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The sterically bulky aryloxide ligand OAr* (OAr* =

We present the design and implementation of libkrylov, an open-source library for solving matrix-free eigenvalue, linear, and shifted linear equations using Krylov subspace methods. The primary objectives of libkrylov are flexible API design and modular structure, which enables integration with specialized matrix--vector evaluation ``engines''. Libkrylov features pluggable preconditioning, orthonormalization, and tunable convergence control. Diagonal (conjugate gradient, CG), Davidson, and Jacobi--Davidson preconditioners are available, along with orthonormal and nonorthonormal (nKs) schemes. All functionality of libkrylov is exposed via Fortran and C application programming interfaces (APIs). We illustrate the performance of libkrylov for eigenvalue calculations arising in the time-dependent density functional theory (TDDFT) in the Tamm--Dancoff approximation (TDA) and discuss the convergence behavior as a function of preconditioning and orthonormalization methods.

To determine if a C5Me5 complex of Y(II) could be isolated and to examine the synthetic accessibility of heteroleptic Y(II) complexes, the reduction of (C5Me5)2YIII(NR2) (R = SiMe3) with potassium ...

Density functional theory (DFT) calculations on four known and seven hypothetical U(II) complexes indicate the importance of coordination geometry in favoring 5f36d1 versus 5f4 electronic ground states. The known [Cp″3U]-, [Cptet3U]-, and [U(NR2)3]- [Cp″ = C5H3(SiMe3)2, Cptet = C5Me4H, and R = SiMe3] anions were found to have 5f36d1 ground states, while a 5f4 ground state was found for the known compound (NHAriPr6)2U. The UV-visible spectra of the known 5f36d1 compounds were simulated via time-dependent DFT and are in qualitative agreement with the experimental spectra. For the hypothetical U(II) compounds, the 5f36d1 configuration is predicted for [U(CHR2)3]-, [U(H3BH)3]-, [U(OAr')4]2-, and [(C8H8)U]2- (OAr' = O-C6H2tBu2-2,6-Me-4). In the case of [U(bnz')4]2- (bnz' = CH2-C6H4tBu-4), a 5f3 configuration with a ligand-based radical was found as the ground state.

The capacity of X-ray photoelectron spectroscopy (XPS) to provide information on the electronic structure of molecular organometallic complexes of Ln(II) ions (Ln = lanthanide) has been examined for the first time. XPS spectra were obtained on the air-sensitive molecular trivalent 4fn Cp'3LnIII complexes (Ln = Sm, Eu, Gd, Tb; Cp' = C5H4SiMe3) and compared to those of the highly reactive divalent complexes, [K(crypt)][Cp'3LnII] (crypt = 2.2.2-cryptand), which have either 4fn+1 (Sm, Eu) or 4fn5d1 electron configurations (Gd, Tb). The Ln 4d, Si 2p, and C 1s regions of the Ln(III) and Ln(II) complexes were identified and compared. The metal 4d peaks of these molecular lanthanide complexes were used diagnostically to compare oxidation states. The valence region of the Gd(III) and Gd(II) complexes was also examined with XPS and density function theory/random phase approximation (DFT/RPA) calculations, and this led to the tentative assignment of a signal from the 5d1 electron consistent with a 4f75d1 electron configuration for Gd(II).

An analytical implementation of static dipole polarizabilities within the generalized Kohn–Sham semicanonical projected random phase approximation (GKS-spRPA) method for spin-restricted closed-shell and spin-unrestricted open-shell references is presented. General second-order analytical derivatives of the GKS-spRPA energy functional are derived using a Lagrangian approach. By resolution-of-the-identity and complex frequency integration methods, an asymptotic [Formula: see text] scaling of operation count and [Formula: see text] scaling of storage is realized, i.e., the computational requirements are comparable to those for GKS-spRPA ground state energies. GKS-spRPA polarizabilities are assessed for small molecules, conjugated long-chain hydrocarbons, metallocenes, and metal clusters, by comparison against Hartree–Fock (HF), semilocal density functional approximations (DFAs), second-order Møller–Plesset perturbation theory, range-separated hybrids, and experimental data. For conjugated polydiacetylene and polybutatriene oligomers, GKS-spRPA effectively addresses the “overpolarization” problem of semilocal DFAs and the somewhat erratic behavior of post-PBE RPA polarizabilities without empirical adjustments. The ensemble averaged GKS-spRPA polarizabilities of sodium clusters (Na n for n = 2, 3, …, 10) exhibit a mean absolute deviation comparable to PBE with significantly fewer outliers than HF. In conclusion, analytical second-order derivatives of GKS-spRPA energies provide a computationally viable and consistent approach to molecular polarizabilities, including systems prohibitive for other methods due to their size and/or electronic structure.

