Efficient two-component self-consistent field procedures and gradients: implementation in TURBOMOLE and application to

Isolation of a planar π-aromatic Bi5- ring in a cobalt-based inverse-sandwich-type complex

Monocyclic π-aromatic compounds are ubiquitous throughout almost all fields of natural sciences-as synthons in industrial processes, as ligands of metal complexes for catalysis or sensing and as bioactive molecules. Planar organocycles stand out through their specific way of overcoming electron deficiency by a non-localizable set of (4n + 2)π electrons. By contrast, all-metal aromatic monocycles are still rare, as metal atoms prefer to form clusters with multiply bonded atoms instead. This limits the knowledge and potential of corresponding compounds in chemical syntheses or for innovative materials. Here we report the successful generation of Bi5-, the heaviest analogue of (C5H5)-. Its use as a ligand in [{IMesCo}2(µ,η5:η5-Bi5)] (1) was realized by reacting (TlBi3)2- with [(IMes)2CoCl] (where IMes is bis(1,3-(2,4,6-trimethylphenyl))imidazol-2-ylidene) in ortho-difluorobenzene. Compound 1 is mixed-valence Co0/CoI as verified by µ-SQUID measurements and density functional theory, and embeds the planar Bi5- cycle in an inverse-sandwich-type manner. Capturing Bi5- represents a landmark in the chemistry of all-metal aromatic molecules and defines a new era for aromatic compounds.

Application of the noncollinear Scalmani-Frisch formalism to current density functional theory

We generalize the noncollinear formalism proposed by Scalmani and Frisch [J. Chem. Theory Comput. 8, 2193 (2012)] to include the particle and spin current densities for meta-generalized gradient approximations and local hybrid functionals. This allows us to fully include the impact of spin-orbit coupling in relativistic calculations and for applications to finite magnetic fields. For the latter, we use London atomic orbitals to ensure gauge origin invariance. It is shown that this formalism is superior to the more common canonical noncollinear approach in relativistic calculations, as it naturally includes all three spin current densities in the closed-shell limit and avoids the projection onto the spin magnetization vector. This is important to easily restore rotational invariance in this limit. In addition, the Scalmani-Frisch approach can be made numerically stable and may lead to a nonvanishing local magnetic torque. However, both formalisms are rotationally invariant for open-shell systems and in finite magnetic fields.

A General and Transferable Local Hybrid Functional for Electronic Structure Theory and Many-Fermion Approaches

Density functional theory has become the workhorse of quantum physics, chemistry, and materials science. Within these fields, a broad range of applications needs to be covered. These applications range from solids to molecular systems, from organic to inorganic chemistry, or even from electrons to other Fermions, such as protons or muons. This is emphasized by the plethora of density functional approximations that have been developed for various cases. In this work, two new local hybrid exchange-correlation density functionals are constructed from first-principles, promoting generality and transferability. We show that constraint satisfaction can be achieved even for admixtures with full exact exchange, without sacrificing accuracy. The performance of the new functionals CHYF-PBE and CHYF-B95 is assessed for thermochemical properties, excitation energies, Mössbauer isomer shifts, NMR spin-spin coupling constants, NMR shieldings and shifts, magnetizabilities, and EPR hyperfine coupling constants. Here, the new density functional shows excellent performance throughout all tests and is numerically robust only requiring small grids for converged results. Additionally, both functionals can easily be generalized to arbitrary Fermions as shown for electron-proton correlation energies. Therefore, we outline that density functionals generated in this way are general purpose tools for quantum mechanical studies.

Uncovering chemical homology of superheavy elements: a close look at astatine

The fascination with superheavy elements (SHE) spans the nuclear physics, astrophysics, and theoretical chemistry communities. Extreme relativistic effects govern these elements' chemistry and challenge the traditional notion of the periodic law. The experimental quest for SHE critically depends on theoretical predictions of these elements' properties, especially chemical homology, which allows for successful prototypical experiments with more readily available lighter homologues of SHE. This work is a comprehensive quantum-chemical investigation into astatine (At) as a non-intuitive homologue of element 113, nihonium (Nh). Combining relativistic coupled-cluster and density functional theory approaches, we model the behaviour of At and AtOH in thermochromatographic experiments on a pristine gold surface. Insights into the electronic structure of AtOH and NhOH and accurate estimates of At-gold and AtOH-gold adsorption energies rationalise recent experimental findings and justify the use of At as a chemical homologue of Nh for the successful design of future experiments on Nh detection and chemical characterisation.

