Toward the Next Generation of Density Functionals: Escaping the Zero-Sum Game by Using the Exact-Exchange Energy Density.

ConspectusKohn-Sham density functional theory (KS DFT) is arguably the most widely applied electronic-structure method with tens of thousands of publications each year in a wide variety of fields. Its importance and usefulness can thus hardly be overstated. The central quantity that determines the accuracy of KS DFT calculations is the exchange-correlation functional. Its exact form is unknown, or better "unknowable", and therefore the derivation of ever more accurate yet efficiently applicable approximate functionals is the "holy grail" in the field. In this context, the simultaneous minimization of so-called delocalization errors and static correlation errors is the greatest challenge that needs to be overcome as we move toward more accurate yet computationally efficient methods. In many cases, an improvement on one of these two aspects (also often termed fractional-charge and fractional-spin errors, respectively) generates a deterioration in the other one. Here we report on recent notable progress in escaping this so-called "zero-sum-game" by constructing new functionals based on the exact-exchange energy density. In particular, local hybrid and range-separated local hybrid functionals are discussed that incorporate additional terms that deal with static correlation as well as with delocalization errors. Taking hints from other coordinate-space models of nondynamical and strong electron correlations (the B13 and KP16/B13 models), position-dependent functions that cover these aspects in real space have been devised and incorporated into the local-mixing functions determining the position-dependence of exact-exchange admixture of local hybrids as well as into the treatment of range separation in range-separated local hybrids. While initial functionals followed closely the B13 and KP16/B13 frameworks, meanwhile simpler real-space functions based on ratios of semilocal and exact-exchange energy densities have been found, providing a basis for relatively simple and numerically convenient functionals. Notably, the correction terms can either increase or decrease exact-exchange admixture locally in real space (and in interelectronic-distance space), leading even to regions with negative admixture in cases of particularly strong static correlations. Efficient implementations into a fast computer code (Turbomole) using seminumerical integration techniques make such local hybrid and range-separated local hybrid functionals promising new tools for complicated composite systems in many research areas, where simultaneously small delocalization errors and static correlation errors are crucial. First real-world application examples of the new functionals are provided, including stretched bonds, symmetry-breaking and hyperfine coupling in open-shell transition-metal complexes, as well as a reduction of static correlation errors in the computation of nuclear shieldings and magnetizabilities. The newest versions of range-separated local hybrids (e.g., ωLH23tdE) retain the excellent frontier-orbital energies and correct asymptotic exchange-correlation potential of the underlying ωLH22t functional while improving substantially on strong-correlation cases. The form of these functionals can be further linked to the performance of the recent impactful deep-neural-network "black-box" functional DM21, which itself may be viewed as a range-separated local hybrid.

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.

Spin-Symmetry Breaking and Hyperfine Couplings in Transition-Metal Complexes Revisited Using Density Functionals Based on the Exact-Exchange Energy Density.

A small set of mononuclear manganese complexes evaluated previously for their Mn hyperfine couplings (HFCs) has been analyzed using density functionals based on the exact-exchange energy density─in particular, the spin symmetry breaking (SSB) found previously when using hybrid functionals. Employing various strong-correlation corrected local hybrids (scLHs) and strong-correlation corrected range-separated local hybrids (scRSLHs) with or without additional corrections to their local mixing functions (LMFs) to mitigate delocalization errors (DE), the SSB and the associated dipolar HFCs of [Mn(CN)4]2-, MnO3, [Mn(CN)4N]-, and [Mn(CN)5NO]2- (the latter with cluster embedding) have been examined. Both strong-correlation (sc)-correction and DE-correction terms help to diminish SSB and correct the dipolar HFCs. The DE corrections are more effective, and the effects of the sc corrections depend on their damping factors. Interestingly, the DE-corrections reduce valence-shell spin polarization (VSSP) and thus SSB by locally enhancing exact-exchange (EXX) admixture near the metal center and thereby diminishing spin-density delocalization onto the ligand atoms. In contrast, sc corrections diminish EXX admixture locally, mostly on specific ligand atoms. This then reduces VSSP and SSB as well. The performance of scLHs and scRSLHs for the isotropic Mn HFCs has also been analyzed, with particular attention to core-shell spin-polarization contributions. Further sc-corrected functionals, such as the KP16/B13 construction and the DM21 deep-neural-network functional, have been examined.

Structure and Photophysics of N-Tolanyl-phenochalcogenazines and their Radical Cations.

