Carbon dioxide capture from open air using covalent organic frameworks.

Capture of CO2 from the air offers a promising approach to addressing climate change and achieving carbon neutrality goals1,2. However, the development of a durable material with high capacity, fast kinetics and low regeneration temperature for CO2 capture, especially from the intricate and dynamic atmosphere, is still lacking. Here a porous, crystalline covalent organic framework (COF) with olefin linkages has been synthesized, structurally characterized and post-synthetically modified by the covalent attachment of amine initiators for producing polyamines within the pores. This COF (termed COF-999) can capture CO2 from open air. COF-999 has a capacity of 0.96 mmol g-1 under dry conditions and 2.05 mmol g-1 under 50% relative humidity, both from 400 ppm CO2. This COF was tested for more than 100 adsorption-desorption cycles in the open air of Berkeley, California, and found to fully retain its performance. COF-999 is an exceptional material for the capture of CO2 from open air as evidenced by its cycling stability, facile uptake of CO2 (reaches half capacity in 18.8 min) and low regeneration temperature (60 °C).

Chemically accurate predictions for water adsorption on Brønsted sites of zeolite H-MFI.

We investigate the adsorption of water molecules in the zeolite H-MFI at isolated Brønsted acid sites (BAS) for loadings of 1, 2, and 3 H2O/BAS. We consider two approaches to the O3Al-O(H)-Si sites: the Brønsted-type approach of H2O to the acidic proton and the Lewis-type approach to the aluminium atom of the AlO4 tetrahedron. From the twelve crystallographically inequivalent framework sites for Al, a representative set of six active site positions is chosen. For them, we calculate CCSD(T)-quality adsorption energies at MP2-quality adsorption structures for different approaches, 48 in total. The Brønsted-type approach is favoured for most cases but the Lewis-type approach has similar stability for some framework positions. We predict heats of adsorption per molecule ranging from 60 to 76, 56 to 65, and 56 to 64 kJ mol-1 for loadings of 1, 2, and 3 H2O/BAS, respectively. For 1 H2O/BAS, the experimental result (70 kJ mol-1) falls into the range of our predictions, whereas for 2 and 3 H2O/BAS, the measured adsorption heats per molecule (74 and 70 kJ mol-1, respectively) are larger than our predictions. For 2 H2O/BAS, the ion-pair structure generated by proton transfer to the water dimer competes with the neutral adsorption complex. The DFT adsorption energies (PBE+D2) deviate significantly from the CCSD(T)-quality reference energies, by up to 25 kJ mol-1 for 1 H2O/BAS, 25 kJ mol-1 per H2O for 2 H2O/BAS, and 18 kJ mol-1 per H2O for 3 H2O/BAS. Specifically, PBE+D2 overstabilises the ion-pair structure, i.e. in many cases the PBE+D2 error is much larger for ionic than for neutral adsorption structures.

Spectroscopic Signatures of Internal Hydrogen Bonds of Brønsted-Acid Sites in the Zeolite H-MFI.

The location of Brønsted-acid sites (bridging OH groups, b-OH) at different crystallographic positions of zeolite catalysts influences their reactivity due to varying confinement. Selecting the most stable b-OH conformers at each of the 12 T-sites (T=Si/Al) of H-MFI, a representative set of 26 conformers is obtained which includes free b-OH groups pointing into the empty pore space and b-OH groups forming H-bonds across five- or six-membered rings of TO4 tetrahedra. Chemically accurate coupled-cluster-quality calculations for periodic models show that the strength of internal H-bonds and, hence, the OH bond length vary substantially with the framework position. For 11 of the 19 H-bonded b-OH groups examined, our predictions fall into the full width at half maximum range of the experimental signals at 3250±175 cm-1 and 7.0±1.4 ppm which supports previously debated assignments of these signals to H-bonded b-OH sites.

Infrared photodissociation spectroscopy of (Al2O3)2-5FeO+: influence of Fe-substitution on small alumina clusters.

