The Interaction of Water with Free Mn4O4+ Clusters: Deprotonation and Adsorption‐Induced Structural Transformations

As the biological activation and oxidation of water takes place at an inorganic cluster of the stoichiometry CaMn₄O₅, manganese oxide is one of the materials of choice in the quest for versatile, earth‐abundant water splitting catalysts. To probe basic concepts and aid the design of artificial water‐splitting molecular catalysts, a hierarchical modeling strategy was employed that explores clusters of increasing complexity, starting from the tetramanganese oxide cluster Mn₄O₄⁺ as a molecular model system for catalyzed water activation. First‐principles calculations in conjunction with IR spectroscopy provide fundamental insight into the interaction of water with Mn₄O₄⁺, one water molecule at a time. All of the investigated complexes Mn₄O₄(H₂O)_n⁺ (n=1–7) contain deprotonated water with a maximum of four dissociatively bound water molecules, and they exhibit structural fluxionality upon water adsorption, inducing dimensional and structural transformations of the cluster core.     

Hydration preferences for Mn4Ca cluster models of photosystem II: location of potential substrate-water binding sites

Density functional theory calculations are reported on a set of three model structures of the Mn₄Ca cluster in the water‐oxidizing complex of Photosystem II (PSII), which share the structural formula [CaMn₄C₉H₁₀N₂O₁₆]^q+ ? (H₂O)_n (q=?1, 0, 1, 2, 3; n=0–7). In these calculations we have explored the preferred hydration sites of the Mn₄Ca cluster across five overall oxidation states (S₀ to S₄) and all feasible magnetic‐coupling arrangements to identify the most likely substrate–water binding sites. We have also explored charge‐compensated structures in which the overall charge on the cluster is maintained at q=0 or +1, which is consistent with the experimental data on sequential proton loss in the real system. The three model structures have skeletal arrangements that are strongly reminiscent, in their relative metal‐atom positions, of the 2.9‐, 3.7‐, and 3.5 Å‐resolution crystal structures, respectively, whereas the charge states encompassed in our study correspond to an assignment of (Mn^III)₃Mn^II for S₀ and up to (Mn^IV)₃Mn^III for S₄. The three models differ principally in terms of the spatial relationship between one Mn (Mn(4)) and a generally robust Mn₃Ca tetrahedron that contains Mn(1), Mn(2), and Mn(3). Oxidation‐state distributions across the four manganese atoms, in most of the explored charge states, are dependent on details of the cluster geometry, on the extent of assumed hydration of the clusters, and in some instances on the imposed magnetic‐coupling between adjacent Mn atoms. The strongest water‐binding sites are generally those on Mn(4) and Ca. However, one structure type displays a high‐affinity binding site between Ca and Mn(3), the S‐state‐dependent binding‐energy pattern of which is most consistent with the substrate water‐exchange kinetics observed in functional PSII. This structure type also permits another water molecule to access the cluster in a manner consistent with the substrate–water interaction with the Mn cluster, seen in electron spin‐echo envelope modulation (ESEEM) studies of the functional enzyme in the S₀ and S₂ states. It also rationalizes the significant differences in hydrogen‐bonding interactions of the substrate water observed in the FTIR measurements of the S₁ and S₂ states. We suggest that these two water‐binding sites, which are molecularly close, model the actual substrate‐binding sites in the enzyme.     

Structures,Unimolecular Fragmentations,and Reactivities of the Self‐Assembled Multimetallic/Peptide Complexes [Mnn(GlyGly‐H)2n−1]+ and [Mnn+1(GlyGly‐H)2n]2+