Investigation of Isolated IrF5 -, IrF6 - Anions and M[IrF6] (M=Na, K, Rb, Cs) Ion Pairs by Matrix-Isolation Spectroscopy and Relativistic Quantum-Chemical Calculations

The molecular IrF5 -, IrF6 - anions and M[IrF6] (M=Na, K, Rb, Cs) ion pairs were prepared by co-deposition of laser-ablated alkali metal fluorides MF with IrF6 and isolated in solid neon or argon matrices under cryogenic conditions. The free anions were obtained as well by co-deposition of IrF6 with laser-ablated metals (Ir or Pt) as electron sources. The products were characterized in a combined analysis of matrix IR spectroscopy and electronic structure calculations using two-component quasi-relativistic DFT methods accounting for spin-orbit coupling (SOC) effects as well as multi-reference configuration-interaction (MRCI) approaches with SOC. Inclusion of SOC is crucial in the prediction of spectra and properties of IrF6 - and its alkali-metal ion pairs. The observed IR bands and the computations show that the IrF6 - anion adopts an Oh structure in a nondegenerate ground state stabilized by SOC effects, and not a distorted D4h structure in a triplet ground state as suggested by scalar-relativistic calculations. The corresponding "closed-shell" M[IrF6] ion pairs with C3v symmetry are stabilized by coordination of an alkali metal ion to three F atoms, and their structural change in the series from M=Na to Cs was proven spectroscopically. There is no evidence for the formation of IrF7, IrF7 - or M[IrF7] (M=Na, K, Rb, Cs) ion pairs in our experiments.

The p-block challenge: assessing quantum chemistry methods for inorganic heterocycle dimerizations

The elements of the p-block of the periodic table are of high interest in various chemical and technical applications like frustrated Lewis-pairs (FLP) or opto-electronics. However, high-quality benchmark data to assess approximate density functional theory (DFT) for their theoretical description are sparse. In this work, we present a benchmark set of 604 dimerization energies of 302 "inorganic benzenes" composed of all non-carbon p-block elements of main groups III to VI up to polonium. This so-called IHD302 test set comprises two classes of structures formed by covalent bonding and by weaker donor-acceptor (WDA) interactions, respectively. Generating reliable reference data with ab initio methods is challenging due to large electron correlation contributions, core-valence correlation effects, and especially the slow basis set convergence. To compute reference values for these dimerization reactions, after thorough testing, we applied a computational protocol using state-of-the-art explicitly correlated local coupled cluster theory termed PNO-LCCSD(T)-F12/cc-VTZ-PP-F12(corr.). It includes a basis set correction at the PNO-LMP2-F12/aug-cc-pwCVTZ level. Based on these reference data, we assess 26 DFT methods in combination with three different dispersion corrections and the def2-QZVPP basis set, five composite DFT approaches, and five semi-empirical quantum mechanical methods. For the covalent dimerizations, the r2SCAN-D4 meta-GGA, the r2SCAN0-D4 and ωB97M-V hybrids, and the revDSD-PBEP86-D4 double-hybrid functional are found to be the best-performing methods among the evaluated functionals of the respective class. However, since def2 basis sets for the 4th period are not associated to relativistic pseudo-potentials, we obtained significant errors in the covalent dimerization energies (up to 6 kcal mol-1) for molecules containing p-block elements of the 4th period. Significant improvements were achieved for systems containing 4th row elements by using ECP10MDF pseudopotentials along with re-contracted aug-cc-pVQZ-PP-KS basis sets introduced in this work with the contraction coefficients taken from atomic DFT (PBE0) calculations. Overall, the IHD302 set represents a challenge to contemporary quantum chemical methods. This is due to a large number of spatially close p-element bonds which are underrepresented in other benchmark sets, and the partial covalent bonding character for the WDA interactions. The IHD302 set may be helpful to develop more robust and transferable approximate quantum chemical methods in the future.