The utility of γ irradiation for generating unstable, low oxidation state molecular species containing rare-earth metal ions in frozen solution has been examined. The method was evaluated by irradiating Ln(III) precursors (Ln = Sc, Y, and La) in a solid matrix of 2-methyltetrahydrofuran at 77 K with a 700 keV

It has been known for more than a decade that the gauge variance of the kinetic energy density τ leads to additional terms in the magnetic orbital rotation Hessian used in linear-response time-dependent density functional theory (TDDFT), affecting excitation energies obtained with τ-dependent exchange–correlation functionals. While previous investigations found that a correction scheme based on the paramagnetic current density has a small effect on benchmark results, we report more pronounced effects here, in particular, for the popular M06-2X functional and for some other meta-generalized gradient approximations (mGGAs). In the first part of this communication, this is shown by a reassessment of a set of five Ni(II) complexes for which a previous benchmark study that did not impose gauge invariance has found surprisingly large errors for excitation energies obtained with M06-2X. These errors are more than halved by restoring gauge invariance. The variable importance of imposing gauge invariance for different mGGA-based functionals can be rationalized by the derivative of the mGGA exchange energy integrand with respect to τ. In the second part, a large set of valence excitations in small main-group molecules is analyzed. For M06-2X, several selected n → π* and [Formula: see text] excitations are heavily gauge-dependent with average changes of −0.17 and −0.28 eV, respectively, while [Formula: see text] excitations are marginally affected (−0.04 eV). Similar patterns, but of the opposite signs, are found for SCAN0. The results suggest that reevaluation of previous gauge variant TDDFT results based on M06-2X and other mGGA functionals is warranted.

We report the synthesis and characterization of the trinuclear 4d-4f compounds [Co(C5Me5)2][(C5Me5)2Ln(μ-S)2Mo(μ-S)2Ln(C5Me5)2], 1-Ln (Ln = Y, Gd, Tb, Dy), containing the highly polarizable MoS43- bridging unit. UV-Vis-NIR diffuse reflectance spectra and DFT calculations of 1-Ln reveal a low-energy metal-to-metal charge transfer transition assigned to charge transfer from the singly occupied 4dz2 orbital of MoV to the empty 5d orbitals of the lanthanides (4d in the case of 1-Y), mediated by sulfur-based 3p orbitals. Electron paramagnetic resonance spectra collected for 1-Y in a tetrahydrofuran solution show large 89Y hyperfine coupling constants of A⊥ = 23 MHz and A|| = 26 MHz, indicating the presence of significant yttrium-localized unpaired electron density. Magnetic susceptibility data support similar electron delocalization and ferromagnetic Ln-Mo exchange for 1-Gd, 1-Tb, and 1-Dy. This ferromagnetic exchange gives rise to an S = 15/2 ground state for 1-Gd and one of the largest magnetic exchange constants involving GdIII observed to date, with JGd-Mo = +16.1(2) cm-1. Additional characterization of 1-Tb and 1-Dy by ac magnetic susceptibility measurements reveals that both compounds exhibit slow magnetic relaxation. Although a Raman magnetic relaxation process is dominant for both 1-Tb and 1-Dy, an extracted thermal relaxation barrier of Ueff = 68 cm-1 for 1-Dy is the largest yet reported for a complex containing a paramagnetic 4d metal center. Together, these results provide a potentially generalizable route to enhanced nd-4f magnetic exchange, revealing opportunities for the design of new nd-4f single-molecule magnets and bulk magnetic materials.

Oxaloacetic acid (OAA) is a 3-oxocarboxylic acid formed from the oxidation of succinic acid. OAA and other 3-oxocarboxylic acids experience a decarboxylation reaction in aqueous solutions, which ca...

The allyl complexes (C5Me5)2Ln(η3-C3H5) (Ln = Y, Dy, Tb) react with benzoxazole, C7H5NO, by deprotonation and ring-opening to yield dark red complexes identified by X-ray crystallography as the 2-i...

Reduction of (C5Me5)2UIII(NR2) and (C5Me5)UIII(NR2)2 (R = SiMe3) with potassium graphite in the presence of 2.2.2-cryptand (crypt) generates dark solutions that have UV–visible spectra consistent w...

Lanthanide triflates have been used to incorporate NdIII and SmIII ions into the 2.2.2-cryptand ligand (crypt) to explore their reductive chemistry. The Ln(OTf)3 complexes (Ln=Nd, Sm; OTf=SO3 CF3 ) react with crypt in THF to form the THF-soluble complexes [LnIII (crypt)(OTf)2 ][OTf] with two triflates bound to the metal encapsulated in the crypt. Reduction of these LnIII -in-crypt complexes using KC8 in THF forms the neutral LnII -in-crypt triflate complexes [LnII (crypt)(OTf)2 ]. DFT calculations on [NdII (crypt)]2+ ], the first NdII cryptand complex, assign a 4f4 electron configuration to this ion.