Complexes of Mn²⁺ with deprotonated GlyGly are investigated by sustained off‐resonance irradiation collision‐induced dissociation (SORI‐CID), infrared multiple‐photon dissociation spectroscopy, ion–molecule reactions, and computational methods. Singly [Mn_n(GlyGly‐H)_2n?1]⁺ and doubly [Mn_n+1(GlyGly‐H)_2n]²⁺ charged clusters are formed from aqueous solutions of MnCl₂ and GlyGly by electrospray ionization. The most intense ion produced was the singly charged [M₂(GlyGly‐H)₃]⁺ cluster. Singly charged clusters show extensive fragmentations of small neutral molecules such as water and carbon dioxide as well as dissociation pathways related to the loss of NH₂CHCO and GlyGly. For the doubly charged clusters, however, loss of GlyGly is observed as the main dissociation pathway. Structure elucidation of [Mn₃(GlyGly‐H)₄]²⁺ clusters has also been done by IRMPD spectroscopy as well as DFT calculations. It is shown that the lowest energy structure of the [Mn₃(GlyGly‐H)₄]²⁺ cluster is deprotonated at all carboxylic acid groups and metal ions are coordinated with carbonyl oxygen atoms, and that all amine nitrogen atoms are hydrogen bonded to the amide hydrogen. A comparison of the calculated high‐spin (sextet) and low‐spin (quartet) state structures of [Mn₃(GlyGly‐H)₄]²⁺ is provided. IRMPD spectroscopic results are in agreement with the lowest energy high‐spin structure computed. Also, the gas‐phase reactivity of these complexes towards neutral CO and water was investigated. The parent complexes did not add any water or CO, presumably due to saturation at the metal cation. However, once some of the ligand was removed via CO₂ laser IRMPD, water was seen to add to the complex. These results are consistent with high‐spin Mn²⁺ complexes.     

Functional chemical models of multielectron water oxidation in photosynthesis

The study of water oxidation by Mn _n ^IV clusters, which are functional chemical models of the manganese cofactor (enzyme that oxidizes water in photosystem II of natural photosynthesis) has demonstrated that a Mn₂^IV cluster oxidizes two water molecules to form one oxygen molecule, Mn₄^IVoxidizes four water molecules to form two O₂ molecules, and Mn₈^IVoxidizes eight water molecules to form four O₂ molecules. A Mn₆^IV cluster oxidizes six water molecules to two ozone molecules, whereas Mn₁₂^IV oxidizes twelve water molecules to four ozone molecules. The six-electron oxidation of water to ozone is also observed in photosynthesis in red and brown sea algae under conditions of water deficit. It is hypothesized that, in the case of water deficit in algae, the manganese cofactor with four manganese ions turns into the cofactor with six manganese ions.     

Electronic Structure of Manganese Complexes of the Redox‐Non‐innocent Tetrazene Ligand and Evidence for the Metal‐Azide/Imido Cycloaddition Intermediate

The first synthetic manganese tetrazene complexes are described as a redox pair comprising anionic [Mn(N₄Ad₂)₂]^? ( 1 ) and neutral Mn(N₄Ad₂)₂ ( 2 ) complexes (N₄Ad₂=[Ad‐N?N=N?N‐Ad]^2?). Compound 1 is obtained in two forms as lithium salts, one as a cationic Li₂Mn cluster, and one as a Mn–Li 1D ionic polymer. Compound 1 is electronically described as a Mn^III center with two [N₄Ad₂]^2? ligands. The one‐electron oxidized 2 is crystalized in two morphologies, one as pure 2 and one as an acetonitrile adduct. Despite similar composition, the behavior of 2 differs in the two morphologies. Compound 2 ‐ MeCN is relatively air and temperature stable. Crystalline 2 , on the other hand, exhibits a compositional, dynamic disorder wherein the tetrazene metallacycle ring‐opens into a metal imide/azide complex detectable by X‐ray crystallography and FTIR spectroscopy. Electronic structure of 2 was examined by EPR and XPS spectroscopies and DFT calculations, which indicate 2 is best described as a Mn^III ion with an anion radical delocalized across the two ligands through spin‐polarization effects.     

Molecular Vibrations of an Oxygen-Evolving Complex and Its Synthetic Mimic

Bio-inspired catalysis for artificial photosynthesis has been widely studied for decades, in particular, with the purpose of using bio-disposable and non-toxic metals as building blocks. The characterisation of such catalysts has been achieved by using different kinds of spectroscopic methods, from X-ray crystallography to NMR spectroscopy. An artificial Mn₄CaO₄ cubane cluster with dangling Mn₄ was synthesised in 2015 [Zhang et al. Science 2015 , 348, 690–693]; this cluster showed many structural similarities to that of the natural oxygen-evolving complex. An accurate structural and spectroscopic comparison between the natural and artificial systems is highly relevant to understand the catalytic mechanism. Among data from different techniques, the differential FTIR spectra (S_n+1−S_n) of photosystem II are still lacking a complete interpretation. The availability of IR data of the artificial cluster offers a unique opportunity to assign absolute absorption spectra on a well-defined and easier to interpret analogous moiety. The present work aims to investigate the novel inorganic compound as a model system for an oxygen-evolving complex through measurement of its spectroscopic properties. The experimental results are compared with calculations by using a variety of theoretical methods (normal mode analysis, effective normal mode analysis) in the S₁ state. We underline the similarities and the differences in the computational spectra based on atomistic models of Mn₄CaO₅ and Mn₄CaO₄ complexes.     