Novel Computational Chemistry Infrastructure for Simulating Astatide in Water: From Basis Sets to Force Fields Using Particle Swarm Optimization

Using the example of astatine, the heaviest naturally occurring halogen whose isotope At-211 has promising medical applications, we propose a new infrastructure for large-scale computational models of heavy elements with strong relativistic effects. In particular, we focus on developing an accurate force field for At- in water based on reliable relativistic density functional theory (DFT) calculations. To ensure the reliability of such calculations, we design novel basis sets for relativistic DFT, via the particle swarm optimization algorithm to optimize the coefficients of the new basis sets and the polarization-consistent basis set idea's extension to heavy elements to eliminate the basis set error from DFT calculations. The resulting basis sets enable the well-grounded evaluation of relativistic DFT against "gold-standard" CCSD(T) results. Accounting for strong relativistic effects, including spin-orbit interaction, via our redesigned infrastructure, we elucidate a noticeable dissimilarity between At- and I- in halide-water force field parameters, radial distribution functions, diffusion coefficients, and hydration energies. This work establishes the framework for the systematic development of polarization-consistent basis sets for relativistic DFT and accurate force fields for molecular dynamics simulations to be used in large-scale models of complex molecular systems with elements from the bottom of the periodic table, including actinides and even superheavy elements.

TURBOMOLE: Today and Tomorrow

TURBOMOLE is a highly optimized software suite for large-scale quantum-chemical and materials science simulations of molecules, clusters, extended systems, and periodic solids. TURBOMOLE uses Gaussian basis sets and has been designed with robust and fast quantum-chemical applications in mind, ranging from homogeneous and heterogeneous catalysis to inorganic and organic chemistry and various types of spectroscopy, light-matter interactions, and biochemistry. This Perspective briefly surveys TURBOMOLE's functionality and highlights recent developments that have taken place between 2020 and 2023, comprising new electronic structure methods for molecules and solids, previously unavailable molecular properties, embedding, and molecular dynamics approaches. Select features under development are reviewed to illustrate the continuous growth of the program suite, including nuclear electronic orbital methods, Hartree-Fock-based adiabatic connection models, simplified time-dependent density functional theory, relativistic effects and magnetic properties, and multiscale modeling of optical properties.

Reducing Exact Two-Component Theory for NMR Couplings to a One-Component Approach: Efficiency and Accuracy

The self-consistent and complex spin-orbit exact two-component (X2C) formalism for NMR spin-spin coupling constants [ J. Chem. Theory Comput. 17, 2021, 3874-3994] is reduced to a scalar one-component ansatz. This way, the first-order response term can be partitioned into the Fermi-contact (FC) and spin-dipole (SD) interactions as well as the paramagnetic spin-orbit (PSO) contribution. The FC+SD terms are real and symmetric, while the PSO term is purely imaginary and antisymmetric. The relativistic one-component approach is combined with a modern density functional treatment up to local hybrid functionals including the response of the current density. Computational demands are reduced by factors of 8-24 as shown for a large tin compound consisting of 137 atoms. Limitations of the current ansatz are critically assessed for Sn, Pb, Pd, and Pt compounds, i.e. the one-component treatment is not sufficient for tin compounds featuring a few heavy halogen atoms.

Investigating the Heaviest Halogen: Lessons Learned from Modeling the Electronic Structure of Astatine's Small Molecules

We present a systematic study of electron-correlation and relativistic effects in diatomic molecular species of the heaviest halogen astatine (At) within relativistic single- and multireference coupled-cluster approaches and relativistic density functional theory. We establish revised reference ab initio data for the ground states of At₂, HAt, AtAu, and AtO⁺ using a highly accurate relativistic effective core potential model and in-house basis sets developed for accurate modeling of molecules with large spin-orbit effects. Spin-dependent relativistic effects on chemical bonding in the ground state are comparable to the binding energy or even exceed it in At₂. Electron-correlation effects near the equilibrium internuclear separation are mostly dynamical and can be adequately captured using single-reference CCSD(T). However, bond elongation in At₂ and, especially, AtO⁺ results in rapid manifestation of its multireference character. While useful for evaluating the spin-orbit effects on the ground-state bonding and properties, the two-component density functional theory lacks predictive power, especially in combination with popular empirically adjusted exchange-correlation functionals. This drawback supports the necessity to develop new functionals for reliable quantum-chemical models of heavy-element compounds with strong relativistic effects.