The study focuses on the structural and photophysical characteristics of neutral and oxidized forms of N-tolanyl-phenochalcogenazines PZX-tolan with X=O, S, Se, and Te. X-ray crystal structure analyses show a pseudo-equatorial (pe) structure of the tolan substituent in the O, S, and Se dyads, while the Te dyad possesses a pseudo-axial (pa) structure. DFT calculations suggest the pe structure for O and S, and the pa structure for Se and Te as stable forms. Steady-state and femtosecond-time resolved optical spectroscopy in toluene solution indicate that the O and S dyads emit from a CT state, whereas the Se and Te dyads emit from a tolan-localized state. The T1 state is tolan-localized in all cases, showing phosphorescence at 77 K. The heavy atom effect of chalcogens induces intersystem crossing from S1 to Tx, resulting in a decreasing S1 lifetime from 2.1 ns to 0.42 ps. The T1 states possess potential for singlet oxygen sensitization with a high quantum yield (ca. 40 %) for the O, S, and Se dyads. Radical cations exhibit spin density primarily localized at the heterocycle. EPR measurements and quasirelativistic DFT calculations reveal a very strong g-tensor anisotropy, supporting the pe structure for the S and Se derivatives.

Revisiting Gauge-Independent Kinetic Energy Densities in Meta-GGAs and Local Hybrid Calculations of Magnetizabilities.

In a recent study [J. Chem. Theory Comput. 2021, 17, 1457-1468], some of us examined the accuracy of magnetizabilities calculated with density functionals representing the local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA (mGGA), as well as global hybrid (GH) and range-separated (RS) hybrid functionals by assessment against accurate reference values obtained with coupled-cluster theory with singles, doubles, and perturbative triples [CCSD(T)]. Our study was later extended to local hybrid (LH) functionals by Holzer et al. [J. Chem. Theory Comput. 2021, 17, 2928-2947]; in this work, we examine a larger selection of LH functionals, also including range-separated LH (RSLH) functionals and strong-correlation LH (scLH) functionals. Holzer et al. also studied the importance of the physically correct handling of the magnetic gauge dependence of the kinetic energy density (τ) in mGGA calculations by comparing the Maximoff-Scuseria formulation of τ used in our aforementioned study to the more physical current-density extension derived by Dobson. In this work, we also revisit this comparison with a larger selection of mGGA functionals. We find that the newly tested LH, RSLH, and scLH functionals outperform all of the functionals considered in the previous studies. The various LH functionals afford the seven lowest mean absolute errors while also showing remarkably small standard deviations and mean errors. Most strikingly, the best two functionals are scLHs that also perform remarkably well in cases with significant multiconfigurational character, such as the ozone molecule, which is traditionally excluded from statistical error evaluations due to its large errors with common density functionals.

Range-Separated Local Hybrid Functionals with Small Fractional-Charge and Fractional-Spin Errors: Escaping the Zero-Sum Game of DFT Functionals.

Extending recent developments on strong-correlation (sc) corrections to local hybrid functionals to the recent accurate ωLH22t range-separated local hybrid, a series of highly flexible strong-correlation-corrected range-separated local hybrids (scRSLHs) has been constructed and evaluated. This has required the position-dependent reduction of both short- and long-range exact-exchange admixtures in regions of space characterized by strong static correlations. Using damping procedures provides scRSLHs that retain largely the excellent performance of ωLH22t for weakly correlated situations and, in particular, for accurate quasiparticle energies of a wide variety of systems while reducing dramatically static-correlation errors, e.g., in stretched-bond situations. An additional correction to the local mixing function to reduce delocalization errors in abnormal open-shell situations provides further improvements in thermochemical and kinetic parameters, making scRSLH functionals such as ωLH23tdE or ωLH23tdP promising tools for complex molecular or condensed-phase systems, where low fractional-charge and fractional-spin errors are simultaneously important. The proposed rung 4 functionals thereby largely escape the usual zero-sum game between these two quantities and are expected to open new areas of accurate computations by Kohn-Sham DFT. At the same time, they require essentially no extra computational effort over the underlying ωLH22t functional, which means that their use is only moderately more demanding than that of global, local, or range-separated hybrid functionals.

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.

Strong-correlation density functionals made simple.