Efficient Olefin Epoxidation by Robust Re4 Cluster‐Supported MnIII Complexes with Peracids: Evidence of Simultaneous Operation of Multiple Active Oxidant Species,MnVO,MnIVO,and MnIII?OOC(O)R

Two new tetranuclear chalcocyanide cluster complexes, [{Mn(saloph)H₂O}₄Re₄Q₄(CN)₁₂]?4 CH₃OH? 8 H₂O (saloph=N,N′‐o‐phenylenebis(salicylidenaminato), Q=Se ( 1 ‐Se), Te ( 2 ‐Te)), have been synthesized by the diffusion of a methanolic solution of [PPh₄]₄[Re₄Q₄(CN)₁₂] into a methanolic solution of [Mn(saloph)]⁺. The structure of 2 ‐Te has been determined by X‐ray crystallography. These rhenium cluster‐supported [Mn^III(saloph)] complexes have been found to efficiently catalyze a wide range of olefin epoxidations under mild experimental conditions in the presence of meta‐chloroperbenzoic acid (mCPBA). Olefin epoxidation by these catalysts is proposed to involve the multiple active oxidants Mn^V?O, Mn^IV?O, and Mn^III? OOC(O)R. Evidence in support of this interpretation has been derived from reactivity and Hammett studies, H₂¹⁸O‐exchange experiments, and the use of peroxyphenylacetic acid as a mechanistic probe. Moreover, it has been observed that the participation of Mn^V?O, Mn^IV?O, and Mn^III? OOC(O)R can be controlled by changing the substrate concentration. This mechanism provides the greatest congruity with related oxidation reactions that employ certain Mn complexes as catalysts.     

A one‐dimensional chain structure based on unusual tetranuclear manganese(II) clusters

The title coordination polymer, poly[bis(μ₄‐biphenyl‐2,2′‐dicarboxylato)(dipyrido[3,2‐a:2′,3′‐c]phenazine)manganese(II)], [Mn₂(C₁₄H₈O₄)₂(C₁₈H₁₀N₄)]_n, was obtained through the reaction of MnCl₂·4H₂O, biphenyl‐2,2′‐dicarboxylic acid (H₂dpdc) and dipyrido[3,2‐a:2′,3′‐c]phenazine (L) under hydrothermal conditions. The asymmetric unit contains two crystallographically unique Mn^II ions, one unique L ligand and two unique dpdc ligands. One Mn ion is six‐coordinated by four O atoms from three different dpdc ligands and two N atoms from one L ligand, adopting a distorted octahedral coordination geometry. The distortions from ideal octahedral geometry are largely due to the presence of chelating ligands and the resulting acute N—Mn—N and O—Mn—O angles. The second Mn ion is coordinated in a distorted trigonal bipyramidal fashion by five O atoms from four distinct dpdc ligands. Four Mn^II ions are bridged by the carboxylate groups of the dpdc ligands to form an unusual tetranuclear Mn^II cluster. Clusters are further connected by the aromatic backbone of the dicarboxylate ligands, forming a one‐dimensional chain structure along the b axis. The title compound is the first example of a chain structure based on a tetranuclear Mn^II cluster.     

Visible‐Light‐Driven Water Oxidation by a Molecular Manganese Vanadium Oxide Cluster

Photosynthetic water oxidation in plants occurs at an inorganic calcium manganese oxo cluster, which is known as the oxygen evolving complex (OEC), in photosystem II. Herein, we report a synthetic OEC model based on a molecular manganese vanadium oxide cluster, [Mn₄V₄O₁₇(OAc)₃]^3?. The compound is based on a [Mn₄O₄]⁶⁺ cubane core, which catalyzes the homogeneous, visible‐light‐driven oxidation of water to molecular oxygen and is stabilized by a tripodal [V₄O₁₃]^6? polyoxovanadate and three acetate ligands. When combined with the photosensitizer [Ru(bpy)₃]²⁺ and the oxidant persulfate, visible‐light‐driven water oxidation with turnover numbers of approximately 1150 and turnover frequencies of about 1.75 s^?1 is observed. Electrochemical, mass‐spectrometric, and spectroscopic studies provide insight into the cluster stability and reactivity. This compound could serve as a model for the molecular structure and reactivity of the OEC and for heterogeneous metal oxide water‐oxidation catalysts.     

