtained from experiments: firstly, we investigate the dynamics of the photoinduced ring-opening of provitamin D (Pro) and cyclohexadiene (CHD) and the subsequent rotational isomerization. In agreement with recent experiments and CC2 calculations, only the bright S1 state is involved in the ring-opening reaction. Our calculations confirm the experimentally reported 5:1 ratio between the excited state lifetimes of Pro and CHD. The longer lifetimes of Pro are attributed to steric constraints of the steroid skeleton and to temperature effects, both emerging directly from our simulations. For CHD and Pro, we present an explanation of the biexponential decay recently reported by Sension and coworkers [Tang et al., J. Phys. Chem., 2011, 134, 104503]: our calculations suggest that the fast and slow components arise from a reactive and an unreactive reaction pathway, respectively. Secondly, we assess the wavelength dependent photochemistry of previtamin D (Pre). Using replica exchange molecular dynamics we sample the Pre conformers present at thermal equilibrium. Based on this ensemble we explain the conformation dependent absorption and the essential features of Pre photochemistry. Consistent with the experiments, we find ring-closure to occur mostly after excitation of the cZc conformers and at lower energies, whereas Z/Eisomerization of the central double bond preferably occurs after excitation at higher energies. For the isomerization we provide the first theoretical evidence of the proposed hula-twist mechanism. Our results show that LR-TDDFT-SH is a highly valuable tool for studying the photochemistry of moderately large systems, even though challenges remain in the vicinity of conical intersections.

In the present work, the validity of the helicity rule relating the absolute configuration of the bridgehead carbon atom in bicyclic β-lactams to the sign of the 220 nm band observed in their electronic circular dichroism (ECD) spectra is examined for ring-expanded cephalosporin analogues. To this end, a series of model compounds with a seven-membered ring condensed with the β-lactam unit was synthesized. A key step of their synthesis was either the ring-closing metathesis (RCM) or the free radical cyclization leading to the seven-membered ring with an S, O, or C atom at the 6 position in the bicyclic skeleton. To investigate the scope and limitations of the simple, empirically established helicity rule, a combination of ECD spectroscopy, variable-temperature ECD measurements, X-ray analysis, and time-dependent density functional theory (TD-DFT) calculations was used. A comparison of the experimental ECD spectra with the spectra simulated by TD-DFT calculations gives a reasonable interpretation of the Cotton effects observed in the 240−215 nm spectral range. The results suggest that the helicity rule does not apply to the investigated compounds because of the planarity of their amide chromophore. Thus, these compounds do not constitute an exception to the rule that was established for bi- and polycyclic β-lactams with the nonplanar amide chromophore only.

The failure of semilocal density functional theory for medium- and long-range noncovalent molecular interactions is a long-standing challenge for computational chemistry. Here, we assess the performance of the random phase approximation (RPA), a parameter-free fifth-rung functional, for reaction energies governed by changes in medium- and long-range noncovalent interactions. Our benchmark data include relative energies of alkane isomers, two sets of isomerization reactions testing intramolecular dispersion, a set of dimers of biological importance, a hierarchy of n-homodesmotic reactions, and the predissociation of a ruthenium-based Grubbs catalyst with bulky ligands. The RPA results are an order of magnitude more accurate than those of popular semilocal functionals such as PBE or B3LYP and more systematic than those of semiempirical functionals parametrized for weak interactions, such as B2PLYP-D or M06-2X. In conclusion, RPA is highly promising for thermochemical applications, particularly if noncovalent interactions are important.Keywords: density functional theory; dispersion interactions; electron correlation; electronic structure theory; isodesmic reactions; medium-range interactions; random phase approximation; thermochemistry; van der Waals interactions;

We investigate the S1 state potential energy surface of 2-pyridone dimer (2PY)2 using time-dependent density functional and coupled cluster theory. Although the ground and S2 excited states of (2PY)2 have C2h symmetry, the S1 state shows symmetry breaking and localization of the excitation on one of the two monomers upon relaxation of the geometry. This localization is rationalized using a simple diabatic curve crossing model. As a consequence of the symmetry breaking, S1 to S0 transitions become optically allowed. We hypothesize that the band at 30 776 cm−1 observed in the excitation spectrum of (2PY)2 might be attributed to the S1 state rather than the S2 state; the S2 state origin is predicted 3000−4000 cm−1 above the S1 state by hybrid density functional and coupled cluster methods. Asymmetric transfer of one hydrogen atom leads to a second S1 state minimum that can rapidly decay to the ground state. This suggests that photoinduced tautomerization of (2PY)2 occurs in a stepwise fashion, with only one hydrogen transfer taking place on the S1 surface.