Lanthanide-based dinitrogen reduction chemistry has been expanded by the discovery of the first end-on Ln2(μ-η1:η1-N2) complexes, whose synthesis and reactivity help explain the reduction of N2 by ...

Heteroleptic U(III) complexes supported by bis(cyclopentadienyl) frameworks have been synthesized to examine their suitability as precursors to U(II) complexes. The newly synthesized (C

The THF-soluble [An(crypt)(OTf)2][OTf] complexes for An = Np and Pu were synthesized from AnI3(THF)4 starting materials based on pilot studies of the An = U system. 5f3 U(iii), 5f4 Np(iii), and 5f5 Pu(iii) electron configurations are indicated by DFT analysis of their UV-visible-NIR spectra.

Density functional theory (DFT) calculations on four known and seven hypothetical U(II) complexes indicate the importance of coordination geometry in favoring 5f

Prompted by recent reports of large errors in noncovalent interaction (NI) energies obtained from many-body perturbation theory (MBPT), we compare the performance of second-order Møller–Plesset MBPT (MP2), spin-scaled MP2, dispersion-corrected semilocal density functional approximations (DFA), and the post-Kohn–Sham random phase approximation (RPA) for predicting binding energies of supramolecular complexes contained in the S66, L7, and S30L benchmarks. All binding energies are extrapolated to the basis set limit, corrected for basis set superposition errors, and compared to reference results of the domain-based local pair-natural orbital coupled-cluster (DLPNO-CCSD(T)) or better quality. Our results confirm that MP2 severely overestimates binding energies of large complexes, producing relative errors of over 100% for several benchmark compounds. RPA relative errors consistently range between 5-10%, significantly less than reported previously using smaller basis sets, whereas spin-scaled MP2 methods show limitations similar to MP2, albeit less pronounced, and empirically dispersion-corrected DFAs perform almost as well as RPA. Regression analysis reveals a systematic increase of relative MP2 binding energy errors with the system size at a rate of approximately 0.1% per valence electron, whereas the RPA and dispersion-corrected DFA relative errors are virtually independent of the system size. These observations are corroborated by a comparison of computed rotational constants of organic molecules to gas-phase spectroscopy data contained in the ROT34 benchmark. To analyze these results, an asymptotic adiabatic connection symmetry-adapted perturbation theory (AC-SAPT) is developed which uses monomers at full coupling whose ground-state density is constrained to the ground-state density of the complex. Using the fluctuation–dissipation theorem, we obtain a nonperturbative “screened second-order” expression for the dispersion energy in terms of monomer quantities which is exact for non-overlapping subsystems and free of induction terms; a first-order RPA-like approximation to the Hartree, exchange, and correlation kernel recovers the macroscopic Lifshitz limit. The AC-SAPT expansion of the interaction energy is obtained from Taylor expansion of the coupling strength integrand. Explicit expressions for the convergence radius of the AC-SAPT series are derived within RPA and MBPT and numerically evaluated. Whereas the AC-SAPT expansion is always convergent for nondegenerate monomers when RPA is used, it is found to spuriously diverge for second-order MBPT, except for the smallest and least polarizable monomers. The divergence of the AC-SAPT series within MBPT is numerically confirmed within RPA; prior numerical results on the convergence of the SAPT expansion for MBPT methods are revisited and support this conclusion once sufficiently high orders are included. The cause of the failure of MBPT methods for NIs of large systems is missing or incomplete “electrodynamic” screening of the Coulomb interaction due to induced particle–hole pairs between electrons in different monomers, leaving the effective interaction too strong for AC-SAPT to converge. Hence, MBPT cannot be considered reliable for quantitative predictions of NIs, even in moderately polarizable molecules with a few tens of atoms. The failure to accurately account for electrodynamic polarization makes MBPT qualitatively unsuitable for applications such as NIs of nanostructures, macromolecules, and soft materials; more robust non-perturbative approaches such as RPA or coupled cluster methods should be used instead whenever possible.