Diverse Ligand‐Functionalized Mixed‐Valent Hexamanganese Sandwiched Silicotungstates with Single‐Molecule Magnet Behavior

Under hydrothermal conditions, replacement of the water molecules in the [Mn^III₄Mn^II₂O₄(H₂O)₄]⁸⁺ cluster of mixed‐valent Mn₆ sandwiched silicotungstate [(B‐α‐SiW₉O₃₄)₂Mn^III₄Mn^II₂O₄(H₂O)₄]^12? ( 1 a ) with organic N ligands led to the isolation of five organic–inorganic hybrid, Mn₆‐substituted polyoxometalates (POMs) 2 – 6 . They were all structurally characterized by IR spectroscopy, elemental analysis, thermogravimetric analysis, diffuse‐reflectance spectroscopy, and powder and single‐crystal X‐ray diffraction. Compounds 2 – 6 represent the first series of mixed‐valent {Mn^III₄Mn^II₂O₄(H₂O)_4?n(L)_n} sandwiched POMs covalently functionalized by organic ligands. The preparation of 1 – 6 not only indicates that the double‐cubane {Mn^III₄Mn^II₂O₄(H₂O)_4?n(L)_n} clusters are very stable fragments in both conventional aqueous solution and hydrothermal systems and that organic functionalization of the [Mn^III₄Mn^II₂O₄(H₂O)₄]⁸⁺ cluster by substitution reactions is feasible, but also demonstrates that hydrothermal environments can promote and facilitate the occurrence of this substitution reaction. This work confirms that hydrothermal synthesis is effective for making novel mixed‐valent POMs substituted with transition‐metal (TM) clusters by combining lacunary Keggin precursors with TM cations and tunable organic ligands. Furthermore, magnetic measurements reveal that 3 and 6 exhibit single‐molecule magnet behavior.     

Cerium(IV)‐Driven Water Oxidation Catalyzed by a Manganese(V)–Nitrido Complex

The study of manganese complexes as water‐oxidation catalysts (WOCs) is of great interest because they can serve as models for the oxygen‐evolving complex of photosystem II. In most of the reported Mn‐based WOCs, manganese exists in the oxidation states III or IV, and the catalysts generally give low turnovers, especially with one‐electron oxidants such as Ce^IV. Now, a different class of Mn‐based catalysts, namely manganese(V)–nitrido complexes, were explored. The complex [Mn^V(N)(CN)₄]²⁻ turned out to be an active homogeneous WOC using (NH₄)₂[Ce(NO₃)₆] as the terminal oxidant, with a turnover number of higher than 180 and a maximum turnover frequency of 6 min⁻¹. The study suggests that active WOCs may be constructed based on the Mn^V(N) platform.     

Evidence of a Photo‐Radical Pathway Responsible of the Rearrangement of a Manganese(III)‐Schiff Base Complex in Solution

A new Mn^III‐Schiff base complex, [MnL(OH₂)](ClO₄) ( 1 ) (H₂L = N, N′‐bis‐(3‐Br‐5‐Cl‐salicylidene)‐1, 2‐diimino‐2‐methylethane), an inorganic model of the catalytic center (OEC, Oxygen Evolving Complex) in photosystem II (PSII), has been synthesized and characterized by elemental analysis, IR and EPR spectroscopy, mass spectrometry, magnetic susceptibility measurement and the study of its redox properties by cyclic and normal pulse voltammetry. This complex mimics reactivity (showing a relevant photolytic activity), and also some structural characteristics (parallel‐mode Mn^III EPR signal from partially assembled OEC cluster) of the natural OEC. The complex 1 was found to rearrange in solution into a crystallographically solved square‐pyramidal complex, [MnLL′] ( 2 ) (HL′ = 6‐bromo‐4‐chloro‐2‐cyanophenol), through a process, which probably liberates radical species (detected by EPR), and provokes a C—N bond cleavage in the ligand. A photo‐radical mechanism is discussed to explain this rearrangement.     