The Davydov or exciton splitting of vertical excitation energies is commonly used to estimate the excitation energy transfer rate between chromophores. Here we investigate the S1−S2 Davydov splitting in 2-pyridone dimer as a function of the monomer separation, R. We assess the ability of various functionals to reproduce the Davydov splitting at finite R predicted by the approximate coupled cluster singles doubles method CC2. While semilocal functionals fail qualitatively because of spurious charge-transfer intruder states, global hybrids with a large fraction of exact exchange, such as BHandH-LYP, reproduce the CC2 splittings within few wavenumbers. We analyze our results by comparison to lowest-order intermolecular perturbation theory in the spirit of Förster and Dexter. At equilibrium hydrogen bond distance, the Förster−Dexter splittings are too small by up to a factor of 2.

[2.2]Paracyclophanes with chiral ketimine side chains constitute a class of highly versatile and enantioselective ligands for catalytic carbon−carbon bond forming reactions. Proper matching of the side chain and [2.2]paracyclophane configurations induces chiral cooperativity, which is key to high selectivities. Here we show that the absolute configuration of both chirotropic elements may be fully resolved by CD spectroscopy and time-dependent density functional calculations. Different ketimine side chain conformations of the diastereomers perturb the planar chiral [2.2]paracyclophane chromophore. This leads to characteristic changes in the measured CD spectra and the specific rotation allowing for the simultaneous assignment of the absolute configuration of both chiral elements. Our results give rise to a simple rule relating sign and magnitude of the specific rotation and the first band of the CD spectra to the absolute configuration of both chiral elements. We infer a tautomeric equilibrium between an ortho-hydroquinone-imine and an ortho-quinone-enamine from strong solvatochromism observed in the CD spectra.

We present the first unconstrained nonadiabatic molecular dynamics (NAMD) simulations of photocatalytic water oxidation by small hydrated TiO2 nanoparticles using Tully surface hopping and time-dependent density functional theory. The results indicate that ultrafast electron–proton transfer from physisorbed water to the photohole initiates the photo-oxidation on the S1 potential energy surface. The new mechanism readily explains the observation of mobile hydroxyl radicals in recent experiments. Two key driving forces for the photo-oxidation reaction are identified: localization of the electron–hole pair and stabilization of the photohole by hydrogen bonding interaction. Our findings illustrate the scope of recent advances in NAMD methods and emphasize the importance of explicit simulation of electronic excitations.

Reduction of the Th3+ complex Cp′′3Th, 1 [Cp′′ = C5H3(SiMe3)2], with potassium graphite in THF in the presence of 2.2.2-cryptand generates [K(2.2.2-cryptand)][Cp′′3Th], 2, a complex containing thorium in the formal +2 oxidation state. Reaction of 1 with KC8 in the presence of 18-crown-6 generates the analogous Th2+ compound, [K(18-crown-6)(THF)2][Cp′′3Th], 3. Complexes 2 and 3 form dark green solutions in THF with ε = 23000 M−1 cm−1, but crystallize as dichroic dark blue/red crystals. X-ray crystallography revealed that the anions in 2 and 3 have trigonal planar coordination geometries, with 2.521 and 2.525 Å Th–(Cp′′ ring centroid) distances, respectively, equivalent to the 2.520 Å distance measured in 1. Density functional theory analysis of (Cp′′3Th)1− is consistent with a 6d2 ground state, the first example of this transition metal electron configuration. Complex 3 reacts as a two-electron reductant with cyclooctatetraene to make Cp′′2Th(C8H8), 4, and [K(18-crown-6)]Cp′′.

A new option for stabilizing unusual Ln2+ ions has been identified in the reaction of Cp′3Ln, 1-Ln (Ln = La, Ce; Cp′ = C5H4SiMe3), with potassium graphite (KC8) in benzene in the presence of 2.2.2-cryptand. This generates [K(2.2.2-cryptand)]2[(Cp′2Ln)2(μ-η6:η6-C6H6)], 2-Ln, complexes that contain La and Ce in the formal +2 oxidation state. These complexes expand the range of coordination environments known for these ions beyond the previously established examples, (Cp′′3Ln)1− and (Cp′3Ln)1− (Cp′′ = C5H3(SiMe3)2-1,3), and generalize the viability of using three anionic carbocyclic rings to stabilize highly reactive Ln2+ ions. In 2-Ln, a non-planar bridging (C6H6)2− ligand shared between two metals takes the place of a cyclopentadienyl ligand in (Cp′3Ln)1−. The intensely colored (ε = ∼8000 M−1 cm−1) 2-Ln complexes react as four electron reductants with two equiv. of naphthalene to produce two equiv. of the reduced naphthalenide complex, [K(2.2.2-cryptand)][Cp′2Ln(η4-C10H8)].