Recent work on incorporating strong-correlation (sc) corrections into the scLH22t local hybrid functional [A. Wodynski and M. Kaupp, J. Chem. Theory Comput. 18, 6111-6123 (2022)] used a hybrid procedure, applying a strong-correlation factor derived from the reverse Becke-Roussel machinery of the KP16/B13 and B13 functionals to the nonlocal correlation term of a local hybrid functional. Here, we show that adiabatic-connection factors for strong-correlation-corrected local hybrids (scLHs) can be constructed in a simplified way based on a comparison of semi-local and exact exchange-energy densities only, without recourse to exchange-hole normalization. The simplified procedure is based on a comparative analysis of Becke's B05 real-space treatment of nondynamical correlation and that in LHs, and it allows us to use, in principle, any semi-local exchange-energy density in the variable used to construct local adiabatic connections. The derivation of competitive scLHs is demonstrated based on either a modified Becke-Roussel or a simpler Perdew-Burke-Ernzerhof (PBE) energy density, leading to the scLH23t-mBR and scLH23t-tPBE functionals, which both exhibit low fractional spin errors while retaining good performance for weakly correlated situations. We also report preliminary attempts toward more detailed modeling of the local adiabatic connection, allowing a reduction of unphysical local maxima in spin-restricted bond-dissociation energy curves (scLH23t-mBR-P form). The simplified derivations of sc-factors reported here provide a basis for future constructions and straightforward implementation of exchange-correlation functionals that escape the zero-sum game between low self-interaction and static-correlation errors.

Excited states and spin-orbit coupling in chalcogen substituted perylene diimides and their radical anions.

While spin-orbit coupling does not play a decisive role in the photophysics of unsubstituted perylene diimides (PDI), this changes dramatically when two phenylselenyl or phenyltelluryl substituents were attached to the PDI bay positions. In the series of PhO-, PhS-, PhSe-, and PhTe-substituted PDIs we observed strongly decreasing fluorescence quantum yield as a consequence of strongly increasing intersystem crossing (ISC) rate, measured by transient absorption spectroscopy with fs- and ns-time resolution as well as by broadband fluorescence upconversion. Time-dependent density functional calculations suggest increasing spin-orbit coupling due to the internal heavy-atom effect as the reason for fast ISC. In case of the selenium PDI derivative we found significant singlet oxygen sensitization via the PDI triplet state. The corresponding radical anions of the chalcogen substituted PDIs were also prepared and investigated by optical and EPR spectroscopy. Here, the increasing SOC results in an increase of the g-tensor anisotropy, and of the isotropic g-value in solution, albeit quasirelativistic density functional calculations show only a relatively small fraction of the spin density to be located on the chalcogen atom.

Local Hybrid Functional Applicable to Weakly and Strongly Correlated Systems.

The recent idea (Wodynski, A.; Arbuznikov, A. V.; Kaupp M. J. Chem. Phys. 2021, 155, 144101) to augment local hybrid functionals by a strong-correlation (sc) factor obtained from the adiabatic connection in the spirit of the KP16 model has been extended and applied to generate the accurate sc-corrected local hybrid functional scLH22t. By damping small values of the ratio between nondynamical and dynamical correlation entering the correction factor, it has become possible to avoid double counting of nondynamical correlation for weakly correlated situations and thereby preserve the excellent accuracy of the underlying LH20t local hybrid for such cases almost perfectly. On the other hand, scLH22t improves substantially over LH20t in reducing fractional-spin errors (FSEs), in providing improved spin-restricted bond dissociation curves, and in treating some typical systems with multireference character. The obtained FSEs are similar to those of the KP16/B13 model and slightly larger than for B13, but performance for weakly correlated systems is better than for these two related methods, which are also difficult to use self-consistently. The recent DM21 functional based on the training of a deep neural network still performs somewhat better than scLH22t but allows no physical insights into the origins of reduced FSEs. Examination of local mixing functions (LMFs) for the corrected scLH22t and uncorrected LH20t functionals provides further insights: in weakly correlated situations, the LMF remains essentially unchanged. Strong-correlation effects manifest in a reduction of the LMF values in certain regions of space, even to the extent of producing negative LMF values. It is suggested that this is the mechanism by which also DM21, which may be viewed as a range-separated local hybrid, is able to reduce FSEs.

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.

Local hybrid functionals augmented by a strong-correlation model.