The infrared photodissociation spectra of He-tagged (Al2O3)nFeO+ (n = 2-5), are reported in the Al-O and Fe-O stretching and bending spectral region (430-1200 cm-1) and assigned based on calculated harmonic IR spectra from density functional theory (DFT). The substitution of Fe for an Al center occurs preferentially at 3-fold oxygen coordination sites located at the cluster rim and with the Fe atom in the +III oxidation state. The accompanying elongation of metal oxygen bonds leaves the Al-O network structure nearly unperturbed (isomorphous substitution). Contrary to the Al2FeO4+ (n = 1), valence isomerism is not observed, which is attributed to a smaller M:O ratio (M = Al, Fe) and consequently decreasing electron affinities with increasing cluster size.

Gas-Phase Mechanism of O.- /Ni2+ -Mediated Methane Conversion to Formaldehyde.

The gas-phase reaction of NiAl2 O4 + with CH4 is studied by mass spectrometry in combination with vibrational action spectroscopy and density functional theory (DFT). Two product ions, NiAl2 O4 H+ and NiAl2 O3 H2 + , are identified in the mass spectra. The DFT calculations predict that the global minimum-energy isomer of NiAl2 O4 + contains Ni in the +II oxidation state and features a terminal Al-O.- oxygen radical site. They show that methane can react along two competing pathways leading to formation of either a methyl radical (CH3 ⋅) or formaldehyde (CH2 O). Both reactions are initiated by hydrogen atom transfer from methane to the terminal O.- site, followed by either CH3 ⋅ loss or CH3 ⋅ migration to an O2- site next to the Ni2+ center. The CH3 ⋅ attaches as CH3 + to O2- and its unpaired electron is transferred to the Ni-center reducing it to Ni+ . The proposed mechanism is experimentally confirmed by vibrational spectroscopy of the reactant and two different product ions.

Insights into Reaction Kinetics in Confined Space: Real Time Observation of Water Formation under a Silica Cover.

We offer a comprehensive approach to determine how physical confinement can affect the water formation reaction. By using free-standing crystalline SiO2 bilayer supported on Ru(0001) as a model system, we studied the water formation reaction under confinement in situ and in real time. Low-energy electron microscopy reveals that the reaction proceeds via the formation of reaction fronts propagating across the Ru(0001) surface. The Arrhenius analyses of the front velocity yield apparent activation energies (Eaapp) of 0.32 eV for the confined and 0.59 eV for the nonconfined reaction. DFT simulations indicate that the rate-determining step remains unchanged upon confinement, therefore ruling out the widely accepted transition state effect. Additionally, H2O accumulation cannot explain the change in Eaapp for the confined cases studied because its concentration remains low. Instead, numerical simulations of the proposed kinetic model suggest that the H2 adsorption process plays a decisive role in reproducing the Arrhenius plots.

The Chemical Nature of Ti4O10-: Vibrational Predissociation Spectroscopy Combined with Global Structure Optimization.

The gas-phase infrared spectrum of Ti4O10- is studied in the spectral range from 400 cm-1 to 1250 cm-1 using cryogenic ion trap vibrational spectroscopy, in combination with density functional theory (DFT). The infrared photodissociation (IRPD) spectrum of D2-tagged Ti4O10- provides evidence for a structure of lower symmetry that contains a superoxo group (1121 cm-1) and two terminal Ti=O moieties. DFT combined with a genetic algorithm for global structure optimization predicts two isomers which feature a superoxo group: the Cs symmetric global minimum-energy structure and a similar isomer (C1) that is slightly higher in energy. Coupled cluster calculations confirm the relative stability. Comparison of the harmonic DFT spectra (different functionals) with the IRPD spectrum suggests that both of these isomers contribute. Earlier assignments to the adamantane-like C3v isomer with three terminal Ti-O• - groups in a quartet state are not confirmed. They were based on the infrared multiple photon photodissociation (IRMPD) spectrum of bare Ti4O10- and local DFT structure optimizations.

Adsorption of CH4 on the Pt(111) surface: Random phase approximation compared to density functional theory.