Local hybrid functionals are a relatively recent class of exchange-correlation functionals that use a real-space dependent admixture of exact exchange. Here, we present the first implementation of time-dependent density functional theory excited-state gradients for these functionals. Based on the ansatz of a fully variational auxiliary Lagrangian of the excitation energy, the working equations for the case of a local hybrid functional are deduced. For the implementation, we derive the third-order functional derivatives used in the hyper-kernel and kernel-gradients following a seminumerical integration scheme. The first assessment for a test set of small molecules reveals competitive performance for excited-state structural parameters with typical mean absolute errors (MAEs) of 1.2 pm (PBE0: 1.4 pm) for bond lengths as well as for vibrational frequencies with typical MAEs of 81 cm-1 (PBE0: 76 cm-1). Excellent performance was found for adiabatic triplet excitation energies with typical MAEs of 0.08 eV (PBE0: 0.32 eV). In a detailed case analysis of the first singlet and triplet excited states of formaldehyde the conceptional (dis-)advantages of the local hybrid scheme for excited-state gradients are exposed.

Reduction of Th(OC6H2tBu2-2,6-Me-4)4 using either KC8 or Li in THF forms a new example of a crystallographically characterizable Th(III) complex in the salts [K(THF)5(Et2O)][Th(OC6H2tBu2-2,6-Me-4)4] and [Li(THF)4][Th(OC6H2tBu2-2,6-Me-4)4]. Surprisingly, in each structure the four aryloxide ligands are arranged in a square-planar geometry, the first example of this coordination mode for an f element complex. The Th(III) ion and four oxygen donor atoms are coplanar to within 0.05 A with O–Th–O angles of 89.27(8) to 92.02(8)° between cis ligands. The ligands have Th–O–C(ipso) angles of 173.9(2) to 178.6(4)°, and the aryl rings make angles of 58.5 to 65.1° with the ThO4 plane. The effect of the eight tert-butyl substituents in generating the unusual structure through packing and/or dispersion forces is discussed. EPR spectroscopy reveals an axial signal consistent with a metal-based radical in a planar complex. DFT calculations yield a C4-symmetric structure that accommodates a low-lying SOMO of 6dz2 characte...

Spins in molecules are particularly attractive targets for next-generation quantum technologies, enabling chemically programmable qubits and potential for scale-up via self-assembly. Here we report the observation of one of the largest hyperfine interactions for a molecular system, A

Spins in molecules are particularly attractive targets for next-generation quantum technologies, enabling chemically programmable qubits and potential for scale-up via self-assembly. Here, we demonstrate chemical control of the degree of s-orbital mixing into the spin-bearing d-orbital associated with a series of spin-½ La(II) and Lu(II) molecules. Increased s-orbital character reduces spin-orbit coupling and enhances the electron-nuclear Fermi contact interaction. Both outcomes are beneficial for quantum applications: the former reduces spin-lattice relaxation, while the latter gives rise to a record molecular hyperfine interaction for Lu(II) that, in turn, generates a massive 9 GHz hyperfine clock transition and an order of magnitude increase in phase memory time. These findings suggest new strategies for development of molecular quantum technologies, akin to trapped ion systems.

Lanthanide triflates have been used to incorporate Nd

Lanthanide-based dinitrogen reduction chemistry has been expanded by the discovery of the first end-on Ln

[Y(N(SiMe3)2)3] reacts with (Ad,MeArOH)3mes to form the Y3+ complex [((Ad,MeArO)3mes)Y], 1-Y. This complex reacts with potassium metal in the presence of 2.2.2-cryptand to give a cocrystallized mixture of [K(2.2.2-cryptand)][((Ad,MeArO)3mes)Y], 2-Y, and [K(2.2.2-cryptand)][((Ad,MeArO)3mes)YH], 3-Y. The electron paramagnetic resonance spectrum of this crystalline mixture exhibits an isotropic signal at 77 K (giso = 2.000, Wiso = 1.8 mT), suggesting that 2-Y is best described as a Y3+ complex of the tris(aryloxide)mesitylene radical ((Ad,MeArO)3mes)4–. Evidence of the hydride ligand in 3-Y was obtained by 89Y–1H heteronuclear multiple quantum coherence NMR spectroscopy, and a coupling constant of JYH = 93 Hz was observed. A single crystal of 3-Y was also obtained in pure form and structurally characterized for comparison with the crystal data on the mixed component 2-Ln/3-Ln crystals. The origin of the hydride in 3-Ln is unknown, but further studies of the reduction of 1-La, previously found to form 2-La, r...

