Electrophotocatalytic perfluoroalkylation by LMCT excitation of Ag(II) perfluoroalkyl carboxylates.

Molecular Ag(II) complexes are superoxidizing photoredox catalysts capable of generating radicals from redox-reticent substrates. In this work, we exploited the electrophilicity of Ag(II) centers in [Ag(bpy)2(TFA)][OTf] and Ag(bpy)(TFA)2 (bpy, 2,2'-bipyridine; OTf, CF3SO3-) complexes to activate trifluoroacetate (TFA) by visible light-induced homolysis. The resulting trifluoromethyl radicals may react with a variety of arenes to forge C(sp2)-CF3 bonds. This methodology is general and extends to other perfluoroalkyl carboxylates of higher chain length (RFCO2-; RF, CF2CF3 or CF2CF2CF3). The photoredox reaction may be rendered electrophotocatalytic by regenerating the Ag(II) complexes electrochemically during irradiation. Electrophotocatalytic perfluoroalkylation of arenes at turnover numbers exceeding 20 was accomplished by photoexciting the Ag(II)-TFA ligand-to-metal charge transfer (LMCT) state, followed by electrochemical reoxidation of the Ag(I) photoproduct back to the Ag(II) photoreactant.

Oxidation Chemistry of Bicarbonate and Peroxybicarbonate: Implications for Carbonate Management in Energy Storage.

Carbonate formation presents a major challenge to energy storage applications based on low-temperature CO2 electrolysis and recyclable metal-air batteries. While direct electrochemical oxidation of (bi)carbonate represents a straightforward route for carbonate management, knowledge of the feasibility and mechanisms of direct oxidation is presently lacking. Herein, we report the isolation and characterization of the bis(triphenylphosphine)iminium salts of bicarbonate and peroxybicarbonate, thus enabling the examination of their oxidation chemistry. Infrared spectroelectrochemistry combined with time-resolved infrared spectroscopy reveals that the photoinduced oxidation of HCO3- by an Ir(III) photoreagent results in the generation of the short-lived bicarbonate radical in less than 50 ns. The highly acidic bicarbonate radical undergoes proton transfer with HCO3- to furnish the carbonate radical anion and H2CO3, leading to the eventual release of CO2 and H2O, thus accounting for the appearance of H2O and CO2 in both electrochemical and photochemical oxidation experiments. The back reaction of the carbonate radical subsequently oxidizes the Ir(II) photoreagent, leading to carbonate. In the absence of this back reaction, dimerization of the carbonate radical provides entry into peroxybicarbonate, which we show undergoes facile oxidation to O2 and CO2. Together, the results reported identify tangible pathways for the design of catalysts for the management of carbonate in energy storage applications.

Taming the Chlorine Radical: Enforcing Steric Control over Chlorine-Radical-Mediated C-H Activation.

Chlorine radicals readily activate C-H bonds, but the high reactivity of these intermediates precludes their use in regioselective C-H functionalization reactions. We demonstrate that the secondary coordination sphere of a metal complex can confine photoeliminated chlorine radicals and afford steric control over their reactivity. Specifically, a series of iron(III) chloride pyridinediimine complexes exhibit activity for photochemical C(sp3)-H chlorination and bromination with selectivity for primary and secondary C-H bonds, overriding thermodynamic preference for weaker tertiary C-H bonds. Transient absorption spectroscopy reveals that Cl· remains confined through formation of a Cl·|arene complex with aromatic groups on the pyridinediimine ligand. Furthermore, photocrystallography confirms that this selectivity arises from the generation of Cl· within the steric environment defined by the iron secondary coordination sphere.

Templated Growth of a Spin-Frustrated Cluster Fragment of MnBr2 in a Metal-Organic Framework.

The metal-organic framework Zr6O4(OH)4(bpydc)6 (bpydc2- = 2,2'-bipyridine-5,5'-dicarboxylate) is used to template the growth of a cluster fragment of the two-dimensional solid MnBr2, which was predicted to exhibit spin frustration. Single-crystal and powder X-ray diffraction analyses reveal a cluster with 19 metal ions arranged in a triangular lattice motif. Static magnetic susceptibility measurements indicate antiferromagnetic coupling between the high-spin (S = 5/2) MnII centers, and dynamic magnetic susceptibility data suggest population of low-lying excited states, consistent with magnetic frustration. Density functional theory calculations are used to determine the energies for a subset of thousands of magnetic configurations available to the cluster. The Yamaguchi generalized spin-projection method is then employed to construct a model for magnetic coupling interactions within the cluster, enabling facile determination of the energy for all possible magnetic configurations. The confined cluster is predicted to possess a doubly degenerate, highly geometrically frustrated ground state with a total spin of STotal = 5/2.