We investigate the adsorption of CH4 on the Pt(111) surface for two adsorption modes, hcp (hexagonal closed packed) hollow tripod and top monopod in a (√3 × âˆš3)R30° surface cell that corresponds to experimental surface coverage. Surface structures are optimized with density functional theory using the Perdew-Burke-Ernzerhof (PBE) functional augmented with the many-body dispersion scheme of Tkatchenko (PBE+MBD). Whereas the Random Phase Approximation (RPA) predicts a clear preference of about 5 kJ mol-1 for the hcp tripod compared to the top monopod structure, in agreement with vibrational spectra, PBE+MBD predicts about equal stability for the two adsorption structures. For the hcp tripod, RPA yields an adsorption energy of -14.5 kJ mol-1, which is converged to within 1.0 ± 0.5 kJ mol-1 with respect to the plane wave energy cutoff (500 eV), the k-point mesh (4 × 4 × 1), the vacuum layer (about 10.3 Å, with extrapolation to infinite distance), and the number of Pt layers (3). Increments for increasing the number of Pt layers to 4 (+1.6 kJ mol-1) and the k-point mesh to 6 × 6 × 1 (-0.6 kJ mol-1) yield a final estimate of -13.5 ± 2.1 kJ mol-1, which agrees to within 2.2 ± 2.1 kJ mol-1 with experiment (-15.7 ± 1.6), well within the chemical accuracy range.

Dimerization of Linear Butenes and Pentenes in an Acidic Zeolite (H-MFI).

Quantum chemical evidence is produced to show that dimerization of linear butenes and pentenes at zeolitic Brønsted sites in H-MFI yields alkanes featuring cyclohexane rings rather than branched alkenes. The absence of any C=C double bond in the formed cyclic alkane explains the observations that oligomerization stops at the dimer. The calculated reaction enthalpies for the dimerization of 2-pentene in the gas phase are -84 kJ mol-1 for branched alkenes, but -153 and -154 kJ mol-1 for alkyl-cyclopentane and -hexane, respectively. Together with calculated adsorption enthalpies of the dimers, -111 and -127 kJ mol-1 , respectively, this implies surface dimer formation enthalpies of -264 and -281 kJ mol-1 , respectively, in close agreement with the experimental value of -285 kJ mol-1 . In contrast, the predicted enthalpy for formation of branched alkoxides, -198 kJ mol-1 , deviates by 87 kJ mol-1 from experiment. Calculated IR spectra for the Brønsted OH group show the observed conversion of the band at approximately 3000 cm-1 (hydrogen bond with alkene) to a less intense band at approximately 3450-3500 cm-1 (interaction with alkane).

Valence and Structure Isomerism of Al2FeO4+: Synergy of Spectroscopy and Quantum Chemistry.

We provide spectroscopic and computational evidence for a substantial change in structure and gas phase reactivity of Al3O4+ upon Fe-substitution, which is correctly predicted by multireference (MR) wave function calculations. Al3O4+ exhibits a cone-like structure with a central trivalent O atom (C3v symmetry). The replacement of the Al- by an Fe atom leads to a planar bicyclic frame with a terminal Al-O•- radical site, accompanied by a change from the Fe+III/O-II to the Fe+II/O-I valence state. The gas phase vibrational spectrum of Al2FeO4+ is exclusively reproduced by the latter structure, which MR wave function calculations correctly identify as the most stable isomer. This isomer of Al2FeO4+ is predicted to be highly reactive with respect to C-H bond activation, very similar to Al8O12+ which also features the terminal Al-O•- radical site. Density functional theory, in contrast, predicts a less reactive Al3O4+-like "isomorphous substitution" structure of Al2FeO4+ to be the most stable one, except for functionals with very high admixture of Fock exchange (50%, BHLYP).

Elucidating Surface Structure with Action Spectroscopy.

Surface Action Spectroscopy, a vibrational spectroscopy method developed in recent years at the Fritz Haber Institute is employed for structure determination of clean and H2O-dosed (111) magnetite surfaces. Surface structural information is revealed by using the microscopic surface vibrations as a fingerprint of the surface structure. Such vibrations involve just the topmost atomic layers, and therefore the structural information is truly surface related. Our results strongly support the view that regular Fe3O4(111)/Pt(111) is terminated by the so-called Fetet1 termination, that the biphase termination of Fe3O4(111)/Pt(111) consists of FeO and Fe3O4(111) terminated areas, and we show that the method can differentiate between different water structures in H2O-derived adsorbate layers on Fe3O4(111)/Pt(111). With this, we conclude that the method is a capable new member in the set of techniques providing crucial information to elucidate surface structures. The method does not rely on translational symmetry and can therefore also be applied to systems which are not well ordered. Even an application to rough surfaces is possible.

Isomerization and Selective Hydrogenation of Propyne: Screening of Metal-Organic Frameworks Modified by Atomic Layer Deposition.