It has been suspected since the early days of the random-phase approximation (RPA) that corrections to RPA correlation energies result mostly from short-range correlation effects and are thus amenable to perturbation theory. Here we test this hypothesis by analyzing formal and numerical results for the most common beyond-RPA perturbative corrections, including the bare second-order exchange (SOX), second-order screened exchange (SOSEX), and approximate exchange kernel (AXK) methods. Our analysis is facilitated by efficient and robust algorithms based on the resolution-of-the-identity (RI) approximation and numerical frequency integration, which enable benchmark beyond-RPA calculations on medium- and large-size molecules with size-independent accuracy. The AXK method systematically improves upon RPA, SOX, and SOSEX for reaction barrier heights, reaction energies, and noncovalent interaction energies of main-group compounds. The improved accuracy of AXK compared with SOX and SOSEX is attributed to stronger screening of bare SOX in AXK. For reactions involving transition-metal compounds, particularly 3d transition-metal dimers, the AXK correction is too small and can even have the wrong sign. These observations are rationalized by a measure α̅ of the effective coupling strength for beyond-RPA correlation. When the effective coupling strength increases beyond a critical α̅ value of approximately 0.5, the RPA errors increase rapidly and perturbative corrections become unreliable. Thus, perturbation theory can systematically correct RPA but only for systems and properties qualitatively well captured by RPA, as indicated by small α̅ values.

A new series of Ln2+ complexes has been synthesized that overturns two previous generalizations in rare-earth metal reduction chemistry: that amide ligands do not form isolable complexes of the highly reducing non-traditional Ln2+ ions, and that yttrium is a good model for the late lanthanides in these reductive reactions. Reduction of Ln(NR2 )3 (R=SiMe3 ) complexes in THF under Ar with M=K or Rb in the presence of 2.2.2-cryptand (crypt) forms crystallographically characterizable [M(crypt)][Ln(NR2 )3 ] complexes not only for the traditional Tm2+ ion and the configurational crossover ions, Nd2+ and Dy2+ , but also for the non-traditional Gd2+ , Tb2+ , Ho2+ , and Er2+ ions. Crystallographic data as well as UV/Vis, magnetic susceptibility, and density functional theory studies are consistent with the accessibility of 4fn 5d1 configurations for Ln2+ ions in this tris(silylamide) ligand environment. The Dy2+ complex, [K(crypt)][Dy(NR2 )3 ], has a higher magnetic moment than previously observed for any monometallic complex: 11.67 μB .

A multivariate adiabatic connection (MAC) framework for describing dispersion interactions in a system consisting of N non-overlapping monomers is presented. By constraining the density to the physical ground-state density of the supersystem, the MAC enables a rigorous separation of induction and dispersion effects. The exact dispersion energy is obtained from the zero-temperature fluctuation–dissipation theorem and partitioned into increments corresponding to the interaction energy gained when an additional monomer is added to a K-monomer system. The total dispersion energy of an N-monomer system is independent of any partitioning into subsystems. This statement of dispersion size consistency is shown to be an exact constraint. The resulting additive separability of the dispersion energy results from multiplicative separability of the generalized screening factor defined as the inverse generalized dielectric function. Many-body perturbation theory (MBPT) is found to violate dispersion size-consistency because perturbative approximations to the generalized screening factor are nonseparable; on the other hand, random phase approximation-type methods produce separable generalized screening factors and therefore preserve dispersion size-consistency. This result further explains the previously observed increase in relative errors of MBPT for dispersion interactions as the system size increases. Implications for electronic structure theory and applications to supramolecular materials and condensed matter are discussed.

The synthesis of 4f n Ln3+ complexes of the tris(aryloxide) mesitylene ligand, ((Ad,MeArO)3mes)3-, with Ln = La, Ce, Pr, Sm, and Yb, and their reduction with potassium have revealed that this ligand system can be redox active with some metals. Protonolysis of [Ln(N(SiMe3)2)3] (Ln = La, Ce, Pr, Sm, Yb) with the tris(phenol) (Ad,MeArOH)3mes yielded the Ln3+ complexes [((Ad,MeArO)3mes)Ln] (Ln = La, Ce, Pr, Sm, Yb), 1-Ln. Single electron reduction of each 4f n complex, 1-Ln, using potassium yielded the reduced products, [K(2.2.2-cryptand)][((Ad,MeArO)3mes)Ln] (Ln = La, Ce, Pr, Sm, Yb), 2-Ln. The Sm and Yb complexes have properties consistent with the presence of Ln2+ ions with traditional 4f n+1 electron configurations. However, the La, Ce, and Pr complexes appear to formally contain Ln3+ ions and ((Ad,MeArO)3mes)4- ligands. Structural comparisons of the [((Ad,MeArO)3mes)Ln] and [((Ad,MeOAr)3mes)Ln]1- complexes along with UV-vis absorption and EPR spectroscopy as well as density functional theory calculations support these ground state assignments.