The strong-correlation factor of the recent KP16/B13 exchange-correlation functional has been adapted and applied to the framework of local hybrid (LH) functionals. The expression identifiable as nondynamical (NDC) and dynamical (DC) correlations in LHs is modified by inserting a position-dependent KP16/B13-style strong-correlation factor qAC(r) based on a local version of the adiabatic connection. Different ways of deriving this factor are evaluated for a simple one-parameter LH based on the local density approximation. While the direct derivation from the LH NDC term fails due to known deficiencies, hybrid approaches, where the factor is determined from the B13 NDC term as in KP16/B13 itself, provide remarkable improvements. In particular, a modified B13 NDC expression using Patra's exchange-hole curvature showed promising results. When applied to the simple LH as a first attempt, it reduces atomic fractional-spin errors and deficiencies of spin-restricted bond dissociation curves to a similar extent as the KP16/B13 functional itself while maintaining the good accuracy of the underlying LH for atomization energies and reaction barriers in weakly correlated situations. The performance of different NDC expressions in deriving strong-correlation corrections is analyzed, and areas for further improvements of strong-correlation corrected LHs and related approaches are identified. All the approaches evaluated in this work have been implemented self-consistently into a developers' version of the Turbomole program.

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

Molecular platinum fluorides PtFn , 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 (3 B2g , D2h ) coexists with an electronic singlet state (1 A1g , D4h ) in solid neon matrices.

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.

Density Functional Calculations of Electron Paramagnetic Resonance g- and Hyperfine-Coupling Tensors Using the Exact Two-Component (X2C) Transformation and Efficient Approximations to the Two-Electron Spin-Orbit Terms.

A two-component quasirelativistic density functional theory implementation of the computation of hyperfine and g-tensors at exact two-component (X2C) and Douglas-Kroll-Hess method (DKH) levels in the Turbomole code is reported and tested for a series of smaller 3d1, 4d1, and 5d1 complexes, as well as for some larger 5d7 Ir and Pt systems in comparison with earlier four-component matrix-Dirac-Kohn-Sham results. A main emphasis is placed on efficient approximations to the two-electron spin-orbit contributions, comparing an existing implementation of two variants of Boettger's "scaled nuclear spin-orbit" (SNSO) approximation in the code with a newly implemented atomic mean-field spin-orbit (AMFSO) approximation. The different variants perform overall comparably well with the four-component data. The AMFSO approximation has the added advantage of being able to include the spin-other-orbit contributions arising from the Gaunt term of relativistic electron-electron interactions. These are of comparably larger importance for the 3d complexes than for their heavier homologues. The excellent agreement between X2C and four-component electron paramagnetic resonance parameter results provides the opportunity to treat large systems efficiently and accurately with the computationally more expedient two-component quasirelativistic methodology.

Structural studies on radiopharmaceutical DOTA-minigastrin analogue (CP04) complexes and their interaction with CCK2 receptor.

BACKGROUND: The cholecystokinin receptor subtype 2 (CCK-2R) is an important target for diagnostic imaging and targeted radionuclide therapy (TRNT) due to its overexpression in certain cancers (e.g., medullary thyroid carcinoma (MTC)), thus matching with a theranostic principle. Several peptide conjugates suitable for the TRNT of MTC have been synthesized, including a very promising minigastrin analogue DOTA-(DGlu)6-Ala-Tyr-Gly-Trp-Met-Asp-Phe-NH2 (CP04). In this contribution, we wanted to see whether CP04 binding affinity for CCK-2R is sensitive to the type of the complexed radiometal, as well as to get insights into the structure of CP04-CCK2R complex by molecular modeling. RESULTS: In vitro studies demonstrated that there is no significant difference in CCK-2R binding affinity and specific cellular uptake between the CP04 conjugates complexed with [68Ga]Ga3+ or [177Lu]Lu3+. In order to investigate the background of this observation, we proposed a binding model of CP04 with CCK-2R based on homology modeling and molecular docking. In this model, the C-terminal part of the molecule enters the cavity formed between the receptor helices, while the N-terminus (including DOTA and the metal) is located at the binding site outlet, exposed in large extent to the solvent. The radiometals do not influence the conformation of the molecule except for the direct neighborhood of the chelating moiety. CONCLUSIONS: The model seems to be in agreement with much of structure-activity relationship (SAR) studies reported for cholecystokinin and for CCK-2R-targeting radiopharmaceuticals. It also explains relative insensitivity of CCK-2R affinity for the change of the metal. The proposed model partially fits the reported site-directed mutagenesis data.

Noncollinear Two-Component Quasirelativistic Description of Spin Interactions in Exchange-Coupled Systems. Mapping Generalized Broken-Symmetry States to Effective Spin Hamiltonians.