Various metal oxide clusters upward of 8 atoms (Cu, Cd, Co, Fe, Ga, Mn, Mo, Ni, Sn, W, Zn, In, and Al) were incorporated into the pores of the metal-organic framework (MOF) NU-1000 via atomic layer deposition (ALD) and tested via high-throughput screening for catalytic isomerization and selective hydrogenation of propyne. Cu and Co were found to be the most active for propyne hydrogenation to propylene, and synergistic bimetallic combinations of Co and Zn, along with standalone Zn and Cd, were established as the most active for conversion to the isomerized product, propadiene. The combination of Co and Zn in NU-1000 diminished the propensity for full hydrogenation to propane as well as coking compared to its individual components. This study highlights the potential for high-throughput screening to survey monometallic and bimetallic cluster combinations that best affect the efficient transformation of small molecules, while discerning mechanistic differences in isomerization and hydrogenation by different metals.

Ab Initio Calculations for Molecule-Surface Interactions with Chemical Accuracy.

Atomistic understanding of complex surface phenomena such as heterogeneous catalysis or storage and separation of energy-relevant gases in nanoporous materials (zeolites; metal-organic frameworks, MOFs) requires knowledge about reaction energies and energy barriers for elementary steps. This is difficult to obtain from experiment since the number of possible chemical, adsorption/desorption, and diffusion steps coupled to complex reaction networks is large, and so is the number of possible surface sites. Here is an important role of quantum chemistry which can provide rate and equilibrium constants for elementary steps "ab initio." To be useful, the predictions have to reach chemical accuracy (4 kJ/mol) which is difficult to achieve because realistic models of the surface systems may comprise of the order of a thousand atoms. While density functional theory (DFT) as a rule cannot be trusted to yield results within chemical accuracy limits, methods that are accurate enough (Coupled Cluster with Single, Double, and perturbative Triple Substitution, CCSD(T)) cannot be applied because of their exponential scaling with system size. This Account presents a hybrid high-level-low-level quantum method that combines DFT with dispersion for the full periodic system with second order Møller-Plesset perturbation theory (MP2) for the reaction site within a mechanical embedding scheme. In addition, to check if MP2 is accurate enough, we calculate Coupled Cluster (CC) corrections with Single, Double, and perturbatively treated Triple substitutions (CCSD(T)) for sufficiently small models of the reaction site. This multilevel hybrid MP2:DFT-D+ΔCC method is shown to yield chemical accuracy for a set of 12 molecule-surface interaction systems for which reliable experimental data are available. For CO/MgO(001), the history of the experiment-theory comparison illustrates two problems: (i) Do experiment and theory look at the same surface site? (ii) Does theory calculate the same quantity as derived from experiment? The hybrid MP2:DFT-D+ΔCC data set generated includes the MgO(001) surface, the Mg2(dobdc) metal-organic framework, and the proton forms of the CHA and MFI zeolites interacting with the H2, N2, CO, CO2, CH4, and C2H6 molecules. It serves two purposes. First, it will be useful for testing density functionals with respect to their performance for molecule-surface interactions. Second, it establishes the hybrid MP2:DFT-D+ΔCC method as a reliable and powerful tool for ab initio predictions of adsorption and reaction energies as well as energy barriers when testing reaction mechanisms. For adsorption of small molecules in MOFs, isotherm predictions have reached a level of accuracy that deviations between theoretical predictions and experiments indicate sample imperfections. For elementary steps of the industrially important methanol-to-olefin process, our hybrid MP2:PBE+D+ΔCC calculations yield rate constants in agreement with experiment within chemical accuracy limits, finally achieving for molecule-surface reactions which was possible so hitherto only for gas phase reactions involving not more than 10 atoms.

Including dispersion in density functional theory for adsorption on flat oxide surfaces, in metal-organic frameworks and in acidic zeolites.