A Local Hybrid Exchange Functional Approximation from First Principles

Local hybrid functionals are a more flexible class of density functional approximations allowing for a position-dependent admixture of exact exchange. This additional flexibility, however, comes with a more involved mathematical form and a more complicated design. A common denominator for previously constructed local hybrid funtionals is usage of thermochemical benchmark data to construct these functionals. Herein, we design a local hybrid functional without relying on benchmark data. Instead, we construct it in a more ab initio manner, following the principles of modern meta-generalized gradient approximations and considering theoretical constrains. To achieve this, we make use of the density matrix expansion and a local mixing function based on an approximate correlation length. The accuracy of the developed density functional approximation is assessed for thermochemistry, excitation energies, polarizabilities, magnetizabilities, NMR spin-spincoupling constants, NMR shieldings and shifts, as well as EPR g-tensors and hyperfine coupling constants. Here, the new exchange functional shows a robust performance and is especially well suited for atomization energies, barrier heights, excitation energies, NMR coupling constants, and EPR properties, whereas it looses some ground for the NMR shifts.Therefore, the designed functional is a major step forwards for functionals that have been designed from first principles.

Investigation of Molecular Iridium Fluorides IrFn (n=1-6): A Combined Matrix-Isolation and Quantum-Chemical Study

The photo-initiated defluorination of iridium hexafluoride (IrF6 ) was investigated in neon and argon matrices at 6 K, and their photoproducts are characterized by IR and UV-vis spectroscopies as well as quantum-chemical calculations. The primary photoproducts obtained after irradiation with λ=365 nm are iridium pentafluoride (IrF5 ) and iridium trifluoride (IrF3 ), while longer irradiation of the same matrix with λ=278 nm produced iridium tetrafluoride (IrF4 ) and iridium difluoride (IrF2 ) by Ir-F bond cleavage or F2 elimination. In addition, IrF5 can be reversed to IrF6 by adding a F atom when exposed to blue-light (λ=470 nm) irradiation. Laser irradiation (λ=266 nm) of IrF4 also generated IrF6 , IrF5 , IrF3 and IrF2 . Alternatively, molecular binary iridium fluorides IrFn (n=1-6) were produced by co-deposition of laser-ablated iridium atoms with elemental fluorine in excess neon and argon matrices under cryogenic conditions. Computational studies up to scalar relativistic CCSD(T)/triple-ζ level and two-component quasirelativistic DFT computations including spin-orbit coupling effects supported the formation of these products and provided detailed insights into their molecular structures by their characteristic Ir-F stretching bands. Compared to the Jahn-Teller effect, the influence of spin-orbit coupling dominates in IrF5 , leading to a triplet ground state with C4v symmetry, which was spectroscopically detected in solid argon and neon matrices.

Quasi-Relativistic Calculation of EPR g Tensors with Derivatives of the Decoupling Transformation, Gauge-Including Atomic Orbitals, and Magnetic Balance

We present an exact two-component (X2C) ansatz for the EPR g tensor using gauge-including atomic orbitals (GIAOs) and a magnetically balanced basis set expansion. In contrast to previous X2C and four-component relativistic ansätze for the g tensor, this implementation results in a gauge-origin-invariant formalism. Furthermore, the derivatives of the relativistic decoupling matrix are incorporated to form the complete analytical derivative of the X2C Hamiltonian. To reduce the associated computational costs, we apply the diagonal local approximation to the unitary decoupling transformation (DLU). The quasi-relativistic X2C and DLU-X2C Hamiltonians accurately reproduce the results of the parent four-component relativistic theory when accounting for two-electron picture-change effects with the modified screened nuclear spin-orbit approximation in the respective one-electron integrals and integral derivatives. According to our benchmark studies, the uncontracted Dyall and segmented-contracted Karlsruhe x2c-type basis sets perform well when compared to large even-tempered basis sets. Moreover, (range-separated) hybrid density functional approximations such as LC-ωPBE and ωB97X-D are needed to match the experimental findings. The impact of the GIAOs depends on the distribution of the spin density, and their use may change the Δg shifts by 10-50% as shown for [(C₅Me₅)₂Y(μ-S)₂Mo(μ-S)₂Y(C₅Me₅)₂]^-. Routine calculations of large molecules are possible with widely available and comparably low-cost hardware as demonstrated for [Pt(C₆Cl₅)₄]^- with 3003 basis functions and three spin-(1/2) La(II) and Lu(II) compounds, for which we observe good agreement with the experimental findings.