How Radical Are "Radical" Photocatalysts? A Closed-Shell Meisenheimer Complex Is Identified as a Super-Reducing Photoreagent.

Super-reducing excited states have the potential to activate strong bonds, leading to unprecedented photoreactivity. Excited states of radical anions, accessed via reduction of a precatalyst followed by light absorption, have been proposed to drive photoredox transformations under super-reducing conditions. Here, we investigate the radical anion of naphthalene monoimide as a photoreductant and find that the radical doublet excited state has a lifetime of 24 ps, which is too short to facilitate photoredox activity. To account for the apparent photoreactivity of the radical anion, we identify an emissive two-electron reduced Meisenheimer complex of naphthalene monoimide, [NMI(H)]-. The singlet excited state of [NMI(H)]- is a potent reductant (-3.08 V vs Fc/Fc+), is long-lived (20 ns), and its emission can be dynamically quenched by chloroarenes to drive a radical photochemistry, establishing that it is this emissive excited state that is competent for reported C-C and C-P coupling reactivity. These results provide a mechanistic basis for photoreactivity at highly reducing potentials via singlet excited state manifolds and lays out a clear path for the development of exceptionally reducing photoreagents derived from electron-rich closed-shell anions.

Capturing the Complete Reaction Profile of a C-H Bond Activation.

The activation of C-H bonds requires the generation of extremely reactive species, which hinders the study of this reaction and its key intermediates. To overcome this challenge, we synthesized an iron(III) chloride-pyridinediimine complex that generates a chlorine radical proximate to reactive C-H bonds upon irradiation with light. Transient spectroscopy confirms the formation of a Cl·|arene complex, which then activates C-H bonds on the PDI ligand to yield HCl and a carbon-centered radical as determined by photocrystallography. First-principles molecular dynamics-density functional theory calculations reveal the trajectory for the formation of a Cl·|arene intermediate. Together, these experimental and computational results show the complete reaction profile for the preferential activation of a C-H bond in the solid state.

Network-Forming Liquids from Metal-Bis(acetamide) Frameworks with Low Melting Temperatures.

Molten phases of metal-organic networks offer exciting opportunities for using coordination chemistry principles to access liquids and glasses with unique and tunable structures and properties. Here, we discuss general thermodynamic strategies to provide an increased enthalpic and entropic driving force for reversible, low-temperature melting transitions in extended coordination solids and illustrate this approach through a systematic study of a series of bis(acetamide)-based networks with record-low melting temperatures. The low melting temperatures of these compounds are the result of weak coordination bonds, conformationally flexible bridging ligands, and weak electrostatic interactions between spatially separated cations and anions, which collectively reduce the enthalpy and increase the entropy of fusion. Through a combination of crystallography, spectroscopy, and calorimetry, enthalpic trends are found to be dictated by the strength of coordination bonds and hydrogen bonds within each compound, while entropic trends are strongly influenced by the degree to which residual motion and positional disorder are restricted in the crystalline state. Extended X-ray absorption fine structure (EXAFS) and pair distribution function (PDF) analysis of Co(bba)3[CoCl4] [bba = N,N'-1,4-butylenebis(acetamide)], which features a record-low melting temperature for a three-dimensional metal-organic network of 124 °C, provide direct evidence of metal-ligand coordination in the liquid phase, as well as intermediate- and extended-range order that support its network-forming nature. In addition, rheological measurements are used to rationalize differences in glass-forming ability and relaxation dynamics. These results provide new insights into the structural and chemical factors that influence the thermodynamics of melting transitions of extended coordination solids, as well as the structure and properties of coordination network-forming liquids.

Fluoroarene Separations in Metal-Organic Frameworks with Two Proximal Mg2+ Coordination Sites.