We examine the performance of nine commonly used methods for including dispersion interactions in density functional theory (DFT): three different parametrizations of damped 1/Rn terms (n = 6, 8, …) added to the DFT energy (Grimme's D2 and D3 parameterizations as well as that of Tkatchenko and Scheffler), three different implementations of the many-body dispersion approach (MBD, MBD/HI and MBD/FI), the density-dependent energy correction, called dDsC, and two "first generation" van der Waals density functionals, revPBE-vdW and optB86b-vdW. As test set we use eight molecule-surface systems for which agreement has been reached between experiment and hybrid QM:QM calculations within chemical accuracy limits (±4.2 kJ mol-1). It includes adsorption of carbon monoxide and dioxide in the Mg2(2,5-dioxido-1,4-benzenedicarboxylate) metal-organic framework (Mg-MOF-74, CPO-27-Mg), adsorption of carbon monoxide as well as of monolayers of methane and ethane on the MgO(001) surface, as well as adsorption of methane, ethane and propane in H-chabazite (H-CHA). D2 with Ne parameters for Mg2+, D2(Ne), MBD/HI and MBD/FI perform best. With the PBE functional, the mean unsigned errors are 6.1, 5.6 and 5.4 kJ mol-1, respectively.

Hydrogen Atom or Proton Coupled Electron Transfer? C-H Bond Activation by Transition-Metal Oxides.

The C-H bond activation in oxidative dehydrogenation of propane by heterobimetallic oxide clusters (first-row transition metals), deposited on the zirconium oxide node of the NU-1000 metal organic framework, was investigated by multireference wave function theory. The redox-active part of the systems studied has the composition (CoO)(MO)(OH)2 with M = Ti, Mn, Fe, Co, Ni, Cu, Zn. In this series, the energy of H transfer from propane to the metal oxide (ΔE) varies from -26 kcal/mol for M = Cu, Zn to 85 kcal/mol for M = Ti. This is accompanied by a change in the mechanism from hydrogen atom transfer, M2+(dn) O•- → M2+(dn) OH-, for M = Cu, Zn to proton coupled electron transfer, Mm+(dn) O2- → M(m-1)+(dn+1) OH-, for M = Ni, Co, Fe, Mn, Ti. Whereas for M = Ni (ΔE = -13 kcal/mol) Ni+III is reduced to Ni+II, for M = Co, Fe, Mn (ΔE = 1, 10, 6 kcal/mol, respectively) it is Co+III that is reduced to Co+II. For M = Ti, Ti maintains its +IV oxidation state and Co+II is reduced to Co+I.

Structure and Reactivity of Al-O(H)-Al Moieties in Siloxide Frameworks: Solution and Gas-Phase Model Studies.

Even though aluminas and aluminosilicates have found widespread application, a consistent molecular understanding of their surface heterogeneity and the behavior of defects resulting from hydroxylation/dehydroxylation remains unclear. Here, we study the well-defined molecular model compound, [Al3 (µ2 -OH)3 (THF)3 (PhSi(OSiPh2 O)3 )2 ], 1, to gain insight into the acid-base reactivity of cyclic trinuclear Al3 (µ2 -OH)3 moieties at the atomic level. We find that, like zeolites, they are sufficiently acidic to catalyze the isomerization of olefins. DFT and gas phase vibrational spectroscopy on solvent-free and deprotonated 1 show that the six-membered ring structure of its Al3 (µ2 -OH)3 core is unstable with respect to deprotonation of one of its hydroxy groups and rearranges into two edge-sharing four-membered rings. This renders AlIV -O(H)-AlIV units strong acid sites, and all results together suggest that their acidity is similar to that of zeolitic SiIV -O(H)-AlIV groups.

Ab Initio Prediction of Proton Exchange Barriers for Alkanes at Brønsted Sites of Zeolite H-MFI.

A hybrid of high level and low level quantum mechanics (QM) methods has been employed to predict intrinsic and apparent energy barriers for the direct proton exchange mechanism of methane, ethane, propane, n-butane, and i-butane on Brønsted sites of H-MFI. The specific hybrid MP2:PBE+D2 + ΔCC implementation used is known to yield the so-called "chemical accuracy" (±4 kJ/mol). Whereas the apparent enthalpy barriers decrease with increasing C number from 104 to 63 kJ/mol, in line with the decreasing heat of adsorption, the intrinsic enthalpy barriers are constant within 124-127 kJ/mol at 500 K. For methane, ethane, propane, and n-butane, we find the expected agreement of apparent barriers with activation energies from batch recirculation reactor experiments. The activation energies derived from NMR experiments (103-113 kJ/mol) are similarly constant as the predicted intrinsic barriers but systematically lower. For i-butane the predicted intrinsic and apparent barriers for the direct proton exchange step are the same as for n-butane with deviations of 2-5 kJ/mol, while the experiments yield values that are 50-60 kJ/mol lower, far outside the estimated range of combined experimental and computational uncertainty (±14 kJ/mol). A change to the indirect proton exchange mechanism, in which a hydride ion is transferred between the alkane and a tert-butyl carbenium ion can be excluded, because we confirm previous findings that the barrier for dehydrogenation that would create a tert-butyl cation from i-butane is much too high, 188 and 132 kJ/mol for the intrinsic and apparent enthalpy barriers, respectively, at 500 K. The possible role of extraframework- and framework-bound alumina species is discussed.