Studies of the First Electronically Excited State of 3-Fluoropyridine and Its Ionic Structure by Means of REMPI, Two-Photon MATI, One-Photon VUV-MATI Spectroscopy and Franck-Condon Analysis

3-Fluoropyridine (3-FP) has been investigated by means of two-photon resonance-enhanced multi photon ionization (REMPI), mass-analyzed threshold ionization (MATI) and one-photon vacuum-ultraviolet (VUV) MATI spectroscopy. The aim was the determination of the effect of m-fluorine substitution on the vibronic structure of the first electronically excited and ionic ground state. The S₁ excitation energy has been determined to be 35 064 ± 2 cm^-1 (4.3474 ± 0.0002 eV). Strong evidence of a distinct vibronic coupling via ν_16b and ν_{[Wag.out.,16a]} to one or both of the lowest ¹ππ* states has been found, which results in a warped S₁ minimum structure with C₁ symmetry. The adiabatic ionization energy of the ionic ground state (14a', n_N-LP orbital) has been determined to be 76 579 ± 6 cm^-1 (9.4946 ± 0.0007 eV), which is the first value reported for this state. The origin of the D₁ state (4a'', π-orbital) is located close by at 77 129 cm^-1 (9.5628 eV). As a result of the D₀-D₁ vicinity, the ionic ground state is coupled to the D₁ state via ν_{[Wag.out.,16a]} and ν_10a, which induces a twisted D₀ geometry with C₁ symmetry. Furthermore, for the first time two-photon and one-photon MATI spectra are presented together, which yield a much better understanding of the ionic vibronic structure in comparison to either of these experiments alone.

NMR Coupling Constants Based on the Bethe-Salpeter Equation in the GW Approximation

We present the first steps to extend the Green's function GW method and the Bethe-Salpeter equation (BSE) to molecular response properties such as nuclear magnetic resonance (NMR) indirect spin-spin coupling constants. We discuss both a nonrelativistic one-component and a quasi-relativistic two-component formalism. The latter describes scalar-relativistic and spin-orbit effects and allows us to study heavy-element systems with reasonable accuracy. Efficiency is maintained by the application of the resolution of the identity approximation throughout. The performance is demonstrated using conventional central processing units (CPUs) and modern graphics processing units (GPUs) for molecules involving several thousand basis functions. Our results show that a large amount of Hartree-Fock exchange is vital to provide a sufficient Kohn-Sham starting point to compute the GW quasi-particle energies. As the GW-BSE approach is generally less accurate for triplet excitations or related properties such as the Fermi-contact interaction, the admixture of the Kohn-Sham correlation kernel through the contracted BSE (cBSE) method improves the results for NMR coupling constants. This leads to remarkable results when combined with the eigenvalue-only self-consistent variant (evGW) and Becke's half and half functional (BH&HLYP) or the CAM-QTP family. The developed methodology is used to calculate the Karplus curve of tin molecules, illustrating its applicability to extended chemically relevant molecules. Here, the GW-cBSE method improves upon the chosen BH&HLYP Kohn-Sham starting points.

Hyperfine Coupling Constants in Local Exact Two-Component Theory

We present a highly efficient implementation of the electron-nucleus hyperfine coupling matrix within the one-electron exact two-component (X2C) theory. The complete derivative of the X2C Hamiltonian is formed, that is, the derivatives of the unitary decoupling transformation are considered. This requires the solution of the response and Sylvester equations, consequently increasing the computational costs. Therefore, we apply the diagonal local approximation to the unitary decoupling transformation (DLU). The finite nucleus model is employed for both the scalar potential and the vector potential. Two-electron picture-change effects are modeled with the (modified) screened nuclear spin-orbit approach. Our implementation is fully integral direct and OpenMP-parallelized. An extensive benchmark study regarding the Hamiltonian, the basis set, and the density functional approximation is carried out for a set of 12-17 transition-metal compounds. The error introduced by DLU is negligible, and the DLU-X2C Hamiltonian accurately reproduces its four-component "fully" relativistic parent results. Functionals with a large amount of Hartree-Fock exchange such as CAM-QTP-02 and ωB97X-D are generally favorable. The pure density functional r²SCAN performs remarkably and even outperforms the common hybrid functionals TPSSh and CAM-B3LYP. Fully uncontracted basis sets or contracted quadruple-ζ bases are required for accurate results. The capability of our implementation is demonstrated for [Pt(C₆Cl₅)₄]^- with more than 4700 primitive basis functions and four rare-earth single-molecule magnets: [La(OAr*)₃]^-, [Lu(NR₂)₃]^-, [Lu(OAr*)₃]^-, and [TbPc₂]^-. Here, the results with the spin-orbit DLU-X2C Hamiltonian are in an excellent agreement with the experimental findings of all Pt, La, Lu, and Tb molecules.