We report on the efficient turbomole implementation of quadratic response properties within the time-dependent density functional theory (TDDFT) context that includes the static and dynamic dipole hyperpolarizability, ground-to-excited-state two-photon absorption amplitudes (through a single residue) and state-to-state one-photon absorption amplitudes (through a double residue). Our implementation makes full use of arbitrary (including non-Abelian) point-group symmetry as well as permutational symmetry and enables the calculation of nonlinear properties with hybrid density functionals for molecules with hundreds of atoms and thousands of basis functions at a cost that is a fixed multiple of the cost of the corresponding linear properties. Using the PBE0 hybrid density functional, we show that excited-state absorption spectra computed within the pseudowavefunction approach contain the qualitative features of transient absorption spectra tracking excimer formation in perylene diimide dimers, two-photon absorption cross sections for a series of highly twisted fused porphyrin chains are semiquantitatively reproduced, and the computed dynamic hyperpolarizability of several calix[4]arene stereoisomers yield simulated hyper-Raleigh scattering signals consistent with experiment. In addition, we show that the incorrect pole structure of adiabatic TDDFT properties can cause incorrect excited-state absorption spectra and overly resonant hyperpolarizabilities, and discuss possible remedies.

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.

Dense linear systems and eigenvalue problems with extremely large dimensions, i.e., well over a million degrees of freedom or unknowns, underlie many grand challenges in science and engineering, from quantum molecular and materials sciences to fluid dynamics. This project develops, validates, and deploys the general-purpose open-source software library libkrylov for solving these linear systems and eigenvalue problems based solely on vector operations. We will give an overview of the already implemented and planned functionality of libkrylov including the recently developed non-orthonormal Krylov subspace methods, as well as design, data structures, and interfaces. The current implementation uses compile-time polymorphism and user-defined procedure encapsulation to enable high degrees of efficiency, generic coding, and ease of use.

TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy-cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe-Salpeter methods, second-order Møller-Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE's functionality, including excited-state methods, RPA and Green's function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE's current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE's development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted.

Reduction of Cp′3ThCl, Cp′3ThBr, and Cp′3ThI (Cp′ = C5H4SiMe3) with potassium graphite generates dark blue solutions with reactivity and spectroscopic properties consistent with the formation of Cp′3Th. The EPR and UV-visible spectra of the solutions are similar to those of crystallographically-characterized tris(cyclopentadienyl) Th(III) complexes: [C5H3(SiMe3)2]3Th, (C5Me4H)3Th, (C5tBu2H3)3Th, and (C5Me5)3Th. Density functional theory (DFT) analysis indicates that the UV-visible spectrum is consistent with Cp′3Th and not [Cp′3ThBr]1−. Although single crystals of Cp′3Th have not been isolated, the blue solution reacts with Me3SiCl, I2, and HCCPh to afford products expected from Cp′3Th, namely, Cp′3ThCl, Cp′3ThI, and Cp′3Th(CCPh), respectively. Reactions with MeI give mixtures of Cp′3ThI and Cp′3ThMe. Evidence for further reduction of the blue solutions to a Cp′-ligated Th(II) complex has not been observed. The crystal structures of Cp′3ThMe and (Cp′3Th)2(μ-O) were also determined as part of these studies.

We report an efficient analytical implementation of first-order nonadiabatic derivative couplings between arbitrary Born-Oppenheimer states in the hybrid time-dependent density functional theory (TDDFT) framework using atom-centered basis functions. Our scheme is based on quadratic response theory and includes orbital relaxation terms neglected in previous approaches. Simultaneous computation of multiple derivative couplings and energy gradients enables efficient multistate nonadiabatic molecular dynamics simulations in conjunction with Tully's fewest switches surface hopping (SH) method. We benchmark the thus obtained multistate TDDFT-SH scheme by simulating ultrafast decay of UV-photoexcited thymine, for which accurate gas-phase data from ultrafast spectroscopy experiments are available. The calculations predict a fast 153 fs decay from the bright S2 to the dark S1 excited state, followed by a much slower 14 ps S1 deactivation to the ground state; statistical uncertainties were estimated using bootstrap sampling. These results agree well with the experimentally observed time constants of 100-200 fs and 5-7 ps, respectively, unlike previous multiconfigurational self-consistent field and second-order algebraic diagrammatic construction calculations. Furthermore, our results support the S1-trapping hypothesis [J. J. Szymczak et al., J. Phys. Chem. A, 2009, 113, 12686-12693]. For thymine, the computational cost of a single TDDFT-SH time-step including the lowest 3 states, all couplings and gradients, is ∼5 times larger than the cost of a single Born-Oppenheimer dynamics time step for the ground state in our implementation. Thus, ps nonadiabatic dynamics simulations using multistate hybrid TDDFT-SH for systems with up to ∼100 atoms are possible without drastic approximations on single workstation nodes. Our implementation will be made available through Turbomole.