A Two-Dimensional 'Zigzag' Silica Polymorph on a Metal Support.

We present a new polymorph of the two-dimensional (2D) silica film with a characteristic 'zigzag' line structure and a rectangular unit cell which forms on a Ru(0001) metal substrate. This new silica polymorph may allow for important insights into growth modes and transformations of 2D silica films as a model system for the study of glass transitions. Based on scanning tunneling microscopy, low energy electron diffraction, infrared reflection absorption spectroscopy, and X-ray photoelectron spectroscopy measurements on the one hand, and density functional theory calculations on the other, a structural model for the 'zigzag' polymorph is proposed. In comparison to established monolayer and bilayer silica, this 'zigzag' structure system has intermediate characteristics in terms of coupling to the substrate and stoichiometry. The silica 'zigzag' phase is transformed upon reoxidation at higher annealing temperature into a SiO2 silica bilayer film which is chemically decoupled from the substrate.

Ab initio study of methanol and ethanol adsorption on Brønsted sites in zeolite H-MFI.

We examine the interaction of methanol and ethanol with a bridging OH group of H-MFI (Al12-O20(H)-Si3 site). The computational standard approach for molecule-surface interaction uses density functional theory with inclusion of dispersion for energies and harmonic vibrational frequencies for entropies and finite temperature effects for enthalpies. At 300 K, this yields -117 and -135 kJ mol-1 for adsorption enthalpies of methanol and ethanol, respectively, and 59 and 61 kJ mol-1, respectively for their entropy terms -T·ΔS. To reach chemical accuracy (±4 kJ mol-1) we go beyond this approach. The energies are calculated using a hybrid QM:QM scheme (QM - quantum mechanics) which combines plane-wave density functional theory accounting for the periodicity of the system with wave function-based methods (Møller-Plesset perturbation and Coupled Cluster theories). Finite temperature and entropy contributions are calculated from anharmonic vibrational partition functions. This yields as final predictions for methanol and ethanol -84 and -104 kJ mol-1, respectively, for the enthalpies of adsorption, 56 and 48 kJ mol-1, respectively, for the -T·ΔS term, and -28 and -56 kJ mol-1, respectively, for the Gibbs free energies at 300 K.

Chemically accurate adsorption energies for methane and ethane monolayers on the MgO(001) surface.

A hybrid QM:QM method that combines MP2 as high-level method on cluster models with density functional theory (PBE+D2) as low-level method on periodic models is applied to adsorption of methane and ethane on the MgO(001) surface for which reliable experimental desorption enthalpies are available. Two coverages are considered, monolayer (every second Mg2+ ion occupied) and one quarter coverage (one of eight Mg2+ ions occupied). Structure optimizations are performed at the hybrid MP2:(PBE+D2) level, with the MP2 energies and forces counterpoise corrected for basis set superposition error and extrapolated to the complete basis set limit. For the MP2 calculations on the adsorbate monolayer a two-body expansion of the lateral molecule-molecule interactions is applied. Higher order correlation effects are evaluated at the hybrid MP2:(PBE+D2) equilibrium structures as coupled cluster [CCSD(T)] - MP2 differences adopting smaller basis sets. The final adsorption energies obtained for monolayer coverage are -14.0 ± 1.0 and -23.3 ± 0.6 kJ mol-1 for CH4·MgO(001) and C2H6·MgO(001), respectively. They agree within 1 kJ mol-1 - well within chemical accuracy limits - with reference energies of -15.0 ± 0.6 and -24.4 ± 0.6 kJ mol-1, respectively. The latter have been derived from measured desorption enthalpy barriers, taking zero-point vibrational energy (ZPVE) and thermal enthalpy contributions into account.