Fluoroarenes are widely used in medicinal, agricultural, and materials chemistry, and yet their production remains a critical challenge in organic synthesis. Indeed, the nearly identical physical properties of these vital building blocks hinders their purification by traditional methods, such as flash chromatography or distillation. As a result, the Balz-Schiemann reaction is currently employed to prepare fluoroarenes instead of more atom-economical C-H fluorination reactions, which produce inseparable mixtures of regioisomers. Herein, we propose an alternative solution to this problem: the purification of mixtures of fluoroarenes using metal-organic frameworks (MOFs). Specifically, we demonstrate that controlling the interaction of fluoroarenes with adjacent coordinatively unsaturated Mg2+ centers within a MOF enables the separation of fluoroarene mixtures with unparalleled selectivities. Liquid-phase multicomponent equilibrium adsorption data and breakthrough measurements coupled with van der Waals-corrected density functional theory calculations reveal that the materials Mg2(dobdc) (dobdc4- = 2,5-dioxidobenzene-1,4-dicarboxylate) and Mg2(m-dobdc) (m-dobdc4- = 2,4-dioxidobenzene-1,5-dicarboxylate) are capable of separating the difluorobenzene isomers from one another. Additionally, these frameworks facilitate the separations of fluoroanisoles, fluorotoluenes, and fluorochlorobenzenes. In addition to enabling currently unfeasible separations for the production of fluoroarenes, our results suggest that carefully controlling the interaction of isomers with not one but two strong binding sites within a MOF provides a general strategy for achieving challenging liquid-phase separations.

Substituent Effects on Exchange Coupling and Magnetic Relaxation in 2,2'-Bipyrimidine Radical-Bridged Dilanthanide Complexes.

Systematic analysis of related compounds is crucial to the design of single-molecule magnets with improved properties, yet such studies on multinuclear lanthanide complexes with strong magnetic coupling remain rare. Herein, we present the synthesis and magnetic characterization of the series of radical-bridged dilanthanide complex salts [(Cp*2Ln)2(µ-5,5'-R2bpym)](BPh4) (Ln = Gd, Dy; R = NMe2 (1), OEt (2), Me (3), F (4); bpym = 2,2'-bipyrimidine). Modification of the substituent on the bridging 5,5'-R2bpym radical anion allows the magnetic exchange coupling constant, JGd-rad, for the gadolinium compounds in this series to be tuned over a range from -2.7 cm-1 (1) to -11.1 cm-1 (4), with electron-withdrawing or -donating substituents increasing or decreasing the strength of exchange coupling, respectively. Modulation of the exchange coupling interaction has a significant impact on the magnetic relaxation dynamics of the single-molecule magnets 1-Dy through 4-Dy, where stronger JGd-rad for the corresponding Gd3+ compounds is associated with larger thermal barriers to magnetic relaxation (Ueff), open magnetic hysteresis at higher temperatures, and slower magnetic relaxation rates for through-barrier processes. Further, we derive an empirical linear correlation between the experimental Ueff values for 1-Dy through 4-Dy and the magnitude of JGd-rad for the corresponding gadolinium derivatives that provides insight into the electronic structure of these complexes. This simple model applies to other organic radical-bridged dysprosium complexes in the literature, and it establishes clear design criteria for increasing magnetic operating temperatures in radical-bridged molecules.

Metal-Organic Phase-Change Materials for Thermal Energy Storage.

The development of materials that reversibly store high densities of thermal energy is critical to the more efficient and sustainable utilization of energy. Herein, we investigate metal-organic compounds as a new class of solid-liquid phase-change materials (PCMs) for thermal energy storage. Specifically, we show that isostructural series of divalent metal amide complexes featuring extended hydrogen bond networks can undergo tunable, high-enthalpy melting transitions over a wide temperature range. Moreover, these coordination compounds provide a powerful platform to explore the specific factors that contribute to the energy density and entropy of metal-organic PCMs. Through a systematic analysis of the structural and thermochemical properties of these compounds, we investigated the influence of coordination bonds, hydrogen-bond networks, neutral organic ligands, and outer-sphere anions on their phase-change thermodynamics. In particular, we identify the importance of high densities of coordination bonds and hydrogen bonds to achieving a high PCM energy density, and we show how metal-dependent changes to the local coordination environment during melting impact the entropy and enthalpy of metal-organic PCMs. These results highlight the potential of manipulating order-disorder phase transitions in metal-organic materials for thermal energy storage.