Investigation of the complex vibronic structure in the first excited and ionic ground states of 3-chloropyridine by means of REMPI and MATI spectroscopy and Franck-Condon analysis

3-Chloropyridine (3-CP) has been investigated by means of resonance-enhanced multi-photon ionization (REMPI) and mass-analyzed threshold ionization (MATI) spectroscopy to elucidate the effect of m-chlorine substitution on the vibronic structure of the first electronically excited and ionic ground states. The S₁ excitation energy has been determined to be 34 840 ± 2 cm^-1 (4.3196 ± 0.0002 eV) with a difference of less than 0.2 cm^-1 between both isotopomers, which is the first reported value for this transition in the gas phase so far. The S₁ state has been assigned to the ¹π* ← n transition. It is subject to strong vibronic coupling via ν_16b to one or both of the lowest ¹ππ* states. In addition, strong coupling via at least one more non-totally symmetric vibration is very likely to exist but the vibration could not be identified yet. Overall, the coupling results in a minimum S₁ structure with C₁ symmetry. The adiabatic ionization energy of the n_N-LP orbital (14a') has been determined to be 75 879 ± 6 cm^-1 (9.4078 ± 0.0007 eV) with a difference of less than 2 cm^-1 between the two isotopomers, which is the first value reported for this state so far. The ionic ground state exhibits a distinct vibronic coupling via ν_16a and ν_10a to either the D₁ state (4a'') and/or D₂ state (3a''), which results in a twisted D₀ geometry with C₁ symmetry. As a consequence of the warped geometry in both S₁ and D₀ states, very complicated MATI spectra were obtained when exciting S₁ states at higher wavenumbers.

Reliable TDDFT Protocol Based on a Local Hybrid Functional for the Prediction of Vibronic Phosphorescence Spectra Applied to Tris(2,2'-bipyridine)-Metal Complexes

An efficient computational protocol for the prediction of vibrationally resolved phosphorescence spectra is developed and validated for five tris(2,2'-bipyridine)-metal complexes ([M(bpy)₃]ⁿ⁺, where M = Zn, Ru, Rh, Os, Ir). The outstanding feature of this protocol is the use of full linear-response time-dependent density functional theory (TDDFT) for the excited-state triplet calculation, i.e., the commonly seen strategies employing the Tamm-Dancoff approximation (TDA) or unrestricted density functional theory (DFT) calculations for the T₁ state are not needed. This is achieved by the use of a local hybrid functional (LH12ct-SsirPW92) that features a real-space dependent admixture of exact exchange governed by a local mixing function. The excellent performance of this LH for triplet excitation energies known from previous studies transfers to a remarkable mean absolute error of 0.06 eV for the phosphorescence 0-0 energies investigated herein, while the popular B3PW91 functional gives an error of 0.27 eV in TDDFT and 0.09 eV in unrestricted DFT calculations, respectively. The advantages of the local hybrid are particularly apparent for excited states with a mixed-valence character. The influence of spin-orbit coupling was found to be significant for [Os(bpy)₃]²⁺ red-shifting the 0-0 energy for phosphorescence by 0.17 eV, while the effect is negligible for the other complexes (<0.03 eV). The influence of the basis-set and integration-grid sizes is evaluated, and a computationally lighter protocol is validated that leads to drastic savings in computation time with negligible loss in accuracy.