We provide a consistent mapping of noncollinear two-component quasirelativistic DFT energies with appropriate orientations of localized spinor quantization axes for multinuclear exchange-coupled transition-metal complexes onto an uncoupled anisotropic effective spin Hamiltonian. This provides access to the full exchange interaction tensor between the centers of spin-coupled systems in a consistent way. The proposed methodology may be best viewed as a generalized broken-symmetry density functional theory approach (gBS-DFT). While the calculations provided are limited to trinuclear systems ([M3O(OOCH)6(H2O)3]+, where M = Cr(III), Mn(III), Fe(III)) with C3 symmetry, the method provides a general framework that is extendable to arbitrary systems. It offers an alternative to previous approaches to single-ion zero-field splittings, and it provides access to the less often examined antisymmetric Dzyaloshinskii-Moriya exchange interaction. Spin-orbit coupling is included self-consistently. This will be of particular importance for complexes involving 4d or 5d transition metal centers or possibly also for f-block elements, where a perturbational treatment of spin-orbit coupling may not be valid anymore. While a comparison with experimental data was indirect due to simplifications in the chosen model structures, the agreement obtained indicates the essential soundness of the presented approach.

The Relativistic Effects on the Carbon-Carbon Coupling Constants Mediated by a Heavy Atom.

The (2)JCC, (3)JCC, and (4)JCC spin-spin coupling constants in the systems with a heavy atom (Cd, In, Sn, Sb, Te, Hg, Tl, Pb, Bi, and Po) in the coupling path have been calculated by means of density functional theory. The main goal was to estimate the relativistic effects on spin-spin coupling constants and to explore the factors which may influence them, including the nature of the heavy atom and carbon hybridization. The methods applied range, in order of reduced complexity, from the Dirac-Kohn-Sham (DKS) method (density functional theory with four-component Dirac-Coulomb Hamiltonian), through DFT with two- and one-component zeroth-order regular approximation (ZORA) Hamiltonians, to scalar effective core potentials (ECPs) with the nonrelativistic Hamiltonian. The use of DKS and ZORA methods leads to very similar results, and small-core ECPs of the MDF and MWB variety reproduce correctly the scalar relativistic effects. Scalar relativistic effects usually are larger than the spin-orbit coupling effects. The latter tend to influence the most the coupling constants of the sp(3)-hybridized carbon atoms and in compounds of the p-block heavy atoms. Large spin-orbit coupling contributions for the Po compounds are probably connected with the inverse of the lowest triplet excitation energy.

The selectivity of diglycolamide (TODGA) and bis-triazine-bipyridine (BTBP) ligands in actinide/lanthanide complexation and solvent extraction separation - a theoretical approach.

Theoretical calculations (density functional theory with the scalar relativistic ZORA Hamiltonian) have been performed to obtain the energy and Gibbs free energy of formation of cationic 1 : 3 complexes of americium(iii) and europium(iii) with a tri-O-dentate diglycolamide ligand TEDGA (a model of TODGA extractant), as well as the free energy of their partition between water and an organic diluent. The distribution of electron density over the atoms, bonds, and molecular orbitals was analyzed by means of Mulliken population analysis, the localization procedure of natural bond orbitals, and the Quantum Theory of Atoms-in-Molecules. The stabilities of both [M(TEDGA)(3)](3+) complexes are similar to each other. On the other hand, our recent data for a similar pair of cationic Am/Eu complexes with a softer (HSAB) tetra-N-dentate ligand C2-BTBP show that the [Am(C2-BTBP)(2)](3+) complex is significantly more stable in aqueous solution than its Eu counterpart. The decisive factor stabilizing the Am(3+) complexes over their Eu(3+) analogues is the charge transfer from the ligands, somewhat greater on the 6d(Am(III)) than on 5d(Eu(III)) orbitals. The covalency of M-N bonds in the [M(C2-BTBP)(2)](3+) complexes is greater than that of M-O bonds in [M(TEDGA)(3)](3+), but the latter is not negligible, in particular in the bonds with the oxygen atoms of the amide groups in TEDGA. The analysis of charge distribution over the whole molecules of the complexes shows that the TEDGA molecule is not hard as expected, but a relatively soft Lewis base, only slightly harder than BTBP. This conclusion has been confirmed by the calculation of the chemical hardness of the ligands. Moreover, the comparison of the results of bonding analysis with the calculated energies of complex formation in water and in the gas phase allows us to conclude that the population analysis, QTAIM topological parameters, and SOPT stabilization energy, as well as Wiberg and overlap-weighted NAO indices are the tools for analyzing the covalency rather than the total bond strength.