Multielectron C-H photoactivation with an Sb(v) oxo corrole.

Pnictogen complexes are ideal for mediating multi-electron chemical reactions in two-electron steps. We report an Sb(v) bis-µ-oxo corrole that photochemically oxidises the C-H bonds of organic substrates. In the case of toluene, the substrate is oxidised to benzaldehyde, a rare example of a four-electron photoreaction.

Double Hangman Iron Porphyrin and the Effect of Electrostatic Nonbonding Interactions on Carbon Dioxide Reduction.

Hangman porphyrins influence the reaction rates of small molecule activation by positioning a functional group in the secondary coordination sphere of the metal center. Electrocatalysis by hangman porphyrins has examined only one face modification of the macrocycle with a hanging group, thus allowing for circumvention of secondary sphere effects by reaction of the small molecule on the opposite face of the hangman cleft. We now report the synthesis and characterization of a double hangman Fe porphyrin in which both faces of the macrocycle are modified with a hanging group. With this double hangman architecture, we are able to unequivocally examine the role of electrostatic interactions on the carbon dioxide reduction reaction (CO2RR) and show that CO2RR rates are significantly attenuated, consistent with the initial reduction of CO2 to generate the anion, whose binding is diminished within the negatively charged carboxylic groups of the hangman cleft. The results demonstrate the pronounced role that nonbonding electrostatic interactions may play in CO2RR and highlight the need to manage deleterious electrostatic interactions during catalytic turnover.

Crystallographic characterization of the metal-organic framework Fe2(bdp)3 upon reductive cation insertion.

Precisely locating extra-framework cations in anionic metal-organic framework compounds remains a long-standing, yet crucial, challenge for elucidating structure-performance relationships in functional materials. Single-crystal X-ray diffraction is one of the most powerful approaches for this task, but single crystals of frameworks often degrade when subjected to post-synthetic metalation or reduction. Here, we demonstrate the growth of sizable single crystals of the robust metal-organic framework Fe2(bdp)3 (bdp2- = benzene-1,4-dipyrazolate) and employ single-crystal-to-single-crystal chemical reductions to access the solvated framework materials A2Fe2(bdp)3·yTHF (A = Li+, Na+, K+). X-ray diffraction analysis of the sodium and potassium congeners reveals that the cations are located near the center of the triangular framework channels and are stabilized by weak cation-π interactions with the framework ligands. Freeze-drying with benzene enables isolation of activated single crystals of Na0.5Fe2(bdp)3 and Li2Fe2(bdp)3 and the first structural characterization of activated metal-organic frameworks wherein extra-framework alkali metal cations are also structurally located. Comparison of the solvated and activated sodium-containing structures reveals that the cation positions differ in the two materials, likely due to cation migration that occurs upon solvent removal to maximize stabilizing cation-π interactions. Hydrogen adsorption data indicate that these cation-framework interactions are sufficient to diminish the effective cationic charge, leading to little or no enhancement in gas uptake relative to Fe2(bdp)3. In contrast, Mg0.85Fe2(bdp)3 exhibits enhanced H2 affinity and capacity over the non-reduced parent material. This observation shows that increasing the charge density of the pore-residing cation serves to compensate for charge dampening effects resulting from cation-framework interactions and thereby promotes stronger cation-H2 interactions.

Confinement of atomically defined metal halide sheets in a metal-organic framework.

The size-dependent and shape-dependent characteristics that distinguish nanoscale materials from bulk solids arise from constraining the dimensionality of an inorganic structure1-3. As a consequence, many studies have focused on rationally shaping these materials to influence and enhance their optical, electronic, magnetic and catalytic properties4-6. Although a select number of stable clusters can typically be synthesized within the nanoscale regime for a specific composition, isolating clusters of a predetermined size and shape remains a challenge, especially for those derived from two-dimensional materials. Here we realize a multidentate coordination environment in a metal-organic framework to stabilize discrete inorganic clusters within a porous crystalline support. We show confined growth of atomically defined nickel(II) bromide, nickel(II) chloride, cobalt(II) chloride and iron(II) chloride sheets through the peripheral coordination of six chelating bipyridine linkers. Notably, confinement within the framework defines the structure and composition of these sheets and facilitates their precise characterization by crystallography. Each metal(II) halide sheet represents a fragment excised from a single layer of the bulk solid structure, and structures obtained at different precursor loadings enable observation of successive stages of sheet assembly. Finally, the isolated sheets exhibit magnetic behaviours distinct from those of the bulk metal halides, including the isolation of ferromagnetically coupled large-spin ground states through the elimination of long-range, interlayer magnetic ordering. Overall, these results demonstrate that the pore environment of a metal-organic framework can be designed to afford precise control over the size, structure and spatial arrangement of inorganic clusters.