Matrix Isolation Spectroscopic and Relativistic Quantum Chemical Study of Molecular Platinum Fluorides PtFn (n=1-6) Reveals Magnetic Bistability of PtF4

Molecular platinum fluorides PtF_n, n=1–6, are prepared by two different routes, photo‐initiated fluorine elimination from PtF₆ embedded in solid noble‐gas matrices, and the reaction of elemental fluorine with laser‐ablated platinum atoms. IR spectra of the reaction products isolated in rare‐gas matrices under cryogenic conditions provide, for the first time, experimental vibrational frequencies of molecular PtF₃, PtF₄ and PtF₅. Photolysis of PtF₆ enabled a highly efficient and almost quantitative formation of molecular PtF₄, whereas both PtF₅ and PtF₃ were formed simultaneously by subsequent UV irradiation of PtF₄. The vibrational spectra of these molecular platinum fluorides were assigned with the help of one‐ and two‐component quasirelativistic DFT computation to account for scalar relativistic and spin–orbit coupling effects. Competing Jahn‐Teller and spin–orbit coupling effects result in a magnetic bistability of PtF₄, for which a spin‐triplet (³B_2g, D_2h) coexists with an electronic singlet state (¹A_1g, D_4h) in solid neon matrices.

NMR Indirect Spin-Spin Coupling Constants in a Modern Quasi-Relativistic Density Functional Framework

A quasi-relativistic implementation of NMR indirect spin-spin coupling constants is presented. The exact two-component (X2C) Hamiltonian and its diagonal local approximation to the unitary decoupling transformation (DLU) are utilized together with the (modified) screened nuclear spin-orbit approach. In a restricted kinetic balance, the finite nucleus model is available for both the scalar and vector potentials. The implementation supports density functionals up to the fourth rung of Jacob's ladder, i.e., (range-separated) hybrid and local hybrid functionals based on a seminumerical ansatz. We assess the quality of our quasi-relativistic X2C approach by comparison with "fully" relativistic four-component results for small main-group molecules and alkynyl compounds. The mean absolute error introduced by the DLU scheme is less than 0.05 × 10¹⁹ T J^-2 of the reduced coupling constant for the small main-group molecules and 0.5 Hz for the alkynyl compounds. Thus, the error is significantly smaller than finite nucleus size effects for heavy elements. The basis set convergence and the impact of different density functional approximations are further studied. We propose a simple scheme to develop segmented-contracted relativistic all-electron basis sets for NMR spin-spin couplings. Our implementation allows us to perform calculations of extended molecules with reasonable computational effort, which is illustrated for the ¹J(¹¹⁹Sn, ³¹P) coupling constant of a low-valent tin phosphinidenide complex. The corresponding results are in good agreement with the experimental findings.

Assessing the Accuracy of Local Hybrid Density Functional Approximations for Molecular Response Properties

A comprehensive overview of the performance of local hybrid functionals for molecular properties like excited states, ionization potentials within the GW framework, polarizabilities, magnetizabilities, NMR chemical shifts, and NMR spin-spin coupling constants is presented. We apply the generalization of the kinetic energy, τ, with the paramagnetic current density to all magnetic properties and the excitation energies from time-dependent density functional theory. This restores gauge invariance for these properties. Different ansätze for local mixing functions such as the iso-orbital indicator, the correlation length, the Görling-Levy second-order limit, and the spin polarization are compared. For the latter, we propose a modified version of the corresponding hyper-generalized gradient approximation functional of Perdew, Staroverov, Tao, and Scuseria (PSTS) [Phys. Rev. A 2008, 78, 052513] to allow for a numerically stable evaluation of the exchange-correlation kernel and hyperkernel. The PSTS functional leads to a very consistent improvement compared to the related TPSSh functional. It is further shown that the "best" choice of the local mixing function depends on the studied property and molecular class. While functionals based on the iso-orbital indicator lead to rather accurate excitation energies and ionization energies, the results are less impressive for NMR properties, for which a considerable dependence on the considered molecular test set and nuclei is observed. Johnson's local hybrid functional based on the correlation length yields remarkable results for NMR shifts of compounds featuring heavy elements and also for the excitation energies of organic compounds.

TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations

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.