The existence of divalent bis(pentaisopropylcyclopentadienyl) actinocene compounds, An(CpiPr5)2 for An = (Th, U, Pu, Am, Bk, No, Lr), is assessed by density functional theory (DFT) calculations with scalar-relativistic small core pseudopotentials. The calculations predict ground states with significant 6d occupation for Th, U, and Lr, whereas Am, Bk, and No exhibit 5f ground states. A mixed ground state with predominant 5f character is found for Pu. The complexes exhibit a linear coordination geometry and high S10 symmetry except for Pu(CpiPr5)2 and Am(CpiPr5)2, which are found to be bent by 11 and 12 degrees , respectively. Absorption spectra are simulated with time-dependent density functional theory (TD-DFT) and compared to experimental spectra of known tris(C4H4SiMe3) and tris(C5H3(SiMe3)2) compounds [M. E. Fieser et al., J. Am. Chem. Soc. 2015, 137, 369-382] as well as recently synthesized divalent lanthanide analogs Dy(CpiPr5)2 and Tb(CpiPr5)2 [C. Gould et al., J. Am. Chem. Soc. 2019, accepted]. Thermodynamic stability is assessed by calculation of adiabatic reduction potentials of the trivalent precursors [An(CpiPr5 )2] +, and the feasibility of further reduction to obtain as yet unknown monovalent molecular actinide complexes is discussed.

The existence of divalent bis(pentaisopropylcyclopentadienyl) actinocene compounds, An(CpiPr5)2 for An = (Th, U, Pu, Am, Bk, No, Lr), is assessed by density functional theory (DFT) calculations with scalar-relativistic small core pseudopotentials. The calculations predict ground states with significant 6d occupation for Th, U, and Lr, whereas Am, Bk, and No exhibit 5f ground states. A mixed ground state with predominant 5f character is found for Pu. The complexes exhibit a linear coordination geometry and high S10 symmetry except for Pu(CpiPr5)2 and Am(CpiPr5)2, which are found to be bent by 11 and 12 degrees , respectively. Absorption spectra are simulated with time-dependent density functional theory (TD-DFT) and compared to experimental spectra of known tris(C4H4SiMe3) and tris(C5H3(SiMe3)2) compounds [M. E. Fieser et al., J. Am. Chem. Soc. 2015, 137, 369-382] as well as recently synthesized divalent lanthanide analogs Dy(CpiPr5)2 and Tb(CpiPr5)2 [C. Gould et al., J. Am. Chem. Soc. 2019, accepted]. Thermodynamic stability is assessed by calculation of adiabatic reduction potentials of the trivalent precursors [An(CpiPr5 )2] +, and the feasibility of further reduction to obtain as yet unknown monovalent molecular actinide complexes is discussed.

The divalent metallocene complexes Ln(CpiPr5)2 (Ln = Tb, Dy) were synthesized through the KC8 reduction of Ln(CpiPr5)2I intermediates and represent the first examples of neutral, linear metallocene...

Optimized and stringent chemical methods to profile nascent RNA expression are still in demand. Herein, we expand the toolkit for metabolic labeling of RNA through application of inverse electron demand Diels-Alder (IEDDA) chemistry. Structural examination of metabolic enzymes guided the design and synthesis of vinyl-modified nucleosides, which we systematically tested for their ability to be installed through cellular machinery. Further, we tested these nucleosides against a panel of tetrazines to identify those which are able to react with a terminal alkene, but are stable enough for selective conjugation. The selected pairings then facilitated RNA functionalization with biotin and fluorophores. We found that this chemistry not only is amenable to preserving RNA integrity but also endows the ability to both tag and image RNA in cells. These key findings represent a significant advancement in methods to profile the nascent transcriptome using chemical approaches.

Reduction of Th(OC

A mechanism explaining the photobasicity of 5-methoxyquinoline (5-MeOQ) is proposed on the basis of nonadiabatic molecular dynamics simulations using time-dependent hybrid density functional theory (TDDFT) and fewest switches surface hopping (SH) and analysis of existing ultrafast spectroscopy experiments. According to the TDDFT- SH simulations, the rate-determining step is hole transfer from photoexcited 5-MeOQ to adjacent water molecules within ∼ 5 ps, followed by rapid electron-coupled pro- ton transfer and deactivation to the ground state. This fast redox-catalyzed proton transfer mechanism is consistent with simple thermodynamic arguments, correlated wavefunction calculations, and recent isotope substitution time-resolved fluorescence experiments. Although energetically feasible, direct protonation of 5-MeOQ in the S1 state appears to be too slow to contribute significantly to 5-MeOQ photobasicity in aqueous solution.