Magnetic “Molecular Oligomers” Based on Decametallic Supertetrahedra: A Giant Mn49 Cuboctahedron and its Mn25Na4 Fragment

Two nanosized Mn₄₉ and Mn₂₅Na₄ clusters based on analogues of the high‐spin (S=22) [Mn^III₆Mn^II₄(μ₄‐O)₄]¹⁸⁺ supertetrahedral core are reported. Mn₄₉ and Mn₂₅Na₄ complexes consist of eight and four decametallic supertetrahedral subunits, respectively, display high virtual symmetry (O_h), and are unique examples of clusters based on a large number of tightly linked high nuclearity magnetic units. The complexes also have large spin ground‐state values (Mn₄₉: S=61/2; Mn₂₅Na₄: S=51/2) with the Mn₄₉ cluster displaying single‐molecule magnet (SMM) behavior and being the second largest reported homometallic SMM.     

Diaquadichloridobis(1H‐imidazole)manganese(II) at 100 K

The mononuclear title complex, [MnCl₂(C₃H₄N₂)₂(H₂O)₂], is located on a crystallographic inversion center. The Mn^II ion is coordinated by two imidazole ligands [Mn—N = 2.2080 (9) Å], two Cl atoms [Mn—Cl = 2.5747 (3) Å] and two water molecules [Mn—O = 2.2064 (8) Å]. These six monodentate ligands define an octahedron with almost ideal angles: the adjacent N—Mn—O, N—Mn—Cl and O—Mn—Cl angles are 90.56 (3), 92.04 (2) and 90.21 (2)°, respectively. Hydrogen bonds between the coordinated water molecules and Cl atoms form a two‐dimensional network parallel to (100) involving R₄²(8) rings. The two‐dimensional networks link into a three‐dimensional framework through weaker N—H...Cl interactions. Thermogravimetric analysis results are in accordance with the water‐coordinated character of the substance and its dehydration in two successive steps.     

[Mn12O12(O2CMe)12(NO3)4(H2O)4]: facile synthesis of a new type of Mn12 complex

The title dodecanuclear Mn complex, namely dodeca‐μ₂‐acetato‐κ²⁴O:O′‐tetraaquatetra‐μ₂‐nitrato‐κ⁸O:O′‐tetra‐μ₄‐oxido‐octa‐μ₃‐oxido‐tetramanganese(IV)octamanganese(III) nitromethane tetrasolvate, [Mn₁₂(CH₃COO)₁₂(NO₃)₄O₁₂(H₂O)₄]·4CH₃NO₂, was synthesized by the reaction of Mn²⁺ and Ce⁴⁺ sources in nitromethane with an excess of acetic acid. This compound is distinct from the previously known single‐molecule magnet [Mn₁₂O₁₂(O₂CMe)₁₆(H₂O)₄], synthesized by Lis [Acta Cryst. (1980), B 36 , 2042–2044]. It is the first Mn₁₂‐type molecule containing nitrate ligands to be directly synthesized without the use of a preformed cluster. Additionally, this molecule is distinct from all other known Mn₁₂ complexes due to intermolecular hydrogen bonds between the nitrate and water ligands, which give rise to a three‐dimensional network. The complex is compared to other known Mn₁₂ molecules in terms of its structural parameters and symmetry.     

A Gas‐Phase CanMn4−nO4+ Cluster Model for the Oxygen‐Evolving Complex of Photosystem II

One of the fundamental processes in nature, the oxidation of water, is catalyzed by a small CaMn₃O₄?MnO cluster located in photosystem II (PS II). Now, the first successful preparation of a series of isolated ligand‐free tetrameric Ca_nMn_4?nO₄⁺ (n=0–4) cluster ions is reported, which are employed as structural models for the catalytically active site of PS II. Gas‐phase reactivity experiments with D₂O and H₂¹⁸O in an ion trap reveal the facile deprotonation of multiple water molecules via hydroxylation of the cluster oxo bridges for all investigated clusters. However, only the mono‐calcium cluster CaMn₃O₄⁺ is observed to oxidize water via elimination of hydrogen peroxide. First‐principles density functional theory (DFT) calculations elucidate mechanistic details of the deprotonation and oxidation reactions mediated by CaMn₃O₄⁺ as well as the role of calcium.     