Noncollinear Relativistic Two-Component X2C Calculations of Hyperfine Couplings Using Local Hybrid Functionals. Importance of the High-Density Coordinate Scaling Limit

Local hybrid functionals with position-dependent exact-exchange admixture have been implemented in the noncollinear spin form into a two-component X2C code and are evaluated for the hyperfine coupling tensors of a series of 3d, 4d, and 5d transition-metal complexes. One aim is to see if the potential of local hybrid functionals toward an improved balance between core-shell and valence-shell spin polarization, recently identified in nonrelativistic computations on 3d complexes (Schattenberg, C.; Maier, T. M.; Kaupp, M. J. Chem. Theory Comput. 2018, 14, 5653-5672), can be extended to the hyperfine couplings of heavier metal centers. The correctness of the two-component implementation is first established by comparison to previous computations for 3d systems with or without notable spin-orbit contributions to their hyperfine tensors, and the good performance of a standard "t-LMF" local mixing function is confirmed. However, when moving to 4d and 5d metal centers, the performance of such local mixing functions deteriorates. This is likely due to their violation of the homogeneous coordinate scaling condition in the high-density limit, which is particularly important for the core shells of heavier atoms. A local mixing function that respects this high-density limit performs notably better for heavier metal centers. However, it brings in much too high exact-exchange admixtures for the 3d systems and is too inflexible to simultaneously provide reasonable chemical accuracy in other areas. These results point to the ongoing need to develop improved local mixing functions and local hybrid functionals that exhibit favorable properties in different areas of space defined by very high and much lower electron densities.

{[CuSn5 Sb3 ](2-) }2 : A Dimer of Inhomogeneous Superatoms

Reaction of the binary Zintl anion (Sn2 Sb2 )(2-) with the β-diketiminato complex [LCu(NCMe)] (L=nacnac=[(N(C6 H3 (i) Pr2 -2,6)C(Me))2 CH](-) ) in ethylenediamine or DMF affords the ternary cluster dimer {[CuSn5 Sb3 ](2-) }2 (1) as its [K(crypt-222)](+) salt. The chemical formulation of 1 is supported by energy-dispersive X-ray spectroscopy (EDX) and quantum chemical calculations. Each monomeric part of the dimer represents a trimetallic "[CuSn5 Sb3 ](2-) " cluster, with an architecture in between a tricapped trigonal prism and a capped square antiprism. As shown by quantum chemical investigations, the presence of Sb atoms and, in particular, of Cu atoms in the cluster skeleton makes the monomeric unit behave like an inhomogeneous superatom, which clearly prefers to dimerize, thereby producing a relatively short, yet virtually non-bonding Cu⋅⋅⋅Cu distance.

Structure of Amido Pyridinium Betaines: Persistent Intermolecular C-H⋅⋅⋅N Hydrogen Bonding in Solution

A hydrogen bond of the type C-H⋅⋅⋅X (X=O or N) is known to influence the structure and function of chemical and biological systems in solution. C-H⋅⋅⋅O hydrogen bonding in solution has been extensively studied, both experimentally and computationally, whereas the equivalent thermodynamic parameters have not been enumerated experimentally for C-H⋅⋅⋅N hydrogen bonds. This is, in part, due to the lack of systems that exhibit persistent C-H⋅⋅⋅N hydrogen bonds in solution. Herein, a class of molecule based on a biologically active norharman motif that exhibits unsupported intermolecular C-H⋅⋅⋅N hydrogen bonds in solution has been described. A pairwise interaction leads to dimerisation to give bond strengths of about 7 kJ mol^-1 per hydrogen bond, which is similar to chemically and biologically relevant C-H⋅⋅⋅O hydrogen bonding. The experimental data is supported by computational work, which provides additional insight into the hydrogen bonding by consideration of electrostatic and orbital interactions and allowed a comparison between calculated and extrapolated NMR chemical shifts.

Extending DFT-based genetic algorithms by atom-to-place re-assignment via perturbation theory: a systematic and unbiased approach to structures of mixed-metallic clusters

Energy surfaces of metal clusters usually show a large variety of local minima. For homo-metallic species the energetically lowest can be found reliably with genetic algorithms, in combination with density functional theory without system-specific parameters. For mixed-metallic clusters this is much more difficult, as for a given arrangement of nuclei one has to find additionally the best of many possibilities of assigning different metal types to the individual positions. In the framework of electronic structure methods this second issue is treatable at comparably low cost at least for elements with similar atomic number by means of first-order perturbation theory, as shown previously [F. Weigend, C. Schrodt, and R. Ahlrichs, J. Chem. Phys. 121, 10380 (2004)]. In the present contribution the extension of a genetic algorithm with the re-assignment of atom types to atom sites is proposed and tested for the search of the global minima of PtHf12 and [LaPb7Bi7](4-). For both cases the (putative) global minimum is reliably found with the extended technique, which is not the case for the "pure" genetic algorithm.