Thermodynamic Separation of 1-Butene from 2-Butene in Metal-Organic Frameworks with Open Metal Sites.

Most C4 hydrocarbons are obtained as byproducts of ethylene production or oil refining, and complex and energy-intensive separation schemes are required for their isolation. Substantial industrial and academic effort has been expended to develop more cost-effective adsorbent- or membrane-based approaches to purify commodity chemicals such as 1,3-butadiene, isobutene, and 1-butene, but the very similar physical properties of these C4 hydrocarbons make this a challenging task. Here, we examine the adsorption behavior of 1-butene, cis-2-butene, and trans-2-butene in the metal-organic frameworks M2(dobdc) (M = Mn, Fe, Co, Ni; dobdc4- = 2,5-dioxidobenzene-1,4-dicarboxylate) and M2(m-dobdc) (m-dobdc4- = 4,6-dioxidobenzene-1,3-dicarboxylate), which all contain a high density of coordinatively unsaturated M2+ sites. We find that both Co2(m-dobdc) and Ni2(m-dobdc) are able to separate 1-butene from the 2-butene isomers, a critical industrial process that relies largely on energetically demanding cryogenic distillation. The origin of 1-butene selectivity is traced to the high charge density retained by the M2+ metal centers exposed within the M2(m-dobdc) structures, which results in a reversal of the cis-2-butene selectivity typically observed at framework open metal sites. Selectivity for 1-butene adsorption under multicomponent conditions is demonstrated for Ni2(m-dobdc) in both the gaseous and the liquid phases via breakthrough and batch adsorption experiments.

Cooperative adsorption of carbon disulfide in diamine-appended metal-organic frameworks.

Over one million tons of CS2 are produced annually, and emissions of this volatile and toxic liquid, known to generate acid rain, remain poorly controlled. As such, materials capable of reversibly capturing this commodity chemical in an energy-efficient manner are of interest. Recently, we detailed diamine-appended metal-organic frameworks capable of selectively capturing CO2 through a cooperative insertion mechanism that promotes efficient adsorption-desorption cycling. We therefore sought to explore the ability of these materials to capture CS2 through a similar mechanism. Employing crystallography, spectroscopy, and gas adsorption analysis, we demonstrate that CS2 is indeed cooperatively adsorbed in N,N-dimethylethylenediamine-appended M2(dobpdc) (M = Mg, Mn, Zn; dobpdc4- = 4,4'-dioxidobiphenyl-3,3'-dicarboxylate), via the formation of electrostatically paired ammonium dithiocarbamate chains. In the weakly thiophilic Mg congener, chemisorption is cleanly reversible with mild thermal input. This work demonstrates that the cooperative insertion mechanism can be generalized to other high-impact target molecules.

Elucidating CO2 Chemisorption in Diamine-Appended Metal-Organic Frameworks.

The widespread deployment of carbon capture and sequestration as a climate change mitigation strategy could be facilitated by the development of more energy-efficient adsorbents. Diamine-appended metal-organic frameworks of the type diamine-M2(dobpdc) (M = Mg, Mn, Fe, Co, Ni, Zn; dobpdc4- = 4,4'-dioxidobiphenyl-3,3'-dicarboxylate) have shown promise for carbon-capture applications, although questions remain regarding the molecular mechanisms of CO2 uptake in these materials. Here we leverage the crystallinity and tunability of this class of frameworks to perform a comprehensive study of CO2 chemisorption. Using multinuclear nuclear magnetic resonance (NMR) spectroscopy experiments and van-der-Waals-corrected density functional theory (DFT) calculations for 13 diamine-M2(dobpdc) variants, we demonstrate that the canonical CO2 chemisorption products, ammonium carbamate chains and carbamic acid pairs, can be readily distinguished and that ammonium carbamate chain formation dominates for diamine-Mg2(dobpdc) materials. In addition, we elucidate a new chemisorption mechanism in the material dmpn-Mg2(dobpdc) (dmpn = 2,2-dimethyl-1,3-diaminopropane), which involves the formation of a 1:1 mixture of ammonium carbamate and carbamic acid and accounts for the unusual adsorption properties of this material. Finally, we show that the presence of water plays an important role in directing the mechanisms for CO2 uptake in diamine-M2(dobpdc) materials. Overall, our combined NMR and DFT approach enables a thorough depiction and understanding of CO2 adsorption within diamine-M2(dobpdc) compounds, which may aid similar studies in other amine-functionalized adsorbents in the future.