Generalized-Kohn-Sham (GKS) orbital energies obtained self-consistently from the random phase approximation energy functional with a semicanonical projection (spRPA) were recently shown to rival the accuracy of GW quasiparticle energies for valence ionization potentials. Here, we extend the scope of GKS-spRPA correlated one-particle energies from frontier-orbital ionization to core orbital ionization energies, which are notoriously difficult for GW and other response methods due to strong orbital relaxation effects. For a benchmark consisting of 23 1s core electron binding energies (CEBEs) of second-row elements, chemical shifts estimated from GKS-spRPA one-particle energies yield mean absolute deviations from experiment of 0.2 eV, which are significantly more accurate than the standard GW and comparable to Δ self-consistent field theory without semiempirical adjustment of the energy functional. For small ammonia clusters and cytosine tautomers, GKS-spRPA based chemical shifts capture subtle variations in covalent and noncovalent bonding environments; GKS-spRPA 1s CEBEs for these systems agree with equation-of-motion coupled cluster singles and doubles and ADC(4) results within 0.2-0.3 eV. Two perturbative approximations to GKS-spRPA orbital energies, which reduce the scaling from O(N6) to O(N5) and O(N4), are introduced and tested. We illustrate the application of GKS-spRPA orbital energies to larger systems by using oxygen 1s CEBEs to probe solvation and packing effects in condensed phases of water. GKS-spRPA predicts a lowering of the oxygen 1s CEBE of approximately 1.6-1.7 eV in solid and liquid phases, consistent with liquid-jet X-ray photoelectron spectroscopy and gas phase cluster experiments. The results are rationalized by partitioning GKS-spRPA electron binding energies into static, relaxation, and correlation parts.

The interaction of water with polycyclic aromatic hydrocarbons, from benzene to graphene, is investigated using various exchange-correlation functionals selected across generalized gradient approximation (GGA), meta-GGA, and hybrid families within the density functional theory (DFT) hierarchy. The accuracy of the different functionals is assessed through comparisons with high-level electronic structure methods, including random phase approximation (RPA), diffusion Monte Carlo (DMC), and coupled-cluster with single, double, and perturbative triple excitations (CCSD(T)). Relatively large variations are found in the interaction energies predicted by different DFT models, with GGA functionals underestimating the interaction strength for configurations with the water oxygen pointing toward the aromatic molecules, and the meta-GGA B97M-rV and hybrid ωB97M-V functionals providing nearly quantitative agreement with CCSD(T) values available for the water-benzene, water-coronene, and water-circumcoronene dimers, which, in turn, are within ∼1 kcal/mol of the corresponding RPA and DMC results. Similar trends among GGA, meta-GGA, and hybrid functionals are observed for the larger polycyclic aromatic hydrocarbon molecules considered in this analysis (up to C216H36). By performing absolutely localized molecular orbital energy decomposition analyses (ALMO-EDA) of the DFT results, it is found that, independently of the number of carbon atoms and exchange-correlation functional, the dominant contributions to the interaction energies between water and polycyclic aromatic hydrocarbon molecules are the electrostatic and dispersion terms while polarization and charge transfer effects are negligibly small. Calculations carried out with GGA and meta-GGA functionals indicate that, as the number of carbon atoms increases, the interaction energies slowly converge to the corresponding values obtained for an infinite graphene sheet. Importantly, water-graphene interaction energies calculated with the B97M-rV functional appear to deviate by more than 1 kcal/mol from the available RPA and DMC values.

This Perspective reviews recent efforts toward selfconsistent calculations of ground-state energies within the random phase approximation (RPA) in the (generalized) Kohn-Sham (KS) density functional theory context. Since the RPA correlation energy explicitly depends on the non-interacting KS potential, an additional condition to determine the energy as a functional of the density is necessary. This observation leads to the concept of functional selfconsistency (FSC), which requires that the KS density equals the interacting density defined as the functional derivative of the ground-state energy with respect to the external potential. While all existing selfconsistent RPA schemes violate FSC, the recent generalized KS semicanonical projected RPA (GKS-spRPA) method takes a step toward satisfying it. This leads to systematic improvements in densities, binding energy curves, reference state stability, and molecular properties compared to non-selfconsistent RPA as well as optimized effective potential RPA. GKS-spRPA orbital energies accurately approximate valence and core ionization potentials, and even electron affinities of non-valence bound anions. The computational cost and performance of GKS-spRPA are compared to those of related selfconsistent schemes, including GW and orbital optimization methods, and limitations are discussed. Large differences between KS and interacting densities observed in the absence of FSC and the well-rounded performance of GKS-spRPA suggest that the KS potential as a density functional should be defined via the FSC condition for explicitly potential-dependent density functionals.