Poly[[diaqua(μ3‐3‐nitrophthalato)calcium(II)] monohydrate]

The title 3‐nitrophthalate–calcium coordination polymer, {[Ca(C₈H₃NO₆)(H₂O)₂]·H₂O}_n, crystallizes as a one‐dimensional framework. The Ca^II centre has a distorted pentagonal–bipyramidal geometry, being seven‐coordinated by five O atoms from three different 3‐nitrophthalate groups and by two water molecules, resulting in a one‐dimensional zigzag chain along the a‐axis direction by the interconnection of the four O atoms from the two carboxylate groups. There is a D3 water cluster composed of the coordinated and the solvent water molecules within such chains. Adjacent chains are aggregated into two‐dimensional layers via hydrogen bonds in the c‐axis direction. The whole three‐dimensional structure is further stabilized by weak O—H...O hydrogen bonds between the O atoms of the nitro group and the water molecules.     

Tetraaquabis(d‐camphor‐10‐sulfonato)calcium(II)

The structure of the title compound, [Ca(C₁₀H₁₅O₄S)₂(H₂O)₄], is the first example in which two d ‐camphor‐10‐sulfonate anions are coordinated to a metal ion, in this case with direct Ca—O bonding. The molecule has crystallographically imposed twofold symmetry with the Ca atom on the twofold axis. Hydrogen bonds are formed between the coordinated water molecules and the O atoms of the SO₃⁻ groups of adjacent molecules, leading to the formation of a two‐dimensional layered network. The compound displays sharp wavelength‐selective transparency in the UV–visible spectrum, offering the potential for application as an optical filter.     

A novel bridged asymmetric binuclear manganese(II) complex with DTPB [DTPB is 1,1,4,7,7‐pentakis(1H‐benz­imidazol‐2‐yl­methyl)‐1,4,7‐tri­aza­heptane]

The crystal structure of the title compound, tetra­chloro­[μ‐1,1,4,7,7‐pentakis(1H‐benzimidazol‐2‐yl­methyl)‐1,4,7‐tri­azaheptane]­dimanganese(II) methanol pentasolvate tetrahydrate, [Mn₂Cl₄(C₄₄H₄₃N₁₃)]·5CH₄O·4H₂O, contains an ­asymmetric dinuclear Mn^II–DTPB [DTPB is 1,1,4,7,7‐pentakis(1H‐benzimidazol‐2‐yl­methyl)‐1,4,7‐tri­aza­heptane] complex with an intra‐ligand bridging group (–NCH₂CH₂N–), as well as several solvate mol­ecules (methanol and water). Both Mn^II cations have similar distorted octahedral coordination geometries. One Mn^II cation is coordinated by a Cl⁻ anion and five N atoms from the ligand, and the other is coordinated by three Cl⁻ anions and three N atoms of the same ligand. The Mn⋯Mn distance is 7.94 Å. A Cl⋯H—O⋯H—O⋯H—N hydrogen‐bond chain is also observed, connecting the two parts of the complex.     

Homoleptic Two‐Coordinate Silylamido Complexes of Chromium(I), Manganese(I), and Cobalt(I)

Anionic two‐coordinate complexes of first‐row transition‐metal(I) centres are rare molecules that are expected to reveal new magnetic properties and reactivity. Recently, we demonstrated that a N(SiMe₃)₂^? ligand set, which is unable to prevent dimerisation or extraneous ligand coordination at the +2 oxidation state of iron, was nonetheless able to stabilise anionic two‐coordinate Fe^I complexes even in the presence of a Lewis base. We now report analogous Cr^I and Co^I complexes with exclusively this amido ligand and the isolation of a [Mn^I{N(SiMe₃)₂}₂]₂^2? dimer that features a Mn?Mn bond. Additionally, by increasing the steric hindrance of the ligand set, the two‐coordinate complex [Mn^I{N(Dipp)(SiMe₃)}₂]^? was isolated (Dipp=2,6‐iPr₂‐C₆H₃). Characterisation of these compounds by using X‐ray crystallography, NMR spectroscopy, and magnetic susceptibility measurements is provided along with ligand‐field analysis based on CASSCF/NEVPT2 ab initio calculations.