Separation of Xylene Isomers through Multiple Metal Site Interactions in Metal-Organic Frameworks.

Purification of the C8 alkylaromatics o-xylene, m-xylene, p-xylene, and ethylbenzene remains among the most challenging industrial separations, due to the similar shapes, boiling points, and polarities of these molecules. Herein, we report the evaluation of the metal-organic frameworks Co2(dobdc) (dobdc4- = 2,5-dioxido-1,4-benzenedicarboxylate) and Co2( m-dobdc) ( m-dobdc4- = 4,6-dioxido-1,3-benzenedicarboxylate) for the separation of xylene isomers using single-component adsorption isotherms and multicomponent breakthrough measurements. Remarkably, Co2(dobdc) distinguishes among all four molecules, with binding affinities that follow the trend o-xylene > ethylbenzene > m-xylene > p-xylene. Multicomponent liquid-phase adsorption measurements further demonstrate that Co2(dobdc) maintains this selectivity over a wide range of concentrations. Structural characterization by single-crystal X-ray diffraction reveals that both frameworks facilitate the separation through the extent of interaction between each C8 guest molecule with two adjacent cobalt(II) centers, as well as the ability of each isomer to pack within the framework pores. Moreover, counter to the presumed rigidity of the M2(dobdc) structure, Co2(dobdc) exhibits an unexpected structural distortion in the presence of either o-xylene or ethylbenzene that enables the accommodation of additional guest molecules.

Unexpected Diffusion Anisotropy of Carbon Dioxide in the Metal-Organic Framework Zn2(dobpdc).

Metal-organic frameworks are promising materials for energy-efficient gas separations, but little is known about the diffusion of adsorbates in materials featuring one-dimensional porosity at the nanoscale. An understanding of the interplay between framework structure and gas diffusion is crucial for the practical application of these materials as adsorbents or in mixed-matrix membranes, since the rate of gas diffusion within the adsorbent pores impacts the required size (and therefore cost) of the adsorbent column or membrane. Here, we investigate the diffusion of CO2 within the pores of Zn2(dobpdc) (dobpdc4- = 4,4'-dioxidobiphenyl-3,3'-dicarboxylate) using pulsed field gradient (PFG) nuclear magnetic resonance (NMR) spectroscopy and molecular dynamics (MD) simulations. The residual chemical shift anisotropy for pore-confined CO2 allows PFG NMR measurements of self-diffusion in different crystallographic directions, and our analysis of the entire NMR line shape as a function of the applied field gradient provides a precise determination of the self-diffusion coefficients. In addition to observing CO2 diffusion through the channels parallel to the crystallographic c axis (self-diffusion coefficient D∥ = (5.8 ± 0.1) × 10-9 m2 s-1 at a pressure of 625 mbar CO2), we unexpectedly find that CO2 is also able to diffuse between the hexagonal channels in the crystallographic ab plane (D⊥ = (1.9 ± 0.2) × 10-10 m2 s-1), despite the walls of these channels appearing impermeable by single-crystal X-ray crystallography and flexible lattice MD simulations. Observation of such unexpected diffusion in the ab plane suggests the presence of defects that enable effective multidimensional CO2 transport in a metal-organic framework with nominally one-dimensional porosity.

A Terminal Fluoride Ligand Generates Axial Magnetic Anisotropy in Dysprosium Complexes.

The first dysprosium complexes with a terminal fluoride ligand are obtained as air-stable compounds. The strong, highly electrostatic dysprosium-fluoride bond generates a large axial crystal-field splitting of the J=15/2 ground state, as evidenced by high-resolution luminescence spectroscopy and correlated with the single-molecule magnet behavior through experimental magnetic susceptibility data and ab initio calculations.