Isostructural vanadium, niobium and tantalum complexes of bis(3,5-di-tert-butyl-2-phenol)amine ([ONO]H3), were prepared and characterized to evaluate the impact of the metal ion on redox-activity of the ligand platform. New vanadium and niobium complexes with the general formula, [ONO]MCl2L (M = V, L = THF, 1-V; M = Nb, L = Et2O, 1-Nb) were prepared and structurally analysed by X-ray crystallography. The solid-state structures indicate that the niobium derivative is electronically analogous to the tantalum analog 1-Ta, containing a reduced (ONO) ligand and a niobium(V) metal ion, [ONOcat]NbVCl2(OEt2); whereas, the vanadium derivative is best described as a vanadium(IV) complex, [ONOsq]VIVCl2(THF). One-electron oxidation was carried out on all three metal complexes to afford [ONO]MCl3 derivatives (3-V, 3-Nb, 3-Ta). For all three derivatives, oxidation occurs at the (ONO) ligand. In the cases of niobium and tantalum, electronically similar complexes characterized as [ONOsq]MVCl3 were obtained and for vanadium, ligand-based oxidation led to the formation of a complex best described as [ONOq]VIVCl3. All complexes were characterized by spectroscopic and electrochemical methods. DFT and TD-DFT calculations were used to probe the electronic structure of the complexes and help verify the different electronic structures stemming from changes to the coordinated metal ion.

Adiabatic nuclear potential energy surfaces (PESs) defined via the Born–Oppenheimer (BO) approximation are a fundamental concept underlying chemical reactivity theory. For a wide range of excited-state phenomena such as radiationless decay, energy and charge transfer, and photochemical reactions, the BO approximation breaks down due to strong couplings between two or more BO PESs. Non-adiabatic molecular dynamics (NAMD) is the method of choice to model these processes. We review new developments in quantum–classical dynamics, analytical derivative methods, and time-dependent density functional theory (TDDFT) which have lead to a dramatic expansion of the scope of ab initio NAMD simulations for molecular systems in recent years. We focus on atom-centered Gaussian basis sets allowing highly efficient simulations for molecules and clusters, especially in conjunction with hybrid density functionals. Using analytical derivative techniques, forces and derivative couplings can be obtained with machine precision in a given basis set, which is crucial for accurate and stable dynamics. We illustrate the performance of surface-hopping TDDFT for photochemical reactions of the lowest singlet excited states of cyclohexadiene, several vitamin D derivatives, and a bicyclic cyclobutene. With few exceptions, the calculated quantum yields and excited state lifetimes agree qualitatively with experiment. For systems with ∼50 atoms, the present TURBOMOLE implementation allows NAMD simulations with 0.2–0.4 ns total simulation time using hybrid density functionals and polarized double zeta valence basis sets on medium-size compute clusters. We close by discussing open problems and future directions.

We investigate the photodynamics of vitamin D derivatives by a fully analytical implementation of the linear response time-dependent density functional theory surface hopping method (LR-TDDFT-SH). Our study elucidates the dynamics of the processes involved in vitamin D formation at the molecular level and with femtosecond resolution. We explain the major experimental findings and provide new insights that cannot directly be obtained from experiments: firstly, we investigate the dynamics of the photoinduced ring-opening of provitamin D (Pro) and cyclohexadiene (CHD) and the subsequent rotational isomerization. In agreement with recent experiments and CC2 calculations, only the bright S1 state is involved in the ring-opening reaction. Our calculations confirm the experimentally reported 5:1 ratio between the excited state lifetimes of Pro and CHD. The longer lifetimes of Pro are attributed to steric constraints of the steroid skeleton and to temperature effects, both emerging directly from our simulations. For CHD and Pro, we present an explanation of the biexponential decay recently reported by Sension and coworkers [Tang et al., J. Phys. Chem., 2011, 134, 104503]: our calculations suggest that the fast and slow components arise from a reactive and an unreactive reaction pathway, respectively. Secondly, we assess the wavelength dependent photochemistry of previtamin D (Pre). Using replica exchange molecular dynamics we sample the Pre conformers present at thermal equilibrium. Based on this ensemble we explain the conformation dependent absorption and the essential features of Pre photochemistry. Consistent with the experiments, we find ring-closure to occur mostly after excitation of the cZc conformers and at lower energies, whereas Z/Eisomerization of the central double bond preferably occurs after excitation at higher energies. For the isomerization we provide the first theoretical evidence of the proposed hula-twist mechanism. Our results show that LR-TDDFT-SH is a highly valuable tool for studying the photochemistry of moderately large systems, even though challenges remain in the vicinity of conical intersections.